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## Trofimchuk, Sergei I.

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 Author ID: trofimchuk.sergei-i Published as: Trofimchuk, Sergei; Trofimchuk, S. I.; Trofimchuk, Sergei I.; Trofimchuk, S.; Trofimchuk, Sergej I.; Trofimchuk, Sergeĭ; Trofımchuk, Sergei External Links: MGP
 Documents Indexed: 115 Publications since 1982 Reviewing Activity: 100 Reviews
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#### Co-Authors

 7 single-authored 18 Samoĭlenko, Anatoliĭ Mykhaĭlovych 13 Liz, Eduardo 11 Pinto, Manuel 11 Tkachenko, Victor Ivanovich 10 Ronto, N. I. 9 Ivanov, Anatoli F. 9 Trofimchuk, Elena 9 Volpert, Vitaly A. 8 Gupta, Chaitan P. 6 Hasík, Karel 4 Faria, Teresa 4 Kolyada, Sergiǐ Fedorovych 4 Snoha, L’ubomír 3 Beuter, Anne 3 Gómez, Carlos Alexis 3 Gopalsamy, Kondalsamy 3 Gyori, Istvan 3 Kopfová, Jana 3 Nábělková, Petra 3 Rogovchenko, Yuri V. 3 Solar, Abraham 2 Aguerrea, Maitere 2 Bantsur, N. K. 2 Bocharov, Gennady A. 2 Gomez, Adrian 2 Hernández, Eduardo M. 2 Martínez, Clotilde 2 Perestyuk, Mykola Oleksiĭovych 2 Robledo, Gonzalo 2 Ronto, M. I. 2 Trofimchuk, E. P. 1 Alvarado, Pedro 1 Antonyuk, Oleksandra Viktorivna 1 Balossier, Anne 1 Berezans’kyĭ, Yuriĭ Makarovych 1 Bessonov, Nick 1 Bessonov, Nikolai 1 Boĭchuk, Oleksandr Andriĭovych 1 Braverman, Elena 1 Cabada, Alberto 1 Chladná, Zuzana 1 Franco, Daniel H. T. 1 Hakl, Robert 1 Hutlyans’kyi, V. Ya. 1 Khruslov, Eugene Yakovlevich 1 Kochubeĭ, Anatoliĭ Naumovych 1 Korolyuk, Volodymyr Semenovych 1 Kushnir, Roman M. 1 Lukovsky, Ivan Oleksandrovych 1 Makarov, Volodymyr Leonidovych 1 Mal’kov, V. A. 1 Mammadov, Musa A. 1 Marchenko, V. O. 1 Meyerhans, Andreas 1 Nenya, O. I. 1 Nieto Roig, Juan Jose 1 Nikitin, A. H. 1 Oliveira, José J. 1 Parasyuk, Igor O. 1 Pastur, Leonid Andreevich 1 Portenko, Mykola Ivanovych 1 Prado, Humberto E. 1 Ronto, Andrei 1 Rontó, Miklós 1 Sharkovs’kyĭ, Oleksandr Mykolaĭovych 1 Šotola, Jakub 1 Touaoula, Tarik Mohamed 1 Valenzuela, Gabriel
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#### Serials

 14 Ukraïns’kyĭ Matematychnyĭ Zhurnal 10 Journal of Mathematical Analysis and Applications 10 Ukrainian Mathematical Journal 9 Journal of Differential Equations 7 Discrete and Continuous Dynamical Systems 3 Nonlinearity 3 Proceedings of the American Mathematical Society 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of Dynamics and Differential Equations 3 Publications of the University of Miskolc. Series D. Natural Sciences. Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 2 Mathematical Biosciences 2 Applied Mathematics and Computation 2 Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Dynamic Systems and Applications 2 SIAM Journal on Mathematical Analysis 2 Journal of Difference Equations and Applications 2 Neliniĭni Kolyvannya 1 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 1 Mathematical Methods in the Applied Sciences 1 Fundamenta Mathematicae 1 Funkcialaj Ekvacioj. Serio Internacia 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Quarterly of Applied Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Ergodic Theory and Dynamical Systems 1 Applied Mathematics Letters 1 Differential and Integral Equations 1 Journal of Global Optimization 1 Journal of Nonlinear Science 1 Dopovidi Akademiï Nauk Ukraïni 1 The Canadian Applied Mathematics Quarterly 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Georgian Mathematical Journal 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Differential Equations and Dynamical Systems 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Cubo Matemática Educacional 1 Mathematical Biosciences and Engineering 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Theoretical Biology 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 78 Ordinary differential equations (34-XX) 41 Biology and other natural sciences (92-XX) 36 Partial differential equations (35-XX) 20 Dynamical systems and ergodic theory (37-XX) 9 Difference and functional equations (39-XX) 5 General topology (54-XX) 4 Numerical analysis (65-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 2 Real functions (26-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX)

#### Citations contained in zbMATH Open

99 Publications have been cited 1,124 times in 659 Documents Cited by Year
A sharper condition for the solvability of a three-point second order boundary value problem. Zbl 0874.34014
Gupta, Chaitan P.; Trofimchuk, Sergej I.
1997
Nonmonotone travelling waves in a single species reaction–diffusion equation with delay. Zbl 1217.35102
Faria, Teresa; Trofimchuk, Sergei
2006
Almost periodic solutions of Lasota-Wazewska-type delay differential equation. Zbl 0936.34058
Gopalsamy, K.; Trofimchuk, Sergei I.
