S.S. Chern's Books

Exterior Differential Systems

By: Robert L. Bryant,S.S. Chern,Robert B. Gardner,Hubert L. Goldschmidt,P.A. Griffiths

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Exterior Differential Systems

By: Robert L. Bryant,S.S. Chern,Robert B. Gardner,Hubert L. Goldschmidt,P.A. Griffiths

This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.

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483

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Springer Science & Business Media

Published Date

ISBN 10

1461397146

ISBN 13

9781461397144

Fish Nutrition in Aquaculture

By: S.S. de Silva,T.A. Anderson

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Fish Nutrition in Aquaculture

By: S.S. de Silva,T.A. Anderson

Aquaculture is a growing industry. A vital component of the subject is feeding the organisms under cultivation. This book provides a thorough review of the scientific basis and applied aspects of fish nutrition in a user-friendly format. It will be of great use to individuals working or training in the industry, and to fish feed manufacturing personnel.

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346

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Springer Science & Business Media

Published Date

ISBN 10

041255030X

ISBN 13

9780412550300

Plant Pathology in India

By: S.S. Chahal,R.K. Khetarpal,T.S. Thind

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Plant Pathology in India

By: S.S. Chahal,R.K. Khetarpal,T.S. Thind

The book makes a modest attempt to highlight the major achievements. The first chapter highlights the status of plant pathology in India before 1905 and sets the stage for an overview of the developments made in the last 100 years. Chapters on significant achievements and current status of knowledge has been contributed by leading experts on mycology, bacteriology, virology and nematology, and also on epidemiological research, fungicide research, biological control, host plant resistance against pathogens and on the application of biotechnological approaches for management of plant diseases. This covered the major broad areas of research in plant pathology. Besides, non conventional chapters encompassing the areas of international co-operation, policy issues and uncommon opportunities are also included along with the role of professional societies of plant pathology in India. Though the volume by no way is a complete account of the vast ocean of information available on various aspects of the subject, it is anticipated that the diverse areas covered in this volume will serve as a roadmap for the younger generation of plant pathologists and policy makers alike who have greater challenges ahead to resolve the pathological problems for augmenting production, ensuring bio-security and facilitating trade in under the changing global trade regime.

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463

Publisher

Scientific Publishers

Published Date

ISBN 10

938817237X

ISBN 13

9789388172370

Exterior Differential Systems

By: Robert L. Bryant,S.S. Chern,Robert B. Gardner,Hubert L. Goldschmidt,P.A. Griffiths

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Exterior Differential Systems

By: Robert L. Bryant,S.S. Chern,Robert B. Gardner,Hubert L. Goldschmidt,P.A. Griffiths

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

483

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461397146

ISBN 13

9781461397144

Book's by S.S. Chern

Exterior Differential Systems

Exterior Differential Systems

Fish Nutrition in Aquaculture

Fish Nutrition in Aquaculture

Plant Pathology in India

Plant Pathology in India

Exterior Differential Systems

Exterior Differential Systems

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