The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

Chen, Jun

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Monograph

Persistent identifier:: 856566209

Author:: Chen, Jun

Title:: The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

Sub title:: May 23 - 25, 2001, Bangkok, Thailand

Scope:: VI, 434 Seiten

Year of publication:: 2001

Place of publication:: Pathumthani, Thailand

Publisher of the original:: AIT

Identifier (digital):: 856566209

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: A FRAMEWORK FOR AUTOMATED CHANGE DETECTION SYSTEM. Haigang SUI, Deren LI, Jianya GONG

Document type:: Monograph

Structure type:: Chapter

258 HISTORY OF THE THEORY OF DETERMINANTS functions of n-f-h variables shall be connected by an equation inde pendent of the said variables is that the Jacobian of the functions with respect to any n of the variables shall vanish. Two of them bear on the theorem concerning the condensation of the Jacobian into one product (Hist., i. p. 391). The first is familiar, namely, he alters x = pcos 6 ( z — fp 2 —a?—y 2 y — p sin 0 sin \js - into i x — p cos 0 z = p sin 0 cos \fsj [ y = P sin 0 sin xfs, and so obtains d(x,y,z) _ dz dx dy d(p,0,\fs) ~ dp’dd'd^ e z • ( — p sin 6) • p sin 6 COS \[s In the second the data are — p 2 sin 0. x x = cos <p x X 2 — Sin <p x COS 0 2 x 3 = sin 0 X sin 0 2 cos 03 X n — sin 0 X sin 02 . . . . sin 0 n _! COS 0„J , and the result d(x x , x 2 , • • • j x n ) o(0i, 02> • • • > 0n) = sin n 0! • Sm n—1 02 • sin n_2 03 .... sin 1 0 n . What may be viewed as an illustration of another theorem of Jacobi’s (Hist., i. p. 389) is the result ^(x x x n \ x 2 x~\ . . . , x n _ y x- 1 ) _ 1 d(x u x. 2 , . . . , x n ) x’n +19 where æ 1 2 +æ 2 2 + . . . +^n 2 = 1. WOLSTENHOLME, J. (1863). [Question 4892. Educ. Times, xxviii. p. 252 ; or Math, from Educ.„ Times, xxvi. pp. 104-105.] The theorem here dealt with is that of § 15 of Jacobi’s memoir of 1841 (Hist., i. pp. 378-380). Any fresh interest is due to the example given in illustration of the simplest case of the theorem,, namely, the Jacobian of a 2 -[-6 2 +c 2 , ax-\-by -\-cz, x z -\-y 2 -\-z 2 , bz—cy, cx—az, ay—bx: Y

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fullscreen: The period 1861 to 1880 (Vol. 3)

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