The discrete-time maximum principle : a survey and some new results

In this paper we present a review of the development of the discrete maximum principle. In the presentation, the emphasis is on a geometrical interpretation. The crucial assumptions in the theory developed are pointed out, and the attempts to overcome the limitation in the resulting theorems ore exposed. Following the review, we present a new approach to optimization of the multi-stage optimization problems called the ’ upper boundary approach ’. The classical methods of solving this problem are shown to fit smoothly into the new approach. Moreover, using this approach a number of new results have been developed, among these a new generalized version of the discrete maximum principle. The new version does not require the assumption of directional convexity.     

Stabilization of linear multivariable constant delay-differential systems

The article presents the iterative method of stabilizing control signal selection in the form of the state-feedback of a multivariable linear time-invariant plant with delays. The proposed method is based on the consecutive assignment of the single system eigenvalues λ_j so that its stabilizability will be preserved for a given iteration step and the assigned eigenvalues will not be changed, even though a dynamical element identified by the matrix K_j(z) (where z is an elementary delay operator) is placed into the state feedback. To illustrate the abovementioned method, a simplified example is given.     

INFLUENCE OF WATER ACTIVITY ON THE ACOUSTIC PROPERTIES OF BREAKFAST CEREALS

Corn and wheat bran flakes were compressed in a plastic cylinder and the generated vibrations were measured by a piezoelectric accelerometer. Amplitude–time records were thoroughly analyzed and the total acoustic energy in arbitrary units, number of acoustic events and energy of a single acoustic event were calculated. Relationships between the time of compression, frequency and sound intensity are presented as acoustograms. All parameters, except the energy of a single acoustic event, were strongly dependent on water activity (A_w). The flakes differed essentially in their ability to propagate vibrations. At low A_w's, both types of flakes were alike, but at higher A_w's, corn flakes damped high‐frequency waves while wheat bran flakes did not show this property.     

CONTEXTUAL INFORMATION RETRIEVAL USING A GRAPH MODEL OF A SENTENCE AND ROUGH SETS

Abstract

A uniform data structure is defined to represent sentence components (words) for a parallel processor of the natural language. The basic notation of rough sets is used for the representation of sentence elements in the computer, to exhibit their context and to select proper meanings. An approximation space reflecting the context of any word in a sentence is defined by induction from the most general meanings of words adjoining that word in the graph model of the sentence and from a contextual knowledge base. The contextual knowledge base specifies the meaning of each word with respect to the most general words expected to adjoin that word in the graph model of the sentence.     

