Knowledge talk:WikiProject Mathematics/equivlistrevert

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Next, all articles that have had '/equiv' changed to something else should have that specific change reverted, preferably with added prose that clarifies the use of 'equiv' if it is ambiguous.

2021: 265: 5285: 4136: 5866: 510: 5849: 4246: 5824: 3914: 3858: 3569:: A few months later, well before Maupertuis' work appeared in print, Euler independently defined action in its modern abbreviated form \mathcal{S}_{0} \ 2671: 2589: 1103:\left\{ x | ( x \in x ) \. The proof proceeds:. \begin{matrix} \mbox{1.} & ( X \in. Again a particular case of this paradox is when Y is in fact a 2092:: In this case, occlude_open(1) is true, making the antecedent of the fourth formula above false for t = 1; therefore, the constraint that open(t-1) \ 4272: 2178: 5380:\frac{F/A}{\Delta x/h. where F/A is shear stress and Δx/h is shear strain. Shear modulus is usually measured in ksi (thousands of pounds per square 2201:

dX+\bold{A}X. Also, \delta_\varepsilon \bold{F}=\varepsilon \bold{F , which means F transforms covariantly. One thing to note is that not all gauge

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Q_{k+K} \quad;\quad \Pi_k. for any integer n. A phonon with wave number k is thus equivalent to an infinite "family" of phonons with wave numbers

2156: 259:\frac{\mathrm{entropy}}{\mathrm{. with p and ρ as the pressure and density from the energy density tensor Tμν, and g * as the effective number of 5717:\frac{U}{\sqrt{gh}} ,. where. U = velocity of the flow; g = acceleration due to gravity (9.81 m/s² or 32.2 ft/s²); h = depth of flow relative to 1267:-\frac{\ddot{a} a }{\. where a is the scale factor of the universe and the dots indicate derivatives by proper time. Recent measurements of dark 6375:{hc\over\lambda kT }. then. {x\over 1-e^{-x}}-5=. This equation cannot be solved in terms of elementary functions. It can be solved in terms of 6235:: Virtual displacements and strains as variations of the real displacements and strains using variational notation such as \delta\ \mathbf {u} \ 5899:\frac{T_H - T_C}{T_H}. The equation shows that higher efficiency is achieved with greater temperature differential between hot and cold working 4902:

measure on E that is quasi-invariant under all translations by elements of E, then either \dim E < + \infty or μ is the trivial measure \mu \

4113:

Binomial\left(1,\frac{1}{2. are independent, identially distributed for each i, and if. y_i = E((\sum_{k=1}^{i}. then the sequences (X_i)_{i\geq

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2 B\,. where B\, is the highest frequency component contained in the signal. To avoid aliasing, the sampling rate must exceed the Nyquist rate:

3578: 2636: 772:\chi(z) = {c \over H_0} \. where c is the speed of light and H0 is the Hubble constant. By using sin and sinh functions, proper motion distance 585:\frac{\mu v}{\sigma}. where:. μ is the viscosity of the liquid; v is a characteristic velocity; σ is the surface or interfacial tension between 6484:\frac{\mbox {tensile stress}}{\mbox. where Y is the Young's modulus (modulus of elasticity) measured in pascals; F is the force applied to the 3492:\int \!\!\! \int \mathbf. where \Phi_m \ is the magnetic flux and B is the magnetic field density. We know from Gauss's law for magnetism that 1578:\frac{p(p-1. This is referred to as Lo's condition in the literature. This follows from the fact that the sum of the lables of the vertices is 5933:\left(\frac{q^2}{mc. where q is the charge per particle, and m is the mass per particle. Note that this is the square of the classical radius 4625:\{1,...1,0,. in which x ones are followed by m-x zeros. For example, in the case of two thresholds, the permissible patterns in this response 3826:\frac{e^2}{\hbar c (. cannot take on a different numerical value no matter what system of units are used. Judiciously choosing units can only 3791:\prod_{i=0}^n v_i^{x_i. The idea here is that when the vi are relatively prime and much smaller than the modulus p this problem can be solved 3545: 2024:: where ρ is the charge density and \vec{J} is the current density. The 4-current satisfies the continuity equation. J^{\alpha}_{,\alpha} \, \ 1474: 4863:\sum_j \langle j|_B \left( |\ . ρA is sometimes called the reduced density matrix of ρ on subsystem A. Colloquially, we "trace out" system B 2538:: \operatorname{sech}(x) = \frac{1}{\. Hyperbolic cosecant, pronounced "cosheck" or "cosech". \operatorname{csch}(x) = \frac{1}{\. where. i \ 2278:\frac{1}{2}\eta^{\. in the +--- sign convention. The theories of ghost condensate predict specific non-gaussianities of the cosmic microwave 6087: 5406:

1\ \mbox{mod}\ N.\. Therefore, N | (a r − 1). Suppose we are able to obtain r, and it is even. Then. a^r - 1 = (a^{r/2} - 1: \Rightarrow N\

4850:{x^2}\mbox{ (mod }. Otherwise, q is called a quadratic non-residue. For prime moduli, roughly half of the residue classes are of each type. 3931: 3535:: It extends the range of the cup product. On differential forms the triple product is formally defined as. MP(\omega_1,\omega_2,\omega_3) \ 3366:\begin{bmatrix} 58 && 26 \. whose determinant is 2340. Taking the logarithm and multiplying by the constants αkB gives the entropy. 1591:\frac {stress} {strain}. where λ is the elastic modulus; stress is the force causing the deformation divided by the area to which the force 161:-R \left( \frac{\partial ~ln. This results in an Ea that is in principle a function of T (since the Arrhenius equation is not exact) but in 6458:\frac {\partial \vec r and the end-to-end distance \vec R = \int_{0}^{l}\hat t . It can be shown that the orientation correlation function 6302:\frac{2\pi}{\lambda} = \. where λ is the wavelength in the medium, ν (Greek letter nu) is the frequency, vp is the phase velocity of wave, 6268:\frac{N_iv_i}{V}. where the total volume of the system is the sum of the contributions from all the chemical species. V = \sum_j N_jv_j \, 6201:: If the letters A–Z are taken to be the numbers 0–25, and addition is performed modulo 26, then Vigenère encryption can be written,. C_i \ 4757:

Pr(T=1 | X=x). The propensity score was introduced by Rosenbaum and Rubin (1983) to provide an alternative method for estimating treatment

4207: 4173:\frac{f_s}{2 f_H} \. or. f_s = 2 \beta f_H \ . where. fs is the sampling frequency; fH is the bandwidth or highest frequency of the signal 3852:

0~, \quad 1\leq i. where the left-hand side denotes the i-th homotopy group. The requirement of being path-connected can also be expressed

3161:{v_0^2 \over c^2 }. and the terms on the right are evaluated at the retarded time. t' = t - {R \over c} . The second term, proportional to 1374:

n \mathrm{U} \. But, ultimately, people always work with dimensionless numbers in reading measuring instruments and manipulating (changing

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H(X,Y) - H . Intuitively, the combined system contains H(X,Y) bits of information. If we learn the value of X, we have gained H(X) bits of

17: 6362:\frac{T-T_c}{T_c} measures the temperature relative to the critical point. . Derivation. The scaling hypothesis is that near the critical 5687:: More specifically, given a modulus N of unknown factorization, and a ciphertext C, it is infeasible to find any pair (M,e) such that C \ 5217:\sum_{k=1}^\infty. which coincides with Riemann's zeta-function when z = 1. The Lerch transcendent is given by. \Phi(z, s, q) = \sum_{k=0 5144:{1 \over {{1 \over m_1. with the force the actual one. Applying the gravitational formula we get that the position of the first body with 4943:\frac{e}{m \omega x_0}. These equations can be solved as follows:. u(t;\delta) = [u_0 \cos \delta t -: v(t;\delta) = [u_0 \cos \delta t + 4347:

i_a(x - \Delta x,. then, the discrete Fourier transform of the images will be shifted relatively in phase:. \mathbf{I}_b(u,v) = \mathbf{I

4227:\alpha_{\mathrm{max}} \cos 2 . In other words, the parametric oscillator phase-locks to the pumping signal f(t). Taking θ(t) = θeq (i.e., 1929:-1 \. then N is prime. Conversely, if the above congruence does not hold, and in addition. \left(\frac{a}{N}\right)=- (See Jacobi symbol) 4498: 3505:\int_0^t {\. In other words, as time progresses the signal traces out a trajectory in k-space with the velocity vector of the trajectory 2958:\mathbf{r} \times \mathbf . where \mathbf{r} is the position vector of the particle and \mathbf{p} = m \mathbf{v} is the momentum of the 2658: 2414:-\nabla \phi is the velocity and is vorticity-free. The second equation leads to the Euler equations. \frac{\partial \vec{v}}{\partial t 2207: 1820:

1\mod n. This follows from Lagrange's theorem and the fact that a belongs to the multiplicative group of \mathbb{Z}/n\mathbb{Z} iff a is

1528:\mathbf{a} - \mathbf{. creating a triangle with sides a, b, and c. According to the law of cosines, we have. c^2 = a^2 + b^2 - 2 ab \cos 1490:: When x is 1, the function is called the sigma function or sum-of-divisors function, and the subscript is often omitted. \sigma_{0}(n) \ 1438:: Given an integer k, one defines the residue class of an integer n as the set of all integers congruent to n modulo k: \hat{n}=\{m | m \ 1233:

E_{k}(r_. A given pair of rotamers A and B at positions k and l, respectively, cannot both be in the final solution (although one or the

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4 \pi \rho G T^2 is a definite number, of order unity, where ρ is the mean density of matter in the universe, and T is the Hubble time.

3392:\frac{1}{\sqrt{1 - v. is called the Lorentz factor and c is the speed of light in a vacuum. This expression differs from the expression 3106:

H^{~e}_{b\. Thus, the Lanczos potential tensor is a gravitational field analog of the vector potential A for the electromagnetic field.

2287:: The Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. It is defined as:. G \ 2265:\ \vdash \forall x \. which does not mean the same as. P(x) \leftrightarrow \forall x \, P(x) \. which is wrong because here P(x) could 1681:\begin{pmatrix} \psi_x \\. is the Jones vector in the x-y plane. Here θ is an angle that determines the tilt of the ellipse and αx − αy 1387:\sum_{k=-\infty}. for some given period T. Some authors, notably Bracewell, refer to it as the Shah function (probably because its graph 952:\frac{g_s^2(. where β0 is a constant computed by Wilczek, Gross and Politzer. Conversely, the coupling increases with decreasing energy 6061:\varnothing' , the Turing jump of the empty set, is Turing equivalent to the halting problem. For each n, the set \varnothing^{(n)} is 5174:

corresponding to {intersection, orthogonal sum, orthogonal complement, inclusion, and orthogonality} respectively, where Q_1 \bot Q_2 \

3784: 3379:\frac{dt}{d\tau} = \. where. \beta = \frac{u}{c} is the velocity in terms of the speed of light,: u is the velocity as observed in the 2665:. where H(h | l) is the conditional entropy (equivocation) of variable h (before the process started) given the variable l (before the 1860: 1757:\pm 1. (where mod refers to the modulo operation). The motivation for this definition is the fact that all prime numbers p satisfy the 1481:

1 + \sum_{j=1}. The problem has therefore been reduced to finding the roots of a rational function f(λ). This equation is known as the

1043:\int f^*. where the integral is over the appropriate values of t. The cross-correlation is similar in nature to the convolution of two 572:\frac{\partial {\mathcal L}}{. This definition of the canonical momentum ensures that one of the Euler-Lagrange equations has the form 6179:-{1\over e}{\. It is unfortunate that the effective action Γeff and the vertex function Γμ happen to be described by the same letter. 4526:\frac{\omega}{. so the plasma waves can accelerate electrons that are moving with speed nearly equal to the phase velocity of the wave. 4010:\frac{b}{\sqrt{ac}. The factor 2 is present so that the solutions can be parameterized in terms of ζ. In the context of mechanical or 3908:\left. The components Ilm and Slm are the mass and current multipoles, respectively. − 2Ylm is the spin-weight -2 spherical harmonic. 2725:-\sum_{\mathcal. which is an alternating (inclusion-exclusion) sum over all subsets \mathcal{T}\subseteq \mathcal{V} , where \left\vert 1625:\frac{ \partial A_b }{ \partial. where A^a = ( \frac{\phi}{c} , \ and A_a \, = \eta_{ a b } A^b = ( -\ where \, \eta is the Minkowski 1030:\int f^*. where the integral is over the appropriate values of t. The cross-covariance is similar in nature to the convolution of two 318:{\bar x_1 - \bar x_2 \over \sqrt. where \bar x_1 and \bar x_2 are the two sample means, and s1 and s2 are their standard deviations. 109:

B_{(p-1). where Bn is the nth Bernoulli number. There are some generalisations of these basic results, in the papers of the authors.

6027:& (C_x -. where use was made of the fact that (-\lambda\ + 1)^2 = (\lambda\ - . Substituting these quadrances into the equation 5963:\sum_{odd \ \ l}(K^{l. Any two-body terms commute: ,F]: = 0, ,G]: = 0 This is done in order to be able to make the Suzuki-Trotter 4539:\cos(x) \. are most neatly written using the "∓" sign. In ISO-8859-1,7,8,9,13,15 and 16, the plus-minus symbol is given by the code 4240:\frac{\partial V}{\partial n_i. and ni is the number of moles of component i. As noted, T and P are held constant when taking these 4049:\sqrt{n_o^2 - n_c^ ,. where no is the refractive index along the central axis of the fiber. Note that when this definition is used, 3326: 3237:\frac{\sqrt{2}}{. where Ln(x) is a Legendre polynomial. These functions are eigenfunctions of the singular Sturm-Liouville problem: 2652:\frac{1}{\sqrt{1 - v. The Lorentz transformation is equivalent to the Galilean transformation in the limit c \rightarrow \infty or, 1451:: The familiar base change formula for ordinary logarithms remains valid: If c is another generator of G, then we have. \log_c (g) \ 993: 453:: Alice generates two large prime numbers p \, and q \, such that p \ne q , randomly and independently of each other, where (p, q) \ 1077:\left. We further define a primary prime to be one which is congruent to -1 modulo 3. Then for distinct primary primes π and θ the 348:

B_n+B_{n+1}. Each Bell number is a sum of "Stirling numbers of the second kind". B_n=\sum_{k=1}^n S(n,k). The Stirling number S(n,

148:\forall n [n \in Z \ . Not every implicitly arithmetical set is arithmetical, however. In particular, the truth set of first order 4789: 2951: 2630:

P_+ - P_- is called the (real phase) metric operator or fundamental symmetry, and may be used to define the Hilbert inner product

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d\theta^2+\sin^. Define the tortoise coordinate r * by. r^* = r + 2GM\ln\left|\frac{r. The tortoise coordinate approaches −∞ as r

785:\sqrt{a} x + i \sqrt{b} ,. we then have. \begin{matrix} |z|^2 &=& z z^*. so. ax2 + by2 + c = | z | 2 + c. . External link 60: 5037:(65539 V_j) \mod 2^. with V0 odd. It is widely considered to be one of the most ill-conceived random number generators designed. 2041:\left(\frac{1}{c. and is sometimes also represented as D. The square of D is the four-Laplacian, which is called the d'Alembertian 1766:: a(p − 1)/2 ≡ −1 (mod p). Euler's criterion can be concisely reformulated using the Legendre symbol:. \left(\frac{a}{p}\right) \ 431:\ln(S/S_0) \,. is a normal random variable with mean μT and variance σ2T. It follows that the mean of S is. E(S) = S_0 e^{rT} \, 392:\max_{|z| \leq 1. The inequality is named after Sergei Natanovich Bernstein and finds uses in the field of approximation theory. 6308: 5730:

i\theta^\dagger\gamma. where C is the charge conjugation matrix, which is defined by the property that when it conjugates a gamma

5678:-1\mod. It should be noted, however, that Guy uses a definition with only the first condition. Because not all primes pass that 5610: 5419:\langle\left(I-\langle. The only exception being if a squeezed coherent state can be formed through correlated photon generation. 2826:

1 - (1 - a)(1 - b. \neg a, 1 − a. As an example, \phi = a \wedge b \vee \neg c would be converted into a polynomial as follows:

2529:\frac{. where rij is the distance between particles i and i, and where the angular brackets \langle \ldots \rangle represent an 1668:\left( a^{2} +. where σ can represent any of the three variables (λ,μ,ν). Using this function, the scale factors can be written 1558: 1314:

n(\vec r) if \,\!V_s is chosen to be. V_s = V + U + \left(T - T_s\right). Thus, one can solve the so-called Kohn-Sham equations

555:: The preceding reasoning is not valid if σ vanishes identically on C. In such a case, we could allow a trial function \varphi \ 5545:\frac{j_{\lambda}}. where jλ is the emission coeffisient, κλ is the absorption coeffisient (also known as the opacity (optics)). 5097:{ \operatorname{tr}(\mathbf{M}). is the stability parameter. The eigenvalues are the solutions of the characteristic equation. 4366: 4210:: Work in units where the gravitational "constant" measured today far from gravitating matter is unity so set G_{\mbox{today}}\ 2172:\partial\! and the fermionic action is given by. \int d^dx \overline{\psi}iD\!\! In Euclidean space, the partition function is 526:\sqrt{\frac{g}{\theta}\ , where θ is potential temperature, g is the local acceleration of gravity, and z is geometric height. 5532:. where. \left(\frac{a}{p}\right). is the Legendre symbol. The Jacobi symbol is a generalisation of the Legendre symbol where 4569:

0 satisfies the conditions i)-iii). Otherwise, in the case of finite measure μ given Z - Poisson random variable with rate μ(E)

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0 then we can write the zero norm as \sum_{i=1}^n x_i^0 . It follows that the zero norm of x is simply the number of non-zero

3426:\frac{1}{\sqrt{1 - \ . The second of these can be written as:. \vec{r'} = \vec{r} + \left(. These equations can be expressed in 2343:\frac{\partial \omega}{\partial k}. where:. vg is the group velocity: ω is the wave's angular frequency: k is the wave number 5367:

x * F_x + x' * F_x' ,. where F is any function and Fxand Fx' are positive and negative Shannon cofactors of F, respectively.

