In a mathematical programming problem, an optimum (maxi­ mum or minimum) of a function is sought, subject to con­ straints on the values of the variables. In the quarter century since G. B. Dantzig introduced the simplex method for linear programming, many real-world problems have been modelled in mathematical programming terms. Such problems often arise in economic planning - such as scheduling industrial production or transportation - but various other problems, such as the optimal control of an interplanetary rocket, are of similar kind. Often the problems involve nonlinear func­ tions, and so need methods more general than linear pro­ gramming. This book presents a unified theory of nonlinear mathe­ matical programming. The same methods and concepts apply equally to 'nonlinear programming' problems with a finite number of variables, and to 'optimal control' problems with e. g. a continuous curve (i. e. infinitely many variables). The underlying ideas of vector space, convex cone, and separating hyperplane are the same, whether the dimension is finite or infinite; and infinite dimension makes very little difference to the proofs. Duality theory - the various nonlinear generaliz­ ations of the well-known duality theorem of linear program­ ming - is found relevant also to optimal control, and the , PREFACE Pontryagin theory for optimal control also illuminates finite dimensional problems. The theory is simplified, and its applicability extended, by using the geometric concept of convex cones, in place of coordinate inequalities.

Mathematical programming and control theory (Chapman and Hall mathematics series)

Science & Math

B.D. Craven

Mathematics

Wiley : distributed in the U.S.A. by Halsted Press

In the second century, Galen recognized that nerve and muscle were functionally inseparable since contraction of muscle occurred only if the nerves supplying that muscle were intact. He therefore concluded that the shortening of a muscle was controlled by the central nervous sytem while the extension of a muscle could occur in the absence of innervation. Nerves, he thought, were the means of transport for animal spirits to the muscles; the way in which animal spirits may bring about contraction dominated the study of muscle physiology from that time until the historical discovery of Galvani that muscle could be stimulated electrically and that nerve and muscle were themselves a source of electrical energy. It is now well known that nerves conduct electrically and that transmission from nerve to striated muscle is mediated by the chemical which is liberated from nerve terminals onto the muscle membrane. In vertebrates this chemical is acetylcholine (ACh). Thus the concept of spirits that are released from nerves and control muscle contraction directly, is no longer tenable. Nevertheless the concept of 'substances' transported down nerv~s which directly control many aspects of muscle has not been abandoned, and has in fact been frequently reinvoked to account for the long-term regula­ tion of many characteristics of muscle (see review by Gutmann, 1976) and for the maintenance of its structural integrity.

Nerve-muscle interaction

Medical Books

Gerta Vrbova

T. Gordon

G. Vrobova

R. Jones

Medicine

Providing a broad coverage of the principles of sampling inspection and quality control, this latest edition has been revised throughout. Particular emphasis is given to the inclusion of tables and nomograms enabling the setting of numerical exercises.

Sampling inspection and quality control

Business & Money

Wetherill, G. Barrie

Management & Leadership

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