Special Issue: Quantum Interference

A general theory of optical image evaluation seems now to be within reach of investigation as a result of the introduction into this field of the powerful methods of Fourier analysis. The most important practical application of such a theory is to the quality evaluation of optical systems. To be realistic, such a quality evaluation must be defined relative to the statistical properties of a prescribed object set and a prescribed receiving surface. A simplification results from the fact that, in the majority of applications, the quality of a high-grade optical system can be satisfactorily assessed by its power to reproduce low-contrast fine detail. This leads to the idea of assessing the system by means of its averaged performance on low contrast random object sets occupying isoplanatism patches in different parts of the field. As is well-known, fine detail is in general reproduced in a metamorphosed form, which however can usually be interpreted correctly by a practised operator. Two distinct types of quality evaluation result according as we demand that the image shall resemble the object as closely as possible, or that it shall give the maximum amount of information about the object without regard to the amount of work (image interpretation) which may be needed to extract this information. In the second type of evaluation, an essentially unique evaluation of image quality exists, viz. that based on the mean information content of the images of a prescribed low-contrast object set; in the first, there is no unique evaluation, but a number of different evaluations of image quality can be made, each of which leads to a corresponding quality evaluation for the optical system. An exploratory study of the relative merits of these evaluations, and of thier interrelations, seems to be an urgent task for the theoretical optician. A beginning to this study is attempted in the present paper. Three simple and natural assessments of the first type are considered, and it is shown that in small-field systems the third assessment (correlation quality) is related in an interesting way to a generalised form of Strehl definition. For such systems, the first assessment (relative structural content) is known to agree with assessment by information content in the limiting case of a random object set whose images are almost completely smothered in random noise. The second assessment (fidelity) is connected with the other two by a simple mathematical relation. The discussion includes consideration of the effects of image spread and noise in the receiving surface. Il paraît maintenant possible de commencer à bâtir une théorie générale de la qualité des images optiques, du fait de l'introduction dans ce domaine des méthodes puissantes de l'analyse de Fourier. L'application pratique la plus importante d'une telle théorie est la détermination de la qualité des systèmes optiques. Pour être réaliste, une telle évaluation de qualité doit être définie à partir de propriétés statistiques d'ensembles d'objets et des propriétés d'une surface réceptrice donnée. Une simplification résulte du fait que, dans la majorité des applications, la qualité des bons systèmes optiques peut être déterminée de façon satisfaisante par leur aptitude à reproduire de petits détails de faible contraste. Ceci conduit à l'idée d'évaluer la qualité d'un système à l'aide de la moyenne des résultats obtenus sur des objets aléatoires de faible contraste occupant des régions isoplanétiques dans différentes parties du champ. Il est bien connu que les fins détails subissent généralement une transformation, mais qu'un observateur entraîné peut souvent les interpréter correctement. Deux types de méthodes d'estimation de la qualité en résultent, suivant que l'on demande que l'image ressemble à l'objet d'aussi près que possible, ou que l'on obtienne le maximum d'information sur l'objet, sans tenir compte de l'importance du travail d'interprétation qui peut être nécessaire pour extraire cette information. Dans le deuxième cas une évaluation unique existe: celle qui est basée sur le calcul de la quantité moyenne d'information dans les images d'un ensemble donné d'objets de faible contraste. Dans le premier cas, il n y a pas d'évaluation unique, mais un certain nombre de méthodes peuvent être employées, chacune conduisant à une évaluation de la qualité du système optique. Une étude des mérites relatifs de ces critères et de leurs relations paraît s'imposer au théoricien. On présente dans l'article ci-dessous, le début d'une telle étude. Trois critères naturels et simples (appartenant à la première catégorie) sont envisagés et l'on montre que dans les systèmes à faible champ le 3 e critère (critère de corrélation) est relié de façon intéressante à une forme généralisée du critère de Strehl. Pour de tels systèmes, on sait que le premier critère (évaluation du ‘ contenu structural ’) s'accorde avec celui qui résulte du calcul de l'information dans le cas limite d'un ensemble d'objets aléatoires dont les images sont presque complètement masquées par le bruit. Le second critère (fidélité) est relié aux deux autres par une relation mathématique simple. La discussion tient compte des effets de la diffusion de l'image et du bruit introduits par la surface réceptrice. Dank der leistungsfähigen Methode der Fourier analyse scheint es jetzt möglich zu sein, eine allgemeine Theorie für die Beurteilung der Bildgüte aufzustellen. Die wichtigste praktische Anwendung einer solchen Theorie richtet sich auf die Leistungsbewertung optischer Systeme. Um in einem realen Rahmen zu bleiben, muss sich diese Leistungsbewertung auf die statistischen Eigenschaften einer vorgegebenen Objektmenge und einer festgelegten Auffangfläche beziehen. Eine Vereinfachung ergibt sich aus dem Umstand, dass bei der Mehrzahl der Anwendungen die Leistung eines wohlkorrigierten optischen Systems hinreichend gut durch seine Wiedergabe kontrastarmer Einzelheiten beurteilt werden kann. Das führt auf den Gedanken, ein optisches System nach der durchschnittlichen Wiedergabe zufälliger kontrastarmer Feinstrukturen in den verschiedenen Isoplanasiebereichen des Gesichtsfeldes zu beurteilen. Bekanntlich wird feines Detail im allgemeinen in einer veränderten Form wiedergegeben, die jedoch gewöhnlich von einem erfahrenen Beobachter richtig gedeutet werden kann. Es ergeben sich zwei verschiedene Arten der Gütebeurteilung eines Bildes, je nachdem ob man verlangt, entweder, dass das Bild dem Objekt möglichst ähnlich ist, oder, dass es den grössten Informationsgehalt berü das Objekt liefert, ohne Rücksicht auf den dabei erforderlichen Arbeitsaufwand (Bilddeutung). Bei der zweiten Art der Qualitätsabschätzung gibt es eine im wesentlichen eindeutige Bewertung der Bildgüte, nämlich diejenige, die auf dem mittleren Informationsinhalt der Bilder einer statistisch vorgeschriebenen Menge kontrastarmer Objekte beruht. Die erste Art jedoch bringt keine eindeutige Bewertung, sondern man kann eine Anzahl verschiedener Bildgütekriterien aufstellen, von denen jede zu einer entsprechenden Gütebewertung des optischen Systems führt. Die Untersuchung der jeweiligen Vorzüge dieser Bewertungen und ihrer gegenseitigen Beziehungen scheint für den theoretischen Optiker eine dringende Aufgabe zu sein. Einen Anfang dazu soll die vorliegende Arbeit geben. Es werden drei einfache und naheliegenden Gütekriterien der ersten Art betrachtet. Es zeigt sich, dass das dritte davon (Korrelationsgüte) bei Systemen mit kleinem Ges ichtsfeld in eigenartiger Weise mit einer verallgemeinerten Form der Strehlschen Definitionshelligkeit in Verbindung steht. Für solche Systeme ist bekanntlich das erste Kriterium (relativer Strukturinhalt) im Grenzfall in Übereinstimmung mit der Beurteilung nach dem Informationsinhalt, wenn man sich auf zufällige Objektmengen beschränkt, deren Bilder fast vollständig in den statistischen Schwankungen (noise) untergehen. Das zweite Kriterium (Objekttreue) steht zu den beiden anderen in einer einfachen mathematischen Beziehung. Schliesslich wird noch der Einfluss der Bildverbreiterung und der statistischen Schwankungen in der Auffangfläche betrachtet.     

