Computational experience with known variable metric updates

Variable metric methods from the Broyden family are well known and commonly used for unconstrained minimization. These methods have good theoretical and practical convergence properties which depend on a selection of free parameters. We demonstrate, using extensive computational experiments, the influence of both the Biggs stabilization parameter and Oren scaling parameter on 12 individual variable metric updates, two of which are new. This paper focuses on a class of variable metric updates belonging to the so-called preconvex part of the Broyden family. These methods outperform the more familiar BFGS method. We also experimentally demonstrate the efficiency of the controlled scaling strategy for problems of sufficient size and sparsity.     

The NNTMM code: Mathematical modeling, optimization, and data analysis through neural networks

The concept, functional capabilities, graphic interface, and application technology for the NNTMM code (Neural Network Tool for Mathematical Modeling), designed for analyzing large amounts of experimental and computational data in an interactive mode, are described. The software can be used to solve a wide range of applied problems where automated extraction of meaningful information from randomly presented data is required, along with data classification, clear representation of established relationships and dependences, analysis of parameter importance, and prediction. Examples of using the NNTMM code to analyze data in controlled nuclear fusion problems are presented.     

Thermoelectric properties of n-Bi2Te3 − x − y Se x S y solid solutions under high pressure

The thermoelectric properties of n-Bi₂Te_{3 ? x ? y} Se _x S _y solid solutions with atomic substitutions in the tellurium sublattice (x = 0.27, 0.3, y = 0, and x = y = 0.09) have been studied under a pressure to 8 GPa. It has been found that the Seebeck coefficient and the resistance decrease with increasing P, and power factor χ increases in all compositions and becomes maximal at pressures of 2–4 GPa. It has been shown that the power factor χ, which is proportional to the product of the effective mass of the density of states m/m m/m ₀ and the charge carrier mobility μ₀ in the form (m/m ₀)^3/2μ₀, increases with increasing pressure mainly due to the increase in the mobility and also depends on the solid solution composition. In the composition with substitution Te → Se + S (x = y = 0.09), the peculiarity of the dependence of m/m ₀ on P in the pressure range corresponding to maximal values of the power factor can be explained by the existence of an electronic topological transition. The increase in the power factor under pressure in n-type Bi₂Te_{3 ? x ? y} Se _x S _y solid solutions combined with similar data for p-type Bi_{2 ? x} Sb _x Te₃ solid solutions obtained earlier, including the estimations of possible changes in the thermal conductivity with increasing pressure, give grounds to design thermoelements with improved value of the thermoelectric figure-of-merit, which can be 50–70% at pressures of 2–4 GPa.     

Solvability of the power flow problem in DC overhead wire circuit modeling

Applications of Mathematics - Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include...     

Long-service-life plasma arc torch

An arc plasma torch having a long service life is described. Its water-cooled copper electrodes are coated with a film of a nanostructured carbon material. Electron microscopy and Raman spectroscopy instrumental studies of the electrode coating showed that it consisted of the composite nanosized carbon material including largely single-walled and multi-walled carbon nanotubes and other carbon forms with a certain amount of copper atoms intercalated in the carbon matrix.     

Lagrangean relaxation based heuristics for lot sizing with setup times

We consider a lot sizing problem with setup times where the objective is to minimize the total inventory carrying cost only. The demand is dynamic over time and there is a single resource of limited capacity. We show that the approaches implemented in the literature for more general versions of the problem do not perform well in this case. We examine the Lagrangean relaxation (LR) of demand constraints in a strong reformulation of the problem. We then design a primal heuristic to generate upper bounds and combine it with the LR problem within a subgradient optimization procedure. We also develop a simple branch and bound heuristic to solve the problem. Computational results on test problems taken from the literature show that our relaxation procedure produces consistently better solutions than the previously developed heuristics in the literature.     

Photochemistry of 2-alkoxymethyl-5-methylphenacyl chloride and benzoate

Irradiation of 2-(alkoxymethyl)-5-methyl-alpha-chloroacetophenones (1a-c) and 2-(methoxymethyl)-5-methylphenacyl benzoate (1d) in dry, nonnucleophilic solvents afforded 3-alkoxy-6-methylindan-1-ones (3a-c) in very high chemical yields. 3-Methylisobenzofuran-1(3H)-one (2) was, however, isolated as a major photoproduct in the presence of trace amounts of water. Quenching experiments and laser flash spectroscopy revealed that the indanone derivatives 3 are formed by 1,5-hydrogen migration from the lowest triplet excited state of the acetophenones 1 and cyclization of the resulting photoenols. In contrast, production of the lactone 2 in wet solvents was found to result from two consecutive photochemical transformations. The photoenols produced by photolysis of 1a-c add water as a nucleophile to form 2-acetyl-4-methylbenzaldehyde (4), which is further converted to 2 via a second, singlet state photoenolization process. Exhaustive photolysis of 1a in methanol produced the acetal 2-(dimethoxymethyl)-5-methylacetophenone (7a) as the exclusive product. The remarkable selectivity of these photoreactions may well be useful in synthetic organic chemistry.