While the very first consensus protocols for the synchronous model were designed to match the worst-case lower bound, deciding in exactly t + 1 rounds in all runs, it was soon realized that they could be strictly improved upon by early stopping protocols. These dominate the first ones, by always deciding in at most t + 1 rounds, but often much faster. A protocol is unbeatable if it can’t be str...

Abstract We prove the following result: Let K be a strictly convex body in Euclidean space ℝ n , ≥ 3, and let L hypersurface which is image of an embedding sphere

We say that a subset of C n is hypoconvex if its complement is the union of complex hyperplanes. We say it is strictly hypoconvex if it is smoothly bounded hypoconvex and at every point of the boundary the real Hessian of its defining function is positive definite on the complex tangent space at that point. Let Bn be the open unit ball in C . Suppose K is a C compact manifold in ∂B1 × C , n > 1...

A Deza graph $\Gamma$ with parameters $(v,k,b,a)$ is a $k$-regular $v$ vertices such that any two distinct have $b$ or $a$ common neighbours, where $b \ge a$. of diameter 2 which not strongly regular called strictly graph. We find all 139 graphs up to 21 vertices.

Let S be a site. We introduce the notion of extension of strictly commutative Picard S-stacks. Applying this notion to 1-motives, we get the notion of extension of 1-motives and we prove the following conjecture of Deligne: if MRZ(k) denotes the integral version of the neutral Tannakian category of mixed realizations over an algebraically closed field k, then the subcategory of MRZ(k) generated...

In this paper we prove that for each k, the expressive power of k–ary fixed–point logic, i.e. the fragment of fixed–point logic whose fixed–point operators are restricted to arity ≤ k, strictly exceeds the power of (k − 1)–ary fixed–point logic. This solves a problem that was posed by Chandra and Harel in 1982. Our proof has a rather general form that applies to several variants of fixed–point ...

The opinions expressed in this paper do not necessarily reflect the position of Summary We prove the existence of an increasing equilibrium, and study the comparative statics of correlation in the k-double auction with affiliated private values. This is supposedly the simplest bilateral trading mechanism that allows for dependence in valuations between buyers and sellers. In the case k ∈{0 ,1} ...

Solution : Assume, without loss of generality |x2 − x1| ≥ 2−n+1. Then there exists an integer k ∈ {1, . . . , 2 − 1}, such that x1 < k · 2−n < (k + 1)2−n < x2. Of course PX((x1, x2)) ≥ P(k · 2−n ≤ X(ω) ≤ (k + 1)2−n) . (4) The integer k admits the unique binary expansion k = ∑n i=1 ki2 n−i. Then P(k · 2−n ≤ X(ω) ≤ (k + 1)2−n) = P(Cn,(k1...,kn)) = p 1(1− p)0 , (5) with n0(k) and n1(k) the number ...

V. D. Milman proved in [14] that the product of two strictly singular operators on L p [0, 1] (1 p < ∞) or on C[0, 1] is compact. In this note we utilize Schreier families S ξ in order to define the class of S ξ-strictly singular operators, and then we refine the technique of Milman to show that certain products of operators from this class are compact, under the assumption that the underlying ...