5184: 5084:\mathbf{S}-\mathbf{ for simplicity, then. |\mathbf{V}+t\mathbf{d}|^{. \mathbf{V}^2+t^2\mathbf{d}. d^2t^2+2\mathbf{V}\cdot t\ 4792:: All that remains is to prove it for − π < x < 0, this can be done by squaring the symmetry identities to get \sin^2x\ 4492:\frac{h}{2\pi} = \. The figures cited here are the 2002 CODATA-recommended values for the constants and their uncertainties. 4296:

the group consisting of all the Pauli matrices X = σ1,Y = σ2,Z = σ3, together with multiplicative factors \pm1,\pm i :. G_1 \

4029: 3754:. where r_{1}+r_{2}+\cdots+r_{N. The central k-order moments are given as follows. (a) If k is odd, \mu _{1,\dots,N}(X-\mu . 3747: 3167: 2803: 2555:\sqrt{-1}. is the imaginary unit. The complex forms in the definitions above derive from Euler's formula. . Useful relations 2108:\frac. We get:. v_1 \cdot v_2 = \frac{A_1 A_2}{2}\left. So, you can see the sum ( f_1 + f_2\, ) and difference ( f_1 - f_2\, 1017:(T-T_{c})/T_c,\. where T is the temperature and Tc its critical value, at which a second-order phase transition is observed. 911: 632:\frac{\left. ,, etc. represent the chemical activities of the reactants and products, which can sometimes be approximated by 542:: However, this one operator is sufficient to define all the other logical operators:. \begin{matrix} A \Rightarrow B & \ 5792:(dx^a)_\mu. is defined with respect to the connection form B. Here, d is the exterior derivative of the ath component of x, 5204:\rho \overline{ u'_i u'. The divergence of this stress is the force density on the fluid due to the turbulent fluctuations. 5191:

K_x(y). is called a reproducing kernel for the Hilbert space. In fact, K is uniquely determined by the above condition (*).

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s. Taking the square root of each side of the line element gives the above definition of d\tau\ . After that, take the path

4445:: An application of Grönwall's lemma to |\varphi(t)-\psi(t)| , where \varphi and ψ are two solutions, shows that \varphi(t)\ 3839:\frac. where \mathbf{v} is the velocity of the fluid. The first term on the right-hand side of the equation is the ordinary 3259:: L0 is the proper length (the length of the object in its rest frame),: L1 is the length observed by an observer,: \gamma \ 2231:: E0 and I0 are, respectively, the electric field amplitude and intensity at the center of the beam at its waist, i.e. E_0 \ 1129:

can be joined correctly if and only if the dihedral angle between the planes was roughly the tetrahedral bond angle \delta \

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v^s {. Once again this shows that the covariant derivative of a vector field is not just simply obtained by differentiating

519: 6070:: By contrast, subtracting equation (2) from equation (1) results in an equation that describes how the vector \mathbf{r} \ 5525: 4631: 2992:\left[\. The K-function is closely related to the Gamma function and the Barnes G-function; for natural numbers n, we have 2444:: Maupertuis' principle uses an integral over the generalized coordinates known as the abbreviated action \mathcal{S}_{0} \ 2377: 2313:: The strain rate γ is the rate of change streaming velocity in the x-direction, with respect to the y-coordinate, \gamma \ 2304:

E - T S - \mu N. Where E is the energy, T is the temperature of the system, S is the entropy, μ is the chemical potential,

659: 4634:: When the final time tf is fixed and the Hamiltonian does not depend explicitly on time ( \frac{\partial H}{\partial t} \ 4442: 1985:: Fermions, such as electrons and protons, compose the "stuff" of matter and have half-integer spin (the unit being \hbar\ 1090:

C. so that the following defines a 0-current:. T(f) = f(0).\,. In particular every signed measure μ with finite mass is a

487:. One occasionally encounters an expression like. - i \hbar \nabla |\psi\rang. This is something of an abuse of notation, 6014:\;\tan. to simplify certain integrals containing the radical expressions. \sqrt{a^2-x^2}. \sqrt{a^2+x^2}. \sqrt{x^2-a^2} 5956: 5279:\sqrt{\frac{h^2}{2. m_e\, is the mass of an electron; T\, is the temperature of the gas; k_B\, is the Boltzmann constant 3895:

m_{i} . The phase that is responsible for oscillation is often written as (with c and \hbar restored) . \frac{\Delta m^2\,

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1 \mod. When d=2, this is called the quadratic residuosity problem. . Applications. The semantic security of the Benaloh

2390: 2384:\langle\psi(t. where the last step was obtained by expanding \left| \psi\left(t\right) \right\rangle in terms of the basis 2002:(\alpha _{then}. In the seven years since their results were first announced, extensive analysis has yet to identity any 1700: 1327:

over the infinite dimensional "functional manifold". The Einstein summation convention is used. In other words,. A^i B_i\

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can be identified with a corresponding directional derivative. We can therefore define a vector precisely:. \mathbf{a} \

5007:: Lubotzky, Phillips and Sarnak show how to construct an infinite family of p + 1-regular Ramanujan graphs, whenever p \ 444:(m(r^e))^d\ (. The author of the message can then remove the blinding factor to reveal s, the valid RSA signature of m: 361:

it is computationally infeasible to determine whether z is an rth residue mod n, i.e. if there exists an x such that z \

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g (g, n . Note that the variation consists of defining \bar g in terms of g(g,n − 1) instead of in terms of g(n − 1,g).

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M. Because of the continuity equation. \partial_\mu M^{\alpha\beta\mu}_0= ,. we get. \partial_\mu S^{\alpha\beta\mu}=T

4783:-1 \. then p is prime. This is a practical test because if p is prime, any chosen a has about a 50% chance of working. 4744:\{ (\alpha + m \beta ). All of these exchange symmetries amount to exchanging pairs of rows in the coefficient matrix. 4548:: The parameter λ is not only the mean number of occurrences \langle k \rangle , but also its variance \sigma_{k}^{2} \ 3674:

of the classical logic (CPC) is Lewis' S5, whereas its largest modal companion is the logic. \mathbf{Triv}=\mathbf K+A\

2248:: In particular, he was looking for relationships between p and q such that q should be a cubic residue of p (i.e. x^3\ 1500: 5617:- (\sin{\theta}. The spin-weighted spherical harmonics are then defined in terms of the usual spherical harmonics as: 4096: 2780:: Of special importance is the conversion rule, which says that given \Gamma\vdash t : \sigma and \Gamma\vdash \sigma\ 2326:: Green used the lowercase blackletter \mathfrak{l} , \mathfrak{r} and \mathfrak{f} for these relations, and wrote a \ 1880: 1173: 1156: 1139: 5630:

const \. If one takes the inverse of Equation 8 it can be observed that the inverse of std Kt/V is proportional to the

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The full dimensionality of these spaces can be exploited to obtain the definition of the perturbers, by diagonalizing

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e. To specify the connection it is enough to specify the Christoffel symbols Γkij. Since {\mathbf e}_i are coordinate

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d\mathbf{A}+\mathbf. This action is diffeomorphically invariant and gauge invariant. Its Euler-Lagrange equations are

4411:: (known as Dirac's constant or Planck's reduced constant); \mathbf{k} is the wave vector (with the wave number k \ 3064:

d\theta^2+\sin^. Kruskal-Szekeres coordinates are defined by replacing t and r by new time and radial coordinates:

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x). Then for a\in\R , a is nonnegative if and only if \mathcal{R}\models\varphi . In conjunction with a formula that

666:\frac{f}{A}. s = distance from lens to point source. s + Δs = distance from lens to external focal plane of sensor 6109: 5551: 5050:\. (where the ai and bi are nonnegative integers.) When we have generated enough of these relations (it's generally 4882: 3993:: Probability density function (pdf), \frac{e^{-(x^2+\lambda^2. Cumulative distribution function (cdf). Mean, \mu\ 3990: 3767: 3230: 2645: 2407: 2159:

f_i^1 (1). One seeks conditions on the existence of a collection of solutions u1, ..., un-r such that the gradients

1350: 834:: By analogy with the classical conditional entropy, one defines the conditional quantum entropy as S(\rho|\sigma) \ 831: 798:(\lambda z_1,\lambda. That is, these are homogeneous coordinates in the traditional sense of projective geometry. 4973:: I_\nu(s)=I_\nu(s_0)e^{. where τ(s1,s2) is the optical depth of the atmosphere between s1 and s2:. \tau(s_1,s_2) \ 4714:-1\mod. A strong probable prime to base a is called a strong pseudoprime to base a. Every strong probable prime to 3333:\eta^{ar , and this is used to calculate the Riemann tensor:. 2R^a{}_{bcd} = h^a_{d,. Using Rbd = δcaRabcd gives 3207:

4a_2. and the set of coordinates i such that ai belongs to any fixed residue class (mod 4) is a word in the binary

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alive(1) must be added to formalize the implicit assumption that loading the gun only changes the value of loaded

4262:: with creation and annihilation operators a^{\dagger}(\phi_i) and a(φi) we define the number operator \hat{n_i} \ 1163:

if one knows theta, r and z in terms of Cartesian coordinates, but the general equation is given below. \nabla \

730:: . Jump to: navigation, search. Colonel General is a senior military rank which is used in some of the world’s 6007: 4103:

1 \mod p \} . For any element x in (\mathbb{Z}/p^2\mathbb{Z}) , we have xp-1 mod p2 is in H, since p divides xp

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s - \langle s\ ; this is the fluctuation term of the spin. If we multiply out the RHS, we obtain one term that's

3498: 3299:\mathbf{x} is aligned with a right eigenvector \mathbf{r}_{k} of the matrix \mathbf{A} , the dynamics are simple 3051:\Box A)\to\Box A generates an incomplete logic, because it corresponds to the same class of frames as GL (viz. 2777: 2467: 6192:\operatorname{trace}_{V}(T) is the row-transfer matrix. Two rows of vertices in the square lattice vertex model 1804:

e^{ix} .\. Considering that i is constant, the first and second derivatives of f(x) are. f'(x) = i e^{ix} \: f

6020: 4737: 4575: 3133: 2420: 1813: 1307: 1146:

if one knows θ, r and z in terms of Cartesian coordinates, but the general equation is given below:. \nabla \

539: 193: 6388:\sqrt{P^2} is a Casimir invariant of the Poincaré group. So, we can classify the irreps into whether m : --> 1850:: As in normal Ewald summation, a generic interaction potential is separated into two terms \phi(\mathbf{r}) \ 1634:: More formally, the electromagnetic tensor may be written in terms of the 4-vector potential Aa:. F_{ a b } \ 170:: Equality would hold if the product xy were antisymmetric (if the product were the Lie bracket, that is, xy \ 6381: 6368: 5892: 5336: 5272: 5223: 5103: 4259: 3901: 2797:\frac{1}{kT} where k is the Boltzmann constant and T is the temperature. The inverse temperature is actually 2592:

be reasonably easy to collect ordered pairs into sets. . Relations. Relations are sets whose members are all

1597: 971: 791: 39: 2839:

d\vec v/dt results in the famous equation \vec F = m \, \vec a \,, which states that the acceleration of an

4889:

AB - BA . Using the above, we can prove the identities. H = \hbar \omega \left(a^{\dagger}a: \left = 1 .

2699:\phi^\prime(t) \. and the instantaneous frequency (Hz) is. f(t) = \frac{1}{2 \pi} \ . . Phase unwrapping 1468:\mathbf x(kT): \mathbf x = e^{\mathbf AkT}\mathbf: \mathbf x = e^{\mathbf A(: \mathbf x = e^{\mathbf AT} 385: 6321: 5905: 4895: 4682: 4306: 3832: 3435:: The charge and fields in Lorentz-Heaviside units are related to the quantities in cgs units by. q_{LH} \ 3432: 3292: 2718: 2705: 2692: 2480: 1995: 1674: 1661: 206: 187:

1 \mbox{ atkinson} \times. where g is the standard acceleration of gravity (metres per second squared).

131:: If the relation R(n_1,\ldots,n_l,m_1,\ldots, m_k) is \Sigma^0_n then the relation S(n_1,\ldots, n_l) \ 2852:

b may be used to emphasise that a is not identically equal to b. ≝, a ≝ b, a is by definition equal to b

1942:\psi^{\dagger} \ . Given the expression for ψ(x) we can construct the Feynman propagator for the fermion 4816:\langle g^2. \langle \overline\psi\psi\rangle \simeq (-0.23). \langle (gG)^4\rangle\simeq 5:10\langle 4618: 4558: 4153: 3566: 3419: 2461:

kc is the angular frequency. We now have Helmholtz's equation for the spatial variable \mathbf{r} and a

2258: 2135: 1969: 1948: 1631: 1618: 1571: 1367: 1260: 552: 371: 311: 128: 4505:

1/\left(kT\right) . The denominator Z\left(\beta\right) , is the partition function of a single mode

1867:\left(-W\left=-. \frac{d}{dk}\Gamma_k=\frac{1}. is the ERGE. As there are infinitely many choices of 897:{\overline A}^{T}. where A^T \,\! denotes the transpose and \overline A \,\! denotes the matrix with 6490: 6464: 5972:: Definitions necessary for this theorem: A congruence on tree languages is a relation such that u_i \ 5684: 5244: 5210: 5124: 5056: 5017: 4949: 4923:\frac{n'_i}{\sum_j n . The above equations for the quasispecies then become for the discrete version: 4876:\sum_{i}. The bosonic field operators obey the commutation relation. \left[\phi(\mathbf{r}) , \phi( 4220: 4003: 3938:

of objects 1 and 2: r21 = | r2 − r1 | is the distance between objects 2 and 1: \mathbf{\hat{r}}_{21} \

3511: 2886: 2441: 1737: 1083: 778: 672: 5020:: The distance between both branes is only −ln(W)/k, though. In another coordinate system,. \varphi\ 4334:

I(t)\cdot \cos(2\pi ft). = I(t)\cdot \cos(2\pi ft) +. where f\, represents a carrier frequency, and

3599: 6493:: has solutions {0, 1} in Z, Q, or R, but in Z6 the solution set is {0, 1, 3, 4} since 32 − 3 = 6 \ 5805:

are commutative, while IF/THEN is not. For comparison, there are 8 commutative two-argument binary

5504: 4869: 4856: 4545: 4233: 3888: 3606:\. is the 4-gradient. Repeated indices are summed over according to Einstein summation convention. 3269: 3213: 2731: 2598: 2310: 1716: 1226: 958: 714: 625: 493: 354: 5869:\mu \left( B_{r_{0}} (0) \ by local finiteness. This is a contradiction, and completes the proof. 513:

Fleet • Fleet Admiral (FADM), Marshal of the Royal Air Force (MRAF). OF-9, General (Gen), General

6342: 5818:\varepsilon , which is a non-real root of 1 (see conic quaternions for examples and references). 5306: 5150: 4387: 4119: 3305: 2790: 2752: 2639:

that the inductance is a purely geometrical quantity independent of the current in the circuits.

2568: 2548: 2535: 2522: 2114: 1435: 1273: 890: 844: 818: 398: 180: 167: 115: 3468: 46:\oint p_{k} dq_{k}. where the integration is over all possible values of qk, given the energy 6103:: . Jump to: navigation, search. Polish Prime Minister Tadeusz Mazowiecki making the V sign. 5926: 5875: 5710: 5671: 5651:& |L|e^{. Under a rotation \theta \rightarrow \theta+\theta' of the polarization ellipse, 4983: 4970: 4912: 4822: 4644: 4519: 4485: 4042: 4016: 3969: 3948: 3797: 3256: 3019: 2964: 2454: 2323: 2008: 1776: 1763: 1552:\. Using this form of the mass, we can again simply write E = mrelc2, even for moving objects. 1448: 865: 638: 154: 6198: 6396: 5946:Δ t is that same time interval as measured in the "stationary" system of reference,: \gamma \ 5399: 4032:: If \nu_1 \le \nu_2 and \nu_1 \ge \nu_2 then we say ν1 is equivalent to ν2 and write \nu_1 \ 3984:\frac{\partial\mathcal{L}. which is called the Noether current associated with the symmetry. 3963:\frac{\partial\mathcal{L}. which is called the Noether current associated with the symmetry. 1201: 594:: Since what we now have here is a SO(p,q) gauge theory, the curvature F defined as \bold{F}\ 6507: 6438: 5636: 5623: 5360: 5197: 4843: 4340: 3705: 3612: 3174:

a (a+1) \ . Lauricella also indicated the existence of ten other hypergeometric functions

3112: 2284: 2068: 2047: 1750: 1647:: 1eV = 1V \times q_e which indicates why the eV is fundamentally a unit of energy since V \ 1070: 1036: 1010: 945: 765: 6477: 6130: 6067: 5743: 4776: 4750: 4455: 4186: 4106: 3044: 2811: 2271: 2245: 1797: 1487: 1096: 1023: 804: 721:

S(\ where S(\mathcal{N} \rho) is the von Neumann entropy of the output and S({\mathcal N}

578: 480: 141: 1744:\frac{k_{u}}{k_ can be used to determine the conformational stability ΔG by the equation 6451: 6261: 6172: 6147: 5785: 5764: 5657: 5538: 5004: 4532: 3867: 3667: 3243: 3077: 2903: 2819: 2349: 2297: 2165: 2101: 1935: 1847: 1687: 1584: 1320: 727: 693: 437: 324: 290: 81: 5771:(dx^a)_\mu. is defined with respect to the connection form B. Here, d is the exterior 6315:

0 suffices for convergence in condition 2, and we obtain: \, P(z) = \prod_n (z-z_n) .

