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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 ...
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.
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 ...
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 ...
Let g : C” – C and h: C” – C be polar weighted homogeneous polynomials. Consider the polynomial on C" X (C" defined by f(z,w) = g(z) –– h(w), which is also a polar weighted homogeneous polynomial (Example 2.6). Let x = f_1(1) C C” x C", ...
The polar SFE component has same trend with total SFE , but the dispersive SFE component is on the contrary exactly . The polar SFE component is also lower than the dispersive SFE component . This is resulting from hydrogen bonding ...
Jacques Azema, Michel Emery, Marc Yor. SOME POLAR SETS FOR THE BROWNIAN SHEET By DAVAR KHOSHNEVISAN * Department of Mathematics The University of Utah Salt Lake City , UT . 84112 , U.S.A. ...
Longitude [ E ] 40 60 20 80 Heiss Island 80 Lovozaro Latitude N ) oval and polar cap area . The midpoint moves inside the polar cap during appreciable geomagnetic disturbances . The path appears to be polar - auroral , since its receiver ...