Intersections Of Thick Cantor Sets

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Intersections Of Thick Cantor Sets

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Author : Roger Kraft
language : en
Publisher: American Mathematical Soc.
Release Date : 1992-01-01

Intersections Of Thick Cantor Sets written by Roger Kraft and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.

In this work, the author proves two theorems about difference sets of Cantor sets, both of which involve the concept of the thickness of a Cantor set. The first gives conditions on the thicknesses of two Cantor sets that determine if the intersection of the two Cantor sets must contain a Cantor set or if the intersection may, in a nontrivial way, be as small as one point. The second theorem states that if the product of the thicknesses of two Cantor sets is strictly greater than one, then for a generic point t in their difference set, *G. (*G' + t) contains a Cantor set.

Intersections Of Thick Cantor Sets

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Author : Roger Kraft
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Intersections Of Thick Cantor Sets written by Roger Kraft and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

The concept of thickness assigns to every Cantor set in the real line a number from 0 to [infinity symbol]. It was known that for some pairs of numbers the intersection of Cantor sets with such numbers as thicknesses may be just one point and that, in some other cases, with certain conditions, the intersection must contain a Cantor set. The author gives a complete answer to the problem of determining all pairs of thicknesses for which the intersection may be a single point and all the pairs of thicknesses for which the intersection must contain a Cantor set. He also considers the problem of how often, as one Cantor set is being translated over another one, the intersection of the two Cantor sets contains a Cantor set.

G Categories

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Author : Robert Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

G Categories written by Robert Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

A [italic]G-category is a category on which a group [italic]G acts. This work studies the 2-category [italic]G-cat of [italic]G-categories, [italic]G-functors (functors which commute with the action of [italic]G) and [italic]G-natural transformations (natural transformations which commute with the [italic]G-action). There is a particular emphasis on the relationship between a [italic]G-category and its stable subcategory, the largest sub-[italic]G-category on which [italic]G operates trivially. Also contained here are some very general applications of the theory to various additive [italic]G-categories and to [italic]G-topoi.

Prime Ideals In Skew And Q Skew Polynomial Rings

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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Prime Ideals In Skew And Q Skew Polynomial Rings written by K. R. Goodearl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

New methods are developed to describe prime ideals in skew polynomial rings [italic capital]S = [italic capital]R[[italic]y; [lowercase Greek]Tau, [lowercase Greek]Delta]], for automorphisms [lowercase Greek]Tau and [lowercase Greek]Tau-derivations [lowercase Greek]Delta] of a noetherian coefficient ring [italic capital]R.

Extension Of Positive Definite Distributions And Maximum Entropy

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Author : Jean-Pierre Gabardo
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Extension Of Positive Definite Distributions And Maximum Entropy written by Jean-Pierre Gabardo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.

Elliptic Regularization And Partial Regularity For Motion By Mean Curvature

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Author : Tom Ilmanen
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Elliptic Regularization And Partial Regularity For Motion By Mean Curvature written by Tom Ilmanen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

We study Brakke's motion of varifolds by mean curvature in the special case that the initial surface is an integral cycle, giving a new existence proof by mean of elliptic regularization. Under a uniqueness hypothesis, we obtain a weakly continuous family of currents solving Brakke's motion. These currents remain within the corresponding level-set motion by mean curvature, as defined by Evans-Spruck and Chen-Giga-Goto. Now let [italic capital]T0 be the reduced boundary of a bounded set of finite perimeter in [italic capital]R[superscript italic]n. If the level-set motion of the support of [italic capital]T0 does not develop positive Lebesgue measure, then there corresponds a unique integral [italic]n-current [italic capital]T, [partial derivative/boundary/degree of a polynomial symbol][italic capital]T = [italic capital]T0, whose time-slices form a unit density Brakke motion. Using Brakke's regularity theorem, spt [italic capital]T is smooth [script capital]H[superscript italic]n-almost everywhere. In consequence, almost every level-set of the level-set flow is smooth [script capital]H[superscript italic]n-almost everywhere in space-time.

Phantom Homology

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Author : Melvin Hochster
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Phantom Homology written by Melvin Hochster and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly Cohen-Macaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to well-behaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic $p$. The book would be suitable for use in an advanced graduate course in commutative algebra.

Behavior Of Distant Maximal Geodesics In Finitely Connected Complete 2 Dimensional Riemannian Manifolds

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Author : Takashi Shioya
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Behavior Of Distant Maximal Geodesics In Finitely Connected Complete 2 Dimensional Riemannian Manifolds written by Takashi Shioya and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.

Unraveling The Integral Knot Concordance Group

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Author : Neal W. Stoltzfus
language : en
Publisher: American Mathematical Soc.
Release Date : 1977

Unraveling The Integral Knot Concordance Group written by Neal W. Stoltzfus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.

The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.

Degenerate Principal Series For Symplectic Groups

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Author : Chris Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Degenerate Principal Series For Symplectic Groups written by Chris Jantzen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

This paper is concerned with induced representations for $p$-adic groups. In particular, Jantzen examines the question of reducibility in the case where the inducing subgroup is a maximal parabolic subgroup of $Sp_{2n (F)$ and the inducing representation is one-dimensional. Two different approaches to this problem are used. The first, based on the work of Casselman and of Gustafson, reduces the problem to the corresponding question about an associated finite-dimensional representation of a certain Hecke algebra. The second approach is based on a technique of Tadi\'c and involves an analysis of Jacquet modules. This is used to obtain a more general result on induced representations, which may be used to deal with the problem when the inducing representation satisfies a regularity condition. The same basic argument is also applied in a case-by-case fashion to nonregular cases.