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Directory of People » Elena Braverman

Elena Braverman

photograph of Elena Braverman

Job Title:

  • Associate Professor

Phone:

  • +1 (403) 220-3956

Office:

  • MS 444

Email:

Web site:

Degrees:

  • 1990 - Ph.D. - Urals State University
  • 1983 - M.Sc. - University of Perm, Russia
  • 1981 - B.Sc. - University of Perm, Russia

Research Interests:

  • Delay differential equations, delay equations of population dynamics, logistic equations
  • Impulsive equations, integro-differential equations, equations with distributed delay
  • Numerical solution of partial differential equations, spectral methods of numerical analysis,Fourier transform, wavelets

Masters Students:

  • Sergey Zhukovskiy (2008)
  • Reneeta Mamdani (2007)
  • Damir Kinzebulatov (2006)

Teaching:

Past Courses:

  • AMAT307 - DIFFERENTIAL EQUATION ENGINEERS
  • MATH251 - Calculus I
  • MATH253 - CALCULUS II
  • MATH311 - LINEAR METHODS II
  • MATH331 - MULTIVARIATE CALCULUS
  • MATH349 - CALCULUS III
  • MATH411 - Linear Spaces With Applications
  • PMAT545 - ANALYSIS III
Representative Publications:
Journal Paper
Berezansky, Leonid and Braverman, Elena. "On stability of some linear and nonlinear delay differential equations" J. Math. Anal. Appl. 314.2 (2006): 391-411
Berezansky, L. and Braverman, Elena. "On persistence of a delay differential equation with positive and negative coefficients" Functional Differential Equations 12.1-2 (2005): 95-107
Berezansky, L. , Braverman, Elena and Idels, L. . "Delay differential equations with {H}ill's type growth rate and linear harvesting" Computers & Mathematics with Applications. An International Journal 49.4 (2005): 549-563
Berezansky, L. and Braverman, Elena. "On exponential dichotomy, {B}ohl-{P}erron type theorems and stability of difference equations" J. Math. Anal. Appl. 304.2 (2005): 511-530
Braverman, Elena, Israeli, M. and Averbuch, A. . "A hierarchical 3-{D} direct {H}elmholtz solver by domain decomposition and modified {F}ourier method" SIAM Journal on Scientific Computing 26.5 (2005): 1504-1524 (electronic)
Berezansky, Leonid , Braverman, Elena and Liz, Eduardo . "Sufficient conditions for the global stability of nonautonomous higher order difference equations" Journal of Difference Equations and Applications 11.9 (2005): 785-798
Braverman, Elena, Epstein, Boris , Israeli, Moshe and Averbuch, Amir . "A fast spectral subtractional solver for elliptic equations" Journal of Scientific Computing 21.1 (2004): 91-128
Berezansky, Leonid and Braverman, Elena. "On impulsive {B}everton-{H}olt difference equations and their applications" Journal of Difference Equations and Applications 10.9 (2004): 851-868
Berezansky, L. , Braverman, Elena and Idels, L. . "Delay differential logistic equations with harvesting" Mathematical and Computer Modelling 39.11-12 (2004): 1243-1259
Berezansky, L. and Braverman, Elena. "On {B}ohl-{P}erron type theorems for linear difference equations" Functional Differential Equations 11.1-2 (2004): 19-28
Berezansky, L. , Braverman, Elena and Idels, L. . "Delay differential logistic equations with a nonlinear harvesting function" Functional Differential Equations 10.1-2 (2003): 83-94
Berezansky, Leonid and Braverman, Elena. "Linearized oscillation theory for a nonlinear delay impulsive equation" Journal of Computational and Applied Mathematics 161.2 (2003): 477-495
Berezansky, L. and Braverman, Elena. "Oscillation and other properties of linear impulsive and nonimpulsive delay equations" Applied Mathematics Letters. An International Journal of Rapid Publication 16.7 (2003): 1025-1030
Berezansky, Leonid and Braverman, Elena. "Linearized oscillation theory for a nonlinear delay impulsive equation" Journal of Computational and Applied Mathematics 161.2 (2003): 477-495
Berezansky, Leonid and Braverman, Elena. "Oscillation criteria for a linear neutral differential equation" Journal of Mathematical Analysis and Applications 286.2 (2003): 601-617
Berezansky, Leonid and Braverman, Elena. "Oscillation for equations with positive and negative coefficients and distributed delay. {II}. {A}pplications" Electronic Journal of Differential Equations (2003): No. 47, 25 pp. (electronic)
Berezansky, Leonid and Braverman, Elena. "Oscillation for equations with positive and negative coefficients and with distributed delay. {I}. {G}eneral results" Electronic Journal of Differential Equations (2003): No. 12, 21 pp. (electronic)
Berezansky, Leonid and Braverman, Elena. "On oscillation of a food-limited population model with time delay" Abstract and Applied Analysis1 (2003): 55-66
Berezansky, Leonid and Braverman, Elena. "Linearized oscillation theory for a nonlinear nonautonomous delay differential equation" Journal of Computational and Applied Mathematics 151.1 (2003): 119-127
