Quantum-corrected finite entropy of noncommutative acoustic black holes

In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1$2+1$-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.     

Correlation functions from a unified variational principle: Trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.     

键阻断原理构建中孔A型沸石

采用不同类型的有机硅烷化SiO₂作为基本合成单元, 制备了具有晶内中孔的A型沸石。考察了反应碱度、Si/Al比、晶化时间等合成条件对产品的影响。结果表明, 甲氨基丙基三甲氧基硅烷是合成中孔A型沸石的最佳硅烷化试剂;硅烷化试剂的应用, 使中孔沸石晶化过程可以通过“键阻断原理”有效控制;沸石的中孔尺寸可以通过不同类型的有机硅烷化试剂进行调控; 一定范围内, 其外比表面积、中孔体积随SiO₂表面硅烷化度的增加而增加。通过沸石晶化过程中的“键阻断”, 可以制备具有晶内中孔的A型沸石。     

键阻断原理构建中孔A型沸石

采用不同类型的有机硅烷化SiO2作为基本合成单元,制备了具有晶内中孔的A型沸石。考察了反应碱度、Si/Al比、晶化时间等合成条件对产品的影响。结果表明,苯胺基丙基三甲氧基硅烷是合成中孔A型沸石的最佳硅烷化试剂;硅烷化试剂的应用,使中孔沸石晶化过程可以通过"键阻断原理"有效控制;沸石的中孔尺寸可以通过不同类型的有机硅烷化试剂进行调控;一定范围内,其外比表面积、中孔体积随SiO2表面硅烷化度的增加而增加。通过沸石晶化过程中的"键阻断",可以制备具有晶内中孔的A型沸石。     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.     

Tighter uncertainty principles for periodic signals in terms of frequency

In this study, we propose some new uncertainty principles for periodic signals with sharper lower bounds than those in the existing ones. The improved lower bounds, in particular, are related to the frequency of the signal. Three examples are employed to demonstrate sharpness of the new uncertainty principles. Copyright © 2014 John Wiley & Sons, Ltd.     

A stochastic control model of investment,production, and consumption on a finite horizon

In this paper, we consider a stochastic control problem on a finite time horizon. The unit price of capital obeys a logarithmic Brownian motion, and the income from production is also subject to the random Brownian fluctuations. The goal is to choose optimal investment and consumption policies to maximize the finite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. A dynamic programming principle is used to derive a time‐dependent Hamilton–Jacobi–Bellman equation. The Leray–Schauder fixed point theorem is used to obtain existence of solution of the HJB equation. At last, we derive the optimal investment and consumption policies by the verification theorem. The main contribution in this paper is the use of PDE technique to the finite time problem for obtaining optimal polices. Copyright © 2014 John Wiley & Sons, Ltd.     

复微分方程组的代数解

本文研究了一类复微分方程组的代数解的存在问题.利用最大模原理和Nevanlinna值分布理论,得到了一个结论,推广和改进了一些文献的结果,例子表明结论精确.