1841:(a=open \wedge t=. Circumscription can simplify this specification, as only necessary 1707:

mz. \mathsf{NatInd}\ P\ mz\ ms\ (\mathsf{ ...And in ASCII: NatInd : all P : Nat -: -->

1116:

C-O-H and H-N=C=O . It forms in a reaction between potassium cyanate and formic acid.

6274: 6211: 5969: 5386: 5043: 4703: 4661: 3625: 3532: 3455: 3398: 3372: 3154: 3099: 2336: 1982: 1976:\gamma^\mu A_. using the Einstein summation notation where γ are the gamma matrices. 1826: 1461: 1414: 1393: 918:

t_1 \in \Phi and let TΦ := \{ \; \overline t \; |\; t \ where TS is the set of terms

3250:. Additionally, the Legendre symbol is a Dirichlet character. . Related functions 3119:

e^{s T} \. where T = 1/f_s \ is the sampling period (in units of time e.g. seconds)

6355: 6244: 5982: 5939: 5798: 5665:

T , then the stopped Brownian motion Bτ- will evolve as per usual up until time T,

5393:\overline{\overline{(p \cdot p. "p implies q" is equivalent to "(p NAND q) NAND p" 5373: 5323: 4668:

z'-z = 1/3 \,\. which indicates that the trait of sightedness is increasing in the

4596: 4472: 4327: 3819: 3684: 3646: 3485: 3385: 3196: 2926: 2228: 2089: 2034: 1922: 1294: 424: 4466:

series resistance of quartz crystal units by zero-phase technique in a pi-network

1246:{hc_sR\over2Lk} = {hc_s\over2Lk}\sqrt. We then have the specific internal energy: 401:: The next step is to consider the equation for u under small perturbations \eta \ 6417: 6232: 6185: 5697: 5313:

0.42e to the carbonyl carbon and oxygen, respectively, and charges of \pm q_{2} \

5137: 4936: 4720: 4166: 4055: 3632:-. whose solution is I = I_{0} e^{-x/\ell} , where x is the distance traveled by 3359: 2832: 2194: 1644: 374:: Probability mass function. Cumulative distribution function. Parameters, p: --> 252: 5292:

p_2(x) ? This problem can be solved by reducing it to the problem of polynomial

3224:\cos \theta . This expansion is used to develop the normal multipole expansion. 2617:

P_3.P_1,. but if the points are expressed in homogeneous coordinates then these

6094:\{c_i \neq c_j| i \neq j; i . Then T \cup S is a collection of L(C)-sentences. 4160:\sqrt{ equal the square roots of the diagonal components of the metric tensor. 2487:(u:v:w). Remark: In some European countries (x:y:z) is customarily represented 1340:: where the (unnormalized) sinc function is defined by \operatorname{sinc}(x) \ 6054: 6033: 5572: 5077: 4763: 4475:: c \ is the speed of light in the vacuum,: h \ is Planck's constant,: \hbar \ 4421: 4289: 3845: 3339: 3320:\alpha . This represents a wave polarized at an angle θ with respect to the x 2222:\sum_{k=1}^{N} \left. Since \sqrt{K} is the local curvature of the trajectory 1521: 1337: 1239: 1109: 1000:\frac{1}{\sqrt{2 as the "creation operator" or the "raising operator" and: a \ 341: 234: 4728:

0). Then it is easy to show that. \Pr(Y=1 | X=x) = \Phi(x. Retrieved from "

851:\sim \left( p_1 \wedge p_2 \wedge. which is by De Morgan's law equivalent to 645:

U(S,V,N_1,..N_n). By referring to U as the internal energy, it is emphasized

6514:

E(k^n) = \frac{1}{. The series on the right is just a series representation

6295: 5723: 5477:\alpha . This represents a wave polarized at an angle θ with respect to the 5412: 5330:

q/f that depends only on the properties of the particle and the surrounding

4809: 2985: 2865: 2708:: That is, the instantaneous angular frequency is defined to be. \omega(t) \ 1380: 1049: 500:

Card(. Härtig: "The φs are equinumerous with the ψs". (Q_Ix)(\phi x,\psi x)\

297:\forall F [\forall x (aRx . Frege's first result is then that this relation 5511:(\mu_1+\mu_2)/2.\,. Then the raw moments mk are. m_1=\left.\Delta\right.\, 5326:: Hence, it is generally possible to define a sedimentation coefficient s \ 5259:\frac{T-T_c}{T_c} measures the temperature relative to the critical point. 5131:

p^{*}(z) . If the coefficients ai are real then this reduces to ai = an−i.

2364:\lambda_{z}^{2} - \frac{. which is always non-negative and zero only for a 6289:

l_w x_w. where lw is the activity coefficient of water and xw is the mole

5811: 3874:

k \ln \Omega,. where Ω is the number of states available to the molecule.

3726: 3560:\frac{x-x_0}{. Because a 2x2 matrix has 2 eigenvectors, we obtain 2 axes. 2998: 2845: 2501: 1901: 1541: 1357:& \mbox{SHA-1. Since g has order q we have. \begin{matrix} g^k & \ 3585:

D_a F_{ . The second equality in the source-free Maxwell equation is the

2872:\rho^{i}(x,u)\frac. A vector field is called horizontal, meaning all the 200:\delta(\omega - \omega_0) , this becomes:. R(1) = \frac{1}{2\pi} \: R(1) 67:{2\over\sqrt. where \omega(\phi)\; is a different dimensionless function 6432:\frac{R\Omega}{U_1}. One key difference between actual turbines and the 6345:: For example, if we order \mathbb{Z} by divisibility, we end up with n\ 6251:\frac{e^{-. and L(x;γ) is the centered Lorentzian profile:. L(x;\gamma)\ 4956:\big [ y(t . We have explicitly included the dependence on the weights. 4479:\frac{h}{2 \pi} \ is the reduced Planck's constant or Dirac's constant, 4428:

Q if Q can be obtained from P by renaming one or more bound names in P.

4130:\left(e^{ of A can be defined via one of several equivalent approaches: 3774:

c^{\phi(n)/p_i} \mod . Thus. \begin{matrix} c^{\phi(n)/p_i}. where m_i \

2015:\phi(x,t) . Similarly. x0 = x(0). is written for x = φ(x,0), and so on. 474:\frac{1}{kT}. where k is Boltzmann's constant and T is the temperature. 96:\phi '(t) = {d. The amplitude function, and the instantaneous phase and 26:

This is a list of all articles that were originally listed on equivlist.

6090:: Then let C be an infinite set of constants not in L of size κ and S \ 5343:

3 \mod 4 , it is much more efficient to use the following identity: x \

4156:: where D is the dimension and the scaling functions h_{k}(\mathbf{q})\ 1908:\ 0 \ ({\rm . A stronger result is Wilson's theorem, which states that 611:

T_n\left(\frac{x-1. where Tn(x) is a Chebyshev polynomial of the first

463: 411: 6218:\frac{1}{2} \sum_{k=. The average of this derivative over a time τ is 5704:\frac{\Gamma (n+1, -1. where Γ denotes the incomplete gamma function, 3699:

1 \,. Mole fractions are one way of representing the concentrations of

2583:\lang x | n \rang. The most important property of these wavefunctions 1895:\ln(1/R) . The order of integration and summation may be interchanged 6116:\sum_{H} Q(H) \ ,. then the likelihood is simply this bound plus the 5825:

Theoretical and experimental justification for the Schrödinger equation

5425: 4582:\frac{2\pi}{T} . An alternative definition of the continuous Fourier 2150:

x^q \mod \Phi ,. where q is the order of the residue field OK mod φ.

1344:\frac{\operatorname{ . Now, substituting in \frac{2\pi}{\lambda} = k 331:\psi * \ ;; if \alpha \models \neg \mu , then (\psi * \mu) * \alpha \ 4462:

444 (1973) Basic method for the measurement of resonance freq &

3778:

m \mod p_i . Since pi is chosen to be small, mi can be recovered be

3712:

m r^2\,. where. m is its mass,: and r is its perpendicular distance

2911: 2427:(q_{1}, q_{2. that need not transform like a vector under rotation. 272:-\left ( A^{0} . The term on the left is the notation for the inner 6100: 5585: 4408: 4353: 3733:\frac{\ . Now, assume these elasticities to be constant over time. 2129:\frac{\rho}{\rho_c} = \. This term originally was used as a means to 1963:{ 1 \over {\sqrt {1 - {{ . The magnitude of the 4-velocity is one, 1122: 914:: Define a binary relation on the set of S-terms t0˜t1 iff \; t_0 \ 736: 6349:

m if and only if n=\pm m , so that (\mathbb{Z},\mid)\;\;\approx .

5700:: Subfactorials can also be calculated in the following ways: !n \ 5484:

Sinusoidal plane-wave solutions of the electromagnetic wave equation

5463:

Sinusoidal plane-wave solutions of the electromagnetic wave equation

5440:

4. — giving a value of 4. The sampled value was then transmitted,

4697:|\delta_k|^2 . For scalar fluctuations, n + 1 is referred to as the 4253:

rR(r) , with a centrifugal term \hbar^2l(l+1)/2m_0r^2 added to V,

1188:\int d\theta \int \rho d\rho \. If the cylindrical multipoles are 405:

u - u_{0} from perfectly circular orbits. On the right-hand side,

196:: If we model the power spectrum as a single frequency S(\omega) \ 6411:. And so primality is determined by the quadratic residues of p. 5886:

1 - \frac{Q_{out}. where \eta_{th} \, is the thermal efficiency,

5588:: In 5 Euclidean dimensions, the relevant isomorphism is Spin(5)\ 5389:: "p or q" is equivalent to "(p NAND p) NAND (q NAND q)", p + q \ 5230:\frac{d\mathbf{r}. The time derivative of position in a rotating 3479:

0 \mod 9 so the resulting number z = n - c\, is a multiple of 9.

743:\frac{\pi^2\textit{, (1). where E = modulus of elasticity of the 679:\begin{pmatrix} \psi_x \\. is the Jones vector in the x-y plane. 5750:

yx\,. The distance from x to y is the same as that from y to x.

5558:\left|\mathbf{r} - \mathbf{r is the distance between the charge 5030: 4837:

4ac-b^2. is the negative of the discriminant. When q < 0, then

4729: 4313:

2 \frac{\mathrm{atanh} \ \xi}. where the parameter ξ is defined

4126:

where t is the "time parameter", the ordered exponential OE(t):\

3653:

H(s) \Big|_. be the complex frequency response of system H (s).

3405:{ 1 \over {\sqrt {1 - {{ . The magnitude of the 4-velocity is a 1723:\frac{\left^c \. The law of chemical equilibrium says that this 1612:\sqrt{\frac{3e^2\rho}{. is called the Fermi-Thomas screening wave 5153:: Zelinsky wondered if there exists a refactorable number n_0 \ 5067:

For any triangle \bar{A_{1}}\bar{A_{2}} define the cross c_{3}\

4197:

However, Hadamard matrices have been shown to exist for all m \

2083:\langle (A-\langle A\. and similarly for the variance of B(ω), 2062:\langle (A-\langle A\. and similarly for the variance of B(ω), 1507:

y^2\quad(\hbox{mod }. where n is the integer to be factorized.

939:\langle A^2-\langle A. and similarly for the variance of B(ω), 717:: The coherent information is defined as I(\rho, \mathcal{N}) \ 5754:

This can be done as xy \le zu \leftrightarrow \forall v ( zv \

5110:\frac{k_{-1}}{. where k1 and k-1 are the forward and backward 4083:

x(nT) = \cos(\pi. are in every case just alternating –1 and +1,

4075:

x(nT), \quad n\in (integers). The sampling theorem leads to a

2979:\frac{J}{M}. where. M is the mass of the black hole: J is the 2897:

S(. These definitions parallel the use of the classical joint

2516:- N k H. so, according to the H-theorem, S can only increase. 6336:\frac{1}{. The stress-energy operator is defined as a vertex 5490:\alpha . This represents a wave polarized at an angle θ with 4990:\frac{1}. The radius of gyration is also proportional to the 1400:|E| - mc^2. The first spanning eigenstate in each eigenspace 379:

1-p\,. Support, k=\{0,1\}\,. Probability mass function (pmf)

3350:"p or q" is equivalent to "(p NOR q) NOR (p NOR q)", p + q \ 3038:(\neg J \wedge J) \vee (\neg J (by the law of distributivity) 3026:{\rm false} \vee (\neg J \wedge \ (because J \wedge \neg J \ 1916:\begin{matrix} \underbrace{ n!^ ,. or as,. n\$ =n!^{(4)}n! \, 807:: (Fundamental theorem of arithmetic); Also, (n-1)! \,\,\, \ 246:

R_N \,. The reconstruction of a signal from its samples can

6255:\frac{\gamma}{. The defining integral can be evaluated as: 6001:

portfolio beta. Like the Sharpe ratio, the Treynor ratio (T)

4147:\Phi \wedge \Phi \ , we see that φ is satisfiable as well. 3518:\frac{D}{s^{2. Defining the dimensionless variables \zeta \ 2893:

S(. and the quantum mutual information:. S(\rho^A:\rho^B) \

2810:(ax_{i-1}^{-. where. 0 \le x_{i} < m. Retrieved from " 1731:\frac{k_{f}}{k_{b}. Since the rate constants are constant by 1604:\sqrt{\frac{\rho e^2}{. The associated length λD ≡ 1/k0 is 4655:

P \ ,. The duals of these schemata, involving existential

4321:\frac{p^{2/3}. The frictional coefficient is related to the 3413:{dv^{\mu} \ . The 4-acceleration is always perpendicular to 2712:\phi^\prime(t) \. and the instantaneous frequency (Hz) is 2011:: In fact, notationally, one has strict equivalence: x(t)\ 4612:\sum_{k=1}^n{1\over. The problem terms now contain −ln(−μ) 4402:{1 \over \sqrt{2}}. then a circular polarization state can 2812:

http://en.wikipedia.org/Inversive_congruential_generator%22

6445:(x + : there are two sets of labels for the equations.) 6222:

which is clearly equal and opposite to \mathbf{F}_{kj} \

2393:: Compute xp = x mod p, xq = x mod q. If x_p^{(p-1)/2} \ 2214:\frac{1}{2} \sum_{k=. Since the line element ds2 in the 1515:\prod_{k}p. where the products are taken over all k for 6281:

p / p_0. where p is the vapor pressure of water in the

3005:

e^{iH\tau} . A combination of time translation with an

1791:

I_{k}\omega_{k} , taking the cross product and using the

1429:\psi^\dagger \gamma_0. is called the Dirac adjoint of ψ. 1408:\psi^\dagger \gamma_0. is called the Dirac adjoint of ψ. 1361:& g^{{. Finally, the correctness of DSA follows from 884:-{i\over2}(x^2\. Where Mμν are the Lorentz generators, 653:

A(T,V,N_1,..N_n). In terms of the Helmholtz free energy,

266:

Basic introduction to the mathematics of curved spacetime

6424:\frac{U_1-U_2}{U_1}. a is the axial induction factor. 2876:

The jet bundle J^{r}\pi\, is co-ordinated by (x,u,w) \

2771:\frac{6}{a b^{2}} \. The J coefficients are the Jeffery 2746:\frac{ . The following is general to all bunched beams, 2508:\int { P ({\ln P}) d^. where P(v) is the probability. 2356:\frac{1}{N+1}. where r_{m}^{(i)} is the mth Cartesian 2022:

Formulation of Maxwell's equations in special relativity

1176:: where the interior multipole moments are defined Q \ 6124:\prod_i Q_i(H_i) ,. where Hi is a disjoint part of the 5860:

c t . The acceleration \mathbf{f} is independent of m.

