Mathematics, Volume 13, Issue 8

Deep neural networks (DNNs) have achieved high accuracy in various applications, but with the rapid growth of AI and the increasing scale and complexity of datasets, their computational cost and power consumption have become even more significant cha...

This paper presents a Finite Element Method (FEM) framework for solving the screened Poisson equation with a Dirac delta function as the forcing term. The singularity introduced by the delta function poses challenges for standard numerical methods, p...

The calibration of ultrasound probes is essential for three-dimensional ultrasound reconstruction and navigation. However, the existing calibration methods are often cumbersome and inadequate in accuracy. In this paper, a hybrid mathematical model, D...

The nonlinear deformation and vibrations of elastic plates represent a fundamental problem in structural vibration analysis, frequently encountered in engineering applications and classical mathematical studies. In the field of studying the nonlinear...

Bi-Frobenius algebras are a class of Frobenius algebras and Frobenius coalgebras with some compatible conditions. In this paper, we construct a class of bi-Frobenius algebras generated by n elements on graded algebra A. The comultiplication and couni...

In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a long-standing open problem from convex and discrete geometry, the construction of ε-nets for the space of convex bodies endowed with the Banach&ndash...

The increasing complexity of cloud service composition demands innovative approaches that can efficiently optimize both functional requirements and quality of service (QoS) parameters. While several methods exist, they struggle to simultaneously mini...

This article discusses the problem of numerically solving the Navier–Stokes equations, the heat conduction equation, and the transport equation in the orthogonal coordinates of a free curve. Since the numerical solution domain is complex, the c...

In this study, we propose a new nonlinear polarization model that modifies the polarization equation to account for the material’s nonlinear response. Specifically, the nonlinear restoring force in our model is reformulated as an electric field...

The computational prediction of RNA three-dimensional (3D) structures remains a significant challenge, largely due to the limited understanding of RNA folding pathways. Although the scarcity of resolved native RNA structures has hindered the effectiv...