1999
A global stability criterion for scalar functional differential equations. Zbl 1069.34109
Liz, Eduardo; Tkachenko, Victor; Trofimchuk, Sergei
2003
Noninvertible minimal maps. Zbl 1031.37014
Kolyada, Sergiĭ; Snoha, L’ubomír; Trofimchuk, Sergeĭ
2001
Existence of a solution to a three-point boundary value problem and the spectral radius of a related linear operator. Zbl 0944.34009
Gupta, Chaitan P.; Trofimchuk, Sergej I.
1998
Global attractivity in $$x'(t)=-\delta x(t)+pf(x(t-\tau))$$. Zbl 0965.34064
Győri, István; Trofimchuk, Sergei I.
1999
Monotone traveling wavefronts of the KPP-Fisher delayed equation. Zbl 1218.34075
2011
Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima. Zbl 1025.34078
Ivanov, Anatoli; Liz, Eduardo; Trofimchuk, Sergei
2002
Global continuation of monotone wavefronts. Zbl 1292.34063
2014
On uniqueness of semi-wavefronts. Zbl 1311.45008
Aguerrea, Maitere; Gomez, Carlos; Trofimchuk, Sergei
2012
A global stability criterion for a family of delayed population models. Zbl 1093.34038
Liz, Eduardo; Pinto, Manuel; Tkachenko, Victor; Trofimchuk, Sergei
2005
Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay. Zbl 1162.34056
Trofimchuk, Elena; Tkachenko, Victor; Trofimchuk, Sergei
2008
On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation. Zbl 1007.34063
Győri, Istvàn; Trofimchuk, Sergei I.
2002
Global stability in difference equations satisfying the generalized Yorke condition. Zbl 1068.39026
Tkachenko, Victor; Trofimchuk, Sergei
2005
Global stability in discrete population models with delayed-density dependence. Zbl 1086.92045
Liz, Eduardo; Tkachenko, Victor; Trofımchuk, Sergei
2006
Separation dichotomy and wavefronts for a nonlinear convolution equation. Zbl 1296.45005
Gomez, Carlos; Prado, Humberto; Trofimchuk, Sergei
2014
Existence and stability of almost periodic solutions for quasilinear delay systems and the Halanay inequality. Zbl 0965.34063
Liz, Eduardo; Trofimchuk, Sergei
2000
Global attractivity and persistence in a discrete population model. Zbl 0977.39005
Győri, I.; Trofimchuk, S. I.
2000
Admissable wavefront speeds for a single species reaction-diffusion equation with delay. Zbl 1154.34032
Trofimchuk, Elena; Trofimchuk, Sergei
2008
Positive travelling fronts for reaction-diffusion systems with distributed delay. Zbl 1206.34086
Faria, Teresa; Trofimchuk, Sergei
2010
Wright type delay differential equations with negative Schwarzian. Zbl 1034.34091
Liz, Eduardo; Pinto, Manuel; Robledo, Gonzalo; Trofimchuk, Sergei; Tkachenko, Victor
2003
Minimality of nonautonomous dynamical systems. Zbl 1092.37011
Kolyada, S.; Snoha, L.; Trofimchuk, S.
2004
A generalization of the monotone method for second order periodic boundary value problem with impulses at fixed points. Zbl 0953.34020
Cabada, Alberto; Nieto, Juan J.; Franco, Daniel; Trofimchuk, Sergei I.
2000
On the geometry of wave solutions of a delayed reaction-diffusion equation. Zbl 1171.35121
Trofimchuk, Elena; Alvarado, Pedro; Trofimchuk, Sergei
2009
Uniqueness of fast travelling fronts in reaction-diffusion equations with delay. Zbl 1152.35403
Aguerrea, Maitere; Trofimchuk, Sergei; Valenzuela, Gabriel
2008
A note on global attractivity in models of hematopoiesis. Zbl 0893.92012
Gopalsamy, K.; Trofimchuk, S. I.; Bantsur, N. K.
1998
Mackey-Glass type delay differential equations near the boundary of absolute stability. Zbl 1022.34071
Liz, Eduardo; Trofimchuk, Elena; Trofimchuk, Sergei
2002
A global attractivity criterion for nonlinear non-autonomous difference equations. Zbl 1103.39017
Tkachenko, Victor; Trofimchuk, Sergei
2006
Pushed traveling fronts in monostable equations with monotone delayed reaction. Zbl 1267.34136
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2013
Traveling waves for a model of the Belousov-Zhabotinsky reaction. Zbl 1271.34066
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2013
Solvability of a multipoint boundary value problem and related a priori estimates. Zbl 0922.34014
Gupta, Chaitan P.; Trofimchuk, Sergej I.
1998
Traveling waves for a bistable reaction-diffusion equation with delay. Zbl 1411.34090
Trofimchuk, Sergei; Volpert, Vitaly
2018
Traveling waves in the nonlocal KPP-Fisher equation: different roles of the right and the left interactions. Zbl 1347.34102
Hasik, Karel; Kopfová, Jana; Nábělková, Petra; Trofimchuk, Sergei
2016
Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima. Zbl 0970.34069
Pinto, Manuel; Trofimchuk, Sergei
2000
Global stability of a class of scalar nonlinear delay differential equations. Zbl 1231.34126
Ivanov, Anatoli; Liz, Eduardo; Trofimchuk, Sergei
2003
Almost periodic evolution systems with impulse action at state-dependent moments. Zbl 1350.35011
Hakl, Robert; Pinto, Manuel; Tkachenko, Viktor; Trofimchuk, Sergei
2017
Slowly oscillating wavefronts of the KPP-Fisher delayed equation. Zbl 1308.34085
Hasik, Karel; Trofimchuk, Sergei
2014
On a generalized Yorke condition for scalar delayed population models. Zbl 1074.34069
Faria, Teresa; Liz, Eduardo; Oliveira, José J.; Trofimchuk, Sergei
2005
Attractivity properties of infinite delay Mackey-Glass type equations. Zbl 1032.34073
Liz, Eduardo; Martínez, Clotilde; Trofimchuk, Sergei
2002
Proper minimal sets on compact connected 2-manifolds are nowhere dense. Zbl 1171.37008
Kolyada, Sergiĭ; Snoha, L’ubomír; Trofimchuk, Sergeĭ
2008
Interplay between reaction and diffusion processes in governing the dynamics of virus infections. Zbl 1406.92553
Bocharov, G.; Meyerhans, A.; Bessonov, N.; Trofimchuk, S.; Volpert, V.
