Article
Mathematics
Xiaosheng Wu, Pengzhen Yang
Summary: According to the Hardy-Littlewood Conjecture, the most likely common differences among primes will increase indefinitely, and every prime can divide all sufficiently large most likely common differences.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2021)
Article
Mathematics, Applied
Jiamin Li, Jianya Liu
Summary: This paper proves a partial case of the k-tuple conjecture by Hardy and Littlewood, and provides a better conditional result under the Elliott-Halberstam conjecture.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics
Li Zhu
Summary: This study improves on Zhao's result for k = 169 by proving that for k = 30, every sufficiently large even integer can be represented as a sum of eight cubes of primes and k powers of 2.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Alessandro Gambini
Summary: The inequality problem with prime variables under certain conditions is studied, and it is proved that the inequality has infinitely many solutions.
Article
Mathematics
Yuhui Liu
Summary: This study proves that every sufficiently large even integer can be represented as a pair of equations consisting of eight prime cubes and 609 powers of 2, and each sufficiently large even integer can be expressed as the sum of eight cubes of primes and 157 powers of 2. These findings refine the results of previous studies by Z. X. Liu (2013) and X. D. Zhao and W. X. Ge (2020).
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Li Zhu
Summary: It has been proven that every sufficiently large even integer can be represented as a sum of two squares of primes, two cubes of primes, two fourth powers of primes and 17 powers of 2.
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Li Zhu
Summary: It has been proven that, when k = 50, any sufficiently large even integers can be represented as the sum of a pair of eight cubes of primes and k powers of 2, which is an improvement over the previous result for k = 658.
Article
Mathematics
Trevor d. Wooley
Summary: This paper investigates a set of non-zero integers and establishes the existence of lines with integral coordinates on a specific affine surface under certain conditions. This conclusion overcomes the traditional convexity barrier and plays an important role in solving the problem.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Libo Li, Zhiwei Hao, Xinru Ding
Summary: In this paper, we introduce the generalized grand Morrey spaces in the framework of probability space setting, and provide the Doob maximal inequalities on these spaces. We also discuss the boundedness of fractional integral operators for regular martingales in this new framework.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Mathematics
Mikhail Dyachenko, Erlan Nursultanov, Sergey Tikhonov, Ferenc Weisz
Summary: This article obtains Fourier inequalities in the weighted L-p spaces for any 1 < p < infinity involving the Hardy-Cesaro and Hardy-Bellman operators. These results are extended to product Hardy spaces for p <= 1. Additionally, the boundedness of the Hardy-Cesaro and Hardy-Bellman operators in various spaces (Lebesgue, Hardy, BMO) is discussed. A key tool used is an appropriate version of the Hardy-Littlewood-Paley inequality.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Helmut Maier, Michael Th Rassias
Summary: This paper proves, on the assumption of the Generalized Riemann Hypothesis, that every sufficiently large odd integer can be represented in a specific form. The proof combines various methods including the infinitude of primes, Piatetski-Shapiro primes, and the Hardy-Littlewood circle method.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2023)
Article
Mathematics
X. Han, H. Liu
Summary: This article proves a mathematical problem on how to represent a series of even positive integers using prime numbers. By improving previous research, better approximations are provided, and two different results are obtained.
SBORNIK MATHEMATICS
(2023)
Article
Mathematics, Applied
Xuetong Su, Jiabao Yang, Huanmin Yao
Summary: This paper focuses on solving a class of quasilinear degenerate parabolic problems using the shifted Legendre reproducing kernel Galerkin method. The method linearizes the quasilinear term, discretizes the time derivative using finite difference scheme, constructs basis functions using shifted Legendre polynomials, and obtains the approximate solution using Galerkin method. The paper also discusses error estimates and stability analysis of the method, and provides numerical examples to demonstrate its feasibility and reliability.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics
Aleksei Kulikov
Summary: This study presents a contractive Hardy-Littlewood type inequality for functions from H-p(T), with 0 < p <= 2, which is sharp in the first two Taylor coefficients and asymptotically at infinity.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Cesar E. Torres Ledesma, Jose Vanterler da C. Sousa
Summary: This paper investigates the Hardy-Littlewood type and the integration by parts results for psi-Riemann-Liouville fractional integrals. It also examines the integration by parts for the psi-Riemann-Liouville and psi-Hilfer fractional derivatives. Additionally, Sobolev-type inequalities involving the psi-Riemann-Liouville and psi-Hilfer fractional derivatives in weighted space are explored.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
