Minimal Generating Sets for Relative Ideals in Numerical Semigroups of Multiplicity Eight

Abstract

Let S be a numerical semigroup and let I be a relative ideal of S. Let S ? I denote the dual of I and let μ _S (?) represent the size of a minimal generating set. We investigate the inequality μ _S (I)μ _S (S ? I) ≥ μ _S (I + (S ? I)) under the assumption that S has multiplicity 8. We will show that if I is non-principal, then the strict inequality μ _S (I)μ _S (S ? I) > μ _S (I + (S ? I)) always holds.     

A novel result on regularity of time-periodic Lagrangians

The regularity of the Peierls barrier $h_c^{\infty }$ for time-periodic Lagrangian systems is equivalent to the convergence of the associated Lax-Oleinik semigroup. In this paper, we established a novel result on the regularity, which has been applied to the convergence and nonconvergence of the Lax-Oleinik semigroup for time-periodic Lagrangians.     

半群P_n(k)的正则性和Green关系

设P_n是X_n={1,…,n}上的部分变换半群.对任意1≤k≤n,令P_n(k)={α∈P_n:(x∈dom(α)x≤k■xα≤k},则易验证P_n(k)是P_n的子半群.刻画了半群P_n(k)的正则元的特征,并且描述了这个半群上的Green关系.     

图上曲率维数不等式的若干等价性质

本文研究局部有限图上的曲率维数不等式CD(n,K)的若干等价性质,包括梯度估计、Poincaré不等式和逆Poincaré不等式.还得到了局部有限图上的修正曲率维数不等式CDE′(∞,K)的其中一个等价性质,即梯度估计.     

奇异变换半群Sing_n的非群平方幂等元秩

设Sing_n是[n]上的奇异变换半群.证明了半群Sing_n是由秩为n-1的非群平方幂等元生成的,且它的非群平方幂等元秩为(n(n-1))/2.     

Existence of anti-periodic mild solutions for semilinear evolution equations

In this paper we study the existence of anti-periodic mild solutions for a class of semilinear evolution equations in Banach spaces and extend some related results in this direction. An example is given to illustrate our results.     

一类变换半群的正则元和Green关系

设T_X为X上的全变换半群,E为X上的等价关系,令T_E(X)={f∈T_X:■(x,y)∈E,(f(x),f(y))∈E},则T_E(X)是T_X的子半群,如果X是一个全序集,E是X上的一个凸等价关系,设OP_E(X)为T_E(X)中所有保向映射作成的半群。对于有限全序集X上一类特殊的凸等价关系E,本文刻画了半群OP_E(X)的正则元的特征,并且描述了这个半群上的Green关系。     

具有Kelvin-Voigt阻尼的弱耦合系统的能量衰减估计

研究具有 Kelvin-Voigt 阻尼的弱耦合系统。首先在合适的假设条件下,应用线性算子半群理论证明了系统的适定性;进而运用线性算子半群的频域定理证明了具有Kelvin-Voigt阻尼的弱耦合梁―弦系统的能量是一致指数衰减的。