Related papers: The Euler and Springer numbers as moment sequences
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
Inversion sequences, also known as subexcedant sequences, form a fundamental class of objects in enumerative combinatorics. In this paper, we study the joint distribution of five statistics on inversion sequences. While several statistics…
In this paper, the singularity formation of classical solutions for the compressible Euler equations with general pressure law is considered. The gradient blow-up of classical solutions is shown without any smallness assumption by the…
We describe fermions in terms of a classical statistical ensemble. The states $\tau$ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
We investigate the properties of the moments of the cot function using the central factorial numbers. Using a new integral representation of the central factorial numbers, we find a new way to express these moments in terms of recursive…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Angular momentum is taught in every classical mechanics course. It is a difficult topic with misconceptions commonly forming significant barriers to student success. My intention in writing this paper is to combat some of the most common…
In this paper, we solve in the convergence set, the fractional logistic equation making use of Euler's numbers. To our knowledge, the answer is still an open question. The key point is that the coefficients can be connected with Euler's…
We consider the series of reciprocals of those positive integers with exactly $k$ occurrences of a given $b$-ary digit $d$ (Irwin series), and obtain geometrically convergent representations for their sums. They are expressed in terms of…
In this paper we are interested in unraveling the mathematical connections between the stochastic derivation of Schr\"odinger equation and ours. It will be shown that these connections are given by means of the time-energy dispersion…
We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
This is a survey article on the Springer correspondence for symmetric spaces. We discuss various generalization of the theory of the Springer correspondence for reductive groups to symmetric spaces and exotic symmetric spaces associated to…
Exact rational partitions are presented for Bernoulli and Euler numbers as novel sums involving Faulhaber and Sali\'e coefficients.
The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we…
Recently, a number of statistical problems have found an unexpected solution by inspecting them through a "modal point of view". These include classical tasks such as clustering or regression. This has led to a renewed interest in…
In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin.…
A generalized Euler equation of fluid dynamics is derived for describing many-body states of quantum mechanics. The Eulerian Eq. can be viewed as representing the interaction of two substates, where each substate has its own velocity and…