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Acta Mathematica Hungarica
Volume/Issue:
Volume 114: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-006-0516-8
Authors:
E. Balanzario
,
M. Garaev
, and
R. Zuazua

Abstract  

We prove that for any given c, 1 < c < 17/11, almost all natural numbers are representable in the form [x c] + [p c], where x is a natural number and p is a prime.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 116: Issue 4
DOI:
https://doi.org/10.1007/s10474-007-6041-6
Authors:
G. Lü
and
Y. Xu

Abstract  

We sharpen Hua’s result by proving that each sufficiently large odd integer N can be written as

\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$N = p_1^3 + \cdots + p_9^3 with \left| {p_j - \sqrt[3]{{N/9}}} \right| \leqq U = N^{\tfrac{1} {3} - \tfrac{1} {{198}} + \varepsilon }$$ \end{document}
, where p j are primes. This result is as good as what was previously derived from the Generalized Riemann Hypothesis.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 126: Issue 3
DOI:
https://doi.org/10.1007/s10474-009-9061-6
Author:
F. Zhao

Abstract  

We prove that almost all integers N satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 5; 6; 7; 8, i.e., N = p 1 3 + ... + p j 3 with |p i − (N/j)1/3| ≦
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$N^{1/3 - \delta _j + \varepsilon }$$ \end{document}
(1 ≦ i ≦ j), for δ j = 1/45; 1/30; 1/25; 2/45, respectively.
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Acta Mathematica Hungarica
Volume/Issue:
Volume 129: Issue 3
DOI:
https://doi.org/10.1007/s10474-010-0028-4
Authors:
T. H. Chan
,
A. V. Kumchev
, and
M. Wierdl

Abstract

A classical additive basis question is Waring’s problem. It has been extended to integer polynomial and non-integer power sequences. In this paper, we will consider a wider class of functions, namely functions from a Hardy field, and show that they are asymptotic bases.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 130: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-010-0002-1
Author:
Zhixin Liu

Abstract

Let p i be prime numbers. In this paper, it is proved that for any integer k≧5, with at most exceptions, all positive even integers up to N can be expressed in the form . This improves the result for some c>0 due to Lu and Shan [12], and it is a generalization for a series of results of Ren and Tsang [15], [16] and Bauer [1–4] for the problem in the form . This method can also be used for some other similar forms.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 122: Issue 3
DOI:
https://doi.org/10.1007/s10474-008-8019-4
Authors:
G. Lü
and
H. Sun

Abstract  

We sharpen Hua’s theorem with five squares of primes by proving that every sufficiently large integer N congruent to 5 modulo 24 can be written in the form
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$N = p_1^2 + p_2^2 + p_3^2 + p_4^2 + p_5^2$$ \end{document}
 with p 1 ≦
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$N^{\tfrac{{49}} {{288}}}$$ \end{document}
.
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Acta Mathematica Hungarica
Volume/Issue:
Volume 132: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-010-0064-0
Authors:
Zhixin Liu
and
Guangshi Lü

Abstract

It is proved that every sufficiently large even integer is a sum of one prime, one square of prime, two cubes of primes and 161 powers of 2.

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Journal of Behavioral Addictions
Volume/Issue:
Volume 5: Issue 4
DOI:
https://doi.org/10.1556/2006.5.2016.077
Authors:
Jeong-Yu Kim
,
Jo-Eun Jeong
,
Je-Keun Rhee
,
Hyun Cho
,
Ji-Won Chun
,
Tae-Min Kim
,
Sam-Wook Choi
,
Jung-Seok Choi
, and
Dai-Jin Kim

Anxiety Inventory; BIS-11, Barratt’s Impulsivity Scale version 11. * p  < .05 (Mann–Whitney U test). Genetic

Open access
Journal of Behavioral Addictions
Volume/Issue:
Volume 5: Issue 1
DOI:
https://doi.org/10.1556/2006.5.2016.004
Authors:
Sebastiano Costa
,
Heather A. Hausenblas
,
Patrizia Oliva
,
Francesca Cuzzocrea
, and
Rosalba Larcan

maternal model, the originally significant path from psychological control to eating disorder (β = .11; p  > .05), and exercise dependence (β = .10; p  > .05) was no longer significant after including maladaptive perfectionism as a mediator. Instead in

Open access
Journal of Behavioral Addictions
Volume/Issue:
Volume 7: Issue 4
DOI:
https://doi.org/10.1556/2006.7.2018.109
Authors:
Kagan Kircaburun
and
Mark D. Griffiths

social media use (β = 0.18, p  < .001); Machiavellianism was associated with online gaming (β = 0.11, p  < .05) and online sex (β = 0.09, p  < .05). Those high in spitefulness scored higher on online sex (β = 0.10, p  < .05), online gambling (β = 0

Open access