Studies on pyrrolidinones. Synthesis of 1,2,3,5,11,11a-hexahydroindolizino[7,6-b]indole-3,11-dione

Condensation of N-trimethylsilylindole with methyl N-trimethylsilyloxymethylpyroglutamate is the best method to obtain methyl N-indolylmethylpyroglutamate. Friedel-Crafts cyclization of the corresponding acid yields a new ketone (1,2,3,5,11,11a-hexahydroindolizino[7,6-b] indole-3,11-dione).     

Mixed-ligand complexes of copper(I) with diimines and phosphines: Effective catalysts for the coupling of phenylacetylene with halobenzene

New copper(I) mixed-ligand complexes 1–4 of the formula Cu(N–N)PR₃X, where N–N = 1,10-phenanthroline (phen), 2,2′-bipyridine (bpy), 5,5′-dimethyl-2,2′-bipyridine (5,5′dimbpy) and PR₃ = tricyclohexylphosphine, tris(2-cyanoethyl)phosphine and isopropyldiphenylphosphine, have been synthesized. The complexes were characterized by EA, IR, NMR and single crystal X-ray diffraction. The solution fluorescence emission spectra were measured. The single crystal X-ray analysis showed that the copper(I) ion is four-coordinate with a distorted tetrahedral geometry. The complexes catalyze the formation of diphenylacetylene from the coupling of halobenzene with phenylacetylene. The complex Cu(5,5′-dimethylbpy)P{(cyhexyl)₃}I showed the highest catalytic activity. At room temperature all four complexes exhibit, in dichloromethane, emission maxima in the 329–344 nm range, corresponding to intra-ligand excited states.     

Local Convergence Properties of Douglas–Rachford and Alternating Direction Method of Multipliers

The Douglas–Rachford and alternating direction method of multipliers are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of Douglas–Rachford (resp. alternating direction method of multipliers) when the involved functions (resp. their Legendre–Fenchel conjugates) are moreover partly smooth. More precisely, when the two functions (resp. their conjugates) are partly smooth relative to their respective smooth submanifolds, we show that Douglas–Rachford (resp. alternating direction method of multipliers) (i) identifies these manifolds in finite time; (ii) enters a local linear convergence regime. When both functions are locally polyhedral, we show that the optimal convergence radius is given in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified submanifolds. Under polyhedrality of both functions, we also provide conditions sufficient for finite convergence. The obtained results are illustrated by several concrete examples and supported by numerical experiments.     

Comparison of two methods for determination of tomato paste solids: vacuum oven versus microwave oven

Two analytical procedures used to determine total, soluble, and insoluble solids in tomato paste were evaluated. The microwave oven (MO) method was compared to the vacuum oven (VO) method. The VO method is tedious and measured the three solids fractions in the paste directly, while the MO method measured the total solids directly but used an equation to calculate the water-soluble and -insoluble solids. The MO method was faster and less labor-intensive, and yielded small but statistically significant higher values for total and insoluble solids and lower statistically significant values for soluble solids.     

Optimizing capacity,pricing and location decisions on a congested network with balking

In this paper, we consider the problem of making simultaneous decisions on the location, service rate (capacity) and the price of providing service for facilities on a network. We assume that the demand for service from each node of the network follows a Poisson process. The demand is assumed to depend on both price and distance. All facilities are assumed to charge the same price and customers wishing to obtain service choose a facility according to a Multinomial Logit function. Upon arrival to a facility, customers may join the system after observing the number of people in the queue. Service time at each facility is assumed to be exponentially distributed. We first present several structural results. Then, we propose an algorithm to obtain the optimal service rate and an approximate optimal price at each facility. We also develop a heuristic algorithm to find the locations of the facilities based on the tabu search method. We demonstrate the efficiency of the algorithms numerically.     

A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis

In this paper, we develop an efficient matrix method based on two‐dimensional orthonormal Bernstein polynomials (2D‐OBPs) to provide approximate solution of linear and nonlinear weakly singular partial integro‐differential equations (PIDEs). First, we approximate all functions involved in the considerable problem via 2D‐OBPs. Then, by using the operational matrices of integration, differentiation, and product, the solution of Volterra singular PIDEs is transformed to the solution of a linear or nonlinear system of algebraic equations which can be solved via some suitable numerical methods. With a small number of bases, we can find a reasonable approximate solution. Moreover, we establish some useful theorems for discussing convergence analysis and obtaining an error estimate associated with the proposed method. Finally, we solve some illustrative examples by employing the presented method to show the validity, efficiency, high accuracy, and applicability of the proposed technique.     

Catalytic study of the copper-based magnetic nanocatalyst on the aerobic oxidation of alcohols in water

A copper-based magnetic nanocatalyst has been prepared by co-precipitation method and characterized by FESEM, EDS, TEM, XRD, XRF, ICP–OES, FTIR, and BET analysis. This new nanocatalyst displays a good activity toward the aerobic oxidation of a wide range of alcohols in water. Moreover, it is recyclable up to five following runs by simple filtration without any significant loss of its catalytic activity.