On ideals and quotients of A \mathcal{T} -algebras

Some results on A -algebras are given. We study the problem when ideals, quotients and hereditary subalgebras of A -algebras are A -algebras or A -algebras, and give a necessary and sufficient condition of a hereditary subalgebra of an A -algebra being an A -algebra.     

ExponentialL 2-convergence of quantum Markov semigroups on\mathcal{B}(h)

With a quantum Markov semigroup (Τ _t ) _t≥0 on , whichhas a faithful normal invariant state ρ, we associate semigroupsT ^(s) (s∈[0],[1]) on the set of Hilbert-Schmidt operators onh defined by the rule . This allows us to use spectral theory to study the infinitesimal generatorL ^(s) of the semigroupT ^(s) and deduce information on the rate of the decay to equilibrium of Τ by means of estimates of the spectral gap ofL ^(s) . Fors=1/2, this method is applied to a class of quantum Markov semigroups on . We prove simple but reasonably general sufficient conditions, as well as necessary and sufficient conditions, for the gap(L ^(1/2)) to be positive. The exact value of the gap(L ^(1/2)) is computed or estimated for a certain class of equations motivated by classical probability or physical applications. Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 523–538, October, 2000.     

关于$\mathcal{F}$-S-可补子群

设$\mathcal{F}$是一个群类. 群$G$的子群$H$称为在$G$中$\mathcal{F}$-S-可补的，如果存在$G$的一个子群$K$,使得$G=HK$且$K/K\cap{H_G}\in\mathcal{F}$, 其中$H_G=\bigcap_{g\in G}H^g$是包含在$H$中的$G$的最大正规子群．本文利用子群的$\mathcal{F}$-S-可补性, 给出了有限群的可解性, 超可解性和幂零性的一些新的刻画. 应用这些结果, 我们可以得到一系列推论, 其中包括有关已知的著名结果.     

\mathcal{Q}-Universal Quasivarieties of Graphs

It is proved that a quasivariety K of undirected graphs without loops is -universal if and only if K contains some non-bipartite graph.     

On sandwich sets and congruences on regular semigroups

Let S be a regular semigroup and E(S) be the set of its idempotents. We call the sets S(e, f)f and eS(e, f) one-sided sandwich sets and characterize them abstractly where e, f ∈ E(S). For a, a′ ∈ S such that a = aa′a, a′ = a′aa′, we call S(a) = S(a′a, aa′) the sandwich set of a. We characterize regular semigroups S in which all S(e; f) (or all S(a)) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every a ∈ S, we also define E(a) as the set of all idempotets e such that, for any congruence ϱ on S, aϱa ² implies that aϱe. We study the restrictions on S in order that S(a) or be trivial. For , we define on S by a b if . We establish for which S are or congruences.     

A New \mathcal{N}\mathcal{P} -Complete Problem and Public-Key Identification

The appearance of the theory of zero-knowledge, presented by Goldwasser, Micali and Rackoff in 1985, opened a way to secure identification schemes. The first application was the famous Fiat-Shamir scheme based on the problem of modular square roots extraction. In the following years, many other schemes have been proposed, some Fiat-Shamir extensions but also new discrete logarithm based schemes. Therefore, all of them were based on problems from number theory. Their main common drawback is high computational load because of arithmetical operations modulo large integers. Implementation on low-cost smart cards was made difficult and inefficient.With the Permuted Kernels Problem (PKP), Shamir proposed the first efficient scheme allowing for an implementation on such low-cost smart cards, but very few others have afterwards been suggested.In this paper, we present an efficient identification scheme based on a combinatorial -complete problem: the Permuted Perceptrons Problem (PPP). This problem seems hard enough to be unsolvable even with very small parameters, and some recent cryptanalysis studies confirm that position. Furthermore, it admits efficient zero-knowledge proofs of knowledge and so it is well-suited for cryptographic purposes. An actual implementation completes the optimistic opinion about efficiency and practicability on low-cost smart cards, and namely with less than 2KB of EEPROM and just 100 Bytes of RAM and 6.4 KB of communication.     

On the Circumference of 2-Connected $$\mathcal{P}_{3}$$-Dominated Graphs

Let G be a connected graph. For at distance 2, we define , and , if then . G is quasi-claw-free if it satisfies , and G is P ₃-dominated() if it satisfies , for every pair (x, y) of vertices at distance 2. Certainly contains as a subclass. In this paper, we prove that the circumference of a 2-connected P ₃-dominated graph G on n vertices is at least min or , moreover if then G is hamiltonian or , where is a class of 2-connected nonhamiltonian graphs.     

On irreducible p,q‐representations of Lie algebras \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {G} (0,1)$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {G} (0,0)$\end{document}

In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model.     

