Let G be a connected graph. For a vertex v ∈ V (G) and an ordered k-partition Π = {S1, S2, ..., Sk} of V (G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v, S1), d(v, S2), ..., d(v, Sk)). The k-partition Π is said to be resolving if the k-vectors r(v|Π), v ∈ V (G), are distinct. The minimum k for which there is a resolving k-partition of V (G) is called the partition d...

One of the approaches used to partition inputs consists in modifying and limiting the input set using an external transcoder. This method is strictly related to output coding. This paper presents an optimal output coding in PAL-based programmable transcoders. The algorithm can be used to implement circuits in PAL-based CPLDs.

Growing applications of phenylalanine dehydrogenase (PheDH) enzyme in the medical and pharmaceutical industries encourages researchers to seek simple, fast and economical alternative purification methods. With goal of finding a new technique, the extraction and purification of recombinant Bacillus badius PheDH in polyethylene glycol 6000 (PEG-6000) and ammonium sulfate aqueous two-phase systems...

in this paper, the bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (iemtl) through expansion methods (collocation method, partition method, galerkin method). the method is discussed in detail and illustrated by solving some numerical examples. comparison between the exact and approximated results obtained from these methods is...

In [46], Witten related topological string theory on the cotangent bundle T M of a three manifold M to the Chern–Simons gauge theory on M . Gopakumar and Vafa [11] related the topological string theory on the deformed conifold (the cotangent bundle T S of the 3–sphere) to that on the resolved conifold (the total space of OP1. 1/ ̊OP1. 1/! P ). These works lead to a duality between the topologica...

for a graph g, let d(g) be the set of all strong orientations of g. the orientationnumber of g is min {d(d) |d belongs to d(g)}, where d(d) denotes the diameterof the digraph d. in this paper, we determine the orientation number for some subgraphs of complete bipartite graphs.

The partition function of the Potts model can be expressed in terms of famous combinatorial graph polynomials for restricted Hamiltonians. We investigate the Hamiltonian with variable edge interaction and external magnetic field, for which the partition function is the V-polynomial. Because the partition function is a polynomial, we can use motivic methods from algebraic geometry to characteriz...

In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is car...

This paper addresses the classical graph partitioning problem applied to the air network : One considers an air transportation network with aircraft inducing a control workload. This network has to be partitioned into K balanced sectors for which the cutting ow is minimized .