相关论文: Differences and similarities between Shape Dynamic…
We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a…
The version of electrodynamics is constructed in which faster-than-light motions of fields and particles with real masses are possible. Transformational properties of 3-velocity, momentum, energy and electromagnetic field are presented in…
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
We demonstrate the use of similarity domains (SDs) for shape modeling and skeleton extraction. SDs are recently proposed and they can be utilized in a neural network framework to help us analyze shapes. SDs are modeled with radial basis…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
The analogy between vorticity and magnetic fields has been a subject of interest to researchers for a considerable period of time, mainly because of the structural similarities between the systems of equations that govern the evolution of…
Position representation is crucial for building position-aware representations in Transformers. Existing position representations suffer from a lack of generalization to test data with unseen lengths or high computational cost. We…
Recent advancements in deep learning have been primarily driven by the use of large models trained on increasingly vast datasets. While neural scaling laws have emerged to predict network performance given a specific level of computational…
To establish a relation between two approaches to the construction of Riemann k-wave solutions of hydrodynamic-type systems, namely the symmetry reduction method and the generalized method of characteristics.
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
We propose a generalization of spin algebra using multi-index objects, and a dynamical system analogous to matrix theory. The system has a solution described by generalized spin representation matrices and possesses a symmetry similar to…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
This preprint deals with the symmetry of parametrized families of systems and the changes therein as the parameter changes. There are (at least ?) two kinds of symmetry: generic and specific which behave in almost totally opposite ways as…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
We compare the nature of electromagnetic fields and of gravitational fields in linearized general relativity. We carry out this comparison both mathematically and visually. In particular the "lines of force" visualizations of…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a…
A brief survey of the author's works on the quantum theory of magnetism. Theoretical foundation and applications of the generalized spin-fermion (sp-d) exchange lattice model to various magnetic systems, e.g., rare-earth metals and…
In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…