Singular continuous Floquet operator for periodic quantum systems

Consider the Floquet operator of a time independent quantum system, acting on a separable Hilbert space, periodically perturbed by a rank one kick: e−iH₀Te−iκT|?〉〈?| where T is the period, κ the coupling constant, and H₀ is a pure point self-adjoint operator, bounded from below. Under some hypotheses on the vector ?, cyclic w.r.t. H₀ we prove the following:

•

If the gaps between the eigenvalues (λn) are such that λn+1−λn?Cn−γ for some γ∈]0,1[ and C>0, then the Floquet operator of the perturbed system is purely singular continuous T-a.e.

•

If H₀ is the Hamiltonian of the one-dimensional rotator on L²(R/T₀Z) and the ratio is irrational, then the Floquet operator is purely singular continuous as soon as κT≠0(2π).

We also establish an integral formula for the family .     

Operational variables of size exclusion columns with semirigid and rigid packings

Systematic studies on operation variables affecting GPC separations using the semirigid Microstyragel (Waters Associates) and the rigid silica packings (DuPont) of about equivalent porosity are reported. The dependence of (a) flow rate, (b) injection volume, and (c) concentration on elution volume and theoretical plates are examined.     

二自由度反射式光纤传感探头的结构设计

采用五光纤特殊排列方式,研制了全自动补偿光纤二自由度传感探测器.分析了二自由度的探测方法,给出了可能的结构排列方案.理论上,给出了探测响应函数,与实验结果进行了对比.可用于二自由度非接触测量场合。     

用连续记录的方法测量高Tc超导材料的转变温度

本文介绍了用连续测量和记录的方法，准确测量高Ｔｃ超导材料的转变温度和实验装置。     

高精度光学对准测量装置的设计

设计了一套光学对准测量装置,该装置主要由面阵CCD相机、光学镜头、图像处理模块、LED红光光源、球面反光镜组成。介绍了测量原理,测量目标采用等腰三角形排列,通过面阵CCD对目标所反射的图像进行采集,由图像处理模块对该图像进行实时处理,能够同时得到X、Y、Z以及旋转角度等四维坐标数据。推导了光斑图像坐标和被测平面距离等计算公式,并进行了对准精度分析。结果表明,该装置位置误差〈1mm,角度误差为0．24°,实现了高精度、自动、快速对准测量。     

目标表面发射率对红外热像仪测温精度的影响

介绍了红外热像仪测温原理,分析了影响红外热像仪测温精度的因素,计算了不同表面发射率下红外热像仪的测温误差曲线。理论分析表明,目标表面发射率越高,红外热像仪测温精度越高。实验改变表面发射率的设置,计算了不同表面发射率对应的总辐射亮度,得到TP8型长波红外热像仪能够精确测温时,目标表面发射率必须大于0.5的结果。最后,对表面发射率分别为0.96、0.93和0.3的3种材料进行实际测温,结果表明,材料表面发射率较高时,红外热像仪具有较好的测温精度。     

ON JENSEN’S INEQUALITY FOR g-EXPECTATION

Briand et al. gave a counterexample showing that given g, Jensen's inequalityfor g-expectation usually does not hold in general. This paper proves that Jensen'sinequality for g-expectation holds in general if and only if the generator g(t,z) issuper-homogeneous in z. In particular, g is not necessarily convex in z.     

Curved fronts in the Belousov–Zhabotinskii reaction–diffusion systems in R2

In this paper we consider a diffusion system with the Belousov–Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in ${\mathbb{R}}^2$ by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in ${\mathbb{R}}^2$.     

An adjustable approach to fuzzy soft set based decision making

Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy-Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated.     

Comparison of two randomized policy M/G/1 queues with second optional service, server breakdown and startup

The problem addressed in this paper is to compare the minimum cost of the two randomized control policies in the M/G/1 queueing system with an unreliable server, a second optional service, and general startup times. All arrived customers demand the first required service, and only some of the arrived customers demand a second optional service. The server needs a startup time before providing the first required service until the system becomes empty. After all customers are served in the queue, the server immediately takes a vacation and the system operates the (T, p)-policy or (p, N)-policy. For those two policies, the expected cost functions are established to determine the joint optimal threshold values of (T, p) and (p, N), respectively. In addition, we obtain the explicit closed form of the joint optimal solutions for those two policies. Based on the minimal cost, we show that the optimal (p, N)-policy indeed outperforms the optimal (T, p)-policy. Numerical examples are also presented for illustrative purposes.