Sulfamic acid catalyzed solvent-free synthesis of 10-aryl-7,7-dimethyl-6,7,8,10-tetrahydro-9H-[1,3]-dioxolo [4,5- <Emphasis Type="Italic">b</Emphasis>]xanthen-9-ones and 12-aryl-9,9-dimethyl-8,9,10,12-tetrahydro-11H-benzo[<Emphasis Type="Italic">a</Emphasis>]xanthen-11-ones

Three-component one-pot synthesis of some novel 10-aryl-7,7-dimethyl-6,7,8,10-tetrahydro-9H-[1,3]-dioxolo[4,5-b]xanthen-9-ones, which have not been published before, and 12-aryl-9,9-dimethyl-8,9,10,12-tetrahydro-11H-benzo[a]xanthen-11-ones from condensation of 3,4-methylenedioxyphenol or β-naphthol, aldehydes and dimedone under solvent-free conditions at 120 °C is reported.     

A variable step implicit block multistep method for solving first-order ODEs

A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss-Seidel approach is used for the implementation of the proposed method in the PE(CE)^m mode. The method is presented in a simple form of Adams type and all coefficients are stored in the code in order to avoid the calculation of divided difference and integration coefficients. Numerical examples are given to illustrate the efficiency of the proposed method.     

A heuristic procedure for the Capacitated m-Ring-Star problem

In this paper we propose a heuristic method to solve the Capacitated m-Ring-Star Problem which has many practical applications in communication networks. The problem consists of finding m rings (simple cycles) visiting a central depot, a subset of customers and a subset of potential (Steiner) nodes, while customers not belonging to any ring must be “allocated” to a visited (customer or Steiner) node. Moreover, the rings must be node-disjoint and the number of customers allocated or visited in a ring cannot be greater than the capacity Q given as an input parameter. The objective is to minimize the total visiting and allocation costs. The problem is a generalization of the Traveling Salesman Problem, hence it is NP-hard. In the proposed heuristic, after the construction phase, a series of different local search procedures are applied iteratively. This method incorporates some random aspects by perturbing the current solution through a “shaking” procedure which is applied whenever the algorithm remains in a local optimum for a given number of iterations. Computational experiments on the benchmark instances of the literature show that the proposed heuristic is able to obtain, within a short computing time, most of the optimal solutions and can improve some of the best known results.     

Quenching of IR luminescence of erbium, neodymium, and ytterbium beta-diketonate complexes by ligand C-H and C-D bonds

The effect of CH and CD quenching on the luminescence lifetime of Er(3+) Nd(3+) and Yb(3+) in the Cs[Ln(HFA)(4)] system has been quantified, and we have shown that for Er(3+) ions the quenching is dominated by the nearest neighbor CH oscillators, whereas for Nd(3+) ions the roles of more distant CH oscillators and nearest neighbor CD oscillators are important.     

New synthetic protocols for the preparation of unsymmetrical bisindoles

Novel unsymmetrical bisindoles were synthesized by a solvent-free C-C bond-formation reaction under mild conditions. Starting from aziridines or hydroxyl precursors, indoles have been used as C-nucleophiles to form new pharmacologically interesting bisindoles via an electrophilic aromatic substitution pathway in good to excellent yields. [reaction: see text]     

ChemInform Abstract: X2Y2 Isomers: Tuning Structure and Relative Stability Through Electronegativity Differences (X: H,Li, Na,F, Cl,Br, I; Y: O,S, Se,Te).

Density functional calculations on XYYX and X₂YY isomers of the X₂Y₂ species (X: H, Li, Na, F, Cl, Br, I; Y: O, S, Se, Te) show that the XYYX isomers are more stable than the X₂YY forms except for X = F and Y = S and Te, for which the F₂SS and F₂TeTe isomers are slightly more stable.     

A new parametric method for ranking fuzzy numbers

Ranking fuzzy numbers is important in decision-making, data analysis, artificial intelligence, economic systems and operations research. In this paper, to overcome the limitations of the existing studies and simplify the computational procedures an approach to ranking fuzzy numbers based on α$\alpha$-cuts is proposed. The approach is illustrated by numerical examples, showing that it overcomes several shortcomings such as the indiscriminative and counterintuitive behavior of existing fuzzy ranking approaches.     

Second Maximum Sum of Element Orders of Finite Nilpotent Groups

In [1 Amiri , H. , Jafarian Amiri , S. M. , Isaacs , I. M. ( 2009 ). Sums of element orders in finite groups . Communications in Algebra 37 : 2978 – 2980 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]], the authors proved that the maximum sum of element orders on finite groups of the same order occurs in cyclic group. In this paper we obtain the structure of groups having maximum sum of element orders on noncyclic nilpotent group of the same order.     

Relativistic symmetries in the Rosen-Morse potential and tensor interaction using the Nikiforov-Uvarov method

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen- Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ(κ± 1)r 2 . In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov-Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.