Existence of positive homoclinic solutions for damped differential equations

This paper is concerned with the existence of positive homoclinic solutions for the second-order differential equation

$$\begin{aligned} u^{\prime \prime }+cu^{\prime }-a(t)u+f(t,u)=0, \end{aligned}$$

where \(c\ge 0\) is a constant and the functions a and f are continuous and not necessarily periodic in t. Under other suitable assumptions on a and f, we obtain the existence of positive homoclinic solutions in both cases sub-quadratic and super-quadratic by using critical point theorems.

     

Numerical study of the flow and heat transfer in a Reiner-Rivlin fluid on a rotating porous disk

An unsteady flow and heat transfer to an infinite porous disk rotating in a Reiner—Rivlin non-Newtonian fluid are considered. The effect of the non-Newtonian fluid characteristics and injection (suction) through the disk surface on velocity and temperature distributions and heat transfer is considered. Numerical solutions are obtained over the entire range of the governing parameters.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 85–95, January–February, 2005.     

Unsteady hydromagnetic channel flow of dusty fluid with temperature dependent viscosity and thermal conductivity

In the present paper the unsteady flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. A constant pressure gradient and an external uniform magnetic field is applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.On leave from Department of Mathematics and Physics, Faculty of Engineering, El-Fayoum University, Egypt     

Studies and X‐ray Determinations with 2‐(Acetonylthio)benzothiazole: Synthesis of 2‐(Benzothiazol‐2‐ylthio)‐1‐phenylethanone and 2‐(Acetonylthio)Benzothiazole by C―S Bond Cleavage of 2‐(Acetonylthio)benzothiazole in KOH

New route for the synthesis of 2‐(benzothiazol‐2‐ylthio)‐1‐phenylethanone ( 6 ) and 2‐(acetonylthio)benzothiazole ( 1 ) by using phenacyl bromide and α‐chloroacetone, respectively, through carbon–sulfur bond cleavage reactions in a basic medium has been generated. Treatment of 1 with malononitrile and elemental sulfur afforded the corresponding derivative of 2‐amino‐3‐cyanothiophene ( 12 ), whereas treatment of 1 with cyanoacetohydrazide afforded the corresponding derivative of cyanoacetylhydrazone derivative ( 13 ). The structure of the synthesis compounds has been established on the basis of elemental analyses, ¹H‐NMR, ¹³C‐NMR, correlation spectroscopy, heteronuclear single quantum coherence, MS spectra, and X‐ray crystallographic investigations.     

Synthesis of Some Novel Imidazopyrazole and Pyrazolopyrimidine Derivatives

5‐Amino‐3‐anilino‐1H‐pyrazole‐4‐carbonitrile 1 was alkylated with various halo reagents under phase transfer conditions to give the corresponding imidazopyrazole derivatives 2a , 2b , 2c , 3 , 4 , 5 , 6 . Pyrazolo[1,5‐a] pyrimidine derivatives 11 , 12 , 13 , 14 were prepared by treating compound 1 with different dicarbonyl reagents, namely, diethymalonate, ethyl 3‐oxo‐3‐phenylpropanoate, pentane‐2,4‐dione or ethyl 3‐oxobutanoate.     

Evaluation of antileishmanial, cytotoxic and antioxidant activities of essential oils extracted from plants issued from the leishmaniasis-endemic region of Sned (Tunisia)

In this study, we tested 10 essential oils (EOs) extracted from 10 plants issued from Sned region (Tunisia) to evaluate both their leishmanicidal effects against Leishmania major and L. infantum, and their cytotoxicity against murine macrophage cell line RAW 264.7 (ATCC, TIB-71). The antioxidant activity was also monitored by the DDPH method, while the chemical composition of active EO was assessed by GC-MS analysis. The results showed that the EOs obtained from Thymus hirtus sp. algeriensis (rich on monoterpenoids, especially linalool at 17.62% and camphor at 13.82%) is significantly active against both L. major and L. infantum, whereas Ruta chalepensis EO (rich on 2-undecanone at 84.28%) is only active against L. infantum. Both oil extracts showed low cytotoxicity towards murine macrophages. The characteristic ratios (IC?? Raw264.7 cells/IC?? L. infantum and IC?? Raw264.7 cells/IC?? L. major) were, respectively, 2.7 and 1.57 for T. hirtus sp. algeriensis, and 1.34 and 0.19 for R. chalepensis. However, when measuring the antioxidant effects (DDPH method), the two latter EOs presented a moderate 2,2-diphenyl-2-picrylhydrazyl hydrate scavenging effects compared to EOs from Eucaliptus globulus, Pinus halepensis, Pituranthos tortuosus, Rosmarinus officinalis, Tetraclinis articulata or to BHT.     

Biocalorimetry as a process analytical technology process analyser; robust in-line monitoring and control of aerobic fed-batch cultures of crabtree-negative yeast cells

Control of bioprocesses requires reliable and robust on- or in-line monitoring tools providing real-time information on process dynamics. Heat generation related to metabolic activity of living systems is currently gaining importance in bioprocess industry due to its non-invasive and essentially instantaneous characteristics. This study deals with monitoring and control of pure aerobic fed-batch cultures of three Crabtree-negative yeast strains, Kluyveromyces marxianus, Candida utilis and Pichia pastoris, based on in-line measured, metabolic heat flow signals. A high resolution biocalorimeter (BioRC1) was developed from a standard bench-scale heat flow calorimeter (RC1). The BioRC1 was equipped with in-line (dielectric spectroscopy, pH probe and dissolved oxygen probe) and at-line (exit gas analyser) sensors to characterise the growth behaviour of the yeast cells. Both metabolic heat flow and biomass profiles exhibited similar behaviour proving the significance of employing heat flow signal as a key-parameter for the system under investigation. A simple estimator for biomass concentration and specific growth rate was formulated based on heat flow values. In order to evaluate the potential of calorimetry as a reliable and powerful process monitoring tool, the robustness, reliability as well as the broad applicability of the developed estimators was assessed through comparison with off-line measurement techniques and showed promising results for general applicability with a wide range of bioprocesses.     

Global synchronization of fractional‐order and integer‐order N component reaction diffusion systems: Application to biochemical models

This study considers the problem of control and synchronization between fractional‐order and integer‐order, N‐components reaction‐diffusion systems with nonidentical coefficients and different nonlinear parts. The control scheme is designed using the Lyapunov direct method. The results are exemplified by two significant biochemical models, namely, the fractional‐order Lengyel‐Epstein model and the Gray‐Scott model. To illustrate the effectiveness of the proposed scheme, numerical simulations are performed in one and two space dimensions using Homotopy Analysis Method (HAM).     

The effect of a generalized nonlinear incidence rate on the stochastic SIS epidemic model

In this paper, we aim to analyze the classical SIS epidemic model with a generalized force of infection (including nonmonotonic cases), where the transmission rate is perturbed by white noise. Using Feller's test for explosions, we prove that the disease dies out with probability one without any restriction on the model parameters.