Related papers: Uniqueness sequences for multidimensional vector-v…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
We completely describe the size and large intersection properties of the Holder singularity sets of Levy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a Levy process. The Holder…
In this paper we give sufficient conditions to ensure uniqueness of limit cycles for a class of planar vector fields. We also exhibit a class of examples with exactly one limit cycle.
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
Multivariate time series forecasting focuses on predicting future values based on historical context. State-of-the-art sequence-to-sequence models rely on neural attention between timesteps, which allows for temporal learning but fails to…
Torse-forming vector fields are generalizations of some important vector fields. In this paper, we present some techniques to transform a proper torse-forming vector field into its special cases. Concrete examples are given.
Two-way relationships between transformations and quadratic forms on Wiener spaces are investigated with the help of change of variables formulas on Wiener spaces. Further the evaluation of Laplace transforms of quadratic forms via Riccati…
The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of…
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
In this paper, we introduce a graph structure called linear dependence graph of a finite dimensional vector space over a finite field. Some basic properties of the graph like connectedness, completeness, planarity, clique number, chromatic…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
We first prove that the Legendre transform is the only continuous and $\mathrm{SL}(n)$ contravariant valuation that behaves as a conjugation of two important translations on super-coercive, lower semi-continuous, and convex functions. Then…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…