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, + ∞[.     

Mathematical study of a bacteria–fish model with level of infection structure

In this paper, we propose a mathematical model to study a bacteria–fish system, based upon the interactions between Clostridium botulinum and tilapia, Oerochromis mossambicus. The fish population is divided into susceptible and infected, and the infected fish population is considered structured by the level of infection. The model is thus a system with the infected fish equation being an evolution equation, while those corresponding to the susceptible fish and bacteria in water are ordinary differential equations. The model is firstly transformed into a system with distributed delay for susceptible fish and bacteria and, further, under some assumptions, into a system with discrete delay. The study of this system gives us some results concerning the existence, uniqueness, positivity and boundedness of solutions; we also discuss the existence and stability of its equilibrium points, including conditions for the appearance of Hopf bifurcation. The theoretical results are illustrated by some numerical simulations.     

A simple route to synthesize nanocrystalline nickel ferrite (NiFe2O4) in the presence of octanoic acid as a surfactant

Nanocrystalline nickel ferrite (NiFe₂O₄) powder was prepared by a co-precipitation method from Ni and Fe chlorides. The as-prepared samples were characterized by powder X-ray diffractometry (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR) and vibrating sample magnetometry (VSM). SEM and TEM indicated that the particles were spherical with particle sizes in the range 25 ± 5 nm. The magnetic properties of the sample were measured by using a vibrating sample magnetometer, which showed that the sample exhibited typical ferromagnetic behavior at room temperature, while a finite coercivity of 245.5 Oe was present at 300 K. The saturation magnetization of the sample (23.13 emu/g) was significantly lower than that for the reported multidomain bulk particles (55 emu/g), reflecting the ultrafine nature of the sample.     

ACTIVATED NITRILES IN HETEROCYCLIC SYNTHESIS: NOVEL SYNTHESIS OF PYRROLO[1,2-c]IMIDAZOLE AND PYRANO[2,3-d]IMIDAZOLE DERIVATIVES

Abstract

Several new pyrrolo[1,2-ylidene ethyl cyanoacetate (lc, d) with each of (2) and (11) afforded the 5-ylidene-2-thiohydantoins (Sa, b), (Wn. b) respectively. Compounds Sn, b react with each of malononitrile and ethyl cyanoacet-ate to give the corresponding pyrroloimidazole derivatives (h,b) and (an, b) respectively. The structure of the isolated products were established by elemental analyse and spectral data studies.     

First principle calculation of accurate native defect levels in CaF<Subscript>2</Subscript>

We report on the first principle density functional calculation of the charge transition levels of native defects (vacancies and interstitials) in CaF₂ structure. The transition level was defined as the Fermi level where two charge states of given defect have the same formation energy. The common error in the band gap inherited to semiclocal density functional has been accounted for by incorporating the hybrid density functional method, leading to correct placement of the transition levels within the band gap. The band gap size from hybrid calculation has been validated using the full potential, Linearized Augmented Planewave method with the Modified-Becke-Johnson exchange potential. Prior to level calculations, we ensured that an agreement between the formation energies from small (95–97 atoms) and large (323–325 atoms) supercells was achieved after applying the Makov-Payne correction method. Our calculated transition level for the anion vacancy was 2.97 eV below the conduction band, agreeing with the experimental optical absorption band at 3.3 eV associated with the electron transition from the ground state F-center to the conduction band in CaF₂.     

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.     

Evanescent-wave in perturbed optical fibers

Two adjacent components may express the total electromagnetic fields of an optical fiber. The first one is defined as a summation over bound modes describing the spatial steady state where the light energy is guided along a non-absorbing waveguide. The second component is the radiation field, which describes the spatial transient. Since total internal reflection on a straight fiber is malfunctioned by bending, therefore the evanescent wave which represents the second component has been investigated in a bent single-mode fiber. The decay constant and phase propagation constant of the evanescent field are determined for the first time as a function of curvature at two standard operating wavelengths 1300 and 1550 nm using an interferometric technique.     

Melting and solidification characteristics of Zr-, Ni-, and Mn-containing 354-type Al-Si-Cu-Mg cast alloys

This study investigated the effects of adding Zr, as a base alloying element, besides Ni and Mn in different amounts and combinations on the melting and solidification characteristics of 354-type Al-Si-Cu-Mg alloys. Differential scanning calorimetry (DSC) was used to characterise the sequence of reactions occurring during the heating and/or cooling cycles; whereas scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) techniques were used to observe and identify existing intermetallic phases. Nickel proved to have a retarding effect on the kinetics of precipitation of the α-Al network and the eutectic Al-Si structure. Also, the presence of Ni consumed a considerable amount of Cu to form Al-Cu-Ni particles instead of Al₂Cu particles. Results revealed that solution treatment at 495°C for 5?h was sufficient to dissolve a large amount of Al₂Cu particles in the α-Al matrix, which is mandatory for a successful aging treatment of the alloys studied. Additions of these transition elements produced new intermetallic phases such as (Al,Si)₃(Ti,Zr), (Al,Si)₃Zr, Al₉FeNi, Al₃Ni, Al₃CuNi, and Al₉FeSi₃Ni₄Zr, in addition to the other phases, namely α-Al, eutectic silicon, Al₂Cu, Mg₂Si, Q-phase (Al₅Cu₂Mg₈Si₆), commonly observed in 354-type alloys, and Fe-based intermetallic phases including β-Al₅FeSi, α-Al₁₅(Fe, Mn)₃Si₂, and π-Al₈FeMg₃Si_6. Superheating the melt at 800°C instead of 750°C had an advantageous effect in that Al₃Zr particles originating from the Al-15%Zr master alloy were dissolved and hence coarse Zr-containing particles were barely spotted in the microstructures examined.