Using involutory and idempotent matrices over finite fields to construct cartesian authentication codes

Two constructions of Cartesian authentication codes form involutory and idempotent matrices over finitefields are presented and their size Parameters are computed. Moreover, assume that the encoding rules are chosen ac-cording to a uniform Probablity distribution, the PI and Ps which dend the largest Probablities of a successful impersonation attack and a successful substitution attack respectively of these codes are also computed. Finially, it is Provedthat thase two Cartesian authentication codes are isomorphic.

Generalized n-idempotents and Hyper-generalized n-idempotents

For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.

ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.

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.

A CLASS OF NATURALLY ORDERED ABUNDANT SEMIGROUPS WITH A GREATESTIDEMPOTENT

On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3].

RIESZ IDEMPOTENT OF (n, k)-QUASI-*-PARANORMAL OPERATORS

A bounded linear operator T on a complex Hilbert space H is called（n, k）-quasi-*-paranormal if ║T;（T;x） ║;║ T;x║;≥║ T*（T;x）║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properties and contains the classes of n-*-paranormal operators and quasi-*-paranormal operators. The aim of this note is to show that every Riesz idempotent E;with respect to a non-zero isolated spectral point λ of an（n, k）-quasi-*-paranormal operator T is self-adjoint and satisfies ran E;= ker（T- λ） = ker（T- λ）*.

THE EXISTENCE OF OVERLARGE SETS OF IDEMPOTENT QUASIGROUPS

A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.

Idempotent Elements of the Semigroups BX(D) Defined by Semilattices of the Class ∑3 (X,8) When Z7=Ø

In this paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.

Idempotent Elements of the Semigroups Bx(D) Defined by Semilattices of the Class ∑3(x,8) When Z7‡Ø

In the paper, complete semigroup binary relation is defined by semilattices of the class . We give a full description of idempotent elements of given semigroup. For the case where X is a finite set and , we derive formulas by calculating the numbers of idempotent elements of the respective semigroup.

On the Number of Idempotent Partial Contraction Mappings of a Finite Chain

Let be the partial symmetric semigroup on and let and be its subsemigroups of order-preserving contractions and order-preserving, order-decreasing contractions mappings of , respectively. In this paper we investigate the cardinalities of and , the set idempotents of and , respectively. We also investigate the cardinalities of certain equivalences on and .

On Primitive Idempotents of the Strong Endomorphism Monoid of a Graph

In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.

Some results on derivations of MV-algebras

In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].

保持等价关系的变换半群的一些结果

给出了保持等价关系的变换半群上的格林关系L,R,H和格林*-关系L^(*),R^(*),H^(*)相容的充要条件,刻画了这类半群的左(右,完全)正则性,得到了这类半群的全体幂等元(正则元,富足元)构成子半群的等价描述.

具有中间幂等元的r-宽大半群

讨论了r-宽大半群上的中间幂等元及其相关幂等元的性质.借此,证明了具有弱型A可乘中间幂等元u的r-宽大半群是自然序r-宽大半群,其中u是最大幂等元.

半群CSP_(n,k)的秩和k方幂等元秩

设自然数n≥3,P_(n)和S_(n)是有限链X_(n)上的部分变换半群和对称群.对任意的正整数k满足3≤k≤n,令C_(k)=g_(k)是X_(n)上的k-局部循环群且CSP_(n,k)=C_(k)∪(P_(n)\S_(n)),易证CSP_(n,k),是部分变换半群P_(n)的子半群.通过分析半群CSP_(n,k),的格林关系和幂等元,获得了半群CSP_(n,k),的极小生成集和k方幂等元极小生成集,进一步确定了半群CSP_(n,k),的秩和k方幂等元秩.

幂等矩阵的等价条件及其推广

归纳证明了幂等矩阵的一些等价条件,并对一个幂等矩阵只有充分条件成立的结论给出必要条件不成立的例子,进一步探讨得到幂等矩阵的两个充要条件.

Linear Maps Preserving Idempotency of Products of Matrices on Upper Triangular Matrix Algebras

Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.

A Qualitative Perstective on Idempotency Defect of Two Level System Interacting with Laser and Quantized Field

Entanglement due to the interaction of a two level atom with a laser and quantized field is investigated. The role of the nonlinearity due to these interactions is discussed. It is found that the nonlinearity changes strongly the behavior of the entanglement also the detuning parameters have important role in the structure of the measure of entanglement.

k次幂等矩阵下Yang-Baxter矩阵方程所有解

令A是一个k次幂等矩阵并考虑Yang-Baxter矩阵方程AXA=XAX.基于先前关于可对角化系数矩阵的Yang-Baxter矩阵方程解的结果,可以推导得到方程的所有解.

Onto Orthogonal Projections in the Space of Polynomials Pn[x]

In this article, I consider projection groups on function spaces, more specifically the space of polynomials Pn[x]. I will show that a very similar construct of projection operators allows us to project into the subspaces of Pn[x] where the function h ∈Pn[x] represents the closets function to f ∈Pn[x] in the least square sense. I also demonstrate that we can generalise projections by constructing operators i.e. in Rn+1 using the metric tensor on Pn[x]. This allows one to project a polynomial function onto another by mapping it to its coefficient vector in Rn+1. This can be also achieved with the Kronecker Product as detailed in this paper.