Pseudopolarity of Generalized Matrix Rings over a Local Ring

Pseudopolar rings are closely related to strongly -regular rings, uniquelystrongly clean rings and semiregular rings. In this paper, we investigate pseudopolar-ity of generalized matrix rings Ks（R） over a local ring R. We determine the conditionsunder which elements of Ks（R） are pseudopolar. Assume that R is a local ring. It isshown that A ∈ Ks（R） is pseudopolar if and only if A is invertible or A^2 ∈ J（Ks（R））or A is similar to a diagonal matrix [ u 0 0 j ]; where lu -rj and lj-ru are injectiveand u 2 U（R） and j ∈ J（R）. Furthermore, several equivalent conditions for Ks（R）over a local ring R to be pseudopolar are obtained.

Using Normal Form of Idempotent Matrices over Finite Local Ring Z/p^kZ to Construct Cartesian Authentication Codes

In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.

Artinian Local Rings Whose Annihilating-ideal Graphs Are Star Graphs

In this paper, a necessary and sufficient condition is given for a commutative Artinian local ring whose annihilating-ideal graph is a star graph. Also, a complete char- acterization is established for a finite local ring whose annihilating-ideal graph is a star graph.

A REMARK ON THE HENSELIZATION OF A REGULAR LOCAL RING

The author gives simple characterization of the Henselization of an excellent regular localring.

Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings

In this paper, we first propose the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields. We then study the deep hole problem of generalized Reed-Solomon (RS) codes over finite local rings. Several different classes of deep holes are constructed. The relationship between finite geometry and deep holes of RS codes over finite local rings are also studied.

On Finite Local Rings with Clique Number Four

We study the algebraic structure of rings R whose zero-divisor graph T(R)has clique number four.Furthermore,we give complete characterizations of all the finite commutative local rings with clique number 4.

The Isomorphisms of Orthogonal Groups over Local Rings

1. Introduction Since O’Meara worked out the automorphisms of orthogonal groups Ωn(V) over fields in [4] by using well-known residual space method, many results about the isomorphisms and automorphisms of orthogonal groups over integral domains have been achieved. Refer to O’Meara, Hahn for example. B. R. McDonald, in [12], determined the automorphisms of O(V) over local rings with 2 a unit by using involutions.

On Semilocal Group Rings

Let R be an associative ring with identity. R is said to be semilocal if R/J（R） is （semisimple） Artinian, where J（R） denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.

The structure of a class of Z-local rings

A local ring R is called Z-local if J(R)= Z(R) and J(R)2= 0. In this paper the structure of a class of Z-local rings is determined.

Localized states of flattened quantum elliptic rings and their optical properties

A flattened elliptic ring containing an electron is studied. The emphasis is placed on clarifying the effect of the flattening. The localized states are classified into four types according to their inherent nodes. When the ring becomes more flattened, the total probability of dipole absorption of each state is found to be reduced. Furthermore, each spectral line of absorption is found to shift towards red and may split into a few lines, and these lines as a whole become more diffusive.

Uniquely strongly clean triangular matrix rings

An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.

Some Characterizations of GVNL Rings

A ring R is called a GVNL-ring if a or 1-a is π-regular for every a∈R,as a common generalization of local and π-regular rings.It is proved that if R is a GVNL ring,then either(1-e)R(1-e) or eRe is a π-regular ring for every idempotent e of R.We prove that the center of a GVNL ring is also GVNL and every abelian GVNL ring is SGVNL.The formal power series ring R[x] is GVNL if and only if R is a local ring.

Reverse mathematics and local rings

In this paper,we study local rings from the perspective of reverse mathematics.We define local rings in a first-order way by usingΠ_2~0 properties of invertible elements,where for a ring R possibly not commutative,R is left(resp.right)local if for any non-left(resp.non-right)invertible elements x,y∈R,x+y is not left(resp.right)invertible;R is local if for any non-invertible elements x,y∈R,x+y is not invertible.Firstly,we solve a question of Sato on characterizations of commutative local rings in his Ph D thesis(Question 6.22 in Sato(2016))and prove that the statement“a commutative ring is local if and only if it has at most one maximal ideal”is equivalent to ACA_0 over RCA_0.We also obtain a nice corollary in computable mathematics,i.e.,there is a computable non-local ring with exactly two maximal ideals such that each of them Turing computes the Halting set K.Secondly,we study the equivalence among left local rings,right local rings,and local rings,showing that these three kinds of first-order local rings are equivalent over the weak basis theory RCA_0.Finally,we extend the results of reverse mathematics on commutative local rings to noncommutative rings.

