Characteristics of high energy interactions II. Production spectra of Gamma-rays in graphite

Twenty high energy nuclear interactions produced in the graphite units of an emulsion chamber were recorded. The emulsion chamber was exposed to cosmic rays at an atmospheric depth of 10 g cm⁻² for about 7 hr over Hyderabad, India. Fourteen interactions which radiated energyΣ E _r⩾1000 GeV in the form ofγ-rays were analysed in detail. The median energy 〈Σ E _r〉 of the interactions was 1600 GeV. Results concerning the multiplicity, the transverse and longitudinal momentum distributions, and the fractional energy distribution ofγ-rays in these interactions are presented. The average transverse momentum ofπ ⁰—mesons <pt _π ⁰> is found to increase very slowly with the primary energyE ₀ and it can be approximated by the function <pt _π ⁰>=0·238E ₀ ^0.06 .     

PHOBOS at RHIC: Some global observations

Particle production in Au+Au collisions has been measured in the PHOBOS experiment at RHIC for a range of collision energies for a large span of pseudorapidities, |η| < 5.4. Three empirical observations have emerged from this data set which require theoretical examination. First, there is clear evidence of limiting fragmentation. Namely, particle production in central Au + Au collisions, when expressed as dN/dη′ ( η′ ≡ – y_beam), becomes energy independent at high energy for a broad region of η′ around η′ = 0. This energy-independent region grows with energy, allowing only a limited region (if any) of longitudinal boost-invariance. Second, there is a striking similarity between particle production in e⁺e⁻and Au + Au collisions (scaled by the number of participating nucleon pairs). Both the total number of produced particles and the longitudinal distribution of produced particles are approximately the same in e⁺e⁻and in scaled Au + Au. This observation This presentation is based in large part on the PHOBOS summary talk by M Baker at the16th Int. Conf. on Ultrarelativistic Nucleus- Nucleus Collisions, Quark Matter 2002, Nantes, France was not predicted and has not been explained. Finally, particle production has been found to scale approximately with the number of participating nucleon pairs for (N _part ) > 65. This scaling occurs both for the total multiplicity and for highp _T particles (3 <p _T < 4.5 GeV/c). This presentation is based in large part on the PHOBOS summary talk by M Baker at the16th Int. Conf. on Ultrarelativistic Nucleus-Nucleus Collisions, Quark Matter 2002, Nantes, France     

一个半正Sturm-Liouville边值问题的n个解的存在性

通过构造与非线性项有关的辅助函数并考察这个辅助函数在有界集上的性质，对于Sturm-Liouville边值问题建立了几个解的存在性，其中非线性项是下有界的．同时，给出了正解和非平凡解的一个判别方法．主要工具是锥压缩与锥拉伸型的Krasnosel’skii不动点定理．     

方程w"-w+f(t,w)=O的Dirichlet边值问题的正解存在性与多解性

考察了下列常微分方程的Dirichlet边值问题的正解[w″(t)-w(t) f(t,w(t))=0,0≤t≤1 w(0)=w(1)=0建立了n正解的存在性，其中n是一个任意的自然数。     

Multi-Faithful Spanning Trees of Infinite Graphs

For an end and a tree T of a graph G we denote respectively by m() and m _T () the maximum numbers of pairwise disjoint rays of G and T belonging to , and we define tm() := min{m _T(): T is a spanning tree of G}. In this paper we give partial answers — affirmative and negative ones — to the general problem of determining if, for a function f mapping every end of G to a cardinal f() such that tm() f() m(), there exists a spanning tree T of G such that m _T () = f() for every end of G.     

弹性理论中上三角无穷维Hamilton算子根向量组的完备性

考虑弹性力学中一类上三角无穷维Hamilton算子.首先,给出此类Hamilton算子特征值的几何重数和代数指标,进而得到代数重数.其次,根据Hamilton算子特征值的代数重数确定其特征(根)向量组完备的形式,得到此类Hamilton算子特征(根)向量组的完备性是由内部算子特征向量组决定.最后,将所得结果应用到弹性力学问题中.     

临界群与二阶差分方程解的多重性

研究了一类二阶非线性差分方程两点边值问题解的多重性.当该问题的非线性项在无穷远点具有特殊的渐近线性性质时,利用变分方法,结合临界群与Morse理论,同时考虑正、负能量泛函的临界点,不论该问题是否发生共振,均证明了它至少存在两个非零解.     

半正二阶三点边值问题的解和正解

考察了非线性二阶三点边值问题的n个解和正解的存在性,其中允许非线性项有一个负的下界并且n是一个任意的自然数．主要结论表明该问题可以具有n个解或者正解,只要非线性项在某些有界集上的“高度”是适当的．     

Multiplicity and stability of standing waves for the nonlinear Schrödinger‐Poisson equation with a harmonic potential

In this paper, we study the multiplicity, stability, and quantitative properties of normalized standing waves for the nonlinear Schrödinger‐Poisson equation with a harmonic potential.     

The multiplicity of abelian covers of splice quotient singularities

From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group.