Recently, an exact Green’s function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was derived. Here, we use the obtained Green’s function to calculate exact expressions for the survival probability, the time-dependent reaction rate coefficient for the initially unbound pair and the survival probability of t...

We consider the following integer feasibility problem: Given positive integer numbers a0 a1 an, with gcd a1 an = 1 and a = a1 an , does there exist a vector x ∈ n≥0 satisfying a x = a0? We prove that if the coefficients a1 an have a certain decomposable structure, then the Frobenius number associated with a1 an, i.e., the largest value of a0 for which a x= a0 does not have a nonnegative integer...

Spectroscopic factors and asymptotic normalization coefficients ~ANCs! have been determined for bound states in O using the N(He,d)O reaction. These results are used to calculate the astrophysical S factor for direct capture in the N(p ,g)O reaction. We also discuss how uncertainties in optical-model parameters influence both the spectroscopic factors and the ANCs, and the effect that this has ...

In this paper we give the coefficients estimates, distortion properties, radii of starlikeness and convexity for classes of functions with varying argument of coefficients defined by convolution and subordination.

We develop a methodology to optimally design a financial issue to hedge non-tradable risk on financial markets. Economic agents assess their risk using monetary risk measure. The inf-convolution of convex risk measures is the key transformation in solving this optimization problem. When agents’ risk measures only differ from a risk aversion coefficient, the optimal risk transfer is amazingly eq...

We introduce and investigate two new general subclasses of multivalently analytic functions of complex order by making use of the familiar convolution structure of analytic functions. Among the various results obtained here for each of these function classes, we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the classes introd...

The polynomials that arise as coefficients when a power series is raised to the power x include many important special cases, which have surprising properties that are not widely known. This paper explains how to recognize and use such properties, and it closes with a general result about approximating such polynomials asymptotically.

Relative to the Gaussian measure on R, entropy and Fisher information are famously related via Gross’ logarithmic Sobolev inequality (LSI). These same functionals also separately satisfy convolution inequalities, as proved by Stam. We establish a dimension-free inequality that interpolates among these relations. Several interesting corollaries follow: (i) the deficit in the LSI satisfies a conv...

A procedure for suboptimizing the choice of convolution codes is described. It is known that random convolution codes that have been passed through a binary symmetric channel, or a binary erasure channel, have a low probability of error and are easily decoded, but no practical procedure for finding the optimum convolution code for long code lengths is known. A convolution code is defined by its...