On right S-Noetherian rings and S-Noetherian modules

In this paper we study right S-Noetherian rings and modules, extending notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings. Two characterizations of right S-Noetherian rings are given in terms of completely prime right ideals and point annihilator sets. We also prove an existence result for completely prime point annihilators of certain S-Noetherian modules with the following consequence in commutative algebra: If a module M over a commutative ring is S-Noetherian with respect to a multiplicative set S that contains no zero-divisors for M, then M has an associated prime.     

Recollements and homological dimensions

We investigate the behavior of the homological dimensions under recollements of derived categories of algebras. In particular, we establish a series of new bounds among the self-injective dimensions or ?-dimensions of the algebras linked by recollements of derived module categories.     

Applications of fractional complex transform and $\left( \frac{G^{\prime }}{G}\right) $-expansion method for time-fractional differential equations

In this paper, the fractional complex transform and the $\left( \frac{G^{\prime }}{G}\right) $-expansion method are employed to solve the time-fractional modfied Korteweg-de Vries equation (fmKdV),Sharma-Tasso-Olver, Fitzhugh-Nagumo equations, where $G$ satisfies a second order linear ordinary differential equation. Exact solutions are expressed in terms of hyperbolic, trigonometric and rational functions. These solutions may be useful and desirable to explain some nonlinear physical phenomena in genuinely nonlinear fractional calculus.     

More results on Hermite-Hadamard type inequality through} $( \alpha ,m)$-preinvexity

We establish various inequalities for n-times differentiable mappings that are connected with illustrious Hermite-Hadamard integral inequality for mapping whose absolute values of derivatives are $\left( {\alpha ,m} \right)$-preinvex function. The new integral inequalities are then applied to some special means     

An Extended Dienylium Terminus to Nucleophilic Addition with Tricarbonyl [3-(1-5-η-4-Isopropoxycyclohexa-2, 4-Dienyl) Ethyl Acetate] Iron Hexafluorophosphate

A study of the regioselectivity in nucleophilic addition to tricarbonyl (dienylium) iron complexes having an acetoxyethyl group (or methoxyethyl group) is reported. Reaction of the acetoxyethyl dienylium complex with the potassium salt of methyl 2-oxocylopentanecarboxylate was found to give a new product and a mechanism is proposed. The regioselectivity to nucleophilic addition was shown to be dependent on the use of an alcohol protecting group as in tricarbonyl (dienylium) iron complexes (5) and (15).     

基于多方参与的“碳核查”业务权利寻租行为监管及控制研究

针对“碳核查”业务权利寻租问题,考虑政府、控排企业及第三方核查企业对其治理的影响,运用演化博弈理论分析各参与主体在“碳核查”业务权利寻租问题治理过程中的决策行为。研究结果表明:碳核查”业务权利寻租行为的发生受各主体不同决策行为的共同作用,如何约束控排企业的行为是解决“碳核查”业务权利寻租问题的关键;中低强度的复查抽检率无法有效约束控排企业的寻租行为,而高复查抽检率则可有效约束控排企业的寻租行为;因寻租成本不同,控排企业及第三方核查企业对政府惩罚力度的敏感性不同;中高强度的复查率及惩罚力度,有助于降低控排企业及第三方核查企业权力寻租行为的发生。     

McCoy环的扩张(英文)

A ring R is said to be right McCoy if the equation f(x)g(x)=0,where f(x)and g(x)are nonzero polynomials of R[x],implies that there exists nonzero s∈R such that f(x)s=0.It is proven that no proper(triangular)matrix ring is one-sided McCoy.It is shown that for many polynomial extensions,a ring R is right McCoy if and only if the polynomial extension over R is right McCoy.     

The minimal polynomial of a matrix

Let Rbe a finite dimensional central simple algebra over a field FA be any n× n matrix over R. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomial q_A(λ) of A over F. By using q_A(λ), this paper discusses the structure of right (left) eigenvalues set of A, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix.     

Nests with the partial factorization property

It is proved that a nest on a separable complex Hilbert space has the left (resp. right) partial factorization property, which means that for every invertible operator from onto a Hilbert space there exists an isometry (resp. a coisometry) from into such that both and are in the associated nest algebra if and only if it is atomic (resp. countable).

     

弱交换富足序半群(Ⅰ)

本文将序半群上的 Ｇｒｅｅｎ’ｓ－关系推广为 Ｇｒｅｅｎ’ｓ＊一关系．给出主序（左、右）＊－理想、主序＊－滤特征描述和弱交换富足序半群的特征．用这些特征证明了一类弱交换富足序半群的结构定理：若序半群Ｓ满足 ,则Ｓ是弱交换富足序半群当且仅当Ｓ是左（右）单序半群｛（ｅ）（Ｓ）｝的半格．