We give an explicit formula (i.e., an explicit expression for the formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. Introduction We will denote by C((t)) (resp. C({t})) the field C[[t]][t] (resp. C{t}[t]) of formal (resp. convergent) Laurent series of the variable t, ...

Let ρ(x) = x− [x], χ = χ(0,1), λ(x) = χ(x) logx, and M(x) = ∑ k≤x μ(k), where μ is the Möbius function. Norms are in Lp(0,∞), 1 < p < ∞. For M1(θ) = M(1/θ) it is noted that ζ(s) ≠ 0 in s > 1/p is equivalent to ‖M1‖r < ∞ for all r ∈ (1,p). The space is the linear space generated by the functions x ρ(θ/x) with θ ∈ (0,1]. Define Gn(x)= ∫ 1 1/nM1(θ)ρ(θ/x)θ−1dθ. For all p ∈ (1,∞) we prove the two ar...

We present tight bounds on the spanning ratio of a large family of ordered θ-graphs. A θ-graph partitions the plane around each vertex into m disjoint cones, each having aperture θ = 2π/m. An ordered θ-graph is constructed by inserting the vertices one by one and connecting each vertex to the closest previously-inserted vertex in each cone. We show that for any integer k ≥ 1, ordered θ-graphs w...

A nested sequence of projectors and corresponding braid matricesˆR(θ): (1) Odd dimensions. Abstract A basis of N 2 projectors, each an N 2 × N 2 matrix with constant elements, is implemented to construct a class of braid matricesˆR(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors P α appearing in the spectral decomposition ofˆR(θ) leads...

Following [3] we confirm a conjecture of Yde Venema by piecing together results from various authors. Specifically, we show that if A is a residually finite, finitely generated modal algebra such that HSP(A) has equationally definable principal congruences, then the profinite completion of A is the MacNeille completion of A, and ♦ is smooth. Specific examples of such modal algebras are the free...

A pseudo-primitive word with respect to an antimorphic involution θ is a word which cannot be written as a catenation of occurrences of a strictly shorter word t and θ(t). Properties of pseudo-primitive words are investigated in this paper. These properties link pseudo-primitive words with essential notions in combinatorics on words such as primitive words, (pseudo)-palindromes, and (pseudo)-co...

Let (M,F) be a foliated m + n-dimensional manifold M with n-dimensional foliation F . Let V be a finite dimensional vector space over R. We describe all canonical (Folm,n-invariant) V -valued 1-forms Θ: TP r(M,F) → V on the r-th order adapted frame bundle P r(M,F) of (M,F). All manifolds and maps are assumed to be of class C∞. A definition of foliations can be found in [2]. Let Folm,n be the ca...

In this paper we continue the combinatorial study of models of particles jumping on a row of cells which we initiated with the standard totally asymmetric simple exclusion process or TASEP (Journal of Combinatorial Theory, Series A, 110(1):1–29, 2005). We consider here the parallel TASEP, in which particles can jump simultaneously. On the one hand, the interest in this process comes from highwa...

Let A be a finite or countable alphabet and let θ be a literal (anti)morphism onto A∗ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ-invariant for short). We establish a formula which allows to embed any non-complete θ-invariant code into a complete one: this brings a positive answer to the open ...

The goal of this paper is to compute the full HOD of models of AD of the form L(℘(R)) below “ADR + Θ is regular”. As part of this computation, we give a computation of HOD|Θ left open in [3] for Θ a successor in the Solovay sequence. Our work, when combined with [3], shows that in AD models of the form L(℘(R)) below “ADR + Θ is regular”, HOD satisfies GCH.