Abstract:
We prove that, unlike in several space dimensions, there is no critical (nonlinear) diffusion coefficient for which solutions to the one dimensional quasilinear Smoluchowski-Poisson equation with small mass exist globally while finite time blowup could occur for solutions with large mass.

Abstract:
We find conditions under which measures belong to . Next we show that measures generated by Prandtl, Kaden as well as Pullin spirals, objects considered by physicists as incompressible flows generating vorticity, satisfy assumptions of our theorem, thus they are (locally) elements of . Moreover, as a by-product, we prove an embedding of the space of Morrey type measures in .

Abstract:
This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behaviour of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.

Abstract:
La evolución de las características ecológicas de las especies es uno de los temas más intensamente estudiados, pero su complejidad suele limitar estos estudios a evidencias indirectas de las adaptaciones reales de los organismos. Recientemente, métodos moleculares como los "micro-arrays" y la secuenciación a gran escala han incrementado de manera notable el conocimiento de los genomas y las vías metabólicas. Con ello, ha sido posible por primera vez estudiar con detalle la interacción a nivelmolecular de los organismos con su medio. Sin embargo, la investigación de los procesos bioquímicos asociados a cuestiones ecológicas y evolutivas relacionando a los organismos con sus hábitats se suele limitar a los llamados "organismos modelo". Los últimos avances en proteómica han permitido un enorme incremento de su uso en ecología y biología evolutiva. Estas metodologías son en muchos aspectos perfectamente aplicables a estudios ecológicos, ofreciendo la posibilidad de trabajar con una amplia gama de organismos. En este trabajo hacemos una breve revisión de las principales metodologías y de cómo la proteómica se ha utilizado hasta la fecha en diferentes estudios ecológicos y evolutivos en organismos no-modelo.

Abstract:
The Debye temperature, T_D, of sigma-phase Fe_(100-x)Mo_x compounds with 47 < x < 56.7 was determined from the temperature dependence of the centre shift of M\"ossbauer spectra recorded in the temperature range of 80 - 300 K. Its compositional dependence shows a weak increase with x whose rate, in a linear approximation, is equal to 3.1 K/at%. The results are compared with the corresponding ones found previously for the sigma-phase in Fe-Cr and Fe-V compounds.

Abstract:
Fe-gluconate was studied by means of the M\"ossbauer spectroscopy in the temperature interval of 80-305K. The measured spectra were analyzed in terms of two subspectra and, alternatively, two distributions of the quadrupole splitting. The major component (ca.85%) was identified as due to high-spin Fe2+ ions while the identification of the minor component (ca.15%) was not unique: some characteristics are in favour of the high-spin Fe3+ state while other ones are consistent with the low-spin Fe2+ state. Values of the Debye temperature were determined for both phases from a temperature dependence of the center shift as well as from that of the spectral area. The force constant for the high-spin ferrous atoms was evaluated to be equal to 44 N/m (243 cm-1).

Abstract:
Distribution of Cr atoms in Fe_{100-x}Cr_x alloys with x \le 25 within the first two coordination shells, 1NN-2NN, around probe 57Fe atoms was studied by means of the M\"ossbauer Spectroscopy. Clear evidence was found that the distribution is characteristic of a given atomic configuration. Only the configurations with Cr atoms situated in 2NN exhibit a quiasi-random distribution, while those with Cr atoms present in 1NN shell and those with Cr atoms in both shells is evidently not random showing clastering or anticlastering features. These findings are novel and much more complete than the up-to-date knowledge according to which there is an inversion of the short-range order parameter at x = 11. The inversion in the present study was found only for the configuration with one Cr atom in 1NN. On average, Cr atoms are distributed almost randomly within the 1NN-2NN volume for x \eq ~10, and do cluster for larger x.

Abstract:
Effect of a thermal history of Fe(100-x)Cr(x) (x < 20) samples on a Cr atoms distribution within the first (1NN) and the second (2NN) neighbor-shells was studied with the M\"ossbauer spectroscopy. The distribution was expressed in terms of the Cowley-Warren short-range order (SRO) parameters: for 1NN, for 2NN and for 1NN-2NN. It was shown to be characteristic of the thermal treatment and of the neigbor shell. For quenched samples, is positive for all x-values, while shows inversion at x about 8 from positive to weakly negative. Similar character has , but the degree of ordering in 1NN-2NN is lower than that in 2NN. Isochronally annealed samples exhibit similar behvior for x > ~8, but significantly different for x < ~8 where the inversion both in and occurs at x about 3, yet in the opposite direction. The follows the trend predicted by Erhart et. al. [PRB 77, 134206 (2008)]. A clear-cut inversion induced by an isothermal annealing at 415 C was found for the Fe85Cr15 sample.

Abstract:
A review is presented on physical properties of the sigma-phase in Fe-Cr and Fe-V alloy systems as revealed both with experimental -- mostly with the Mossbauer spectroscopy -- and theoretical methods. In particular, the following questions relevant to the issue have been addressed: identification of sigma and determination of its structural properties, kinetics of alpha-to-sigma and sigma-to-alpha phase transformations, Debye temperature and Fe-partial phonon density of states, Curie temperature and magnetization, hyperfine fields, isomer shifts and electric field gradients.

Abstract:
57Fe site Mossbauer Spectroscopy (MS) was used to investigate a dynamics of 57Fe atoms embedded into chromium lattice as impurities. From the Mossbauer spectra recorded in the temperature range of 80 to 350 K, a temperature dependence of the Lamb-Mossbauer factor, f, was determined. The latter revealed an unusual dynamics of 57Fe atoms viz. harmonic mode below T = 145 K with a characteristic effective Debye temperature, Qeff = 185 K and anharmonic one above T o 145 K. The latter mode exists in two clearly separated temperature intervals with slightly different Qeff - values viz. (i) 156 K for 145 K < T < 240 K and the record-high anharmonic coefficient e = 18 * 10-4 K-1 and (ii) 152 K for T > 240 K and e = 13.6 * 10-4 K-1. Based on the Visscher's theory, the record-low values of relative binding force constants for Fe atoms were determined as 0.0945, 0.0673 and 0.0634, respectively. It is suggested that the unusual dynamics observed in this study might be related to the underlying spin- and charge- and strain-density waves of chromium.