Further generalization of the Dubovicki-Milutin theorem

Combining the results of Walczak (Ref. 1) and Lasiecka (Refs. 2 and 3), we extend the well-known Dubovicki-Milutin theorem in two directions: (i) We allow for treatment of several equality constraints in optimization problems; and (ii) We assume less regularity of optimization problems by requiring the existence of external cones instead of tangent cones. An example of an optimization problem is also considered.     

Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay

A distributed control problem for the parabolic operator withan infinite number of variables and time delay is considered.The performance index has an integral form. Constraints on controlsare imposed. To obtain optimality conditions for the Neumannproblem, the generalization of the Dubovitskii–Milyutintheorem given by Walczak in WALCZAK, S. Folia Mathematics, 1,187–196 and WALCZAK, S. J. Optim. Theory Appl., 42, 561–582was applied.     

Time-Optimal Control of Infinite Order Distributed Parabolic Systems Involving Multiple Time-Varying Lags

In this article, a time-optimal control problem for linear infinite order distributed parabolic systems involving multiple time-varying lags appearing both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.     

Optimal control of a system governed by a parabolic equation with an infinite number of variables

A distributed control problem for a parabolic operator with an infinite number of variables is considered. The performance index is more general than the quadratic one an has an integral form. Making use of the Dubovicki-Milutin theorem, necessary and sufficient conditions of optimality are derived for the Dirichlet problem.     

On the robust Newton’s method with the Mann iteration and the artistic patterns from its dynamics

Nonlinear Dynamics - There are two main aims of this paper. The first one is to show some improvement of the robust Newton’s method (RNM) introduced recently by Kalantari. The RNM is a...     

Optimality conditions for n x n infinite-order parabolic coupled systems with control constraints and general performance index

W. Kotarski Institute of Informatics, Silesian University, Bedzinska 60, 41-200 Sosnowiec, Poland Email: bahaa_gm{at}hotmail.com Email: kotarski{at}gate.math.us.edu.pl Received on March 14, 2006; Accepted on December 20, 2006 A distributed control problem for n x n parabolic coupled systemsinvolving operators with infinite order is considered. The performanceindex is more general than the quadratic one and has an integralform. Constraints on controls are imposed. Making use of theDubovitskii–Milyutin theorem, the necessary and sufficientconditions of optimality are derived for the Dirichlet problem.Yet, the problem considered here is more general than the problemsin El-Saify & Bahaa (2002, Optimal control for n x n hyperbolicsystems involving operators of infinite order. Math. Slovaca,52, 409–424), El-Zahaby (2002, Optimal control of systemsgoverned by infinite order operators. Proceeding (Abstracts)of the International Conference of Mathematics (Trends and Developments)of the Egyptian Mathematical Society, Cairo, Egypt, 28–31December 2002. J. Egypt. Math. Soc. (submitted)), Gali &El-Saify (1983, Control of system governed by infinite orderequation of hyperbolic type. Proceeding of the InternationalConference on Functional-Differential Systems and Related Topics,vol. III. Poland, pp. 99–103), Gali et al. (1983, Distributedcontrol of a system governed by Dirichlet and Neumann problemsfor elliptic equations of infinite order. Proceeding of theInternational Conference on Functional-Differential Systemsand Related Topics, vol. III. Poland, pp. 83–87) and Kotarskiet al. (200b, Optimal control problem for a hyperbolic systemwith mixed control-state constraints involving operator of infiniteorder. Int. J. Pure Appl. Math., 1, 241–254).     

Ion chromatographic methods for the detection of starch hydrolysis products in ruminal digesta.

Dionex high-performance ion chromatographic methods were evaluated for separation and quantitation of plant sugars and starch digestion products in the ruminal digesta of cattle. Mono- and disaccharides were eluted from a Dionex CarboPac PA1 column with sodium hydroxide used isocratically or as a pH gradient. Maltooligosaccharides which had a degree of polymerization (DP) less than 30 glucose residues were eluted in 60 min by a sodium hydroxide eluent containing a sodium acetate gradient. Carbohydrates were detected amperometrically. Responses were linear (r2 greater than 0.99) for glucose, disaccharides and maltooligosaccharides (DP less than 8). Precipitation and solid-phase extraction methods were evaluated for clean-up of samples of feedstuffs, ruminal contents, and bacterial culture fluids. Perchloric acid precipitation hydrolyzed sucrose but did not affect recoveries of cellobiose, isomaltose or maltose. Ethanol in concentrations of 79 and 86% precipitated maltooligosaccharides having chain lengths larger than 14 and 9 glucose residues, respectively. Maltooligosaccharide recoveries from solid-phase extraction columns varied with maltooligosaccharide size and column packing. Recoveries were greater than 94% for short chains (DP less than 6) eluted from phenyl-substituted columns and variable for all oligosaccharides eluted from C18 columns. Applications of these methods are presented and include: (1) detection of sugars in ruminant feed, (2) monitoring changes in ruminal sugars after feeding and (3) monitoring changes in extracellular sugars and oligosaccharides in the culture fluids of the ruminal bacterium, Bacteroides ruminicola.     

Optimal control of a system governed by a parabolic equation with an infinite number of variables and time delay

A distributed control problem with delay for the parabolic operator with an infinite number of variables is considered. The performance index has an integral form. Constraints on controls are assumed. To obtain optimality conditions, the generalization of the Dubovicki-Milutin theorem given by Walczak in Ref. 1 was applied.     

Newton’s method with fractional derivatives and various iteration processes via visual analysis

Numerical Algorithms - The aim of this paper is to visually investigate the dynamics and stability of the process in which the classic derivative is replaced by the fractional...