2018
Asymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction. Zbl 1388.35104
Solar, Abraham; Trofimchuk, Sergei
2015
Monotone waves for non-monotone and non-local monostable reaction-diffusion equations. Zbl 1343.34158
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2016
A priori estimates for the existence of a solution for a multi-point boundary value problem. Zbl 0967.34006
Gupta, Chaitan P.; Trofimchuk, Sergei
2000
Almost periodic sampled-data systems. Zbl 0834.34016
Samoilenko, A. M.; Trofimchuk, S. I.
1993
An extension of Wright’s $$3/2$$-theorem for the KPP-Fisher delayed equation. Zbl 1322.34079
Hasik, Karel; Trofimchuk, Sergei
2015
Speed selection and stability of wavefronts for delayed monostable reaction-diffusion equations. Zbl 06643386
Solar, Abraham; Trofimchuk, Sergei
2016
Solvability of a multi-point boundary value problen of Neumann type. Zbl 0993.34009
Gupta, Chaitan P.; Trofimchuk, Sergei
1999
Positive heteroclinics and traveling waves for scalar population models with a single delay. Zbl 1106.92059
Faria, Teresa; Trofimchuk, Sergei
2007
On the existence of non-monotone non-oscillating wavefronts. Zbl 1295.35168
Ivanov, Anatoli; Gomez, Carlos; Trofimchuk, Sergei
2014
A simple approach to the wave uniqueness problem. Zbl 1410.34189
Solar, Abraham; Trofimchuk, Sergei
2019
Generalized solutions of impulse systems and the phenomenon of pulsations. Zbl 0735.34014
Samojlenko, A. M.; Perestyuk, N. A.; Trofimchuk, S. I.
1991
Delay reaction-diffusion equation for infection dynamics. Zbl 1418.35228
Bessonov, Nick; Bocharov, Gennady; Touaoula, Tarik Mohammed; Trofimchuk, Sergei; Volpert, Vitaly
2019
A note on global attractivity in models of hematopoiesis. Zbl 0933.92013
Gopalsamy, K.; Trofimchuk, S. I.; Bantsur, N. K.
1998
Almost periodic solutions to linear abstract impulse systems. Zbl 0853.34073
Trofimchuk, S. I.
1995
The theory of the numerical-analytic method: Achievements and new trends of development. IV. Zbl 0940.34027
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1998
Global attractivity in Goodwin’s oscillator with finite delay. Zbl 1042.34576
Liz, Eduardo; Martínez, Clotilde; Trofimchuk, Sergei
2001
Global stability of a nonlinear difference equation. Zbl 1092.39009
Nenya, O. I.; Tkachenko, V. I.; Trofimchuk, S. I.
2004
Yorke and Wright $$3/2$$-stability theorems from a unified point of view. Zbl 1066.34077
Liz, Eduardo; Tkachenko, Victor; Trofimchuk, Sergei
2003
Bounded and periodic solutions of weakly nonlinear impulse evolution systems. Zbl 0631.34050
Rogovchenko, Yu. V.; Trofimchuk, S. I.
1987
Global continuation of monotone waves for bistable delayed equations with unimodal nonlinearities. Zbl 1423.34082
Trofimchuk, Sergei; Volpert, Vitaly
2019
Construction of minimal non-invertible skew-product maps on 2-manifolds. Zbl 1353.37020
Šotola, Jakub; Trofimchuk, Sergei
2016
The theory of the numerical-analytic method: Achievements and new trends of development. I. Zbl 0933.34009
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
$$L_p$$-perturbations of invariant subbundles for linear systems. Zbl 1029.34007
Trofimchuk, Sergei; Pinto, Manuel
2002
On periodic solutions of autonomous difference equations. Zbl 0985.39010
Ronto, A. N.; Rontó, M.; Samoilenko, A. M.; Trofimchuk, S. I.
2001
Periodic solutions of weakly nonlinear systems with impulse interaction. Zbl 0715.34084
Rogovchenko, Yu. V.; Trofimchuk, S. I.
1989
Impulse systems with fixed shock times of general disposition: Existence, uniqueness of solution, and the well-posedness of the Cauchy problem. Zbl 0722.34008
Trofimchuk, E. P.; Trofimchuk, S. I.
1990
Theory of the numerical-analytic method: achievements and new directions of development. Zbl 0897.34014
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
Periodic solutions of a discretized differential delay equation. Zbl 1194.34129
Ivanov, Anatoli F.; Trofimchuk, Sergei I.
2010
Global stabilization in nonlinear discrete systems with time-delay. Zbl 1277.39028
Ivanov, Anatoli F.; Mammadov, Musa A.; Trofimchuk, Sergei I.
2013
Estimate of the travelling wave speed for an integro-differential equation. Zbl 1407.35045
Bessonov, N.; Beuter, A.; Trofimchuk, S.; Volpert, V.
2019
Modeling of post-stroke stimulation of cortical tissue. Zbl 1409.92029
Beuter, A.; Balossier, A.; Trofimchuk, S.; Volpert, V.
