We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence. We follow [4] in defi...

Let Mg be the moduli space of smooth, genus g curves over an algebraically closed field K of zero characteristic. Denote by Mg(G) the subset of Mg of curves δ such that G (as a finite non-trivial group) is isomorphic to a subgroup of Aut(δ) and let M̃g(G) be the subset of curves δ such that G ∼= Aut(δ) where Aut(δ) is the full automorphism group of δ. Now, for an integer d ≥ 4, let MPl g be the ...

Byzantine vector consensus requires that non-faulty processes reach agreement on a decision (or output) that is in the convex hull of the inputs at the non-faulty processes. Recent work has shown that, for n processes with up to f Byzantine failures, when the inputs are d-dimensional vectors of reals, n ≥ max (3f + 1, (d+ 1)f + 1) is the tight bound for synchronous systems, and n ≥ (d+ 2)f + 1 ...

Given two comparative maps, that is two sequences of markers each representing a genome, the Maximal Strip Recovery problem (MSR) asks to extract a largest sequence of markers from each map such that the two extracted sequences are decomposable into non-intersecting strips (or synteny blocks). This aims at defining a robust set of synteny blocks between different species, which is a key to unde...

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

A homomorphism of an automaton A without outputs onto a subau-tomaton B of A is called a retract homomorphism if it leaves the elements of B fixed. An automaton A is called a retractable automaton if, for every subautomaton B of A, there is a retract homomorphism of A onto B. In [1] and [3], special retractable automata are examined. The purpose of this paper is to give a construction for state...

Let u(x) x ∈ Rq be a symmetric non-negative definite function which is bounded away from zero but which may have u(0) = ∞. Let px,δ(·) be the density of an Rq valued canonical normal random variable with mean x and variance δ and let {Gx,δ; (x, δ) ∈ Rq× [0, 1]} be the mean zero Gaussian process with covariance EGx,δGy,δ′ = ∫ ∫ u(s− t)px,δ(s)py,δ′(t) ds dt. A finite positive measure μ on Rq is s...

In this paper, we deal with second-order stochastic dominance (SSD) portfolio efficiency with respect to all portfolios that can be created from a considered set of assets. Assuming scenario approach for distribution of returns several SSD portfolio efficiency tests were proposed. We introduce a δ-SSD portfolio efficiency approach and we analyze the stability of SSD portfolio efficiency and δ-S...

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.