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Statement by Mr. Beernaert , Minister , in regard to the efforts made to give effect to the Resolution passed by the Polar Congress of 1906 , that an « International Polar Commission » should be organised . Demission of office by the President ...
Let r and O be polar coordinates for R " , 0 r < 0,0 eS " -1 ( the unit sphere in R " ) . A domain D in R " is a starlike domain ( with respect to the origin ) if there exists a function B : S " -1 → R , ß continuous and strictly positive , so that D = { re : 0 sr ...
Let ( r , oi , oz ) , O S rSR , 0 SØ 51,0 5 oz < 27 , be polar coordinates in Gr . Let the function x = x ( r , , Ø2 ) be the transformation from the polar coordinate to the orthogonal coordinate . We put f . ( r , 01 , 02 , t ) = f ( x ( r , 01 , 2 ) , t ) and set f ' ( ro ...
Note that , in the situation under consideration , when the polar set V of the form w is a smooth ( k – 1 ) - dimensional ... 4 Pairing to Smooth Forms It is clear that the ( would - be ) polar homology groups of a complex manifold X should have a  ...
POLAR SETS OF SOME GAUSSIAN PROCESSES by MICHEL (JEBER. 1. INTRODUCTION . Let S be a bounded set of R", N=1, and consider X (., s) a centered gaussian process defined on S. Je associate to it the process (1) X* = ( X1, X2, ...
Śl Polar Morse–Smale vector fields Let X G *(M), r = 1, be a polar Morse–Smale vector field. ... cycle of X. If M is a k—torus and X is a polar Morse–Smale vector field on M then X has 2k stable cycles which intersect each other at the source.
Contributing further to the polar gradient of the bioelectric field may be the fact that conductivity is much greater up and down the stem than across the stem ( HOPE and ROBERTSON 1953), and such conductivity might limit lateral transport ...
For such a group of substances the substituent effect can be assumed to be polar only . Equation ( 4 ) reduces to ( 5 ) . Having established the rules that govern the polar effect of substituents , we can consider substituents that cause both polar ...
The representation theorem 3 allows to prove the following invariance properties ( propositions 17 and 18 ) . PROPOSITION 17 . Let 21 22 be open subsets of so and F a compact subset of z , N zz Then F is polar in 21 if and only if it is polar in ...
Let ( 1 , 0 ) be polar co - ordinates ; then = xQ - YF is never zero , and the system ( 1 . 5 ) can be written as a first order equation in polar coordinates ( 7 , 0 ) : ur - sir , euar lP cos 0 + ļ sin ) ( Qcos O - P sin o ) ( 2 . 4 ) ( 2 . 4 ) DA If both P and Q are ...