Local solvability of the -equation with boundary regularity on weakly q-convex domains

We consider weakly q-convex domains with smooth boundary and show that the -equation is locally solvable with regularity up to the boundary for smooth forms of degree (p,s) for s≥q.     

The uniqueness of blow-up solution for radially symmetric semilinear elliptic equation

In this paper we establish a blow up rate of the large positive solutions of the singular boundary value problem -Δu=λu-b(x)u^p,u_|∂Ω=+∞$-\mathrm{\Delta }u=\lambda u-b(x)u^p,u{|}_{\mathrm{\partial }\Omega }=+\infty$ with a ball domain and radially function b(x)$b(x)$. All previous results in the literature assumed the decay rate of b(x)$b(x)$ to be approximated by a distance function near the boundary ∂Ω$\mathrm{\partial }\Omega$. Obtaining the accurate blow up rate of solutions for general b(x)$b(x)$ requires more subtle mathematical analysis of the problem.     

Er~(3+)/Yb~(3+)共掺杂磷酸盐微晶玻璃的光谱性质

采用高温熔融法生长了Er3+/Yb3+共掺杂的磷酸盐微晶玻璃,测量了微晶玻璃室温下的吸收光谱。由此吸收谱,根据Judd-O felt理论,计算了Er3+/Yb3+共掺杂磷酸盐微晶玻璃的强度参数、自发辐射几率、荧光分支比等光谱参数,得到了吸收截面曲线,并根据M cCumber理论得到1 540 nm附近的积分发射截面。样品的强度参数为Ω2=6.33×10-20cm2,Ω4=1.41×10-20cm2,Ω6=1.09×10-20cm2。1 540 nm对应的积分发射截面峰值为1.8×10-20cm2。另外,还测量了Er3+/Yb3+共掺杂磷酸盐微晶玻璃在980 nm激发下的上转换光谱,讨论了Er3+/Yb3+共掺杂磷酸盐微晶玻璃的上转换发光和能量传递过程。     

离心泵启动过程瞬态特性与流动的实验研究

为获得离心泵在启动过程中的瞬时性能和内部非定常流动状态,建立了离心泵瞬态性能测试实验台。分别对启动过程的瞬时流量、扬程、转速和功率进行采集,同时采用PIV测试系统对叶轮上部二维瞬时速度矢量场进行了拍摄和记录。给出了三种转速下的瞬时外部性能和内部流动测试结果,并对瞬时外部性能和内部瞬时流动结构的演化进行了对比说明,同时分析和讨论了实验误差产生的原因。     

A parallel global optimization method and its implementation on a transputer system

This paper deals with a new parallel method for solving one-dimensional global optimization problems. We present the formulation of the decision rules of this method, the conditions for its nonredundant parallelization, the generalization for solving multi-dimensional problems and its implementation on a transputer system. There is also an account of some numerical experiments.     

Minimum degree thresholds for bipartite graph tiling

Given a bipartite graph H and a positive integer n such that v(H) divides 2n, we define the minimum degree threshold for bipartite H‐tiling, δ₂(n, H), as the smallest integer k such that every bipartite graph G with n vertices in each partition and minimum degree δ(G)≥k contains a spanning subgraph consisting of vertex‐disjoint copies of H. Zhao, Hladký‐Schacht, Czygrinow‐DeBiasio determined δ₂(n, K_{s, t}) exactly for all s?t and suffi‐ciently large n. In this article we determine δ₂(n, H), up to an additive constant, for all bipartite H and sufficiently large n. Additionally, we give a corresponding minimum degree threshold to guarantee that G has an H‐tiling missing only a constant number of vertices. Our δ₂(n, H) depends on either the chromatic number χ(H) or the critical chromatic number χ_cr(H), while the threshold for the almost perfect tiling only depends on χ_cr(H). These results can be viewed as bipartite analogs to the results of Kuhn and Osthus [Combinatorica 29 (2009), 65–107] and of Shokoufandeh and Zhao [Rand Struc Alg 23 (2003), 180–205]. © 2011 Wiley Periodicals, Inc. J Graph Theory     

The difference between Schrödinger equation derived from Schrödinger map and Landau-Lifshitz equation

We provide an explicit blow up solution of Schrödinger equation derived from Schrödinger map. Consequently we show the non-equivalence between the Schrödinger equation and Landau-Lifshitz equation. We also find that two class of equivariant solutions of Landau-Lifshitz equation are static.     

A rainbow blow‐up lemma

We prove a rainbow version of the blow‐up lemma of Komlós, Sárközy, and Szemerédi for μn‐bounded edge colorings. This enables the systematic study of rainbow embeddings of bounded degree spanning subgraphs. As one application, we show how our blow‐up lemma can be used to transfer the bandwidth theorem of Böttcher, Schacht, and Taraz to the rainbow setting. It can also be employed as a tool beyond the setting of μn‐bounded edge colorings. Kim, Kühn, Kupavskii, and Osthus exploit this to prove several rainbow decomposition results. Our proof methods include the strategy of an alternative proof of the blow‐up lemma given by Rödl and Ruciński, the switching method, and the partial resampling algorithm developed by Harris and Srinivasan.     

Global nonexistence of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms

This work is concerned with a system of viscoelastic wave equations with nonlinear damping and source terms acting in both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy.     

Blow up behavior for a semilinear parabolic equation with localized source

In this paper, we investigate the blow-up behavior of solutions of a parabolic equation with localized reactions. We completely classify blow-up solutions into the total blow-up case and the single point blow-up case, and give the blow-up rates of solutions near the blow-up time which improve or extend previous results of several authors. Our proofs rely on the maximum principle, a variant of the eigenfunction method and an initial data construction method.