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Some Comparisons of Dirichlet, Neumann and Buckling Eigenvalues on Riemannian Manifolds
In this paper, we study some comparisons of Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds. By introducing a new parameter, we...
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The number of representations of arithmetic progressions by integral quadratic forms
Let f be a positive definite integral quadratic forms and let r ( n , f ) be the number of representations of an integer n by f . In this article, we...
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Infinite series on quadratic skew harmonic numbers
By combining hypergeometric series computations with partial fraction decompositions, we present full solutions to the evaluation problems about two...
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Necessary conditions for turnpike property for generalized linear–quadratic problems
In this paper, we develop several necessary conditions of turnpike property for generalized linear–quadratic (LQ) optimal control problem in...
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Dirichlet-Neumann and Neumann-Neumann Methods for Elliptic Control Problems
Consider the state y (x) governed by the elliptic partial differential equation (PDE).
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Some Quadratic Problems
The problem that Hypernumbermotivates the study of ‘hypernumbers’ in the next few essays comes from the prehistory of mathematics.
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Ideals in Quadratic Number Fields
This chapter presents the arithmetic of ideals and the class group of quadratic number fields; as an application, we solve equations of...
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Multiple Solutions for an Elliptic Equation from the Antarctic Circumpolar Current
In this paper, a mathematical model of the second order elliptic equation of the Antarctic Circumpolar Current with Dirichlet boundary is...
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On the Prescription of Boundary Conditions for Nonlocal Poisson’s and Peridynamics Models
We introduce a technique to automatically convert local boundary conditions into nonlocal volume constraints for nonlocal Poisson’s and peridynamic...
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Lagrange’s Theorem
The aim of this chapter is to study questions related to the periodicity of geometric and regular continued fractions. The main object here is to...
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Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does...
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On signatures of elliptic curves and modular forms
In [
4 ], the first and second authors studied the signatures of Dirichlet characters and elliptic curves. In this paper we improve their lower bound... -
On the Attainability of the Best Constant in Fractional Hardy-Sobolev Inequalities Involving the Spectral Dirichlet Laplacian
We prove the attainability of the best constant in the fractional Hardy-Sobolev inequality with a boundary singularity for the spectral Dirichlet...