In [13] it was demonstrated that the Proper Forcing Axiom implies that there is a five element basis for the class of uncountable linear orders. The assumptions needed in the proof have consistency strength of at least infinitely many Woodin cardinals. In this paper we reduce the upper bound on the consistency strength of such a basis to something less than a Mahlo cardinal, a hypothesis which ...

The Itapecuru is a relatively large river in the northeastern Brazilian state of Maranhão. During several expeditions to this basin, we collected 69 fish species belonging to 65 genera, 29 families and 10 orders. Characiformes and Siluriformes were the orders with the largest number of species and Characidae, Loricariidae, Cichlidae, Auchenipteridae and Pimelodidae were the richest families. Ab...

We consider the problem of determining finite integer sets which are knapsack-solvable in linear time (that is, it is possible to determine in linear time, for any integer b, whether b can be expressed as a sum of distinct elements of that set) and where the largest element is as small as possible. We study the condition that the k-subsets (for fixed k) when lexicographically ordered have incre...

We make use of binary encoding of a phase wave front for the generation of diffractive elements. Binary encoding enables to introduce a constant phase shift between different diffraction orders. We describe the main features of phase wave front encoding and then suggest to apply them for a design of a diffractive alignment element. The proposed positioning tool is a modified version of the hype...

A finite semifield D is a finite nonassociative ring with identity such that the set D∗ = D \ {0} is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield planes of orders 64 and 81 by means of computational methods. These computer-assisted results yield to a complete classification (up to isotopy) of 81-element finite s...

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element method of arbitrary order. We prove that the proposed Hessian recovery method preserves polynomials of degree k + 1 on general unstructured meshes and superconverges at a rate of O(hk) on mildly structured meshes. In addition, the method is proved to be ultraconvergent (two orders hi...

We consider the limit distribution of the orders of the k largest components in the Erdős-Rényi random graph inside the “critical window” for arbitrary k. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function.

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...