On microfunctions at the boundary along CR manifolds

Let X be a complex analytic manifold, a C ² submanifold, an openset with C ² boundary .Denote by (resp. ) the microlocalization along M (resp. ) of the sheaf of holomorphic functions.In the literature (cf. [A-G], [K-S 1,2])one encounters two classical results concerning the vanishing of the cohomology groups .The most general gives the vanishing outside a range of indices j whose length is equal to (with being the number of respectively positive, negative and null eigenvalues for themicrolocal Levi form ).The sharpest result gives the concentration in a single degree, provided that the difference is locally constant for near p (with for z the base point of p).The first result was restated for the complex in [D'A-Z 2], in the case codim We extend it here to any codimension and moreover we also restate for the second vanishing theorem.We also point out that the principle of our proof, related to a criterion for constancy of sheaves due to [K-S 1], is a quite new one.     

On copies of c 0 in the bounded linear operator space

In this note we study some properties concerning certain copies of the classic Banach space c ₀ in the Banach space of all bounded linear operators between a normed space X and a Banach space Y equipped with the norm of the uniform convergence of operators.     

Interpolation of Intersections Generated by a Linear Functional

Let (X ₀, X ₁) be a Banach couple such that X ₀ ∩ X ₁ is dense in X ₀ and X ₁. By (X ₀, X ₁)_θ,q , 0 < θ < 1, 1 ⩽ q < ∞, we denote the spaces of the real interpolation method. Let ψ be a nonzero linear functional defined on some linear space M ⊂ X ₀ + X ₁ and such that ψ ∈ (X ₀ ∩ X ₁)*, and let N = Ker ψ. We examine conditions under which the natural formula

Image inverse d'un D-module and Newton Polygon)

We show that, under conditions about the microcharacteristic variety of a coherent -module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic -module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.     

Optimal Ternary Linear Rate 1/2 Codes

In this paper, we classify all optimal linear[n, n/2] codes up to length 12. We show that thereis a unique optimal [10, 5, 5] code up to equivalence.     

The Local Stark Conjecture at a Real Place

A refinement of the rank 1 Abelian Stark conjecture has been formulated by B.Gross. This conjecture predicts some -adic analytic nature of a modification of the Stark unit. The conjecture makes perfect sense even when is an Archimedean place. Here we consider the conjecture when is a real place, and interpret it in terms of 2-adic properties of special values of L-functions. We prove the conjecture for CM extensions; here the original Stark conjecture is uninteresting, but the refined conjecture is nontrivial. In more generality, we show that, under mild hypotheses, if the subgroup of the Galois group generated by complex conjugations has less than full rank, then the refined conjecture implies that the Stark unit should be a square. This phenomenon has been discovered by Dummit and Hayes in a particular type of situation. We show that it should hold in much greater generality.     

Polynomials with All Zeros Real and in a Prescribed Interval

We provide a characterization of the real-valued univariate polynomials that have only real zeros, all in a prescribed interval [a,b]. The conditions are stated in terms of positive semidefiniteness of related Hankel matrices.     

A Modal Logic Based on Linearly Ordered f-Spaces

A modal logic associated with the -spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered -frames, and the class of all strictly linearly ordered -frames.     

A Unified Fixed Point Theory in Generalized Convex Spaces

Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.     

On <Emphasis Type="Italic">p</Emphasis>-nilpotency of finite groups*

Let be a class of groups. A subgroup H of a group G is called -s-supplemented in G, if there exists a subgroup K of G such that G = HK and K/K ∩ H_G belongs to where H_G is the maximal normal subgroup of G which is contained in H. The main purpose of this paper is to study some subgroups of Fitting subgroup and generalized Fitting subgroup -s-supplemented and some new criterions of p-nilpotency of finite groups are obtained. *This research is supported by the grant of NSFC and TianYuan Fund of Mathematics of China (Grant #10626047).     

