相关论文: A generalization of Wolstenholme's harmonic series…
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
The global regularity for the viscous Boussinesq equations is proved.
This paper provides a complete solution to Skolem's problem for the $k$-generalized Lucas sequence $(L_n^{(k)})_{n \in \mathbb{Z}}$ with a primary focus on its behavior at negative indices. We characterize the zero-distribution of this…
We prove some weighted $L_p$ estimates for generalized harmonic extensions in the half-space.
The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.
In these notes we address the study of the log-concave operator acting on Lucas Sequences of first kind. We will find for which initial values a generic Lucas sequence is log-concave, and using this we show when the same sequence is…
We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the…
We derive generalizations of a couple of inverse tangent summation identities involving Fibonacci and Lucas numbers. As byproducts we establish many new inverse tangent identities involving the Fibonacci and Lucas numbers.
We prove a generalization of the Wallis product for a sequence of real numbers related to arc lengths of clover curves. Our proof generalizes a common argument given for the original Wallis product using a sequence of definite integrals.
In this paper, we shall find a new connection between $n$th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discuss the recent work been done in sequences and their…
In this article we obtain the classification of the congruences of lines with one-dimensional focal locus. It turns out that one can restrict to study the case of $\mathbb{P}^3$.
We shall show that the sum of the series formed by the so-called hyperharmonic numbers can be expressed in terms of the Riemann zeta function. More exactly, we give summation formula for the general hyperharmonic series.
In terms of the derivative operator and three hypergeometric series identities, several interesting summation formulas involving generalized harmonic numbers are established.
We study the convergence of the Hermite series of measurable functions on the real line. We characterize the norm convergence of truncated partial Hermite sums in rearrangement invariant spaces provided that the truncations vanish…
Recent work has generalized the Furstenberg correspondence between sets of integers and dynamical systems to versions which involve sequences of finite graphs or sequences of $L^\infty$ functions. We give a unified version of the theorem…
We propose two inductive approaches for determining the cohomology of Deligne-Lusztig varieties in the case of the general linear group
Some explicit expressions are given for the theta series of Niemeier lattices. As an application, we present some of their congruence relations.