Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

线性规划的对偶基线算法

In this paper,we studied the dual form of the basic line algorthm for linear programs.It can be easily implemented in tableau that similar to the primal/dual simplex method.Different from primal simplex method or dual simplex method,the dual basic line algorithm can keep primal feasibility and dual feasibility at the same time in a tableau,which makes it more efficient than the former ones.Principles and convergence of dual basic line algorthm were discussed.Some examplex and computational experience were given to illustrate the efficiency of our method.     

若干中点迭代法的收敛性

The King-Werner iteration xn 1= xn -F‘(1/2(xn yn))^-1 F(xn);yn 1=xn 1-F‘(1/2(xn yn))^-1F(xn 1) which is used for solving the operator eqution in Banach space F(x) = 0 requires the inverse of the opterator‘s derivative.Now in this paper a deformation King-Werner method without use of inverse is presented and the convergence of this method is proved with the skill of the majoring function. In addition, for the existed convergent theorem the convergent condtions are amended. The corresponding convergence theorem holds also with the amended conditions and its error bounds is obtained. At last a midpoint method of order 1 √2 : yn=xn-F‘(xn)^-1F(xn);xn 1=xn-F‘(xn yn/2)^-1F(xn) which is studied by D.Chen and I.K.Argros is convergent withby milder conditions by recurence relations.     

On Möbius form and Möbius isoparametric hypersurfaces

An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.     

主平移不变空间的特征

Shifts-invariant spaces in L1 (R) are investigated. First,based on a study of the system of linearly difference operators, the method of constructing generators with linearly independent shifts is provided. Then the characterizations of the closed shift-invariant subspaces in L1 (R) are given in terms of such generators and the local basis of shift-invariant subspaces.     

Ass（M／N） and Ann（M／N） on the Noetherian Module M

Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relationbetween associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary andsufficient conditions of Ass(M/N)=Ann(M/N).     

Trees, unicyclic graphs and bicyclic graphs with exactly two Q-main eigenvalues

The signless Laplacian matrix of a graph G is defined to be the sum of its adjacency matrix and degree diagonal matrix, and its eigenvalues are called Q-eigenvalues of G. A Q-eigenvalue of a graph G is called a Q-main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this work, all trees, unicyclic graphs and bicyclic graphs with exactly two Q-main eigenvalues are determined.     

三维De Sitter与Anti-de Sitter空间中的等参曲面

A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfaces in S13 and H13.     

On Two Conjectures Concerning the Veronese Generating submanifolds

The notion of finite type submanifolds was introduced by B.Y.Chen.In this paper the con-jectures on scalar curvature of Veronses generating submanifolds in E^6 and the minimal conjecture on Veronese space-like submanifold ∑ and Veronese pseudo-Riemannian submanifold-↑∑ in E1^6 are proved.We have ∑ is minimal in H^5.-↑∑ is minimal in S1^5,∑ and -↑∑ are of 1-type in E1^6.     

一类六角系统图的特征多项式及应用

Let Ln be the hexagonal chain graph,Fnbe the hexacyclic system graph and Mn be the M¨obius hexacyclic system graph. Derflinger and Sofer gave the spectra of Ln and Fn by using group theoretical method. Later, Gutman gave the spectra of them using a polynomial result due to Godsil and McKay. In this paper, we give a simple and direct method to determine the characteristic polynomial and spectra of Fn and Ln. By the method, we give the characteristic polynomial and spectrum of Mn that is new. Additionally, the exact values of total π-electron energy and the nullities of Ln, Fn and Mn are obtained, and the bounds for the energy of Ln and Mn are also considered.     

Annihilator Primes and Foundation Primes

ABSTRACT

Let R be a Noetherian ring and M a finitely generated R -module. In this article, we introduce the set of prime ideals Fnd  M , the foundation primes of M . Using the fact that this set is nicely organized by foundation levels, we present an approach to the problem of understanding Annspec  M , the annihilator primes of M , via Fnd  M . We show: (1) Fnd  M is a finite set containing Annspec  M . Further, suppose that moreover every ideal of R has a centralizing sequence of generators; now, Annspec  M is equal to the set Ass  M of associated primes of M. Then: (2) For an arbitrary P  ∈ Fnd  M , P  ∈ Annspec  M if and only if there is no Q  ∈ Annspec  M such that P contains Q , and at the same time, the minimal foundation level on which appears P is greater than the minimal foundation level on which appears Q .     

