Utilization of 2-ylidene-4-thiazolidinones in the synthesis of heterocyclic compounds. Part I: Synthesis of pyrazoles

2-Ylidene and 2,5-diylidene-4-thiazolidinones 2a–d were synthesized and converted into pyrazole derivatives 4a–d by reaction with hydrazine hydrate. A mechanism of this novel conversion is suggested.     

Cohomology of q-Deformed Witt–Virasoro Superalgebras of the Hom Type

Ukrainian Mathematical Journal - We study Virasoro-type extensions of the q-deformed Witt Hom–Lie superalgebras. Moreover, we provide the cohomology of q-deformed Witt–Virasoro...     

Coactions on Hochschild homology of Hopf-Galois extensions and their coinvariants

Let B⊆A be an H-Galois extension, where H is a Hopf algebra over a field K. If M is a Hopf bimodule then , the Hochschild homology of A with coefficients in M, is a right comodule over the coalgebra C_H=H/[H,H]. Given an injective left C_H-comodule V, our aim is to understand the relationship between and . The roots of this problem can be found in Lorenz (1994) [15], where and are shown to be isomorphic for any centrally G-Galois extension. To approach the above mentioned problem, in the case when A is a faithfully flat B-module and H satisfies some technical conditions, we construct a spectral sequence

     

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.     

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.     

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.     

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.