Berezansky, Leonid and Braverman, Elena. "Oscillation properties of a logistic equation with distributed delay" Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal 4.1 (2003): 1-19
Berezansky, Leonid and Braverman, Elena. "On oscillation of a food-limited population model with time delay [MR1954246]" (2003): 55-66
Berezansky, Leonid and Braverman, Elena. "On oscillation of an impulsive logistic equation" Dynamics of Continuous, Discrete \& Impulsive Systems. Series A. Mathematical Analysis 9.3 (2002): 377-396
Averbuch, A. , Braverman, Elena, Coifman, R. and Israeli, M. . "Fast evaluation of 2-{D} and 3-{D} oscillatory integrals with local {F}ourier bases" International Journal of Pure and Applied Mathematics 3.1 (2002): 1-28
Berezansky, Leonid , Domshlak, Yury and Braverman, Elena. "On oscillation properties of delay differential equations with positive and negative coefficients" Journal of Mathematical Analysis and Applications 274.1 (2002): 81-101
Berezansky, L. and Braverman, Elena. "Non-oscillation properties of a linear neutral differential equations" Functional Differential Equations 9.3-4 (2002): 275-288
Berezansky, L. and Braverman, Elena. "On oscillation of a differential equation with infinite number of delays" Zeitschrift f\"ur Analysis und ihre Anwendungen. Journal for Analysis and its Applications 21.3 (2002): 803-816
Israeli, Moshe , Braverman, Elena and Averbuch, Amir . "A hierarchical 3-{D} {P}oisson modified {F}ourier solver by domain decomposition" Journal of Scientific Computing 17.1-4 (2002): 471-479
Berezansky, Leonid and Braverman, Elena. "On oscillation of a generalized logistic equation with several delays" Journal of Mathematical Analysis and Applications 253.2 (2001): 389-405
Averbuch, A. , Braverman, Elena, Israeli, M. and Coifman, R. . "On efficient computation of multidimensional oscillatory integrals with local Fourier bases" Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 47.5 (2001): 3491-3502
Berezansky, L. and Braverman, Elena. "On oscillation of equations with distributed delay" Zeitschrift f\"ur Analysis und ihre Anwendungen. Journal for Analysis and its Applications 20.2 (2001): 489-504
Berezansky, L. and Braverman, Elena. "On oscillation of a multiplicative delay logistic equation" Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 47.2 (2001): 1199-1209
Averbuch, A. , Braverman, Elena, Israeli, M. and Coifman, R. . "On efficient computation of multidimensional oscillatory integrals with local {F}ourier bases" Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 47.5 (2001): 3491-3502
Berezansky, L. and Braverman, Elena. "Oscillation of a second-order delay differential equation with middle term" Applied Mathematics Letters. An International Journal of Rapid Publication 13.2 (2000): 21-25
Berezansky, Leonid and Braverman, Elena. "On oscillation of a logistic equation with several delays" Journal of Computational and Applied Mathematics 113.1-2 (2000): 255-265
Averbuch, A. , Braverman, Elena, Coifman, R. , Israeli, M. and Sidi, A. . "Efficient computation of oscillatory integrals via adaptive multiscale local {F}ourier bases" Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications 9.1 (2000): 19-53
Averbuch, A. , Braverman, Elena and Israeli, M. . "Parallel adaptive solution of a {P}oisson equation with multiwavelets" SIAM Journal on Scientific Computing 22.3 (2000): 1053-1086 (electronic)
Berezansky, Leonid and Braverman, Elena. "Oscillation properties of a logistic equation with several delays" Journal of Mathematical Analysis and Applications 247.1 (2000): 110-125
Braverman, Elena, Israeli, M. and Averbuch, A. . "A fast spectral solver for a {$3$}{D} {H}elmholtz equation" SIAM Journal on Scientific Computing 20.6 (1999): 2237-2260 (electronic)
Berezansky, L. and Braverman, Elena. "Nonoscillation of a second order linear delay differential equation with a middle term" Functional Differential Equations 6.3-4 (1999): 233-247
Berezansky, Leonid , Braverman, Elena and Ak{\c{c}}a, Haydar . "On oscillation of a linear delay integro-differential equation" Dynamic Systems and Applications 8.2 (1999): 219-234
Berezansky, L. and Braverman, Elena. "On oscillation of a second order impulsive linear delay differential equation" Journal of Mathematical Analysis and Applications 233.1 (1999): 276-300
Braverman, Elena, Israeli, M. , Averbuch, A. and Vozovoi, L. . "A fast {$3$}{D} {P}oisson solver of arbitrary order accuracy" Journal of Computational Physics 144.1 (1998): 109-136
Berezansky, L. and Braverman, Elena. "Some oscillation problems for a second order linear delay differential equation" Journal of Mathematical Analysis and Applications 220.2 (1998): 719-740
