How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main argument brought in favor of this statement.     

Thermal effects and band spreading in capillary electro-separation

Summary Four Capillary Electroseparation methods are distinguished. All have an ultimate efficiency limited only by axial diffusion and are in principle capable of achieving 10⁶ plates in <1 hour.The main limitation to performance arises from Ohmic heating of the electrolyte. While forced convection at 10ms^–1 is recommended to keep tubes cool, the parabolic temperature profile within the electrolyte limits the tube bore which can be used. A simple limiting expression is derived: (d_c/m)³ (E/kV m^–1)³ (c/mol dm^–3) <3.3×10⁹.Values of constants underlined     

某些离解能、电子亲合能等的G2计算与评价

PoPle及其合作者创立的Gaussian再简称GZ）理论［‘－’］，以其相对可靠的化学精度和相应较小的计算量已经引起了实验和理论化学家们的广泛关注问．p。ple等人在他们的GZ文章中强调了GZ的理论计算结果在研究离解能等化学问题中与精确实验数据之间的偏差普遍不大于全8．狄J规厂‘．我们近期的研究表明＊’1，＊2和优（＊则在计算一般化学反应能量中，绝大多数情况下，分别都能保证结果与实验偏差在全8．4和士13kJ·mol‘以内．近年来，已有大量的研究工作表明，GZ的理论结果已广泛用于未知实验数据的预测、已有实验数据的评价和修正等…     

The circular chemistry conceptual framework: A way forward to sustainability in industry 4.0

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Green chemistry and sustainability metrics in the pharmaceutical manufacturing sector

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A path following algorithm for a class of convex programming problems

We present a primal-dual path following interior algorithm for a class of linearly constrained convex programming problems with non-negative decision variables. We introduce the definition of a Scaled Lipschitz Condition and show that if the objective function satisfies the Scaled Lipschitz Condition then, at each iteration, our algorithm reduces the duality gap by at least a factor of (1–/n), where is positive and depends on the curvature of the objective function, by means of solving a system of linear equations which requires no more than O(n³) arithmetic operations. The class of functions having the Scaled Lipschitz Condition includes linear, convex quadratic and entropy functions.     

Computational complexity of LCPs associated with positive definite symmetric matrices

Murty in a recent paper has shown that the computational effort required to solve a linear complementarity problem (LCP), by either of the two well known complementary pivot methods is not bounded above by a polynomial in the size of the problem. In that paper, by constructing a class of LCPs—one of ordern forn 2—he has shown that to solve the problem of ordern, either of the two methods goes through 2 ⁿ pivot steps before termination.However that paper leaves it as an open question to show whether or not the same property holds if the matrix,M, in the LCP is positive definite and symmetric. The class of LCPs in whichM is positive definite and symmetric is of particular interest because of the special structure of the problems, and also because they appear in many practical applications.In this paper, we study the computational growth of each of the two methods to solve the LCP, (q, M), whenM is positive definite and symmetric and obtain similar results.This research is partially supported by Air Force Office of Scientific Research, Air Force Number AFOSR-78-3646. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon.     

Second order algorithms for the posynomial geometric programming dual,part I: Analysis

In this paper we analyse algorithms for the geometric dual of posynomial programming problems, that make explicit use of second order information. Out of two possible approaches to the problem, it is shown that one is almost always superior. Interestingly enough, it is the second, inferior approach that has dominated the geometric programming literature.This work was partially supported by the National Research Council of Canada, Grant A3552 and National Science Foundation Grant ENG78-21615.Earlier versions of this paper were presented at the Optimization Days Conference in Montreal (May 1976) and the TIMS meeting in Athens (July 1977).