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Normality concerning the sequence of multiple functions

ANALYSIS AND MATHEMATICAL PHYSICS 2025年第2期15卷 1-13页

作者： Wei, Dongmei Li, Fei Xu, Yan Nanjing Normal Univ Inst Math Sch Math Nanjing 210023 Peoples R China

Let {fn}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{f_n\}$$\end{document} be a sequence of meromorphic functions defined in a domain D, and let {psi n}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{\psi _n\}$$\end{document} be a sequence of holomorphic functions on D, whose zeros are multiple, such that psi n ->psi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi _n\rightarrow \psi $$\end{document} converges locally uniformly in D, where psi(not equivalent to 0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi (\not \equiv 0)$$\end{document} is holomorphic in D. If, (1) fn not equal 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_n\ne 0$$\end{document} and fn(k)not equal 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_n<^>{(k)}\ne 0$$\end{document};(2) all zeros of fn(k)-psi n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa

关键词： Meromorphic function Normal family Multiple function sequence of functions

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Normality Concerning the sequence of functions

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Acta Mathematica Sinica,English Series 2017年第8期33卷 1154-1162页

作者： Bing Mao DENG De Gui YANG Ming Liang FANG Institute of Applied Mathematics South China Agricultural UniversityGuangzhou 510642P.R.China

Let {fn} be a sequence of functions meromorphic in a domain D, let {hn} be a sequence of holomorphic functions in D, such that hn（z） x h（z）, where h（z） 0 is holomorphic in D, and let k be a positive integer. If for each n ∈ N＋, fn（z） ≠ 0 and fn（k）（z） - hn（z） has at most k distinct zeros （ignoring multiplicity） in D, then {fn} is normal in D.

关键词： Meromorphic function normality sequence of functions

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Lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed space

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2014年第3期26卷 1289-1299页

作者： Karakaya, Vatan Simsek, Necip Gursoy, Faik Erturk, Muzeyyen Yildiz Tech Univ Dept Engn Math TR-34220 Istanbul Turkey Istanbul Commerce Univ Dept Math Istanbul Turkey Yildiz Tech Univ Dept Math TR-34220 Istanbul Turkey

In this paper we study lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces. We define concept of lacunary statistical pointwise convergence and lacunary statistical uniform... 详细信息

关键词： Intuitionistic fuzzy normed spaces statistical convergence sequence of functions

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ON PROJECTIONS IN L1 AND L-INFINITY

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CONSTRUCTIVE APPROXIMATION 1985年第4期1卷 297-303页

作者： SHEKHTMAN, B UNIV CALIF RIVERSIDE DEPT MATH RIVERSIDE CA 92521 USA

Let (X n ) be an increasing sequence ofn-dimensional subspaces inL ∞. LetP n be a sequence of projections fromL 1 orL t8 ontoX n , written in the integral form(p n f)(t)=∫K n (s,t)f(s)ds. We prove that if ∥... 详细信息

Let (X _n) be an increasing sequence ofn-dimensional subspaces inL _∞. LetP _n be a sequence of projections fromL ₁ orL _t8 ontoX _n, written in the integral form(p _n f)(t)=∫K _n (s,t)f(s)ds. We prove that if ∥K _n?K _n?1∥_∞0(logn), then sup∥p _n∥=∞. This theorem extends some results of Olevskii [3] and Kwapien and Szarek [2].

关键词： 41A35 41A45 41A65 Projections sequences of projections Norms of projections Increasing sequence of subspaces sequence of functions

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Rational solutions to the Pfaff lattice and Jack polynomials

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ERGODIC THEORY AND DYNAMICAL SYSTEMS 2002年第5期22卷 1365-1405页

作者： Adler, M Kuznetsov, VB Van Moerbeke, P Brandeis Univ Dept Math Waltham MA 02454 USA Univ Leeds Dept Appl Math Leeds LS2 9JT W Yorkshire England Catholic Univ Louvain Dept Math B-1348 Louvain Belgium

The finite Pfaff lattice is given by a commuting Lax pair involving, a finite matrix L (zero above the first subdiagonal) and a projection onto sp(N). The lattice admits solutions such that the entries of the matrix L are rational in the time parameters t1, t2,..., after conjugation by a diagonal matrix. The sequence of polynomial tau-functions, solving the problem, belongs to an intriguing chain of subspaces of Schur polynomials, associated to Young diagrams, dual with respect to a finite chain of rectangles. Also, this sequence of tau-functions is given inductively by the action of a fixed vertex operator. As an example, one such sequence is given by Jack polynomials for rectangular Young diagrams, while another chain starts with any two-column Jack polynomial.

