相关论文: Dimensional Analysis and Physical Laws

This review aims to provide a very short and pedestrian introduction to some of the basics of extra-dimensional physics. The hope is to facilitate access and to be, in some respects, complementary to the many already existing reviews on…

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…

A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…

We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…

A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…

In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…

Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…

The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…

Properties and examples of the dual transformation between two planes, which is such that the coordinates of a point in the original plane give the coefficients of a line in the dual plane and the coefficients of a line in the original…

A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…

The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…

In a world increasingly awash with data, the need to extract meaningful insights from data has never been more crucial. Functional Data Analysis (FDA) goes beyond traditional data points, treating data as dynamic, continuous functions,…

Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…

Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…

The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…

This article is based on papers discussing different aspects of extra dimensional environments. In addition to the results, we review some of the concepts on which models with large extra dimensions are based.