1. Višja matematika v fizikiMilan Ambrožič, Robert Repnik, Mitja Slavinec, 2017, reviewed university, higher education or higher vocational education textbook Abstract: V fiziki se da vse zakone in izreke, povezane s fizikalnimi količinami, ki so odvisne od kraja in časa, zapisati z diferencialnimi enačbami. Le-te so lahko navadne ali parcialne, skalarne ali vektorske, velikokrat pa gre celo za sistem več ali mnogo sklopljenih diferencialnih enačb, odvisno od dimenzije in kompleksnosti fizikalnega problema. Medtem ko so diferencialne enačbe lokalna oblika zapisa fizikalnih zakonov, zajemajo integralske enačbe cel prostor ali čas ali pa določeno prostorsko in časovno območje. Značilen zgled zapisa enačb v obeh oblikah so Maxwellove enačbe v elektromagnetizmu ali pa variacijski račun, povezan z minimizacijo proste energije. S postavitvijo in reševanjem (analitičnim ali numeričnim) teh enačb lahko zajamemo vsa področja fizike, od mehanike in gibanja točkastih teles, kjer posebna fizikalna veja analitična mehanika vpelje koncepte posplošenih koordinat in impulzov, Lagrangiana in Hamiltoniana, do obravnave skalarnih in vektorskih polj v elektromagnetizmu in valovni optiki, kvantni fiziki, termodinamiki, fiziki tekočin, teoriji verjetnosti itd.
Keywords: navadne diferencialne enačbe, parcialne diferencialne enačbe, variacijski račun, Euler-Lagrangeove enačbe, verjetnost
Published in DKUM: 10.04.2017; Views: 1890; Downloads: 215
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2. Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan: Delay-dependent stability analysis for uncertain neutral systems with time-varying delays. (English). - [J] Math. Comput. Simul. 75, No. 1-2, 15-27 (2007). [ISSN 0378-4754]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, asimptotična stabilnost, mathematics, ordinary differential equations, neutral delay-differential system
Published in DKUM: 10.07.2015; Views: 1498; Downloads: 40
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3. Faria, Teresa: Asymptotic stability for delayed logistic type equations. (English). - [J] Math. Comput. Modelling 43, No. 3-4, 433-445 (2006). [ISSN 0895-7177]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, populacijska dinamika, mathematics, differential equations, delayed logistic equation, delayed population model, global asymptotic stability
Published in DKUM: 10.07.2015; Views: 1807; Downloads: 25
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4. Balachandran, K.; Ravikumar, R.: Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces. (English). - [J] Tamkang J. Math. 37, No. 3, 193-205 (2006). [ISSN 0049-2930]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, polgrupe nelinearnih operatorjev, mathematics, differential equations, delay integrodifferential equation, nonlocal condition
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5. Voigt, Jürgen: The modulus semigroup for linear delay equations II. (English). - [J] Note Mat. 25, No. 2, 191-208 (2006).[ISSN 1123-2536; ISSN 1590-0932]Miklavž Mastinšek, 2007, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, teorija operatorjev, funkcijska diferencialna enačba, teorija perturbacij, mathematics, ordinary differential equations, operator theory, functional differential equation, modulus semigroup, perturbation theory
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6. Karunanithi, S.; Anthoni, S.M.: Existence of mild solutions of nonlinear functional integro-differential equations of neutral type. (English). - [CA] Sahadevan, R. (ed.) et al., Nonlinear systems. Proceedings of the 8th Ramanujan symposium on recent developments in nonlinear systems, University of Madras, Chennai, India, February 14-16, 2001. Boca Raton, FL: Chapman and Hall/CRC; New Delhi: Narosa Publishing House. 207-219 (2002). [ISBN 0-8493-1722-3; ISBN 81-7319-456-4]Miklavž Mastinšek, 2005, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, nelinearni funkcional, integro-diferencialna enačba, nevtralni tip, mathematics, ordinary differential equations, nonlinear functional, integro-differential equation, neutral type, mild solution
Published in DKUM: 10.07.2015; Views: 1065; Downloads: 27
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7. Agarwal, Shruti; Bahuguna, Dhirendra: Existence and uniqueness of strong solutions to nonlinear nonlocal functional differential equations. - Electron. J. Differ. Equ. 2004, Paper No. 52, 9 p., electronic only (2004). [ISSN 1072-6691]Miklavž Mastinšek, 2005, review, book review, critique Keywords: matematika, analiza, nelinearne navadne diferencialne enačbe, nelokalni problemi, mathematics, analysis, nonlocal problem, accretive operator, method of lines
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8. Xu, Rui; Chaplain, M. A. J.; Chen, Lansun: Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with infinite delays. -Appl. Math. Comput. 130, no. 2-3, 295-309 (2002). [ISSN 0096-3003]Miklavž Mastinšek, 2004, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, Lotka-Volterrov sistem, stabilnost, funkcional Ljapunova, mathematics, ordinary differential equations, Lotka-Volterra system, Lyapunov functional, global asymptotic stability, infinite delays
Published in DKUM: 10.07.2015; Views: 1278; Downloads: 18
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9. Megan, M.; Sasu, A. L.; Sasu, B.; Pogan, A.: Exponential stability and unstability of semigroups of linear operators in Banach spaces. - Math. Inequal. Appl. 5, no. 3, 557-567 (2002). [ISSN 1331-4343]Miklavž Mastinšek, 2004, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, ▫$C_0$▫-polgrupe, stabilnost, mathematics, ordinary differential equations, ▫$C_0$▫-semigroups, uniform exponential stability
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10. Mastinšek, Miklavž: Structural operators for abstract functional differential equations. - Semigroup theory and applications, Proc. Conf. Trieste/Italy, Lect. Notes Pure Appl. Math. 116, 303-314 (1989)Miklavž Mastinšek, 1990, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, ulomljene potence operatorjev, strukturni operatorji, mathematics, ordinary differential equations, fractional powers of operators, structural operators, abstract functional differential equations
Published in DKUM: 10.07.2015; Views: 1010; Downloads: 43
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