The GHS inequality and the Riemann hypothesis

LetV(t) be the even function on (–, ) which is related to the Riemann xi-function by (x/2)=4 _– exp(ixt–V(t))dt. In a proof of certain moment inequalities which are necessary for the validity of the Riemann Hypothesis, it was previously shown thatV'(t)/t is increasing on (0, ). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely thatV' is convex on [0, ). The possible relevance of the convexity ofV' to the Riemann Hypothesis is discussed.Communicated by Richard Varga.     

Generalized reinhardt domains

In this paper we investigate a class of Lie group actions on , the so-calledpolar actions, that naturally generalize the standard actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain containing the origin of we also compute its automorphism group. Supported in part by NSF Grant 8602020     

Optimal monotone hysteretic Markov policies in anM/M/1 queueing model with switching costs and finite time horizon

In anM/M/1 queueing model, a decision maker can choosem pairs of arrival- and service rates. He can change his action at any time epoch, a switch of action costs an amount depending on the size of the switch. Besides that there are continuously incurring costs. Over a finite time horizon, there exists an optimal monotone hysteretic Markov policy. This is shown essentially by the technique of time discretization.The work producing this article was done during a half year stay at the University of Leiden, The Netherlands, with Prof. Arie Hordijk. A technical report (a more detailled version of this article) was written there [6]. The opportunity for this stay was given by the University of Bonn, Germany, where the author, at that time, worked as scientific assistant of Prof. M. Schäl.     

Convergence rates for the approximations of the solutions to algebraic Riccati Equations with unbounded coefficients: case of analytic semigroups

Summary Approximations schemes for the solutions of the Algebraic Riccati Equations will be considered. We shall concentrate on the case when the input operator is unbounded and the dynamics of the system is described by an analytic semigroup. The main goal of the paper is to establish the optimal rates of convergence of the underlying approximations. By optimal, we mean such approximations which would reconstruct the optimal regularity of the original solutions as well as the best approximation properties of the finite-dimensional subspaces. It turns out that, if one aims to obtain the optimal rates in the case of unbounded input operators, the choice of the approximations to the generator, as well as to the control operator, is very critical. While the convergence results hold with any consistent approximations, the optimal rates require a careful selection of the approximating schemes. Our theoretical results will be illustrated by several examples of boundary/point control problems where the optimal rates of convergence are achieved with the appropriate numerical algorithms.Research partially supported by the NSF Grant DMS-8301668 and by the AFOSR Grant AFOSR 89-0511     

Finite elements for parabolic equations backwards in time

Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a boundary value problem in time-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.     

Simultaneous determination of C1−C8 n-alkyl acetates and corresponding mono-, di- and trichloroacetates on glass capillary columns with programmed temperature rise

Summary Gas chromatography of mixtures of aliphaticn-alkyl acetates (CH₃–COOR), chloroacetates (CHCl₂–COOR), dichloroacetates (CHCl₂–COOR) and trichloroacetates (CCl₃–COOR), where the alcohol chain length (R) varied between 1 and 8, has been studied on SE-30, Carbowax 20M and OV-351 glass capillary columns with programmed temperatures from 50°C at 2, 4, 6, 8 and 10°C/min. Compounds in the homologous series are eluted in the direct order from methyl ton-octyl acetate. The isomeric chloro esters are eluted on SE-30 according to their boiling points in the order: mono-, di- and trichloro isomer, whereas on polar columns di- and trichloro esters are eluted in the reverse order. The complete separation of all 32 individual components from the mixture could not be reached by any single column, the best separation occurred on SE-30. The mixture can, however, be separated by using columns with polar and non-polar stationary phases. The relative retention times for the compounds are given and the retention order discussed.     

A Comprehensive Review with Updated Future Perspectives on the Ethnomedicinal and Pharmacological Aspects of Moringa oleifera

Moringa oleifera is an ancient remedy plant, known as the miraculous plant due to its many prominent uses and significant health benefits. It is a nutrient-rich plant, with exceptional bioactive compounds, such as polyphenols that possess several medicinal properties. Many significant studies have been carried out to evaluate the ethnomedicinal and pharmacological properties of M. oleifera in various applications. Therefore, this comprehensive review compiles and summarizes important findings from recent studies on the potential properties of different parts of M. oleifera. The pharmacological properties of M. oleifera have been studied for various potential biological properties, such as cardio-protective, anti-oxidative, antiviral, antibacterial, anti-diabetic and anti-carcinogenic effects. Therefore, the potential of this plant is even more anticipated. This review also highlights the safety and toxicity effects of M. oleifera treatment at various doses, including in vitro, in vivo and clinical trials from human studies.     

HL-2M偏滤器结构动力学分析

用有限元软件分析了动载荷作用下的偏滤器结构动力学响应。通过对动力学和静力学计算结果的对比,确定载荷的动态放大因子。计算结果表明,所设计的偏滤器结构在瞬态电磁力载荷作用下能满足设计准则的要求。     

HL-2M装置等离子体放电反馈控制系统

通过对HL-2M装置极向场线圈的参数和初始等离子放电控制需求的分析,基于实时采集系统和反射内存实时数据传输的先进控制集成技术,完成了整个HL-2M初始等离子体放电反馈控制系统的设计。新系统实现了稳定的1ms控制周期和实时数据传输,同时解决了实时控制周期和数据传输的延迟。实验结果表明新设计的等离子控制系统能满足初始等离子体极向场线圈电流控制的需求。     

线性规划中大M法的参数M估值问题

在线性规划的单纯形法中,为求初始的可行基有著名的大M法,即惩罚因子法.在通常的运筹学教材中,只说明当M充分大时,大M法是有效的,并没有给出参数M的确切估计值.现给出一个确定的常数M0,并证明当M>M0时,大M法收敛于原问题的最优解.