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Apr 24, 2025Open Access
In this paper, a new concept is proposed: semi-primitive root. The basic theory system of semi-primal roots is established, and the congruence equations and propositions of indefinite equations are solved by the theory of semi-primal roots. The security problem of using the same value to digitally sign multiple different information in discrete logarithm encryption is solved.
Apr 09, 2025Open Access
This paper is devoted to the normalized solutions of a planer L2-critical Schrödinger-Poisson system with an external potential V(x) =❘X❘ 2 and in-homogeneous attractive interactions K(x)∈(0,1). Applying the constraint variational method, we prove that the normalized solutions exist if and only if the interaction strength a satisfies a∈(0,a *):=∥Q∥ 2L2...
Feb 18, 2025Open Access
Many kinds of explicit and exact solutions of the nonlinear Newell equation, including the solitary wave solution, the singular traveling wave solution, and the triangle function-type periodic wave solutions, are presented by a direct trial function approach.
Dec 18, 2024Open Access
In this paper, three examples of non-Hermitian Hamiltonians were presented on which an approach was applied based on the Heisenberg equation of motion, namely a first-order equation in the coordinate and momentum.
Dec 16, 2024Open Access
The knowledge system of high school mathematics is extensive, logically rigorous, highly abstract, and challenging. Reasoning-based teaching is the primary method, with blackboard teaching and PPT teaching being common instructional tools. This study, based on cognitive load theory, explores the effectiveness of these two teaching methods in high school mathematics classrooms. First, it explains the concept of cognitive load, including intrinsic, extraneous, and germane cognitive load. Then, it ...
Oct 28, 2024Open Access
Soon, the edition will have the challenge of publishing the prompts of the authors. The theorem of Thales and the theorem of Pythagoras do not escape the rule, and they seem to have been preceded by several millennia. Asking the true paternity of those geometrical realities makes it possible to show that a * b = R2 according to the terms defined by the Theorem of the Circle or Theorem of Apollo stating the constant product of two segments of perpendicular tangents for a...
Oct 23, 2024Open Access
In this paper, we report the study of I-V characteristics for some metal work functions. The Schottky barrier structure is controlled by the metal work function using the MATLAB programming language. The study of the effect of metal work function proved its influence on device performance, and a significant dependence was observed between this parameter and the electrical parameters at room temperature. The temperature effect on the electrical characteristics of n-AlGaAs Schottky diodes has been...
Sep 30, 2024Open Access
West Lake is renowned worldwide for its picturesque scenery and profound cultural heritage. This paper uses two famous scenic spots, Leifeng Pagoda and Broken Bridge, as examples to explore the mathematical culture embedded in the landscapes of West Lake. We analyze not only the architectural structure and geometric aesthetics of Leifeng Pagoda and Broken Bridge but also employ mathematical knowledge to understand these structures. This includes using the theorem of similar triangles to measure ...
Sep 24, 2024Open Access
In mathematics, the Fekete-Szeg？ inequality is an inequality for the coefficients of univalent analytic functions found by Fekete and Szeg？ (1933), related to the Bieberbach conjecture. Finding similar estimates for other classes of functions is called the Fekete-Szeg？ problem. In this paper, I study to solve the Fekete-Szeg？ problem for #9474;a 3 - μa 22│ -functional inequalities with μ is real or complex by the generalized linear differential operator. That...
Sep 06, 2024Open Access
In this paper, we use partial differential equations to deal with constraint optimal control problems. We construct extremal flows by differential-algebraic equation to approximate the optimal objective value of constraint optimal control problems. We prove a convergent theorem for an approximation approach to the optimal objective value of a state-constraint optimal control problem.
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