Related papers: Comment on the history of the stretched exponentia…
In their interesting article (Physical Review A, Vol. 101, 023843 (2020)) Conforti et al. present doubly periodic (elliptic) solutions of the nonlinear Schr\"odinger equation, based on an earlier article by Akhmediev et.al. (Theoretical and…
The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed…
A history of two Rolle Theorems, about the root of derivative and about root interval from 1690 till the end of XIX century.
The stretched exponential relaxation function is used to analyze the relaxation of the glassy state data. Due to the singularity of this function at the origin, this function is inconvenient for data analysis. Concerning this, a Prony…
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a…
These notes arose from a mini lecture series the author gave at the Early Career Researchers Workshop on Geometric Analysis and PDEs, held in January 2020 at the Matrix institute of the University of Melbourne. We discussed some classical…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities,…
The preceding Comment by Xu et al. (Phys. Rev. Lett. 122, 059803 (2019); arXiv:1808.05390) erroneously applies the entropic stress expression in our Letter (T.C. O'Connor et al., Phys. Rev. Lett. 121, 047801 (2018); arXiv:1806.09509) to…
We consider a discrete version of X-ray transform going back, in particular, to Strichartz (1982). We suggest non-overdetermined reconstruction for this discrete transform. Extensions to weighted (attenuated) analogues are given.…
Here an extended form of the reaction rate probability integral, in the case of nonresonant thermonuclear reactions with the depleted tail and the right tail cut off, is considered. The reaction rate integral then can be looked upon as the…
This expository article is an introduction to Landau's problem of bounding the derivative, knowing bounds for the function and its second derivative, and some of its variants and generalizations. Connexions with convex and functional…
Twenty five years ago, several authors proposed to describe the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across…
In the 1990's exponential-type error bounds appeared in the theory of radial basis functions. This kind of error bounds is very powerful. However it only measures the difference between the approximant and approximand. Mathematicians and…
We study statistical distributions in a mechanical model for an earthquake fault introduced by Burridge and Knopoff [R. Burridge and L. Knopoff, {\sl Bull. Seismol. Soc. Am.} {\bf 57}, 341 (1967)]. Our investigations on the size (moment),…
In [Arch. Math. 7, 28 (1956), Utilitas Math. 15, 51 (1979)] Carlitz introduced the degenerate Bernoulli numbers and polynomials by replacing the exponential factors in the corresponding classical generating functions with their deformed…
We start with a short survey of the basic properties of the Mittag-Leffler functions. Then we focus on the key role of these functions to explain the after-effects and relaxation phenomena occurring in dielectrics and in viscoelastic…
In 1989 H.Karcher rewrote the theory of elliptic functions through an approach that is much more geometrical than analytical. Therewith he obtained an optimal control over the behaviour and image values of these functions, which allowed for…
There are two parts for this paper. In the first part, we extend some results in a recent paper by Du, Guth, Li and Zhang to a more general class of phase functions. The main methods are Bourgain-Demeter's $l^2$ decoupling theorem and…
This article is a survey of Ecalle's theory of flexion units. In particular, we provide complete proofs of several key assertions that were stated without proof in Ecalle's original works.