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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Equidistance Relations: A New Bridge Between Geometric And Algebraic Structures, Thomas Q. Sibley
Equidistance Relations: A New Bridge Between Geometric And Algebraic Structures, Thomas Q. Sibley
Mathematics Faculty Publications
This paper investigates the transformations of certain geometric structures into algebraic ones and conversely. The algebraic notion of absolute value corresponds with the geometric one of equidistance. Further, latin squares with absolute values correspond to regular equidistance relations, "near groups" yield 1 point homogenous equidistance relations, and "near commutative groups" yield 2-point homogenous equidistance relations.
Ultrafilter Limits And Finitely Additive Probability, Thomas Q. Sibley
Ultrafilter Limits And Finitely Additive Probability, Thomas Q. Sibley
Mathematics Faculty Publications
Ultrafilter limits provide the natural convergence notion for finitely additive probability. The finitely additive infinitely divisible laws are closed under ultrafilter limits. The characteristic function of any convolution of finitely additive probability measures is the product of their characteristic functions.
Nonmeasurable Sets And Pairs Of Transfinite Sequences, Branko Ćurgus, Harry I. Miller
Nonmeasurable Sets And Pairs Of Transfinite Sequences, Branko Ćurgus, Harry I. Miller
Mathematics Faculty Publications
Many proofs of the fact that there exist Lebesgue nonmeasurable subsets of the real line are known. The oldest proof of this result is due to Vitali [4]. The cosets (under addition) of Q, the set of rational numbers, constitute a partition of the line into an uncountable family of disjoint sets, each congruent to Q under translation, Vitali's proof shows that V is nonmeasurable, if V is a set having one and only one element in common with each of these cosets.
Conjugate Type Boundary Value Problems For Functional-Differential Equations, Paul W. Eloe, Louis J. Grimm
Conjugate Type Boundary Value Problems For Functional-Differential Equations, Paul W. Eloe, Louis J. Grimm
Mathematics Faculty Publications
Two-point boundary value problems (BVPs) for delay differential equations have been studied extensively, beginning with the work of G. A. Kamenskiï, S. B. Norkin and others which was motivated by variational problems and problems in oscillation theory. L. J. Grimm and K. Schmitt and Ju. I. Kovac and L. I. Savcenko employed solutions of various differential inequalities for the study of two-point problems with retarded argument. In this paper, we show how a bilateral iteration procedure can be developed to yield existence and inclusion theorems for multipoint boundary value problems of conjugate type for nonlinear functional-differential equations.