Related papers: Generalized solutions of variational problems and …
In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of…
In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
The mean value inequality is characteristic for upper semicontinuous functions to be subharmonic. Quasinearly subharmonic functions generalize subharmonic functions. We find the necessary and sufficient conditions under which subsets of…
Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved…
Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms…
In standard construction of hyperrational numbers using an ultrapower we assume that the ultrafilter is selective. It makes possible to assign real value to any finite hyperrational number. So, we can consider hyperrational numbers with…
You can invent striking and challenging problems with unique solution by building some symmetry into functional equations. Some are suitable for high school; others could generate college-level projects involving computer algebra. The…
Determination of quasi-invariant generalized functions is important for a variety of problems in representation theory, notably character theory and restriction problems. In this note, we review some new and easy-to-use techniques to show…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. H\"{o}rmander). In the hyperfunction case our work can be summarized as follows. We construct a differential algebra that…
We introduce the notion of "functional extension" of a set X, by means of two natural algebraic properties of the operator * on unary functions. We study the connections with ultrapowers of structures with universe X, and we give a simple…
The Schrodinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
We obtain several Euler-Lagrange equations for variational functionals defined on a set of H\"older curves. The cases when the Lagrangian contains multiple scale derivatives, depends on a parameter, or contains higher-order scale…
The fundamental quasisymmetric functions in superspace are a generalization of the fundamental quasisymmetric functions involving anticommuting variables. We obtain the action of the product, coproduct, and antipode on the fundamental…