2018
Nonstandard quasi-monotonicity: an application to the wave existence in a neutral KPP-Fisher equation. Zbl 1443.34065
Hernández, Eduardo; Trofimchuk, Sergei
2020
Minimal sets of fibre-preserving maps in graph bundles. Zbl 1378.54036
Kolyada, Sergii; Snoha, L’ubomír; Trofimchuk, Sergei
2014
On the minimal speed of front propagation in a model of the Belousov-Zhabotinsky reaction. Zbl 1312.34104
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2014
Krylov-Bogolyubov averaging of asymptotically autonomous differential equations. Zbl 1058.34056
Samoilenko, Anatoliy; Pinto, Manuel; Trofimchuk, Sergei
2005
Periodic solutions of abstract impulsive systems with non-fixed moments of impulsive effect. Zbl 0859.34044
Ronto, M.; Trofimchuk, S. I.
1995
Weak hyperbolicity of delay differential equations and the 3/2-type stability conditions. Zbl 1142.34382
Trofimchuk, Sergei I.; Ivanov, Anatoli F.
2000
Unbounded functions with almost periodic differences. Zbl 0782.42009
Samojlenko, A. M.; Trofimchuk, S. I.
1991
Spaces of piecewise-continuous almost-periodic functions and almost- periodic sets on the line. I. Zbl 0774.42006
Samojlenko, A. M.; Trofimchuk, S. I.
1991
The theory of the numerical-analytic method: Achievements and new trends of development. III. Zbl 0934.34034
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
Cortical waves and post-stroke brain stimulation. Zbl 1425.92038
Bessonov, Nikolai; Beuter, Anne; Trofimchuk, Sergei; Volpert, Vitaly
2019
Nonlinearly determined wavefronts of the Nicholson’s diffusive equation: when small delays are not harmless. Zbl 1443.34073
Chladná, Zuzana; Hasík, Karel; Kopfová, Jana; Nábělková, Petra; Trofimchuk, Sergei
2020
On global dynamics in a periodic differential equation with deviating argument. Zbl 1338.34126
Ivanov, Anatoli F.; Trofimchuk, Sergei I.
2015
A cyclic system with delay and its characteristic equation. Zbl 07198709
Braverman, Elena; Hasik, Karel; Ivanov, Anatoli F.; Trofimchuk, Sergei I.
2020
Numerical-analytic method for nonlinear differential equations. Zbl 0926.34010
Ronto, M.; Trofimchuk, S.
1998
The theory of the numerical-analytic method: Achievements and new trends of development. V. Zbl 0937.39003
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1999
The theory of the numerical-analytic method: achievements and new trends of development. VI. Zbl 0940.34010
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1999
The theory of the numerical-analytic method: achievements and new trends of development. VII. Zbl 0940.34026
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1999
Global stability in a regulated logistic growth model. Zbl 1181.37026
Trofimchuk, E.; Trofimchuk, S.
2005
Linear extensions that satisfy the transversality condition. Zbl 0599.34060
Trofimchuk, S. I.
1984
Spaces of piecewise-continuous almost-periodic functions and almost- periodic sets on the real line. II. Zbl 0793.42008
Samojlenko, A. M.; Trofimchuk, S. I.
1992
The theory of a numerical-analytic method: Achievements and new trends of development. II. Zbl 0933.34034
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
Theory of a numerical-analytic method: achievements and new directions of development. Zbl 0915.34030
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
Periodic solutions and their stability of a differential-difference equation. Zbl 1192.34089
Ivanov, Anatoli F.; Trofimchuk, Sergei
2009
Traveling waves solutions for partial neutral differential equations. Zbl 1426.35064
Hernández, Eduardo; Trofimchuk, Sergei
2020
Existence of bistable waves for a nonlocal and nonmonotone reaction-diffusion equation. Zbl 07183658
Trofimchuk, Sergei; Volpert, Vitaly
2020
On the geometric diversity of wavefronts for the scalar Kolmogorov ecological equation. Zbl 07341376
Hasík, Karel; Kopfová, Jana; Nábělková, Petra; Trofimchuk, Sergei
2020
Nonstandard quasi-monotonicity: an application to the wave existence in a neutral KPP-Fisher equation. Zbl 1443.34065
Hernández, Eduardo; Trofimchuk, Sergei
2020
Nonlinearly determined wavefronts of the Nicholson’s diffusive equation: when small delays are not harmless. Zbl 1443.34073
Chladná, Zuzana; Hasík, Karel; Kopfová, Jana; Nábělková, Petra; Trofimchuk, Sergei
2020
A cyclic system with delay and its characteristic equation. Zbl 07198709
Braverman, Elena; Hasik, Karel; Ivanov, Anatoli F.; Trofimchuk, Sergei I.
2020
Traveling waves solutions for partial neutral differential equations. Zbl 1426.35064
Hernández, Eduardo; Trofimchuk, Sergei
2020
Existence of bistable waves for a nonlocal and nonmonotone reaction-diffusion equation. Zbl 07183658
Trofimchuk, Sergei; Volpert, Vitaly
2020
On the geometric diversity of wavefronts for the scalar Kolmogorov ecological equation. Zbl 07341376
Hasík, Karel; Kopfová, Jana; Nábělková, Petra; Trofimchuk, Sergei
2020
A simple approach to the wave uniqueness problem. Zbl 1410.34189
Solar, Abraham; Trofimchuk, Sergei
2019
Delay reaction-diffusion equation for infection dynamics. Zbl 1418.35228
Bessonov, Nick; Bocharov, Gennady; Touaoula, Tarik Mohammed; Trofimchuk, Sergei; Volpert, Vitaly
2019
Global continuation of monotone waves for bistable delayed equations with unimodal nonlinearities. Zbl 1423.34082
Trofimchuk, Sergei; Volpert, Vitaly
2019
Estimate of the travelling wave speed for an integro-differential equation. Zbl 1407.35045
Bessonov, N.; Beuter, A.; Trofimchuk, S.; Volpert, V.
