Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory

We consider one-dimensional problem for the thermoelastic diffusion theory and we obtain polynomial decay estimates. Then we show that the solution decays exponentially to zero as time goes to infinity; that is, denoting by E(t) the first-order energy of the system, we show that positive constants C ₀ and c ₀ exist which satisfy E(t) ≤ C ₀ E(0)e ^{?c ₀ t} .     

A weighted Hardy inequality and nonexistence of positive solutions

In this article, we prove that the following weighted Hardy inequality $$\begin{array}{ll}\big(\frac{|{d-p}|}{p}\big)^{p}\, \int\limits_{\Omega}\, \frac{|{u}|^{p}}{|{x}|^{p}}\;d\mu \\ \quad \quad \le \int\limits_{\Omega}\,|{\nabla u}|^{p}\;d\mu+ \big(\frac{|{d-p}|}{p}\big)^{p-1}\,\textrm{sgn}(d-p)\,\int\limits_{\Omega}|{u}|^{p}\,\frac{(x^{t}Ax)^{p/2}}{|{x}|^{p}}\; d\mu \quad \quad \quad (1) \end{array}$$ holds with optimal Hardy constant ${\big(\frac{|d-p|}{p}\big)^{p}}$ for all ${u \in W^{1,p}_{\mu,0}(\Omega)}$ if the dimension d ≥ 2, 1 < p < d, and for all ${u \in W^{1,p}_{\mu,0}(\Omega{\setminus}\{0\})}$ if p > d ≥ 1. Here we assume that Ω is an open subset of ${\mathbb{R}^{d}}$ with ${0 \in \Omega}$ , A is a real d × d-symmetric positive definite matrix, c > 0, and $$ d \mu: = \rho(x) \,dx \qquad \textrm{with} \quad \rho(x) = c \cdot \exp(-\frac{1}{p}(x^{t}Ax)^{p/2}), \quad x \in\Omega.\quad \quad (2) $$ If p > d ≥ 1, then we can deduce from (1) a weighted Poincaré inequality on ${W^{1,p}_{\mu,0}(\Omega \setminus\{0\})}$ . Due to the optimality of the Hardy constant in (1), we can establish the nonexistence (locally in time) of positive weak solutions of a p-Kolmogorov parabolic equation perturbed by a singular potential in dimension d = 1, for 1 < p <  + ∞, and when Ω =  ]0, + ∞[.     

A multiobjective stochastic program for hospital bed planning

In this paper, we study hospital bed capacity management for a set of existing hospitals when the demand for beds is random. We propose a multiobjective stochastic program model to assign beds to hospital departments. We consider three objective functions to be minimized, which are the cost of creation and management of new beds and the number of nurses and physicians working in these hospitals, subject to demand satisfaction of three kinds of health-care specialities. A certainty equivalent program was derived based on a mixture between the chance constrained approach, the recourse approach and the goal programming approach. Empirical results using real data from 157 Tunisian national hospitals are reported.     

Effect of different dopant elements (Al,Mg and Ni) on microstructural,optical and electrochemical properties of ZnO thin films deposited by spray pyrolysis (SP)

In the present work we studied the influence of the dopant elements and concentration on the microstructural and electrochemical properties of ZnO thin films deposited by spray pyrolysis. Transparent conductive thin films of zinc oxide (ZnO) were prepared by the spray pyrolysis process using an aqueous solution of zinc acetate dehydrate [Zn(CH₃COO)₂·2H₂O] on soda glass substrate heated at 400 ± 5 °C. AlCl₃, MgCl₂ and NiCl₂ were used as dopant. The effect of doping percentage (2–4%) has been investigated. Afterwards the samples were thermally annealed in an ambient air during one hour at 500 °C. X-ray diffraction showed that films have a wurtzite structure with a preferential orientation along the (0 0 2) direction for doped ZnO. The lattice parameters a and c are estimated to be 3.24 and 5.20 ?, respectively. Transmission allowed to estimate the band gaps of ZnO layers. The electrochemical studies revealed that the corrosion resistance of the films depended on the concentration of dopants.     