Dominated polynomials on $\mathcal{L}_P $ -spaces

It is well known that continuous bilinear forms on C(K) × C(K) are 2-dominated. This paper shows that generalizations of this result are not to be expected. The main result asserts that for every -space E(1 p ), every n 2, every r > 0 and every Banach space F , there exists an n-homogeneous polynomial P : E F such that P is not of type [_r], hence P is neither r-dominated nor r-semi-integral (if n = 2 and p = , F is supposed to contain an isomorphic copy of some , 1_q < ).Received: 24 November 2003     

On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors

A class of structured multi-linear system defined by strong $\mathcal{M}_z$-tensors is considered. We prove that the multi-linear system with strong $\mathcal{M}_z$-tensors always has a nonnegative solution under certain condition by the fixed point theory. We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors, such as strong $\mathcal{M}$-tensors, $\mathcal{H}^+$-tensors, strictly diagonally dominant tensors with positive diagonal elements. Numerical examples are presented to illustrate our theoretical results.     

Fundamentals for symplectic $$ \mathcal{A} $$-modules. Affine Darboux theorem

In his [9–11], the first author shows that the sheaf-theoreti-cally based Abstract Differential Geometry incorporates and generalizes classical differential geometry. Here, we undertake to explore the implications of Abstract Differential Geometry to classical symplectic geometry. The full investigation will be presented elsewhere.      

拟正则半群的圈积嵌入与矩阵同余

给出了拟正则半群的圈积嵌入．研究了幂等元集 Ｅ Ｓ 生成的子半群〈 Ｅ Ｓ〉上的矩阵同余可扩张为 Ｓ上的矩阵同余的条件． 特别地,如果〈 Ｅ Ｓ〉上的最小矩阵同余可扩张为 Ｓ上的矩阵同余,那么〈 Ｅ Ｓ〉上的每个矩阵同余可扩张为 Ｓ上的矩阵同余     

A Korovkin type approximation theorems via $$\mathcal{I}$$ -convergence

Using the concept of -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.     

Euler Characteristics of Local Systems on \mathcal{M}> 2

We calculate the Euler characteristics of the local systems S ^k S ² on the moduli space ₂ of curves of genus 2, where is the rank 4 local system R ¹ _* .     

A note on maximal regular subsemigroups of the finite transformation semigroups \mathcal{T}(n,r)

Let $\mathcal{T}_{n}$ be the semigroup of all full transformations on the finite set X _n ={1,2,…,n}. For 1≤r≤n, set $\mathcal {T}(n, r)=\{ \alpha\in\mathcal{T}_{n} | \operatorname{rank}(\alpha)\leq r\}$ . In this note we show that, for 2≤r≤n?2, any maximal regular subsemigroup of the semigroup $\mathcal{T} (n,r)$ is idempotent generated, but this may not happen in the semigroup $\mathcal{T}(n, n-1)$ .     

The Abelian category of quotients of $$\mathcal{L}\mathfrak{F}$$ -spaces

We construct the category of quotients of -spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.     

On the 0-dimensional irreducible components of the singular locus of \mathcal{A}_g

In this short note we give a characterization of extremal principally polarized abelian varieties determining an isolated point in Sing The case g = 5 is treated in depth.Received: 14 June 2004     

Global solution with \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$ \mathcal {C}^{k}$\end{document}‐estimates for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\bar{\partial }$\end{document}‐equation on q‐convex intersections

We construct a global solution with $\mathcal {C}^{k}$‐estimates for the $\bar{\partial }$‐equation on q‐convex intersections.     

On the Intertwining of \partial{\mathcal{D}}-Isometries

Let be a strictly pseudoconvex bounded domain in with C ² boundary . If a subnormal m-tuple T of Hilbert space operators has the spectral measure of its minimal normal extension N supported on , then T is referred to as a -isometry. Using some non-trivial approximation theorems in the theory of several complex variables, we establish a commutant lifting theorem for those -isometries whose (joint) Taylor spectra are contained in a special superdomain Ω of . Further, we provide a function-theoretic characterization of those subnormal tuples whose Taylor spectra are contained in Ω and that are quasisimilar to a certain (fixed) -isometry T (of which the multiplication tuple on the Hardy space of the unit ball in is a rather special example). Submitted: September 9, 2007. Revised: October 10, 2007. Accepted: October 24, 2007.     

Compact solutions to the equation Tx = y in a weakly closed $$ \mathcal{T}(\mathcal{N}) $$-module

Given two vectors x, y in a Hilbert space and a weakly closed -module , we provide a necessary and sufficient condition for the existence of a compact operator T in satisfying Tx = y.