In this paper, we study the boundedness of the G-fractional integral operators J(G)(alpha) on R+ = [0, infinity) in the generalized Morrey G-spaces M-p,M-nu,M-lambda(R+). We characterize the strong and weak types of boundedness of J(G)(alpha) on the generalized G-Morrey spaces, respectively.
Recent developments in the theory of dynamical systems and their attractors for the Caputo fractional differential equations are reviewed.
Lyapunov functions characterize the stability of attractors in dynamical systems. Their analytical construction for general systems, however, remains a formidable task. Therefore, numerous numerical methods for their computation have been developed. We give a short overview of the theory of Lyapunov functions and discuss how they can be parameterized using linear programming in the so-called CPA method. We discuss a few of the many extensions of the CPA method, in particular to differential inclusions, and we discuss how the linear programming problem generated in the CPA method can often be solved very efficiently. We give numerous concrete examples to illustrate the technique of the CPA method.
Topological insulators are materials whose electronic properties are governed by topological invariants rather than local geometric features. In this note, we review the mathematical foundations underlying topological insulators, emphasizing the connection with vector bundles and K-theory. We discuss how "real" and "quaternionic" vector bundles arise naturally in the presence of time-reversal symmetry, and summarize our recent results about the conditions under which stable isomorphism implies isomorphism for these bundles. Finally, we describe ongoing work concerning the G-equivariant K-theory for finite groups, highlighting new phenomena that occur in this context.
We study relatively compact sets in weighted Musielak-Orlicz sequence spaces. The characterization of such sets is given in the case of weighted Musielak-Orlicz sequence spaces. As an application, we establish a necessary and sufficient condition on weight functions for the compactness of a discrete Hardy operator on weighted Musielak-Orlicz sequence spaces. In particular, we get similar results for the dual operator of a discrete Hardy operator. The results are illustrated by a number of corollaries.
In this paper, we consider several classes of Brownian functionals, including non-smooth functionals (therefore, it is impossible to use the well-known Clark-Ocone formula), depending both on the trajectory and on the last moment of time. We also propose a new method for obtaining a constructive stochastic integral representation for smooth, as well as for non-smooth functionals.
Let {k is an element of Z(n): 1 <= Pi(n)(j=1) |k(j)|(gamma j) <= R gamma 1+& centerdot;& centerdot;& centerdot;+gamma n }, where gamma(1), . . . , gamma(n) > 0, be a "hyperbolic cross" dilated homothetically as R -> +infinity. In our study, their Lebesgue constants are, as expected, always of power growth R-p, p > 0, sometimes several times larger than a logarithmic factor. Surprisingly, contrary to the expected p = n-1/2 in any case, p may become, for an appropriate choice of gamma(1), . . . , gamma(n), arbitrarily larger than that fraction. In many cases, the estimates of the Lebesgue constants are exact in the sense that the upper and lower bounds differ from each other only by their coefficients.
In the present note, several results concerning the richness of intersections of Mazurkiewicz type sets in R-2 with various irreducible plane algebraic curves are discussed. Mazurkiewicz type sets are considered here with respect to the family of all straight lines in R-2 and also with respect to the family of all circles in R-2.
The vector spaces of generalized theta-series with spherical polynomials of order nu, corresponding to certain diagonal and non-diagonal quadratic forms in six variables, are considered. An upper bound on the dimension of these spaces is established.
Under certain conditions, it is shown that if a ground set E is equipped with an involution s and a measure & micro;, then there exists a partition of E into two s-congruent & micro;-nonmeasurable subsets. On the other hand, no such partition consists of sets that are absolutely nonmeasurable with respect to the class M-& micro;.
In this note, we present Rubio de Franc & imath;a's extrapolation results in one-sided setting, in grand Lebesgue, Lorentz and ball Banach function spaces. These results can be applied, for example, to obtain the boundedness for one-sided operators of Harmonic Analysis in these spaces.
In this paper, we introduce some new weighted maximal Fejer mean operators of the Walsh-Fourier series. We prove that for some "optimal" weights, (H-p-L-p) type inequalities hold for these operators when 0 < p < 1/2. We also prove the sharpness of this result. As a consequence, we obtain some new and well-known results.
The multidimensional characteristic problem in the conical domain for a class of high-order nonlinear equations of composite type is considered. The theorems on the existence, uniqueness and nonexistence of solutions of this problem are proved.
Let X be a Banach function space over a locally compact abelian group admitting a family of coverings. We show that if the Hardy-Littlewood maximal operator M is bounded on the space X, then its boundedness on the associate space X ' is equivalent to a certain condition A(infinity).
In this paper, we focus on the introduction, study and characterization of functions defined on binary sets in binary topological spaces. As a part of our applications, we demonstrate how a binary soft set can be viewed as a special case of the functions defined here. Furthermore, we propose a method for improving decision-making. Additionally, we present an algorithm for identifying binary topologies.
This paper studies the dynamic problem of frictional contact between a perfectly locking thermo-visco elastic material and a heat conductive foundation. The contact is described by the normal compliance condition, and the friction is modeled by the nonlo cal Coulomb friction law. The mathematical model of the dynamic process is presented, and the variational formulation is derived. The existence and uniqueness of the weak solution are established. The continuous dependence of the solution on the friction coefficient, as well as on the initial displacement and temperature data, is studied. Finally, a fully discrete finite element scheme for the variational problem is proposed, and error estimates for the approximate solution are derived.
In this work, we introduce a new subclass of meromorphic bi-quasi-subordinate functions by utilizing the (p, q)-Jackson derivative, specifically defined in the exterior of the unit disc. We derive coefficient bounds for these functions and explore several special consequences of our findings. By providing some new results in this area, this work extends the understanding of meromorphic function classes and their behavior under generalized derivatives, offering new insights and potential applications in complex analysis.
The paper considers the theory of the surface of metric tangent fibers for the space T(V-n). Analogues of the Gauss-Weingarten derivation formulas, as well as analogues of the generalized Gauss, Peterson-Codazzi-Mainardi equations, are found.
In this paper, we study algorithmic problems in tensor completions G circle times N-2,N-R R of finitely generated torsion-free nilpotent groups G of class 2 in the quasivariety N-2,N-R of R-exponential 2-nilpotent groups over a computable field of characteristic zero with a computable additive basis. We show that the word problem, the conjugacy problem, and the power problem are decidable in G circle times N-2,N-R R. Note that these results do not hold for arbitrary finitely generated torsion-free 2-nilpotent R-groups. In fact, there are two generated torsion-free 2-nilpotent R-groups for which these problems are undecidable.
In this study, our main aim is to generalize the inverse Minkowski's type inequality with the help of a unified integral operator containing the Mittag-Leffler function in its kernel. Some related inequalities are also discussed. The established results are valid for various types of fractional integral operators derived from unified integral operators.