2019
Cortical waves and post-stroke brain stimulation. Zbl 1425.92038
Bessonov, Nikolai; Beuter, Anne; Trofimchuk, Sergei; Volpert, Vitaly
2019
Traveling waves for a bistable reaction-diffusion equation with delay. Zbl 1411.34090
Trofimchuk, Sergei; Volpert, Vitaly
2018
Interplay between reaction and diffusion processes in governing the dynamics of virus infections. Zbl 1406.92553
Bocharov, G.; Meyerhans, A.; Bessonov, N.; Trofimchuk, S.; Volpert, V.
2018
Modeling of post-stroke stimulation of cortical tissue. Zbl 1409.92029
Beuter, A.; Balossier, A.; Trofimchuk, S.; Volpert, V.
2018
Almost periodic evolution systems with impulse action at state-dependent moments. Zbl 1350.35011
Hakl, Robert; Pinto, Manuel; Tkachenko, Viktor; Trofimchuk, Sergei
2017
Traveling waves in the nonlocal KPP-Fisher equation: different roles of the right and the left interactions. Zbl 1347.34102
Hasik, Karel; Kopfová, Jana; Nábělková, Petra; Trofimchuk, Sergei
2016
Monotone waves for non-monotone and non-local monostable reaction-diffusion equations. Zbl 1343.34158
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2016
Speed selection and stability of wavefronts for delayed monostable reaction-diffusion equations. Zbl 06643386
Solar, Abraham; Trofimchuk, Sergei
2016
Construction of minimal non-invertible skew-product maps on 2-manifolds. Zbl 1353.37020
Šotola, Jakub; Trofimchuk, Sergei
2016
Asymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction. Zbl 1388.35104
Solar, Abraham; Trofimchuk, Sergei
2015
An extension of Wright’s $$3/2$$-theorem for the KPP-Fisher delayed equation. Zbl 1322.34079
Hasik, Karel; Trofimchuk, Sergei
2015
On global dynamics in a periodic differential equation with deviating argument. Zbl 1338.34126
Ivanov, Anatoli F.; Trofimchuk, Sergei I.
2015
Global continuation of monotone wavefronts. Zbl 1292.34063
2014
Separation dichotomy and wavefronts for a nonlinear convolution equation. Zbl 1296.45005
Gomez, Carlos; Prado, Humberto; Trofimchuk, Sergei
2014
Slowly oscillating wavefronts of the KPP-Fisher delayed equation. Zbl 1308.34085
Hasik, Karel; Trofimchuk, Sergei
2014
On the existence of non-monotone non-oscillating wavefronts. Zbl 1295.35168
Ivanov, Anatoli; Gomez, Carlos; Trofimchuk, Sergei
2014
Minimal sets of fibre-preserving maps in graph bundles. Zbl 1378.54036
Kolyada, Sergii; Snoha, L&rsquo;ubomír; Trofimchuk, Sergei
2014
On the minimal speed of front propagation in a model of the Belousov-Zhabotinsky reaction. Zbl 1312.34104
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2014
Pushed traveling fronts in monostable equations with monotone delayed reaction. Zbl 1267.34136
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2013
Traveling waves for a model of the Belousov-Zhabotinsky reaction. Zbl 1271.34066
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2013
Global stabilization in nonlinear discrete systems with time-delay. Zbl 1277.39028
Ivanov, Anatoli F.; Mammadov, Musa A.; Trofimchuk, Sergei I.
2013
On uniqueness of semi-wavefronts. Zbl 1311.45008
Aguerrea, Maitere; Gomez, Carlos; Trofimchuk, Sergei
2012
Monotone traveling wavefronts of the KPP-Fisher delayed equation. Zbl 1218.34075
2011
Positive travelling fronts for reaction-diffusion systems with distributed delay. Zbl 1206.34086
Faria, Teresa; Trofimchuk, Sergei
2010
Periodic solutions of a discretized differential delay equation. Zbl 1194.34129
Ivanov, Anatoli F.; Trofimchuk, Sergei I.
