Transform-based tensor algebras induced by invertible linear transforms provide a unified framework for tensor operations and spectral analysis. This paper investigates how the choice of a unitary transform affects the quantitative tightness of class...
As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a symmetry group of transformations. A gauge theory is dealt...
This work presents a computational framework for the analysis and design of large-scale algorithms utilized in the estimation of acoustic, doubly-dispersive, randomly time-variant, underwater communication channels. Channel estimation results are use...
Induction machines (IMs) are critical components of many industrial processes, what justifies the use of condition-based maintenance (CBM) systems for detecting their faults at an early stage, in order to avoid costly breakdowns of production lines....
With an increase in tracking time, the operating cost of the controller will increase accordingly. Considering the biological applications of Boolean control networks (BCNs), it is necessary to study the control problem of BCNs over finite time. In t...
In this work, we introduce an efficient spectral Galerkin method for solving one-dimensional time-fractional reaction–subdiffusion equations. Traditional fractional operators often pose severe computational challenges and exhibit weak singulari...
This paper proposes a finite element approach to the numerical solution of boundary value problems of linear elasticity theory formulated directly in terms of the stress tensor components. In contrast to the classical finite element formulation, in w...
In this paper, Chebyshev polynomials—which are ultraspherical in the first and second kind and hence symmetric, while the third and fourth order are not ultraspherical and are hence non-symmetric—are used for the simulation of two-dimensi...
Large language models (LLMs) built upon the Transformer architecture have achieved remarkable performance in natural language understanding, text generation and logical reasoning, while their internal working mechanisms remain poorly interpreted. Thi...