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Annals of mathematics, ISSN 0003-486X, 2014, Volume 179, Issue 3, pp. 1121 - 1174
It is proved that $\lim_{n\rightarrow \infty }inf(p_{n+1}-p_n)\textless 7\times 10^7$, where pn is the n-th prime. Our method is a refinement of the recent... 
Integers | Cauchy Schwarz inequality | Prime numbers | Arithmetic progressions | Mathematical theorems | Partial sums | Mathematical functions | Factorization | Estimation methods | MATHEMATICS | ARITHMETIC PROGRESSIONS | LARGE MODULI | NUMBERS
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 06/2018, Volume 25, Issue 2, pp. 313 - 316
A trigonometric sine series with special properties is constructed. One of the properties of this series shows that Bary’s conjecture on subsequences of... 
40A30 | 40A05 | partial sums | Trigonometric series | subsequences of partial sums | MATHEMATICS
Journal Article
Journal Article
1974, Probability and mathematical statistics., ISBN 9780126727500, x, 381 p. --
Book
Journal of mathematical analysis and applications, ISSN 0022-247X, 06/2018, Volume 462, Issue 2, pp. 1073 - 1086
In this article we prove a general result which in particular suggests that, on a simply connected domain Ω in C, all the derivatives and anti-derivatives of... 
Generic property | Universal Taylor series | Differentiation and integration operators | Partial sums | Taylor expansion | Baire's Theorem | MATHEMATICS | MATHEMATICS, APPLIED | UNIVERSAL TAYLOR-SERIES | BOUNDARY-BEHAVIOR
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 9
The aim of the present paper is to consider geometric properties such as starlikeness and convexity of the Cesáro partial sums of certain analytic functions in... 
unit disk | partial sums | Analysis | analytic function | starlike functions | Cesáro partial sums | Mathematics, general | Mathematics | univalent functions | Applications of Mathematics | Starlike functions | Partial sums | Analytic function | Unit disk | Univalent functions | MATHEMATICS | MATHEMATICS, APPLIED | Cesaro partial sums | Disks | Convexity | Analytic functions | Classification | Inequalities | Sums
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 05/2016, Volume 437, Issue 1, pp. 513 - 525
This paper proves that the real projection of each zero of any function P(z) in a large class of exponential polynomials is an interior point of the closure of... 
Exponential polynomials | Partial sums of the Riemann zeta function | Kronecker theorem | Zeros of entire functions | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
IZVESTIYA MATHEMATICS, ISSN 1064-5632, 04/2019, Volume 83, Issue 2, pp. 273 - 286
We prove an exponential integral estimate for the cubic partial sums of multiple Fourier series on sets of large measure. This estimate yields some new... 
MATHEMATICS | multiple Fourier series | exponential integral estimates | SUMMABILITY | cubic partial sums | Fourier series | Sums
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 10/2005, Volume 102, Issue 40, pp. 14150 - 14154
Journal Article
Journal of inequalities and applications, ISSN 1025-5834, 2018, Volume 2018, Issue 1, pp. 1 - 14
Let {X,Xn}n∈N\(\{X, X_{n}\}_{n\in N}\) be a strictly stationary ρ−\(\rho^{-}\)-mixing sequence of positive random variables, under the suitable conditions, we... 
Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables
Journal Article
Integral transforms and special functions, ISSN 1476-8291, 2019, Volume 31, Issue 3, pp. 221 - 231
We establish some supercongruences related to a supercongruence of Van Hamme, such as where p is an odd prime and is the th Euler number. Our proof uses some... 
Whipple's | Euler numbers | WZ-pair | transformation | Supercongruence | gamma function | Q-ANALOG | MATHEMATICS | MATHEMATICS, APPLIED | PARTIAL-SUMS | PROOF | Whipple's F-7 transformation | Congruences
Journal Article
The Annals of statistics, ISSN 0090-5364, 2010, Volume 38, Issue 2, pp. 1034 - 1070
Journal Article
Chaos, solitons and fractals, ISSN 0960-0779, 01/2018, Volume 106, pp. 233 - 242
In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The... 
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | SURE INVARIANCE-PRINCIPLE | PARTIAL-SUMS | PHYSICS, MATHEMATICAL | CENTRAL-LIMIT-THEOREM | DEPENDENCE | Mathematics - Probability
Journal Article
Issues of analysis, ISSN 2306-3432, 12/2018, Volume 25, Issue 2, pp. 131 - 143
In this article, we prove a two-points distortion theorem and obtain sharp coefficient estimates for the families of close-toconvex harmonic mappings whose... 
sectionsб | Univalent Harmonic | closeto-convex | partial sums | convex in one direction | sections
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 7/2018, Volume 186, Issue 3, pp. 453 - 470
Let $$\mathcal {S}_H^0$$ SH0 denote the class of all functions $$f(z)=h(z)+\overline{g(z)}=z+\sum ^\infty _{n=2} a_nz^n +\overline{\sum ^\infty _{n=2}... 
Harmonic functions | Harmonic univalent functions | 30C55 | 30C50 | Mathematics, general | Coefficient bounds | Partial sums | Mathematics | Secondary 30C45 | Primary 31A05 | Affine invariant family | Linear invariant family | MATHEMATICS
Journal Article
Bioinformatics, ISSN 1367-4803, 2017, Volume 33, Issue 5, pp. 654 - 660
Motivation: The local score of a biological sequence analysis is a mathematical tool largely used to analyse biological sequences. Consequently, determining an... 
DISTRIBUTIONS | APPROXIMATION | ALIGNMENT | BIOTECHNOLOGY & APPLIED MICROBIOLOGY | BIOCHEMICAL RESEARCH METHODS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | PARTIAL-SUMS | GOODNESS-OF-FIT | VARIABLES | STRONG LIMIT-THEOREMS | EXCEEDANCES | Sequence Analysis, Protein | Statistics, Nonparametric | Models, Statistical | Statistics | Mathematics
Journal Article
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