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.     

Analytical calculations and properties of γ-rays polymerization of novel acrylates copolymer system

A detailed study of some physical properties of pure PMMA (polymethyl methacrylate) film and MMA/Ani (methyl methacrylate/aniline) films is presented. Films of thicknesses ranged from 0.04 to 0.72 mm for MMA/Ani were prepared while it is 0.68 mm for PMMA. The structure of the sample is analyzed by X-ray diffraction technique and is found to be amorphous (PMMA) and partially crystalline (MMA/Ani). Ultra violet–visible electronic absorption spectra measurements were analyzed to obtain some important parameters such as molar extrication coefficient, oscillator strength, dipole strength and having good thermal stability (T_d >300 °C) was also reported. TGA studies revealed that the thermal stability of polymethyl methacrylate, prepared by radiation polymerization of methyl methacrylate, improved after copolymerization with aniline. Also, optical behavior of film samples was analyzed by obtaining transmission spectra, in the wavelength range of 200–1100 nm. It was found that all studied samples lead to the appearance of a second edge at lower photon energy due to the formation of the induced energy states. From the intensity of absorption interband transitions (B and Q) which are assigned as type π–π^* for both PMMA and MMA/Ani films, the energy gaps E_g1 and E_g2 were calculated respectively. The optical conductivity (σ) was determined and it was found that with the increase of thicknesses optical energy gap decreases monotonically and the refractive index increases.     

On toric locally conformally Kähler manifolds

We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is \(-\infty \), and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold.     

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 \(\mathbb{R }^n\) .     

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.     

Le problème de Yamabe avec singularités

Let (Mn,g) be a compact riemannian manifold of dimension n?3. Under some assumptions, we prove that there exists a positive function φ solution of the Yamabe equation

     

Positron annihilation lifetime study of PTFE/silica composites

Positron annihilation lifetime spectroscopy (PALS) was used to study the microstructure of PTFE/silica composites. The positron lifetimes (τ_n) and intensities (I_n) of PTFE and the composites (30-62% silica) were measured at room temperature as a function of specimen thickness. Four lifetime components were found in PTFE and the composites. The longer lifetime components, τ₃ = 1.4 ns and τ₄ = 4.4 - 4.1 ns, were interpreted to be due to the presence of two different sized free volume cavity distributions within the PTFE/silica composites. A strong silica concentration dependence was found in the bulk intensities (I_3b and I_4b). The I_3b value increased from 13.0% in PTFE to 28.2% in the 62% composite, while the I_4b value decreased from 17.5% in PTFE to 4.5% in the 62% composite. The smaller-void size, free volume fraction (τ₃I_3b) values increased linearly between 0 and 100% silica concentration, while the larger void size, free volume fraction (τ₄I_4b) values decreased nonlinearly with silica concentration. Since silica has a long lifetime component (τ₃ = 1.6 ns), this behavior is ascribed to silica particles occupying the large free volume cavities (370 ų) in the PTFE/silica composites. © 1996 John Wiley & Sons, Inc.