Image space analysis of generalized fractional programs

The solution of a particular nonconvex program is usually very dependent on the structure of the problem. In this paper we identify classes of nonconvex problems involving either sums or products of ratios of linear terms which may be treated by analysis in a transformed space. In each class, the image space is defined by a mapping which associates a new variable with each original ratio of linear terms. In the image space, optimization is easy in certain directions, and the overall solution may be realized by sequentially optimizing in these directions.In addition to these ratio problems, we also show how to use image space analysis to treat the subclass of problems whose objective is to optimize a product of linear terms. For each class of nonconvex problems, we present an algorithm that locates global solutions by computing both upper and lower bounds on the solution and then solving a sequence of linear programming sub-problems. We also demonstrate the algorithms described in this paper by solving several example problems.     

On invexity-type nonlinear programming problems

In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, )-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.The author wishes to thank the referee for helpful comments.     

STRONG DERIVATIVE AND ITS CONSEQUENCES

We introduce strong derivative, the corresponding Z-integrable and other related concepts. Also, we give an improved version of the fundamental theorem of calculus.     

A Review of Fractional Order Entropies

Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful.     

Fractionally differenced models for water quality time series

This paper deals with the selection and evaluation of statistical techniques for use in the modeling and forecasting of water quality time series. The focus is on statistical concepts relevant to the analysis of flows and concentrations. A selection of time series procedures has been used for auditing water quality archival data, including the screening of data sets, correlation and spectrum calculations, and iterative model fitting. A summary is provided of experience with analyzing archival data on the Niagara River and the use of a fractionally differenced model.This paper is the result of a study performed for the International Joint Commission, United States and Canada. The authors gratefully acknowledge the direction and support provided by Dr. Joel L. Fisher.     

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

含吡啶(噻唑)甲基的哌嗪类化合物的合成及生物活性

采用活性基团拼接原理, 分别以2-氯-5-氯甲基吡啶和2-氯-5-氯甲基噻唑为原料, 经过氮烷基化和加成反应, 得到系列含吡啶甲基或噻唑甲基的哌嗪类化合物. 初步测试结果表明: 部分化合物表现出较弱的除草活性和杀豆蚜活性, 但对孑孓显示出较高的的杀灭活性, 其中4f在50 mg/L的浓度下对孑孓的杀死率可达100%.     

Characteristics of high energy interactions II. Production spectra of Gamma-rays in graphite

Twenty high energy nuclear interactions produced in the graphite units of an emulsion chamber were recorded. The emulsion chamber was exposed to cosmic rays at an atmospheric depth of 10 g cm⁻² for about 7 hr over Hyderabad, India. Fourteen interactions which radiated energyΣ E _r⩾1000 GeV in the form ofγ-rays were analysed in detail. The median energy 〈Σ E _r〉 of the interactions was 1600 GeV. Results concerning the multiplicity, the transverse and longitudinal momentum distributions, and the fractional energy distribution ofγ-rays in these interactions are presented. The average transverse momentum ofπ ⁰—mesons <pt _π ⁰> is found to increase very slowly with the primary energyE ₀ and it can be approximated by the function <pt _π ⁰>=0·238E ₀ ^0.06 .     

4种等温物态方程适用性的比较研究

 通过分析现有文献,认为4种两参数的物态方程在高压物理研究中较为流行,它们是Vinet、Baonza、Morse和Born-Meyer（BM）方程。将这4种方程用于拟合50种材料的实验压缩数据,得出了零压下压缩模量及其一阶压力导数的优化取值,并计算了4种方程的平均压力误差。结果表明,Morse方程的精度最高,对50种材料的平均拟合误差为0.557 6%;BM方程次之,平均误差为0.615 1%;Vinet和Baonza方程的误差大一些,分别为0.788 9%和0.833 3%。对8种典型材料计算了压力误差随压强变化的曲线,所得结果与平均误差的趋势一致,也是Morse方程的精度最高。在宽广压力范围的高压物态方程研究中,推荐使用Morse方程。