2010
On the geometry of wave solutions of a delayed reaction-diffusion equation. Zbl 1171.35121
Trofimchuk, Elena; Alvarado, Pedro; Trofimchuk, Sergei
2009
Periodic solutions and their stability of a differential-difference equation. Zbl 1192.34089
Ivanov, Anatoli F.; Trofimchuk, Sergei
2009
Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay. Zbl 1162.34056
Trofimchuk, Elena; Tkachenko, Victor; Trofimchuk, Sergei
2008
Admissable wavefront speeds for a single species reaction-diffusion equation with delay. Zbl 1154.34032
Trofimchuk, Elena; Trofimchuk, Sergei
2008
Uniqueness of fast travelling fronts in reaction-diffusion equations with delay. Zbl 1152.35403
Aguerrea, Maitere; Trofimchuk, Sergei; Valenzuela, Gabriel
2008
Proper minimal sets on compact connected 2-manifolds are nowhere dense. Zbl 1171.37008
Kolyada, Sergiĭ; Snoha, L&rsquo;ubomír; Trofimchuk, Sergeĭ
2008
Positive heteroclinics and traveling waves for scalar population models with a single delay. Zbl 1106.92059
Faria, Teresa; Trofimchuk, Sergei
2007
Nonmonotone travelling waves in a single species reaction–diffusion equation with delay. Zbl 1217.35102
Faria, Teresa; Trofimchuk, Sergei
2006
Global stability in discrete population models with delayed-density dependence. Zbl 1086.92045
Liz, Eduardo; Tkachenko, Victor; Trofımchuk, Sergei
2006
A global attractivity criterion for nonlinear non-autonomous difference equations. Zbl 1103.39017
Tkachenko, Victor; Trofimchuk, Sergei
2006
A global stability criterion for a family of delayed population models. Zbl 1093.34038
Liz, Eduardo; Pinto, Manuel; Tkachenko, Victor; Trofimchuk, Sergei
2005
Global stability in difference equations satisfying the generalized Yorke condition. Zbl 1068.39026
Tkachenko, Victor; Trofimchuk, Sergei
2005
On a generalized Yorke condition for scalar delayed population models. Zbl 1074.34069
Faria, Teresa; Liz, Eduardo; Oliveira, José J.; Trofimchuk, Sergei
2005
Krylov-Bogolyubov averaging of asymptotically autonomous differential equations. Zbl 1058.34056
Samoilenko, Anatoliy; Pinto, Manuel; Trofimchuk, Sergei
2005
Global stability in a regulated logistic growth model. Zbl 1181.37026
Trofimchuk, E.; Trofimchuk, S.
2005
Minimality of nonautonomous dynamical systems. Zbl 1092.37011
Kolyada, S.; Snoha, L.; Trofimchuk, S.
2004
Global stability of a nonlinear difference equation. Zbl 1092.39009
Nenya, O. I.; Tkachenko, V. I.; Trofimchuk, S. I.
2004
A global stability criterion for scalar functional differential equations. Zbl 1069.34109
Liz, Eduardo; Tkachenko, Victor; Trofimchuk, Sergei
2003
Wright type delay differential equations with negative Schwarzian. Zbl 1034.34091
Liz, Eduardo; Pinto, Manuel; Robledo, Gonzalo; Trofimchuk, Sergei; Tkachenko, Victor
2003
Global stability of a class of scalar nonlinear delay differential equations. Zbl 1231.34126
Ivanov, Anatoli; Liz, Eduardo; Trofimchuk, Sergei
2003
Yorke and Wright $$3/2$$-stability theorems from a unified point of view. Zbl 1066.34077
Liz, Eduardo; Tkachenko, Victor; Trofimchuk, Sergei
2003
Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima. Zbl 1025.34078
Ivanov, Anatoli; Liz, Eduardo; Trofimchuk, Sergei
2002
On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation. Zbl 1007.34063
Győri, Istvàn; Trofimchuk, Sergei I.
2002
Mackey-Glass type delay differential equations near the boundary of absolute stability. Zbl 1022.34071
Liz, Eduardo; Trofimchuk, Elena; Trofimchuk, Sergei
2002
Attractivity properties of infinite delay Mackey-Glass type equations. Zbl 1032.34073
Liz, Eduardo; Martínez, Clotilde; Trofimchuk, Sergei
2002
$$L_p$$-perturbations of invariant subbundles for linear systems. Zbl 1029.34007
Trofimchuk, Sergei; Pinto, Manuel
2002
Noninvertible minimal maps. Zbl 1031.37014
Kolyada, Sergiĭ; Snoha, L&rsquo;ubomír; Trofimchuk, Sergeĭ
2001
Global attractivity in Goodwin’s oscillator with finite delay. Zbl 1042.34576
Liz, Eduardo; Martínez, Clotilde; Trofimchuk, Sergei
2001
On periodic solutions of autonomous difference equations. Zbl 0985.39010
Ronto, A. N.; Rontó, M.; Samoilenko, A. M.; Trofimchuk, S. I.
2001
Existence and stability of almost periodic solutions for quasilinear delay systems and the Halanay inequality. Zbl 0965.34063
Liz, Eduardo; Trofimchuk, Sergei
2000
Global attractivity and persistence in a discrete population model. Zbl 0977.39005
Győri, I.; Trofimchuk, S. I.
2000
A generalization of the monotone method for second order periodic boundary value problem with impulses at fixed points. Zbl 0953.34020
Cabada, Alberto; Nieto, Juan J.; Franco, Daniel; Trofimchuk, Sergei I.
2000
Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima. Zbl 0970.34069
Pinto, Manuel; Trofimchuk, Sergei
2000
A priori estimates for the existence of a solution for a multi-point boundary value problem. Zbl 0967.34006
Gupta, Chaitan P.; Trofimchuk, Sergei
2000
Weak hyperbolicity of delay differential equations and the 3/2-type stability conditions. Zbl 1142.34382
Trofimchuk, Sergei I.; Ivanov, Anatoli F.
2000
Almost periodic solutions of Lasota-Wazewska-type delay differential equation. Zbl 0936.34058
Gopalsamy, K.; Trofimchuk, Sergei I.
1999
Global attractivity in $$x'(t)=-\delta x(t)+pf(x(t-\tau))$$. Zbl 0965.34064
Győri, István; Trofimchuk, Sergei I.
1999
Solvability of a multi-point boundary value problen of Neumann type. Zbl 0993.34009
Gupta, Chaitan P.; Trofimchuk, Sergei
1999
The theory of the numerical-analytic method: Achievements and new trends of development. V. Zbl 0937.39003
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1999
The theory of the numerical-analytic method: achievements and new trends of development. VI. Zbl 0940.34010
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1999
The theory of the numerical-analytic method: achievements and new trends of development. VII. Zbl 0940.34026
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1999
Existence of a solution to a three-point boundary value problem and the spectral radius of a related linear operator. Zbl 0944.34009
Gupta, Chaitan P.; Trofimchuk, Sergej I.
