Pairs of positive solutions for nonlinear elliptic equations with the <Emphasis Type="Italic">p</Emphasis>-Laplacian and a nonsmooth potential

In this paper we examine a nonlinear elliptic problem driven by the p-Laplacian differential operator and with a potential function which is only locally Lipschitz, not necessarily C¹ (hemivariational inequality). Using the nonsmooth critical point theory of Chang, we obtain two strictly positive solutions. One solution is obtained by minimization of a suitable modification of the energy functional. The second solution is obtained by generalizing a result of Brezis-Nirenberg about the local C¹₀-minimizers versus the local H¹₀-minimizers of a C¹-functional. Mathematics Subject Classification (2000) 35J50, 35J85, 35R70     

Multiplicity and symmetry results for a nonlinear Schrödinger equation with non‐local regional diffusion

In this paper, we are interested in the nonlinear Schrödinger equation with non‐local regional diffusion (1) where 0 < α < 1 and is a variational version of the regional Laplacian, whose range of scope is a ball with radius ρ(x) > 0. The novelty of this paper is that, assuming f is of subquadratic growth as |u|→+∞, we show that 1 possesses infinitely many solutions via the genus properties in critical point theory. Furthermore, if f(x,u) = γa(x)|u|^{γ ? 1}, where is a nonincreasing radially symmetric function, then the solution of 1 is radially symmetric. Copyright © 2015 John Wiley & Sons, Ltd.     

基于基准可靠度和预防维修次数上限的两参数预防维修策略

本文研究了一类修旧非新的两参数预防维修策略.在预防维修依赖于基准可靠度R的条件下,利用系统的相关可靠性指标建立了平均费用关于R和N(预防维修次数上限)的函数关系.进一步找到了该函数的最小值点,即得到了最优策略(R,N)*.同时通过实例说明了本文的维修策略优于文献[8].     

On a ‐Kirchhoff equation with critical exponent and an additional nonlocal term via truncation argument

We study existence and multiplicity of solutions of the following nonlocal ‐Kirchhoff equation with critical exponent, via truncation argument on the Sobolev space with variable exponent, where Ω is a bounded smooth domain of , , M, f are continuous functions, , and are real parameter.     

O(n) tricriticality in two dimensions

We present exact results for several universal parameters of the tricritical O(n) model in two dimensions. The results apply to the range −2⩽n⩽3/2, and include the central charge and three scaling dimensions, associated with temperature, magnetic field and the introduction of an interface. Since these results are based on an extrapolation of known relations between the O(n) and the Potts model, they cannot be considered as rigorous. For this reason, we perform an accurate numerical analysis of the central charge and the critical exponents. This analysis, which is based on transfer-matrix calculations on the honeycomb lattice, is in a full and precise agreement with the theoretical predictions.      

Holographic Superconductors with Nonlinear Arcsin‐Electrodynamics

Holographic s‐wave superconductors with nonlinear arcsin‐electrodynamics in the background of Schwarzschild anti‐de Sitter black holes are investigated. The analytical Sturm–Liouville eigenvalue problem is explored and the scalar and electromagnetic fields are assumed not to influence the background metric (the probe limit). The critical temperatures of phase transitions depending on the parameter of the model are obtained. It is shown that in this case, the condensation formation becomes easier compared to Born–Infeld nonlinear electrodynamics. The critical exponent near the critical temperature is calculated, which is 1/2. With the help of the matching method, analytic expressions for the condensation value and the critical temperature are derived. The real and imaginary parts of the conductivity in the model, making use of an analytical method, are computed.     

Event-by-event efficiency fluctuations and efficiency correction for cumulants of superposed multiplicity distributions in relativistic heavy-ion collision experiments

We performed systematic studies on the effects of event-by-event efficiency fluctuations on efficiency correction for cumulant analysis in relativistic heavy-ion collision experiments. Experimentally, particle efficiencies of events measured under different experimental conditions should be different. For fluctuation measurements, the final event-by-event multiplicity distributions should be the superposed distributions of various type of events measured under different conditions. We demonstrate efficiency fluctuation effects using numerical simulation, in which we construct an event ensemble consisting of events with two different efficiencies. By using the mean particle efficiencies, we find that the efficiency corrected cumulants show large deviations from the original inputs when the discrepancy between the two efficiencies is large. We further studied the effects of efficiency fluctuations for the cumulants of net-proton distributions by implementing the UrQMD events of Au+Au collisions at sNN~(1/2) = 7.7 GeV in a realistic STAR detector acceptance. We consider the unequal efficiency in two sides of the Time Projection Chamber(TPC), multiplicity dependent efficiency, and the event-by-event variations of the collision vertex position along the longitudinal direction(V_z). When the efficiencies fluctuate dramatically within the studied event sample,the effects of efficiency fluctuations have significant impacts on the efficiency corrections of cumulants with the mean efficiencies. We find that this effect can be effectively suppressed by binning the entire event ensemble into various sub-event samples, in which the efficiency variations are relatively small. The final efficiency corrected cumulants can be calculated from the weighted average of the corrected factorial moments of the sub-event samples with the mean efficiencies.     

势阱中玻色-爱因斯坦凝聚气体的势场有效性和粒子数极限判据

基于最小动量态上的玻色-爱因斯坦凝聚(简称BEC)，给出了指数吸引势场中超冷玻色原子气体的势场有效性和势阱中所装载的原子数目极限判据.此判据给出了当所装载的原子数确定时，所需要的势场强度；或势场给定时，所装载的原子数目的极限. 关键词： 玻色-爱因斯坦凝聚 临界温度 最小动量态     

Heat transfer from a hot moving steel plate by using Cu-Al layered double hydroxide nanofluid based air atomized spray

The current research is focused on the cooling of a hot moving steel plate by using air atomized spray cooling technique. A new type of coolant, Cu-Al LDH nanofluid, has been prepared and used for heat flux removal. Preparation method of nanofluid and its characteristics has been reported. The cooling effectiveness is reported in terms of cooling rate by varying the concentration of nanofluid in five levels. The results indicate that the cooling rate increases at very low concentration of LDH with respect to base fluid. However, beyond a certain concentration a decreasing trend of cooling rate has been observed.

Abbreviations: CHF: Critical heat flux; HTC: Heat transfer coefficients; LDH:Layered double hydroxide; TEM: Transmission electron microscopy.     

London penetration depth and thermal fluctuations in the sulphur hydride 203 K superconductor

Recently, compressed H₂S has been shown to become superconducting at 203 K under a pressure of 155 GPa. One might expect fluctuations to dominate at such temperatures. Using the magnetisation critical current, we determine the ground‐state London penetration depth, λ₀=189 nm, and the superconducting energy gap, Δ₀=27.8 meV, and find these parameters are similar to those of cuprate superconductors. We also determine the fluctuation temperature scale, K, which shows that, unlike the cuprates, of the hydride is not limited by fluctuations. This is due to its three dimensionality and suggests the search for better superconductors should refocus on three‐dimensional systems where the inevitable thermal fluctuations are less likely to reduce the observed .