We calculate the BB parameter, relevant for B 0 –B 0 mixing, from a lattice gauge theory simulation using the static approximation for the heavy quark and the Wilson action for the light quark and gauge fields. Improved sources, produced by an optimized variational technique, most, reduce statistical errors and minimize excited-state contamination of the ground-state signal. Renormalization of ...

We study linear and nonlinear instability of steady incompressible inviscid flows. First, some sufficient conditions of linear instability for a class of shear flows are given. Second, nonlinear instability in the L2-norm of velocity is proved under the assumption that the growth rate exceeds half of the Liapunov exponent of the steady flow, for any bounded domain. We also estimate the growth o...

where 1 < p < N+2 N−2 , N ≥ 3. It is well-known that this equation has a unique positive radial solution. The existence of sign-changing radial solutions with exactly k nodes is also known. However the uniqueness of such solutions is open. In this paper, we show that such sign-changing radial solution is unique when p is close to N+2 N−2 . Moreover, those solutions are non-degenerate, i.e., the...

We propose a natural expansion of the atomic field operator in studying elementary excitations in trapped Bose-Einstein Condensation (BEC) system near T=0K. Based on this expansion, a system of coupled equations for elementary excitations, which is equivalent to the standard linearized GP equation, is given to describe the collective excitation of BEC in a natual way. Applications of the new fo...

We study the interior spike solutions to a steady state problem of the shadow system of the Gierer-Meinhardt system arising from biological pattern formation. We rst show that at a nondegenerate peak point the interior spike solution is locally unique and then we establish the spectrum estimates of the associated linearized operator. We also prove that the corresponding solution to the shadow s...

We consider the energy current correlation function for the FPU-β lattice. For small non-linearity one can rely on kinetic theory. The issue reduces then to a spectral analysis of the linearized collision operator. We prove thereby that, on the basis of kinetic theory, the energy current correlations decay in time as t−3/5. It follows that the thermal conductivity is anomalous, increasing as N ...

The linear quadratic (LQ) optimal control problem is studied for a partial differential equation model of a time-varying plug flow tubular reactor. First some properties of the linearized model around a specific equilibrium profile are studied. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a related...

We study the resolvent equation associated with a linear operator L arising from the linearized equation for perturbations of a steady Navier–Stokes flow U∗. We derive estimates which, together with a stability criterion from [33], show that the stability of U∗ (in the L–norm) depends only on the position of the eigenvalues of L, regardless the presence of the essential spectrum. Mathematics Su...

Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polyhedral domains. Standard finite element approximations are considered. The error constants are independent of the diameters of mesh elements and the small perturbation parameter. In our analysis, we employ sharp bounds on the Green’s function of ...