Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

On the regulator problem for linear degenerate control systems

In this paper, we study the finite-time regulator problem for linear, autonomous, degenerate systems, i.e., systems described by the differential equation with det(K)=0. Two investigations of the regulator problem are presented, which depend on the quadratic cost associated with the differential equation.This work was performed under the auspices of the National Research Council of Italy, Gruppo Nazionale per l'Analisi Funzionale e le Sue Applicazioni, Rome, Italy.     

The alternating basis algorithm for assignment problems

The purpose of this paper is to present a new primal extreme point algorithm for solving assignment problems which both circumvents and exploits degeneracy. The algorithm is based on the observation that the degeneracy difficulties of the simplex method result from the unnecessary inspection of alternative basis representations of the extreme points. This paper characterizes a subsetQ of all bases that are capable of leading to an optimal solution to the problem if one exists. Using this characterization, an extreme point algorithm is developed which considers only those bases inQ. Computational results disclose that the new algorithm is substantially more efficient than previously developed primal and primal-dual extreme point (simplex) methods for assignment problems.     

On affine scaling algorithms for nonconvex quadratic programming

We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.     

ε-optimality criteria for convex programming problems via exact penalty functions

In this paper, we present-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved. We assume the solvability of neither the convex problem nor the dual problem. To derive our criteria, we estimate the size of the penalty parameter in terms of an-solution for the dual problem.     

Convexlike and concavelike conditions in alternative,minimax, and minimization theorems

Convexlike and concavelike conditions are of interest for extensions of the Von Neumann minimax theorem. Since the beginning of the 80's, these conditions also play a certain role in deriving generalized alternative theorems of the Gordan, Motzkin, and Farkas type and Lagrange multiplier results for constrained minimization problems.In this paper, we study various known convexlike conditions for vector-valued functions on a set and investigate convexlike and concavelike conditions for real-valued functions on a product setC×D, where we are mainly interested in the relationships between these conditions. At the end of the paper, we point out several conclusions from our results for the above-mentioned mathematical fields.The author is indebted to Dr. R. Reemtsen and Dr. V. Jeyakumar for their helpful comments during the preparations of this paper.     

Ab initio studies of the protonation of CO,N2 and NO+: Calculation of the minimum energy reaction paths

Ab initio molecular orbital calculations employing a 4-31G basis set have been used to study the minimum energy paths for the formation of HCO⁺, COH⁺, and HCOH²⁺ from CO by protonation. The protonation of N₂ to give NNH⁺ and HNNH²⁺ and of NO⁺ to form HNO²⁺ and NOH²⁺ have also been investigated. All species formed have linear equilibrium geometries and the minimum energy path for approach of the proton is along the line-of-centers of the heavy atoms. Energy barriers to the formation of the various species are given, where appropriate, and changes in geometry, ordering of molecular orbitals and orbital occupancy are discussed.     

Stability theorems for infinitely constrained mathematical programs

The primary concern of this paper is to investigate stability conditions for the mathematical program: findx E ⁿ that maximizesf(x):g ^j(x)0 for somej J, wheref is a real scalarvalued function and eachg is a real vector-valued function of possibly infinite dimension. It should be noted that we allow, possibly infinitely many, disjunctive forms. In an earlier work, Evans and Gould established stability theorems wheng is a continuous finite-dimensional real-vector function andJ=1. It is pointed out that the results of this paper reduce to the Evans-Gould results under their assumptions. Furthermore, since we use a slightly more general definition of lower and upper semicontinuous point-to-set mappings, we can dispense with the continuity ofg (except in a few instances where it is implied by convexity assumptions).     

Salpianthus macrodontus Extracts,a Novel Source of Phenolic Compounds with Antibacterial Activity against Potentially Pathogenic Bacteria Isolated from White Shrimp

This study aimed to evaluate the antibacterial activity in vitro of Salpianthus macrodontus and Azadirachta indica extracts against potentially pathogenic bacteria for Pacific white shrimp. Furthermore, the extracts with higher inhibitory activity were analyzed to identify compounds responsible for bacterial inhibition and evaluate their effect on motility and biofilm formation. S. macrodontus and A. indica extracts were prepared using methanol, acetone, and hexane by ultrasound. The minimum inhibitory concentration (MIC) of the extracts was determined against Vibrio parahaemolyticus, V. harveyi, Photobacterium damselae and P. leiognathi. The polyphenol profile of those extracts showing the highest bacterial inhibition were determined. Besides, the bacterial swimming and swarming motility and biofilm formation were determined. The highest inhibitory activity against the four pathogens was found with the acetonic extract of S. macrodontus leaf (MIC of 50 mg/mL for Vibrio spp. and 25 mg/mL for Photobacterium spp.) and the methanol extract of S. macrodontus flower (MIC of 50 mg/mL for all pathogens tested). Both extracts affected the swarming and swimming motility and the biofilm formation of the tested bacteria. The main phenolic compounds related to Vibrio bacteria inhibition were naringin, vanillic acid, and rosmarinic acid, whilst hesperidin, kaempferol pentosyl-rutinoside, and rhamnetin were related to Photobacterium bacteria inhibition.     

基于串行最小频移键控的8进制调制的研究

提出了一种新型的基于串行结构的最小频移键控调制技术,产生了相位连续,频谱宽度窄,每码元时间有两次π/2相移,类似于传统最小频移键控调制信号,给出了该调制方案的理论推导,并将其应用于8进制的多维多阶调制系统中。理论和仿真分析了不同的8进制调制方案在频谱特性,残留色散容限,自相位调制容限的不同,还分析了其受到系统滤波带宽的影响。最后仿真实现了通过350km的色散完全补偿的光纤120Gb/s的数据传输。