5814:: They allow for powers, roots, and logarithms of j \ 5566:

q \left( r^{\prime} . As with axial multipole moments,

5286:

Schwartz-Zippel lemma and testing polynomial identities

1972:: If A is a covariant vector, i.e. 1-form,. A\!\!\!/\ 1276:: Transposition, (p → q) ⊢ (¬q → ¬p), If p then q is 1004:\frac{1}{\sqrt{2}} \ as the "annihilation operator" or 5801:: Of the four functions defined above, OR, AND, and 3716:

where M is the total mass of the rigid body, R^{2} \

3691:\frac{n_i}{n} = \frac{N_i. where. n = \sum_j n_j \, 3342:: "not p" is equivalent to "p NOR p", \overline{p} \ 3276:\sqrt{\frac{c}{2\pi}. which diverges for all n : --> 1951:: The velocity in spacetime is defined as. v^{\mu} \ 327:: if \alpha \models \mu then (\psi * \mu) * \alpha \ 2121:\left(\frac{\dot{a}. 3\frac{\ddot{a}}{a} = \Lambda 6522:

E(e^{tk}). The series is just the definition of the

5114:

where the two equilibrium concentrations R_{\pm} \

5024:-{\pi \ln(ky)\over \. so that. 0\le \varphi \le \pi 217:

where the interior axial multipole moments I_{k} \

5600:

In 6 Euclidean dimensions, the isomorphism Spin(6)\

4689:\frac{\rho. where \bar{\rho} is the average mass 4193:0 \mathrm{\,mod\,} 4. If m is of the above form, 3925:{d \over ds} + \. and Γ is a Christoffel symbol. 3013:e^. A bit of algebraic manipulation shows that the 1887:\frac{4R}{{(1-R)^ is the coefficient of finesse. 1740:: The dimensionless equilibrium constant K_{eq} \ 28:

First, all math-related articles should be removed.

