幂等剩余格

研究一种特殊的刺余格--幂等刺余格,证明满足幂等性的一般刺余格必是可换剩余格,即不存在非可换的幂等剩余格.讨论幂等剩余格的基本性质以及与各类特殊剩余格之间的关系.在一般剩余格中引入psG-滤子的概念,给出其一组等价条件,并借助psG-滤子刻画幂等刺余格的特征.     

Kleene代数及相关半模结构

Kleene代数在理论计算机科学中具有基础而特殊的重要性,Kleene模、布尔模和动态代数等与Kleene代数密切相关的半模结构在程序的语义逻辑及推理中发挥着十分重要的作用.将半环和半模等代数系统作为基本构架,研究了理论计算机科学中的Kleene代数、Kleene模和归纳~*-半环等重要概念,并将这些对象统一为序~*-半环上称为归纳半模的代数结构.进一步,提出并讨论了弱归纳半模、伪归纳半模以及伪弱归纳半模等相关概念.     

Crown-free Lattices and Their Related Graphs

This paper investigates links between some classes of graphs and some classes of lattices. We show that a co-atomic lattice is crown-free (i.e. dismantlable) if and only if it is a maximal clique lattice of a strongly chordal graph. We also prove that each crown-free lattice that is not a chain contains at least two incomparable doubly-irreducible elements x ₁ and x ₂ such that ↑ x ₁ and ↑ x ₂ are chains.     

Odd Systems of Vectors and Related Lattices

We consider uniform odd systems, i.e. sets of vectors of constant odd norm with odd inner product, and the lattice L(V) linearly generated by a uniform odd system V of odd norm 2t+1. If uu p (mod 4) for all u V, one has v² p (mod 4) if v² is odd and v² 0 (mod 4) if v² is even, for any vector v L(V). The vectors of even norm form a double even sublattice L₀(V) of L(V), i.e. is an even lattice. The closure of V, i.e. all vectors of L(V) of norm 2t+1, are minimal vectors of L(V) for t=1, and they are almost always minimal for t=2. For such t, the convex hull of vectors of the closure of V is an L-polytope of L₀V and the contact polytope of L(V). As an example, we consider closed uniform odd systems of norm 5 spanning equiangular lines.     

Adjoints and pluricanonical adjoints to an algebraic hypersurface

. We develop the theory of canonical and pluricanonical adjoints, of global canonical and pluricanonical adjoints, and of adjoints and global adjoints to an irreducible, algebraic hypersurface V?? ⁿ , under certain hypotheses on the singularities of V. We subsequently apply the results of the theory to construct a non-singular threefold of general type X, desingularization of a hypersurface V of degree six in ?⁴, having the birational invariants q ₁=q ₂=p _g =0, P ₂=P ₃=5. We demonstrate that the bicanonical map ? _|2KX| is birational and finally, as a consequence of the Riemann–Roch theorem and vanishing theorems, we prove that any non-singular model Y, birationally equivalent to X, has the canonical divisors K _Y that do not (simultaneously) satisfy the two properties: (K _Y ³)>0 and K _Y numerically effective.     

Multipliers and Modulus on Banach Algebras Related to Locally Compact Groups

LetGbe a locally compact group. In this paper we study moduli of products of elements and of multipliers of Banach algebras which are related to locally compact groups and which admit lattice structure. As a consequence, we obtain a characterization of operators onL^∞(G) which commute with convolutions whenGis amenable as discrete.     

Extremal Even Unimodular Lattices of Rank 32 and Related Codes

In the paper the asymptotic behaviour of the solutions of a class of neutral differential equations with distributed delay is studied.     

On Polynomials Sharing Preimages of Compact Sets, and Related Questions

In this paper we give a solution of the following problem: under what conditions on infinite compact sets and polynomials f ₁, f ₂ do the preimages f ₁⁻¹{K ₁} and f ₂⁻¹{K ₂} coincide. Besides, we investigate some related questions. In particular, we show that polynomials sharing an invariant compact set distinct from a point have equal Julia sets. Received: May 2006, Accepted: June 2006     

Schroedinger Flows on Compact Hermitian Symmetric Spaces and Related Problems

In this note,we prove that the Schroedinger flow of maps from a closed riemann surface into a compact irreducible Hermitian symmetic space admits a global weak solution.Also,we show the existence of weak solutions to the initial value problem of Heisenberg model with Lie algebra values,which is closely related to the Schroedinger flow on compact Hermitian symmetric spaces.     

