Synthesis,Acidity Constants and Tautomeric Structure of 7‐Arylhydrazono[1,2,4]Triazolo[3,4‐b][1,3,4]thiadiazines in Ground and Excited States

7‐Arylhydrazono[1,2,4]triazolo[3,4‐b][1,3,4]thiadiazines 4 were synthesized from the reactions of 4‐amino‐5‐phenyl‐4H‐[1,2,4]triazole‐3‐thiol 2 and 2‐(2‐naphthyl)‐2‐oxoethanehydrazonoyl bromides 1 and their acid dissociation constants pK and pK*, in the ground and excited states, respectively, were determined. Both pK and pK* constants were correlated by Hammett equation. The pK and the spectral data presented indicate that the title compounds exist predominantly in the hydrazone tautomeric form.     

Combinatorial optimization and Green Logistics

The purpose of this paper is to introduce the area of Green Logistics and to describe some of the problems that arise in this subject which can be formulated as combinatorial optimization problems. The paper particularly considers the topics of reverse logistics, waste management and vehicle routing and scheduling.     

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.     

Existence of Solutions for Impulsive Parabolic Partial Differential Equations

We discuss the propagation of heat along a homogeneous rod of length A under the influence of a nonlinear heat source and impulsive effects at fixed times. This problem is described by an initial-boundary value problem for a nonlinear parabolic partial differential equation subjected to impulsive effects at fixed times. Using Green's function, we convert the problem into a nonlinear integral equation. Sufficient conditions are provided that enable the application of fixed point theorems to prove existence and uniqueness of solutions.     

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.     

Modelling the spontaneous combustion of coal: the adiabatic testing procedure

A general approach is described for modelling problems that involve heat and mass transfer in coal, such as spontaneous combustion. It is based on the TOUGH2 code, which is a general-purpose simulator for modelling multi-component, multi-phase, non-isothermal flow in a porous medium. An equation of state (EOS) module for TOUGH2 is developed, which includes accurate physical properties for all of the gases involved (N₂, oxygen and carbon dioxide). The new simulator is then used to model the adiabatic method for testing the reactivity of coal samples. An important part of the model development is the selection of the approximate representation of the reaction of coal with oxygen. The results show that (i) using dual Arrhenius parameters and (ii) representing the heat-release as an oxidation reaction rather than a purely thermal reaction both significantly improve the match of the model to the experimental data.