Assume Xn is a random sample of n uniform, independent points from a triangle T . The longest convex chain, Y , of Xn is defined naturally (see the next paragraph). The length |Y | of Y is a random variable, denoted by Ln. In this paper we determine the order of magnitude of the expectation of Ln. We show further that Ln is highly concentrated around its mean, and that the longest convex chains...

The "/-ray decay of the giant dipole resonance ( G D R ) buil t on highly excited states has not only become a very impor tan t tool for the study o f nuclear shape effects as a function o f tempera ture and angular m o m e n t u m [ 1 ], but is also sensit ive to react ion dynamical effects [2 ]. For example, a reduct ion of the fission probabi l i ty at the early stages of the decay of a high...

Colonies are an abundant form of bacterial multicellularity; however, relatively little is known about the initial stages of their construction. We have previously described that colony development of the soil bacterium Bacillus subtilis is a highly ordered process, typically initiating with the formation of extending cell chains arranged in a Y shape structure. Furthermore, we demonstrated tha...

Assume Xn is a random sample of n uniform, independent points from a triangle T . The longest convex chain, Y , of Xn is defined naturally (see the next paragraph). The length |Y | of Y is a random variable, denoted by Ln. In this paper we determine the order of magnitude of the expectation of Ln. We show further that Ln is highly concentrated around its mean, and that the longest convex chains...

Let X be a topological vector space, Y = IR n , n 2 IN, A a continuous linear map from X to Y , C X, B a convex set dense in C, and d 2 Y a data point. We derive conditions which guarantee that the set B \ A ?1 (d) is nonempty and dense in C \ A ?1 (d). Some applications to shape preserving interpolation and approximation are described.

This work reports about the assessment of two shape descriptors, namely the fractal dimension and the normalized multiscale bending energy, for applications in biological shape analysis. Both descriptors are brie y reviewed and some preliminary results of their application to the morphometric characterization of neural cells are presented. The methodology for the evaluation of the shape measure...

Formation micro imager (FMI) can directly reflect changes of wall stratums and rock structures. Conventionally, FMI images mainly are analyzed with manual processing, which is extremely inefficient and incurs a heavy workload for experts. Iranian reservoirs are mainly carbonate reservoirs, in which the fractures have an important effect on permeability and petroleum production. In this paper, a...

The aim of the study was to assess the influence of gap shape on biomechanical results in extra-articular distal humeral fracture: with contact on the posterior part (by anterior gap) and contact on ulnar column (by radial gap). The goal was to examine if and to what extent did displacements decrease in comparison with previously examined parallel gap without bony contact. The finite element an...

Abstract. Let I be a finite interval, r, n ∈ N, s ∈ N0 and 1 ≤ p ≤ ∞. Given a set M , of functions defined on I, denote by ∆+M the subset of all functions y ∈ M such that the s-difference ∆τ y(·) is nonnegative on I, ∀τ > 0. Further, denote by W r p the Sobolev class of functions x on I with the seminorm ‖x‖Lp ≤ 1. We obtain the exact orders of the Kolmogorov and the linear widths, and of the s...

Alloyed Zn(1-x-y)Cd(x)Mn(y)Se nanocrystals exhibiting bright intrinsic dual emission attractive for ratiometric optical nanothermometry are reported. Relative to earlier materials with related dual emission, these alloy nanocrystals require shorter syntheses, contain less Cd(2+), and show dual emission that is less sensitive to nanocrystal shape, size, or surfaces.