This note constructs the short primality tests of a few classes of integers. The running time complexity of any one of these tests is [log ] − 1 modular multiplications, exactly the same as the Pepin's test. In addition, it also will be shown that there are infinitely many primes with a short...

We used scaled factorial moments to search for intermittency in the log expression ratios (LERs) for thousands of genes spotted on cDNA microarrays (gene chips). Results indicate varying levels of intermittency in gene expression. The observation of intermittency in the data analyzed provides a...

Macroscopic properties of thermosetting polymers are strongly affected by thermal degradation. However, modelling the dynamics of thermal degradation is difficult due to an intrinsic coupling between reaction kinetics and heat transfer in polymeric materials. In this paper we consider...

The study of deterministic and stochastic dynamic problems in control theory can be reduced to partial differential equations by using Bellman's approach. The resulting PDE-based mathematical models are difficult to solve numerically, and most existing approaches cannot provide accuracy expected...

We consider left shift transform on the space = Σ of two-sided sequences over a compact alphabet Σ. We give an important and sufficient condition on ∈ which guarantees the restriction of onto orbit closure of to be a Toeplitz flow

Since an H-separable extension | is of depth two, we associate to it dual bialgebroids := End and := ( ⊗ ) over the centralizer as in [12, Kadison-Szlachányi]. We show that has an antipode and is a Hopf algebroid. is also Hopf algebroid under the condition that the centralizer is an Azumaya...

Cutting and packing problems appears as application birth in industry, transport, manufacture, as in ensemble of domains of mathematics, physics, biology. In this article we consider a guillotine cutting problem of separating of rectangle sheet to strips that can be rotated over right angle. We...

A base for a space is said to be if, whenever ∈ and () is a sequence of pairwise distinct elements of each containing , the collection {∩ : ∈ } is a local base at . We answer questions raised by Alleche and Arhangel'skii by showing that a pseudocompact TychonofF space with a sharp base...