Related papers: Rapid Decay for Odometers
We discuss issues in rare and radiative kaon decays. The interest is to extract useful short-distance information and uncover underlying dynamics. We emphasize channels where either we can understand non-perturbative aspects of QCD or there…
Motivated by the local formulae for asymptotic expansion of heat kernels in spectral geometry, we propose a definition of Ricci curvature in noncommutative settings. The Ricci operator of an oriented closed Riemannian manifold can be…
Novel relativistic expressions are used to calculate the weak decay constants of pseudoscalar and vector mesons within the constituent quark model. Meson wave functions satisfy the quasipotential equation with the complete relativistic…
In this article, we give a geometric description for any invertible operator on a finite dimensional inner--product space. With the aid of such a description, we are able to decompose any given conformal transformation as a product of…
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional…
In this paper we study the derived sets for the rational deformations of multiple zeta-star values. By using the theory of bounded variation functions, we will give function decompositions which describe the metric structure of the derived…
In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions are extremely important for some reasons. First, its…
We discuss the theoretical framework required for the computation of radiative corrections to semileptonic decay rates in lattice simulations, and in particular to those for $K_{\ell3}$ decays. This is an extension of the framework we have…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
This paper reviews the current status of experimental measurements of radiative kaon decays. Several experiments at BNL, CERN and FNAL have recently or will soon complete data collection; as a result, several new results are available.
The two-body decay rate of a weakly decaying particle (such as the kaon) is shown to be proportional to the square of a well-defined transition matrix element in finite volume. Contrary to the physical amplitude, the latter can be extracted…
We discuss strong decays of baryon resonances within the concept of relativistic constituent quark models. In particular, we follow a Poincare-invariant approach along the point form of relativistic quantum mechanics. Here, we focus on…
This is a survey article of the recent progresses on the metric behaviour of Ricci-flat K\"{a}hler-Einstein metrics along degenerations of Calabi-Yau manifolds.
We show how an operation of inf-convolution can be used to approximate convex functions with $C^{1}$ smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some…
This is a limited overview of quantum non-demolition (QND) measurements, with brief discussions of illustrative examples meant to clarify the essential features. In a QND measurement, the predictability of a subsequent value of a precisely…
Indecomposable but reducible representations of several Lie algebras of local scale-transformations, including the Schr\"odinger and conformal Galilean algebras, and some of their applications in physical ageing are reviewed. The physical…
Using light to measure an object's motion is central to operating mechanical sensors that probe forces and fields. Cavity optomechanical systems embed mechanical resonators inside optical resonators. This enhances the sensitivity of…
We investigate the feasibility of performing quantum non-demolition (QND) measurements in relativistic quantum systems, using the one-dimensional Dirac oscillator as a specific example. We derive general expressions for its QND observables…
On-chip actuation and readout of mechanical motion is key to characterize mechanical resonators and exploit them for new applications. We capacitively couple a silicon nitride membrane to an off resonant radio-frequency cavity formed by a…
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…