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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville Properties on gradient shrinking Ricci solitons with constant scalar curvature
常标量 曲率梯度收缩 Ricci孤子 Liouville性质
2023/11/13
In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
SOME SPECTRAL PROPERTIES OF PSEUDO-DIFFERENTIAL OPERATORS ON THE SIERPINSKI GASKET
Analysis on fractals localized eigenfunctions Sierpiński gasket Szego limit theorem
2015/12/10
We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Ourresults used in a fundamental way the existence of loc...
On removability properties of $ψ$-uniform domains in Banach spaces
Uniform domain uniform domain removability property quasihyperbolic metric
2012/6/9
Suppose that $E$ and $E'$ denote real Banach spaces with the same dimension at least 2. The main aim of this paper is to show that a domain $D$ in $E$ is a $\psi$-uniform domain if and only if $D\back...
An expression for the Homflypt polynomial and some related properties
Homflypt polynomial Conway polynomial skein relation
2010/12/13
Associated with each oriented link is the two variable Homflypt polynomial. Formulas for the coefficient polynomials of the three lowest v-degrees are presented that shows they are determined by the w...
Amusing properties of Klein-Gordon solutions on manifolds with variable geometry
properties Klein-Gordon solutions on manifolds variable geometry
2010/12/16
This work develops the recent proposition to use dimensional reduction from the four-imensional space-time to the one with a smaller number of dimensions (1 + d); d < 3 at high enough energy.To this g...
Complements, Approximations, Smoothings and Invariance Properties
Nonsmooth analysis epi-Lipschitz complement approximations invariance differential inclusion smoothing proximal smoothness ]tangentiality feedback convolution Hamiltonian-Jacobi inequalities
2009/2/5
Proximal methods are used to determine the relationship between normal cones to a closed set in $\Re^n$ and those to the closure of its complement. The geometry of outer and inner set approximations i...
On some Properties of Paramonotone Operators
variational inequalities]monotone operators convex programming
2009/1/23
An operator $T\colon\mathbb{R}^n\to\mathbb{R}^n$ is paramonotone iff it is monotone and $\langle T(x)-T(y),x-y \rangle=0$ implies $T(x)=T(y)$. This definition can be extended to operators defined in a...
Some Geometric Properties in Orlicz Sequence Spaces equipped with Orlicz Norm
Orlicz sequence space rotundity local uniform rotundity compact local uniform rotundity property H smoothness copy of $l_\infty$
2009/1/20
It is proved that for any reflexive Banach space $X$, both $X$ and $X^{*}$ are CLUR if and only if both $X$ and $X^{*}$ have property H. Criteria for rotundity, local uniform rotundity, compact l...
Topological Properties of a New Graph Topology
Kuratowski convergence $\tau$-convergence Back's convergence
2009/1/19
In [10, 11, 12] a new graph topology $\tau$ was introduced which is useful in applications to differential equations. In this paper we study topological properties of $\tau$ and relations between $\ta...
Bounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties
conical hull intersection property Bounded Linear Regularity Distinct Properties
2009/1/16
Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed conve...
On the Algebraic Properties of Convex Bodies and Some Applications
(differences of) convex bodies Minkowski operations quasilinear spaces (differences of) support functions
2009/1/13
We extend the set of convex bodies up to differences (factorized pairs) of convex bodies; thereby (Minkowski) multiplication by real scalar is extended in a natural way. We show that differences of co...
Certain Properties of Generalized Orlicz Spaces
Banach Function spaces generalized Orlicz class generalized Orlicz space Luxemburg norm Young function Young's inequality imbedding convergence separability
2010/1/22
In the context of generalized Orlicz spaces , the concepts of inclusion, convergence and separability are studied.
A Remark on the Asymptotic Properties of Positive Homogeneous Maps on Homogeneous Lattices
Lyapunov Exponents asymptotic stability
2010/3/1
An abstract version of Lyapunov exponents is defined for positive homogeneous maps on Homogeneous Lattices and a sufficient condition is given for the asymptotic stability of the map.