单调Minkowski泛函与Henig真有效性的标量化

没有凸锥的闭性和点性假设,该文考虑由一般凸锥生成的单调Minkowski泛函并研究其性质.由此,在偏序局部凸空间的框架下,通过利用单调连续Minkowski泛函和单调连续半范,该文分别获得了一般集合及锥有界集合的弱有效点的标量化.利用此弱有效性的标量化,该文分别推导出一般集合及锥有界集合的Henig真有效点的标量化.进而,当序锥具备有界基时,该文获得局部凸空间中超有效性的一些标量化结果.最后,该文给出Henig真有效性和超有效性的稠密性结果.这些结果推广并改进了有关的已知结果.     

On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

The paper concerns L ¹-convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials (−4≤γ<0), with and without angular cutoff. We prove the time-averaged L ¹-convergence to equilibrium for all weak solutions whose initial data have finite entropy and finite moments up to order greater than 2+|γ|. For the usual L ¹-convergence we prove that the convergence rate can be controlled from below by the initial energy tails, and hence, for initial data with long energy tails, the convergence can be arbitrarily slow. We also show that under the integrable angular cutoff on the collision kernel with −1≤γ<0, there are algebraic upper and lower bounds on the rate of L ¹-convergence to equilibrium. Our methods of proof are based on entropy inequalities and moment estimates. E.A. Carlen work partially supported by US National Science Foundation grant DMS 06-00037. M.C. Carvalho work partially supported by POCI/MAT/61931/2004. X. Lu work partially supported by NSF of China grant 10571101.     

Modal analysis of a super-elliptical Bragg waveguide with a small number of periodic cladding layers based on a very simple analytical technology

Using a simple matrix method and replacing the boundary condition by a matrix equation, the characteristic equation of an unconventional Bragg waveguide, namely a super-elliptical Bragg waveguide, has been obtained analytically. Computed results are shown in the form of dispersion curves and are compared with the dispersion curves of a standard step index fiber and a standard Bragg fiber having circular core [V. Singh, B. Prasad, S.P. Ojha. Analysis of the modal characteristics of a Bragg fiber with a small number of claddings using a very simple analytical approach, Microw. Opt. Technol. Lett. 46 (2005) 271-275 [1]]. It is seen that the correspondence between the cutoff values for the standard step index fiber and the new super-elliptical Bragg fiber is quite close for the lowest mode under the weak guidance condition.     

Effect of curvature of the boundary on the modal dispersion of a single-mode dielectric waveguide of core cross-section bounded by involuted spirals

In this paper, we are presenting an analytical study of the effect of curvature of the spiral shape on the modal dispersion characteristics of the waveguide whose core cross-section is bounded by two involuted spirals of the form 1/r=ξθ, where ξ is a constant and represents the curvature of the spiral taken to design the waveguide into consideration. This study has been done under the weak guidance approximation. Analyzing the dispersion curves for different curvature we found that this waveguide supports only the single mode, and their cutoff value decreases as the the curvature of the spiral increases.     

Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions

Using a Wang-Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- (J_nn) and next-nearest-neighbor (J_nnn) antiferromagnetic interactions. We consider the case R=J_nnn/J_nn=1, for which the pure model is known to have a columnar ground state where rows of nearest-neighbor spins up and down alternate and undergo a weak first-order phase transition from the ordered to the paramagnetic state. With the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first-order phase transition to a second-order phase transition and using the Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging, under random bonds, continuous transition shows a strongly saturating specific heat behavior, corresponding to a negative exponent α, and belongs to a new distinctive universality class with ν=1.135(11), γ/ν=1.744(9), and β/ν=0.124(8). Thus, our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional (2d) systems without and with quenched disorder.     

Influences of CO2 laser annealing on mechanical and laser-induced damage properties of ZrO2 thin films

Zirconium dioxide (ZrO₂) thin films were deposited on BK7 glass substrates by the electron beam evaporation method. A continuous wave CO₂ laser was used to anneal the ZrO₂ thin films to investigate whether beneficial changes could be produced. After annealing at different laser scanning speeds by CO₂ laser, weak absorption of the coatings was measured by the surface thermal lensing (STL) technique, and then laser-induced damage threshold (LIDT) was also determined. It was found that the weak absorption decreased first, while the laser scanning speed is below some value, then increased. The LIDT of the ZrO₂ coatings decreased greatly when the laser scanning speeds were below some value. A Nomarski microscope was employed to map the damage morphology, and it was found that the damage behavior was defect-initiated both for annealed and as-deposited samples. The influences of post-deposition CO₂ laser annealing on the structural and mechanical properties of the films have also been investigated by X-ray diffraction and ZYGO interferometer. It was found that the microstructure of the ZrO₂ films did not change. The residual stress in ZrO₂ films showed a tendency from tensile to compressive after CO₂ laser annealing, and the variation quantity of the residual stress increased with decreasing laser scanning speed. The residual stress may be mitigated to some extent at proper treatment parameters.     

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system     

TEA CO2激光器序列带的输出特性

 采用双光栅谐振腔和增长放电增益区,进行了TEA CO₂激光器弱线输出特性研究。在CO₂,N₂,He气体体积比为0.16∶0.21∶0.63,总压强为57.3 kPa情况下,获得6条11 μm波长附近弱线(序列带和热带)激光输出,谱线脉宽为400 ns左右。研究了011-030带的P19线的输出波形和能量,结果表明：谱线输出能量随光栅中心的位移变化而变化,当光栅中心在放电区中心轴线上时输出最强,最大输出能量达几百mJ。     

基于弱相互作用的石墨化CNT/PMMA复合材料的热电传输性能

从理论上计算了碳纳米管(CNT)与聚甲基丙烯酸甲酯(PMMA)的相互作用及浸润性, 并测试了CNT/PMMA复合材料的电学、热学和光学性能. 发现石墨化CNT/PMMA复合材料具有较好的导热和导电性能, 其渗流阈值在0.8%左右, 当CNT质量分数为3%时, 复合材料的导热系数提高193%. 这种电学及热学性能的提高一方面与石墨化CNTs的规整结构有关, 另一方面与石墨化CNT-PMMA体系的弱相互作用、CNT间的有效接触以及高效的CNT网络输运性能有密切关系. 研究结果表明, 通过调控CNT与聚合物基体的表面性质、相互作用及浸润性, 可以有效地构建优化的CNT输运网络, 获得性能优异的功能复合材料.     

Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property

We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2^No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. Mathematics Subject Classification: 03B55, 03C90.