We call a coloring of the edge set of a graph G a b-bounded coloring if no color is used more than b times. We say that a subset of the edges of G is rainbow if each edge is of a different color. A graph has property A(b, H) if every b-bounded coloring of its edges has a rainbow copy of H. We estimate the threshold for the random graph Gn,p to have property A(b, H).

In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the n-th order delay differential equations ( r(t) [ x(n−1)(t) ]γ)′ = q(t)f ( x(τ(t)) ) . Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations....

In this paper we describe the successful application of the ProB validation tool on an industrial case study. The case study centres on the San Juan metro system installed by Siemens. The control software was developed and formally proven with B. However, the development contains certain assumptions about the actual rail network topology which have to be validated separately in order to ensure ...

We provide an explicit formula for a large class of exponential Bsplines. Also, we characterize the cases where the integer-translates of an exponential B-spline form a partition of unity up to a multiplicative constant. As an application of this result we construct explicitly given pairs of dual Gabor frames.

TB-9Sb is a translocation between the B chromosome and chromosome 9 in maize. Certain deletions of B chromatin from the translocation cause a sharp decrease in B-9 transmission compared to the rate for standard TB-9Sb. The deletions remove components of a B chromosome genetic system that serves to suppress meiotic loss in the female. At least two distinct B-chromosome regions suppress meiotic l...

We prove the following theorems: 1. There exists an ω-covering with the property s0. 2. Under cov(N ) = 2 there exists X such that ∀B∈Bor[B ∩ X is not an ω-covering or X \B is not an ω-covering]. 3. Also we characterize the property of being an ω-covering.

Given a checkpoint and communication pattern of a distributed execution, the \No Z-Cycle" property (N ZC) states that there does not exist a dependency between a checkpoint and itself. In other words, there does not exist a non-causal sequence of messages that starts after a checkpoint and terminates before that checkpoint. From an operational point of view, this property corresponds to the fac...

ProB is a model checking tool for the B Method. In this paper we present an extension of ProB that supports checking of specifications written in a combination of CSP and B. We explain how the notations are combined semantically and give an overview of the implementation of the combination. We illustrate the benefit that appropriate use of CSP, in conjunction with our tool, gives to B developme...

The classical Erdős-Ko-Rado theorem states that if k ≤ ⌊n/2⌋ then the largest family of pairwise intersecting k-subsets of [n] = {0, 1, . . . , n} is of size ( n−1 k−1 ) . A family of k subsets satisfying this pairwise intersecting property is called an EKR family. We generalize the EKR property and provide asymptotic lower bounds on the size of the largest family A of k-subsets of [n] that sat...

The problem of designing new peptides that possess specific properties, such as bactericidal activity, is of wide interest. Recently, attention has focused on the use of Computer-Aided Molecular Design techniques in parallel with more traditional 'synthesise and test' methods. These techniques may typically use Genetic Algorithms to optimise molecules based on Neural Network models that predict...