The Method Of Layer Potentials For The Heat Equation In Time Varying Domains
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| Author | : John L. Lewis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 170 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803603 |
This memoir consists of three papers in which we develop the method of layer potentials for the heat equation in time-varying domains. In Chapter I we show certain singular integral operators on [italic]L[superscript italic]p are bounded. in Chapter II, we develop a modification of the David buildup scheme to obtain [italic]L[superscript italic]p boundedness of the double layer heat potential on the boundary of our domains. In Chapter III, we use the results of the first two chapters to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure.
| Author | : Kenji Matsuki |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 146 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803417 |
In this paper we provide a unified way of looking at the apparently sporadic Weyl groups connected with the classical geometry of surfaces, namely those with 1) the rational double points, 2) the Picard groups of Del Pezzo surfaces, 3) the Kodaira-type degenerations of elliptic curves, and 4) the Picard-Lefschetz reflections of [italic]K3-surfaces, by putting them together into the picture of 3-dimensional birational geometry in the realm of the recently established Minimal Model Theory for 3-folds.
| Author | : Christian Krattenthaler |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 122 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821826131 |
A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to [italic]x + [italic]y = 0. In some cases these determinants can be evaluated to result in simple products. As applications we compute the generating function for tableaux with [italic]p odd rows, with at most [italic]c columns, and with parts between 1 and [italic]n. Moreover, we compute the generating function for the same kind of tableaux which in addition have only odd parts. We thus also obtain a closed form for the generating function for symmetric plane partitions with at most [italic]n rows, with parts between 1 and [italic]c, and with [italic]p odd entries on the main diagonal. In each case the result is a simple product. By summing with respect to [italic]p we provide new proofs of the Bender-Knuth and MacMahon (ex-)conjectures, which were first proved by Andrews, Gordon, and Macdonald. The link between nonintersecting lattice paths and tableaux is given by variations of the Knuth correspondence.
| Author | : Huaxin Lin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 102 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821826115 |
We show that the Weyl-von Neumann theorem for unitaries holds for [lowercase Greek]Sigma-unital [italic capital]A[italic capital]F-algebras and their multiplier algebras.
| Author | : Freddy Dumortier |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 117 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180443X |
In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon >0$ and for decreasing $a$, the limit cycle created in a Hopf bifurcation at $a = 0$ stays of ``small size'' for a while before it very rapidly changes to ``big size'', representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.
| Author | : Carlos Andradas |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 130 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821826123 |
A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a description is possible locally around every point, by means of analytic inequalities varying with the point, the set is called semianalytic. If one single system of strict inequalities is enough, either globally or locally at every point, the set is called basic. The topic of this work is the relationship between these two notions. Namely, Andradas and Ruiz describe and characterize, both algebraically and geometrically, the obstructions for a basic semianalytic set to be basic semialgebraic. Then they describe a special family of obstructions that suffices to recognize whether or not a basic semianalytic set is basic semialgebraic. Finally, they use the preceding results to discuss the effect on basicness of birational transformations.
| Author | : I-Chiau Huang |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 73 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821826085 |
Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.
| Author | : Gilles Pisier |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 119 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180474X |
In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]OH) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.
| Author | : Hans J. Baues |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 194 |
| Release | : 1980 |
| Genre | : Mathematics |
| ISBN | : 0821822306 |
The homology of iterated loop spaces [capital Greek]Omega [superscript]n [italic]X has always been a problem of major interest because it gives some insight into the homotopy of [italic]X, among other things. Therefore, if [italic]X is a CW-complex, one has been interested in small CW models for [capital Greek]Omega [superscript]n [italic]X in order to compute the cellular chain complex. The author proves a very general model theorem from which he can derive models, in addition to very technical proofs of the model theorem for several other models.
| Author | : Jin Nakagawa |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 90 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821804723 |
In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an explicit expression of the Dirichlet series. Using this expression, its analytic properties are deduced. He also presents an asymptotic formula for the number of orders in a quartic field with index less than a given positive number.
