Commuting graphs of matrices over semirings

We calculate diameters and girths of commuting graphs of the set of all nilpotent matrices over a semiring, the group of all invertible matrices over a semiring, and the full matrix semiring.     

Inequalities for Gondran-Minoux rank and idempotent semirings

The rank-sum, rank-product, and rank-union inequalities for Gondran-Minoux rank of matrices over idempotent semirings are considered. We prove these inequalities for matrices over quasi-selective semirings without zero divisors, which include matrices over the max-plus semiring. Moreover, it is shown that the inequalities provide the linear algebraic characterization for the class of quasi-selective semirings. Namely, it is proven that the inequalities hold for matrices over an idempotent semiring S without zero divisors if and only if S is quasi-selective. For any idempotent semiring which is not quasi-selective it is shown that the rank-sum, rank-product, and rank-union inequalities do not hold in general. Also, we provide an example of a selective semiring with zero divisors such that the rank-sum, rank-product, and rank-union inequalities do not hold in general.     

Frozen divided difference scheme for solving systems of nonlinear equations

The development of an inverse first-order divided difference operator for functions of several variables, as well as a direct computation of the local order of convergence of an iterative method is presented. A generalized algorithm of the secant method for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed. Furthermore, a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced.     

On the computational efficiency index and some iterative methods for solving systems of nonlinear equations

In this paper two new iterative methods are built up and analyzed. A generalization of the efficiency index used in the scalar case to several variables in iterative methods for solving systems of nonlinear equations is revisited. Analytic proofs of the local order of convergence based on developments of multilineal functions and numerical concepts that will be used to illustrate the analytic results are given. An approximation of the computational order of convergence is computed independently of the knowledge of the root and the necessary time to get one correct decimal is studied in our examples.     

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.     

Structures and stabilities of the donor–acceptor complexes HXPY (X=Al,B; Y=H,F, OH)

The optimized geometries, complexation energies, etc. of HXPY (X?=?Al, B; Y?=?H, F, OH) donor–acceptor complexes have been investigated at the B3LYP/6-311+G(d,p), MP2/6-311+G(d,p) and/or CCSD(T)/6-311+G(d,p) levels. The results show that HBPY (Y?=?H, F, OH) is more stable than the corresponding HAlPY (Y?=?H, F, OH), F (or OH) substitution on phosphorus results in decreasing complex stability, and the stronger the electron-attracting nature of the substitution atom, the more stable the complex. Moreover, the thermodynamic and kinetic properties of the formation reaction of these donor–acceptor complexes were also examined within the temperature range 200–800?K using the general statistical thermodynamics and Eyring transition state theory with Wigner correction. It is concluded that the formation of HBPY is thermodynamically favoured over that of the corresponding HAlPY, especially at low temperature, and is kinetically favoured over that of the relevant HAlPY (Y?=?H, F, OH), especially at high temperature.     

Carbon-13 Assignments and Revision of the Stereostructures of the Cadinanes 2-Hydroxy-8α-angeloyloxycalamenene and 2-Hydroxy-8α-hydroxycalamenene

The two known cadinanes 2-hydroxy-8α-hydroxycalamenene and 2-hydroxy-8α-angeloyloxycalamenene were isolated from a Louisiana population of Heterotheca subaxillaris.

Their ¹³C NMR spectra were fully assigned by the application of HETCOR, COLOC, COSY, NOESY and DEPT experiments. It was shown on the basis of NOESY experiments that both cadinanes require revision at the stereogenic centre C-7.     

Binding Study of Phenformin with Bovine Serum Album Using a Combined Technique of Equilibrium Dialysis with Flow-Injection Chemiluminescence Detection

ABSTRACT

The interaction between phenformin hydrochloride and bovine serum albumin (BSA) was investigated by the methods of chemiluminescence combined with equilibrium dialysis technique. A novel N-bromosuccinimide (NBS)–eosin Y (EY) chemiluminescence (CL) method was established for the determination of phenformin. The mechanism of this chemiluminescence system was proposed. Optimization studies were performed to determine the phenformin. Under the optimal conditions, the CL intensity was linear for a phenformin concentration over the range of 4.6 × 10^?8 to 5.0 × 10^?5 g/mL. The detection limit was 1.5 × 10^?8 g/mL. The data obtained by the present equilibrium dialysis–CL system were analyzed using the Klotz plot and the Scatchard analysis. The results showed that the Klotz plot and the Scatchard plot are linear with good correlation coefficient, indicating that the phenformin has only one type of binding site on BSA. The binding parameters were the number of the binding sites n (1.02) and the estimated association constant K (2.66 × 10⁴ L/mol). The chemiluminescence system combined with equilibrium dialysis developed in this work demonstrated its use for determination of interaction between drug and protein by using relatively simple instrument.     

偏最小二乘分光光度法同时测定镍基合金中的铈和钇

以对乙酰基偶氮氯膦（ＣＰＡｐＡ）为显色剂，研究了同时测定Ｃｅ和Ｙ的最佳条件，由于二者吸收光谱严重重叠，本文运用偏最小二乘法实现了Ｃｅ和Ｙ的同时测定，结果满意。     

Copper Tetrahydrosalen Complex Encapsulated in Zeolite Y： an Effective Heterogeneous Catalyst for the Oxidation of Cycloalkanes

In the last decade, encapsulation of transition metal complexes in zeolites and related materials has been paid much attention, because this type of materials could serve as functional mimic enzymes, possessing both homogeneous-catalysis and heterogeneous…