The spectra and branching ratios of the weak semi-leptonic B meson decays to the first excited D mesons are predicted, taking into account the confined effects of quarks using the covariant oscillator quark model (COQM). In the COQM the same relation between general weak transition form factors as that in HQET is derived, and the concrete form of the IsgurWise function is given with no free par...

Stability analyses and error estimates are carried out for a number of commonly used numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all the schemes we considered are either unconditionally energy stable, or conditionally energy stable with reasonable stability conditions in the semi-discretized versions. Error estimates for selected schemes with a spectral-Ga...

Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable...

We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the leading coefficients are measurable in one variable and have small BMO semi-norms in the other variables, variable exponents p(x) satisfy log-Hölder continuity, and the boundarie...

We review recent results on the hydrodynamical model for semiconductors. The derivation of the mathematical model from the semi-classical Boltzmann equation in terms of the moment method is performed, and the mathematical analysis of the asymptotic behavior of both classical solutions and entropy weak solutions is given on spatially bounded domain or whole space.

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation o...

In the domain of qualitative constraint reasoning, a subfield of AI which has evolved in the last 25 years, a large number of calculi for efficient reasoning about space and time has been developed. Reasoning problems in such calculi are usually formulated as constraint satisfaction problems. For temporal and spatial reasoning, these problems often have infinite domains, which need to be abstra...

We give a detailed comparison between the notion of a weak Hopf algebra (also called a quantum groupoid by Nikshych and Văınerman), and that of a ×R-bialgebra due to Takeuchi (and also called a bialgebroid or quantum (semi)groupoid by Lu and Xu). A weak bialgebra is the same thing as a ×R-bialgebra in which R is Frobenius-separable. We extend the comparison to cover module and comodule theory, ...

We study a class of semi-linear mean curvature equations −Mu = H + λf(u) where M is the mean curvature operator. We show that there exists an extremal parameter λ∗ such that this equation admits a minimal weak solutions for all λ ∈ [0, λ∗], while no weak solutions exists for λ > λ∗. In the radial case, we then show that minimal solutions are classical solutions for all λ ∈ [0, λ∗] and that anot...

As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the subdifferential of the sum of these functions is the sum of their subdifferentials. This note is devoted to proving ...