A New Form of Fuzzy Compact Spaces and Related Topics via Fuzzy Idealization

Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have been introduced to fuzzy topological spaces in the last twenty years but not have been studied using fuzzy ideals so,the main aim of our work in this paper is to define and study some new various types of fuzzy compactness with respect to fuzzy ideals namely fuzzy L-compact and L*-compact spaces. Also fuzzy compactness with respect to ideal is useful as unification and generalization of several others widely studied concepts. Possible application to superstrings and E∞ space-time are touched upon.     

Lattices, Diophantine equations and applications to rational surfaces

In this article,we study certain quadratic Diophantine equations in Picard lattices of blow-ups of the complex projective plane,and describe their relations with root systems and Weyl group orbits of quasiminuscule fundamental weights.We apply these to study the geometry of certain rational surfaces.     

On the Ternary Approach to Clifford Structures and Ising Lattices

We continue to modify and simplify the Ising-Onsager-Zhang procedure for analyzing simple orthorhombic Ising lattices by considering some fractal structures in connection with Jordan and Clifford algebras and by following Jordan-von Neumann-Wigner (JNW) approach. We concentrate on duality of complete and perfect JNW-systems, in particular ternary systems, analyze algebras of complete JNW-systems, and prove that in the case of a composition algebra we have a self-dual perfect JNW-system related to quaternion or octonion algebras. In this context, we are interested in the product table of the sedenion algebra.     

Zonal Functions for the Unitary Groups and Applications to Hermitian Lattices

We study the decomposition of the space L²(Sⁿ⁻¹) under the actions of the complex and quaternionic unitary groups. We give an explicit basis for the space of zonal functions, which in the second case takes account of the action of the group of quaternions of norm 1. We derive applications to hermitian lattices.     

A Poset-based Approach to Embedding Median Graphs in Hypercubes and Lattices

A median graph G is a graph where, for any three vertices u, v and w, there is a unique node that lies on a shortest path from u to v, from u to w, and from v to w. While not obvious from the definition, median graphs are partial cubes; that is, they can be isometrically embedded in hypercubes and, consequently, in integer lattices. The isometric and lattice dimensions of G, denoted as dim _I (G) and dim _Z (G), are the smallest integers k and r so that G can be isometrically embedded in the k-dimensional hypercube and the r-dimensional lattice respectively. Motivated by recent results on the cover graphs of distributive lattices, we study these parameters through median semilattices, a class of ordered structures related to median graphs. We show that not only does this approach provide new combinatorial characterizations for dim _I (G) and dim _Z (G), they also have nice algorithmic consequences. Assume G has n vertices and m edges. We prove that dim _I (G) can be computed in O(n + m) time, and an isometric embedding of G on a hypercube with dimension dim _I (G) can be constructed in O(n × dim _I (G)) time. The algorithms are extremely simple and the running times are optimal. We also show that dim _Z (G) can be computed and an isometric embedding of G on a lattice with dimension dim _Z (G) can be constructed in O( n ×dim_I(G) + dim_I(G)^2.5)O( n \times dim_I(G) + dim_I(G)^{2.5}) time by using an existing algorithm of Eppstein’s that performs the same tasks for partial cubes. We are able to speed up his algorithm by using our framework to provide a new “interpretation” to the algorithm. In particular, we note that its main part is essentially a generalization of Fulkerson’s method for finding a smallest-sized chain decomposition of a poset.     

Interval Reductions and Extensions of Orders: Bijections to Chains in Lattices

We discuss bijections that relate families of chains in lattices associated to an order P and families of interval orders defined on the ground set of P. Two bijections of this type have been known:(1) The bijection between maximal chains in the antichain lattice A(P) and the linear extensions of P.(2) The bijection between maximal chains in the lattice of maximal antichains A_M(P) and minimal interval extensions of P.We discuss two approaches to associate interval orders with chains in A(P). This leads to new bijections generalizing Bijections 1 and 2. As a consequence, we characterize the chains corresponding to weak-order extensions and minimal weak-order extensions of P.Seeking for a way of representing interval reductions of P by chains we came upon the separation lattice S(P). Chains in this lattice encode an interesting subclass of interval reductions of P. Let S_M(P) be the lattice of maximal separations in the separation lattice. Restricted to maximal separations, the above bijection specializes to a bijection which nicely complements 1 and 2.(3) A bijection between maximal chains in the lattice of maximal separations S_M(P) and minimal interval reductions of P.