Applications of Nonlinear Partial Differential Equations in - download pdf or read online

By Edited by R. Finn

ISBN-10: 082181317X

ISBN-13: 9780821813171

ISBN-10: 1441962131

ISBN-13: 9781441962133

ISBN-10: 1519561741

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ISBN-13: 9781519621191

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ISBN-10: 5019637947

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By Edited by R. Finn

ISBN-10: 082181317X

ISBN-13: 9780821813171

ISBN-10: 1441962131

ISBN-13: 9781441962133

ISBN-10: 1519561741

ISBN-13: 9781519561749

ISBN-10: 1519621191

ISBN-13: 9781519621191

ISBN-10: 2119576556

ISBN-13: 9782119576553

ISBN-10: 2719631612

ISBN-13: 9782719631614

ISBN-10: 3219303293

ISBN-13: 9783219303292

ISBN-10: 5019637947

ISBN-13: 9785019637942

ISBN-10: 7019642993

ISBN-13: 9787019642995

Show description

Read Online or Download Applications of Nonlinear Partial Differential Equations in Mathematical Physics. Proceedings of Symposia in Applied Mathematics Volume XVII PDF

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Extra info for Applications of Nonlinear Partial Differential Equations in Mathematical Physics. Proceedings of Symposia in Applied Mathematics Volume XVII

Sample text

Obviously, X+ Θ = X9 λθ = 0. The vectors ^(1, 0, 0, . . , 0), e2(09 1, 0, . . , 0), . . , en(09 0, . . ; 0, 1) or alternatively, e i(&11> ^i2> · · · > δφ . . , Ó in ), where ôtJ is the Kronecker delta: (0 for Ï V j , for 1 = j , are called 101ft vectors. The following equation holds for any vector X = (χ^ x29 . . , x ^ : n z = Σ *^· t-1 «-DIMENSIONAL SPACES AND FUNCTIONS DEFINED THERE 41 The norm \\X\\ of the vector X is the number n 11*11= / £ * î . 3) equal to the distance ρ(Χ, 0) from the point X to Θ.

Xk be linearly independent elements o f £ n ( l ^ k < Λ). 22) with arbitrary real ci is called a k-dimensional linear manifold. e. a set of elements of the form X = Axt (jq 5* 0) is a straight line passing through Θ and xv Part of this straight line — the set of elements of the form X = λχΐ9 λ > 0, — is called a ray. A displaced k-dimensional manifold or k-dimensional plane is a set of elements X of the form (2·23) Z = X0+ Σ *Λ with fixed and linearly independent Xl9 Xl9 . . , Xk and arbitrary values of the numbers c1?

See Chapter IV, § 2, sec. 3 for the Gram determinant for functions. Manifolds. , Xk be linearly independent elements o f £ n ( l ^ k < Λ). 22) with arbitrary real ci is called a k-dimensional linear manifold. e. a set of elements of the form X = Axt (jq 5* 0) is a straight line passing through Θ and xv Part of this straight line — the set of elements of the form X = λχΐ9 λ > 0, — is called a ray. A displaced k-dimensional manifold or k-dimensional plane is a set of elements X of the form (2·23) Z = X0+ Σ *Λ with fixed and linearly independent Xl9 Xl9 .

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Applications of Nonlinear Partial Differential Equations in Mathematical Physics. Proceedings of Symposia in Applied Mathematics Volume XVII by Edited by R. Finn


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