Constrained extremum problems with infinite dimensional image. Selection and saddle point

The paper deals with Image Space Analysis for constrained extremum problems having infinite dimensional image. It is shown that the introduction of selection for point- to-set maps and of quasi-multipliers allows one to establish sufficient optimality conditions for problems, where the classic ones fail.      

Constrained Extremum Problems with Infinite-Dimensional Image: Selection and Necessary Conditions

This paper deals with image space analysis for constrained extremum problems having an infinite-dimensional image. It is shown that the introduction of selection for point-to-set maps and of quasi multipliers allows one to establish optimality conditions for problems where the classical approach fails.     

Semi-analytical modeling of non-premixed counterflow combustion of metal dust

In this study, a semi-analytical model is developed for non-premixed combustion of metal dusts in counterflow configuration. Combustion domain is divided into three separate zones, each of which possesses corresponding mass and energy conservation equations as well as boundary and jump conditions. Metal dust, assumed to be aluminum, undergoes an Arrhenius-type reaction with oxidizer, when it is heated enough to reach the ignition temperature. Dimensionless forms of conservation equations are derived and utilized to elucidate the combustion characteristics. The effects of oxidizer Lewis number and fuel mass concentration on the flame position and temperature are discussed thoroughly. In addition, temperature distribution of the whole domain is calculated by numerically solving the system of partial differential equations. In order to track particles through combustion domain, Lagrangian equations of motion are solved either mathematically or numerically, considering thermophoretic, weight, buoyancy and drag forces. The effects of thermophoretic force on the particle path are investigated, and the deviation of particle from carrier neutral gas direction is obtained. The results showed a great agreement with the data reported in the literature highlighting the fact that the presented model is an efficient one to accurately model the non-premixed counterflow combustion of metal dust.

     

Reaction and Morphology Development Influenced by Diffusion in a Thermoplastic/Thermoset Blend

Diglycidyl ether of bisphenol A (DGEBA) and 4,4′-methylenebis [2,6-diethylaniline] (MDEA) are miscible in polystyrene at 177 °C. We have studied how their diffusion rate in a molten polystyrene matrix influences their polymerization rate and the morphology of the thermoset particles formed at the end of the reaction. The global composition of the blend was 60 wt% of PS and 40 wt% of epoxy-amine. The diffusional control of the reaction was evidenced by comparing the time of reaction of an initially homogeneous mixture with that of different bi-layer samples. The reaction was controled by the diffusion for relatively thick layers (>0.3. mm). A gradient of morphology was obtained due to the diffusionnal control of the reaction. The asymetricity of this gradient may be explained by three factors: differences in diffusion coefficients, in thermodynamic interactions and in viscosity.     

Numerical simulation of the anisotropic elastic field generated by a misfit dislocations along a NiSi2/Si/(001)GaAs heterotwin interface

The purpose of this work is the numerical resolution, in the case of anisotropic elasticity, of the problem of a misfit dislocation located between an infinite substrate and two-layer composite. This case is obtained where the period of a network of misfit dislocations is taken as much greater than the thickness of the two foils. As a result, in the vicinity of the dislocation, the limiting boundary conditions will be close to those of Volterra translation dislocation. The elastic fields of displacement and stress are calculated for various orientations of the burger's vector, by inversion of a 30 x 30 computed matrix. Before this calculation, we tested the precision of the results of the program by comparing the interfacial relative displacement obtained from it with the results of the analytical expression describing this same displacement. The composite NiSi2/Si/(001)GaAs the subject of several investigations, is treated as an example.     

Self-affine surface morphology of plastically deformed metals

We analyze the surface morphology of metals after plastic deformation over a range of scales from 10 nm to 2 mm using atomic force microscopy and scanning white-light interferometry. We demonstrate that an initially smooth surface during deformation develops self-affine roughness over almost 4 orders of magnitude in scale. The Hurst exponent H of one-dimensional surface profiles initially decreases with increasing strain and then stabilizes at H approximately 0.75. We show that the profiles can be mathematically modeled as graphs of a fractional Brownian motion. Our findings can be understood in terms of a fractal distribution of plastic strain within the deformed samples.     

Some Cohen–Macaulay and Unmixed Binomial Edge Ideals

We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some classes of graphs. We compute the depth of the binomial edge ideal of a generalized block graph. We also characterize all generalized block graphs whose binomial edge ideals are Cohen–Macaulay and unmixed. So that we generalize the results of Ene, Herzog, and Hibi on block graphs. Moreover, we study unmixedness and Cohen–Macaulayness of the binomial edge ideal of some graph products such as the join and corona of two graphs with respect to the original graphs.     

On the coupling of the homotopy perturbation method and Laplace transformation

In this paper, a Laplace homotopy perturbation method is employed for solving one-dimensional non-homogeneous partial differential equations with a variable coefficient. This method is a combination of the Laplace transform and the Homotopy Perturbation Method (LHPM). LHPM presents an accurate methodology to solve non-homogeneous partial differential equations with a variable coefficient. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as HPM, VIM, and ADM. The approximate solutions obtained by means of LHPM in a wide range of the problem’s domain were compared with those results obtained from the actual solutions, the Homotopy Perturbation Method (HPM) and the finite element method. The comparison shows a precise agreement between the results, and introduces this new method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.     

Composition operators acting on Besov spaces on the real line

We study the composition operator \(T_f(g):= f\circ g\) on Besov spaces \(B_{{p},{q}}^{s}(\mathbb{R })\) . In case \(1 < p< +\infty ,\, 0< q \le +\infty \) and \(s>1+ (1/p)\) , we will prove that the operator \(T_f\) maps \(B_{{p},{q}}^{s}(\mathbb{R })\) to itself if, and only if, \(f(0)=0\) and \(f\) belongs locally to \(B_{{p},{q}}^{s}(\mathbb{R })\) . For the case \(p=q\) , i.e., in case of Slobodeckij spaces, we can extend our results from the real line to \(\mathbb{R }^n\) .