A. D. Polyanin (Bauman Moscow State Technical University/Ishlinsky Institute for Problems in Mechanics) :


Articles:

001.92 Disadvantages of citation index and Hirsch and using other scientometrics

Polyanin A. D. (Bauman Moscow State Technical University/Ishlinsky Institute for Problems in Mechanics)


doi: 10.18698/2309-3684-2014-1-131144


The paper deals with the citation index and h-index, which are the main scientometric indices, currently used for evaluating the performance of scientists and university professors. The author indicates their main disadvantages and considers a number of illustra-tive examples. The study shows that the normalized citation index (taking into account the presence of co-authors) has a number of important advantages in comparison with other scientometric indices. The author proposes new indices — the maximum citation indices, which can be easily calculated, have a simple and clear interpretation and have a number of distinct advantages in comparison with the h-index.


Polyanin A. Disadvantages of citation index and Hirsch and using other scientometrics. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 131-144



517.9+532+536 Nonlinear delay reaction-diffusion equations of hyperbolic type: Exact solutions and global instability

Polyanin A. D. (Bauman Moscow State Technical University/Ishlinsky Institute for Problems in Mechanics), Sorokin V. G. (Bauman Moscow State Technical University), Vyazmin A. V. (Moscow State University of Mechanical Engineering)


doi: 10.18698/2309-3684-2014-4-5373


In the article we explored nonlinear hyperbolic delay reaction-diffusion equations with varying transfer coefficients. A number of generalized separable solutions were obtained. Most of the equations considered contain arbitrary functions. Global nonlinear instability conditions of solutions of hyperbolic delay reaction-diffusion systems were determined. The generalized Stokes problem for a linear delay diffusion equation with periodic boundary conditions was solved.


Polyanin A., Sorokin V., Vyazmin A. Nonlinear delay reaction-diffusion equations of hyperbolic type: Exact solutions and global instability. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 53-73



517.9:532:536 Nonlinear delay reaction-diffusion equations with varying transfer coefficients: generalized and functional separable solutions

Polyanin A. D. (Bauman Moscow State Technical University/Ishlinsky Institute for Problems in Mechanics), Zhurov A. I. (Cardiff University/Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences)


doi: 10.18698/2309-3684-2015-4-337


We present a number of new simple separable, generalized separable, and functional separable solutions to one-dimensional nonlinear delay reaction-diffusion equations with varying transfer coefficients of the formut = [G(u)ux ]x  F(u,w),where w = u(x,t) and w = u(x,t  ), with  denoting the delay time. All of the equations considered contain one, two, or three arbitrary functions of a single argument. The generalized separable solutions are sought in the form =1 = () () N
n n n u   x  t , withn (x) and n (t) to be determined in the analysis using a new modification of the functional constraints method. Some of the results are extended to nonlinear delay reaction-diffusion equations with time-varying delay  = (t). We also present exact solutions to more complex, three-dimensional delay reactiondiffusion equations of the formut = div[G(u)u] F(u,w).Most of the solutions obtained involve free parameters, so they may be suitable for solving certain problems as well as testing approximate analytical and numerical methods for non-linear delay PDEs.


Polyanin A., Zhurov A. Nonlinear delay reaction-diffusion equations with varying transfer coefficients: generalized and functional separable solutions. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 3-37