无条件C的广义αη-单调性的判别标准

用α和η关于第一分量是仿射的且是斜对称的条件代替条件C,得到如下结论:(1)如果一个函数的梯度是(严格)αη-伪单调的,则该函数是(严格)伪αη-不变凸的;(2)如果一个函数的梯度是拟αη-单调的,则该函数是拟αη-不变凸的.     

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.     

代数$\Omega$-范畴的等价范畴

本文基于$\Omega$-范畴研究了(连续) $\mathcal{I}$-余万备$\Omega$-范畴的一些性质. 我们给出了双完备$\Omega$-范畴和逼近双模的概念并讨论了它们的性质, 证明了任何$\mathcal{I}$-余万备$\Omega$-范畴都是双完备$\Omega$-范畴. 得到了代数$\Omega$-范畴范畴等价于双完备$\Omega$-范畴.     

$\alpha$阶星象亚纯函数

令$S(p)$表示单位圆盘$\mathbb{D}$上在$p\in(0,1)$处有一个简单极点的单叶亚纯函数全体.令$\alpha\in[0,1)$,我们用$\Sigma^{*}(p,\omega_{0},\alpha)$表示$f\in S(p)$使得$\hat{\mathbb{C}}\setminus f(\mathbb{D})$是关于不动点$\omega_{0}\neq0$, $\infty$星象的$\alphga$阶区域的函数全体.在本文中,$f\in\Sigma^{*}(p,\omega_{0},\alpha)$的一些解析刻画条件和系数估计被考虑.     

$\beta$阶星象函数和凸象函数的几个充分条件的扩展

本文目的是研究了两个新算子$\mathcal{E}_{\alpha, \lambda}^{\gamma}$和$H_{m}^{l}(\alpha_1)$的星形和凸性的几个充分条件, 分别与定义在单位圆盘的广义Mittag-Leffler函数$E_{\alpha, \lambda}^{\gamma}$和广义超几何函数有关.本文得出的结果与早期的一些已知结果建立联系.     

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.     

相对平坦模的$\aleph$-积

设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中$0\leq A相似文献   

非广义$\mathcal {H}$-张量的判定准则[英文]

给出判定非广义$\mathcal {H}$-张量的充要条件, 从理论上彻底解决了不可约非广义$\mathcal {H}$-张量的判定问题, 并给出判定不可约非广义$\mathcal {H}$-张量的具体算法. 最后, 利用数值算例表明了结果的有效性.     

分裂的$\delta$-Jordan 李三系

本文研究了任意分裂的$\delta$-Jordan李三系的结构,其为分裂的李三系的结构的推广. 利用这种三系的根连通, 得到了带有对称根系的分裂的 $\delta$-Jordan 李三系可以表示成 $T=U+\sum_{[\alpha]\in \Lambda^{1}/\sim} I_{[\alpha]}$,其中$U$是0根空间$T_{0}$的子空间,任意$I_{[\alpha]}$为$T$的理想, 并且满足 当$[\alpha]\neq [\beta]$时, $\{I_{[\alpha]},T,I_{[\beta]}\}=\{I_{[\alpha]},I_{[\beta]},T\}=\{T,I_{[\alpha]},I_{[\beta]}\}=0$.     

$\mathbb{Z}^{k}$-作用一维子系统的Lipschitz跟踪性

本文主要研究了$\mathbb{Z}^{k}$-作用一维子系统的跟踪性质. 文中运用两种等价的方式引入了$\mathbb{Z}^{k}$-作用一维子系统的伪轨以及跟踪性的概念. 对于一个闭黎曼流形上的光滑$\mathbb{Z}^{k}$-作用$T$, 我们通过诱导的非自治动力系统提出了Anosov方向的概念. 借助Bowen几何的方法, 我们证明了$T$沿着任意Anosov方向具有Lipschitz跟踪性.     

广义 $d$-$\rho$-$(\eta,\theta)$-type I 一致凸非可微多目标规划

In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.     

强拟\alpha-预不变凸函数

研究了一类重要的广凸函数------强拟$\alpha$-预不变凸函数,讨论了它与拟\,$\alpha$-预不变凸函数、严格拟\,$\alpha$-预不变凸函数及半严格拟\,$\alpha$-预不变凸函数之间的关系,并在中间点的强拟\,$\alpha$-预不变凸性下得到了它的三个重要的性质定理,同时给出了强拟\,$\alpha$-预不变凸函 数在数学规划中的两个重要应用,这些结果在一定程度上完善了对强拟\,$\alpha$-预不变凸函数的研究.     

赋$\beta$-范空间中的最佳逼近问题

本文讨论赋$\beta$-范空间中的最佳逼近问题.以[1]引进的共轭锥为工具,借助[2]中关于$\beta$-次半范的Hahn-Banach延拓定理,第二节给出赋$\beta$-范空间的闭子空间中最佳逼近元的特征,第三节得到赋$\beta$-范空间中任何凸子集或子空间均为半Chebyshev集的充要条件是空间本身严格凸,文章最后证明了严格凸的赋$\beta$-范空间中任何有限维子空间都是Chebyshev集.     

Higher-Order (F,α,β,ρ,d,E)-Convexity in Fractional Programming

In this paper we define higher order (F,α,β,ρ,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,α,β,ρ,d)-convexity. Here, we establish Mond-Weir and Wolfe duality for (NP) and utilize these duality in nonlinear fractional programming problem.     

$\alpha$-可分解4-圈系统

An m-cycle system of order v and index λ, denoted by m-CS（v,λ）, is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS（v,λ） is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m｜λv（v-1）/2,2｜λ（v -1）,m｜αv,α｜λ（v-1）/2. It is shown in this paper that these conditions are also sufficient when m = 4.     

α-TRANSIENCE AND α-RECURRENCE FOR RANDOM WALKS AND LEVY PROCESSES

The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasi-symmetric if and only if X is not α-recurrent for all α< 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.     

两类具有标量旗曲率的弱Berwald度量

In this paper, we study the （α,β）-metrics of scalar flag curvature in the form of F = α ＋ εβ ＋ κβ^2/α （ε and k ≠ 0 are constants） and F = α^2/α-β. We prove that these two kinds of metrics are weak Berwaldian if and only if they are Berwaldian and their flag curvatures vanish. In this case, the metrics are locally Minkowskian.     

具有对称自同态的环及其扩张

Let R be a ring with an endomorphism α and an α-derivation δ. We introduce the notions of symmetric α-rings and weak symmetric α-rings which are generalizations of symmetric rings and weak symmetric rings, respectively, discuss the relations between symmetricα-rings and related rings and investigate their extensions. We prove that if R is a reduced ring and α(1) = 1, then R is a symmetric α-ring if and only if R[x]/(x n) is a symmetric ˉα-ring for any positive integer n. Moreover, it is proven that if R is a right Ore ring, α an automorphism of R and Q(R) the classical right quotient ring of R, then R is a symmetric α-ring if and only if Q(R) is a symmetric ˉα-ring. Among others we also show that if a ring R is weakly 2-primal and(α, δ)-compatible, then R is a weak symmetric α-ring if and only if the Ore extension R[x; α, δ] of R is a weak symmetric ˉα-ring.