Remark on an infinite semipositone problem with indefinite weight and falling zeros

In this work, we consider the positive solutions to the singular problem $$ \left\{\begin{array}{ll} -\Delta u = am(x)u-f(u) - \dfrac{c}{u^{\alpha}} & {\rm in}\;\Omega,\\ u=0 & {\rm on}\; \partial\Omega, \end{array} \right. $$ where 0?<?α?<?1,a?>?0 and c?>?0 are constants, Ω is a bounded domain with smooth boundary $\partial\Omega$ , Δ is a Laplacian operator, and $f:[0,\infty] \longrightarrow{\mathbb R}$ is a continuous function. The weight functions m(x) satisfies m(x)?∈?C(Ω) and m(x)?>?m ₀?>?0 for x?∈?Ω and also ||m||_?∞??=?l?<?∞. We assume that there exist A?>?0, M?>?0, p?>?1 such that alu???M?≤?f(u)?≤?Au ^p for all u?∈?[0,?∞?). We prove the existence of a positive solution via the method of sub-supersolutions when $m_{0}a>\frac{2\lambda_{1} }{1+\alpha}$ and c is small. Here λ ₁ is the first eigenvalue of operator ??Δ with Dirichlet boundary conditions.     

A DIRECT NUMERICAL SIMULATION OF CHANNEL FLOW TRANSITION UNDER AN EXTERNAL BODY FORCE

This research seeks to increase our understanding on the laminar-turbulent transition under an external body force. Direct numerical simulation by the spectral method with a weak formulation is used to solve the transient 3-D Navier-Stokes equations. Initial disturbances consist of the finite-amplitude 2-D Tollmien-Schlichting wave and two 3-D oblique waves. Competitions among different modes were computed during transition for different Richardson numbers.

It is found that the body force can modify the transition mechanism of flows between two vertical plates. The body force was found to hasten the formation of three-dimensional flow. A non-laminar flow induced by the body force may present when the background flow is still laminar.     

磁场热处理对含钴的尖晶石型铁氧体共振线宽的影响

本文在Haas-Calln所提出的,由于从一个离子到另一个离子的自旋-轨道互作用的变化而引起的铁磁子散射的机构的基础上,考虑了含少量钴的正型尖晶石型铁氧体或Fe₃O₄内,磁场热处理对铁磁共振线宽的影响。由于钴离子在八面体位上有了择优分布,对共振线宽的贡献除了各向同性的部分外,还出现了一各向导性的部分,后者是热处理时所加磁场的方向及M的方向的函数。每百分之一的钴在正型铁氧体中所导致的最大与最小的线宽间的差值约为4奥。     

Analytic Feynman Integrals of Functionals in a Banach Algebra Involving the First Variation

This paper deals with the analytic Feynman integral of functionals on a Wiener space. First the authors establish the existence of the analytic Feynman integrals of functionals in a Banach algebra S_α. The authors then obtain a formula for the first variation of integrals. Finally, various analytic Feynman integration formulas involving the first variation are established.     

Purification and Characterization of Cyclic AMP-Binding Protein from Ganoderma lucidum

Cyclic AMP-binding protein was purified 30 fold from the mycelia of Ganoderma lucidum by the methods of ammonium sulfate precipitation, DEAE-cellulose, phospho-cellulose ion exchange chromatography and Sephacryl S-100 gel filtration. The molecular mass of the purified protein is 34.5 kDa and 17 kDa by Sephacryl S-100 gel filtration and SDS-ployacrylamide gel electrophoresis, respectively. From these results it is suggested that the protein has a homometric dimmer structure. The pI of the purified protein is pH 8.2 by native isoelectric focusing gel. The half-life of the protein activity in 10% glycerol at 4 ℃ is 7 d in crude extract, but its half-life is only 3 d under purifying conditions. The optimal conditions of the protein activity are at 1 ℃ and pH 7.5. Its activity is increased 6 times by 1 mmol/L Zn^2 and is slightly inhibited by cGMP,Cu^2 and Mn^2 .     

Stability of a simple Levi–Civitá functional equation on non-unital commutative semigroups

In this paper, we study the Hyers–Ulam stability of a simple Levi–Civitá functional equation f(x+y)=f(x)h(y)+f(y) and its pexiderization f(x+y)= g(x) h(y)+k(y) on non-unital commutative semigroups by investigating the functional inequalities |f(x+y)?f(x)h(y)?f(y)|≤?? and |f(x+y)?g(x)h(y)?k(y)|≤??, respectively. We also study the bounded solutions of the simple Levi–Civitá functional inequality.     

Application of Modern Colour Measurement Dervices in Coloration Industries

In colour measurement ralated industry, reflectance spectrophotometer is the one of the popular measuring machine for measuring colour and quality control. Colour communications is frequently confusing. This is because the colour appearance is subject to the influence of at least three different phenomena: the light source, the object and the visual system. The variation in either the radiant quantity or the spectral distribution of the source can alter the observed colour. Because of this reason, the objective quantitative tool, colour measurement equipment and communication method; become more important in evaluating of the colour. In fact, based on the advanced in computer system and electronic device, the colour measurement becomes more and more accuracy, especially in spectrophotometer measurement. In this paper, we will focus on the review of modern spectrophotometers in coloration industries.     

关于 STURM-LIOUVILLE 方程的一些概率结果

本文研究 Sturm-Liouville 方程 f″+2qf=0.我们给出了该方程的 Neumann 问题解的概率表示.此表示涉及到 Feynman-Kac 泛函及在0与1处的局部时,特别是包含了一类新的“穿梭”停时.