Kp,q-factorization of complete bipartite graphs

Let K_(m,n) be a complete bipartite graph with two partite sets having m and nvertices, respectively. A K_(p,q)-factorization of K_(m,n) is a set of edge-disjoint K_(p,q)-factorsof K_(m,n) which partition the set of edges of K_(m,n). When p=i and q is a prime number,Wang, in his paper "On K_(1,k)-factorizations of a complete bipartite graph" (Discrete Math,1994, 126; 359-364), investigated the K_(1,q)-factorization of K_(m,n) and gave a sufficientcondition for such a factorization to exist. In the paper "K_(1,k)-factorizations of completebipartite graphs" (Discrete Math, 2002, 259: 301-306), Du and Wang extended Wang'sresult to the case that q is any positive integer In this paper, we give a sufficient conditionfor K_(m,n) to have a K_(p,q)-factorization. As a special case, it is shown that the Martin's BACconjecture is true when p: q=k: (k+1) for any positive integer k.     

Exponential Expansiveness and Complete Admissibility For Evolution Families

Connections between uniform exponential expansiveness and complete admissibility of the pair are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.     

Order Environments of Topological Spaces

In this paper it is proved that a space may be realized as the set of the maximal elements in a continuous poset if and only if it is Tychonoff.     

Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths ≥2 and ≥4 in Algebraic Surfaces

We prove that the varieties of complete pairs of zero-dimensional subschemes of lengths d ₁ 2, d ₂ 4 on a smooth irreducible projective algebraic surface are singular.     

Graphs that are not complete pluripolar

Let be domains in . Under very mild conditions on we show that there exist holomorphic functions , defined on with the property that is nowhere extendible across , while the graph of over is not complete pluripolar in . This refutes a conjecture of Levenberg, Martin and Poletsky (1992).

     

Metric and Complete Metric σ-Frames

A -frame is a lattice in which countable joins exist and binary meets distribute over countable joins. In this paper, the category MFrm, of metric -frames, is introduced, and it is shown to be equivalent to the category MLFrm _u, of metric Lindelöf frames.Finally, it is shown that the complete metric -frames are exactly the cozero parts of complete metric Lindelöf frames.     

Off‐diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n)

An upper bound on the Ramsey number r(K_2,n‐s,K_2,n) where s ≥ 2 is presented. Considering certain r(K_2,n‐s,K_2,n)‐colorings obtained from strongly regular graphs, we additionally prove that this bound matches the exact value of r(K_2,n‐s,K_2,n) in infinitely many cases if holds. Moreover, the asymptotic behavior of r(K_2,m,K_2,n) is studied for n being sufficiently large depending on m. We conclude with a table of all known Ramsey numbers r(K_2,m,K_2,n) where m,n ≤ 10. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 252–268, 2003     

Contractive projections and operator spaces

Parallel to the study of finite-dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces , , generalizing the row and column Hilbert spaces and , and we show that an atomic subspace that is the range of a contractive projection on is isometrically completely contractive to an -sum of the and Cartan factors of types 1 to 4. In particular, for finite-dimensional , this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classification up to complete isometry of atomic w-closed -triples without an infinite-dimensional rank 1 w-closed ideal.

     

Local complete intersections in and Koszul syzygies

We study the syzygies of a codimension two ideal . Our main result is that the module of syzygies vanishing (scheme-theoretically) at the zero locus is generated by the Koszul syzygies iff is a local complete intersection. The proof uses a characterization of complete intersections due to Herzog. When is saturated, we relate our theorem to results of Weyman and Simis and Vasconcelos. We conclude with an example of how our theorem fails for four generated local complete intersections in and we discuss generalizations to higher dimensions.

     

The K-SAT Problem in a Simple Limit

In this work we compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computation can be strongly simplified and the thermodynamic properties can be obtained with a high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, >_c.