A k-factor in a graph G is a spanning regular subgraph in which every vertex has degree exactly k. If a graph G on n vertices has minimum degree δ ≥ n/2 and k is a positive integer such that kn is even and k < (δ + √ 2δn− n2 + 8)/2, then G has a k-factor. Moreover, this is within an additive constant of 1 of being best possible.

Protein isolate is used in the food industry in order to process and stabilise food foams. Thereforethere has been a great deal of interest and research in order to understand the effect of processingparameters on the functional properties of the isolate. The major purpose of this research is to studythe foamability of the different proteins - starch nano-particle system. The results from exper...

Abstract By applying the weight functions, idea of introducing parameters and technique real analysis, a new multiple Hilbert-type integral inequality involving upper limit functions is given. The constant factor related to gamma function proved be best possible in condition. A corollary about case nonhomogeneous kernel some particular inequalities are obtained.

We examine the issue of running algorithms on a hypercube which has both node and edge faults, and we assume a worst case distribution of the faults. We prove that for any constant c, an n-dimensional hypercube (n-cube) with n c faulty components contains a fault-free subgraph that can implement a large class of hypercube algorithms with only a constant factor slowdown. In addition, our approac...

Let rex(n,F) denote the maximum number of edges in an n-vertex graph that is regular and does not contain F as a subgraph. We give lower bounds on rex(n,F), are best possible up to constant factor, when one C4, K2,t, K3,3 or Ks,t for t>s!.

We construct stable configurations of n overlapping discs of radius r in a unit square, with r = O(1/n). By a result of Diaconis, Lebeau, and Michel, this result is best possible, up to a constant factor. A consequence is that the Metropolis algorithm, a well-studied Markov chain on the hardcore model, is not irreducible in this range of parame-

We prove that every graph with maximum degree ∆ can be properly (∆ + 1)-coloured so that no colour appears more than O(log∆/ log log∆) times in the neighbourhood of any vertex. This is best possible up to the constant factor in the O(−) term. We also provide an efficient algorithm to produce such a colouring.

Financial returns exhibit common behavior described at best by factor models, but also fat tails, which may be captured by α-stable distributions. This paper concentrates on estimating factor models with multivariate α-stable distributed and independent factors and idiosyncratic noises under the assumption of time constant distribution (static factor models) or time-varying conditional distribu...

In this paper, by using the way of weight function and the technic of real analysis, a new integral inequality with some parameters and a best constant factor is given, which is a relation to four basic Hilberttype integral inequalities. The equivalent form and the reverse forms are considered. Mathematics Subject Classification: 26D15

In this paper, by using the way of weight function and real analysis techniques, a new integral inequality with some parameters and a best constant factor is given, which is a relation to Hilbert’s integral inequality and some base Hilbert-type integral inequalities. The equivalent form and the reverse forms are considered.