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     

A Distance-Regular Graph with Strongly Closed Subgraphs

Let be a distance-regular graph of diameter d, valency k and r := maxi | (c _i,b _i) = (c ₁,b ₁). Let q be an integer with r + 1 q d – 1.In this paper we prove the following results: Theorem 1 Suppose for any pair of vertices at distance q there exists a strongly closed subgraph of diameter q containing them. Then for any integer i with 1 i q and for any pair of vertices at distance i there exists a strongly closed subgraph of diameter i containing them. Theorem 2 If r 2, then c _2r+3 1.As a corollary of Theorem 2 we have d k ²(r + 1) if r 2.     

Sets of Type (a, b) From Subgroups of ΓL(1, pR)

In this paper k-sets of type (a, b) with respect to hyperplanes are constructed in finite projective spaces using powers of Singer cycles. These are then used to construct further examples of sets of type (a, b) using various disjoint sets. The parameters of the associated strongly regular graphs are also calculated. The construction technique is then related to work of Foulser and Kallaher classifying rank three subgroups of AL(1, p ^R). It is shown that the sets of type (a, b) arising from the Foulser and Kallaher construction in the case of projective spaces are isomorphic to some of those constructed in the present paper.     

The Ergodic Theory of Traffic Jams

We introduce and analyze a simple probabilistic cellular automaton which emulates the flow of cars along a highway. Our Traffic CA captures the essential features of several more complicated algorithms, studied numerically by K. Nagel and others over the past decade as prototypes for the emergence of traffic jams. By simplifying the dynamics, we are able to identify and precisely formulate the self-organized critical evolution of our system. We focus here on the Cruise Control case, in which well-spaced cars move deterministically at maximal speed, and we obtain rigorous results for several special cases. Then we introduce a symmetry assumption that leads to a two-parameter model, described in terms of acceleration () and braking () probabilities. Based on the results of simulations, we map out the (, ) phase diagram, identifying three qualitatively distinct varieties of traffic which arise, and we derive rigorous bounds to establish the existence of a phase transition from free flow to jams. Many other results and conjectures are presented. From a mathematical perspective, Traffic CA provides local, particle-conserving, one-dimensional dynamics which cluster, and converge to a mixture of two distinct equilibria.     

Strongly Mixing Sequences of Measure Preserving Transformations

We call a sequence (T _n ) of measure preserving transformations strongly mixing if tends to P(A)P(B) for arbitrary measurable A, B. We investigate whether one can pass to a suitable subsequence such that almost surely for all (or "many") integrable f.     

On Nonlinear Integro-differential Operators in Generalized Orlicz–Sobolev Spaces

A nonlinear integral operator T of the form (Tf)(s)=∫_G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T.     

Strongly Regular Graphs and Designs with Three Intersection Numbers

We investigate BIBDs with three intersection numbers,x, y, and z, such that the relation on the block set given byA B iff the cardinality of the intersectionof A and B is not equal to x is an equivalence relation. Withsuch a design, we associate a family of strongly regular graphswith the same parameters. Two constructions producing infinitefamilies of such designs are given.     

Group extensions and free actions by finite groups on solvmanifolds

The purpose of this paper is to generalize Yalçin's result [Trans. Amer. Math. Soc. 352 , 2689–2700 (2000)] from tori to solvmanifolds. As a result, we prove that if (?_p)^r acts freely on a solvmanifold M of dimension n, then r ≤ n (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

拟线性双曲抛物耦合组强适定非线性初边值问题

本文用叠代方法得到强适定双曲抛物耦合系统非线性初始边值问题局部解的存在唯一性。     

随机变量序列函数的几乎处处中心极限定理

该文证明了随机元序列的一个一般的几乎处处中心极限定理, 并把这一结论应用于随机变量序列的函数.