Given a standard set δ of a finite size r, we show that the functor associating to a k-algebra B the set of all reduced Gröbner bases with standard set δ is representable. We show that the representing scheme Hilb′ δ k[x]/k is a locally closed stratum in the punctual Hilbert scheme Hilbrk[x]/k. Moreover, we cover the punctual Hilbert scheme by open affine subschemes attached to all standard set...

The stable set polytope of a graph is the convex hull of the 01 vectors corresponding to stable sets of vertices. To any nontrivial facet ∑n i=1 aixi ≤ b of this polytope we associate an integer δ, called the defect of the facet, by δ = ∑n i=1 ai − 2b. We show that for any fixed δ there is a finite collection of graphs (called “basis”) such that any graph with a facet of defect δ contains a sub...

In the rectangle D = (0, a) × (0, b) with the boundary Γ the Dirichlet problem ∂4u ∂x2∂y2 = p(x, y)u + q(x, y), u(x, y) = 0 for (x, y) ∈ Γ is considered, where p and q : D → R are locally summable functions and may have nonintegrable singularities on Γ. The effective conditions guaranteeing the unique solvability of this problem and the stability of its solution with respect to small perturbati...

A collection C of balls in R is δ-inflatable if it is isometric to the intersection U ∩ E of some d-dimensional affine subspace E with a collection U of (d + δ)-dimensional balls that are disjoint and have equal radius. We give a quadratic-time algorithm to recognize 1-inflatable collections of balls in any fixed dimension, and show that recognizing δ-inflatable collections of d-dimensional bal...

OBjEcTIVE: As we previously demonstrated, the inhibitory effect of iodine on thyroid cell growth is mediated by iodolactones, especially 6-iodo-5-hydroxy-eicosatrienoic acid (δ-iodolactone). In this communication we compare the effect of iodide, molecular iodine and δ-iodolactone on growth inhibition and apoptosis on three human thyroid carcinoma cell lines (B-cPAP cells, FTc-133 cells and 8505...

M be a module. In this article we study δ–essential submodules as a dual of δ-small submodules of Zhou where δ = {N ∈ σ[M ] : Rej(N,M) = 0} and M = {N ∈ σ[M ] : N ¿ b N}, and also define μ-M–singular modules as modules N ∈ σ[M ] such that N ∼= K/L for some K ∈ σ[M ] and L is μ–essential in K. By M–M–singular modules and δ–M– singular modules a characterization of GCO–modules, and by FC–M–singul...

We say a pair of integers (a, b) is findable if the following true. For any δ > 0 there exists p0 such that for prime p ≥ and red-blue colouring ℤ/pℤ in which each colour has density at least δ, we can find an arithmetic progression length + b inside whose first elements are red last blue. Szemeredi’s Theorem on progressions implies (0, k) (1, find-able k. prove (2, also However, same not true ...

This article defines the paritions of a finite set structured in a cycle which possesses the property that a pair of points belonging to a class and a pair of points belonging to another class cannot be in a crossed way. It establishes that these partitions form a lattice and it specifies some of the descriptive and enumerative properties of the lattice; it computes in particular the Möbius fun...

We define a cohomology theory for topological semigroups, with seminormed cohomology groups. Our theory can be considered as a topological version of bounded cohomology of discrete semigroups. 1. Definition of the cohomology Bounded cohomology was first defined for discrete groups by F. Trauber and then for topological spaces by M. Gromov [6]. In this paper we establish a topological bounded co...

Main result of this paper is the following theorem: given δ, 0 < δ < 1/3 and n ∈ N there exists an (n + 1) × n inner matrix function F ∈ H∞ (n+1)×n such that I ≥ F ∗(z)F (z) ≥ δI ∀z ∈ D, but the norm of any left inverse for F is at least [δ/(1−δ)]−n ≥ (2δ). This gives a lower bound for the solution of the Matrix Corona Problem, which is pretty close to the best known upper b bound C · δ−n−1 log...