S U M M A R Y We develop a self-consistent thermodynamic description of silicate liquids applicable across the entire mantle pressure and temperature regime. The description combines the finite strain free energy expansion with an account of the temperature dependence of liquid properties into a single fundamental relation, while honouring the expected limiting behaviour at large volume and hig...

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a spher...

for the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. when the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. in this paper we will consider the polynomial planar vector fields ...

the crossing number of a graph  is the minimum number of edge crossings over all possible drawings of  in a plane. the crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and vlsi circuit design. in this paper we introduce vertex centered crossing number and study the same for maximal planar graph.

Histamine-sensitization test method based on histamine-sensitizing death is widely used for controlling residual activity of pertussis toxin in acellular pertussis vaccines. The test method evaluates the residual activity according to the death of mice injected with a test vaccine after histamine challenge and the test result, therefore, depends on the sensitivity of mice. A highly sensitive te...

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph G to evaluate to multiple zeta values. The criterion depends only on the topology of G, and can be checked algorithmically. As a corollary, we reprove the result, due to Bierenbaum and Weinzierl, that the massless 2-loop 2...

Effects of thermal spin disorder and excess Mn on the electronic spectrum of half-metallic NiMnSb are studied using first-principles calculations. Temperature-dependent spin disorder, introduced within the vector disordered local moment model, causes the valence band at the point to broaden and shift upwards, crossing the Fermi level and thereby closing the half-metallic gap above room temperat...

The biplanar crossing number cr2(G) of a graph G is min{cr(G1)+ cr(G2)}, where cr is the planar crossing number and G1 ∪ G2 = G. We show that cr2(G) ≤ (3/8)cr(G). Using this result recursively, we bound the thickness by Θ(G) − 2 ≤ Kcr2(G) log2 n with some constant K. A partition realizing this bound for the thickness can be obtained by a polynomial time randomized algorithm. We show that for an...

The effect of temperature and calcium ions on the denaturation of a recombinant alpha-amylase from Bacillus halmapalus alpha-amylase (BHA) has been studied using calorimetry. It was found that thermal inactivation of BHA is irreversible and that calcium ions have a significant effect on stability. Thus an apparent denaturation temperature ( T (d)) of 83 degrees C in the presence of excess calci...