Quantized fields and gravitational particle creation in f (R) expanding universes

The problem of cosmological particle creation for a spatially flat, homogeneous and isotropic universes is discussed in the context of f (R) theories of gravity. Different from cosmological models based on general relativity theory, it is found that a conformal invariant metric does not forbid the creation of massless particles during the early stages (radiation era) of the universe. (C) 2010 Elsevier B.V. All rights reserved.

WNT5A Mutations in Patients With Autosomal Dominant Robinow Syndrome

Robinow syndrome is a skeletal dysplasia with both autosomal dominant and autosomal recessive inheritance patterns. It is characterized by short stature, limb shortening, genital hypoplasia, and craniofacial abnormalities. The etiology of dominant Robinow syndrome is unknown; however, the phenotypically more severe autosomal recessive form of Robinow syndrome has been associated with mutations in the orphan tyrosine kinase receptor, ROR2, which has recently been identified as a putative WNT5A receptor. Here, we show that two different missense mutations in WNT5A, which result in amino acid substitutions of highly conserved cysteines, are associated with autosomal dominant Robinow syndrome. One mutation has been found in all living affected members of the original family described by Meinhard Robinow and another in a second unrelated patient. These missense mutations result in decreased WNT5A activity in functional assays of zebrafish and Xenopus development. This work suggests that a WNT5A/ROR2 signal transduction pathway is important in human craniofacial and skeletal development and that proper formation and growth of these structures is sensitive to variations in WNT5A function. Developmental Dynamics 239:327-337, 2010. (C) 2009 Wiley-Liss, Inc.

The Immunomodulatory Action of Sialostatin L on Dendritic Cells Reveals Its Potential to Interfere with Autoimmunity

Sialostatin L (SialoL) is a secreted cysteine protease inhibitor identified in the salivary glands of the Lyme disease vector Ixodes scapularis. In this study, we reveal the mechanisms of SialoL immunomodulatory actions on the vertebrate host. LPS-induced maturation of dendritic cells from C57BL/6 mice was significantly reduced in the presence of SialoL. Although OVA degradation was not affected by the presence of SialoL in dendritic cell cultures, cathepsin S activity was partially inhibited, leading to an accumulation of a 10-kDa invariant chain intermediate in these cells. As a consequence, in vitro Ag-specific CD4(+) T cell proliferation was inhibited in a time-dependent manner by SialoL, and further studies engaging cathepsin S(-/-) or cathepsin L(-/-) dendritic cells confirmed that the immunomodulatory actions of SialoL are mediated by inhibition of cathepsin S. Moreover, mice treated with SialoL displayed decreased early T cell expansion and recall response upon antigenic stimulation. Finally, SialoL administration during the immunization phase of experimental autoimmune encephalomyelitis in mice significantly prevented disease symptoms, which was associated with impaired IFN-gamma and IL-17 production and specific T cell proliferation. These results illuminate the dual mechanism by which a human disease vector protein modulates vertebrate host immunity and reveals its potential in prevention of an autoimmune disease. The Journal of Immunology, 2009, 182: 7422-7429.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

Distinguishing links up to link-homotopy by algebraic methods

In this paper we provide a complete algebraic invariant of link-homotopy, that is, an algebraic invariant that distinguishes two links if and only if they are link-homotopic. The paper establishes a connection between the ""peripheral structures"" approach to link-homotopy taken by Milnor, Levine and others, and the string link action approach taken by Habegger and Lin. (C) 2009 Elsevier B.V. All rights reserved.

SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.

Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Isometric immersions into a homogeneous Lorentzian Heisenberg group and rigidity

In this paper we prove an existence result for local and global isometric immersions of semi-Riemannian surfaces into the three dimensional Heisenberg group endowed with a homogeneous left-invariant Lorentzian metric. As a corollary, we prove a rigidity result for such immersions.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Iterative strong coupling of dimensionally heterogeneous models

In this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models, under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone. The novel methodology takes full advantage of the small number of interface unknowns in this kind of problems. Existing algorithms can be viewed as variants of the `natural` staggered algorithm in which each domain transfers function values to the other, and receives fluxes (or forces), and vice versa. This natural algorithm is known as Dirichlet-to-Neumann in the Domain Decomposition literature. Essentially, we propose a framework in which this algorithm is equivalent to applying Gauss-Seidel iterations to a suitably defined (linear or nonlinear) system of equations. It is then immediate to switch to other iterative solvers such as GMRES or other Krylov-based method. which we assess through numerical experiments showing the significant gain that can be achieved. indeed. the benefit is that an extremely flexible, automatic coupling strategy can be developed, which in addition leads to iterative procedures that are parameter-free and rapidly converging. Further, in linear problems they have the finite termination property. Copyright (C) 2009 John Wiley & Sons, Ltd.