Tensor-based methods are receiving a growing interest in scienti c computing for the numerical solution of problems de ned in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analy...

In this paper two independent and unitarily invariant projection matrices P (N) and Q(N) are considered and the large deviation is proven for the eigenvalue density of all polynomials of them as the matrix size N converges to in nity. The result is formulated on the tracial state space TS(A) of the universal C -algebra A generated by two selfadjoint projections. The random pair (P (N); Q(N)) de...

The theory of theta functions for arithmetic groups that act on the Drinfeld upper half-plane is extended to allow degenerate parameters. This is used to investigate the cuspidal divisor class groups of Drinfeld modular curves. These groups are nite for congruence subgroups and may be described through the corresponding quotients of the Bruhat-Tits tree by . The description given is fairly expl...

The number of bound states of the one-dimensional Schrodinger equation is analyzed in terms of the number of bound states corresponding to \fragments" of the potential. When the potential is integrable and has a nite rst moment, the sharp inequalities 1 n+ Pn j=1Nj N Pn j=1Nj are proved, where n is the number of fragments, N is the total number of bound states, and Nj is the number of bound st...

In this paper we investigate those extensions of the bimodal provability logicCSM0 (alias PRL1 or F ) which are subframe logics, i.e. whose general frames are closed under a certain type of substructures. Most bimodal provability logics are in this class. The main result states that all nitely axiomatizable subframe logics containing CSM0 are decidable. We note that, as a rule, interesting syst...

We nd the adjoint of the Askey-Wilson divided di erence operator with respect to the inner product on L 2 ( 1; 1; (1 x 2 ) 1=2 dx) de ned as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic de...

Conservative discretizations of two uid ow problems generally exhibit pressure oscillations In this work we show that these pressure oscillations are induced by the loss of a pressure invariance property under discretiza tion and we introduce a non oscillatory conservative method for barotropic two uid ows The conservative formulation renders the two uid ow problem suitable to treatment by a Go...

The theory of base change is used to give some new examples of the Global Langlands Conjecture. The Galois representations involved have solvable image and are not monomial, although some multiple of them in the Grothendieck group is monomial. Thus, it gives nothing new about Artin's Conjecture itself. An application is given to a question which arises in studying multiplicities of cuspidal rep...

We present an e cient algorithm to determine the maximal class of con uent -transitions in a labelled transition system. Con uent -transitions are inert with respect to branching bisimulation. This allows to use -priorisation, which means that in a state with a con uent outgoing -transition all other transitions can be removed, maintaining branching bisimulation. In combination with the removal...

We examine connections between A-hypergeometric di erential equations and the theory of integer programming. In the rst part, we develop a \hypergeometric sensitivity analysis" for small variations of constraint constants with creation operators and b-functions. In the second part, we study the indicial polynomial (b-function) along the hyperplane x i = 0 via a correspondence between the optima...