Some remarks on quasilinear parabolic problems with singular potential and a reaction term

In this paper we deal with the following quasilinear parabolic problem $$\left\{\begin{array}{l@{\quad}l} (u^\theta)_t - \Delta_p {u} = \lambda \frac{u^{p - 1}}{|x|^{p}} + u^q + f,\,\, u \geq 0 \quad {\rm in} \;\;\Omega \times (0, T),\\ u(x, t) = 0 \quad\qquad\qquad\qquad\qquad\qquad\qquad {\rm on}\; \partial \Omega \times(0, T),\\ u(x, 0) = u_0(x), \,\,\, \qquad\qquad\qquad\qquad\qquad x \in\; \Omega,\end{array}\right.$$ where θ is either 1 or (p ? 1), \({N \geq 3, \,\Omega \subset \mathcal{IR}^N}\) is either a bounded regular domain containing the origin or \({\Omega \equiv \mathcal{IR}^N}\) , 1 < p < N, q > 0 and u ₀ ≥  0, f ≥  0 with suitable hypotheses. The aim of this work is to get natural conditions to show the existence or the nonexistence of nonnegative solutions. In the case of nonexistence result, we analyze blow-up phenomena for approximated problems in connection with the classical Harnack inequality, in the Moser sense, more precisely in connection with a strong maximum principle. We also study when finite time extinction (1 < p < 2) and finite speed propagation (p > 2) occur related to the reaction power.     

A Heroin Epidemic Model: Very General Non Linear Incidence,Treat-Age,and Global Stability

The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems

$$ - \mbox{div} \bigl(\epsilon^{2}\phi\bigl(\epsilon|\nabla u|\bigr)\nabla u \bigr) + V(x)\phi\bigl(\vert u\vert\bigr)u = f(u)\quad\mbox{in } \mathbb{R}^{N}, $$

where \(\epsilon\) is a positive parameter, \(N\geq2\), \(V\), \(f\) are continuous functions satisfying some technical conditions and \(\phi\) is a \(C^{1}\)-function.

     

DEEP CATALYTIC OXIDATION OF BENZENE IN THE PRESENCE OF SEVERAL VOLATILE ORGANIC COMPOUNDS ON METAL OXIDES AND Pt/Al2O3 CATALYSTS

Oxidation of benzene into CO₂ in air has been studied in the temperature range of 300-673 K on supported metal oxides and on 0.7% Pt/Al₂O₃, in the absence and in the presence of several Volatile Organic Compounds (VOCs). On the metal oxides, the deep oxidation of benzene is strongly inhibited in presence of VOCs and O-containing VOCs lead to more toxic VOCs (i.e: acetaldehyde).     

Gradient Estimates for Solutions of Ultraparabolic Equations

We establish a priori estimates for solutions to ultraparabolic equations which play a crucial role in the solvability of the initial value problem. A class of these equations came from population dynamics, namely from a fish larvae model.      

Synthesis and characterization of nanoheterostructures based on oligothiophene functionalized Ru nanoparticles

Monodisperse ruthenium nanoparticles functionalized by electroactive oligothiophenes have been prepared and characterized. Using TEM, UV-visible and FTIR we established that the organization of these nanoparticles into nanospheres can be directly controlled via modulation of the pi-pi interaction between the organic components adsorbed on the surface. This finding also shows that the self-assembled nanoheterostructures may be switched from monodisperse nanoparticles to ordered nanospheres by tuning the pH.     

Mechanically Driven Activation of Polyaniline into Its Conductive Form

Mechanical treatment of polymers produces surface cations and anions which, as demonstrated here for the first time, can drive chemical reactions. In particular, it is shown that such a mechanical treatment transforms nonconductive polyaniline into its conductive form. These results provide a mechanical means of patterning conductive polymers and also coating small polymer objects with conductive polyaniline films preventing accumulation of static electricity.     

1,2,4‐Triazine Chemistry Part IV: Synthesis and Chemical Behavior of 3‐Functionalized 5,6‐Diphenyl‐1,2,4‐triazines towards Some Nucleophilic and Electrophilic Reagents

The synthesis and chemical behavior of 3‐functionalized 5,6‐diphenyl‐1,2,4‐triazines towards some electrophilic and nucleophilic reagents are reviewed. The synthesis, unique features, and medicinal, pharmacological, and biological significance of these constituents are also reported.     

Amphiphilic water soluble cationic ring opening metathesis copolymer as an antibacterial agent

Bacterial infection is a global problem, especially resistance acquired by bacteria against to antibiotics; there is urgent need for the development of antibiotics. Here, we proposed dendron-grafted polymers via ring opening metathesis polymerization (ROMP) featuring different with tailored hydrophobicity/hydrophilicity and cationic charges. Dendritic oxanorbornene derivatives were synthesized having two and six carbon linkers and their corresponding random and block copolymers were prepared having pendant pyridinium salt moieties via ROMP. In total, 12 different water-soluble dendronized cationic polymers featuring hexyl pyridinium moieties were prepared and investigated. Six carbon linker possessing triple charge density and hexyl pyridinium functionality each repeating unit copolymers exhibited high antibacterial activity against Gram-positive bacteria (S. aureus). However, all the polymers were inactive against Gram-negative bacteria (E. coli). Most of the copolymers are non-hemolytic (>HC ₅₀ = 1,000 μg/ml). It was also observed that, there is no significant effect between block copolymers and random copolymers keeping hydrophobicity and cationic charge density constant. Zeta potential was measured to investigate the mechanism in solution via the interaction of polymers with S. aureus, while scanning electron microscope (SEM) measurements image confirms damage of the bacterial cell wall after implementation of biocidal polymer.     

Guaianolide Sesquiterpene Lactones from Centaurothamnus maximus

Centaurothamnus maximus (family Asteraceae), is a leafy shrub indigenous to the southwestern Arabian Peninsula. With a paucity of phytochemical data on this species, we set out to chemically characterize the plant. From the aerial parts, two newly identified guaianolides were isolated: 3β-hydroxy-4α(acetoxy)-4β(hydroxymethyl)-8α-(4-hydroxy methacrylate)-1αH,5αH, 6αH-gual-10(14),11(13)-dien-6,12-olide (1) and 15-descarboxy picrolide A (2). Seven previously reported compounds were also isolated: 3β, 4α, 8α-trihydroxy-4-(hydroxymethyl)-lαH, 5αH, 6βH, 7αH-guai-10(14),11(13)-dien-6,12-olide (3), chlorohyssopifolin B (4), cynaropikrin (5), hydroxyjanerin (6), chlorojanerin (7), isorhamnetin (8), and quercetagetin-3,6-dimethyl ether-4’-O-β-d-pyranoglucoside (9). Chemical structures were elucidated using spectroscopic techniques, including High Resolution Fast Atom Bombardment Mass Spectrometry (HR-FAB-MS), 1D NMR; ¹H, ¹³C NMR, Distortionless Enhancement by Polarization Transfer (DEPT), and 2D NMR (¹H-¹H COSY, HMQC, HMBC) analyses. In addition, a biosynthetic pathway for compounds 1–9 is proposed. The chemotaxonomic significance of the reported sesquiterpenoids and flavonoids considering reports from other Centaurea species is examined.