A search for Fibonacci-Wieferich and Wolstenholme primes

A prime is called a Fibonacci-Wieferich prime if , where is the th Fibonacci number. We report that there exist no such primes . A prime is called a Wolstenholme prime if . To date the only known Wolstenholme primes are 16843 and 2124679. We report that there exist no new Wolstenholme primes . Wolstenholme, in 1862, proved that for all primes . It is estimated by a heuristic argument that the ``probability' that is Fibonacci-Wieferich (independently: that is Wolstenholme) is about . We provide some statistical data relevant to occurrences of small values of the Fibonacci-Wieferich quotient modulo .

     

On finiteness of multiplication modules

Our main aim in this note, is a further generalization of a result due to D. D. Anderson, i.e., it is shown that if R is a commutative ring, and M a multiplication R-module, such that every prime ideal minimal over Ann (M) is finitely generated, then M contains only a finite number of minimal prime submodules. This immediately yields that if P is a projective ideal of R, such that every prime ideal minimal over Ann (P) is finitely generated, then P is finitely generated. Furthermore, it is established that if M is a multiplication R-module in which every minimal prime submodule is finitely generated, then R contains only a finite number of prime ideals minimal over Ann (M).      

一种加快概率素数搜索技巧的改进和推广

对一种快速筛去部分合数的一种算法加以改进和推广，结合利用雅可比符号寻找大素数的算法，给出了一种可以有效的减少判别的奇合数，加快素数搜索过程的有效快速算法．     

关于形如（2^p＋1）／3的素数

设ｐ为奇素数,本文讨论（２＾ｐ＋１）／３的基本性质,并对ｐ〈６０００给出了素数和概率数。     

关于格序群的极大素子群

研究了格序群的极大素子群的性质以及由素子群根系确定的几种格序群类的结构。     

Reductions of Tensor Categories Modulo Primes

We study good (i.e., semisimple) reductions of semisimple rigid tensor categories modulo primes. A prime p is called good for a semisimple rigid tensor category 𝒞 if such a reduction exists (otherwise, it is called bad). It is clear that a good prime must be relatively prime to the Müger squared norm |V|² of any simple object V of 𝒞. We show, using the Ito–Michler theorem in finite group theory, that for group-theoretical fusion categories, the converse is true. While the converse is false for general fusion categories, we obtain results about good and bad primes for many known fusion categories (e.g., for Verlinde categories). We also state some questions and conjectures regarding good and bad primes.     

Asymptotic behaviour of certain sets of prime ideals

Let be ideals of the commutative ring , let be a Noetherian -module and let be a submodule of ; also let be an Artinian -module and let be a submodule of . It is shown that, whenever is a sequence of -tuples of non-negative integers which is non-decreasing in the sense that for all and all , then Ass is independent of for all large , and also Att is independent of for all large . These results are proved without any regularity conditions on the ideals , and so (a special case of) the first answers in the affirmative a question raised by S. McAdam.

     

扩张环上的$\Sigma$-相伴素理想

作为对相伴素理想与幂零相伴素理想的推广,我们在本文中引进了$\Sigma$-相伴素理想的定义,探讨了$\Sigma$-相伴素理想的基本性质,证明了Ore扩张环$R[x;\alpha,\delta]$、斜洛朗多项式环$R[x,x^{-1};\alpha]$及斜幂级数环$R[[x;\alpha]]$的$\Sigma$-相伴素理想都分别可以用环$R$的$\Sigma$-相伴素理想来刻画,从而将相伴素理想与幂零相伴素理想的一些已有结论推广到更一般的情形.     

Strongly Prime Submodules

Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime submodule of M is defined. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of prime ideal. In particular, the Generalized Principal Ideal Theorem is extended to modules.