Formality and Deformations of Universal Enveloping Algebras

We describe enveloping algebras of finite-dimensional Lie algebras which are formal in the sense that their Hochschild complex as a differential graded Lie algebra is quasi-isomorphic to its Hochschild cohomology. For Abelian Lie algebras this is true thanks to the Kontsevich formality theorem. We are using his formality map twisted by the group-like element generated by the linear Poisson structure to simplify the problem, and then study examples. For instance, the universal enveloping algebras of the Lie algebras are formal. We also recover our rigidity results for enveloping algebras from this new angle and present some explicit deformations of linear Poisson structure in low dimensions.     

Sol-gel encapsulation of cells is not limited to silica: long-term viability of bacteria in alumina matrices

A colloidal route to aqueous alumina gels is described, allowing the long-term viability of encapsulated bacteria.     

Electronic transport mechanisms in tetraphenyleprophyrin thin films

Thermally-evaporated thin films of tetraphenylporphyrin, TPP, with thickness range from (175 to 735) nm had been prepared. Annealing temperatures ranging from (273–473) K do not influence the amorphous structure of these films. The influence of environmental conditions: film thickness, temperature and frequency on the electrical properties of TPP thin films had been reported. It was found that dc conductivity increases with increasing temperature and film thickness. The extrinsic conduction mechanism is operating in temperature range of (293–380) K with activation energy of 0.13 eV. The intrinsic one is in temperatures >380 K via phonon assisted hopping of small polaron with activation energy of 0.855 eV. The ac electrical conductivity and dielectric relaxation in the temperature range (293–473) K and in frequency range (0.1–100) kHz had been also studied. It had been shown that theoretical curves generated from correlated barrier hopping (CBH) model gives the best fitting with experimental results. Analysis of these results proved that conduction occurs at low temperatures (300–370) K by phonon assisted hopping between localized states and it is performed by single polaron hopping process at higher temperatures. The temperature and frequency dependence of both the real and imaginary parts of dielectric constant had been reported.     

On the limit cycles for a class of generalized Kukles differential systems

In this paper, we consider the limit cycles of a class of polynomial differential systems of the form $\dot{x}=-y, \hspace{0.2cm} \dot{y}=x-f(x)-g(x)y-h(x)y^{2}-l(x)y^{3},$ where $f(x)=\epsilon f_{1}(x)+\epsilon^{2}f_{2}(x),$ $g(x)=\epsilon g_{1}(x)+\epsilon^{2}g_{2}(x),$ $h(x)=\epsilon h_{1}(x)+\epsilon^{2}h_{2}(x)$ and $l(x)=\epsilon l_{1}(x)+\epsilon^{2}l_{2}(x)$ where $f_{k}(x),$ $g_{k}(x),$ $h_{k}(x)$ and $l_{k}(x)$ have degree $n_{1},$ $n_{2},$ $n_{3}$ and $n_{4},$ respectively for each $k=1,2,$ and $\varepsilon$ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot{x}=-y,$ $\dot{y}=x$ using the averaging theory of first and second order.     

Synthesis and characterization of titanium nitride, niobium nitride, and tantalum nitride nanocrystals via the RAPET (reaction under autogenic pressure at elevated temperature) technique

TiN, NbN, and TaN nanocrystals have been selectively prepared through a simple, solvent-free, and convenient reaction under autogenic pressure at moderate temperature (RAPET) process at 350 °C for 12 h, reacting transition metal chlorides and sodium azide. The nanostructures obtained are characterized by powder X-ray diffraction (PXRD), transmission electron microscopy (TEM), and scanning electron microscopy (SEM). A reaction mechanism is suggested based on the experimental results. These rapid reactions produce nanocrystals of TiN, NbN, and TaN with average sizes of approximately 30, 28, and 27 nm, respectively (as calculated from X-ray line broadening). An octahedral inorganic fullerene was detected among the various structures of the TiN.     

Approximations of non-smooth integral type functionals of one dimensional diffusion processes

In this article, we obtain the weak and strong rates of convergence of time integrals of non-smooth functions of a one dimensional diffusion process. We propose the use of the exact simulation scheme to simulate the process at discretization points. In particular, we also present the rates of convergence for the weak and strong errors of approximation for the local time of a one dimensional diffusion process as an application of our method.     

Influence of high-energy X-ray irradiation on the optical properties of tetraphenylporphyrin thin films

Tetraphenylporphyrin (TPP) thermally evaporated films were irradiated by different doses (0.5–2.5 kGy) of X-ray with energy 6 MeV. The optical properties for TPP were investigated using spectrophotometric measurements of the transmittance and reflectance at normal incidence of light in the wavelength range from 200 to 1100 nm. The absorption spectra recorded in the UV-VIS region of spectra showed different absorption bands, namely four Q-bands in the visible region of the spectrum and a more intense band termed as the Soret band in the near-UV region of the spectrum. Two other bands labeled N and M appear in the UV region. The Soret band showed Davydov splitting. Increasing X-ray irradiation dose influences the optical properties of TPP films. All absorption bands show a continuous blue shift in position and a decrease in intensity with increasing X-ray dose. At 2.5 kGy the B, N, and M bands disappeared. The reduction in the absorbency was calculated as a function of X-ray dose. The energy gap was determined and the type of optical transition was found to be an indirect allowed transition.     

Formation of new metastable transition metal alloys by combination of mechanical alloying and chemical leaching

The leaching of Al atoms from B2 structures of mechanically alloyed Ni and Co aluminides led to the formation of metastable B2 Ni and Co. B2 Ni is strong paramagnet not stable above 470 K. The magnetic moment of Co atom in ferromagnetic B2 phase is smaller than in fcc one. B2 Ni demonstrates high catalytic activity in hydrogenation of organic compounds.