Berezansky, L. and Braverman, Elena. "Explicit conditions of exponential stability for a linear impulsive delay differential equation" Journal of Mathematical Analysis and Applications 214.2 (1997): 439-458
Berezansky, Leonid and Braverman, Elena. "On non-oscillation of a scalar delay differential equation" Dynamic Systems and Applications 6.4 (1997): 567-580
Berezansky, L. and Braverman, Elena. "Oscillation of a linear delay impulsive differential equation" Communications on Applied Nonlinear Analysis 3.1 (1996): 61-77
Berezansky, L. and Braverman, Elena. "On integrable solutions of impulsive delay differential equations" Differential Equations and Dynamical Systems. An International Journal for Theory and Applications 4.1 (1996): 21-42
Berezansky, L. and Braverman, Elena. "Exponential boundedness of solutions for impulsive delay differential equations" Applied Mathematics Letters. An International Journal of Rapid Publication 9.6 (1996): 91-95
Ak{\c{c}}a, H. , Berezansky, L. and Braverman, Elena. "On linear integro-differential equations with integral impulsive conditions" Zeitschrift f\"ur Analysis und ihre Anwendungen. Journal for Analysis and its Applications 15.3 (1996): 709-727
Berezansky, Leonid and Braverman, Elena. "Impulsive stabilization of linear delay differential equations" Dynamic Systems and Applications 5.2 (1996): 263-276
Anokhin, Alexander , Berezansky, Leonid and Braverman, Elena. "Stability of linear delay impulsive differential equations" Dynamic Systems and Applications 4.2 (1995): 173-187
Braverman, Elena and Drakhlin, Michael . "On the variational problem for functionals with deviations of argument" Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 25.11 (1995): 1123-1138
Anokhin, A. , Berezansky, L. and Braverman, Elena. "Exponential stability of linear delay impulsive differential equations" Journal of Mathematical Analysis and Applications 193.3 (1995): 923-941
Berezansky, L. and Braverman, Elena. "Preservation of the exponential stability under perturbations of linear delay impulsive differential equations" Zeitschrift f\"ur Analysis und ihre Anwendungen. Journal for Analysis and its Applications 14.1 (1995): 157-174
Berezansky, L. and Braverman, Elena. "Boundedness and stability of impulsively perturbed delay differential equations" Functional Differential Equations 3.1-2 (1995): 19-30
Berezansky, L. and Braverman, Elena. "On stability of impulsive differential equations with delay" Functional Differential Equations. Israel Seminar 2 (1994): 11-21 (1995)
Berezansky, L. and Braverman, Elena. "Boundedness and stability of impulsively perturbed systems in a {B}anach space" International Journal of Theoretical Physics 33.10 (1994): 2075-2090
Braverman, Elena. "The inner superposition operator in the space of discrete measures" Izvestiya Vysshikh Uchebnykh Zavedeni\u\i. Matematika12 (1991): 80-85
Anokhin, A. V. and Braverman, Elena. "Linear impulsive functional-differential equations" Differentsial\cprime nye Uravneniya 26.11 (1990): 1864-1872, 2018
Book
Berezansky, Leonid , Braverman, Elena and Idels, Lev . On oscillation of nonlinear delay equations of population dynamics Yokohama Publ., Yokohama (2004): 1-14
Israeli, M. , Braverman, Elena and Averbuch, A. . A hierarchical domain decomposition method with low communication overhead , Internat. Center Numer. Methods Eng. (CIMNE), Barcelona (2002): 395-403
Averbuch, A. , Braverman, Elena and Israeli, M. . A new low communication parallel algorithm for elliptic partial differential equations North-Holland (2001): 275-282
Braverman, Elena. On linear neutral type equations with generalized right-hand side 1, Coll. Judea Samaria (1993): 22-32
Braverman, Elena. On the definition of the inner superposition operator in a space of discrete measures Perm. Politekh. Inst. (1990): 131-142
Anokhin, A. V. and Braverman, Elena. Definition of the concept of impulse functional-differential equations Perm. Politekh. Inst. (1989): 35-46
Braverman, Elena. On a boundary value problem for a linear functional-differential equation with impulses Perm. Politekh. Inst. (1988): 50-55
Braverman, Elena. Conditions for the unique solvability of the {C}auchy problem with impulse actions Perm. Politekh. Inst. (1987): 146-150, x
Braverman, Elena. Complete continuity of a linear operator in the space of step functions Perm. Politekh. Inst. (1986): 49-52, v
Braverman, Elena. An inner superposition operator in a special space Perm. Politekh. Inst. (1986): 96-103, viii
Braverman, Elena. Solvability on the half-axis of some nonlinear integral equations with deviating argument Perm. Politekh. Inst. (1984): 30-33, 154-155

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