Molecular Aspects of Catalytic Reactivity. Application of EPR Spectroscopy to Stuies of the Mechanism of Heterogeneous Catalytic Reactions

The basic objective of mechanistic studies of real catalytic processes is to dissect the course of the reaction into individual steps; ascertain their sequence; and determine the stoichiometry, structure, and electronic states of active sites and intermediates. The electron paramagnetic resonance (EPR) technique is at present widely used to explore many of these principal aspects of heterogeneous catalysis and surface chemistry. The extreme sensitivity compared to the usual spectroscopic methods is perhaps its most acknowledged advantage and makes EPR best suited to investigate and characterize low-abundance active sites and intermediates appearing during catalytic reaction. Additional information can be drawn from the theoretical analysis of the experimental spin Hamiltonian parameters within the ligand field and from angular overlap or Newman's superposition models as well as by more sophisticated quantum chemical calculations. The purpose of this paper is to show how catalysis benefits from EPR spectroscopy and to identify the issues and areas explored by this method. A comprehensive literature review is not attempted in this article; instead, attention is directed toward application of EPR for elucidation of the molecular reaction mechanism that can provide a scientific background for understanding many fundamental aspects of catalytic activity. The major events of mechanistic studies which involve the identification of active sites, activation of reagents, and determination of the reaction pathways are illustrated by selected examples and discussed. An approach that is complementary to mechanistic catalytic test studies is also presented. It consists of spectroscopic investigations of a set of partial reactions, driven by external creation of the supposed active sites and intermediates, with the aim of reproducing and verifying the feasibility of the postulated catalytic cycle. Moreover, to assure some consistency of the subject, basic characteristics of EPR spectroscopy related to surface studies and chemical theories of reactivity are concisely reviewed.     

Enzyme—Pretreatment of Pinto Bean High Protein Fraction and Time of Blending Corn Meal Affects Extrudate Properties

High protein fraction of pinto bean, treated with papain and cellulose enzymes (Solvay Enzymes Inc.), was blended with corn meal (30%) and extruded at 120°C. Changes in expansion, texture, color, pH, in vitro protein digestibility, reducing sugars and functional properties of extmdates were recorded. Changes depended on type of enzymes and time of corn incorporation (before or after enzymatic pretreatment). The best texture of the extrudates was obtained using a cellulase enzyme. Papain affected some functional properties such as NSI and WSI. The best improvement in in vitro protein digestibility and reducing sugars was found with a cellulase treatment. Protein and fiber could be modified to improve physicochemical and functional properties of extrudates.     

New Flame-Retardant Polymeric Materials

The production of dibromobutendiol (DBBD) was developed in a wasteless and environmentally friendly way. DBBD is effective as a fire retardant because of the amount of bromine. New unsaturated polyester resin with decreasing flammability was presented. The main monomers were dibromobutendiol and diallylic ether of dibromoneopentylglycol (DAP). Both monomers act effectively against oxygen inhibition, and bromine in their molecules decreased the flammability of obtained products. DAP has been obtained in direct allylation by the use of allyl bromide on the interphase in the presence of proper catalysts—triethylallylammonium chloride. The obtained resins were UV curable. A photocuring system consisting of monoazide or diazide and hydroksyalkylphenone has been applied. The obtaining of new polyurethane foams via reaction of reactive oligomers with DBBD was studied. Well-known difficulties with the solubility of DBBD in polyol systems were solved.     

Extrusion of Pinto Bean High Protein Fraction Pretreated with Papain and Cellulase Enzymes

High protein fraction of pinto bean was pretreated with papain and cellulase enzymes and extruded at a temperature of 120°C. The effect of enzyme type and concentration, moisture and duration of incubation on expansion, texture, color, water absorption and solubility, pH, sugars, nitrogen solubility index and in vitro protein digestibility of the extrudate were investigated. Enzymatic modification had differential effects on nitrogen and carbohydrate components and on some physical and functional preperties of extrudates, depending on type of enzyme and incubation conditions. Results indicated the possibility of controlling protein and fiber hydrolysis at low moisture to obtain a desirable degree of modification to improve extruded products. This method may be used in food applications to obtain new snack type products from beans or their fractions.     

Distributed bottleneck control for repetitive production systems

A bottleneck control problem for general periodic job shops with blocking where each machine has an input buffer of finite capacity is investigated. The job shop considered consists of a set of workflows competing with each other for access to common machines. A distributed buffer control policy that restricts a job entering an input buffer of a local machine in a specific sequence is proposed. The conditions sufficient for design and allocation of dispatching rules are presented. The system time and the rate of machine utilization are considered as the evaluation criteria. Finally, the procedure aimed at scheduling periodic job shops is provided.