Graphs With Few Matching Roots

We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomials.     

Application of N,N'-Diiodo-N,N'-1,2-ethandiylbis(p-toluene sulfonamide)as a New Reagent for Synthesis of2-Arylbenzimidazoles and 2-Arylbenzothiazoles under Solvent-free Conditions

N,N′‐Diiodo‐N,N′‐1,2‐ethandiylbis(p‐toluene sulfonamide) (NIBTS) is a good and new reagent for synthesis of 2‐arylbenzimidazoles and 2‐arylbenzothiazoles at room temperature under solvent‐free condition with good to high yield. Absence of solvent, short reaction times, non‐corrosive, operational simplicity and environmentally friendliness are the main advantages of this procedure.     

Novel isocyanide-based three-component reaction: a facile synthesis of substituted 1H-chromeno[2,3-d]pyrimidine-5-carboxamides

A mild and efficient method for the synthesis of 1H-chromeno[2,3-d]pyrimidine-5-carboxamide derivatives via a one-pot, three-component reaction of an isocyanide, barbituric acid, and a salicylaldehyde in the presence of acetic acid in ethanol/water mixture at 75 °C is reported. This high atom economy reaction led to the construction of one benzopyran ring, and one amide group in a single synthetic step.     

Maximum Order of Triangle‐Free Graphs with a Given Rank

The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle‐free graphs with a given rank and characterize all such graphs achieving the maximum order.     

On edge star sets in trees

Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity m_A(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if m_A(λ)−m_A−e(λ) is negative (resp., 0, positive ), where A−e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=m_A(λ) and A−S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is proved. We prove that neutral edges always exist for eigenvalues of multiplicity more than 1. It is also proved that an edge e=uv is a downer edge for λ,A if and only if u and v are both downer vertices for λ,A; and e=uv is a neutral edge if u and v are neutral vertices. Among other results, it is shown that any edge star set for each eigenvalue of a tree is a matching.     

Benzoylferrocene-modified carbon nanotubes paste electrode as a voltammetric sensor for determination of hydrochlorothiazide in pharmaceutical and biological samples

The electrooxidation of hydrochlorothiazide (HCT) at the surface of a benzoylferrocene modified multi-walled carbon nanotube paste electrode was studied using electrochemical approaches. Under the optimized conditions (pH 7.0), the square wave voltammetric peak current of HCT increased linearly with HCT concentration in the ranges of 6.0?×?10^?7 to 3.0?×?10^?4 M. The detection limit was 9.0?×?10^?8 M HCT. The diffusion coefficient (D?=?1.75?×?10^?5 cm²/s) and electron transfer coefficient (α?=?0.45) for HCT oxidation were also determined. The proposed sensor was successfully applied for the determination of HCT in human urine and tablet samples.     

On FC-Purity and I-Purity of Modules and Köthe Rings

In this article, several characterizations of certain classes of rings via FC-purity and I-purity are considered. Among others results, it is shown that every I-pure injective left R-module is projective if and only if every FC-pure projective left R-module is injective, if and only if, R is a semisimple ring. In particular, the structures of FC-pure projective and I-pure projective modules over a left Artinian ring are completely described. Also, it is shown that every left R-module is FC-pure projective if and only if every indecomposable left R-module is a finitely presented cyclic R-module, if and only if, R is a left Köthe ring. Finally, we introduce FC-pure flatness and I-pure flatness of modules and several characterizations of these notions are given. In particular, we show that a commutative ring R is quasi-Frobenius if and only if R is an Artinian ring and I-pure injective, if and only if, R is an Artinian ring and the injective envelope E(R) is an FC-pure projective R-module.