关键词： .SCHUR POLYNOMIALS rational solutions sequence of functions VERTEX OPERATOR polynomials for rectangular Pfaff lattice Marked proof MOSER Sheet

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ON I-UNIFORM CONVERGENCE OF sequenceS OF functions IN 2-NORMED SPACES

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ROCKY MOUNTAIN JOURNAL OF MATHEMATICS 2020年第5期50卷 1637-1646页

作者： Dundar, Erdinc Arslan, Mukaddes Yegul, Sevim Afyon Kocatepe Univ Dept Math Afyon Turkey

In this work, we discuss various kinds of I-uniform convergence for sequences of functions and introduce the concepts of I*-uniform convergence, I and I*-uniformly Cauchy sequences of functions in 2-normed spaces. The... 详细信息

关键词： sequence of functions I-convergence uniformly convergence 2-normed spaces

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Ideal generalizations of Egoroff's theorem

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ARCHIVE FOR MATHEMATICAL LOGIC 2020年第7-8期59卷 957-977页

作者： Repicky, Miroslav Slovak Acad Sci Math Inst Gresakova 6 Kosice 04001 Slovakia

We investigate the classes of ideals for which the Egoroff's theorem or the generalized Egoroff's theorem holds between ideal versions of pointwise and uniform convergences. The paper is motivated by considera... 详细信息

关键词： Egoroff's theorem Ideal on omega Ideal convergence sequence of functions

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Conformal invariants and partial differential equations

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BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY 2005年第3期42卷 365-393页

作者： Chang, SYA Princeton Univ Dept Math Princeton NJ 08544 USA

Our goal is to study quantities in Riemannian geometry which remain invariant under the conformal change of metrics that is, under changes of metrics which stretch the length of vectors but preserve the angles between any pair of vectors. We call such a quantity conformally invariant . In conjunction with the study of conformal invariants, we are also interested in studying conformally covariant operators , that is, linear dierential operators dened on a manifold which prescribes the change of a geometric quantity under conformal change of metrics.

关键词： .Conformally invariant GAUSSIAN CURVATURE erential operators fully nonlinear blow-up Gauss-Bonnet sequence of functions Conformal invariants conformal geometry conformal covariant boundary operator Conformally covariant Renormalized volume conformal change covariant operators

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Real analysis students' understanding of pointwise convergence of function sequences in a DGS assisted learning environment

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JOURNAL OF MATHEMATICAL BEHAVIOR 2018年 49卷 61-81页

作者： Caglayan, Gunhan New Jersey City Univ Dept Math Jersey City NJ 07305 USA

The purpose of this research study is to understand how math majors conceptualize and make sense of pointwise convergence of sequence of functions in a series of in-depth qualitative interviews. Framed in APOS (Dubinsky & McDonald, 2002) and VA (visual-analytic) strategy coordination (Zazkis, Dubinsky & Dautermann, 1996) theoretical perspectives, the analysis showed that students demonstrated a diversity of mathematical behaviors associated mostly with the process level of understanding in APOS model. Yet a complete understanding of pointwise convergence at object level did not take place, students still also exhibited significant achievements in progression from process to object. The VA coordination also proved a beneficial mechanism in students' making sense of pointwise convergence in a dynamic geometry environment.

关键词： sequence of functions Pointwise convergence Pointwise limit function APOS theory Visual-analytic strategy coordination Dynamic geometry software

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Constructions of Resilient functions Over Finite Fields

Constructions of Resilient Functions Over Finite Fields

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International Symposium on Image Analysis and Signal Processing

作者： Zhang Jie Liu Zhenhua Wen Qiaoyan Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China China Womens Univ Comp Sci Dept Beijing 100101 Peoples R China

ISBN: (纸本)9781424439867

This paper presents some methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. Furthermore, we construct some infinite families of resilient functions with optimal nonlinearity which is particularly well-suited for combining linear feedback shift registers.

关键词： correlation-immune functions resilient functions optimal nonlinearity order linear cord sequence of functions

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