UV/VIS Spectral Studies of Catecholase Activity of Binuclear Copper(II) Complexes [Cu2REP(μ-X)(Y)2]

By means of ultraviolet and visible spectroscopy we have studied the catecholase activity of two binuclear copper(II) complexes of general formula [Cu₂REP(u-X)(Y)₂] (1, X=OH and Y=ClO₄; 2, X=Y=CI), REP =deprotonated 2, 6-bis(1′-(4′-(2″-pyridyl)-2′-thiabutyl))-4-methylphenol. Both complexes promote catalytic autoxidation of 3, 5-di-tert-butylcatechol (3, 5-DTBC) to 3, 5-di-tert-butylquinone (3, 5-DTBQ) in methanol, but not in acetonitrile.     

Chiral,biomimetic total synthesis of (−)-aplysistatin

The marine antineoplastic agent aplysistatin ($\text{6}$) has been prepared enantiospecifically. The key step is the biomimetic cyclization of (2R, 3R)-2-homogeranyl-3,4-dihydroxybutanoic acid 1 4 lactone ($\text{3}$)_with 2,4,4,6-tetrabromocyclohexa-2,5-dienone in nitromethane.     

Dimensions of supercritical branching processes in varying environments

Let ∂Γ be the boundary of a family tree Γ associated with a supercritical branching process in varying environments. In this paper, the Hausdorff dimension, the upper box dimension and the packing dimension of ∂Γ are computed explicitly. In contrast to the (fixed environment) Galton–Watson case, the Hausdorff and upper box dimension may take different values.     

A study on the method of fundamental solutions using an image concept

In this paper, both analytical and semi-analytical solutions for Green’s functions are obtained by using the image method which can be seen as a special case of method of fundamental solutions (MFS). The image method is employed to solve the Green’s function for the annular, eccentric and half-plane Laplace problems. In addition, an analytical solution is derived for the fixed-free annular case. For the half-plane problem with a circular hole and an eccentric annulus, semi-analytical solutions are both obtained by using the image concept after determining the strengths of two frozen image points and a free constant by matching boundary conditions. It is found that two frozen images terminated at the two focuses in the bipolar coordinates for the problems with two circular boundaries. A boundary value problem of an eccentric annulus without sources is also considered. Error distribution is plotted after comparing with the analytical solution derived by Lebedev et al. using the bipolar coordinates. The optimal locations for the source distribution in the MFS are also examined by using the image concept. It is observed that we should locate singularities on the two focuses to obtain better results in the MFS. Besides, whether the free constant is required or not in the MFS is also studied. The results are compared well with the analytical solutions.     

A note on a paper by Molai and Khorram

The aim of this note is to show that the optimization algorithm proposed in [6] may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain.     

Modified particle swarm optimization algorithm with simulated annealing behavior and its numerical verification

The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms.