相关论文: On $\Lambda^{r}$-strong convergence of numerical s…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
In this note, we present a relationship between Lelong numbers and complex singularity exponents. As an application, we obtain a new proof of Siu's semicontinuity theorem for Lelong numbers.
We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial…
We give a proof of the uniform convergence of Fourier series, using the methods of nonstandard analysis.
In this paper we discuss near-perfect numbers of various forms. In particular, we study the existence of near-perfect numbers in the Fibonacci and Lucas sequences, near-perfect values taken by integer polynomials and repdigit near-perfect…
The convolved Fibonacci numbers F_j^(r) are defined by (1-z-z^2)^{-r}=\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers that can be expressed in terms of convolved Fibonacci numbers are considered. These numbers appear in the…
Shmuel Friedland and the author recently presented a formal expansion for lambda_d(p) of the monomer-dimer problem. Herein we prove that if the terms in the expansion are rearranged as a power series in p, then for sufficiently small p this…
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…
This paper deals with two notions: a polarized partition relations $\left( \begin{array}{c} \alpha \beta \end{array} \right) \to \left( \begin{array}{cc} \gamma & \eta \delta & \lambda \end{array} \right)$ and product of generalized strong…
In this paper we present an effective method for computing certain real coefficients $\lambda_{n}$ which appear in a criterion for the Riemann hypothesis proved by Xian-Jin Li. With the use of this method a sequence of over three-thousand…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…
We prove new variants of the Lambert series factorization theorems studied by Merca and Schmidt (2017) which correspond to a more general class of Lambert series expansions of the form $L_a(\alpha, \beta, q) := \sum_{n \geq 1} a_n q^{\alpha…
We establish the weighted fractional Orlicz-Hardy inequalities for various Orlicz functions. Further, we identify the critical cases for each Orlicz function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic…
The paper provides a new test of convergence and divergence of positive series. In particular, it extends the known test by Margaret Martin [%\emph{Bull. Amer. Math. Soc.} \textbf{47} (6), 452--457 (1941)]. \emph{Bull. Amer. Math. Soc.}…
We introduce new classes of general monotone sequences and study their properties. For functions whose Fourier coefficients belong to these classes, we establish Hardy-Littlewood-type theorems.
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
We consider summability methods generated by the class GM(2b). We generalize some related results of P. Pych-Taberska [Studia Math. XCVI (1990), 91-103] on strong approximation of almost periodic functions by their Fourier series and S. M.…
A $1$-Lipschitz map $f$ from a convex compact set to itself has fixed points. This consequence of Brouwer's or Schauder's fixed point theorem has more elementary proofs by approximating $f$ by $\lambda$-contractions, $f_\lambda$. We study…
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
In a previous article, we reduced the unsolved problem of the convergence of Collatz sequences, to convergence of Collatz sequences of odd numbers, that are divisible by 3. In this article, we further reduce this set to odd numbers that are…