Ferdinánd Filip

Selye János University · Department of Mathematics and Informatics

In this paper we study the properties of the unbounded sequence $0 < y_1 \le y_2 \le y_3 \le \cdots$ of positive reals having asymptotic distribution function of the form $x^\lambda$. As a consequence, we immediately get information on the asymptotic behavior of the power means of order $r>0$ of function values of some arithmetic functions, e.g., t...

In this paper we study inequalities between weighted densities of sets of natural numbers corresponding to different weight functions. Depending on the asymptotic relation between the weight functions, we give sharp bounds for possible values of one density when the values of another density are given. In particular, we give a condition for two wei...

In this paper we study ratio block sequences possessing an asymptotic distribution function. By means of these distribution functions we define new families of subsets of N which appear to be admissible ideals. We characterize these ideals using the exponent of convergence and this characterization is useful in decision if a given set belongs to a...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a comprehensive state-of-the-art investigation of the recent advances in data science in emerging economic applications. The analysis is performed on the novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains in...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

This paper provides a state-of-the-art investigation of advances in data science in emerging economic applications. The analysis was performed on novel data science methods in four individual classes of deep learning models, hybrid deep learning models, hybrid machine learning, and ensemble models. Application domains include a wide and diverse ran...

Let \(\mathbb N\) be the set of positive integers, and denote by $$\begin{aligned} \lambda (A)=\inf \{t>0:\sum _{a\in A} a^{-t}<\infty \} \end{aligned}$$the convergence exponent of \(A\subset \mathbb N\). For \(0<q\le 1\), \(0\le q\le 1\), respectively, the admissible ideals \({\mathcal {I}}_{<q}\), \({\mathcal {I}}_{\le q}\) of all subsets \(A\sub...

Let $\mathbb N$ be the set of positive integers, and denote by $\lambda(A)=\inf\{t>0:\sum_{a\in A} a^{-t}<\infty\}$ the convergence exponent of $A\subset\mathbb N$. For $0<q\le 1$, $0\le q\le 1$, respectively, the admissible ideals $\mathcal I(<q)$, $\mathcal I(\leq q)$ of all subsets $A\subset \mathbb N$ with $\lambda(A)<q$, $\lambda(A)\le q$, res...

A comparison theorem for two weighted series is proved. As a consequence, a new result concerning the weighted densities is given. © 2014 Jo´zsef Bukor, Ferdina´nd Filip and Ja´nos T. To´th.

The paper deals with the generalized Gauss composition of arbitrary means. We give sufficient conditions for the existence of this generalized Gauss composition. Finally, we show that these conditions cannot be improved or changed.

In this paper we give necessary and sufficient conditions for the block sequence of the set X = {x 1 < x 2 < … < x n < …} ⊂ ℕ to have an asymptotic distribution function in the form x λ. Key words and phrasesasymptotic distribution function-uniform distribution-block sequence Mathematics subject classification number11B05

The aim of this paper is to investigate the zeros of polynomials P n,k (x)=K k-1 x n +K k x n-1 +⋯+K n+k2 x+K n+k-1 , where the coefficients K i are terms of a linear recursive sequence of k-order (k≥2).

It is known that we can prescribe the lower and upper asymptotic and logarithmic density of a set of positive integers. The only limitation is the inequality between asymptotic and logarithmic density. We generalize this result.

Properties of dispersion of block sequences were investigated by J. T. Tóth, L. Mišík and F. Filip [Math. Slovaca 54, 453–464 (2004; Zbl 1108.11017)]. The present paper is a continuation of the study of relations between the density of the block sequence and so called dispersion of the block sequence.

Distribution functions of ratio block sequences formed from sequences of positive integers are investigated in the paper. We characterize the case when the set of all distribution functions of a ratio block sequence contains c 0, the greatest possible distribution function. Presented results complete some previously published results.

The number L(a, b) = a b ln a ln b for a 6= b and L(a, a) = a, is said to be the logarithmic mean of the positive numbers a, b. We shall say that a sequence (an) 1 n=1 with positive terms is a logarithmic sequence if an = L(an 1, an+1). In the present paper some basic estimations of the terms of logarithmic sequences are investigated.

In this paper we study sequences of the form (an + b)1n=1, where a, b 2 N. We prove many interesting results connection with sequences with infinitely many prime divisors.

The new concept of an irrationality measure of sequences is introduced in this paper by means of the related irrational sequences. The main results are two criteria characterising lower bounds for the irrationality measures of certain sequences. Applications and several examples are included.