1998
A note on global attractivity in models of hematopoiesis. Zbl 0893.92012
Gopalsamy, K.; Trofimchuk, S. I.; Bantsur, N. K.
1998
Solvability of a multipoint boundary value problem and related a priori estimates. Zbl 0922.34014
Gupta, Chaitan P.; Trofimchuk, Sergej I.
1998
A note on global attractivity in models of hematopoiesis. Zbl 0933.92013
Gopalsamy, K.; Trofimchuk, S. I.; Bantsur, N. K.
1998
The theory of the numerical-analytic method: Achievements and new trends of development. IV. Zbl 0940.34027
Ronto, N. I.; Samojlenko, A. M.; Trofimchuk, S. I.
1998
The theory of the numerical-analytic method: Achievements and new trends of development. I. Zbl 0933.34009
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
Theory of the numerical-analytic method: achievements and new directions of development. Zbl 0897.34014
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
The theory of the numerical-analytic method: Achievements and new trends of development. III. Zbl 0934.34034
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
Numerical-analytic method for nonlinear differential equations. Zbl 0926.34010
Ronto, M.; Trofimchuk, S.
1998
The theory of a numerical-analytic method: Achievements and new trends of development. II. Zbl 0933.34034
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
Theory of a numerical-analytic method: achievements and new directions of development. Zbl 0915.34030
Ronto, N. I.; Samoilenko, A. M.; Trofimchuk, S. I.
1998
A sharper condition for the solvability of a three-point second order boundary value problem. Zbl 0874.34014
Gupta, Chaitan P.; Trofimchuk, Sergej I.
1997
Almost periodic solutions to linear abstract impulse systems. Zbl 0853.34073
Trofimchuk, S. I.
1995
Periodic solutions of abstract impulsive systems with non-fixed moments of impulsive effect. Zbl 0859.34044
Ronto, M.; Trofimchuk, S. I.
1995
Almost periodic sampled-data systems. Zbl 0834.34016
Samoilenko, A. M.; Trofimchuk, S. I.
1993
Spaces of piecewise-continuous almost-periodic functions and almost- periodic sets on the real line. II. Zbl 0793.42008
Samojlenko, A. M.; Trofimchuk, S. I.
1992
Generalized solutions of impulse systems and the phenomenon of pulsations. Zbl 0735.34014
Samojlenko, A. M.; Perestyuk, N. A.; Trofimchuk, S. I.
1991
Unbounded functions with almost periodic differences. Zbl 0782.42009
Samojlenko, A. M.; Trofimchuk, S. I.
1991
Spaces of piecewise-continuous almost-periodic functions and almost- periodic sets on the line. I. Zbl 0774.42006
Samojlenko, A. M.; Trofimchuk, S. I.
1991
Impulse systems with fixed shock times of general disposition: Existence, uniqueness of solution, and the well-posedness of the Cauchy problem. Zbl 0722.34008
Trofimchuk, E. P.; Trofimchuk, S. I.
1990
Periodic solutions of weakly nonlinear systems with impulse interaction. Zbl 0715.34084
Rogovchenko, Yu. V.; Trofimchuk, S. I.
1989
Bounded and periodic solutions of weakly nonlinear impulse evolution systems. Zbl 0631.34050
Rogovchenko, Yu. V.; Trofimchuk, S. I.
1987
Linear extensions that satisfy the transversality condition. Zbl 0599.34060
Trofimchuk, S. I.
1984
all top 5

#### Cited by 698 Authors

 45 Trofimchuk, Sergei I. 22 Liz, Eduardo 20 Ge, Weigao 16 Li, Wan-Tong 16 Tkachenko, Victor Ivanovich 15 Berezansky, Leonid M. 15 Braverman, Elena 13 Volpert, Vitaly A. 12 Pinto, Manuel 12 Saker, Samir H. 11 Ma, Ruyun 11 Yi, Taishan 10 Ivanov, Anatoli F. 9 Agarwal, Ravi P. 9 El-Morshedy, Hassan A. 9 Faria, Teresa 9 O’Regan, Donal 9 Xu, Xian 9 Xu, Zhaoquan 8 Henderson, Johnny Lee 8 Snoha, L’ubomír 8 Wang, Zhi Cheng 7 Guo, Yanping 7 Idels, Lev V. 7 Mei, Ming 7 Röst, Gergely 7 Zou, Xingfu 6 Aguerrea, Maitere 6 Finkelshteĭn, Dmitriĭ Leonidovich 6 Liu, Lishan 6 Ruan, Shigui 6 Ruiz-Herrera, Alfonso 6 Sun, Yongping 6 Tkachov, Pasha 6 Trofimchuk, Elena 6 Wei, Junjie 6 Wu, Jianhong 6 Wu, Shiliang 5 Chen, Yuming 5 Feng, Meiqiang 5 Hasík, Karel 5 Hernández, Eduardo M. 5 Jiménez López, Víctor 5 Krisztin, Tibor 5 Lin, Guo 5 Tisdell, Christopher C. 5 Zhai, Chengbo 4 Balibrea, Francisco 4 Dvornyk, A. V. 4 Garab, Ábel 4 Gómez, Carlos Alexis 4 Gupta, Chaitan P. 4 Gyori, Istvan 4 Kolyada, Sergiǐ Fedorovych 4 Kondrat’yev, Yuriĭ Grygorovych 4 Maličký, Peter 4 Muroya, Yoshiaki 4 Shen, Jianhua 4 Solar, Abraham 4 Špitalský, Vladimír 4 Touaoula, Tarik Mohamed 4 Wang, Xiao 4 Yin, Jingxue 4 Yu, Zhixian 4 Zhang, Guang 4 Zhang, Guobao 4 Zhang, Zhongxin 3 Akin, Ethan 3 Bai, Chuanzhi 3 Barragán, Franco 3 Bartha, Ferenc A. 3 Boroński, Jan P. 3 Chen, Haibo 3 Chen, Shihua 3 Dirbák, Matúš 3 Downarowicz, Tomasz 3 Du, Zengji 3 Ducrot, Arnaud 3 Ferreiro, Juan Bosco 3 Franco, Daniel H. T. 3 Giang, Dang Vu 3 Han, Bang-Sheng 3 Hric, Roman 3 Hsu, Cheng-Hsiung 3 Ishiwata, Emiko 3 Ji, Shanming 3 Klimina, Lyubov’ Aleksandrovna 3 Kopfová, Jana 3 Kosmatov, Nickolai 3 Kyrychko, Yuliya N. 3 Li, Pingrun 3 Li, Zhixiang 3 Lian, Hairong 3 Liu, Bing 3 Liu, Bingwen 3 Liu, Sanyang 3 Liu, Yuji 3 Long, Shujun 3 Memarbashi, Reza 3 Myslo, Yu. M. ...and 598 more Authors
