Ural Mathematical Journal (UMJ)
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GROWTH OF –ORDER SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS ON THE COMPLEX PLANE
No full textIn this paper, we study the growth of solutions of higher order linear differential equations with meromorphic coefficients of -order on the complex plane. By considering the concepts of -order and -type, we will extend and improve many previous results due to Chyzhykov–Semochko, Belaïdi, Cao–Xu–Chen, Kinnunen
GENERALIZED ORDER ORIENTED SOME GROWTH PROPERTIES OF COMPOSITE ENTIRE FUNCTIONS
No full textIn this paper we establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized order and generalized lower order where and are continuous non-negative functions on
ON NECESSARY OPTIMALITY CONDITIONS FOR RAMSEY-TYPE PROBLEMS
Get PDFWe study an optimal control problem in infinite time, where the integrand does not depend explicitly on the state variable. A special case of such problem is the Ramsey optimal capital accumulation in centralized economy. To complete the optimality conditions of Pontryagin's maximum principle, so called transversality conditions of different types are used in the literature. Here, instead of a transversality condition, an additional maximum condition is considered
IDENTITIES IN BRANDT SEMIGROUPS, REVISITED
Get PDFWe present a new proof for the main claim made in the author's paper "On the identity bases of Brandt semigroups" (Ural. Gos. Univ. Mat. Zap., 14, no.1 (1985), 38–42); this claim provides an identity basis for an arbitrary Brandt semigroup over a group of finite exponent. We also show how to fill a gap in the original proof of the claim in loc. cit
REGULAR GLOBAL ATTRACTORS FOR WAVE EQUATIONS WITH DEGENERATE MEMORY
Get PDFWe consider the wave equation with degenerate viscoelastic dissipation recently examined in Cavalcanti, Fatori, and Ma, Attractors for wave equations with degenerate memory, J. Differential Equations (2016). Under certain extra assumptions (namely on the nonlinear term), we show the existence of a compact attracting set which provides further regularity for the global attractor and show that it consists of regular solutions
IMPULSE CONTROL OF THE MANIPULATION ROBOT
Get PDFA nonlinear control problem for a manipulation robot is considered. The solvability conditions for the problem are obtained in the class of special impulse controls. To achieve the control goal, the kinetic energy of the manipulation robot is used. When finding analytical formulas for controls, the classical first integrals of Lagrangian mechanics were used. The effectiveness of the proposed algorithm is illustrated by computer simulation
JACOBI TRANSFORM OF -JACOBI–LIPSCHITZ FUNCTIONS IN THE SPACE
No full textUsing a generalized translation operator, we obtain an analog of Younis' theorem [Theorem 5.2, Younis M.S. Fourier transforms of Dini–Lipschitz functions, Int. J. Math. Math. Sci., 1986] for the Jacobi transform for functions from the -Jacobi–Lipschitz class in the space
ORDER OF THE RUNGE-KUTTA METHOD AND EVOLUTION OF THE STABILITY REGION
Get PDFIn this article, we demonstrate through specific examples that the evolution of the size of the absolute stability regions of Runge–Kutta methods for ordinary differential equation does not depend on the order of methods
Amendment to my article "HARMONIC INTERPOLATING WAVELETS IN NEUMANN BOUNDARY VALUE PROBLEM IN A CIRCLE"
Get PDFIn the article indicated, the following omission need to be amended. Namely, on the first page, a footnote to the article title with reference to grant "This work was supported by Russian Science Foundation (project no.14-11-00702)" should be added
ASYMPTOTIC SOLUTIONS OF A PARABOLIC EQUATION NEAR SINGULAR POINTS OF AND TYPES
Get PDFThe Cauchy problem for a quasi-linear parabolic equation with a small parameter multiplying a higher derivative is considered in two cases when the solution of the limit problem has a point of gradient catastrophe. Asymptotic solutions are found by using the Cole–Hopf transform. The integrals determining the asymptotic solutions correspond to the Lagrange singularities of type and the boundary singularities of type . The behavior of the asymptotic solutions is described in terms of the weighted Sobolev spaces