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Full-Text Articles in Physical Sciences and Mathematics
A Class Of Functional Equations And Mielnik Probability Spaces, S. J. Guccione, Caslav V. Stanojevic
A Class Of Functional Equations And Mielnik Probability Spaces, S. J. Guccione, Caslav V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
Let S be the unit sphere of a normed real linear space N and let (S, p) be a Mielnik space of dimension two. For p(x, y) = f(‖x+y‖), x, yєS, where /is a continuous, strictly increasing function from [0, 2] onto [0, 1], it has been shown that (S, p) being two dimensional is equivalent to N being an inner product space. In some polarization problems modeled on the unit sphere of an inner product space, the transition probability p(x, y) may not be as well behaved as p(x, y) = f(‖x + y‖). In order to provide a …
Quasi-Unmixedness And Integral Closure Of Rees Rings, Peter G. Sawtelle
Quasi-Unmixedness And Integral Closure Of Rees Rings, Peter G. Sawtelle
Mathematics and Statistics Faculty Research & Creative Works
For certain Rees rings ℛ of a local domain R, the quasiunmixedness of R is characterized in terms of a certain transform of ℛ being contained in the integral closure of ℛ. © 1976 American Mathematical Society.
On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic
On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
It is shown that to a certain cosine series f, a Rees-Stanojević cosine sumn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for L1 convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Other corollaries are given concerning the well-known integrability conditions. © 1975, American Mathematical Society.
On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic
On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
Rees and Stanojevic introduced a new class of modified cosine sums (equation omitted) and found a necessary and sufficient condition for integrability of these modified cosine sums. Here we show that to every classical cosine series f with coefficients of bounded variation, a Rees-Stanqjevic cosine sum gn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for Lx convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Examples are given using the well-known integrability conditions. © 1976 American …
Univalence Of Derivatives Of Functions Defined By Gap Power Series. Ii, S. M. Shah, S. Y. Trimble
Univalence Of Derivatives Of Functions Defined By Gap Power Series. Ii, S. M. Shah, S. Y. Trimble
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
The Extremal Structure Of Locally Compact Convex Sets, J. C. Hankins, Roy M. Rakestraw
The Extremal Structure Of Locally Compact Convex Sets, J. C. Hankins, Roy M. Rakestraw
Mathematics and Statistics Faculty Research & Creative Works
Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases. © 1976 Pacific Journal of Mathematics. All rights reserved.