On W-solvability for special vectorial Hamilton-Jacobi systems

We study the solvability of special vectorial Hamilton-Jacobi systems of the form F(Du(x))=0 in a Sobolev space. In this paper we establish the general existence theorems for certain Dirichlet problems using suitable approximation schemes called W^1,p-reduction principles that generalize the similar reduction principle for Lipschitz solutions. Our approach, to a large extent, unifies the existing methods for the existence results of the special Hamilton-Jacobi systems under study. The method relies on a new Baire's category argument concerning the residual continuity of a Baire-one function. Some sufficient conditions for W^1,p-reduction are also given along with certain generalization of some known results and a specific application to the boundary value problem for special weakly quasiregular mappings.     

On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

Le saut en zéro de la fonction de décalage spectral

We give a formula for the jump at zero of the spectral shift function associated with Schrödinger operator on manifolds with conical ends. We show that, according to its decay, a zero energy resonant state has a non-integer contribution.     

Subword complexes in Coxeter groups

Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σ and an element in Π determine a subword complex, as introduced in Knutson and Miller (Ann. of Math. (2) (2003), to appear). Subword complexes are demonstrated here to be homeomorphic to balls or spheres, and their Hilbert series are shown to reflect combinatorial properties of reduced expressions in Coxeter groups. Two formulae for double Grothendieck polynomials, one of which appeared in Fomin and Kirillov (Proceedings of the Sixth Conference in Formal Power Series and Algebraic Combinatorics, DIMACS, 1994, pp. 183-190), are recovered in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented.     

A new joint model for longitudinal and survival data with a cure fraction

We develop a new joint cure rate model for longitudinal and survival data. The model allows for multiple longitudinal markers as well as a cure structure for the survival component based on the promotion time cure rate model, as described in Ibrahim et al. (Bayesian Survival Analysis, Springer, New York, 2001). Several characteristics and properties of the new model are discussed and examined. A real dataset from a melanoma clinical trial is given to demonstrate the methodology.     

Separable free quadratic algebras over quadratic integers

The aim of the paper is to determine all free separable quadratic algebras over the rings of integers of quadratic fields in terms of the properties of the fundamental unit in the real case. The paper corrects some earlier published results on the subject.     

Dynamic frictionless contact with adhesion

A model for the dynamic, adhesive, frictionless contact between a viscoelastic body and a deformable foundation is described. The adhesion process is modeled by a bonding field on the contact surface. The contact is described by a modified normal compliance condition. The tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field. The existence of a unique weak solution for the problem is established, together with a partial regularity result. The existence proof proceeds by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

Double complex and gamma-monomials in global function fields

We investigate Γ-monomials of positive characteristic Γ-functions in the global function fields by using Anderson's double complex method. The results are the generalizations of those in the rational function field case.     

Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation.