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
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 integ...
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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.
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...
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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 convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.
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 ∥...
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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].
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...
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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.
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...
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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. Then, we show the relationships between them.
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...
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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 considerations of Korch (Real Anal Exchange 42(2):269-282, 2017).
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...
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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.
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 (Dubins...
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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.
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...
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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.
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