4394:\alpha . This represents a wave polarized at an 2674:\partial_{\beta} \left( SI \right): \Box A^{\mu} \ 6441:: Note that in this webpage, \mbox{Eq.} (4.x) \ 6036:: The negation of conjunction \neg (p \and q) \ 5912:U-TS = \mu n - PV ~. . Gibbs free energy. ~ G \ 5867:There is no infinite-dimensional Lebesgue measure 5157:a \mod m , does there necessarily exist n : --> 1254:{\epsilon\over k}. then one can say. T_E \ne T_D 986:<\sigma, {. where <\sigma, {\mathbf u}: --> 619:\frac{1}{(x+. The orthogonality of the Chebyshev 511:British and United States military ranks compared 135:\forall m_1\cdots is defined to be \Pi^0_{n+1} 5878:: Thermal efficiency is defined as \eta_{th} \ 4651:\exists. and. \forall x ( P \rightarrow Q(x) ) \ 2401:1 mod q, then x is a quadratic residue mod N. 5976:v_i 1 \leq i \leq n \Rightarrow f(u_1 It is of 5127:: A polynomial is called reciprocal if p(z) \ 4998:\frac{1}{. similar to the hydrodynamic radius, 3552:Ax^2+By^2+Cx+Dy+Exy. That can be written as: 978:\frac{df}{. The parallel between the tangent 696:: For example, there are two models of P(a) \ 6044:The negation of disjunction \neg (p \or q) \ 4137:Original proof of Gödel's completeness theorem 598:d\bold{A}+\bold is pointwise gauge covariant. 5852:where dτ is c times the proper time interval 5850:Theoretical motivation for general relativity 5498:{1 \over \sqrt{2}}. Elliptical polarization. 4367:Photon dynamics in the double-slit experiment 4247:Particle in a spherically symmetric potential 3127:x(nT) \ are the discrete samples of x(t) \ . 2054:\. Where \omega\in \mathbb{R}^n and \omega 931:\. Where \omega\in \mathbb{R}^n and \omega 241:x(nT) = x \left( { for integer n \, and T \ 8: 6311:: If the sequence, {zi} is finite then p_i \ 5950:\frac{1}{\sqrt{1 - \ is the Lorentz factor, 3915:Newtonian motivations for general relativity 3859:N-Electron Valence state Perturbation Theory 3526:t/t_{0} , the Mason-Weaver equation becomes 2793:: The inverse temperature is given by \beta\ 2495:a (x:y:z. even though. (x:y:z) \ne a (x:y:z 1938:: where "psi-bar" is defined as \bar{\psi} \ 2672:Inhomogeneous electromagnetic wave equation 2590:Implementation of mathematics in set theory 2075:\frac{1}{\sqrt{. x(t) = \frac{1}{\sqrt{2 \ 209:: where the axial multipole moments M_{k} \ 5660:: Stopping at a deterministic time T : --> 4273:Partition function (statistical mechanics) 3285:\sqrt{\frac{c}. which diverges for t : --> 2912:http://en.wikipedia.org/Josephson_phase%22 2835:: Defining the acceleration to be \vec a \ 2179:Fundamental theorem of Riemannian geometry 1421:- i. To describe a relativistic system, 1112:: Two tautomers exist for cyanic acid, N \ 859:\left( h_1 \wedge h_2 \wedge h_3 \cdots \ 3882:\frac{^y ^z. In an electrochemical cell, 3475:1 \mod 9, n = n_m + n_{ . Hence n - c \ 2457:: where k is the wave vector and \omega \ 2157:Frobenius theorem (differential topology) 5234:where \mathbf{a}_{\mathrm{rotating}} \ 4964:f\left [ x(t). where t is a time index. 4586:Making a change of variables to \tau \ 3942:\ is the unit vector from object 1 to 2 3295:: If the initial vector \mathbf{x}_{0} \ 2637:Inductance/derivation of self inductance 1284:Tautology, p ⊢ (p ∨ ¬p), p is true is 1208:P(a) \ . But, using De Morgan's laws, 470:e^{\beta \. and β defined as:. \beta \ 6166:\operatorname{div}\ \operatorname{grad 5350:Outputs: R, an integer satisfying R^2 \ 5158:n0- such that n is refactorable and n \ 5063:{Q(B,C. See also spread polynomials. 4730:http://en.wikipedia.org/Probit_model%22 3579:Maxwell's equations in curved spacetime 3546:Matrix representation of conic sections 3140:\mathbf{r} \times \mathbf is conserved 1783:\. where \mathbf{I} is the moment of 1475:Divide-and-conquer eigenvalue algorithm 6467:: In other words, a formula alive(0) \ 5916:U-TS+PV = \mu n ~. . Enthalpy. ~ H \ 4415:2\pi/\lambda \! as its magnitude) and 4208:Parameterized post-Newtonian formalism 3148:m \frac{d\mathbf{r as usual and where 2910:\theta_2-\theta_1 . Retrieved from " 1694:is the concentration of free enzyme). 1216:\neg \Diamond \neg p ,: \Diamond p \ 1052:: Now reformulate things so that \psi\ 245:{ 1 \over f_s }. as long as. f_s : --> 18:Knowledge talk:WikiProject Mathematics 4436:(\nu x if x is not a free name of Q. 4330:: A(t)\cdot \cos[2\pi ft + \varphi, \ 3932:Newton's law of universal gravitation 3615:: where we define \mathbf{\Delta(s) \ 3602:: \partial \over { \partial x^a } } \ 3439:\sqrt{4\pi} q_{cgs. \mathbf{E}_{LH} \ 2967:: ds^{2}=-\frac{\Delta}{\rho: \Delta\ 2933:\textbf{: \hat{\textbf{y}}_{k|k} \ 2848:: a ≠ b, a is not equal to b, a \not\ 2682:\partial \over { \partial x^a } } \ 2659:Information flow (information theory) 708:P(b) one would consider the value of 7: 4829:x + \frac{b}{2c} ,. define. -A^2 \ 4647:: \forall x ( P(x) \rightarrow Q ) \ 4499:Planck's law of black body radiation 3800:: p = 2 \quad \mbox{and} \quad d_K \ 3785:Naccache-Stern knapsack cryptosystem 3741:\frac{MRP_t-w_t}{w_t}=\epsilon_ . 3657:\mathcal{H} \lbrace x(t) \rbrace \ 3593:{R^. is the Ricci curvature tensor. 2571:: \Psi^{(S)}_{n_1 n_2 \cdots n_N}, \ 2208:Gauss' principle of least constraint 1861:Exact renormalization group equation 1703:: \mathsf{NatInd}\ P\ mz\ ms\ zero \ 811:\, for all composite numbers n : --> 704:For example, in the formula P(a) \ 75:g^{\alpha\ , l\; is a length scale, 6403:\ -. 1\cdot(p-1)\cdot 2\cdot (p- 5519:\ln(M. which yields the cumulants: 5309:: It assigns charges of \pm q_{1} \ 4369:E_y . and. \mid \mathbf{E} \mid^2 \ 4283:\langle (E -. The heat capacity is 3327:Linearised Einstein field equations 3136:: The angular momentum \mathbf{L} \ 2906:: then the Josephson phase is \phi\ 994:Creation and annihilation operators 504:(Q_Lx. Chang: "The number of φs is 6328:\frac{\delta}{ is not conserved 6324:: The current defined as J^\mu(x)\ 6158:\nabla \cdot: \operatorname{curl} 5300:0. Hence if we can determine that 4790:Pythagorean trigonometric identity 4603:. This converges for Re(s) : --> 4275:kB denoting Boltzmann's constant. 2784:\tau then \Gamma\vdash t : \tau . 2252:q ({\rm mod}\ p) ) or such that q 1651:{W\over q_0} or equivalently V \ 284:A^1 \ . It transforms as a scalar 61:Alternatives to general relativity 24: 6309:Weierstrass factorization theorem 5611:Spin-weighted spherical harmonics 3809:p = 3 \quad \mbox{or} \quad p \ 3805:2 \quad \mbox{and} \quad \left(\ 3144:where the momentum \mathbf{p} \ 3047:: For example, the schema \Box(A\ 2952:Kepler's laws of planetary motion 1559:Eddington-Finkelstein coordinates 6154:\nabla: \operatorname{div} \ \ 5185:Reproducing kernel Hilbert space 4919:\frac{n_i}{\sum_j n_j} . x'_i\ 4266:a^{\dagger}(\phi_i and we have: 4069:Nyquist–Shannon sampling theorem 4030:Numbering (computability theory) 3748:Multivariate normal distribution 3168:Lauricella hypergeometric series 2804:Inversive congruential generator 2330:b (\mathfrak{l}) for a L b (and 1854:\phi_{sr} - a short-ranged part 1638:\frac{ \partial A_b }{ \partial 1167:\mathbf{\hat r}\frac{\partial . 1150:\mathbf{\hat r}\frac{\partial . 912:Consistency (Mathematical Logic) 6088:Upward Löwenheim–Skolem theorem 5526:Solovay-Strassen primality test 4249:equation for the variable u(r)\ 3628:: \frac{dI}{dx} = -I n \sigma \ 2763:K \frac{J_{\alpha}^{\prime. L \ 2378:Hamiltonian (quantum mechanics) 660:Circle of confusion computation 483:: \mathbf{p} \psi(\mathbf{x}) \ 5957:Time-evolving block decimation 5882:\frac{W_{out}}{ or \eta_{th} \ 5046:: \prod_{p_i\in P} p_i^{a_i} \ 4632:Pontryagin's minimum principle 4599:: \operatorname{Li}_{s+1}(z) \ 4279:\langle \delta E^2 \rangle \ 3917:The geodesic equation becomes 2624:Indefinite inner product space 2391:Goldwasser-Micali cryptosystem 1701:Epigram (programming language) 905:\Big(\begin{matrix} a & - 592:Cartan connection applications 566:Canonical commutation relation 174:M(x,y) = ), thus turning the 103:Ankeny-Artin-Chowla congruence 88:\mathcal{F}\left\{s_\mathrm{a 1: 6497:0 (mod 6) and 42 − 4 = 12 \ 6023:: \begin{matrix}Q(AC) & \ 5469:\begin{pmatrix} \psi_x^* . 5251:\lim_{N \rightarrow \infty 4766:: So for our purposes \tau\ \ 4638:0 ), then:. H(x^*(t),u^*(t), 4097:Okamoto-Uchiyama cryptosystem 2738:\frac{ ,: \frac{1}{T_{h}} \ 2431:\mathbf{p} \cdot \mathbf{q} \ 1297:: \varphi=\exists y(y\cdot y\ 1288:. to p is true or p is false 1174:Cylindrical multipole moments 1157:Cylindrical coordinate system 1140:Cylindrical coordinate system 1056:{\phi + i \chi\over \sqrt{ . 687:\left ( {\cos\theta +i\sin . 5779:(dB^a). is gauge invariant. 5528:: \left(\frac{a}{p}\right) \ 5317:0.20e to the amide nitrogen 5168:Relational quantum mechanics 5091:Ray transfer matrix analysis 3312:\begin{pmatrix} \psi_x \\ 3263:\frac{1}{\sqrt{1 - \ is the 3246:: \left(\frac{a}{p}\right) \ 3216:: where we have taken \eta \ 3058:Kruskal-Szekeres coordinates 2941:\textbf{H}: \textbf{i}_{k} \ 2678:\partial_{\beta} \left( cgs 2397:1 mod p and. x_q^{(q-1)/2} \ 1501:Dixon's factorization method 1086:: \Lambda_c^0(\mathbb{R}^n)\ 961:: \nabla_{e_j} {\mathbf v} \ 925:Continuous Fourier transform 605:Chebyshev rational functions 451:Blum-Goldwasser cryptosystem 305:\forall x \forall y \forall 6110:Variational message passing 6074:\mathbf{x}_{1} between the 5843:|R\rangle \langle R | - . 5827:\begin{pmatrix} \zeta_x \\ 5626:: std \frac{K \cdot t}{V} \ 5552:Spherical multipole moments 4883:Quantum harmonic oscillator 4833:\frac{a}{c} - \. where. q \ 4449:\psi(t) , thus proving the 3991:Noncentral chi distribution 3891:: where \Delta m_{ij}^{2} \ 3768:Naccache-Stern cryptosystem 3231:Legendre rational functions 3093:\delta\, then Y=Y_nf_y^3\, 3092:f_y-b^*/200; if f_y : --> 3084:(L^*+16)/116; define f_x\ 2767:\frac{2}{a b^{2} \left. N \ 2742:\frac{ ,: \frac{1}{T_{v}} \ 2646:Inertial frame of reference 2408:Hamiltonian fluid mechanics 2317:\partial u_x /\partial y . 1351:Digital Signature Algorithm 1064:{\chi + i\phi\over\sqrt{ . 880:-x_\mu\partial^\mu , K_\mu\ 832:Conditional quantum entropy 213:q a^{k} contain everything 84:: S_\mathrm{a}(\omega)\,, \ 6540: 6008:Trigonometric substitution 5639:: \begin{matrix} I & \ 4381:\begin{pmatrix} \psi_x \\ 3499:Magnetic resonance imaging 2778:Intuitionistic type theory 2575:\lang x_1 x_2 \cdots x_N; 2468:Higher residuosity problem 1989:\frac{h}{2\pi} where h is 1881:Fabry-Pérot interferometer 1779:: \frac{d\mathbf{L}}{dt} \ 1417:: p_j \psi(\mathbf{x},t) \ 1353:: \begin{matrix} k & \ 1331:\int_M d^dx \sum_\alpha A 6399:: 1\cdot 2\cdots (p-1)\ \ 6021:Triple quad formula proof 4738:Projective transformation 4672:\operatorname{var}(z_i) \ 4576:Poisson summation formula 4552:\langle k^{ (see Table). 4201:0 \mathrm{\,mod\,} 4 for 3976:\int_M d^nx \mathcal{L 3813:1 (cf. Eisenstein prime) 3134:Laplace-Runge-Lenz vector 2971:r^{2}-2Mr+a^{2: \rho^{2}\ 2421:Hamilton-Jacobi equations 2104:: \sin(A) \cdot \sin(B) \ 1310:: Obviously, n_s(\vec r)\ 1308:Density functional theory 540:Calculus of constructions 194:Autocorrelation technique 6141:a^\alpha \frac{\partial 5993:portfolio return,. r_f \ 5893:Thermodynamic efficiency 5647:\begin{matrix} L & \ 5575:: S^{\alpha\beta\mu}(x)\ 5337:Shanks-Tonelli algorithm 5273:Saha ionization equation 5224:Rotating reference frame 5104:Receptor-ligand kinetics 4812:: \langle (gG)^2\rangle\ 4710:1\mod n: a^{d\cdot 2^r}\ 4260:Particle number operator 4139:then, considering \Psi \ 3902:Newman-Penrose formalism 3835:: \frac{D}{Dt}(\star ) \ 3199:: a_1+a_2+\cdots+a_{24}\ 3088:f_y+a^*/500; define f_z\ 2380:: \langle H(t) \rangle \ 2071:: unitary, X_1(\omega) \ 1998:: \Delta \alpha/\alpha \ 1814:Euler's totient function 1598:Electric field screening 1060:But let's redefine \psi\ 972:Covariant transformation 812:5. (Wilson's theorem) 792:Complex projective plane 751:\frac{\pi^{2}E_T, (2) 700:P(b) with domain {a,b}, 496:: (Q_Lx)(\phi x,\psi x)\ 71:where h^{\alpha\beta}\ 54:\oint \frac{\partial w_ 40:Action-angle coordinates 6382:Wigner's classification 6369:Wien's displacement law 6322:Weinberg-Witten theorem 6150:: \operatorname{grad} \ 5997:risk free rate. \beta \ 5906:Thermodynamic equations 5835:{1 \over \sqrt{2}} . 5661:0: if \tau (\omega) \ 5486:: \alpha_x = \alpha_y \ 4896:Quasi-invariant measure 4740:: n \leftrightarrow c \ 4683:Primordial fluctuations 4443:Picard–Lindelöf theorem 4390:: \alpha_x = \alpha_y \ 4307:Perrin friction factors 3833:Navier-Stokes equations 3678:\Box A. More examples: 3433:Lorentz-Heaviside units 3293:Linear dynamical system 3286:0 and is therefore not 2719:Interaction information 2706:Instantaneous frequency 2693:Instantaneous frequency 2481:Homogeneous coordinates 2050:: \mathcal{F}\{f\}(w) \ 1996:Fine-structure constant 1675:Elliptical polarization 1662:Ellipsoidal coordinates 1655:{\triangle E\over q_0} 927:: \mathcal{F}\{f\}(w) \ 520:Brunt-Väisälä frequency 207:Axial multipole moments 118:: where g (g) (n - 1) \ 6389:0-, m = 0 but P0 : --> 6040:p \bar{\and , and the 4619:Polytomous Rasch model 4559:Poisson random measure 4513:\frac{hc}{2L}\sqrt{n_ 4154:Orthogonal coordinates 3750:: \mu _{1,\dots,N}(X)\ 3640:\frac{1}{n\sigma} = \ 3420:Lorentz transformation 2259:Generalization (logic) 2136:Frobenius endomorphism 1970:Feynman slash notation 1949:Fermi-Walker transport 1632:Electromagnetic tensor 1619:Electromagnetic tensor 1572:Edge-graceful labeling 1368:Dimensionless quantity 1261:Deceleration parameter 553:Calculus of variations 386:Bernstein's inequality 372:Bernoulli distribution 312:Behrens-Fisher problem 221:\frac{q}{a^{k contain 129:Arithmetical hierarchy 6491:Zero-product property 6465:Yale shooting problem 6407:\prod_{j=1}^m\ j^2\ \ 5989:Treynor ratio,. r_p \ 5685:Strong RSA assumption 5473:\alpha_x = \alpha_y \ 5245:Rushbrooke inequality 5211:Riemann zeta function 5125:Reciprocal polynomial 5118:E \pm D are given by 5059:: s(\ell_1, \ell_2) \ 5057:Rational trigonometry 5018:Randall-Sundrum model 4986:: \mathbf{r}_{mean} \ 4952:: K_t( \mathbf{w} ) \ 4950:Radial basis function 4300:\{\pm I,\pm iI,\pm X 4221:Parametric oscillator 4036:\nu_2 . . See also 4004:Nondimensionalization 3729:: \epsilon_{SR}^{-1}\ 3567:Maupertuis' principle 3512:Mason-Weaver equation 3329:: where h_{bc,}{}^a \ 3316:\alpha_x = \alpha_y \ 2887:Joint quantum entropy 2525:: \frac{1}{R_{hyd}} \ 1738:Equilibrium unfolding 1204:: \exists x \, P(x) \ 1084:Current (mathematics) 779:Completing the square 759:{F_y}-\frac{F^{, (3) 673:Circular polarization 5726:: \overline{\theta}\ 5505:Skellam distribution 5071:1 - s_{3} . Then: 5011:1\mod 4 is a prime. 