all top 5

#### Cited in 139 Serials

 79 Journal of Mathematical Analysis and Applications 49 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 39 Journal of Differential Equations 34 Applied Mathematics and Computation 26 Applied Mathematics Letters 24 Computers & Mathematics with Applications 22 Journal of Difference Equations and Applications 17 Mathematical and Computer Modelling 15 Advances in Difference Equations 14 Journal of Dynamics and Differential Equations 13 Nonlinear Analysis. Real World Applications 11 Proceedings of the American Mathematical Society 11 Discrete and Continuous Dynamical Systems 10 Journal of Computational and Applied Mathematics 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 9 Topology and its Applications 8 Applicable Analysis 8 Discrete Dynamics in Nature and Society 8 Discrete and Continuous Dynamical Systems. Series B 8 Nonlinear Oscillations 7 Ukrainian Mathematical Journal 7 Chaos, Solitons and Fractals 7 Journal of Mathematical Sciences (New York) 6 Ergodic Theory and Dynamical Systems 6 Journal of Inequalities and Applications 6 Communications in Nonlinear Science and Numerical Simulation 5 Transactions of the American Mathematical Society 5 Nonlinear Dynamics 5 Abstract and Applied Analysis 4 Mathematical Methods in the Applied Sciences 4 Nonlinearity 4 Applied Mathematical Modelling 4 Journal of Nonlinear Science 4 Chaos 4 Qualitative Theory of Dynamical Systems 4 Communications on Pure and Applied Analysis 4 Journal of Applied Mathematics and Computing 4 Mediterranean Journal of Mathematics 4 Boundary Value Problems 4 Discrete and Continuous Dynamical Systems. Series S 3 Journal of the Franklin Institute 3 Mathematical Biosciences 3 Rocky Mountain Journal of Mathematics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal of Integral Equations and Applications 3 SIAM Journal on Applied Mathematics 3 SIAM Journal on Mathematical Analysis 3 Applied Mathematics. Series B (English Edition) 3 Electronic Journal of Differential Equations (EJDE) 3 NoDEA. Nonlinear Differential Equations and Applications 3 Mathematical Biosciences and Engineering 3 International Journal of Biomathematics 2 Journal of Mathematical Physics 2 Theoretical and Mathematical Physics 2 Bulletin of the Iranian Mathematical Society 2 Physica D 2 Acta Mathematicae Applicatae Sinica. English Series 2 International Journal of Mathematics 2 Applications of Mathematics 2 Computational Mathematics and Mathematical Physics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Journal of Computer and Systems Sciences International 2 Complexity 2 Differential Equations and Dynamical Systems 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Acta Mathematica Sinica. English Series 2 Journal of Applied Mathematics 2 Science China. Mathematics 2 Nonlinear Analysis. Theory, Methods & Applications 1 Biological Cybernetics 1 Israel Journal of Mathematics 1 Journal of Mathematical Biology 1 Lithuanian Mathematical Journal 1 Periodica Mathematica Hungarica 1 Studia Mathematica 1 Bulletin of Mathematical Biology 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Polonici Mathematici 1 Automatica 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Functional Analysis 1 Matematički Vesnik 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Quarterly of Applied Mathematics 1 Results in Mathematics 1 SIAM Journal on Control and Optimization 1 Tohoku Mathematical Journal. Second Series 1 Systems & Control Letters 1 Zeitschrift für Analysis und ihre Anwendungen 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Applicandae Mathematicae 1 Journal of Scientific Computing 1 Science in China. Series A 1 European Journal of Applied Mathematics 1 International Journal of Adaptive Control and Signal Processing ...and 39 more Serials
all top 5

#### Cited in 32 Fields

 365 Ordinary differential equations (34-XX) 202 Biology and other natural sciences (92-XX) 171 Partial differential equations (35-XX) 97 Dynamical systems and ergodic theory (37-XX) 86 Difference and functional equations (39-XX) 66 Operator theory (47-XX) 34 General topology (54-XX) 30 Integral equations (45-XX) 22 Numerical analysis (65-XX) 17 Systems theory; control (93-XX) 5 Manifolds and cell complexes (57-XX) 4 Functions of a complex variable (30-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Real functions (26-XX) 3 Abstract harmonic analysis (43-XX) 3 Functional analysis (46-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Probability theory and stochastic processes (60-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)