1219:
1186:
993:
984:
705:
696:
171:
162:
469:
1309:. 8th Workshop STRUCTURAL DYNAMICAL SYSTEMS: Computational Aspects; Edited by Nicoletta Del Buono, Roberto Garrappa and Giulia Spaletta and Nonstandard Applications of Computer Algebra (ACA’2013); Edited by Francisco Botana, Antonio Hernando, Eugenio Roanes-Lozano and Michael J. Wester.
1147:. Четверта наукова конференція Харківського університету Повітряних Сил імені Івана Кожедуба, 16–17 квітня 2008 (The fourth scientific conference of the Ivan Kozhedub Kharkiv University of Air Forces, 16–17 April 2008) (in Russian). Kharkiv, Ukraine:
260:
690:
827:
1355:
1170:]. Материалы XIII Международного молодежного форума «Радиоэлектро-ника и молодежь в XXI веке» (Materials of the 13th international youth forum "Radioelectronics and youth in the 21st century") (in Russian). Kharkiv, Ukraine:
156:
1118:
Soboleva proposed the name "modified hyperbolic tangent" (mtanh, mth), but since other authors used this name also for other functions, some authors have started to refer to this function as "Soboleva modified hyperbolic
977:
903:
1368:
1341:
1443:
1494:
1620:
1290:
531:
1469:
1464:(Thesis). Joint Research Doctorate In Fusion Science And Engineering Cycle XXX (in English, Italian, and Portuguese). Padova, Italy: Centro Ricerche Fusione (CRF),
1207:
1171:
1553:
734:
464:{\displaystyle \operatorname {smht} '(x)\doteq {\frac {ae^{ax}+be^{-bx}}{e^{cx}+e^{-dx}}}-\operatorname {smht} (x){\frac {ce^{cx}-de^{-dx}}{e^{cx}+e^{-dx}}}}
1607:
496:
A family of recurrence-generated parametric
Soboleva modified hyperbolic tangent activation functions (NPSMHTAF, FPSMHTAF) was studied with parameters
1086:
57:
1274:
907:
833:
1634:
1659:
1465:
1343:ПРИМЕНЕНИЕ МОДИФИЦИРОВАННОЙ ФУНКЦИИ ГИПЕРБОЛИЧЕСКОГО ТАНГЕНСА ДЛЯ АППРОКСИМАЦИИ ВОЛЬТАМПЕРНЫХ ХАРАКТЕРИСТИК ПОЛЕВЫХ ТРАНЗИСТОРОВ
1654:
1148:
1537:
1419:
715:
The function is sensitive to ratio of the denominator coefficients and often is used without coefficients in the numerator:
1644:
1585:
1399:
223:
It was also used in economics for modelling consumption and investment, to approximate current-voltage characteristics of
1348:
Using modified hyperbolic tangent function to approximate the current-voltage characteristics of field-effect transistors
197:
512:. It is worth noting that in this case, the function is not sensitive to flipping the left and right-sides parameters:
1649:
1459:
1351:
1081:
1145:Функция для оценки полезности альтернатив в задачах структурной оптимизации территориально распределенных объектов
1065:
1191:[Identification of utility functions in multi-objective choice modelling by using S-shaped functions]
1569:
1070:
224:
1473:
31:
1639:
1581:
1525:
1437:
1395:
1262:
1247:
1302:
1091:
228:
1303:"A discrete mathematical model for chaotic dynamics in economics: Kaldor's model on business cycle"
1060:
1168:
The S-shaped utility function of individual criteria for multi-objective decision-making in design
1488:
1076:
685:{\displaystyle {\frac {e^{ax}-e^{-bx}}{e^{ax}+e^{-bx}}}={\frac {e^{bx}-e^{-ax}}{e^{bx}+e^{-ax}}}}
35:
1599:
1529:
1411:
1322:
1266:
1211:
1589:
1403:
1314:
1164:
S-образная функция полезности част-ных критериев для многофакторной оценки проектных решений
1096:
236:
201:
28:
1235:
1044:
205:
822:{\displaystyle \operatorname {ssht} x={\frac {e^{x}-e^{-x}}{e^{\alpha x}+e^{-\beta x}}}.}
1594:
1188:ИДЕНТИФИКАЦИЯ ЧАСТНОй ПОлЕЗНОСТИ МНОГОФАКТОРНЫХ АлЬТЕРНАТИВ С ПОМОЩЬЮ S-ОБРАЗНЫХ ФУНКЦИй
244:
217:
1628:
1584:"Paisii Hilendarski", Plovdiv, Bulgaria / Institute of Mathematics and Informatics,
1248:"A Family Of Recurrence Generating Activation Functions Based On Gudermann Function"
1510:
232:
1142:
The utility function in problems of structural optimization of distributed objects
1518:
International
Journal of Innovative Science, Engineering & Technology (JISET)
1380:
1318:
151:{\displaystyle \operatorname {smht} x={\frac {e^{ax}-e^{-bx}}{e^{cx}+e^{-dx}}}.}
1246:
Malinova, Anna; Golev, Angel; Iliev, Anton; Kyurkchiev, Nikolay (August 2017).
