Neumann problem for singular degenerate parabolic equations

We prove a comparison theorem for viscosity solutions of singular degenerate parabolic equations with the Neumann boundary condition on a domain not necessarily convex. Our result applies to various level set equations including the Neumann problem for the mean curvature flow equations where every level set of solutions moves by its mean curvature and perpendicularly intersects the boundary of the domain

Quantum Critical Point of Itinerant Antiferromagnet in the Heavy Fermion Ce(Ru_{1-x}Rh_x)_2Si_2

A focus of recent experimental and theoretical studies on heavy fermion systems close to antiferromagnetic (AFM) quantum critical points (QCP) is directed toward revealing the nature of the fixed point, i.e., whether it is an itinerant antiferromagnet [spin density wave (SDW)] type or a locally-critical fixed point. The relevance of the local QCP was proposed to explain the E/T-scaling with an anomalous exponent observed for the AFM QCP of CeCu_{5.9}Au_{0.1}. In this work, we have investigated an AFM QCP of another archetypal heavy fermion system Ce(Ru_{1-x}Rh_x)_2Si_2 with x = 0 and 0.03 (sim x_c) using single-crystalline neutron scattering. Accurate measurements of the dynamical susceptibility Im[chi(Q,E)] at the AFM wave vector Q = 0.35 c^* have shown that Im[chi(Q,E)] is well described by a Lorentzian and its energy width Gamma(Q), i.e., the inverse correlation time depends on temperature as Gamma(Q) = c_1 + c_2 T^{3/2 +- 0.1}, where c_1 and c_2 are x dependent constants, in low temperature ranges.This critical exponent 3/2 proves that the QCP is controlled by the SDW QCP in three space dimensions studied by the renormalization group and self-consistent renormalization theories.Comment: 4 pages, 4 figures, LT24 (Aug. 2005, Orlando

Okishio Theory Revisited in the Light of ‘Axiomatic Externality’

It is well known that Nobuo Okishio played a central role in the world of mathematical Marxian eco-nomics. In this paper, we examine Okishio theory from a methodological perspective. Our focus is the "the-oretical boundary"that separates the economic model from conditions"given from outside". We demonstrate that Okishio’s theory could be"an open"system, but, actually, it only shows the Achilles heel of a capitalist economy. Nevertheless, bearing in mind that the accumulation of capital is at the heart of the workings of a capitalist system, and even if modern capitalism were to be financialised, Okishio’s theory should still provide us with a starting from which to think about this system, because it demonstrates capitalism’s essentially unstable character

Relaxing Constraints on Inflation Models with Curvaton

We consider the effects of the curvaton, late-decaying scalar condensation, to observational constraints on inflation models. From current observations of cosmic density fluctuations, severe constraints on some class of inflation models are obtained, in particular, on the chaotic inflation with higher-power monomials, the natural inflation, and the new inflation. We study how the curvaton scenario changes (and relaxes) the constraints on these models.Comment: 18 pages, 6 figure

Quantum Critical Point of Itinerant Antiferromagnet in Heavy Fermion

A quantum critical point (QCP) of the heavy fermion Ce(Ru_{1-x}Rh_x)_2Si_2 (x = 0, 0.03) has been studied by single-crystalline neutron scattering. By accurately measuring the dynamical susceptibility at the antiferromagnetic wave vector k_3 = 0.35 c^*, we have shown that the energy width Gamma(k_3), i.e., inverse correlation time, depends on temperature as Gamma(k_3) = c_1 + c_2 T^{3/2 +- 0.1}, where c_1 and c_2 are x dependent constants, in a low temperature range. This critical exponent 3/2 +- 0.1 proves that the QCP is controlled by that of the itinerant antiferromagnet.Comment: 4 pages, 3 figure