On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

On Non-Negative Elliptic-Type Differential Inequalities in ℝ n , Vanishing Almost Everywhere on Some Open Subset in ℝ n

It is proved in this article that any generalized solution of a sufficiently general class of elliptic-type differential inequalities in  ⁿ that is non-negative almost everywhere in  ⁿ and vanishes almost everywhere on an open set ⁿ is trivial in  ⁿ .     

On the Self-adjointness of the Product Operators of Two ruth-Order Differential Operators on [0, ＋∞）

In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, ∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.     

On the positive radial solutions of some semilinear elliptic equations on ℝ n

We study the existence and behavior of positive radial solutions of the equationu + f(u) = 0 in ⁿ . This equation arises in various problems in applied mathematics, e.g. in the study of phase transitions, nuclear cores and more recently in population genetics and solitary waves. The important model casef(u) = – u + u ^p, p>1, describes for instance the pressure distribution in a van der Waals fluid. In this case, we obtain fairly complete knowledge of all positive radial solutions.Supported in part by an NSF grant and a research grant from the Graduate School of the University of Minnesota.     

On the relationship between differentiability and absolute continuity of measures on ℝn

Summary We give an elementary proof of the fact that a finite Borel measure on ⁿ is absolutely continuous with a C ¹ density if and only if it has directional derivatives which are continuous almost everywhere. The Radon-Nikodym derivative of a differentiable measure is given in terms of the directional derivatives.     

The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions

In this paper, the space-time Riesz fractional partial differential equations with periodic conditions are considered. The equations are obtained from the integral partial differential equation by replacing the time derivative with a Caputo fractional derivative and the space derivative with Riesz potential. The fundamental solutions of the space Riesz fractional partial differential equation (SRFPDE) and the space-time Riesz fractional partial differential equation (STRFPDE) are discussed, respectively. Using methods of Fourier series expansion and Laplace transform, we derive the explicit expressions of the fundamental solutions for the SRFPDE and the STRFPDE, respectively.     

On the reduction (mod 1) of completely monotone functions (0, ∞)

Summary The Euler-Maclaurin summation formula and its harmonic analysis (Poisson) are applied to the case of functions which are completely monotone on an open half-line. What thus results is a curious class of Fourier series, which can be determined explicitly and which represent completely monotone functions on the first half of the period. A by-product is the complete monotony (on the first half-period) of the Bernoulli functions, whether the index is integral or fractional.     

On a class of totally topologically transitive skew products defined on cells in ℝ n,n ≥ 2

Mathematical Notes - We obtain sufficient conditions for total topological transitivity (transitivity of all iterations) for a class of C 3 skew products defined on cells in ? n , n ≥ 2.     

Additional Note on Partial Regularity of Weak Solutions of the Navier-Stokes Equations in the Class L ∞(0, T, L 3(Ω)3)

We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution u belongs to L (0, T, L ³()³), then the set of all possible singular points of u in is at most finite at every time t₀ (0,T).     

Solvability in the large on (0, ∞) of the fundamental initial-boundary value problem for the two-dimensional equations of the motion of Oldroyd fluids

The unqiue global solvability for t (0, ) is proved for the system describing the two-dimensional motion of an Oldroyd fluid.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 69–72, 1986.     

Towards a theory of global solvability on [0, ∞) of initial-boundary value problems for the equations of motion of oldroyd and Kelvin—Voight fluids

Classical global solvability on [0, ) is proved for initial-boundary value problems (30), (32), (33), and (31), (32), (33) which describe two-dimensional motion of Oldroyd fluids and three-dimensional motion of Kelvin—Voight fluids of orders L = 2, 3, .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 121–141, 1990.     

On the Periodic Structure of Delayed Difference Equations of the Form x n = f ( x n − k ) on I and S 1

The aim of this paper is to give an account of some results recently obtained in Combinatorial Dynamics and apply them to get for k S 2 the periodic structure of delayed difference equations of the form x n = f ( x n m k ) on I and S 1 .     

The (n + 1)2 m -ray algorithm: a new simplicial algorithm for the variational inequality problem on ℝ + m ×S n

In this paper we propose a variable dimension simplicial algorithm for solving the variational inequality problem on the cross product of the nonnegative orthant ₊ ^m of them-dimensional Euclidean space ^m and then-dimensional unit simplexS ⁿ of ⁿ⁺¹. Starting from an arbitrary point (u, v) є ₊ ^m ×S ⁿ, the algorithm generates a piecewise linear path in ₊ ^m ×S ⁿ. The path is traced by making alternately linear programming pivot operations and replacement steps in an appropriate simplicial subdivision of ₊ ^m ×S ⁿ. The algorithm differs from the thus far known algorithm in the number of directions in which it may leave the starting point. More precisely, the algorithm has (n+1)2 ^m rays to leave the starting point whereas the existing algorithm hasn+m+1 rays. A convergence condition is presented and the accuracy estimation of an approximate solution generated is also given.     

On the intrinsic normalizations of the seminonholonomic complexesSN Gr(m, n, (m+1)(n−m)−ϱ). I

Some intrinsic normalizations of seminonholonomic complexes of then-dimensional projective space are considered. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 517–538, October–December, 1999. Translated by R. Lapinskas