Krasnoselskii type fixed point theorems for multi-valued mappings with weakly sequentially closed graph

In this work, using an analogue of Sadovskii’s fixed point result for multi-valued mappings with weakly sequentially closed graph, we prove new multi-valued analogues of Krasnoselskii fixed point theorem for mappings with weakly sequentially closed graph and under weak topology features. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.     

Low-energy electron scattering with the purine bases of DNA/RNA using the R-matrix method

R-matrix calculations on electron collisions with the purine bases found in DNA and RNA (i.e., adenine and guanine) are presented. Resonant anion states of these systems are identified by employing different approximation levels of ab initio theoretical methods, such as the static exchange, the static exchange plus polarization, and the close-coupling methods. The results are compared with other available calculations and experiments. All of these ab initio approximations, which we refer to as a scattering "model," give four shape resonances of (2)A' (π) symmetry within the energy range of 10 eV for both molecules. For adenine, the most sophisticated method, the close-coupling model, gives two very narrow (2)A' (σ) symmetry Feshbach-type resonances at energies above 5 eV. Quantitative results for the total elastic and electronic excitation cross sections are also presented.     

Fracture spacing in layered materials.

We perform an elastostatic analysis of a periodic array of cracks under constant loading. We give an analytical solution and show that there is a limitation to the fracture spacing, due to a transition from an opening to a compressive loading. For this configuration, the threshold of the fracture spacing depends on neither the applied strain nor the elastic parameters of the material. This result shows that, in the general case of layered materials, the physical mechanism that is responsible for the limitation in the density of fractures is related mainly to the geometry of the problem. This is in agreement with observations and with recent numerical results.     

Applications of homogenization techniques to the electrical conduction in biological tissues

We study a family of problems set in a finely mixed periodic medium, modelling electrical conduction in biological tissues. We prove a unified derivation of these different schemes from the Maxwell equations in the quasi-stationary approximation and we investigate the behaviour of the corresponding macroscopic models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Matched asymptotic expansions for the determination of the electromagnetic field near the edge of a patch antenna

We consider a simple but representative model incorporating the main behavior of the electromagnetic field near the edge of a patch antenna. Recall that this kind of antenna is obtained by a metal patch laying on a dielectric substrate covering a ground metallic plane. The functioning principle of such an electric device is based on the matching of an N-dimensional behavior of the field outside the antenna with an (N-1)-dimensional one inside the zone limited by the patch and the ground plane, N = 3 or 2 according to the considered model. In this study, we make use of the technique of matched asymptotic expansions and computation of singularities to describe this behavior for the two-dimensional case. Proved error estimates enable us to give a rigorous background to the underlying asymptotic analysis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of a novel highly efficient flame-retardant coating for cotton fabrics with low combustion toxicity and antibacterial properties

Cellulose - The synthesis of multi-function flame retardants is widely increasing to fulfill industrial and economic goals. In this work, a novel flame retardant, melamine salt of tannic phosphate...     

Newly Generated Atractylon Derivatives in Processed Rhizomes of Atractylodes macrocephala Koidz

Thermally processed rhizomes of Atractylodes macrocephala (RAM) have a long history of use in traditional Chinese medicine (TCM) for treating various disorders, and have been an integral part of various traditional drugs and healthcare products. In TCM, herbal medicines are, in most cases, uniquely processed. Although it is thought that processing can alter the properties of herbal medicines so as to achieve desired functions, increase potency, and/or reduce side effects, the underlying chemical changes remain unclear for most thermally processed Chinese herbal medicines. In an attempt to shed some light on the scientific rationale behind the processes involved in traditional medicine, the RAM processed by stir-frying with wheat bran was investigated for the change of chemical composition. As a result, for the first time, five new chemical entities, along with ten known compounds, were isolated. Their chemical structures were determined by spectroscopic and spectrometric analyses. The possible synthetic pathway for the generation of such thermally-induced chemical entities was also proposed. Furthermore, biological activity evaluation showed that none of the compounds possessed cytotoxic effects against the tested mammalian cancer and noncancer cell lines. In addition, all compounds were ineffective at inhibiting the growth of the pathogenic microorganisms.     

Energetics and structure in I 2 − (CO2) n clusters

We have implemented a model of I ₂ ^? (CO₂) _n (2 ≤n ≤ 17) clusters and present an analysis of the minimum energy structures obtained from a quenching procedure. A discussion of the importance of various potential contributions to the energetics of the clusters is also presented. Given the current state of understanding of structural control of caging and the time scales of recombination and evaporation, this model has important implications for understanding the picosecond dynamics observed by the Lineberger group and for rigorous studies of evaporation rates.     

Pancyclism in Chvátal-Erdös's graphs

LetG = (X, E) be a simple graph of ordern, of stability numberα and of connectivityk withα ≤ k. The Chvátal-Erdös's theorem [3] proves thatG is hamiltonian. We have investigated under these conditions what can be said about the existence of cycles of lengthl. We have obtained several results:

1. IfG ≠ K _k,k andG ≠ C ₅,G has aC _n?1 .
2. IfG ≠ C ₅, the girth ofG is at most four.
3. Ifα = 2 and ifG ≠ C ₄ orC ₅,G is pancyclic.
4. Ifα = 3 and ifG ≠ K _3,3,G has cycles of any length between four andn.
5. IfG has noC ₃,G has aC _n?2 .

     

One-step,stereoselective synthesis of octahydrochromanes via the Prins reaction and their cannabinoid activities

Novel, functionalized octahydrochromane derivatives were synthesized in a single step via the Prins reaction. Enantiomerically pure (+)-isopulegol was reacted with benzaldehyde to stereoselectively yield the corresponding octahydro-2H-chromen-4-ol derivative containing five stereocenters. A total of 10 compounds were synthesized by altering the enantiomer of isopulegol and the substituted benzaldehyde, and the resulting enantiopure octahydrochromanes were screened in vitro against the cannabinoid receptor isoforms CB1 and CB2. Compounds containing an olefin at the C4 position [(+)-3c, (?)-3c, (?)-7c, (?)-9c and (?)-11c] of the octahydrochromane scaffold were found to exhibit reasonable displacement of [³H] CP55,940 from the CB receptors, whereas the corresponding hydroxy analogs [(+)-3a, (+)-3b, (?)-3a, (?)-3b and (+)-5a] had very little or no effect.