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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Two families of $n$-rectangle nonconforming finite elements for sixth-order elliptic equations
六阶椭圆方程 矩形 有限元族
2023/4/13
We propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of ...
THE BASE CHANGE FUNDAMENTAL LEMMA FOR CENTRAL ELEMENTS IN PARAHORIC HECKE ALGEBRAS
PARAHORIC HECKE Algebra
2015/9/29
Let G be an unramified group over a p-adic field F, and let E/F be a finite
unramified extension field. Let θ denote a generator of Gal(E/F). This paper concerns the
ma...
SPLITTING FIELDS OF CHARACTERISTIC POLYNOMIALS OF RANDOM ELEMENTS IN ARITHMETIC GROUPS
SPLITTING FIELDS CHARACTERISTIC POLYNOMIALS RANDOM ELEMENTS ARITHMETIC GROUPS
2015/8/26
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the sp...
A g-element for a graded R-module is a one-form with properties similar to a Lefschetz class in the cohomology ring of a compact complex projective manifold, except that the induced multiplication map...
A sweeping preconditioner for time-harmonic Maxwell’s equations with finite elements
Maxwell’s equations Frequency domain Finite element methods Preconditioners Fast solvers Perfectly matched layers Block LDLt factorization High-frequency waves
2015/7/14
This paper is concerned with preconditioning the stiffness matrix resulting from finite element discretizations of Maxwell’s equations in the high frequency regime. The moving PML sweeping preconditio...
Elements of Polya-Schur theory in finite difference setting
Elements Polya-Schur theory finite difference setting Classical Analysis and ODEs
2012/4/16
In this note we attempt to develop an analog of P\'olya-Schur theory describing the class of univariate hyperbolicity preservers in the setting of linear finite difference operators. We study the clas...
Singular Casimir Elements of the Euler Equation and Equilibrium Points
Singular Casimir Elements Euler Equation Equilibrium Points Analysis of PDEs
2011/10/10
Abstract: The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal...
Singular Casimir Elements of the Euler Equation and Equilibrium Points
the Euler Equation Equilibrium Points Analysis of PDEs
2011/9/21
Abstract: The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal...
Formulae for the determination of the elements of the Eotvos matrix of the Earth's normal gravity field and a relation between normal and actual Gaussian curvature
Eotvos matrix normal gravity field equipotential surfaces Gauss curvature plumbline curvature
2011/9/1
Abstract: In this paper we form relations for the determination of the elements of the E\"otv\"os matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the ...
Abstract: Using the method of commutative algebra, we show that the set $\mathfrak{R}$ of nilpotent elements of a vertex algebra $V$ forms an ideal, and $V/\mathfrak{R}$ has no nonzero nilpotent eleme...
Arithmetical rank of squarefree monomial ideals generated by five elements or with arithmetic degree four
monomial ideal, arithmetical rank, projective dimension
2011/8/24
Abstract: Let $I$ be a squarefree monomial ideal of a polynomial ring $S$. In this paper, we prove that the arithmetical rank of $I$ is equal to the projective dimension of $S/I$ when one of the follo...
Rectangular Mixed Elements for Elasticity with Weakly Imposed symmetry Condition
Rectangular Mixed Elements Elasticity symmetry Condition
2011/1/19
We present new rectangular mixed nite elements for linear elasticity.The approach is based on a modi cation of the Hellinger-Reissner functional in which the symmetry of the stress eld is enforced w...
Two remarks on rectangular mixed finite elements for elasticity
Two remarks rectangular finite elements elasticity
2011/1/19
The lowest order nonconforming rectangular element in three dimen-sions involves 54 degrees of freedom for the stress and 12 degrees of freedom for the displacement.
Dual Raviart-Thomas mixed finite elements
finite volumes mixed finite elements Petrov-Galerkin variational formulation
2011/1/19
For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Ravia...
Irreducible characters taking root of unity values on p-singular elements
Irreducible characters unity values on p-singular elements
2011/1/20
In this paper we study finite p-solvable groups having irreducible com-plex characters χ ∈ Irr(G) which take roots of unity values on the p-singular elements of G.