Given an arbitrary measure μ, this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on L1 μ . However, we have the density if and only if μ is purely atomic. Furthermore, the study presents an example of a Banach space X in which the set of norm attaining operators from X into X∗ is dense in the space of all bounded linea...

Valuations of dense near polygons were introduced in [9]. A valuation of a dense near polygon S = (P,L, I) is a map f from the point-set P of S to the set N of nonnegative integers satisfying very nice properties with respect to the set of convex subspaces of S. In the present paper, we give an alternative definition of the notion valuation and prove that both definitions are equivalent. In the...

We construct a dense point set of n points in the plane with ne( √ logn) halving lines. This improves the bound O(n log n) of Edelsbrunner, Valtr and Welzl from 1997. We also observe that the upper bound on the maximum number of halving lines of dense point set can be improved to O(n). Our construction can be generalized to higher dimensions, for any d we construct a dense point set of n points...

This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time many one reductions It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity It follows that every weakly hard problem has a dense set of such maximally hard instances This extends the theorem ...

A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...

Previous case histories have shown that soil liquefaction severely damaged many structures supported on pile foundations during earthquakes. As a result, evaluating the potential for instability is an important consideration for the safe and resistant design of deep foundation against earthquakes. In this study, the liquefaction susceptibility of saturated sand interacting by single concrete pi...

Assuming that the underlying probability space is non-atomic we prove that products of random matrices (linear cocycles) with simple Lyapunov spectrum form an L p-dense set (1 p < 1) in the space of all cocy-cles satisfying the integrability conditions of the multiplicative ergodic theorem. However, the linear cocycles with one-point spectrum are also L p-dense. Further, in any L 1-neighborhood...

background: serological assay based on dense granular (gra) proteins of toxoplasma gondii (t. gondii) is actually the most popular laboratory diagnostic tool to detection of toxoplasmosis. we aimed to construct a recombinant gra7-ptz57rt plasmid vectors that it is suitable for sub-cloning and gra7 protein production. m aterials and methods: souris mice were used for maintaining of t. gondii tac...

The notion of an A-nowhere dense set for various subsets A of the reals may prove to be of interest in its own right, but this paper will be concerned exclusively with the special case A = Q. Notice that rational perfect sets introduced by Miller in [1] form a subset of the Q-nowhere dense sets since the closure of a set is rational perfect if it is perfect and disjoint from the rationals. On t...