Evaluation Formulas for a Conditional Feynman Integral Over Wiener Paths in Abstract Wiener Space

In this paper, we introduce a simple formula for conditional Wiener integrals over , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral for functionals of the form which are of interest in Feynman integration theories and quantum mechanics.     

\mathcal{Q}-Universal Quasivarieties of Graphs

It is proved that a quasivariety K of undirected graphs without loops is -universal if and only if K contains some non-bipartite graph.     

Solving the Sum-of-Ratios Problem by an Interior-Point Method

We consider the problem of minimizing the sum of a convex function and of p1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and the denominators are positive concave functions. Thus, each fraction is quasi-convex. We give a brief discussion of the problem and prove that in spite of its special structure, the problem is -complete even when only p=1 fraction is involved. We then show how the problem can be reduced to the minimization of a function of p variables where the function values are given by the solution of certain convex subproblems. Based on this reduction, we propose an algorithm for computing the global minimum of the problem by means of an interior-point method for convex programs.     

Resonant Local Systems on Complements of Discriminantal Arrangements and Sl2Representations

We calculate the skew-symmetric cohomology of the complement of a discriminantal hyperplane arrangement with coefficients in local systems arising in the context of the representation theory of the Lie algebra . For a discriminantal arrangement in ^k, the skew-symmetric cohomology is nontrivial in dimension k–1 precisely when the 'master function' which defines the local system on the complement has nonisolated criticalpoints. In symmetric coordinates, the critical set is a union of lines. Generically, the dimension of this nontrivial skew-symmetric cohomology group is equal to the number of critical lines.     

Quasiconformal Mappings and Solutions of the Dispersionless KP Hierarchy

A formalism for studying dispersionless integrable hierarchies is applied to the dispersionless KP (dKP) hierarchy. We relate this formalism to the theory of quasiconformal mappings on the plane and present some classes of explicit solutions of the dKP hierarchy.     

Double Circulant Codes over \mathbb{Z}_4 and Even Unimodular Lattices

With the help of some new results about weight enumerators of self-dual codes over we investigate a class of double circulant codes over , one of which leads to an extremal even unimodular 40–dimensional lattice. It is conjectured that there should be Nine more constructions of the Leech lattice     

Meromorphic approximation theorem in a Stein space

We prove the meromorphic version of the Weil–Oka approximation theorem in a reduced Stein space X and give some characterizations of meromorphically -convex open sets of X. As an application we prove that for every meromorphically -convex open set D of a reduced Stein space X with no isolated points there exists a family of holomorphic functions on X such that the normality domain of coincides with D. Mathematics Subject Classification (2000)  32E10, 32C15, 32E30, 32A19     

Initial Segments in Rogers Semilattices of \Sigma _n^0 -Computable Numberings

S. Goncharov and S. Badaev showed that for , there exist infinite families whose Rogers semilattices contain ideals without minimal elements. In this connection, the question was posed as to whether there are examples of families that lack this property. We answer this question in the negative. It is proved that independently of a family chosen, the class of semilattices that are principal ideals of the Rogers semilattice of that family is rather wide: it includes both a factor lattice of the lattice of recursively enumerable sets modulo finite sets and a family of initial segments in the semilattice of -degrees generated by immune sets.     

Maximal L p –L q Regularity for Parabolic Partial Differential Equations on Manifolds with Cylindrical Ends

We give a short, simple proof of maximal L^p–L^q regularity for linear parabolic evolution equations on manifolds with cylindrical ends by making use of pseudodifferential parametrices and the concept of -boundedness for the resolvent.      

An Application of U(g)-bimodules to Representation Theory of Affine Lie Algebras

Let be the affine Lie algebra associated to the simple finite-dimensional Lie algebra . We consider the tensor product of the loop -module associated to the irreducible finite-dimensional -module V() and the irreducible highest weight -module L _k,. Then L _k, can be viewed as an irreducible module for the vertex operator algebra M _k,0. Let A(L _k,) be the corresponding -bimodule. We prove that if the -module is zero, then the -module is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras.