相关论文: Three analogues of Stern's diatomic sequence

We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.

In this paper, we completely solve the existence of large sets of $(3,\lambda)$-GDDs of type $g^u$ and the existence of a simple $(3,\lambda)$-GDD of type $g^u$.

We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…

We observe that Dickey's stabilizing chain can be naturally included into two-dimensional chain of infinitely many copies of equations of KP hierarchy.

A Sidon sequence is a sequence of integers a_1 < a_2 < a_3 < ... with the property that the sums a_i+a_j (i\le j) are distinct. This work contains a survey of Sidon sequences and their generalizations, and an extensive annotated and…

We prove several theorems concerning arithmetic properties of Stern polynomials defined in the following way: $B_{0}(t)=0, B_{1}(t)=1, B_{2n}(t)=tB_{n}(t)$, and $B_{2n+1}(t)=B_{n}(t)+B_{n+1}(t)$. We study also the sequence…

Models of neutron stars are considered in the case of a uniform density distribution. An algebraic equation, valid for any equation of state, is obtained. This equation allows one to find the approximate mass of a star of a given density…

In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.

Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated…

The widely accepted interpretation of the Stern-Gerlach experiment assumes the objective atomic trajectories (the "classical trajectories") in front of the screen. Following this interpretation, we perform an {\it ab initio} analysis of the…

We prove some identities for the squares of generalized Tribonacci numbers. Various summation identities involving these numbers are derived.

We investigate the following surprisingly widespread phenomenon which we call The Rule of Three: in order for a particular kind of commutation relation to hold for subsequences of elements of a ring labeled by any subset of indices, it is…

There are sequences of directions such that, given any compact set K in R^n, the sequence of iterated Steiner symmetrals of K in these directions converges to a ball. However examples show that Steiner symmetrization along a sequence of…

An l-good sequencing of a Steiner triple system of order v, STS(v), is a permutation of the points of the system such that no l consecutive points in the permutation contains a block. It is known that every STS(v) with v > 3 has a 3-good…

We derive expressions for three-body phase space that are explicitly symmetrical in the masses of the three particles, by three separate methods.

We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.

It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An…

We study the periods of Markov sequences, which are derived from the continued fraction expression of elements in the Markov spectrum. This spectrum is the set of minimal values of indefinite binary quadratic forms that are specially…