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## On the Almost Sure Central Limit Theorem Along Subsequences

Mathematica Pannonica
Authors:
István Berkes
and
Endre Csáki

Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.

Open access

## Trimmed Least Square Estimators for Stable Ar(1) Processes

Mathematica Pannonica
Authors:
Alina Bazarova
,
István Berkes
, and
Lajos Horváth

We prove the weak consistency of the trimmed least square estimator of the covariance parameter of an AR(1) process with stable errors.

Open access

## On the strong law of large numbers and additive functions

Periodica Mathematica Hungarica
Authors:
István Berkes
,
Wolfgang Müller
, and
Michel Weber

## Abstract

Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f, we prove the following weighted strong law of large numbers: if X,X 1,X 2, … is any sequence of integrable i.i.d. random variables, then

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop {\lim }\limits_{N \to \infty } \frac{{\sum\nolimits_{n = 1}^N {f(n)X_n } }} {{\sum\nolimits_{n = 1}^N {f(n)} }} = \mathbb{E}Xa.s.$$ \end{document}

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## Almost sure convergence of the Bartlett estimator

Periodica Mathematica Hungarica
Authors:
István Berkes
,
Lajos Horváth
,
Piotr Kokoszka
, and
Qi-man Shao

## Summary

We study the almost sure convergence of the Bartlett estimator for the asymptotic variance of the sample mean of a stationary weekly dependent process. We also study the a.\ s.\ behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent. We also show that, after appropriate normalization, the estimator converges a.s. in the long-range dependent case as well. In both cases, our conditions involve fourth order cumulants and assumptions on the rate of growth of the truncation parameter appearing in the definition of the Bartlett estimator.

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## Botulism in infancy – survey of literature based on a case report

Orvosi Hetilap
Authors:
Andrea Berkes
,
István Szegedi
,
Edit Szikszay
,
Márta Gulyás
, and
Éva Oláh

A szerzők közleményükben egy ritka, differenciáldiagnosztikai szempontból nehézséget okozó kórképre, a csecsemőkori botulizmusra hívják fel a figyelmet. A bemutatott 6 hónapos csecsemő esetében a botulizmus ételmérgezéses formája a csecsemőkorra jellemző valódi Clostridium botulinum-fertőzéssel keveredve jelent meg. A kórkép súlyossága és az esetünkben is megfigyelt rapid lefolyás miatt a kórismét a pontos anamnézis és klinikai vizsgálat alapján kell felvetni, majd célzott vizsgálatokkal megerősíteni. Az eset ismertetése kapcsán áttekintjük a kórkép mikrobiológiai hátterét, tünettanát, epidemiológiai jellemzőit, a jelenlegi irodalmi ajánlásoknak megfelelő laboratóriumi és elektrofiziológiai vizsgáló módszereket, a felmerülő differenciáldiagnosztikai nehézségeket és a kezelési lehetőségeket. Különös figyelmet fordítunk a csecsemőkori forma speciális jellemzőire, a diagnózis felállításának az életkori sajátosságokból adódó nehézségeire, illetve a terápiás irányelvekkel kapcsolatos kérdésekre. A betegünknél megfigyelt gyors és fatális lefolyás figyelmeztet a korszerű terápia mellett is bekövetkező súlyos szövődményekre. Így a javuló prognosztikai adatok ellenére a betegség megelőzésére kell törekednünk a helyes táplálkozáshigiénés rendszabályok terjesztésével.

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## On trigonometric sums with random frequencies

Studia Scientiarum Mathematicarum Hungarica
Authors:
Alina Bazarova
,
István Berkes
, and
Marko Raseta

We prove that if I k are disjoint blocks of positive integers and n k are independent random variables on some probability space (Ω,F,P) such that n k is uniformly distributed on I k , then $N − 1 / 2 ∑ k = 1 N ( sin 2 π n k x − E ( sin 2 π n k x ) )$ has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0, 1),B, λ), where B is the Borel σ-algebra and λ is the Lebesgue measure. We also investigate the case when n k have continuous uniform distribution on disjoint intervals I k on the positive axis.

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## The personality, motivational, and need-based background of problematic Tinder use

Authors:
Gábor Orosz
,
Mária Benyó
,
,
Edina Nikoletti
,
Éva Gál
,
István Tóth-Király
, and
Beáta Bőthe

### Background and aims

Tinder is a geo-located online dating application, which is present in almost 200 countries and has 10 million daily users. The aim of the present research was to investigate the motivational, personality, and basic psychological need-related background of problematic Tinder use.

### Methods

After qualitative pretest and item construction, in Study 1 (N = 414), confirmatory factor analysis was conducted to corroborate the different motivational factors behind Tinder use. In Study 2 (N = 346), the associations between Big Five traits, Tinder motivations, and problematic Tinder use were examined with structural equation modeling (SEM). In Study 3 (N = 298), the potential role of general self-esteem, relatedness need satisfaction, and frustration in relation to Tinder-use motivations and problematic Tinder use was examined with SEM.

### Results

In Study 1, a 16-item first-order factor structure was identified with four motivational factors, such as sex, love, self-esteem enhancement, and boredom. In Study 2, problematic Tinder use was mainly related to using Tinder for self-esteem enhancement. The Big Five personality factors were only weakly related to the four motivations and to problematic Tinder use. Counterintuitively, Study 3 showed that instead of global self-esteem, relatedness need frustration was the strongest predictor of self-esteem enhancement Tinder-use motivation which, in turn, was the strongest predictor of problematic Tinder use.

### Discussion

Four motivational factors were identified as predictors of problematic use with need frustration being a relevant background variable instead of general personality traits.

Open access

## Szövegkritikai műhelymunka az Eötvös Collegiumban

Antik Tanulmányok
Authors:
Tamás Mészáros
,
László Horváth
,
Hermann Harrauer
,
Christian Gastgeber
,
Erika Juhász
,
Orsolya Hegyi
,
Mercédesz Minda
,
Tamás Németh
,
Lajos Berkes
,
Diotima Preseka
,
Katalin Delbó
,
Anna Farkas
,
István Ikvahidi
, and
Nóra Zergi
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