On the maximal multiplicity of block sizes in a random set partition

We study the asymptotic behavior of the maximal multiplicity M_n = M_n(σ) of the block sizes in a set partition σ of [n] = {1,2,…,n}, assuming that σ is chosen uniformly at random from the set of all such partitions. It is known that, for large n, the blocks of a random set partition are typically of size W = W(n), with We^W = n. We show that, over subsequences {n_k}_{k ≥ 1} of the sequence of the natural numbers, , appropriately normalized, converges weakly, as k→∞, to , where Z₁ and Z₂ are independent copies of a standard normal random variable. The subsequences {n_k}_{k ≥ 1}, where the weak convergence is observed, and the quantity u depend on the fractional part f_n of the function W(n). In particular, we establish that . The behavior of the largest multiplicity M_n is in a striking contrast to the similar statistic of integer partitions of n. A heuristic explanation of this phenomenon is also given.     

Positive solutions for a singular fractional boundary value problem

We investigate the existence of positive solutions for a system of Riemann-Liouville fractional differential equations, supplemented with uncoupled nonlocal boundary conditions which contain various fractional derivatives and Riemann-Stieltjes integrals, and the nonlinearities of the system are nonnegative functions and they may be singular at the time variable. In the proof of our main theorems, we use the Guo-Krasnosel'skii fixed point theorem.     

具有$2$为无符号拉普拉斯特征值的完美匹配单圈图

本文给出了$2$为完美匹配单圈图的无符号拉普拉斯特征值的充分必要条件.     

A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac–Moody algebras

In this paper we study root multiplicities of rank 2 hyperbolic Kac–Moody algebras using the combinatorics of Dyck paths.     

Multiplicity of positive solutions to boundary blow‐up problem with variable exponent and sign‐changing weights

In this paper, we consider the elliptic boundary blow‐up problem where Ω is a bounded smooth domain of are positive continuous functions supported in disjoint subdomains Ω₊,Ω_? of Ω, respectively, a ₊ vanishes on the boundary of satisfies p (x )≥1 in Ω,p (x ) > 1 on ? Ω and , and ε is a parameter. We show that there exists ε ^?>0 such that no positive solutions exist when ε > ε ^?, while a minimal positive solution u _ε exists for every ε ∈(0,ε ^?). Under the additional hypotheses that is a smooth N ? 1‐dimensional manifold and that a ₊,a _? have a convenient decay near Γ, we show that a second positive solution v _ε exists for every ε ∈(0,ε ^?) if , where N ^?=(N + 2)/(N ? 2) if N > 2 and if N = 2. Our results extend that of Jorge Garcá‐Melián in 2011, where the case that p > 1 is a constant and a ₊>0 on ? Ω is considered. Copyright © 2016 John Wiley & Sons, Ltd.     

一个供应链系统可靠性模型时间依赖解的渐近行为

本文研究一个供应链系统可靠性模型的时间依赖解.利用C0-半群理论研究该模型相应算子的谱的特征,获得了该系统模型时间依赖解的渐近行为,推广了文献[8]中的结果.     

A short Proof of Bezout's Theorem in P2

We will give a new short proof of Bezout's Theorem for complex algebraic curves in P ² which is local.     

一类分数阶微分方程多点边值问题正解的存在性

本文研究一类分数阶微分方程的多点边值问题.利用Guo-krasnoselskii不动点定理和Leggett-Williams不动点定理,得到正解的存在性和多重性结果.通过一个简单的例子说明了主要结果的应用.     

500 AMeV 56Fe诱发乳胶核反应弹核碎裂研究

通过利用日本放射线医学综合研究所( NIRS ) 重离子医用加速器( HIMAC) 产生的束流照射国产的核-4型原子核乳胶,对500 AMeV 56Fe诱发乳胶核反应粒子产生进行了研究。讨论了500 AMeV 56Fe诱发乳胶核反应弹核碎片的多重数分布,并与其他结果进行了比较。结果表明,弹核碎片平均多重数随靶核质量的增加而增加,与入射能量无关。A stack of domestic N-4 nuclear emulsion was exposed to 56Fe ions at 500 AMeV at the HIMAC of NIRS. Particle production was investigated in 56Fe-Em interactions. The multiplicity distribution of projectile fragments was given in this paper and compared with other experimental results of heavy ion induced nuclear reactions in nuclear emulsion. The results show that the multiplicity of projectile fragments increase with the increasing target mass, and thereis no dependence on the projectile energy.     

方程w″-w+f(t,w)=0的Dirichlet边值问题的正解存在性与多解性(英文)

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 1w(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 .