Zero-divisor Graphs for Direct Products of Rings

In [1], Joe Warfel investigated the diameter of a zero-divisor graph for a direct product R 1 × R 2 with respect to the diameter of the zero-divisor graph of R 1 and R 2 . But the author only considered those graphs whose diameters ≥ 1 and discussed six cases. This paper further discusses the other nine cases and also gives a complete characterization for the possible diameters for left Artin rings.

HUSTRING网络的双环结构及其路由算法

环形局域网HUSTRING采用令牌传递和寄存器插入相结合的媒介访问控制协议,从而获得了优于令牌环的实时传输性能。本文介绍了HUSTRING 的双环结构,研究了它的拓扑容错性能,并给出其信息包路由选择算法。

Dynamical localization effect in a coupled quantum dot array driven by an AC magnetic field

We have studied the transport properties of a ring-coupled quantum dot array driven by an AC magnetic field, which is connected to two leads, and we give the response of the transport current to the dynamical localization. We found that when the ratio of the magnetic flux to the total quantum dots number is a root of the zeroth order Bessel function, dynamical localization and collapse of quasi-energy occurs and importantly~ the transport current displays a dip which is the signal of dynamical localization. The dynamical localization effect is strengthened as a result of the increase of the quantum dot number, and it is weakened on account of the increase of the dots-lead hopping rate.

弧形绝缘子金属连接环局部机械损坏识别仿真

弧形绝缘子金属连接环通常安装在电力设备上,由于其所处的环境复杂,且存在各种环境干扰因素的影响,使得其局部出现机械损坏时,识别结果不准确。为了精准识别连接环局部机械损坏,提出一种弧形绝缘子金属连接环局部机械损坏识别方法。通过形态学开—闭重构运算对弧形绝缘子金属连接环图像展开建模,使用差分运算获取差分图像,并结合最大熵值法对其分割。根据弧形绝缘子金属连接环的特点,排除非损伤部分对图像识别的干扰。采用基于分形理论的差分盒维法,将图像划分为多个子块并计算其分形维数值,并判断图像是否在数值范围内,从而实现对连接环局部机械损坏的识别。实验结果表明,所提方法可以精准识别弧形绝缘子金属连接环局部机械损坏,具有比较强的适用性。

Artin环局部化结构与一类商环的等价刻画

设R是Artin交换环,m_(i)(1≤i≤k)是R的k个极大理想.通过Artin环的Jacobson根幂零和中国剩余定理得到R到⊕R/m_(i)^(l)的同态是一种同构关系.进一步把Artin环写成有限个局部环Re_(i)的直和,发现这些直和加项与商环R/m_(i)^(l)是同构关系,并且与局部环R_(m_(i))的也是同构关系.

Some Success Applications for Local-Realism Quantum Mechanics: Nature of Covalent-Bond Revealed and Quantitative Analysis of Mechanical Equilibrium for Several Molecules

With local realism quantum mechanics established, we can simply describe an extranuclear electron as a large-scale elastic ring with an elastic phase trajectory. Several small molecules can thus be strictly calculated through the logical method of establishing an accurate mechanical equilibrium equation describing the molecular structure, then solving the strict solutions of this mechanical equation and the corresponding wave equation. The results (bond length and dissociation energy) are in good agreement with observed results—i.e. if it is only coincidence, there should not be such a high probability of agreement between calculated and observed results. The method of local realism quantum mechanics is no longer the semi-empirical method. The method to calculate the electron pairing energy uses a linear regression of the ionization energy obtained through experiment. Nonetheless, it is exciting that there are diatomic molecules such as Na2, K2 and asymmetric HF molecules that possess a non-zero non-bonding electron number in the calculation examples. Moreover, the molecular structures are very intuitive, and the calculation method is much simpler than existing methods.

基于图像取反的同心圆环半径和圆心提取方法

为了解决非定域干涉同心圆环图像的圆心和半径的精确提取问题,提出了一种基于图像取反的暗亮环兼顾的算法,以点光源非定域干涉同心圆环为对象,在平滑降噪预处理基础上,利用霍夫圆变换获得参考圆心,以参考圆心为基础分别在其x方向和y方向上[-50,50]像素范围内每隔5 pixel取一条强度轮廓线,每一条强度轮廓线取反后,分别实现暗环和亮环峰位坐标的精确识别,再利用圆回归拟合得到系列圆心和半径,通过系列圆心和半径的平均运算实现图像最终圆心和半径的精确提取。结果表明,靠近中心的3个亮环和3个暗环各自的圆心坐标非常接近,相对于总平均值的最大偏差为-3.7 pixel,即相对于总平均值的最大相对偏差为-0.15%,重复性很好;相邻两个圆环半径平方比值相对于实际比值的误差在-4.18%~0.36%之间变化,验证了算法的可行性。该研究对实现自动化检测、提高测量精度是有帮助的。