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SCALAR AND DENSITY CONCOMITANTS OF A CERTAIN TENSOR WITH VALENCY (0,3) IN A THREE-DIMENSIONAL SPACE

SCALAR AND DENSITY CONCOMITANTS OF A CERTAIN TENSOR WITH VALENCY (0,3) IN A THREE-DIMENSIONAL SPACE DEMONSTRATIOVal. VUIMATHEMATICANa J1*79E u g e n i a » Stasiak, Irena Stasiak, Urszula Zandecka-PerlSCALAR AND DENSITY CONCOMITANTS OF A CERTAIN TENSORWITH VALENCY (0,3) IN A THREE-DIMENSIONAL SPACE1. IntroductionIn this paper we shall determine the most general, in theclass C , scalar and density concomitant oi the tensor ^ci/ilin a three-dimensional space under the assumotion that thegiven tensor s t i s f i e s the condition(1-1)This problem w i l l be solved with the help of a methodindicated by S.Goiqb in [ 3 ] » which constists in reducing somefunctional equation to a system of partial d i f f e r e n t i a l equations of f i r s t order.2. Scalar and density concomitantsBefore we pass to the basic problem of this paper, we introduce a notation to be used in the sequel. I f a transformation between two admissible coordinate system (pfyi s givenby means of a system of functions(2.1)U = 1 , 2 , 3 . . . n ; - 2! -1' f 2 / f 3',. .n' f ;then the partial derivatives and the Jacobianformation (2.1 ) are denoted as followsA'(2.2)(2.3)4':Js =- 253fi 0ofthe trans-2E.Stasiak, I.Stasiak, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

SCALAR AND DENSITY CONCOMITANTS OF A CERTAIN TENSOR WITH VALENCY (0,3) IN A THREE-DIMENSIONAL SPACE

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References (1)

Publisher
de Gruyter
Copyright
© by Eugenia Stasiak
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1975-0302
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIOVal. VUIMATHEMATICANa J1*79E u g e n i a » Stasiak, Irena Stasiak, Urszula Zandecka-PerlSCALAR AND DENSITY CONCOMITANTS OF A CERTAIN TENSORWITH VALENCY (0,3) IN A THREE-DIMENSIONAL SPACE1. IntroductionIn this paper we shall determine the most general, in theclass C , scalar and density concomitant oi the tensor ^ci/ilin a three-dimensional space under the assumotion that thegiven tensor s t i s f i e s the condition(1-1)This problem w i l l be solved with the help of a methodindicated by S.Goiqb in [ 3 ] » which constists in reducing somefunctional equation to a system of partial d i f f e r e n t i a l equations of f i r s t order.2. Scalar and density concomitantsBefore we pass to the basic problem of this paper, we introduce a notation to be used in the sequel. I f a transformation between two admissible coordinate system (pfyi s givenby means of a system of functions(2.1)U = 1 , 2 , 3 . . . n ; - 2! -1' f 2 / f 3',. .n' f ;then the partial derivatives and the Jacobianformation (2.1 ) are denoted as followsA'(2.2)(2.3)4':Js =- 253fi 0ofthe trans-2E.Stasiak, I.Stasiak,

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 1975

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