Extreme ultraviolet and soft x-ray laser emission from Ni-like Nd ions

We use the energy levels, transition probabilities, and effective collision strengths for the states 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ and 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁹ 4 l (l = s, p, d, and f) of a nickel-like Nd ion to determine reduced population for 55 fine-structure levels over a wide range of electron density values (from 10²⁰ to 4 · 10²² cm ⁻³) at various electron plasma temperatures in the range of 1–2 keV. We find the gain coefficients for those transitions with the positive population inversion factor and show their dependences on the electron density.     

Single-crystal EPR study and DFT structure of the [Mo(CO)5PPh3]+· radical cation

A radical species characterized by a large g-anisotropy and a clearly resolved hyperfine structure with ^95/97Mo and ³¹P nuclei is formed, at 77 K, by radiolysis of a single crystal of Mo(CO)₅PPh₃. The corresponding EPR signals disappear irreversibly with increasing temperature and the angular dependence of the various coupling constants imply a spin delocalization of ～60% and ～4% on the molybdenum and the phosphorus atoms, respectively and are, a priori, consistent with the trapping of a one-electron deficient centre. The ability of DFT to predict the EPR tensors for a 17-electron Mo^(I) species is verified by calculating the g-tensor and the various ¹⁴N and ¹³C coupling tensors previously reported by Hayes for [Mo(CN)₅NO]^3?. Calculations at the B3LYP/ZORA/SOMF level of theory show that, in contrast to Mo(CO)₅PH₃, one-electron oxidation of Mo(CO)₅PPh₃ causes an appreciable change in the geometry of the complex. The g-tensor and the ^95/97Mo and ³¹P isotropic and anisotropic coupling constants calculated for [Mo(CO)₅PPh₃]^+· confirm the trapping of this species in the irradiated crystal of Mo(CO)₅PPh₃; they also show that the conformational modifications induced by the electron release are probably hindered by the nearby complexes.     

Coating of carbon nanotubes on flexible substrate and its adhesion study

The primary goal of this project was to develop a flexible transparent conductor with 100 Ω/sq and 90% transmittance in the wavelength range of 400-700 nm on a flexible substrate. The best result achieved so far was 110 Ω/sq at 88% transmittance using purified single-walled carbon nanotubes (SWNTs) coated on a polyethylene naphthalate (PEN) substrate. The secondary goal was to simplify the overall coating procedure; we successfully reduced the process from five (prior art method) to three steps utilizing a sonication method. We also found that the use of metallic SWNTs significantly improved the conductivity and transmittance compared with the use of mixed SWNTs, i.e., unseparated SWNTs. Furthermore, a possible adhesion mechanism between SWNTs and the surface of PEN was studied; we concluded that a π-π stacking effect and a hydrophobic interaction are the major contributing factors for SWNTs to adhere to the surface of the substrate.     

Combination of partially non-distinct beliefs: The cautious-adaptive rule

The combination rule is critical in an evidence based fusion process. The conjunctive rule is most common eventhough when the cognitive independence – distinctness – assumption is often questionable. A new combination rule is tested here in both discrete and continuous cases, accounting for a partial non-distinctness between evidences. It is based on ‘generalized discounting’, that we define for separable basic belief assignments (bbas) or basic belief densities (bbds), to be applied to the source correlation derived from the cautious rule. This correlation can be specified in both considered cases of consonant bbas/bbds (as proposed by Dubois et al.) and separable bbas/bbds (as proposed by Denœux). Then, the so-called ‘cautious-adaptive’ rule varies between the conjunctive rule and the cautious one, depending on the discounting level. In the Gaussian case with standard deviation σ, the evidence non-distinctness will be parameterized by a factor [0,1] dividing σ. It leads to the generalized discounting needed in the cautious-adaptive formulation.