1019: = 1 the modified hyperbolic tangent function reduces to the conventional
1197:
Problemy
Bioniki: Respublikanskij Mežvedomstvennyj Naučno-Techničeskij Sbornik
187:
1603:
1533:
1415:
1407:
1326:
1270:
1215:
1185:
Beskorovainyi, Vladimir
Valentinovich; Soboleva, Elena Vladimirovna (2010).
1140:
Soboleva, Elena
Vladimirovna; Beskorovainyi, Vladimir Valentinovich (2008).
1461:
Power
Exhaust Data Analysis and Modeling Of Advanced Divertor Configuration
972:{\displaystyle x_{\max }={\frac {1}{2}}\ln {\frac {\alpha +1}{\alpha -1}}.}
186:
This function was originally proposed as "modified hyperbolic tangent" by
1511:"A Note on the Soboleva' Modified Hyperbolic Tangent Activation Function"
898:{\displaystyle x_{\min }={\frac {1}{2}}\ln {\frac {\beta -1}{\beta +1}};}
240:
992:
983:
704:
695:
1255:
International
Journal of Engineering Researches and Management Studies
170:
161:
25:(parametric) Soboleva modified hyperbolic tangent activation function
1379:
Golev, Angel; Djamiykov, Todor; Kyurkchiev, Nikolay (2017-11-23) .
991:
982:
703:
694:
169:
160:
1476:. p. 84. ID 10811. Archived from the original on 2020-06-19
1020:
1568:
Iliev, Anton; Kyurkchiev, Nikolay; Markov, Svetoslav (2017).
1509:
Golev, Angel; Iliev, Anton; Kyurkchiev, Nikolay (June 2017).
473:
The following conditions are keeping the function limited on
1402:, Sofia, Bulgaria: Academic Publications, Ltd.: 1081–1092.
1570:"A Note on the New Activation Function of Gompertz Type"
255:
Derivative of the function is defined by the formula:
1388:
International
Journal of Pure and Applied Mathematics
910:
836:
737:
534:
263:
60:
1528:"Paisii Hilendarski", Plovdiv, Bulgaria: 177–182.
971:
897:
821:
684:
463:
150:
1442:: CS1 maint: DOI inactive as of September 2024 (
1381:"Sigmoidal Functions In Antenna-Feeder Technique"
16:Mathematical activation function in data analysis
1493:: CS1 maint: bot: original URL status unknown (
1265:"Paisii Hilendarski", Plovdiv, Bulgaria: 38–48.
916:
842:
1208:Kharkiv National University of Radioelectronics
1172:Kharkiv National University of Radioelectronics
1206:] (in Russian). Vol. 72, no. 1.
1580:(2). Faculty of Mathematics and Informatics,
1524:(6). Faculty of Mathematics and Informatics,
1394:(4). Faculty of Mathematics and Informatics,
1261:(8). Faculty of Mathematics and Informatics,
191:
8:
1470:Università degli Studi di Napoli Federico II
216:The function has since been introduced into
1340:Tuev, Vasily I.; Uzhanin, Maxim V. (2009).
1398:"Paisii Hilendarski", Plovdiv, Bulgaria /
717:
514:
40:
1593:
1087:List of integrals of hyperbolic functions
940:
924:
915:
909:
866:
850:
841:
835:
801:
785:
770:
757:
750:
736:
667:
651:
633:
617:
610:
592:
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558:
542:
535:
533:
446:
430:
412:
393:
383:
350:
334:
316:
297:
287:
262:
130:
114:
96:
80:
73:
59:
1354:(TPU/ТПУ). pp. 135–138. No. 4/314.
1588:, Sofia, Bulgaria: Biomath Forum (BF).
1307:Mathematics and Computers in Simulation
1132:
1108:
1486:
1435:
1162:Soboleva, Elena Vladimirovna (2009).
1114:
1112:
1043: = 0, the term becomes equal to
7:
1472:/ Instituto Superior Técnico (IST),
21:Soboleva modified hyperbolic tangent
1350:] (in Russian). Tomsk, Russia:
239:temperatures and densities in the
14:
1595:10.11145/10.11145/bmc.2017.10.201
1466:Università degli Studi di Padova
1301:Orlando, Giuseppe (2016-07-01).
1610:from the original on 2020-06-20
1543:from the original on 2020-06-19
1425:from the original on 2020-06-19
1358:from the original on 2017-08-15
1280:from the original on 2022-07-14
1225:from the original on 2022-06-21
1210:(KNURE/ХНУРЕ). pp. 50–54.
