The BKK root count in

The root count developed by Bernshtein, Kushnirenko and Khovanskii only counts the number of isolated zeros of a polynomial system in the algebraic torus . In this paper, we modify this bound slightly so that it counts the number of isolated zeros in . Our bound is, apparently, significantly sharper than the recent root counts found by Rojas and in many cases easier to compute. As a consequence of our result, the Huber-Sturmfels homotopy for finding all the isolated zeros of a polynomial system in can be slightly modified to obtain all the isolated zeros in .

     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

Variable-Energy Photoelectron Spectroscopy of (eta(5)-C(5)H(5))NiNO: Molecular Orbital Assignment and Xalpha-SW Calculations

Variable-energy valence and inner-valence photoelectron spectra have been recorded for the CpNiNO complex (Cp = eta(5)-C(5)H(5)) between 21.2 and 100 eV, using He I radiation and synchrotron radiation. The ground state electronic structure has been calculated by using the Xalpha-SW method. Photoionization cross sections (sigma) have also been calculated for the valence ionizations using the Xalpha-SW method. The theoretical branching ratios (sigma(i)/ summation operatorsigma) have been compared with the observed branching ratios (A(i)()/ summation operatorA) between 21.2 and 100 eV. The assignment of the photoelectron spectrum based on the analysis of intensity variations and width of vibrational peaks is consistent with the ion state orbital ordering 5e(1)(1) < 7a(1)(2) < 3e(2)(3) < 4e(1)(4) (band numbers are in parentheses) and is inconsistent with another recently proposed ordering 5e(1)(1), 5e(1)(2) < 7a(1), 3e(2)(3) < 4e(1)(4), which takes the 5e(1) vibronic effects into consideration. The experimental branching ratio results indicate a Ni 3p resonance effect around 75 eV in the photoionization process. The inner-valence spectrum has also been assigned with the aid of the Xalpha-SW calculations.     

Study of free volume parameters of polystyrenes of different molecular architecture by positron annihilation lifetime measurement

Differences of size, content and size distribution of free volumes in linear branched and three-armed polystyrenes, synthesized by radical and anionic processes, were observed by positron annihilation lifetime measurements. The temperature dependence of an average free volume radius was quite similar among polystyrenes of different architectures and molecular weight distributions. The free volume radius increased with temperature, from 0.27 nm (T:60 K) to 0.29 nm (T:260 K) and 0.30 nm (T _g:363 K), then to 0.35 nm (423 K), showing turning at and transition temperature. The free volume content decreased from 60 K to 220 K to 300 K showing peculiar minimum at 220 K to 300 K depending on the molecular shape, increased above 320 K, upto 340 to 360 K. The free volume contents decreased with an increase of molecular weight and by an addition of oligomer or plasticiser, suggesting differences in relaxation time or molecular motion between the edge and middle portions of molecular chain and filling effect of smaller molecules in free volumes, respectively. The apparent free volume fraction showed clear variations atT andT _g. Size distribution of free volumes suggested more complicated behavior of free volume upon the molecular relaxations and filling effect.