In this paper, we first establish regularity of the heat flow of biharmonic maps into the unit sphere S ⊂ R under a smallness condition of renormalized total energy. For the class of such solutions to the heat flow of biharmonic maps, we prove the properties of uniqueness, convexity of hessian energy, and unique limit at t = ∞. We establish both regularity and uniqueness for Serrin’s (p, q)-sol...

It is shown that the quark mass aligns QCD θ vacuum in such a way that the strong CP is conserved, resolving the strong CP problem. Quantum chromodynamics (QCD) is well established as the fundamental theory for the strong interactions. However, there has been a persistent puzzle with QCD, namely the smallness of the strong CP violation. The most general QCD Lagrangian is given in the form:

Abstract: In this paper, we consider an isentropic Euler-Poisson equations for the bipolar hydrodynamic model of semiconductor devices, which has a non-flat doping profile and insulating boundary conditions. Using a technical energy method and an entropy dissipation estimate, we present a framework for the large time behavior of time-increasing weak entropy solutions. It is shown that the weak ...

In order to achieve integrated condition in the girth welding of high pressure natural gas transmission pipelines, the weld zones and its surrounding area should have good mechanical properties. Residual stresses are an important defect especially in the girth welding of the pipeline. In this study, two API X70 steel pipes (with spiral seam weld) of 56 inches outside diameter and 0.780 inch wal...

background and aims: the safe, potent and effective live vaccines against measles, mumps and rubella as important childhood diseases have been available for several decades. several factors can affect the thermal stability of lyophilized vaccine. methods: in this study, the effect of residual moisture on thermal stability of 61 batches of mmr vaccine was investigated using an accelerated method...

In this paper we study some monotone behavior of the residual (past) entropy of order . We prove that, under some relation between the hazard rates (reversed hazard rates) of two distributions functions F and G, when the residual (past) entropy of order of F is decreasing (increasing) then the residual (past) entropy of G is decreasing (increasing). Using this, several conclusions regarding mo...

In this article we obtain Hölder estimates for solutions to second-order Hamilton-Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estimates are uniform with respect to the smallness of the diffusion and the smoothness of the Hamiltonian. Our work is in the spirit of a result by P. Cardaliaguet and L. Silvestre [5]. We utilize De Giorgi’s method, which...

An effective quantum theory of gravitation in which gravity weakens at energies higher than approximately 10(-3) eV is one way to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from the Newtonian inverse-square force law on distances below approximately 0.05 mm. However, it is shown that this modification also leads to changes in the long-rang...

The following lemma follows the standard paradigm of recurrence results in ergodic theory: given a topological space X which satisfies a suitable ’smallness’ condition (e.g. compactness, μ(X) < ∞), and a transformation T : X → X, there exist points of X which satisfy a certain ’almost-periodicity’ condition under the action of T . Lemma 1. Poincare Recurrence Lemma If (X,β, μ, T ) is an m.p.s. ...