Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory

No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures ρ on Ω having zero mean value and dispersion σ²(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ²(ρ) = hⁿ (for n = 2 we obtain the conventional quantum formalism).     

激发相干态在耗散量子通道中Husimi函数的演化

基于有序算符内的积分技术和量子力学相干态表象,本文研究了激发相干态在耗散量子通道中的Husimi函数的演化情况,首次推导了Husimi函数在耗散量子通道中的解析表达式,并通过绘制图形讨论了各种参数对Husimi函数的影响。     

Morse inequalities, a function space integral approach

In this paper we prove the Morse inequalities in the non-degenerate and degenerate cases. Like the approach of J.-M. Bismut, ours is based on the idea suggested by Witten. In fact, if anything, our approach is closer to Witten's original idea than Bismut's.     

On the elliptic equation on complete Riemannian manifolds and their geometric applications

We study the elliptic equation on complete noncompact Riemannian manifolds with nonnegative. Three fundamental theorems for this equation are proved in this paper. Complete analyses of this equation on the Euclidean space and the hyperbolic space are carried out when is a constant. Its application to the problem of conformal deformation of nonpositive scalar curvature will be done in the second part of this paper.

     

Application of ZnO nanorods loaded on activated carbon for ultrasonic assisted dyes removal: Experimental design and derivative spectrophotometry method

A method based on application of ZnO nanorods loaded on activated carbon (ZnO-NRs-AC) for adsorption of Bromocresol Green (BCG) and Eosin Y (EY) accelerated by ultrasound was described. The present material was synthesized under ultrasound assisted wet-chemical method and subsequently was characterized by FE-SEM, TEM, BET and XRD analysis. The extent of contribution of conventional variables like pH (2.0–10.0), BCG concentration (4–20 mg L⁻¹), EY concentration (3–23 mg L⁻¹), adsorbent dosage (0.01–0.03 g), sonication time (1–5 min) and centrifuge time (2–6 min) as main and interaction part were investigated by central composite design under response surface methodology. Analysis of variance (ANOVA) was adapted to experimental data and guide the best operational conditions mass by set at 6.0, 9 mg L⁻¹, 10 mg L⁻¹, 0.02 g, 4 and 4 min for pH, BCG concentration, EY concentration, adsorbent dosage, sonication and centrifuge time, respectively. At these specified conditions dye adsorption efficiency was higher than 99.5%. The suitability and well prediction of optimum point was tested by conducting five experiments and respective results revel that RSD% was lower than 3% and high quality of fitting was confirmed by t-test. The experimental data were best fitted in Langmuir isotherm equation and the removal followed pseudo second order kinetics. The experimentally obtained maximum adsorption capacities were estimated as 57.80 and 61.73 mg g⁻¹ of ZnO-NRs-AC for BCG and EY respectively from binary dye solutions. The mechanism of removal was explained by boundary layer diffusion via intraparticle diffusion.     

Uniqueness and Sharp Estimates on Solutions to Hyperbolic Systems with Dissipative Source

Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension were constructed (cf. Christoforou, 2006 Christoforou , C. ( 2006 ). Hyperbolic systems of balance laws via vanishing viscosity . J. Diff. Eq. 221 ( 2 ): 470 – 541 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) via the vanishing viscosity method under the assumption that the source term g is dissipative. In this article, we establish sharp estimates on the uniformly Lipschitz semigroup 𝒫 generated by the vanishing viscosity limit in the general case which includes also nonconservative systems. Furthermore, we prove uniqueness of solutions by means of local integral estimates and show that every “viscosity solution” can be constructed as a limit of vanishing viscosity approximations.     

Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces

The stochastic integrals of M- type 2 Banach valued random functions w.r.t. compensated Poisson random measures introduced in (Rüdiger, B., 2004, In: Stoch. Stoch. Rep., 76, 213–242.) are discussed for general random functions. These are used to solve stochastic integral equations driven by non Gaussian Lévy noise on such spaces. Existence and uniqueness of the path wise solutions are proven under local Lipshitz conditions for the drift and noise coefficients on M-type 2 as well as general separable Banach spaces. The continuous dependence of the solution on the initial data as well as on the drift and noise coefficients are shown. The Markov properties for the solutions are analyzed.     

Dynkin Diagram Sequences and Stabilization Phenomena

We continue the study of stabilization phenomena for Dynkin diagram sequences initiated in the earlier work of Kleber and the present author. We consider a more general class of sequences than that of this earlier work, and isolate a condition on the weights that gives stabilization of tensor product and branching multiplicities. We show that all the results of the previous article can be naturally generalized to this setting. We also prove some properties of the partially ordered set of dominant weights of indefinite Kac–Moody algebras, and use this to give a more concrete definition of a stable representation ring. Finally, we consider the classical sequences B _n , C _n , D _n that fall outside the purview of the earlier work, and work out some easy-to-describe conditions on the weights which imply stabilization.     

Analysis of the breakdown mechanism for an ultra high voltage high-side thin layer silicon-on-insulator p-channel low-density metal-oxide semiconductor

This paper discusses the breakdown mechanism and proposes a new simulation and test method of breakdown voltage(BV) for an ultra-high-voltage(UHV) high-side thin layer silicon-on-insulator(SOI) p-channel lateral double-diffused metal-oxide semiconductor(LDMOS).Compared with the conventional simulation method,the new one is more accordant with the actual conditions of a device that can be used in the high voltage circuit.The BV of the SOI p-channel LDMOS can be properly represented and the effect of reduced bulk field can be revealed by employing the new simulation method.Simulation results show that the off-state(on-state) BV of the SOI p-channel LDMOS can reach 741(620) V in the 3-μm-thick buried oxide layer,50-μm-length drift region,and at 400 V back-gate voltage,enabling the device to be used in a 400 V UHV integrated circuit.     

随机过程数值仿真的精度实验与分析

为了考核随机过程数值仿真中采用的混沌多项式展开,小波动态自适应网格等的可靠性和近似程度,本文构造了一个具有解析解的随机过程,随后进行数值仿真。比较了数值仿真结果与解析解,证明两者是相互一致的。说明所采用的数值仿真方法是成立和近似度是可以接受的。所进行比较的随机过程解析解是相对比较简单的,当对更复杂的情况需要进一步数值实验验证。在文中并讨论了影响数值仿真精度和增加数值仿真工作难度的因素。