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.

     

Cleavage of Diethyl Chromonyl α-Aminophosponate with Nitrogen and Carbon Nucleophiles: A Synthetic Approach and Biological Evaluations of a Series of Novel Azoles,Azines, and Azepines Containing α-Aminophosphonate and Phosphonate Groups

A convenient synthetic approach leading to a series of novel substituted azoles, azines, and azepines linked to the α-aminophosphonate moiety was achieved. The methodology depends on ring opening and ring closure (RORC) of the chromone ring of diethyl chromonyl α-aminophosphonate 1 via its reaction with nitrogen nucleophiles such as primary amines and 1,2-, 1,3-, and 1,4-bi-nucleophiles in ethanolic sodium ethoxide. Also, treatment of compound 1 with some acyclic and cyclic active methylene compounds under the same reaction conditions afforded interesting novel isolated and fused pyridine systems bearing phosphonate groups at the α-position. The screening of antimicrobial activity for the synthesized compounds indicates that connection of pyrazole, oxazepine, and benzodiazepine rings with α-aminophosphonate moiety exhibited good antimicrobial effects. Also, evaluation of their antioxidant properties shows that the compounds having 1,5-benzoxazepinyl and 1,5-benzodiazepinyl units in combination with α-aminophosphonic diester moiety are the most powerful antioxidant agents.     

Chirality and numbering of substituted tropane alkaloids

The strict application of IUPAC rules for the numbering of tropane alkaloids is not always applied by authors and there is hence a lot of confusion in the literature. In most cases, the notation of 3, 6/7-disubstituted derivatives has been chosen arbitrarily, based on NMR and MS data, without taking into account the absolute configuration of these two carbons. This paper discusses the problem and the relevance of CD and NMR to determine molecular configurations. We report on the use of (1)H-NMR anisochrony (Δδ) induced by the Mosher's chiral auxiliary reagents (R)-(-)- and (S)-(+)-α-methoxy-α-trifluoromethyl-phenylacetyl chlorides (MTPA-Cl), to determine the absolute configuration of (3R,6R)-3α-hydroxy-6β-senecioyloxytropane, a disubstituted tropane alkaloid isolated from the aerial parts of Schizanthus grahamii (Solanaceae). These analytical tools should help future works in correctly assigning the configuration of additional 3, 6/7 disubstituted tropane derivatives.     

Thermodynamic properties of a relativistic fermi system with a bose condensate at finite temperature

We investigate a procedure for obtaining the thermodynamical potential at finite temperature and density for a relativistic system of fermions in the presence of condensed bosons. After we have considered the formalism based on a relativistic form of the Landau theory of quantum liquids, we analyze a model with the Yukawa interaction between the spinor and the pseudoscalar fields. Finally we discuss our results in relationship to some known cases of condensation in high energy physics.     

Stable Carbodications

Methods developed for the generation and study of stable carbomonocations can also be employed for similar investigations on carbodications. Trivalent (classical) as well as hexacoordinate (non-classical) carbodications studied under long-lived ion conditions are reviewed with special emphasis on their structural features, and investigated primarily by ¹H- and ¹³C-NMR spectroscopy.     

Dielectric relaxation in the odd-numbered polyamides: Nylon 7-7 and nylon 11

Odd-numbered polyamides have dipoles with components that point in the same direction in the planar zigzag conformation (rather than alternating as in the even-numbered polyamides). An investigation of the dielectric properties of two odd nylons was undertaken here to see if dipole correlation resulting from this effect could be detected. It was found that the dielectric constant and relaxation strength associated with the α loss process (amorphous phase glass–rubber relaxation) when normalized for dipole concentration was indeed markedly higher in the odd nylons. The effect of uniaxial orientation induced by solid-state extrusion on the isotropy of the dielectric properties was also studied. A previous study on nylon 6–10 found a reduction in relaxation strength of the α process in both the parallel and perpendicular directions but with the perpendicular direction being much stronger than the parallel. A similar result was found here for the odd polyamides. Thus the reduction in intensity appears to be due to effective reduction in the amount of amorphous material and not due to any change in dipole correlation induced by orientation. The anisotropy in relaxation strength can be explained by a composite material effect resulting from parallel stacking of crystal lamellas and interlamellar amorphous material and without invoking any anisotropy in the amorphous-phase dielectric strength. Thus there is no reason to conclude that the amorphous phase undergoes orientation as a result of the crystal-phase orientation.     

Decay solution for the renewal equation with diffusion

In this paper we consider age structured equation with diffusion under nonlocal boundary condition and nonnegative initial data. We prove existence, uniqueness and the positivity of the solution to the above problem. Our main result is to get an exponential decay of the solution for large times toward such a study state. To this end we prove a weighted Poincaré–Wirtinger’s type inequality in unbounded domain.