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Articles 1 - 17 of 17
Full-Text Articles in Physical Sciences and Mathematics
Measure And Integration, Jose L. Menaldi
Measure And Integration, Jose L. Menaldi
Mathematics Faculty Research Publications
Abstract measure and integration, with theory and (solved) exercises is developed. Parts of this book can be used in a graduate course on real analysis.
Distributions And Function Spaces, Jose L. Menaldi
Distributions And Function Spaces, Jose L. Menaldi
Mathematics Faculty Research Publications
Beginning with a quick recall on measure and integration theory, basic concepts on (a) Function Spaces, (b) Schwartz Theory of Distributions, and (c) Sobolev and Besov Spaces are developed. Moreover, only a few number of (solved) exercises are given. Parts of this book can be used in a graduate course on real analysis.
Spaces Of Sections Of Banach Algebra Bundles, Emmanuel Dror Farjoun, Claude Schochet
Spaces Of Sections Of Banach Algebra Bundles, Emmanuel Dror Farjoun, Claude Schochet
Mathematics Faculty Research Publications
Suppose that B is a G-Banach algebra over 𝔽 = ℝ or ℂ, X is a finite dimensional compact metric space, ζ : P → X is a standard principal G-bundle, and Aζ = Γ(X,P xG B) is the associated algebra of sections. We produce a spectral sequence which converges to π∗(GLoAζ) with
E_2p,q ≅ Ȟp(X ; πq(GLoB)).
A related spectral sequence converging to K∗+1(Aζ) (the real or complex topological …
Continuous Trace C*-Algebras, Gauge Groups And Rationalization, John R. Klein, Claude Schochet, Samuel B. Smith
Continuous Trace C*-Algebras, Gauge Groups And Rationalization, John R. Klein, Claude Schochet, Samuel B. Smith
Mathematics Faculty Research Publications
Let ζ be an n-dimensional complex matrix bundle over a compact metric space X and let Aζ denote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UAζ, the group of unitaries of Aζ. The answer turns out to be independent of the bundle ζ and depends only upon n and the rational cohomology of X. We prove analogous results for the gauge group and the projective gauge group of a principal bundle over a compact metric space X.
Banach Algebras And Rational Homotopy Theory, Gregory Lupton, N. Christopher Phillips, Claude Schochet, Samuel B. Smith
Banach Algebras And Rational Homotopy Theory, Gregory Lupton, N. Christopher Phillips, Claude Schochet, Samuel B. Smith
Mathematics Faculty Research Publications
Let A be a unital commutative Banach algebra with maximal ideal space Max(A). We determine the rational H-type of GLn(A), the group of invertible n x n matrices with coefficients in A, in terms of the rational cohomology of Max(A). We also address an old problem of J. L. Taylor. Let Lcn(A) denote the space of "last columns" of GLn(A). We construct a natural isomorphism
Ȟs(Max(A);ℚ) ≅ π2n-1-s(Lcn(A)) ⊗ ℚ …
Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro
Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro
Mathematics Faculty Research Publications
We use the notion of backward integration, with respect to a general Lévy process, to treat, in a simpler and unifying way, various classical topics as: Girsanov theorem, rst order partial differential equations, the Liouville (or Lyapunov) equations and the stochastic characteristic method.
Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro
Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro
Mathematics Faculty Research Publications
We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-di erential operator with Wentzell boundary conditions.
Notes For Mat 7500 – Winter '93, Revised Winter '06, David Handel
Notes For Mat 7500 – Winter '93, Revised Winter '06, David Handel
Mathematics Faculty Research Publications
These notes developed from a one semester course at Wayne State University, taught several times in the last three decades of the 1900s. The subject matter is analysis on manifolds, consisting of the theory of smooth manifolds, differential forms, integration of forms, the generalized Stokes' Theorem, de Rham cohomology, and some related topics. The course is intended for first or second year graduate students in Mathematics with a background in Advanced Calculus, General Topology, linear algebra (including quotient spaces), and a little elementary group theory (including some familiarity with the symmetric groups). Given the above background, the notes are self-contained. …
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If uα(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that limα→0αuα(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.
The Fine Structure Of The Kasparov Groups Ii: Topologizing The Uct, Claude Schochet
The Fine Structure Of The Kasparov Groups Ii: Topologizing The Uct, Claude Schochet
Mathematics Faculty Research Publications
The Kasparov Groups KK∗(A,B) have a natural structure as pseudopolonais groups. In this paper we analyze how this topology interacts with the terms of the Universal Coefficient Theorem (UCT) and the splitting sof the UCT constructed by J. Rosenberg and the author, as well as its canonical three term decomposition which exists under bootstrap hypotheses. We show that the various topologies on [cursive]Ext^{1}_{ℤ}(K∗(A),K∗(B)) and other related groups mostly coincide. Then we focus attention on the Milnor sequence and the fine structure subgroup of KK∗(A,B). …
Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan
Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan
Mathematics Faculty Research Publications
In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this signi cantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.
Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.
Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi
Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi
Mathematics Faculty Research Publications
We consider the strong solution of a semi linear HJB equation associated with a stochastic optimal control in a Hilbert space H: By strong solution we mean a solution in a L2(μ,H)-Sobolev space setting. Within this framework, the present problem can be treated in a similar fashion to that of a finite-dimensional case. Of independent interest, a related linear problem with unbounded coefficient is studied and an application to the stochastic control of a reaction-diffusion equation will be given.
Regularity Of The Free-Boundary In Singular Stochastic Control, S. A. Williams, P. L. Chow, J. L. Menaldi
Regularity Of The Free-Boundary In Singular Stochastic Control, S. A. Williams, P. L. Chow, J. L. Menaldi
Mathematics Faculty Research Publications
No abstract provided.
Regularizing Effect For Integro-Differential Parabolic Equations, Maria Giovanna Garroni, José Luis Menaldi
Regularizing Effect For Integro-Differential Parabolic Equations, Maria Giovanna Garroni, José Luis Menaldi
Mathematics Faculty Research Publications
No abstract provided.
Generalized Lame-Clapeyron Solution For A One-Phase Source Stefan Problem, José Luis Menaldi, Domingo Alberto Tarzia
Generalized Lame-Clapeyron Solution For A One-Phase Source Stefan Problem, José Luis Menaldi, Domingo Alberto Tarzia
Mathematics Faculty Research Publications
In this paper we obtain a generalized Lamé-Clapeyron solution for a one-phase Stefan problem with a particular type of sources. Necessary and sufficient conditions are given in order to characterize the source term which provides a unique solution. Some estimates on the free boundary and the temperature are presented. In particular, asymptotic expansions are given for small Stefan number and source.
Remarks On Estimates For The Green Function, Jose Luis Menaldi
Remarks On Estimates For The Green Function, Jose Luis Menaldi
Mathematics Faculty Research Publications
No abstract provided.