The E-theoretic descent functor for groupoids

The paper establishes, for a wide class of locally compact groupoids Γ, the E-theoretic descent functor at the C^∗-algebra level, in a way parallel to that established for locally compact groups by Guentner, Higson and Trout. Section 2 shows that Γ-actions on a C₀(X)-algebra B, where X is the unit space of Γ, can be usefully formulated in terms of an action on the associated bundle B^?. Section 3 shows that the functor B→C^∗(Γ,B) is continuous and exact, and uses the disintegration theory of J. Renault. Section 4 establishes the existence of the descent functor under a very mild condition on Γ, the main technical difficulty involved being that of finding a Γ-algebra that plays the role of Cbcont(T,B) in the group case.     

Flow prolongation of some tangent valued forms

We study the prolongation of semibasic projectable tangent valued k-forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r-th order connection on the base manifold, where r is the base order of F. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps.     

Smash Products for Secondary Homotopy Groups

We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered. The second author was partially supported by the Spanish Ministry of Education and Science under MEC-FEDER grants MTM2004-01865 and MTM2004-03629, the postdoctoral fellowship EX2004-0616, and a Juan de la Cierva research contract.     

Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method

In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM soluti...     

Lie algebroid modules and representations up to homotopy

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’s Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.     

A new characterization of for countable spectra of (LB)-spaces

The derived projective limit functor Proj¹ is a very useful tool for investigating surjectivity problems in various parts of analysis (e.g. solvability of partial differential equations).

We provide a new characterization for vanishing Proj¹ on projective spectra of (LB)-spaces which improves a classical result of V. P. Palamodov and V. S. Retakh.

     

A New Homotopy Method for Nonlinear Complementarity Problems

In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method.     

Properties of four partial orders on standard Young tableaux

Let SYTn be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYTn and some of their crucial properties, we prove three main results:

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Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer.

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The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra ²[n−1]. In particular, the Möbius function of these orders on tableaux is (−1)ⁿ⁻³.

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For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and Möbius function.

     

Degenerations of the moduli spaces of vector bundles on curves II (generalized Gieseker moduli spaces)

LetX ₀ be a projective curve whose singularity is one ordinary double point. We construct a birational modelG(n, d) of the moduli spaceU(n, d) of stable torsion free sheaves in the case (n, d)= 1, such that G(n, d) has normal crossing singularities and behaves well under specialization i.e. if a smooth projective curve specializes toX ₀, then the moduli space of stable vector bundles of rankn and degreed onX specializes toG(n, d). This generalizes an earlier work of Gieseker in the rank two case.