Related papers: A probabilistic proof of Euler's pentagonal number…

We give generalizations of a finite version of Euler's pentagonal number theorem and of a q-identity of Gauss.

We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.

We prove several extensions of the Erdos-Fuchs theorem.

This paper does exactly what the title says it does. It expands the given series to arrive at the familiar "pentagonal number" expansion, also known as the pentagonal number theorem, and recalls its application to partition numbers. The…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.

In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.

Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.

This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…

We provide several simple recursive formulae for the moment sequence of infinite Bernoulli convolution. We relate moments of one infinite Bernoulli convolution with others having different but related parameters. We give examples relating…

Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…

We prove a distribution-theoretic conjecture of Robert Coleman, thereby also obtaining an explicit description of the complete set of Euler systems for the multiplicative group over Q.

We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.

In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M. A. Stern.

A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.

A symmetry of $(t,q)$-Eulerian numbers of type $B$ is combinatorially proved by defining an involution preserving many important statistics on the set of permutation tableaux of type $B$. This involution also proves a symmetry of the…

We consider controllability for divergence-free systems that have a conserved quantity and satisfy a H\"ormander condition. It is shown that such systems are controllable, provided that the conserved quantity is a proper function. The proof…

We present a proof given by Euler in his paper {\it ``De serierum determinatione seu nova methodus inveniendi terminos generales serierum"} \cite{E189} (E189:``On the determination of series or a new method of finding the general terms of…