A new class of Ramsey-Turán problems

We introduce and study a new class of Ramsey-Turán problems, a typical example of which is the following one:Let ε>0 and G be a graph of sufficiently large order n with minimum degree δ(G)>3n/4. If the edges of G are colored in blue or red, then for all k∈[4,⌊(1/8−ε)n⌋], there exists a monochromatic cycle of length k.     

Covering and radius-covering arrays: Constructions and classification

The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays, explicit constructions from covering codes are developed. Lower bounds are improved upon using connections to orthogonal arrays, partition matrices, and covering codes, and in specific cases by computation. Consequently for some parameter sets the minimum size of a covering array is determined precisely. For some of these, a complete classification of all inequivalent covering arrays is determined, again using computational techniques. Existence tables for up to 10 columns, up to 8 symbols, and all possible strengths are presented to report the best current lower and upper bounds, and classifications of inequivalent arrays.     

纳米ZnO薄膜的反射及偏振特性研究

用电子束蒸发镀膜法制备了纳米ZnO薄膜．通过测量其X射线衍射谱,计算出纳米ZnO颗粒的平均粒径大小为30nm．实验研究了纳米ZnO薄膜的反射和偏振性质,结果表明：当振动方向平行于入射面的线偏振光（简称P光）入射纳米ZnO薄膜时,不存在严格意义上的布儒斯特角,但对于入射角却存在一个临界角β．当入射角小于β时,反射光的振动面随着入射角的增大向左旋转;当入射角大于β时,振动面转而向右旋转;当振动方向垂直于入射面的线偏振光（简称S光）入射纳米ZnO薄膜时,反射光的振动面始终向左旋转．     

Fitting Height and Character Degree Graphs

Given a group G, Γ(G) is the graph whose vertices are the primes that divide the degree of some irreducible character and two vertices p and q are joined by an edge if pq divides the degree of some irreducible character of G. By a definition of Lewis, a graph Γ has bounded Fitting height if the Fitting height of any solvable group G with Γ(G)=Γ is bounded (in terms of Γ). In this note, we prove that there exists a universal constant C such that if Γ has bounded Fitting height and Γ(G)=Γ then h(G)≤C. This solves a problem raised by Lewis. Research supported by the Spanish Ministerio de Educación y Ciencia, MTM2004-06067-C02-01 and MTM2004-04665, the FEDER and Programa Ramón y Cajal.     

On the triple jump of the set of atoms of a Boolean algebra

We prove the following result concerning the degree spectrum of the atom relation on a computable Boolean algebra. Let be a computable Boolean algebra with infinitely many atoms and be the Turing degree of the atom relation of . If is a c.e. degree such that , then there is a computable copy of where the atom relation has degree . In particular, for every c.e. degree , any computable Boolean algebra with infinitely many atoms has a computable copy where the atom relation has degree .

     

Post's Problem for Reducibilities of Bounded Complexity

In this paper we consider the we known method by E. Post of solving the problem of construction of recursively enumerable sets that have a degree intermediate between the degrees of recursive and complete sets with respect to a given reducibility. Post considered reducibilities ≤_m, ≤_btt, ≤_tt and ≤_T and solved the problem for al of them except ≤_T. Here we extend Post's original method of construction of incomplete sets onto two wide classes of sub‐Turing reducibilities what were studying in [1, 2].     

广义Lienard方程边值问题

By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equation a(t)x＂+F(x,x′)x′+g(x)=e(t),x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α| y|β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application.     

高功率氙灯脉冲放电过程中石英管壁热损伤机理

基于高功率激光装置对脉冲氙灯工程运行可靠性的要求,利用现有的能源模块开展了氙灯放电考核实验。实验结果表明：虽然氙灯运行在安全的能量负载水平,当能源模块单个放电回路的峰值功率超过300 MW时,氙灯石英玻璃管壁存在热损伤风险。肉眼观察到管壁损伤后在反射器对侧的灯管内壁出现乳白色沉积层。经扫描电镜和X射线光电子能谱测试分析,证实热损伤形成的乳白色沉积物为二氧化硅。为探究管壁热损伤机制,采用高速摄影观测了氙灯放电等离子体沟道发展过程。图像显示放大器内金属反射器的几何形状对放电沟道的分布产生了显著影响,尤其是在侧灯箱,灯内电弧沟道会靠近反射器一侧集中分布,因此,导致等离子体对灯管的偏烧。当放电峰值功率超过石英热负载极限时,管壁表面二氧化硅材料会被烧蚀至蒸发、气化,并随后沉积在灯管较冷部位。研究结果表明放电回路的放电峰值功率过高、放大器内金属反射器均会对氙灯造成热损伤。     

On a Conjecture of Kleene and Post

A proof is given that 0 ′ (the argest Turing degree containing a computably enumerable set) is definable in the structure of the degrees of unsolvability. This answers a long‐standing question of Kleene and Post, and has a number of corollaries including the definability of the jump operator.     

UNILATERAL EIGENVALUE PROBLEMS FOR NONLINEARLY ELASTIC PLATES： AN APPROACH VIA PSEUDO-MONOTONE OPERATORS

gi.TheTOpologicalDegreeforGeneralizedMonotoneOperatorsMonotoneoperatortheoryisoftenanefficienttoolforprovingtheexistenceofsolutionstononlinearProblems.Inparticular,thepseudo-monotoneoperatorsintroducedbyBrezis[2]areveryusefulforstudyingnonlinearellipticproblems.Weconsiderherethefollowingclassesofmappingsofgeneralizedmonotonetype.(QM)=theclassofquasi-mollotoneoperators,(S )=theclassofoperatorsoftype(S ),(PM)=theclassofpseudthmonotoneoperators,(LS)=theclassofLeray-Schauderoperators(compac…