Application of lower bound direct method to engineering structures

Direct methods provide elegant and efficient approaches for the prediction of the long-term behaviour of engineering structures under arbitrary complex loading independent of the number of loading cycles. The lower bound direct method leads to a constrained non-linear convex problem in conjunction with finite element methods, which necessitates a very large number of optimization variables and a large amount of computer memory. To solve this large-scale optimization problem, we first reformulate it in a simpler equivalent convex program with easily exploitable sparsity structure. The interior point with DC regularization algorithm (IPDCA) using quasi definite matrix techniques is then used for its solution. The numerical results obtained by this algorithm will be compared with those obtained by general standard code Lancelot. They show the robustness, the efficiency of IPDCA and in particular its great superiority with respect to Lancelot.     

Sequences of nonlinear differential equations with related solutions

Summary A second-order nonlinear differential equation which occurs (together with variants of it) in many problems of applied mathematics, physics and engineering is here reduced to a first-order equation. This equation contains a parameter which is a quadratic rational function of two parameters appearing in the original equation. By applying a certain identity for a quadratic rational function, two (finite or infinite) sequences of nonlinear differential equations are generated whose solutions are determinable whenever the solution of any equation belonging to a sequence is known. The cases amenable to exact solution by quadrature are given. Entrata in Redazione il 16 luglio 1968.     

Energy Decay Rate of Solutions for the Wave Equation with Singular Nonlinearities

In this paper, we study the initial boundary value problem of the wave equation with singular nonlinearities of the form $$u_{tt}-u_{xx}+\sigma(t)|u|^{-r}g(u_{t})+|u|^{-\alpha}u=0\quad\hbox{in}\ I\times \mathbb{R}_+.$$ We prove decay estimates using multiplier method and weighted integral inequalities. We show that the energy of the system is bounded above by a quantity, depending on ??,g,r and ??, which tends to zero (as time goes to infinity). We give many significant examples to illustrate how to derive from our general estimates the polynomial, exponential or logarithmic decay.     

A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates

In the present paper, a new sinusoidal higher-order plate theory is developed for bending of exponential graded plates. The effects due to transverse shear and normal deformations are both included. The number of unknown functions involved in the present theory is only five as against six or more in case of other shear and normal deformation theories. The theory accounts for sinusoidal distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Based on the sinusoidal shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and efficient in predicting the bending response of exponential graded plates.     

Films thickness effect on structural and optoelectronic properties of hydrogenated amorphous germanium (a-Ge:H)

Thin films of hydrogenated amorphous germanium (a-Ge:H) deposited at high growth rate by radiofrequency (RF) glow discharge with 1 sccm GeH₄ diluted in 40 sccm H₂ have been studied. The effect of the films thicknesses on the defect density and on the structural parameters was carefully investigated by means of infrared spectroscopy, optical transmission measurements, and the photothermal deflection spectroscopy (PDS) technique. The results of this investigation show that when the films thicknesses increase, the total hydrogen content (C_H) decreases and the hydrogen-bonding configuration changes. The results of these changes appear clearly on the defects density and on the microstructure parameter of the films, while the disorder parameter E_OV and the optical gap E_T remain practically constant (E_OV ≈ 45 ± 2 meV, E_T = 1.08 ± 0.02 eV). The improvement of these parameters is mainly due to the incorporation of the hydrogen in the bulk of the material as the monohydride groups (Ge-H) rather than the polyhydride groups (Ge-H₂ and Ge-H_2n) when the films thicknesses increase.     

Diffusion processes of trimers on missing row surfaces: \mathrm{Cu }_{3}/\mathrm{Ag }(110) and \mathrm{Ag }_{3}/\mathrm{Cu }(110)

A semi-empirical potential according to the embedded atom, has been applied to investigate the diffusion of trimers by computing the energy barriers for different mechanisms. Our attention was more focused on the leapfrog process which is likely to occur on missing row surfaces. The activation barriers of this mechanism are calculated using drag method at 0K. These barriers are found to be 0.64 and 0.68 eV for hopping out the channel for $\mathrm{Cu }_{3}/\mathrm{Ag }(110) \mathrm{and Ag }_{3}/\mathrm{Cu }$ (110) respectively. While for hopping down at the other side they are about 0.42 and 0.32 eV. Moreover, a deep metastable position is observed during leapfrog diffusion leading to some spectacular trimer motion. At high temperature and essentially for $\mathrm{Cu }_{3}/\mathrm{Ag }$ (110), we also observed a competition between leapfrog process and concerted jump mechanism with a deformation of trimer geometry. Implications of these findings are briefly discussed.     

Spectrophotometric Determination of Metformin via Charge-Transfer Complex with Iodine

Abstract

A spectroscopic method is described for the determination of Metformin based on its formation of molecular complex with iodine in dichloroethane. Quantitative measurements are made at the maximum absorption of 295nm. The molar ratio of the formed metformin-iodine complex is 1:1 as revealed by Job's method. Beers' law is obeyed in the range 2–12 ug.ml^?1 base solution. The proposed method is statistically comparable with the official B. P. method. When applied to pharmaceutical preparation, tablets, average percentage recovery of 99.97 ± 0.81 was obtained.     

A nonlinear problem having a continuous locus of singular points and no multiple solutions

The boundary-value problem ?z″ = (z² ? t²)z′, ? > 0, z(? 1) = α, z(0) = β, t? [?1, 0], has been shown to have a solution, and moreover, depending on the choice of α and β, multiple solutions to it exist. We consider the more general equation f(z, t)z″ = (z^r ? t^s)z′ for a particular non-negative function f(z, t), and integrate the equation exactly. Depending on α and β, we find that either there are no solutions, or that only unique solutions exist. The conclusion is that the presence of a continuous locus of singular points, given by z^r = t^s, does not necessarily produce multiple solutions.     

6-alkoxy-3,4-dihydro-2h-pyrans from substituted α,β-unsaturated esters

Cycloaddition reactions of substituted α,β-unsaturated esters with various electronich olefins lead to 6-alkoxy-3,4-dihydro-2H-pyrans.     

New regiospecific synthesis of 2-trifluoromethyl-1,5 diazapentadiene compounds and of 2-trifluoromethylquinolines, their cyclization products

2-trifluoromethylquinolines 5 are synthesized in high yields using a perfluoroalkylated gem-iodoacetoxy derivative 3 and arylamines 4. The intermediate of this reaction, 2-trifluoromethyl-1,5-diazapentadiene compound 6, was isolated. The procedures are easy, and yields are in general high. This sequence represents a valuable new synthesis of substituted 2-trifluoromethylquinolines and of 2-trifluoromethyl-diazapentadienes (vinamidine compounds).