相关论文: Potential theoretic approach to rendezvous numbers
Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
Potential theory on the complement of a subset of the real axis attracts a lot of attention both in function theory and applied sciences. The paper discusses one aspect of the theory - the logarithmic capacity of closed subsets of the real…
The collection $\mathcal{M}_n$ of all metric spaces on $n$ points whose diameter is at most $2$ can naturally be viewed as a compact convex subset of $\mathbb{R}^{\binom{n}{2}}$, known as the metric polytope. In this paper, we study the…
In this article we propose a general framework for normal approximation using Stein's method. We introduce the new concept of Stein couplings and we show that it lies at the heart of popular approaches such as the local approach,…
The work concentrates on relations, which are general and model independent in chaotic system, between time averages of a few (typically {\it very few}) observables. Equilibrium thermodynamics provides a guide and here is attempted to argue…
Richard Guy asked for the largest set of points which can be placed in the plane so that their pairwise distances are rational numbers. In this article, we consider such a set of rational points restricted to a given hyperbola. To be…
We review the basic concepts of magnetic reconnection and propose a general framework for the astrophysical reconnection at large scales. Magnetic reconnection is the rearrangement of magnetic field topology. The conventional Sweet-Parker…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
The study examines the relationship between Ball's magic numbers and reverses divisors. These numbers are the source of beautiful and curious properties. Activities related to numbers can be a fun way to motivate mathematics students, while…
This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length…
The purpose of this article is to discuss the circle method and its quantitative role in understanding pointwise almost everywhere convergence phenomena for polynomial ergodic averaging operators. Specifically, we will use the circle method…
Alexandrov's inequalities imply that for any convex body $A$, the sequence of intrinsic volumes $V_1(A),\ldots,V_n(A)$ is non-increasing (when suitably normalized). Milman's random version of Dvoretzky's theorem shows that a large initial…
It has been known for a long time that many simple liquids have surprisingly similar structure as quantified, e.g., by the radial distribution function. A much more recent realization is that the dynamics are also very similar for a number…
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on…
Natural numbers satisfying an unusual property are mentioned by the author in [5], in which their infinitude is also proved. In this paper, we start with an arbitrary natural number which is not a multiple of 10 and non-palindromic, form…