We consider the two-dimensional (2-D) (d, IC) runlengthlimited constraint and the 2-D ‘no isolated bits’ constraint (in short, the n.i.b. constraint). A binary array on the square lattice satisfies the two-dimensional (d, IC) constraint if it satisfies the one-dimensional (d, IC) constraint in both vertical and horizontal directions. Similarly, an array on the hexagonal lattice satisfies the tw...

Energy absorption capability of thin-walled structures with various cross sections has been considered by researchers up to now. These structures as energy absorbers are used widely in different industries such as automotive and aerospace and protect passengers and goods against impact. In this paper, mechanical behavior of thin-walled aluminum tubes with and without polyurethane foam filler su...

in a subclass of the scale-parameter exponential family, we consider the sequential pointestimation of a function of the scale parameter under the loss function given as the sum of the weightedsquared error loss and a linear cost. for a fully sequential sampling scheme, second order expansions areobtained for the expected sample size as well as for the regret of the procedure. the former resear...

Problem 1. On the picture below (not to scale, adapted from an actual Chinese drawing from 1000 B.C.) the area of the large square ABCD is 25, and the area of the small square A B C D is 1. Find the length of AA. A A B B C C D D

We prove a nontrivial bound of O(|D|27/56+ ) for the 3-part of the class number of a quadratic field Q( √ D) by using a variant of the square sieve and the q-analogue of van der Corput’s method to count the number of squares of the form 4x3− dz2 for a square-free positive integer d and bounded x, z.