Asymptotically self-similar global solutions of a general semilinear heat equation

We consider the general nonlinear heat equation on where and g satisfies certain growth conditions. We prove the existence of global solutions for small initial data with respect to a norm which is related to the structure of the equation. We also prove that some of those global solutions are asymptotic for large time to self-similar solutions of the single power nonlinear heat equation, i.e. with Received: 23 July 1999 / Accepted: 14 December 2000 / Published online: 23 July 2001     

Cupressus sempervirens Essential Oil: Exploring the Antibacterial Multitarget Mechanisms,Chemcomputational Toxicity Prediction,and Safety Assessment in Zebrafish Embryos

Nowadays, increasing interest has recently been given to the exploration of new food preservatives to avoid foodborne outbreaks or food spoilage. Likewise, new compounds that substitute the commonly used synthetic food preservatives are required to restrain the rising problem of microbial resistance. Accordingly, the present study was conducted to examine the chemical composition and the mechanism(s) of action of the Cupressus sempervirens essential oil (CSEO) against Salmonella enterica Typhimuriumand Staphyloccocus aureus. The gas chromatography analysis revealed α-pinene (38.47%) and δ-3-carene (25.14%) are the major components of the CSEO. By using computational methods, such as quantitative structure–activity relationship (QSAR), we revealed that many CSEO components had no toxic effects. Moreover, findings indicated that α-pinene, δ-3-carene and borneol, a minor compound of CSEO, could inhibit the AcrB-TolC and MepR efflux pump activity of S. enterica Typhimurium and S. aureus, respectively. In addition, our molecular docking predictions indicated the high affinity of these three compounds with active sites of bacterial DNA and RNA polymerases, pointing to plausible impairments of the pathogenic bacteria cell replication processes. As well, the safety profile was developed through the zebrafish model. The in vivo toxicological evaluation of (CSEO) exhibited a concentration-dependent manner, with a lethal concentration (LC₅₀) equal to 6.6 µg/mL.     

Modification of the thermoresistance to spray-drying of a cold-adapted subtilisin by genetic engineering

The thermoresistance of a cold-adapted subtilisin dried by spray-drying was studied. Proteolytic activity of this enzyme was measured before and after spray-drying. Without chemical additives, spray-drying yields ranged from 2–13%. The use of arabic gum and lactose in the composition of the enzyme solutions allowed the strengthening of the enzyme structures and increased water mobility in the product. Increase of water mobility led to a shorter residence time of the product in the spray-drier and a net yield increase was obtained (yield higher than 50%). The effect of two selective mutations on the thermoresistance to spray-drying of the cold-adapted subtilisin was also investigated. Mutation T85D (introduction of an additional link with an ion Ca²⁺ necessary for enzyme activity, by substitution of Asp for Thr 85) had no effect on the thermoresistance of the subtilisin to spray-drying. Mutation H121W (introduction of an additional aromatic link by substitution of Trp for His 121) reduced the drying yield from 66% (not modified subtilisin) to 52%. This higher thermosensitivity could be explained by an increase of the hygroscopic character of the modified subtilisin (mutation H121W).     

Fock Spaces Connected with Spherical Mean Operator and Associated Operators

We define and study the Fock space associated with the spherical mean operator. Next, we establish some results for the Segal-Bergmann transform for this space. Lastly, we prove some properties concerning Toeplitz operators on this space. Received: May 11, 2007. Revised: May 20, 2008. Accepted: May 23, 2008.     

Stabilité de l'écoulement de Hartmann chauffé par le basStability of the Hartmann flow heated from below

A numerical study is conducted in order to determine the influence of a vertical magnetic field, the Reynolds number and a temperature stratification on the instabilities occurring in the Hartmann flow heated from below. For $\mathit{Pr}=0.001$ and $\mathit{Ha}?2.5$, the results show that the vertical magnetic field has a stabilizing effect on both transverse oscillatory travelling waves $(T)$ and longitudinal stationary rolls $(L)$. The temperature stratification is responsible of a destabilization of the transverse $(T)$ modes and the appearance of longitudinal $(L)$ modes non-existent for the isothermal Hartmann flow. Moreover, the extent of the domains of Re where the transverse modes $(T)$ prevail is found to narrow when Ha increases and to widen when Ra increases for a given value of Ha. On the other hand, for the $(L)$ modes, the extent of the domains of Re where they prevail increases when Ha grows. To cite this article: W. Fakhfakh et al., C. R. Mecanique 334 (2006).     

An Efficient Algorithm for the Knapsack Sharing Problem

The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N, where each object j, j = 1,...,n, is associated with a profit p _j and a weight w _j. The set of objects N is composed of m different classes of objects J _i, i = 1,...,m, and N = ^m _i=1 J _i. The aim is to determine a subset of objects to be included in the knapsack that realizes a max-min value over all classes.In this article, we solve the KSP using an approximate solution method based upon tabu search. First, we describe a simple local search in which a depthparameter and a tabu list are used. Next, we enhance the algorithm by introducing some intensifying and diversifying strategies. The two versions of the algorithm yield satisfactory results within reasonable computational time. Extensive computational testing on problem instances taken from the literature shows the effectiveness of the proposed approach.     

Threshold of Effective Degree SIR Model

The effective degree SIR model is a precise model for the SIR disease dynamics on a network. The original ODE model is only applicable for a network with finite degree distributions. The new generating function approach rewrites with model as a PDE and allows infinite degree distributions. In this paper, we first prove the existence of a global solution. Then we analyze the linear and nonlinear stability of the disease-free steady state of the PDE effective degree model, and show that the basic reproduction number still determines both the linear and the nonlinear stability. Our method also provides a new tool to study the effective degree SIS model, whose basic reproduction number has been elusive so far.     

Electrocatalytic and Photocatalytic CO2 Methanation: From Reaction Fundamentals to Catalyst Developments

Transitioning from fossil fuels to renewable energy sources is demanded due to the gradual depletion of petroleum oil/gas and the environmental impact of carbon dioxide (CO₂) emissions into the atmosphere. Electrocatalytic and photocatalytic CO₂ reduction to methane (CH₄) using renewable energy sources is crucial for sustainable chemical/fuel production and greenhouse gas reduction. In recent years, extensive research has focused on understanding the fundamental aspects of the two approaches, such as reaction mechanisms and active sites, and exploring/designing novel catalytic materials. This review initially discusses the reaction fundamentals, including performance evaluation indexes, reactors, and mechanisms, to understand the catalytic reactions. Subsequently, various catalyst preparation strategies and characterization methods are summarized, trying to outline the catalyst design principle based on the obtained understanding of the reaction mechanisms. Finally, research challenges and perspectives for future development in this area are discussed and presented. It is expected to provide a comprehensive understanding of the photo/electrocatalytic CO₂ methanation, valuable knowledge to novice researchers, and a helpful reference for future research endeavors.     

The asymptotic photon propagator in a nonperturbative iteration scheme of quantum electrodynamics

In connection with the possibility of a finite theory of quantum electrodynamics, the asymptotic photon-propagator is investigated in lowest order of a nonperturbative iteration technique. The result is that at this level of approximation the theory cannot be finite.