Existence and multiplicity of positive solutions for a class of singular Kirchhoff type problems with sign‐changing potential

In this paper, the existence and multiplicity of positive solutions are obtained for a class of Kirchhoff type problems with two singular terms and sign‐changing potential by the Nehari method.     

科学缓解学生心理压力 提升化学研究生培养质量

人才强国战略对研究生的综合素质培养有着越来越高的要求,而面对当前研究生承受各种压力、心理问题日益凸显的现状,不仅要重视研究生科研能力培养,更要重视其心理健康的发展,继而培养出全面发展的高素质人才。以吉林大学化学学科为依托,探讨化学研究生的心理压力问题,采用积极心理学方法进行分析,并采取针对措施,缓解化学研究生心理压力,促进研究生心理健康,提升研究生培养质量。     

掺杂对钠离子电池正极材料性能影响机制的研究

钠元素在地壳中的丰度是锂元素的1000倍,资源丰富,价格低廉。同时,钠离子电池负极可采用廉价的铝箔替代铜箔,且低温特性更加优异,在能量型、备用型储能场景均具有较好应用前景,因而钠离子电池被认为是下一代大规模储能技术的理想选择之一。然而,相对锂离子而言,钠离子较大的离子半径和质量极大限制了其在电极材料中的可逆脱嵌,导致电池的工作电压和能量密度相对较低。在钠离子电池材料体系中,正极材料的研究尤为需要长足的进步。本文对现有的典型钠离子电池正极材料进行了综述,包括层状金属氧化物、聚阴离子化合物和普鲁士蓝类化合物,并重点分析了掺杂对钠离子电池正极材料性能的影响。通过元素掺杂可提高材料的循环可逆性、增加其可逆容量、提升钠离子扩散动力学性能,能够在一定程度上改变晶格的性质,增强晶格稳定性、电子导电性、钠离子嵌脱动力学性能等。本文总结了掺杂应用在现有材料中获得的成果,并对正极材料未来的研究方向以及发展前景提出了展望。     

Total positivity and accurate computations with Gram matrices of Said-Ball bases

In this article, it is proved that Gram matrices of totally positive bases of the space of polynomials of a given degree on a compact interval are totally positive. Conditions to guarantee computations to high relative accuracy with those matrices are also obtained. Furthermore, a fast and accurate algorithm to compute the bidiagonal factorization of Gram matrices of the Said-Ball bases is obtained and used to compute to high relative accuracy their singular values and inverses, as well as the solution of some linear systems associated with these matrices. Numerical examples are included.     

Multiple Positive Solutions for a Nonlinear Elliptic Equation Involving Hardy–Sobolev–Maz'ya Term

In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy–Sobolev–Maz'ya term:-Δu- λu/|y|2=|u|pt-1u/|y|t+ μf(x), x ∈Ω,where Ω is a bounded domain in RN(N ≥ 2), 0 ∈Ω, x =(y, z) ∈ Rk× RN-kand pt =N +2-2t N-2(0 ≤ t ≤2). For f(x) ∈ C1(Ω)\{0}, we show that there exists a constant μ* 0 such that the problem possessesat least two positive solutions if μ∈(0, μ*) and at least one positive solution if μ = μ*. Furthermore,there are no positive solutions if μ∈(μ*, +∞).     

Multiple positive solutions for semi‐linear elliptic systems involving sign‐changing weight

In this paper, we study the multiplicity results of positive solutions for a semi‐linear elliptic system involving critical growth terms. With the help of Nehari manifold and Ljusternik‐Schnirelmann category, we investigate how the coefficient h(x) of the critical nonlinearity affects the number of positive solutions of that problem and get a relationship between the number of positive solutions and the topology of the global maximum set of h. Copyright © 2014 John Wiley & Sons, Ltd.     

无创正压通气治疗COPD 合并肺源性心脏病的疗效及对血浆C反应蛋白和脑钠素水平的影响

目的 探讨无创正压通气对慢性阻塞性肺疾病（COPD）合并肺源性心脏病的疗效和对患者血浆C 反应蛋白（CRP）和脑钠素（BNP）水平的影响。方法 将2012 年1 月到2014 年1月收治的120 例COPD 急性加重期合并肺源性心脏病患者随机分为观察组（60 例）和对照组（60 例）,对照组给予常规治疗,观察组在此基础上给予无创正压通气治疗。治疗前和治疗3d 后分别进行动脉血气分析,比较患者血pH 值、PaO2、PaCO2和动脉血氧饱和度（SaO2）在治疗前后的改变,并监测治疗前后血浆CRP和BNP 水平的改变。结果 治疗3d 后,两组患者的pH 值、PaO2、SaO2均较治疗前明显升高,PaCO2较治疗前明显降低,而观察组患者治疗后的动态血气分析指标的改善情况明显优于对照组,均有统计学差异（均P＜0.05）。两组患者的血浆CRP 和BNP 水平均较治疗前明显降低,而观察组患者治疗后的血浆CRP 和BNP 水平明显低于对照组,均有统计学差异（均P＜0.05）。结论 无创正压通气治疗COPD 合并肺源性心脏病,能够有效改善血气指标,提高SaO2和PaO2,同时降低血浆CRP 和BNP 的水平,值得在临床推广应用。     

Positivity of the generalized translation associated with the q-Hankel transform and applications

A new formulation of the Graf-type addition formula related to the third Jackson q-Bessel function gives a solution for the problem of the positivity of the generalized q-translation operator associated with the q-Hankel transform. Next some applications in q-theory are treated, for instance the relationship between the q-Bessel- positive and negative-definite functions. We also show how the positivity of the q-Bessel translation operator plays a central role in q-Fourier analysis, namely in the study of Markov operators in the q-context. The paper concludes with the nonnegative product linearization of the q^?2-Lommel polynomials.     

Pareto严格稳定分布在保险理赔中的应用

本文研究了Pareto严格稳定分布在保险中的应用.利用极大似然估计的方法得到了Pareto严格稳定分布,正态分布和Pareto分布的参数估计.根据信息准则,表明Pareto严格稳定分布能够较好地拟合保险数据.