Search

Abstract: We introduce the notion of a Schur-finite element in a λ-ring. [Copyright &y& Elsevier]

Sufficient conditions for the discreteness of the spectrum of a polar differential operation in the space of vector functions are obtained. [ABSTRACT FROM AUTHOR]

Abstract: Let be a closed and smooth manifold with an involution having fixed point set of the form , where and are submanifolds with dimensions n and 2, respectively, and where and does not bound. The main result of this paper is to establish the upper bound for m, for each n. The existence of these bounds is guaranteed by the famous -theorem of J. Boardman, which establishes that, under the above hypotheses, . [Copyright &y& Elsevier]

Abstract: We offer a new perspective on the splitting principle. We give an easy proof that applies to all classical types of vector bundles and in fact to G-bundles for any compact connected Lie group G. The perspective gives precise calculational information and directly ties the splitting principle to the specification of characteristic classes in terms of classifying spaces. [Copyright &y& Elsevier]

The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematics and mathematical physics, based on a special transformation with an integral term and the generalized splitting principle. The effectiveness of this approach is illustrated by nonlinear diffusion-type equations that contain reaction and convective terms with variable coefficients. The focus is on equations of a fairly general form that depend on one, two or three arbitrary functions (such nonlinear PDEs are most difficult to analyze and find exact solutions). A lot of new functional separable solutions and generalized traveling wave solutions are described (more than 30 exact solutions have been presented in total). It is shown that the method of functional separation of variables can, in certain cases, be more effective than (i) the nonclassical method of symmetry reductions based on an invariant surface condition, and (ii) the method of differential constraints based on a single differential constraint. The exact solutions obtained can be used to test various numerical and approximate analytical methods of mathematical physics and mechanics. [ABSTRACT FROM AUTHOR]