4872:: \phi(\mathbf{r}) \ 4870:Quantum field theory 4857:Quantum entanglement 4546:Poisson distribution 4234:Partial molar volume 4019:: If we define 0^0 \ 3997:\sqrt{\frac{\pi}{2} 3889:Neutrino oscillation 3522:z/z_{0} and \tau \ 3422:: where now \gamma \ 3220:a/r < 1 and x \ 3214:Legendre polynomials 3009:\alpha^{\mu}_{\tau}\ 2988:: \zeta^\prime(a,z)\ 2929:: \textbf{Y}_{k|k} \ 2889:: S(\rho^A|\rho^B) \ 2732:Intrabeam Scattering 2599:Incidence (geometry) 2448:\int \mathbf{ where 2442:Hamilton's principle 2311:Green-Kubo relations 1829:: Clipped(t_1,f,t) \ 1787:Substituting L_{k} \ 1717:Equilibrium constant 1544:: m_{\mathrm{rel}} \ 1227:Dead-end elimination 1073:: \alpha^{(P-1)/3} \ 959:Covariant derivative 876:-i\partial_\mu. D\ 715:Coherent information 626:Chemical equilibrium 494:Branching quantifier 355:Benaloh cryptosystem 335:\psi * \ ;; if \psi 6343:Well-quasi-ordering 6048:p \bar{\or and the 6010:: \sec^2\theta-1\;\ 5920:U+PV = \mu n + TS~ 5307:Secondary structure 5151:Refactorable number 4685:: \delta(\vec{x}) \ 4604:0 and all z except 4388:Photon polarization 4120:Ordered exponential 3600:Maxwell's equations 3306:Linear polarization 2791:Inverse temperature 2753:Intrinsic viscosity 2734:: \frac{1}{T_{p}} \ 2661:: H(h|l) - H(h|l')\ 2569:Identical particles 2549:Hyperbolic function 2536:Hyperbolic function 2523:Hydrodynamic radius 2115:Friedmann equations 2037:: \partial_\alpha \ 1806:(x) = i^2 e^{ix} = 1455:\log_c (b) \cdot \ 1436:Dirichlet character 1280:. to if not q then 1274:Deductive reasoning 1220:\neg \Box \neg p . 891:Conjugate transpose 845:Confirmation holism 819:Conditional entropy 293:: 76: \Vdash aR*b \ 181:Atkinson resistance 168:Associative algebra 116:Anonymous recursion 5927:Thomson scattering 5876:Thermal efficiency 5711:Supercritical flow 5672:Strong pseudoprime 5465:: \langle \psi | \ 5238:\ is the apparent 4984:Radius of gyration 4971:Radiative transfer 4913:Quasispecies model 4823:Quadratic integral 4676:\operatorname{E}( 4645:Prenex normal form 4590:t + nT results in 4520:Plasma oscillation 4432:(\nu x)(P | Q) \ 4214:\alpha/c_0 c_1= . 4043:Numerical aperture 4017:Norm (mathematics) 3955:\int_M \mathrm{ 3798:Narrow class group 3257:Length contraction 3020:Knights and knaves 2965:Kerr-Newman metric 2626:: The operator J \ 2605:L_2 \times L_3 \ 2601:: L_1 \times L_2 \ 2455:Helmholtz equation 2235:|E(0,0)| and I_0 \ 2009:Flow (mathematics) 1449:Discrete logarithm 987:is a real number. 872:-i(x_\mu\ , P_\mu\ 866:Conformal symmetry 639:Chemical potential 399:Bertrand's theorem 301:115: \Vdash I(R) \ 183:: 1 \mbox{ gaul} \ 155:Arrhenius equation 6508:Zeta distribution 6439:WKB approximation 5674:: a^{d\cdot 2^r}\ 5643:& |E_x|^{2 5637:Stokes parameters 5624:Standardized Kt/V 5515:K(t;\mu_1,\mu_2)\ 5361:Shannon expansion 5198:Reynolds stresses 5080:: Let \mathbf{V}\ 4844:Quadratic residue 4535:: \cos(x \pm y) \ 4522:: v \sim v_{ph} \ 4486:Planck's constant 4341:Phase correlation 4236:: \overline V_i \ 3970:Noether's theorem 3949:Noether's theorem 3720:\mathbf{R} \cdot 3706:Moment of inertia 3613:Mean field theory 3589:{R^{ a }}_{ b } \ 3581:: {F_{ab}}_{;a} \ 3458:: Mach8: \Omega \ 3346:\overline{p + p} 3270:Lévy distribution 3113:Laplace transform 3001:: \alpha_\tau(A)\ 2822:: a \vee b, a*b \ 2721:: I(\mathcal{V})\ 2324:Green's relations 2285:Gibbs free energy 2261:: \vdash P(x) \ \ 2069:Fourier transform 2048:Fourier transform 1777:Euler's equations 1764:Euler's criterion 1751:Euler pseudoprime 1133:\cos^{-1}(-1/3 . 1071:Cubic reciprocity 1039:: (f\star g)(x) \ 1037:Cross-correlation 1026:: (f\star g)(x) \ 1011:Critical exponent 948:: \alpha_s(k^2) \ 946:Coupling constant 794:: (z_1,z_2,z_3) \ 766:Comoving distance 559:c , where c is a 6531: 6397:Wilson's theorem 6131:Vector (spatial) 6068:Two-body problem 5613:: \bar\eth\eta \ 5400:Shor's algorithm 4751:Propensity score 4456:Piezoelectricity 4107:Optimal stopping 4099:: H = \{ x : x \ 3904:: {}^{(l)}G(t) \ 3308:: |\psi\rangle \ 3045:Kripke semantics 2937:\textbf{I}_{k} \ 2759:\frac{M}{2}. J \ 2410:: where \vec{v}\ 2272:Ghost condensate 2246:Gaussian integer 2142:x^q \mod \Phi . 1833:\exists a,t [ 1677:: |\psi\rangle \ 1488:Divisor function 1442:n \mod That is, 1202:De Morgan's laws 1180:\lambda , I_{k} 1024:Cross covariance 805:Composite number 675:: |\psi\rangle \ 662:: N = f-number \ 579:Capillary number 546:& \forall x 481:Bra-ket notation 142:Arithmetical set 105:: {u \over t}h \ 6539: 6538: 6534: 6533: 6532: 6530: 6529: 6528: 6478:Young's modulus 6452:Worm-like chain 6262:Volume fraction 6199:Vigenère cipher 6173:Vertex function 6148:Vector operator 6084: 5786:Teleparallelism 5765:Teleparallelism 5744:Tarski's axioms 5740: 5658:Stopped process 5541:: S_{\lambda} \ 5539:Source function 5269: 5005:Ramanujan graph 4933: 4806: 4796:\sin^2(-x) and 4777:Proth's theorem 4533:Plus-minus sign 4187:Paley's theorem 4183: 4093: 4045:: \mathrm{NA} \ 3868:Nernst equation 3764: 3668:Modal companion 3649:: H(j \omega) \ 3501:: {\vec k}(t) \ 3452: 3244:Legendre symbol 3078:Lab color space 3074: 2923: 2904:Josephson phase 2862: 2820:IP (complexity) 2609:L_3 \times L_1 2565: 2470:: x^{(p-1)/d} \ 2374: 2350:Gyration tensor 2298:Grand potential 2191: 2166:Fujikawa method 2102:Frequency mixer 1936:Fermionic field 1925:: a^{(N-1)/2} \ 1877: 1848:Ewald summation 1816:: a^{\phi(n)} \ 1798:Euler's formula 1753:: a^{(n-1)/2} \ 1688:Enzyme kinetics 1585:Elastic modulus 1538: 1511:\prod_{k}x_k^2\ 1383:: \Delta_T(t) \ 1321:DeWitt notation 1229:: U_{kl}^{AB} \ 1198: 1097:Curry's paradox 974:: {\mathbf v} \ 728:Colonel General 694:Circumscription 536: 466:: z(\beta,\mu)\ 438:Blind signature 325:Belief revision 291:Begriffsschrift 280:-A^0 \quad A_1\ 231: 82:Analytic signal 36: 22: 21: 20: 12: 11: 5: 6537: 6535: 6527: 6526: 6505: 6488: 6475: 6462: 6449: 6436: 6415: 6394: 6379: 6366: 6353: 6340: 6319: 6306: 6293: 6275:Water activity 6272: 6259: 6247:: G(x;\sigma)\ 6242: 6230: 6212:Virial theorem 6209: 6196: 6188:: where \tau \ 6183: 6170: 6145: 6128: 6107: 6098: 6083: 6080: 6079: 6078: 6065: 6052: 6031: 6018: 6005: 5980: 5970:Tree automaton 5967: 5954: 5937: 5924: 5903: 5890: 5873: 5864: 5847: 5822: 5809: 5796: 5783: 5775:T^a_{\mu\nu} \ 5762: 5739: 5736: 5735: 5734: 5721: 5708: 5695: 5682: 5669: 5655: 5634: 5621: 5608: 5583: 5570: 5549: 5536: 5523: 5502: 5481: 5460: 5423: 5415:: \Delta I^2 \ 5410: 5397: 5387:Sheffer stroke 5384: 5371: 5358: 5334: 5321: 5304: 5283: 5268: 5265: 5264: 5263: 5242: 5226:: \mathbf{v} \ 5221: 5208: 5195: 5182: 5165: 5148: 5135: 5122: 5101: 5088: 5075: 5054: 5044:Rational sieve 5041: 5028: 5015: 5002: 4981: 4968: 4947: 4932: 4929: 4928: 4927: 4910: 4893: 4880: 4867: 4854: 4841: 4820: 4805: 4802: 4801: 4800: 4787: 4779:: a^{(p-1)/2}\ 4774: 4761: 4748: 4735: 4718: 4704:Probable prime 4701: 4680: 4662:Price equation 4659: 4642: 4629: 4616: 4594: 4573: 4556: 4543: 4530: 4517: 4496: 4483: 4470: 4453: 4440: 4419: 4406: 4385: 4377:|\psi\rangle \ 4364: 4351: 4338: 4325: 4304: 4287: 4270: 4257: 4244: 4231: 4218: 4205: 4182: 4179: 4178: 4177: 4164: 4151: 4134: 4117: 4104: 4092: 4089: 4088: 4087: 4066: 4053: 4040: 4027: 4014: 4001: 3988: 3967: 3951:: \mathcal{S}\ 3946: 3929: 3921:{D \over Ds} \ 3912: 3899: 3886: 3865: 3856: 3843: 3830: 3817: 3804:1. or. p : --> 3795: 3782: 3763: 3760: 3759: 3758: 3745: 3724: 3703: 3682: 3665: 3644: 3626:Mean free path 3623: 3610: 3597: 3576: 3564: 3543: 3533:Massey product 3530: 3509: 3496: 3483: 3471:: Since 10^m \ 3466: 3456:Mach principle 3451: 3448: 3447: 3446: 3430: 3417: 3399:Lorentz scalar 3396: 3383: 3373:Lorentz factor 3370: 3362:: \mathbf{W} \ 3357: 3337: 3324: 3303: 3290: 3277:0 so that the 3267: 3254: 3241: 3228: 3211: 3194: 3165: 3155:Larmor formula 3152: 3131: 3110: 3100:Lanczos tensor 3097: 3073: 3070: 3069: 3068: 3055: 3042: 3017: 2996: 2983: 2962: 2954:: \mathbf{L} \ 2949: 2922: 2919: 2918: 2917: 2901: 2884: 2861: 2858: 2857: 2856: 2843: 2830: 2817: 2801: 2788: 2775: 2750: 2729: 2716: 2703: 2690: 2669: 2656: 2643: 2634: 2621: 2596: 2587: 2564: 2561: 2560: 2559: 2546: 2533: 2520: 2499: 2478: 2465: 2452: 2439: 2423:: \mathbf{q} \ 2418: 2405: 2388: 2373: 2370: 2369: 2368: 2347: 2337:Group velocity 2334: 2321: 2308: 2295: 2282: 2269: 2256: 2243: 2226: 2205: 2190: 2187: 2186: 2185: 2176: 2163: 2154: 2133: 2112: 2099: 2087: 2066: 2045: 2032: 2019: 2006: 1993: 1983:Fine structure 1980: 1967: 1946: 1933: 1920: 1899: 1876: 1873: 1872: 1871: 1858: 1845: 1837:Happens(a,t) \ 1827:Event calculus 1824: 1811: 1795: 1774: 1761: 1748: 1735: 1714: 1698: 1685: 1672: 1659: 1642: 1629: 1616: 1595: 1582: 1569: 1556: 1548:\gamma m_0 \ 1537: 1534: 1533: 1532: 1524:: \mathbf{c} \ 1519: 1498: 1485: 1477:: f(\lambda) \ 1472: 1462:Discretization 1459: 1446: 1433: 1415:Dirac equation 1412: 1394:Dirac equation 1391: 1378: 1370:: \mathrm{Q} \ 1365: 1348: 1335: 1318: 1305: 1292: 1271: 1258: 1237: 1224: 1197: 1194: 1193: 1192: 1171: 1154: 1137: 1120: 1107: 1094: 1081: 1068: 1047: 1034: 1021: 1008: 991: 969: 956: 943: 922: 909: 888: 863: 842: 829: 816: 802: 789: 776: 763: 734: 725: 712: 691: 670: 657: 636: 623: 602: 589: 576: 563: 550: 535: 532: 531: 530: 517: 508: 491: 478: 461: 448: 435: 422: 409: 396: 383: 369: 352: 339: 322: 309: 288: 263: 250: 230: 227: 226: 225: 204: 191: 178: 165: 152: 139: 126: 113: 100: 79: 58: 50:\Delta w_{k} \ 35: 32: 23: 15: 14: 13: 10: 9: 6: 4: 3: 2: 6536: 6525: 6521: 6517: 6513: 6509: 6506: 6504: 6500: 6496: 6492: 6489: 6487: 6483: 6479: 6476: 6474: 6470: 6466: 6463: 6461: 6457: 6454:: \hat t(s) \ 6453: 6450: 6448: 6444: 6440: 6437: 6435: 6431: 6427: 6423: 6419: 6416: 6414: 6410: 6406: 6402: 6398: 6395: 6393: 6390:0- and m = 0 6387: 6384:: The mass m\ 6383: 6380: 6378: 6374: 6370: 6367: 6365: 6361: 6357: 6356:Widom scaling 6354: 6352: 6348: 6344: 6341: 6339: 6335: 6331: 6327: 6323: 6320: 6318: 6314: 6310: 6307: 6305: 6301: 6297: 6294: 6292: 6288: 6284: 6280: 6276: 6273: 6271: 6267: 6263: 6260: 6258: 6254: 6250: 6246: 6245:Voigt profile 6243: 6241: 6238: 6234: 6231: 6229: 6225: 6221: 6217: 6213: 6210: 6208: 6204: 6200: 6197: 6195: 6191: 6187: 6184: 6182: 6178: 6175:: \Gamma^\mu\ 6174: 6171: 6169: 6165: 6161: 6157: 6153: 6149: 6146: 6144: 6140: 6136: 6132: 6129: 6127: 6123: 6119: 6115: 6111: 6108: 6106: 6102: 6099: 6097: 6093: 6089: 6086: 6085: 6081: 6077: 6073: 6069: 6066: 6064: 6060: 6057:: K_\varphi \ 6056: 6053: 6051: 6047: 6043: 6039: 6035: 6032: 6030: 6026: 6022: 6019: 6017: 6013: 6009: 6006: 6004: 6000: 5996: 5992: 5988: 5984: 5983:Treynor ratio 5981: 5979: 5975: 5971: 5968: 5966: 5962: 5958: 5955: 5953: 5949: 5945: 5941: 5940:Time dilation 5938: 5936: 5932: 5928: 5925: 5923: 5919: 5915: 5911: 5907: 5904: 5902: 5898: 5894: 5891: 5889: 5885: 5881: 5877: 5874: 5872: 5868: 5865: 5863: 5859: 5855: 5851: 5848: 5846: 5842: 5838: 5834: 5830: 5826: 5823: 5821: 5817: 5813: 5810: 5808: 5804: 5800: 5799:Ternary logic 5797: 5795: 5791: 5788:: D_\mu x^a \ 5787: 5784: 5782: 5778: 5774: 5770: 5767:: D_\mu x^a \ 5766: 5763: 5761: 5757: 5753: 5749: 5745: 5742: 5741: 5737: 5733: 5729: 5725: 5722: 5720: 5716: 5712: 5709: 5707: 5703: 5699: 5696: 5694: 5690: 5686: 5683: 5681: 5677: 5673: 5670: 5668: 5664: 5659: 5656: 5654: 5650: 5646: 5642: 5638: 5635: 5633: 5629: 5625: 5622: 5620: 5616: 5612: 5609: 5607: 5603: 5599: 5595: 5591: 5587: 5584: 5582: 5578: 5574: 5571: 5569: 5565: 5561: 5557: 5553: 5550: 5548: 5544: 5540: 5537: 5535: 5531: 5527: 5524: 5522: 5518: 5514: 5510: 5506: 5503: 5501: 5497: 5494:|L\rangle \ 5493: 5489: 5485: 5482: 5480: 5476: 5472: 5468: 5464: 5461: 5459: 5455: 5451: 5447: 5443: 5439: 5435: 5431: 5427: 5424: 5422: 5418: 5414: 5411: 5409: 5405: 5401: 5398: 5396: 5392: 5388: 5385: 5383: 5379: 5375: 5374:Shear modulus 5372: 5370: 5366: 5362: 5359: 5357: 5353: 5349: 5346: 5342: 5338: 5335: 5333: 5329: 5325: 5324:Sedimentation 5322: 5320: 5316: 5312: 5308: 5305: 5303: 5299: 5295: 5291: 5287: 5284: 5282: 5278: 5274: 5271: 5270: 5266: 5262: 5258: 5254: 5250: 5246: 5243: 5241: 5237: 5233: 5229: 5225: 5222: 5220: 5216: 5212: 5209: 5207: 5203: 5199: 5196: 5194: 5190: 5186: 5183: 5181: 5177: 5173: 5169: 5166: 5164: 5161: 5156: 5152: 5149: 5147: 5143: 5139: 5136: 5134: 5130: 5126: 5123: 5121: 5117: 5113: 5109: 5105: 5102: 5100: 5096: 5092: 5089: 5087: 5083: 5079: 5076: 5074: 5070: 5066: 5062: 5058: 5055: 5053: 5049: 5045: 5042: 5040: 5036: 5032: 5029: 5027: 5023: 5019: 5016: 5014: 5010: 5006: 5003: 5001: 4997: 4994:R_{g}^{2} \ 4993: 4989: 4985: 4982: 4980: 4977:\int_{s_1}^{ 4976: 4972: 4969: 4967: 4963: 4959: 4955: 4951: 4948: 4946: 4942: 4938: 4935: 4934: 4930: 4926: 4922: 4918: 4914: 4911: 4909: 4905: 4901: 4897: 4894: 4892: 4888: 4884: 4881: 4879: 4875: 4871: 4868: 4866: 4862: 4858: 4855: 4853: 4849: 4845: 4842: 4840: 4836: 4832: 4828: 4824: 4821: 4819: 4815: 4811: 4808: 4807: 4803: 4799: 4795: 4791: 4788: 4786: 4782: 4778: 4775: 4773: 4769: 4765: 4762: 4760: 4756: 4752: 4749: 4747: 4743: 4739: 4736: 4734: 4731: 4726: 4722: 4719: 4717: 4713: 4709: 4705: 4702: 4700: 4696: 4692: 4688: 4684: 4681: 4679: 4675: 4671: 4667: 4663: 4660: 4658: 4654: 4650: 4646: 4643: 4641: 4637: 4633: 4630: 4628: 4624: 4620: 4617: 4615: 4611: 4607: 4602: 4598: 4597:Polylogarithm 4595: 4593: 4589: 4585: 4581: 4577: 4574: 4572: 4568: 4564: 4560: 4557: 4555: 4551: 4547: 4544: 4542: 4538: 4534: 4531: 4529: 4525: 4521: 4518: 4516: 4512: 4508: 4504: 4500: 4497: 4495: 4491: 4487: 4484: 4482: 4478: 4474: 4473:Planck charge 4471: 4469: 4465: 4461: 4457: 4454: 4452: 4448: 4444: 4441: 4439: 4435: 4431: 4427: 4423: 4420: 4418: 4414: 4410: 4407: 4405: 4401: 4397: 4393: 4389: 4386: 4384: 4380: 4376: 4372: 4368: 4365: 4363: 4359: 4355: 4352: 4350: 4346: 4342: 4339: 4337: 4333: 4329: 4328:Phase (waves) 4326: 4324: 4320: 4316: 4312: 4308: 4305: 4303: 4299: 4295: 4291: 4288: 4286: 4282: 4278: 4274: 4271: 4269: 4265: 4261: 4258: 4256: 4252: 4248: 4245: 4243: 4239: 4235: 4232: 4230: 4226: 4222: 4219: 4217: 4213: 4209: 4206: 4204: 4200: 4196: 4192: 4188: 4185: 4184: 4180: 4176: 4172: 4168: 4165: 4163: 4159: 4155: 4152: 4150: 4146: 4142: 4138: 4135: 4133: 4129: 4125: 4121: 4118: 4116: 4112: 4108: 4105: 4102: 4098: 4095: 4094: 4090: 4086: 4082: 4078: 4074: 4070: 4067: 4065: 4061: 4057: 4054: 4052: 4048: 4044: 4041: 4039: 4035: 4031: 4028: 4026: 4022: 