亚BCI-代数的$(\alpha,\beta)$-软理想

首先将软集的参数集赋予亚BCI-代数, 给出了亚BCI-代数的$(\alpha,\beta)$-软理想的概念.当$U=[0,1], \alpha=U, \beta=\phi$时,相应地就得到了亚BCI-代数的犹豫模糊理想的概念.研究了亚BCI-代数的$(\alpha,\beta)$-软理想的一些重要性质.最后讨论了亚BCI-代数的$(\alpha,\beta)$-软理想的同态像和原像的性质.     

具有可反测地线的$(\alpha,\beta)$-度量

本文我们得到了$(\alpha,\beta)$-度量的测地系数$G^{i}(x,y)$和其逆$G^{i}(x,-y)$有相同Douglas曲率的充分必要条件.这个充分必要条件恰好是$(\alpha,\beta)$-度量具有可反测地线的充分必要条件.     

关于空间$S(\Omega,\Sigma,\mu)$与$L^\beta(\Omega,\Sigma,\mu)$上的次加上半连续$\alpha$-正齐性泛函

本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了S（Ω，∑，μ）与L^β（Ω，∑，μ）分别不存在非零的上半连续、次加、α-正齐性泛函（分别有0≤α≤1和β〈α≤1）的充要条件．     

具$w_0$-距离度量空间中$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的最佳逼近点定理

本文提出了一类称为$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的新的非自映射,并引进了关于$\eta$的$\alpha$-逼近可容许映射和关于$\eta$的$(\alpha,d)$正则映射的概念.基于这些新概念,在$w_0$-距离度量空间中研究了此类新压缩最佳逼近点的存在唯一性,并给出了一个新的定理,推广和补充了文[Ayari, M. I. et al. Fixed Point Theory Appl., 2017, 2017: 16]和[Ayari, M. I. et al. Fixed Point Theory Appl., 2019, 2019: 7]中的结果.给出了一个例子来说明主要结果的有效性.进一步地,作为推论得到关于两个映射的最佳逼近点和公共不动点定理.作为其中一个推论的应用,讨论了一类Volterra型积分方程组的求解问题.     

Higher-Order $(F,\alpha, \beta, \rho, d, E) $-Convexity in Fractional Programming

In this paper we define higher order $(F,\alpha, \beta, \rho,d, E)$-convex function with respect to $E$-differentiable function $K$ and obtain optimality conditions for nonlinear programming problem (NP) from the concept of higher order $(F,\alpha, \beta, \rho,d)$-convexity. Here, we establish Mond-Weir and Wolfe duality for (NP) and utilize these duality in nonlinear fractional programming problem.     

广义(ω)性质及亚循环算子

研究了Weyl定理的一种变化形式:广义$(\omega)$性质; 给出了广义$(\omega)$性质成立的充要条件.同时, 广义$(\omega)$性质及算子的亚(超)循环性之间的关系得到了研究.     

一类$L^2(\mathbb{R}^n)$的紧支撑不可分正交小波

本篇文章给出一类$L^{2}(\mathbb{R}^{n})$, $n\geq2$的紧支撑不可分正交小波基的具体构造算法,其中正交小波的伸缩矩阵为$\alpha I_{n}~(\alpha\geq2,\ \alpha \in \mathbb{Z})$, $I_{n}$是$n$阶单位矩阵.最后给出两个不可分正交小波基的构造算例.     

一类具间断系数退化椭圆型方程的$L^{p,\lambda}$正则性

得到一类退化椭圆型方程弱解梯度在其拟线性系数矩阵$A(\cdot,u)$对任意$u$关于$x$一致满足VMO条件下在Morrey空间$L^{p,\lambda}$的内部正则性.     

与强奇异 Calder\''{o}n-Zygmund算子相关的Toeplitz算子的双权估计

研究了与强奇异Calder\'{o}n-Zygmund算子和加权 Lipschitz函数${\rm Lip}_{\beta_0,\omega}$相关的Toeplitz算子$T_b$的sharp极大函数的点态估计,并证明了Toeplitz算子是从 $L^p(\omega)$到$L^q(\omega^{1-q})$上的有界算子.此外, 建立了与强奇异Calder\'{o}n-Zygmund算子和加权 BMO函数${\rm BMO}_{\omega}$相关的Toeplitz算子$T_b$的sharp极大函数的点态估计,并证明了Toeplitz算子是从 $L^p(\mu)$到$L^q(\nu)$上的有界算子.上述结果包含了相应交换子的有界性.     

强正则图的一些性质

文[3]给出了强正则图的概念及有关性质,本文在此基地上利用图的谱性质,得到了强正则图的又一些性质。     

关于一类弱-Berwald的$(\alpha,\beta)$-度量

In this paper, we study an important class of （α,β）-metrics in the form F = （α＋β）^m＋1/α^m on an n-dimensional manifold and get the conditions for such metrics to be weakly- Berwald metrics, where α = √aij（x）y^iy^j is a Riemannian metric and β = bi（x）y^i is a 1-form and m is a real number with m ≠ -1,0,-1/n. Furthermore, we also prove that this kind of （α,β）-metrics is of isotropic mean Berwald curvature if and only if it is of isotropic S-curvature. In this case, S-curvature vanishes and the metric is weakly-Berwald metric.     

关于超代数$(\alpha,\beta,\gamma)$-超导子的一个注记

This paper is concerned with two results for （α, β, γ）-superderivations of general superalgebras over the field of complex numbers.     

The stability of additive $(\alpha,\beta)$-functional equations

In this paper, we investigate the following $(\alpha,\beta)$-functional equations $$ 2f(x)+2f(z)=f(x-y)+\alpha^{-1}f(\alpha (x+z))+\beta^{-1}f(\beta(y+z)),~~~~~~~~~(0.1) $$ $$ 2f(x)+2f(y)=f(x+y)+\alpha^{-1}f(\alpha(x+z)) +\beta^{-1}f(\beta(y-z)),~~~~~~~~~~~(0.2) $$ where $\alpha,\beta$ are fixed nonzero real numbers with $\alpha^{-1}+\beta^{-1}\neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the $(\alpha,\beta)$-functional equations $(0.1)$ and $(0.2)$ in non-Archimedean Banach spaces.     

一类新的具有标量旗曲率Finsler度量

In this paper,we study a new class of general(α,β)-metrics F defined by a Riemannian metric α,a 1-form β and C ∞ function φ(b2,s).We provide the projective factor of a class of general(α,β)-metrics F=αφ(b2,s),and apply these formulae to compute its flag curvature.     

理想上的广义$(\theta,\phi)$-导子的正交性

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized （θ,φ）-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

$2$-Primal环的Ore扩张中的极小素理想和单位元

Let R be an(α,δ)-compatible ring.It is proved that R is a 2-primal ring if and only if for every minimal prime ideal P in R[x;α,δ] there exists a minimal prime ideal P in R such that P = P [x;α,δ],and that f(x) ∈ R[x;α,δ] is a unit if and only if its constant term is a unit and other coefficients are nilpotent.