On <Emphasis Type="Italic">W</Emphasis>-geometry of Toda systems

We describe W-geometry of two-dimensional Toda systems associated with the Lie algebra C _n . __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.     

A Reverse of bessel’s inequality in 2-inner product spaces and some grüss type related results with applications

A reverse of Bessel’s inequality in 2-inner product spaces and companions of Grüss inequality with applications for determinantal integral inequalities are given.     

Dielectrophoretically aligned GaN nanowire rectifiers

We demonstrate GaN nanowire (NW) current rectifiers which were formed by assembling n-GaN nanowires on a patterned p-Si substrate by means of alternating current (ac) dielectrophoresis. The dielectrophoresis was accomplished at a frequency of 10 kHz with three different ac bias voltages (5, 10, and 15 V_p–p), indicating that the number of aligned GaN nanowires increased with increasing ac bias voltage. The n-GaN NW/p-Si diodes showed well-defined current rectifying behavior with a forward voltage drop of 1.2–1.5 V at a current density of 200 A/cm². We observed that the GaN NW diode functioned well as a half-wave rectifier. PACS 71.20.Nr; 73.40.Cg; 73.40.Ei; 73.40.Kp     

Photodecomposition of several compounds commonly used as sunscreen agents

The photolysis reactions of three compounds commonly used as a sunscreen agents, Parsol 1789 (1-[4-(1,1-dimethylethyl)phenyl]-3-(4-methoxyphenyl)-1,3- propanedione), Oxybenzone ((2-hydroxy-4-methoxyphenyl)phenyl-methanone) and Padimate O (2-ethylhexyl-4-(dimethylamino)benzoate), were investigated to provide a chemical background to aid in the understanding of the photosensitization of the sunscreen agents. Photolysis was carried out in cyclohexane for 70–140 h using a mercury vapor lamp (450W) without excluding oxygen.

Irradation of Parsol 1789 in cyclohexane yielded tert-butylbenzene, p-tert-butylbenzoic acid and p-methoxybenzoic acid; products obtained from the combination of the sunscreen with the solvent included the cyclohexyl esters of p-methoxybenzoic acid, p-tert-butylbenzoic acid and methanoic acid; products obtained from the solvent included cyclohexanol, cyclohexanone and dicyclohexyl ether.

Irradiation of Oxybenzone in the cyclohexane for 100 h produced no detectable products by either gas or liquid chromatographic analysis. Oxybenzone was recovered unchanged and no products were observed from the photoinitiated reaction of oxygen with the solvent.

Irradiation of Padimate O in cyclohexane yielded the ethylhexyl esters of p-aminobenzoic acid, p-monomethylaminobenzoic acid and p-dimethylamino (o/m)-methylbenzoic acid, as well as products from the photoinitiated reaction of oxygen with the solvent.     

Kinetic model for hydrocarbon-assisted particulate boron combustion

A kinetic model is presented to describe the high temperature (1800 K < T < 3000 K) surface oxidation of particulate boron in a hydrocarbon combustion environment. The model includes a homogeneous gas-phase B/O/H/C oxidation mechanism consisting of 19 chemical species and 58 forward and reverse elementary reactions, multi-component gas-phase diffusion, and a heterogeneous surface oxidation mechanism consisting of ‘elementary’ adsorption and desorption reaction steps. Thermochemical and kinetic parameters for the surface reactions are estimated from available experimental data and/or elementary transition state arguments. The kinetic processes are treated using a generalized kinetics code, with embedded sensitivity analysis, for the combustion of a one-dimensional (particle radius), spherical particle. Model results are presented for the oxidation of a 200 μm boron particle in a JP-4/air mixture at ambient temperatures of 1400 K and 2000 K. These results include temperature and gas-phase species profiles as a function of radial distance and particle burning rates. © 1994 John Wiley & Sons, Inc.     

A simulated annealing algorithm for resource constrained project scheduling problems

This paper presents a simulated annealing algorithm for resource constrained project scheduling problems with the objective of minimising makespan. In the search algorithm, a solution is represented with a priority list, a vector of numbers each of which denotes the priority of each activity. In the algorithm, a priority scheduling method is used for making a complete schedule from a given priority list (and hence a project schedule is defined by a priority list). The search algorithm is applied to find a priority list which corresponds to a good project schedule. Unlike most of priority scheduling methods, in the suggested algorithm some activities are delayed on purpose so as to extend search space. Solutions can be further improved by delaying certain activities, since non-delay schedules are not dominant in the problem (the set of non-delay schedules does not always include an optimal solution). The suggested algorithm is flexible in that it can be easily applied to problems with an objective function of a general form and/or complex constraints. The performance of the simulated annealing algorithm is compared with existing heuristics on problems prepared by Patterson and randomly generated test problems. Computational results showed that the suggested algorithm outperformed existing ones.     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation considering the Payne effect

The viscoelastic behavior of carbon-black-filled rubber under small oscillatory loads superimposed on large static deformation is dealt with. In this class of problems, as the strain amplitudes of the load increase, the dynamic stiffness decreases, and this phenomenon is known as the Payne effect. Besides the effects of the static deformation and the frequencies of the superimposed dynamic load, the Payne effect is considered in this study. Influence factors are introduced in this model in order to consider the influence of static predeformation, the dynamic-strain-dependent properties, and frequency-dependent properties. For simplicity, separation of the three dominant variables, frequency, prestatic deformation, and dynamic amplitude of strain, is assumed. The Kraus model is used for describing the Payne effect. Dynamic tension tests are executed to obtain the model parameters and also for the verification of the proposed model. The suggested constitutive equation shows reasonable agreement with test data.     

Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.