Dispersive constraints on the shape of the form factors which describe the exclusive decays B̄ → D(∗)l ν̄ are derived by fully exploiting spin symmetry in the groundstate doublet of heavy–light mesons. The analysis includes all twenty B̄(∗) → D(∗) semileptonic form factors. Heavy-quark symmetry, with both short-distance and 1/mQ corrections included, is used to provide relations between the form f...

Baryon form factors can be analyzed in a largely model–independent fashion in terms of two complementary approaches. These are chiral perturbation theory and dispersion relations. I review the status of dispersive calculations of the nucleon electromagnetic form factors in the light of new data. Then, I present the leading one–loop chiral perturbation theory analysis of the hyperon and the stra...

An accurate low-energy dispersive parametrization of the scalar Kπ form factor was constructed some time ago in terms of a single parameter guided by the Callan-Treiman low-energy theorem. A similar twice subtracted dispersive parametrization for the vector Kπ form factor will be investigated here. The robustness of the parametrization of these two form factors will be studied in great detail. ...

Dispersive representations of the Kπ vector and scalar form factors are used to fit the spectrum of τ → Kπν τ obtained by the Belle collaboration incorporating constraints from results for K l 3 decays. The slope and curvature of the vector form factor are obtained directly from the data through the use of a three-times-subtracted dispersion relation. We find λ ′ + = (25.49 ± 0.31) × 10 −3 and ...

nonstandard finite difference schemes for the black-scholes partial differential equation preserving the positivity property are proposed. computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the black-scholes equation. unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.

In this paper, a general framework for surface modeling using geometric partial differential equations (PDEs) is presented. Starting with a general integral functional, we derive an Euler–Lagrange equation and then a geometric evolution equation (also known as geometric flow). This evolution equation is universal, containing several well-known geometric partial differential equations as its spe...

We present precision corrections to dispersion relation bounds on form factors in bottom hadron semileptonic decays and analyze their effects on parameterizations derived from these bounds. We incorporate QCD two-loop and nonperturbative corrections to the two-point correlator, consider form factors whose contribution to decay rates is suppressed by lepton mass, and implement more realistic est...

In the long-wave, weakly nonlinear limit a generic model for the interaction of two waves with nearly coincident linear phase speeds is a pair of coupled Korteweg-de Vries equations. Here we consider the simplest case when the coupling occurs only through linear non-dispersive terms, and for this case delineate the various families of solitary waves that can be expected. Generically, we demonst...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

The Callan-Treiman low-energy theorem offers an opportunity to test electroweak couplings of light quarks to the gauge boson W. To that aim, we introduce a model-independent and accurate dispersive parametrization of the two K ℓ3 form factors. We then discuss three applications to the analysis of K e3 and K µ3 measurements: the prediction of the ratios Γ K µ3 /Γ (K e3), the extraction of | f + ...