1149:Kharkiv University of Air Force
1458:Rubino, Giulio (2018-01-15) .
380:
374:
281:
275:
1:
1586:Bulgarian Academy of Sciences
1400:Technical University of Sofia
190:scientist Elena V. Soboleva (
1635:Elementary special functions
1319:10.1016/j.matcom.2016.01.001
1082:Inverse hyperbolic functions
198:multi-objective optimization
196:) as a utility function for
1352:Tomsk Politehnic University
1174:(KNURE/ХНУРЕ). p. 247.
1676:
1660:Artificial neural networks
1151:(HUPS/ХУПС). p. 121.
1066:e (mathematical constant)
251:Sensitivity to parameters
192:
1499:(2+viii+3*iii+102 pages)
1408:10.12732/ijpam.v116i4.23
1342:
1218:. UDK 519.688: 004.896.
1199:
1187:
1163:
1144:
1027:) function, whereas for
225:field-effect transistors
1410:(inactive 2024-09-19).
1204:Bionics of Intelligence
1071:Equal incircles theorem
27:(SMHTAF), is a special
1655:Functions and mappings
1574:Biomath Communications
1474:Universidade de Lisboa
996:
987:
973:
899:
823:
708:
699:
686:
465:
174:
165:
152:
1582:University of Plovdiv
1526:University of Plovdiv
1396:University of Plovdiv
1263:University of Plovdiv
995:
986:
974:
900:
824:
707:
698:
687:
466:
229:light-emitting diodes
220:theory and practice.
173:
164:
153:
1645:Hyperbolic functions
908:
834:
830:Extremum estimates:
735:
532:
261:
58:
1061:Activation function
50:Right tail control
1650:Analytic functions
1200:БИОНИКА ИНТЕЛЛЕКТА
1077:Hausdorff distance
997:
988:
969:
895:
819:
709:
700:
682:
461:
175:
166:
148:
47:Left tail control
36:hyperbolic tangent
1092:Poinsot's spirals
1001:
1000:
964:
932:
890:
858:
814:
713:
712:
680:
605:
524:Right prevalence
459:
363:
193:Елена В. Соболева
179:
178:
143:
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1616:
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1555:
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1385:
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1366:
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1279:
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1243:
1237:
1233:
1231:
1230:
1224:
1194:
1182:
1176:
1175:
1159:
1153:
1152:
1137:
1120:
1116:
1097:Sigmoid function
1003:With parameters
978:
976:
975:
970:
965:
963:
952:
941:
933:
925:
920:
919:
904:
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851:
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828:
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820:
815:
813:
812:
811:
793:
792:
779:
778:
777:
762:
761:
751:
727:Scaled function
718:
691:
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645:
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624:
611:
606:
604:
603:
602:
584:
583:
570:
569:
568:
550:
549:
536:
521:Left prevalence
515:
470:
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467:
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438:
437:
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422:
401:
400:
384:
364:
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328:
327:
326:
305:
304:
288:
271:
202:choice modelling
195:
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149:
144:
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122:
121:
108:
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106:
88:
87:
74:
41:
23:, also known as
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1674:
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1624:
1613:
1611:
1567:
1564:
1562:Further reading
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1156:
1146:
1139:
1138:
1134:
1129:
1124:
1123:
1117:
1110:
1105:
1073:, based on sinh
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953:
942:
911:
906:
905:
879:
868:
837:
832:
831:
797:
781:
780:
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245:fusion reactors
233:antenna feeders
214:
212:Practical usage
206:decision-making
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126:
110:
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92:
76:
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55:
17:
12:
11:
5:
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1079:
1074:
1068:
1063:
1056:
1053:
1035: = 1 and
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998:
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980:
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948:
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235:, and analyze
218:neural network
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2:
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84:
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64:
61:
54:
53:
49:
46:
43:
42:
39:
37:
34:based on the
33:
30:
26:
22:
1640:Exponentials
1612:. Retrieved
1577:
1573:
1545:. Retrieved
1521:
1517:
1504:
1478:. Retrieved
1460:
1453:
1438:cite journal
1427:. Retrieved
1391:
1387:
1374:
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1289:(11 pages)
38:, given by
1629:Categories
1614:2020-06-19
1552:(6 pages)
1547:2020-06-19
1480:2020-06-19
1448:(12 pages)
1429:2020-06-19
1367:(4 pages)
1362:2015-11-05
1284:2020-06-19
1234:(5 pages)
1229:2020-06-19
1127:References
243:region of
1604:2367-5233
1534:2348-7968
1489:cite book
1416:1311-8080
1327:0378-4754
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1216:0555-2656
1119:tangent".
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518:Equation
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285:≐
273:
188:Ukrainian
132:−
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1356:Archived
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1055:See also
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182:History
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