4018: 4015: 4013: 4009: 4005: 4002: 4000: 3996: 3992: 3989: 3987: 3983: 3979: 3975: 3971: 3968: 3966: 3962: 3958: 3954: 3950: 3947: 3945: 3941: 3937: 3933: 3930: 3928: 3924: 3920: 3916: 3913: 3911: 3907: 3903: 3900: 3898: 3894: 3890: 3887: 3885: 3881: 3877: 3873: 3869: 3866: 3864: 3860: 3857: 3855: 3851: 3847: 3844: 3842: 3838: 3834: 3831: 3829: 3825: 3821: 3820:Natural units 3818: 3816: 3812: 3808: 3803: 3799: 3796: 3794: 3790: 3786: 3783: 3781: 3777: 3773: 3769: 3766: 3765: 3761: 3757: 3753: 3749: 3746: 3744: 3740: 3736: 3732: 3728: 3725: 3723: 3719: 3715: 3711: 3707: 3704: 3702: 3698: 3694: 3690: 3686: 3685:Mole fraction 3683: 3681: 3677: 3673: 3669: 3666: 3664: 3660: 3656: 3652: 3648: 3647:Minimum phase 3645: 3643: 3639: 3635: 3631: 3627: 3624: 3622: 3618: 3614: 3611: 3609: 3605: 3601: 3598: 3596: 3592: 3588: 3584: 3580: 3577: 3575: 3572: 3568: 3565: 3563: 3559: 3555: 3551: 3547: 3544: 3542: 3538: 3534: 3531: 3529: 3525: 3521: 3517: 3513: 3510: 3508: 3504: 3500: 3497: 3495: 3491: 3487: 3486:Magnetic flux 3484: 3482: 3478: 3474: 3470: 3467: 3465: 3461: 3457: 3454: 3453: 3449: 3445: 3442: 3438: 3434: 3431: 3429: 3425: 3421: 3418: 3416: 3412: 3408: 3404: 3400: 3397: 3395: 3391: 3387: 3386:Lorentz force 3384: 3382: 3378: 3374: 3371: 3369: 3365: 3361: 3358: 3356: 3353: 3349: 3345: 3341: 3338: 3336: 3332: 3328: 3325: 3323: 3319: 3315: 3311: 3307: 3304: 3302: 3298: 3294: 3291: 3289: 3284: 3280: 3275: 3271: 3268: 3266: 3262: 3258: 3255: 3253: 3249: 3245: 3242: 3240: 3236: 3232: 3229: 3227: 3223: 3219: 3215: 3212: 3210: 3206: 3202: 3198: 3197:Leech lattice 3195: 3193: 3189: 3185: 3181: 3177: 3173: 3169: 3166: 3164: 3160: 3156: 3153: 3151: 3147: 3143: 3139: 3135: 3132: 3130: 3126: 3122: 3118: 3114: 3111: 3109: 3105: 3101: 3098: 3096: 3091: 3087: 3083: 3080:: define f_y\ 3079: 3076: 3075: 3071: 3067: 3063: 3059: 3056: 3054: 3050: 3046: 3043: 3041: 3037: 3033: 3029: 3025: 3021: 3018: 3016: 3012: 3008: 3004: 3000: 2997: 2995: 2991: 2987: 2984: 2982: 2978: 2974: 2970: 2966: 2963: 2961: 2957: 2953: 2950: 2948: 2944: 2940: 2936: 2932: 2928: 2927:Kalman filter 2925: 2924: 2920: 2916: 2913: 2909: 2905: 2902: 2900: 2896: 2892: 2888: 2885: 2883: 2879: 2875: 2871: 2867: 2864: 2863: 2859: 2855: 2851: 2847: 2844: 2842: 2838: 2834: 2831: 2829: 2825: 2821: 2818: 2816: 2813: 2809: 2805: 2802: 2800: 2796: 2792: 2789: 2787: 2783: 2779: 2776: 2774: 2770: 2766: 2762: 2758: 2754: 2751: 2749: 2745: 2741: 2737: 2733: 2730: 2728: 2724: 2720: 2717: 2715: 2711: 2707: 2704: 2702: 2698: 2695:: \omega(t) \ 2694: 2691: 2689: 2685: 2681: 2677: 2673: 2670: 2668: 2664: 2660: 2657: 2655: 2651: 2647: 2644: 2642: 2638: 2635: 2633: 2629: 2625: 2622: 2620: 2616: 2612: 2608: 2604: 2600: 2597: 2595: 2591: 2588: 2586: 2582: 2578: 2574: 2570: 2567: 2566: 2562: 2558: 2554: 2550: 2547: 2545: 2541: 2537: 2534: 2532: 2528: 2524: 2521: 2519: 2515: 2511: 2507: 2503: 2500: 2498: 2494: 2490: 2486: 2482: 2479: 2477: 2473: 2469: 2466: 2464: 2460: 2456: 2453: 2451: 2447: 2443: 2440: 2438: 2434: 2430: 2426: 2422: 2419: 2417: 2413: 2409: 2406: 2404: 2400: 2396: 2392: 2389: 2387: 2383: 2379: 2376: 2375: 2371: 2367: 2363: 2359: 2355: 2351: 2348: 2346: 2342: 2338: 2335: 2333: 2329: 2325: 2322: 2320: 2316: 2312: 2309: 2307: 2303: 2299: 2296: 2294: 2290: 2286: 2283: 2281: 2277: 2273: 2270: 2268: 2264: 2260: 2257: 2255: 2251: 2247: 2244: 2242: 2238: 2234: 2230: 2229:Gaussian beam 2227: 2225: 2221: 2217: 2213: 2209: 2206: 2204: 2200: 2196: 2193: 2192: 2188: 2184: 2180: 2177: 2175: 2171: 2167: 2164: 2162: 2158: 2155: 2153: 2149: 2145: 2141: 2138:: s_\Phi(x) \ 2137: 2134: 2132: 2128: 2124: 2120: 2116: 2113: 2111: 2107: 2103: 2100: 2098: 2095: 2091: 2090:Frame problem 2088: 2086: 2082: 2078: 2074: 2070: 2067: 2065: 2061: 2057: 2053: 2049: 2046: 2044: 2040: 2036: 2035:Four-gradient 2033: 2031: 2027: 2023: 2020: 2018: 2014: 2010: 2007: 2005: 2001: 1997: 1994: 1992: 1988: 1984: 1981: 1979: 1975: 1971: 1968: 1966: 1962: 1958: 1954: 1950: 1947: 1945: 1941: 1937: 1934: 1932: 1928: 1924: 1923:Fermat number 1921: 1919: 1915: 1911: 1907: 1903: 1900: 1898: 1894: 1890: 1886: 1882: 1879: 1878: 1874: 1870: 1866: 1862: 1859: 1857: 1853: 1849: 1846: 1844: 1840: 1836: 1832: 1828: 1825: 1823: 1819: 1815: 1812: 1810: 1809: 1803: 1799: 1796: 1794: 1790: 1786: 1782: 1778: 1775: 1773: 1769: 1765: 1762: 1760: 1756: 1752: 1749: 1747: 1743: 1739: 1736: 1734: 1730: 1726: 1722: 1718: 1715: 1713: 1710:(all n : Nat 1709:P zero -: --> 1706: 1702: 1699: 1697: 1693: 1689: 1686: 1684: 1680: 1676: 1673: 1671: 1667: 1664:: S(\sigma) \ 1663: 1660: 1658: 1654: 1650: 1646: 1643: 1641: 1637: 1633: 1630: 1628: 1624: 1621:: F_{ a b } \ 1620: 1617: 1615: 1611: 1607: 1603: 1599: 1596: 1594: 1590: 1586: 1583: 1581: 1577: 1573: 1570: 1568: 1564: 1560: 1557: 1555: 1551: 1547: 1543: 1540: 1539: 1535: 1531: 1527: 1523: 1520: 1518: 1514: 1510: 1506: 1502: 1499: 1497: 1493: 1489: 1486: 1484: 1480: 1476: 1473: 1471: 1467: 1464:: \mathbf x \ 1463: 1460: 1458: 1454: 1450: 1447: 1445: 1441: 1437: 1434: 1432: 1428: 1424: 1420: 1416: 1413: 1411: 1407: 1403: 1399: 1395: 1392: 1390: 1386: 1382: 1379: 1377: 1373: 1369: 1366: 1364: 1360: 1356: 1352: 1349: 1347: 1343: 1339: 1336: 1334: 1330: 1326: 1322: 1319: 1317: 1313: 1309: 1306: 1304: 1300: 1296: 1295:Definable set 1293: 1291: 1287: 1283: 1279: 1275: 1272: 1270: 1266: 1262: 1259: 1257: 1253: 1249: 1245: 1241: 1238: 1236: 1232: 1228: 1225: 1223: 1219: 1215: 1211: 1207: 1203: 1200: 1199: 1195: 1191: 1187: 1183: 1179: 1175: 1172: 1170: 1166: 1162: 1158: 1155: 1153: 1149: 1145: 1141: 1138: 1136: 1132: 1128: 1124: 1121: 1119: 1115: 1111: 1108: 1106: 1102: 1098: 1095: 1093: 1089: 1085: 1082: 1080: 1076: 1072: 1069: 1067: 1063: 1059: 1055: 1051: 1048: 1046: 1042: 1038: 1035: 1033: 1029: 1025: 1022: 1020: 1016: 1012: 1009: 1007: 1003: 999: 996:: a^\dagger \ 995: 992: 990: 985: 981: 977: 973: 970: 968: 964: 960: 957: 955: 951: 947: 944: 942: 938: 934: 930: 926: 923: 921: 917: 913: 910: 908: 904: 900: 896: 892: 889: 887: 883: 879: 875: 871: 868:: M_{\mu\nu}\ 867: 864: 862: 858: 854: 850: 846: 843: 841: 837: 833: 830: 828: 824: 820: 817: 815: 810: 806: 803: 801: 797: 793: 790: 788: 784: 780: 777: 775: 771: 767: 764: 762: 758: 754: 750: 746: 742: 738: 735: 733: 729: 726: 724: 720: 716: 713: 711: 707: 703: 699: 695: 692: 690: 686: 682: 678: 674: 671: 669: 665: 661: 658: 656: 652: 648: 644: 640: 637: 635: 631: 627: 624: 622: 618: 615:\omega(x) \ 614: 610: 606: 603: 601: 597: 593: 590: 588: 584: 580: 577: 575: 571: 567: 564: 562: 558: 554: 551: 549: 545: 541: 538: 537: 533: 529: 525: 521: 518: 516: 512: 509: 507: 503: 499: 495: 492: 490: 486: 482: 479: 477: 473: 469: 465: 462: 460: 456: 452: 449: 447: 443: 439: 436: 434: 430: 426: 425:Black-Scholes 423: 421: 417: 414:: \mathbf{F}\ 413: 410: 408: 404: 400: 397: 395: 391: 387: 384: 382: 378: 375:0\, (real) q\ 373: 370: 368: 365:x^r \mod n . 364: 360: 356: 353: 351: 347: 343: 340: 338: 334: 330: 326: 323: 321: 317: 313: 310: 308: 304: 300: 296: 292: 289: 287: 283: 279: 275: 271: 267: 264: 262: 258: 254: 251: 249: 244: 240: 236: 233: 232: 228: 224: 220: 216: 212: 208: 205: 203: 199: 195: 192: 190: 186: 182: 179: 177: 173: 169: 166: 164: 160: 156: 153: 151: 147: 144:: \theta(Z) \ 143: 140: 138: 134: 130: 127: 125: 121: 117: 114: 112: 108: 104: 101: 99: 95: 91: 87: 83: 80: 78: 74: 70: 66: 63:: T^{\mu\nu}\ 62: 59: 57: 53: 49: 45: 41: 38: 37: 33: 31: 29: 19: 6523: 6519: 6515: 6511: 6502: 6498: 6494: 6485: 6481: 6472: 6468: 6459: 6455: 6446: 6442: 6433: 6429: 6425: 6421: 6418:Wind turbine 6412: 6408: 6404: 6400: 6391: 6385: 6376: 6372: 6363: 6359: 6350: 6346: 6337: 6333: 6329: 6325: 6316: 6312: 6303: 6299: 6290: 6286: 6282: 6278: 6269: 6265: 6256: 6252: 6248: 6239: 6236: 6233:Virtual work 6227: 6223: 6219: 6215: 6206: 6205:(P_i + K_i) 6202: 6193: 6189: 6186:Vertex model 6180: 6176: 6167: 6163: 6159: 6155: 6151: 6142: 6138: 6134: 6125: 6121: 6117: 6113: 6104: 6095: 6091: 6075: 6071: 6062: 6058: 6049: 6045: 6041: 6037: 6028: 6024: 6015: 6011: 6002: 5998: 5994: 5990: 5986: 5977: 5973: 5964: 5960: 5951: 5947: 5943: 5934: 5930: 5921: 5917: 5913: 5909: 5900: 5896: 5887: 5883: 5879: 5870: 5861: 5857: 5853: 5844: 5840: 5836: 5832: 5828: 5819: 5815: 5806: 5802: 5793: 5789: 5780: 5776: 5772: 5768: 5759: 5755: 5751: 5747: 5731: 5727: 5718: 5714: 5705: 5701: 5698:Subfactorial 5692: 5691:M^e~mod~N . 5688: 5679: 5675: 5666: 5662: 5652: 5648: 5644: 5640: 5631: 5627: 5618: 5614: 5605: 5601: 5597: 5593: 5589: 5580: 5576: 5567: 5563: 5559: 5555: 5546: 5542: 5533: 5529: 5520: 5516: 5512: 5508: 5499: 5495: 5491: 5487: 5478: 5474: 5470: 5466: 5457: 5453: 5449: 5445: 5441: 5437: 5433: 5429: 5420: 5416: 5407: 5403: 5394: 5390: 5381: 5377: 5368: 5364: 5355: 5351: 5347: 5344: 5340: 5331: 5327: 5318: 5314: 5310: 5301: 5297: 5293: 5289: 5280: 5276: 5260: 5256: 5252: 5248: 5239: 5235: 5231: 5227: 5218: 5214: 5205: 5201: 5192: 5188: 5179: 5178:Q_1 \supset 5175: 5171: 5162: 5159: 5154: 5145: 5141: 5138:Reduced mass 5132: 5128: 5119: 5115: 5111: 5107: 5098: 5094: 5085: 5081: 5072: 5068: 5064: 5060: 5051: 5047: 5038: 5034: 5025: 5021: 5012: 5008: 4999: 4995: 4991: 4987: 4978: 4974: 4965: 4961: 4957: 4953: 4944: 4940: 4937:Rabi problem 4924: 4920: 4916: 4907: 4903: 4899: 4890: 4886: 4877: 4873: 4864: 4860: 4851: 4847: 4838: 4834: 4830: 4826: 4817: 4813: 4797: 4793: 4784: 4780: 4771: 4767: 4758: 4754: 4745: 4741: 4732: 4724: 4721:Probit model 4715: 4711: 4707: 4698: 4694: 4690: 4686: 4677: 4673: 4669: 4665: 4664:: \Delta z \ 4656: 4652: 4648: 4639: 4635: 4626: 4622: 4613: 4609: 4605: 4600: 4591: 4587: 4583: 4579: 4578:: \omega_0 \ 4570: 4566: 4562: 4553: 4549: 4540: 4536: 4527: 4523: 4514: 4510: 4509:\varepsilon\ 4506: 4502: 4493: 4489: 4480: 4476: 4467: 4463: 4459: 4450: 4446: 4437: 4433: 4429: 4425: 4416: 4412: 4403: 4399: 4395: 4391: 4382: 4378: 4374: 4370: 4361: 4357: 4348: 4344: 4343:: i_b(x,y) \ 4335: 4331: 4322: 4318: 4314: 4310: 4301: 4297: 4293: 4284: 4280: 4276: 4267: 4263: 4254: 4250: 4241: 4237: 4228: 4224: 4215: 4211: 4202: 4198: 4194: 4190: 4174: 4170: 4167:Oversampling 4161: 4157: 4148: 4144: 4140: 4131: 4127: 4123: 4114: 4110: 4100: 4084: 4080: 4076: 4072: 4063: 4059: 4056:Nyquist rate 4050: 4046: 4037: 4033: 4024: 4020: 4011: 4007: 3998: 3994: 3985: 3981: 3977: 3973: 3964: 3960: 3956: 3952: 3943: 3939: 3935: 3926: 3922: 3918: 3909: 3905: 3896: 3892: 3883: 3879: 3875: 3871: 3862: 3853: 3849: 3848:: \pi_i(X) \ 3840: 3836: 3827: 3823: 3814: 3810: 3806: 3801: 3792: 3788: 3779: 3775: 3771: 3755: 3751: 3742: 3738: 3734: 3730: 3721: 3717: 3713: 3709: 3700: 3696: 3695:\sum_i x_i \ 3692: 3688: 3679: 3675: 3671: 3662: 3658: 3654: 3650: 3641: 3637: 3633: 3629: 3620: 3616: 3607: 3603: 3594: 3590: 3586: 3582: 3573: 3570: 3561: 3557: 3553: 3549: 3540: 3536: 3527: 3523: 3519: 3515: 3506: 3502: 3493: 3489: 3480: 3476: 3472: 3469:Magic gopher 3463: 3459: 3443: 3440: 3436: 3427: 3423: 3414: 3410: 3406: 3402: 3393: 3389: 3380: 3376: 3367: 3363: 3360:Loop entropy 3354: 3351: 3347: 3343: 3334: 3330: 3321: 3317: 3313: 3309: 3300: 3296: 3287: 3282: 3278: 3273: 3264: 3260: 3251: 3247: 3238: 3234: 3225: 3221: 3217: 3208: 3204: 3200: 3191: 3187: 3183: 3179: 3175: 3171: 3162: 3158: 3149: 3145: 3141: 3137: 3128: 3124: 3120: 3116: 3107: 3103: 3094: 3089: 3085: 3081: 3065: 3061: 3060:: d\Omega^2\ 3052: 3048: 3039: 3035: 3031: 3027: 3023: 3014: 3010: 3006: 3002: 2993: 2989: 2980: 2976: 2975:r^{2}+a^: a\ 2972: 2968: 2959: 2955: 2946: 2942: 2938: 2934: 2930: 2914: 2907: 2898: 2894: 2890: 2881: 2877: 2873: 2869: 2853: 2849: 2840: 2836: 2833:Isaac Newton 2827: 2823: 2814: 2807: 2798: 2794: 2785: 2781: 2772: 2768: 2764: 2760: 2756: 2747: 2743: 2739: 2735: 2726: 2722: 2713: 2709: 2700: 2696: 2687: 2683: 2679: 2675: 2666: 2662: 2653: 2649: 2640: 2631: 2627: 2618: 2614: 2610: 2606: 2602: 2593: 2584: 2580: 2576: 2572: 2556: 2552: 2543: 2539: 2530: 2526: 2517: 2513: 2509: 2505: 2496: 2492: 2488: 2484: 2475: 2471: 2462: 2458: 2449: 2445: 2436: 2432: 2428: 2424: 2415: 2411: 2402: 2398: 2394: 2385: 2381: 2365: 2361: 2357: 2353: 2344: 2340: 2331: 2327: 2318: 2314: 2305: 2301: 2300:: \Phi_{G} \ 2292: 2288: 2279: 2275: 2266: 2262: 2253: 2249: 2240: 2236: 2232: 2223: 2219: 2215: 2211: 2202: 2198: 2195:Gauge theory 2182: 2173: 2169: 2160: 2151: 2147: 2143: 2139: 2130: 2126: 2122: 2118: 2109: 2105: 2096: 2093: 2084: 2080: 2076: 2072: 2063: 2059: 2055: 2051: 2042: 2038: 2029: 2025: 2016: 2012: 2003: 1999: 1990: 1986: 1977: 1973: 1964: 1960: 1956: 1955:{dx^{\mu} \ 1952: 1943: 1939: 1930: 1926: 1917: 1913: 1909: 1905: 1896: 1892: 1888: 1884: 1868: 1864: 1855: 1851: 1842: 1838: 1834: 1830: 1821: 1817: 1807: 1805: 1801: 1792: 1788: 1784: 1780: 1771: 1767: 1758: 1754: 1745: 1741: 1732: 1728: 1724: 1720: 1711: 1704: 1695: 1691: 1682: 1678: 1669: 1665: 1656: 1652: 1648: 1645:Electronvolt 1639: 1635: 1626: 1622: 1613: 1609: 1605: 1601: 1592: 1588: 1579: 1575: 1566: 1562: 1561:: d\Omega^2\ 1553: 1549: 1545: 1529: 1525: 1516: 1512: 1508: 1504: 1495: 1491: 1482: 1478: 1469: 1465: 1456: 1452: 1443: 1439: 1430: 1426: 1422: 1418: 1409: 1405: 1401: 1397: 1396:: \epsilon \ 1388: 1384: 1375: 1371: 1362: 1358: 1354: 1345: 1341: 1332: 1328: 1324: 1315: 1311: 1302: 1298: 1289: 1285: 1281: 1277: 1268: 1264: 1255: 1251: 1247: 1243: 1234: 1230: 1221: 1217: 1213: 1209: 1205: 1189: 1185: 1181: 1177: 1168: 1164: 1160: 1151: 1147: 1143: 1134: 1130: 1126: 1117: 1113: 1104: 1100: 1091: 1087: 1078: 1074: 1065: 1061: 1057: 1053: 1044: 1040: 1031: 1027: 1018: 1014: 1005: 1001: 997: 988: 983: 979: 975: 966: 962: 953: 949: 940: 936: 932: 928: 919: 915: 906: 902: 898: 894: 885: 881: 877: 873: 869: 860: 856: 852: 848: 839: 835: 826: 822: 813: 808: 799: 795: 786: 782: 773: 769: 760: 756: 752: 748: 744: 740: 731: 722: 718: 709: 705: 701: 697: 688: 684: 680: 676: 667: 663: 654: 650: 646: 642: 633: 629: 620: 616: 612: 608: 599: 595: 586: 582: 573: 569: 560: 556: 547: 543: 527: 523: 514: 505: 501: 497: 488: 484: 475: 471: 467: 458: 454: 445: 441: 432: 428: 419: 415: 406: 402: 393: 389: 380: 376: 366: 362: 358: 349: 345: 336: 332: 328: 319: 315: 306: 302: 298: 294: 285: 281: 277: 273: 269: 260: 256: 253:Baryogenesis 247: 242: 238: 222: 218: 214: 210: 201: 197: 188: 184: 175: 171: 162: 158: 149: 145: 136: 132: 123: 119: 110: 106: 97: 93: 89: 85: 76: 72: 68: 64: 55: 51: 47: 43: 27: 25: 6501:0 (mod 6). 6226:-\nabla_{\ 6055:Turing jump 6034:Truth table 5831:|L\rangle \ 5573:Spin tensor 5554:: where R \ 5354:n \mod p . 5275:: \Lambda \ 5213:: Li_s(z) \ 5140:: m_{red} \ 5078:Ray tracing 5033:: V_{j+1} \ 4764:Proper time 4727:1(y^* : --> 4621:: \Omega' \ 4422:Pi-calculus 4398:|L\rangle \ 4290:Pauli group 4006:: 2 \zeta \ 3846:N-connected 3340:Logical NOR 3170:: (a)_{i} \ 3157:: \beta^2 \ 2945:\textbf{H} 2579:\psi_n(x) \ 2483:: (x:y:z) \ 2146:s_\Phi(x) \ 2079:\Delta^2 A\ 2058:\Delta^2 A\ 1891:and \gamma\ 1863:: \Gamma_k\ 1587:: \lambda \ 1522:Dot product 1338:Diffraction 1240:Debye model 1110:Cyanic acid 935:\Delta^2 A\ 838:S(\rho,\ . 388:: \max(X) \ 342:Bell number 235:Bandlimited 92:\omega(t) \ 6332:T^{MN}(x)\ 6296:Wavenumber 6264:: \phi_i \ 6162:\nabla^2 \ 5929:: \sigma \ 5724:Superspace 5436:-2 + 6 \ 5413:Shot noise 5339:: When p \ 5288:: p_1(x) \ 5247:: M(T,H) \ 5200:: R_{ij} \ 5187:: K(x,y) \ 4939:: \kappa \ 4859:: \rho_A \ 4810:QCD vacuum 4373:\left ( . 4223:: \alpha \ 3822:: \alpha \ 3539:\omega_1\ 3488:: \Phi_m \ 3401:: \gamma \ 3388:: \gamma \ 3375:: \gamma \ 3190:F_4,F_D . 2986:K-function 2880:(x^{i}, . 2866:Jet bundle 2648:: \gamma \ 2542:\sqrt{-1} 2352:: S_{mn} \ 1883:: where F\ 1690:: _{tot} \ 1574:: q(q+1) \ 1425:\bar\psi \ 1404:\bar\psi \ 1381:Dirac comb 1050:C-symmetry 847:: \sim O \ 821:: H(Y|X) \ 628:: K_{eq} \ 344:: B_{p+n}\ 5839:\hat{S} \ 5812:Tessarine 5428:: 3 - 5 \ 5106:: K_{d} \ 4885:: \left \ 4565:0 then N\ 4561:: If \mu\ 4169:: \beta \ 3727:Monopsony 3556:a_{1,2} \ 3514:: t_{0} \ 3409:a^{\mu} \ 3233:: R_n(x)\ 3102:: H_{bd}\ 2999:KMS state 2846:ISO 31-11 2806:: x_{i} \ 2502:H-theorem 2491:(x:y:z) \ 1902:Factorial 982:\sigma \ 739:: f_{cr}\ 607:: R_n(x)\ 568:: \pi_i \ 457:3 mod 4. 268:: (A,A) \ 42:: J_{k} \ 6518:M(t;s) \ 6428:\lambda\ 6112:: L(Q) \ 5562:Q_{lm} \ 4753:: p(x) \ 4501:: \beta\ 4488:: \hbar\ 3186:F_3,F_C\ 3182:F_2,F_B\ 2291:H-TS \, 2125:\Omega \ 1959:\gamma \ 1800:: f(x) \ 1708:* =: --> 1494:\tau(n) 1212:\Box p \ 1013:: \tau \ 901:a + ib \ 683:\psi_L \ 464:Bose gas 412:BF model 314:: \tau \ 6510:: m_n \ 6277:: a_w \ 5592:USp(4)\ 5452:9 - 6 \ 5444:4 + 5 \ 5426:SIGSALY 5402:: a^r \ 4960:x(t+1)\ 4356:: Q_k \ 4317:f_{P} \ 4143:\Phi' \ 4058:: f_N \ 3770:: c_i \ 3687:: x_i \ 3281:M(t;c)\ 2339:: v_g \ 2117:: H^2 \ 1600:: k_0 \ 893:: A^* \ 768:: d_p \ 755:f_{cr}\ 747:f_{cr}\ 157:: E_a \ 6120:Q(H) \ 6101:V sign 5856:\tau \ 5746:: xy \ 5713:: Fr \ 5604:SU(4) 5596:Sp(2) 5586:Spinor 5507:: \mu\ 5456:3\mod 4915:: x_i\ 4846:: {q}\ 4706:: a^d\ 4693:P(k) \ 4409:Photon 4354:Phonon 4109:: X_i\ 3980:J^\mu\ 3959:J^\mu\ 3636:\ell \ 3272:: m_n\ 2435:\sum_ 1503:: x^2\ 1242:: T_D\ 1123:Cyclol 737:Column 581:: Ca \ 440:: s' \ 6520:equiv 6512:equiv 6499:equiv 6495:equiv 6482:equiv 6480:: Y \ 6469:equiv 6456:equiv 6443:equiv 6430:equiv 6422:equiv 6409:equiv 6401:equiv 6386:equiv 6373:equiv 6360:equiv 6358:: t \ 6347:equiv 6334:equiv 6326:equiv 6313:equiv 6300:equiv 6298:: k \ 6287:equiv 6285:a_w \ 6279:equiv 6266:equiv 6253:equiv 6249:equiv 6237:equiv 6224:equiv 6216:equiv 6214:: T \ 6203:equiv 6190:equiv 6177:equiv 6164:equiv 6156:equiv 6152:equiv 6139:equiv 6122:equiv 6114:equiv 6092:equiv 6072:equiv 6059:equiv 6046:equiv 6038:equiv 6025:equiv 6012:equiv 5999:equiv 5995:equiv 5991:equiv 5987:equiv 5985:: T \ 5974:equiv 5961:equiv 5959:: G \ 5948:equiv 5931:equiv 5918:equiv 5914:equiv 5910:equiv 5908:: F \ 5897:equiv 5895:: e \ 5884:equiv 5880:equiv 5858:equiv 5841:equiv 5833:equiv 5816:equiv 5803:EQUIV 5790:equiv 5777:equiv 5769:equiv 5756:equiv 5748:equiv 5728:equiv 5715:equiv 5702:equiv 5689:equiv 5676:equiv 5663:equiv 5649:equiv 5641:equiv 5628:equiv 5615:equiv 5602:equiv 5594:equiv 5590:equiv 5577:equiv 5564:equiv 5556:equiv 5543:equiv 5530:equiv 5517:equiv 5509:equiv 5496:equiv 5488:equiv 5475:equiv 5467:equiv 5454:equiv 5450:equiv 5446:equiv 5438:equiv 5434:equiv 5430:equiv 5417:equiv 5404:equiv 5391:equiv 5378:equiv 5376:: G \ 5365:equiv 5363:: F \ 5352:equiv 5345:equiv 5341:equiv 5328:equiv 5315:equiv 5311:equiv 5298:equiv 5290:equiv 5277:equiv 5257:equiv 5249:equiv 5236:equiv 5228:equiv 5215:equiv 5202:equiv 5189:equiv 5176:equiv 5160:equiv 5155:equiv 5142:equiv 5129:equiv 5116:equiv 5108:equiv 5095:equiv 5093:: g \ 5082:equiv 5069:equiv 5061:equiv 5048:equiv 5035:equiv 5031:RANDU 5022:equiv 5009:equiv 4996:equiv 4988:equiv 4975:equiv 4962:equiv 4954:equiv 4941:equiv 4921:equiv 4917:equiv 4904:equiv 4887:equiv 4874:equiv 4861:equiv 4848:equiv 4835:equiv 4831:equiv 4827:equiv 4825:: u \ 4814:equiv 4794:equiv 4781:equiv 4768:equiv 4755:equiv 4742:equiv 4725:equiv 4723:: Y \ 4712:equiv 4708:equiv 4695:equiv 4687:equiv 4674:equiv 4666:equiv 4653:equiv 4649:equiv 4636:equiv 4623:equiv 4610:equiv 4601:equiv 4588:equiv 4580:equiv 4567:equiv 4563:equiv 4550:equiv 4537:equiv 4524:equiv 4511:equiv 4503:equiv 4490:equiv 4477:equiv 4464:equiv 4447:equiv 4434:equiv 4426:equiv 4424:: P \ 4413:equiv 4400:equiv 4392:equiv 4379:equiv 4371:equiv 4358:equiv 4345:equiv 4332:equiv 4319:equiv 4311:equiv 4309:: S \ 4298:equiv 4281:equiv 4264:equiv 4251:equiv 4238:equiv 4225:equiv 4212:equiv 4199:equiv 4191:equiv 4189:: m \ 4171:equiv 4158:equiv 4145:equiv 4141:equiv 4128:equiv 4111:equiv 4101:equiv 4081:equiv 4073:equiv 4071:: x \ 4060:equiv 4047:equiv 4034:equiv 4021:equiv 4008:equiv 3995:equiv 3982:equiv 3974:equiv 3961:equiv 3953:equiv 3940:equiv 3923:equiv 3906:equiv 3893:equiv 3880:equiv 3872:equiv 3870:: S \ 3850:equiv 3837:equiv 3824:equiv 3811:equiv 3802:equiv 3789:equiv 3787:: c \ 3776:equiv 3772:equiv 3752:equiv 3739:equiv 3731:equiv 3718:equiv 3710:equiv 3708:: I \ 3697:equiv 3689:equiv 3676:equiv 3659:equiv 3651:equiv 3638:equiv 3630:equiv 3617:equiv 3604:equiv 3591:equiv 3583:equiv 3571:equiv 3558:equiv 3550:equiv 3548:: Q \ 3537:equiv 3524:equiv 3520:equiv 3516:equiv 3503:equiv 3490:equiv 3477:equiv 3473:equiv 3460:equiv 3441:equiv 3437:equiv 3424:equiv 3411:equiv 3403:equiv 3390:equiv 3377:equiv 3364:equiv 3352:equiv 3344:equiv 3331:equiv 3318:equiv 3310:equiv 3297:equiv 3283:equiv 3274:equiv 3261:equiv 3248:equiv 3235:equiv 3222:equiv 3218:equiv 3205:equiv 3203:4a_1\ 3201:equiv 3188:equiv 3184:equiv 3180:equiv 3172:equiv 3159:equiv 3146:equiv 3138:equiv 3125:equiv 3123:x \ 3117:equiv 3115:: z \ 3104:equiv 3090:equiv 3086:equiv 3082:equiv 3062:equiv 3049:equiv 3036:equiv 3030:{\rm 3028:equiv 3024:equiv 3011:equiv 3003:equiv 2990:equiv 2977:equiv 2973:equiv 2969:equiv 2956:equiv 2943:equiv 2939:equiv 2931:equiv 2908:equiv 2895:equiv 2891:equiv 2878:equiv 2870:equiv 2868:: V \ 2850:equiv 2837:equiv 2824:equiv 2808:equiv 2795:equiv 2782:equiv 2769:equiv 2765:equiv 2761:equiv 2757:equiv 2755:: K \ 2744:equiv 2740:equiv 2736:equiv 2723:equiv 2710:equiv 2697:equiv 2684:equiv 2676:equiv 2663:equiv 2650:equiv 2628:equiv 2615:equiv 2613:P_3 \ 2607:equiv 2603:equiv 2581:equiv 2573:equiv 2553:equiv 2551:: i \ 2540:equiv 2527:equiv 2514:equiv 2506:equiv 2504:: H \ 2493:equiv 2485:equiv 2472:equiv 2459:equiv 2446:equiv 2433:equiv 2425:equiv 2412:equiv 2399:equiv 2395:equiv 2382:equiv 2362:equiv 2354:equiv 2341:equiv 2328:equiv 2315:equiv 2302:equiv 2289:equiv 2276:equiv 2263:equiv 2250:equiv 2237:equiv 2233:equiv 2220:equiv 2212:equiv 2210:: T \ 2199:equiv 2197:: DX\ 2170:equiv 2148:equiv 2140:equiv 2127:equiv 2119:equiv 2106:equiv 2094:equiv 2081:equiv 2073:equiv 2060:equiv 2052:equiv 2039:equiv 2026:equiv 2013:equiv 2000:equiv 1987:equiv 1974:equiv 1961:equiv 1953:equiv 1940:equiv 1927:equiv 1914:equiv 1912:n\$ \ 1906:equiv 1893:equiv 1885:equiv 1865:equiv 1852:equiv 1839:equiv 1831:equiv 1818:equiv 1802:equiv 1789:equiv 1781:equiv 1768:equiv 1755:equiv 1742:equiv 1729:equiv 1721:equiv 1719:: K \ 1705:equiv 1692:equiv 1679:equiv 1666:equiv 1653:equiv 1649:equiv 1636:equiv 1623:equiv 1610:equiv 1608:k_0 \ 1602:equiv 1589:equiv 1576:equiv 1563:equiv 1550:equiv 1546:equiv 1542:E=mc² 1526:equiv 1513:equiv 1505:equiv 1492:equiv 1479:equiv 1466:equiv 1453:equiv 1440:equiv 1427:equiv 1419:equiv 1406:equiv 1398:equiv 1385:equiv 1372:equiv 1359:equiv 1355:equiv 1342:equiv 1329:equiv 1312:equiv 1299:equiv 1286:equiv 1278:equiv 1265:equiv 1263:: q \ 1252:equiv 1250:T_E \ 1244:equiv 1231:equiv 1218:equiv 1214:equiv 1206:equiv 1186:equiv 1178:equiv 1165:equiv 1148:equiv 1131:equiv 1114:equiv 1101:equiv 1099:: X \ 1088:equiv 1075:equiv 1062:equiv 1054:equiv 1041:equiv 1028:equiv 1015:equiv 1002:equiv 998:equiv 984:equiv 976:equiv 963:equiv 950:equiv 937:equiv 929:equiv 916:equiv 903:equiv 895:equiv 882:equiv 878:equiv 874:equiv 870:equiv 857:equiv 849:equiv 836:equiv 823:equiv 809:equiv 796:equiv 783:equiv 781:: z \ 770:equiv 757:equiv 749:equiv 741:equiv 719:equiv 706:equiv 698:equiv 685:equiv 677:equiv 664:equiv 651:equiv 643:equiv 641:: U \ 630:equiv 617:equiv 609:equiv 596:equiv 583:equiv 570:equiv 557:equiv 544:equiv 524:equiv 522:: N \ 502:equiv 498:equiv 485:equiv 472:equiv 468:equiv 455:equiv 442:equiv 429:equiv 427:: X \ 416:equiv 403:equiv 390:equiv 377:equiv 363:equiv 346:equiv 333:equiv 329:equiv 316:equiv 303:equiv 295:equiv 282:equiv 278:equiv 270:equiv 257:equiv 255:: s \ 243:equiv 239:equiv 237:: x \ 219:equiv 211:equiv 198:equiv 185:equiv 172:equiv 159:equiv 146:equiv 133:equiv 120:equiv 107:equiv 94:equiv 86:equiv 73:equiv 65:equiv 52:equiv 44:equiv 16:< 6420:: a\ 6371:: x\ 5432:-2 \ 4906:0 . 4608:H_n\ 3972:: S\ 3737:e_t\ 3661:\ . 3178:F_A\ 2274:: X\ 2239:I(0 276:A_0\ 6524:... 6516:... 6503:... 6486:... 6473:... 6460:... 6447:... 6434:... 6426:... 6413:... 6405:... 6392:... 6377:... 6364:... 6351:... 6338:... 6330:... 6317:... 6304:... 6291:... 6283:... 6270:... 6257:... 6240:... 6228:... 6220:... 6207:... 6194:... 6181:... 6168:... 6160:... 6143:... 6135:... 6126:... 6118:... 6105:... 6096:... 6082:U-Z 6076:... 6063:... 6050:... 6042:... 6029:... 6016:... 6003:... 5978:... 5965:... 5952:... 5944:... 5935:... 5922:... 5901:... 5888:... 5871:... 5862:... 5854:... 5845:... 5837:... 5829:... 5820:... 5807:... 5794:... 5781:... 5773:... 5760:... 5758:uv 5752:... 5732:... 5719:... 5706:... 5693:... 5680:... 5667:... 5653:... 5645:... 5632:... 5619:... 5606:... 5598:... 5581:... 5568:... 5560:... 5547:... 5534:... 5521:... 5513:... 5500:... 5492:... 5479:... 5471:... 5458:... 5448:9 \ 5442:... 5421:... 5408:... 5395:... 5382:... 5369:... 5356:... 5348:... 5332:... 5319:... 5302:... 5294:... 5281:... 5261:... 5255:t \ 5253:... 5240:... 5232:... 5219:... 5206:... 5193:... 5180:... 5172:... 5163:... 5146:... 5133:... 5120:... 5112:... 5099:... 5086:... 5073:... 5065:... 5052:... 5039:... 5026:... 5013:... 5000:... 4992:... 4979:... 4966:... 4958:... 4945:... 4925:... 4908:... 4900:... 4891:... 4878:... 4865:... 4852:... 4839:... 4818:... 4798:... 4785:... 4772:... 4759:... 4746:... 4733:... 4716:... 4699:... 4691:... 4678:... 4670:... 4657:... 4640:... 4627:... 4614:... 4606:... 4592:... 4584:... 4571:... 4554:... 4541:... 4528:... 4515:... 4507:... 4494:... 4481:... 4468:... 4460:... 4451:... 4438:... 4430:... 4417:... 4404:... 4396:... 4383:... 4375:... 4362:... 4349:... 4336:... 4323:... 4315:... 4302:... 4294:... 4285:... 4277:... 4268:... 4255:... 4242:... 4229:... 4216:... 4203:... 4195:... 4175:... 4162:... 4149:... 4132:... 4124:... 4115:... 4085:... 4079:x \ 4077:... 4064:... 4051:... 4038:... 4025:... 4012:... 3999:... 3986:... 3978:... 3965:... 3957:... 3944:... 3936:... 3927:... 3919:... 3910:... 3897:... 3884:... 3878:Q \ 3876:... 3863:... 3854:... 3841:... 3828:... 3815:... 3807:... 3793:... 3780:... 3756:... 3743:... 3735:... 3722:... 3714:... 3701:... 3693:... 3680:... 3672:... 3663:... 3655:... 3642:... 3634:... 3621:... 3608:... 3595:... 3587:... 3574:... 3562:... 3554:... 3541:... 3528:... 3507:... 3494:... 3481:... 3464:... 3444:... 3428:... 3415:... 3407:... 3394:... 3381:... 3368:... 3355:... 3348:... 3335:... 3322:... 3314:... 3301:... 3288:... 3279:... 3265:... 3252:... 3239:... 3226:... 3209:... 3192:... 3176:... 3163:... 3150:... 3142:... 3129:... 3121:... 3108:... 3095:... 3066:... 3053:... 3040:... 3032:... 3022:: \ 3015:... 3007:... 2994:... 2981:... 2960:... 2947:... 2935:... 2915:... 2899:... 2882:... 2874:... 2854:... 2841:... 2828:... 2815:... 2799:... 2786:... 2773:... 2748:... 2727:... 2714:... 2701:... 2688:... 2680:... 2667:... 2654:... 2641:... 2632:... 2619:... 2611:... 2594:... 2585:... 2577:... 2557:... 2544:... 2531:... 2518:... 2512:S \ 2510:... 2497:... 2489:... 2476:... 2463:... 2450:... 2437:... 2429:... 2416:... 2403:... 2386:... 2366:... 2360:b \ 2358:... 2345:... 2332:... 2319:... 2306:... 2293:... 2280:... 2267:... 2254:... 2241:... 2224:... 2218:K \ 2216:... 2203:... 2183:... 2174:... 2161:... 2152:... 2144:... 2131:... 2123:... 2110:... 2097:... 2085:... 2077:... 2064:... 2056:... 2043:... 2030:... 2028:. 2017:... 2004:... 1991:... 1978:... 1965:... 1957:... 1944:... 1931:... 1918:... 1910:... 1904:: \ 1897:... 1889:... 1869:... 1856:... 1843:... 1835:... 1822:... 1808:... 1793:... 1785:... 1772:... 1770:. 1759:... 1746:... 1733:... 1727:K \ 1725:... 1712:... 1696:... 1683:... 1670:... 1657:... 1640:... 1627:... 1614:... 1606:... 1593:... 1580:... 1567:... 1554:... 1530:... 1517:... 1509:... 1496:... 1483:... 1470:... 1457:... 1444:... 1431:... 1423:... 1410:... 1402:... 1389:... 1376:... 1363:... 1346:... 1333:... 1325:... 1316:... 1303:... 1290:... 1282:... 1269:... 1256:... 1248:... 1235:... 1222:... 1210:... 1190:... 1184:U \ 1182:... 1169:... 1161:... 1152:... 1144:... 1135:... 1127:... 1118:... 1105:... 1092:... 1079:... 1066:... 1058:... 1045:... 1032:... 1019:... 1006:... 989:... 980:... 967:... 954:... 941:... 933:... 920:... 907:... 899:... 886:... 861:... 855:T \ 853:... 840:... 827:... 814:... 800:... 787:... 774:... 761:... 753:... 745:... 732:... 723:... 710:... 702:... 689:... 681:... 668:... 655:... 649:A \ 647:... 634:... 621:... 613:... 600:... 587:... 574:... 561:... 548:... 528:... 515:... 506:... 489:... 476:... 459:... 446:... 433:... 420:... 407:... 394:... 381:... 367:... 359:... 350:... 337:... 320:... 307:... 299:... 286:... 274:... 261:... 248:... 223:... 215:... 202:... 189:... 176:... 163:... 150:... 137:... 124:... 111:... 98:... 90:... 77:... 69:... 56:... 48:... 6133:: 5942:: 5170:: 4898:: 4458:: 4292:: 4122:: 3934:: 3670:: 2686:\ 2168:: 1323:: 1159:: 1142:: 1125:: 357:: 5738:T 5296:\ 5267:S 4931:R 4804:Q 4181:P 4091:O 3762:N 3450:M 3072:L 3034:\ 2921:K 2860:J 2563:I 2372:H 2189:G 1875:F 1536:E 1196:D 534:C 229:B 34:A

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