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Hankel and Toeplitz Determinants of Logarithmic Coefficients of inverse functions for Certain Classes of Univalent functions

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IRANIAN JOURNAL OF SCIENCE 2025年第1期49卷 243-252页

作者： Mandal, Sanju Roy, Partha Pratim Ahamed, Molla Basir Jadavpur Univ Kolkata West Bengal India

The Hankel and Toeplitz determinants H2,1(Ff-1/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{2,1}(F_{f<^>{-1}}/2)$$\end{document} and T2,1(Ff-1/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{2,1}(F_{f<^>{-1}}/2)$$\end{document} are defined as: H2,1(Ff-1/2):=Gamma 1 Gamma 3-Gamma 22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{2,1}(F_{f<^>{-1}}/2):=\Gamma _{1}\Gamma _{3} -\Gamma <^>2_{2}$$\end{document} and T2,1(Ff-1/2):=Gamma 12-Gamma 22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{2,1}(F_{f<^>{-1}}/2):=\Gamma <^>2_{1}-\Gamma <^>2_{2}$$\end{document}, where Gamma 1,Gamma 2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma _1, \Gamma _2,$$\end{document} and Gamma 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma _3$$\end{document} are the first, second and third logarithmic coefficients of inverse functions belonging to the class S\documentclass[12pt]{minimal} \u

关键词： Univalent functions Starlike functions Convex functions Hankel determinant Toeplitz determinant Logarithmic coefficients Schwarz functions inverse functions

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inverse functions of pseudo regular mappings and regularity conditions

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MATHEMATICAL PROGRAMMING 2000年第2期88卷 313-339页

作者： Kummer, B Humboldt Univ Math Inst Math Nat Fak 2 D-10099 Berlin Germany

We show that, even for monotone directionally differentiable Lipschitz functionals on Hilbert spaces, basic concepts of generalized derivatives identify only particular pseudo regular (or metrically regular) situations. Thus, pseudo regularity of (multi-) functions will be investigated by other means, namely in terms of the possible inverse functions. Tn this way, we show how pseudo regularity for the intersection of multifunctions can be directly characterized and estimated under general settings and how contingent and coderivatives may be modified to obtain sharper regularity conditions. Consequences for a concept of stationary points as limits of Ekeland points in nonsmooth optimization will be studied, too.

关键词： metric regularity intersection of multifunctions inverse functions descent directions nonsmooth equations Ekeland points generalized derivatives stationary points

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Fast Evaluation Algorithms for Elementary Algebraic and inverse functions Using the FEE Method

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PROBLEMS OF INFORMATION TRANSMISSION 2022年第3期58卷 284-296页

作者： Karatsuba, E. A. Russian Acad Sci Dorodnitsyn Comp Ctr Fed Res Ctr Comp Sci & Control Moscow Russia

We construct new fast evaluation algorithms for elementary algebraic and inverse functions based on application of two methods: A.A. Karatsuba's method of 1960 and the author's FEE method of 1990. The computat... 详细信息

关键词： fast algorithms computational complexity A A Karatsuba's method FEE method Newton's method elementary algebraic functions inverse functions rational function logarithmic function

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Subjective and objective verifications of the inverse functions of binaural room impulse responses

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APPLIED ACOUSTICS 2003年第12期64卷 1141-1158页

作者： Wang, JH Pai, CS Natl Tsing Hua Univ Dept Power Mech Engn Sound & Vibrat Labs Hsinchu Taiwan

The binaural room impulse responses (BRIRs) can be applied to 3-D sound field reconstruction, virtual reality, noise control, et al. Because the BRIRs are non-minimum phase functions, it is difficult to find the exact inverse functions of the BRIRs, especially when there are two or more sources in a reverberant space. In this work, a method was proposed to find the inverse functions of BRIRs with two sound sources in a reverberant space. The concept of time delays and the method of weighted least squares were used to find the causal, however, approximate inverse functions. The accuracy of the inverse functions was first evaluated objectively by a dummy head system. The result shows that the distortion due to crosstalk and room reverberation can be improved by 16similar to18 dB. The inverse functions were also verified subjectively by 20 students. The result of subjective evaluation also shows that the inverse functions can be used successfully to reduce the crosstalk effect and the room reverberation. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： inverse functions BRIR

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Sharp Bounds of Hankel Determinant for the inverse functions on a Subclass of Bounded Turning functions

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MEDITERRANEAN JOURNAL OF MATHEMATICS 2023年第3期20卷 1-18页

作者： Shi, Lei Arif, Muhammad Abbas, Muhammad Ihsan, Muhammad Anyang Normal Univ Sch Math & Stat Anyang 455002 Henan Peoples R China Abdul Wali Khan Univ Mardan Dept Math Mardan 23200 Pakistan

The purpose of this paper is to determine the estimates of some coefficient-related problems for the class BT3e of bounded turning functions connected to a three-leaf shaped domain. We calculate the upper bounds of the second and third order Hankel determinants with the coefficients of the inverse functions. The bounds are proved to be sharp.

关键词： Hankel determinant bounded turning functions inverse functions three leaf-shaped domain

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Families of inverse functions: Coefficient Bodies and the Fekete-Szego Problem

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MEDITERRANEAN JOURNAL OF MATHEMATICS 2022年第2期19卷 1-17页

作者： Elin, Mark Jacobzon, Fiana Ort Braude Coll Dept Math IL-21982 Karmiel Israel

In this paper, we establish the coefficient bodies for a wide class of families of inverse functions. We also completely describe functions that are boundary points of these bodies in small dimensions. We use this to obtain sharp bounds for the Fekete-Szego functionals over some classes of functions defined by quasi-subordination as well as over classes of their inverses. As a biproduct, we derive a formula for ordinary Bell polynomials that seems to be new.

关键词： inverse functions Fekete-Szego functionals Schur parameters Bell polynomials

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Divided differences of inverse functions and partitions of a convex polygon

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MATHEMATICS OF COMPUTATION 2008年第264期77卷 2295-2308页

作者： Floater, Michael S. Lyche, Tom Univ Oslo Dept Informat Ctr Math Applicat N-0316 Oslo Norway

We derive a formula for an n-th order divided difference of the inverse of a function. The formula has a simple and surprising structure: it is a sum over partitions of a convex polygon with n + 1 vertices. The formula provides a numerically stable method of computing divided differences of k-th roots. It also provides a new way of enumerating all partitions of a convex polygon of a certain type, i.e., with a specified number of triangles, quadrilaterals, and so on, which includes Catalan numbers as a special case.

关键词： divided differences inverse functions polygon partitions

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Asymptotic expansions for oscillatory integrals using inverse functions

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BIT NUMERICAL MATHEMATICS 2009年第2期49卷 397-417页

作者： Lyness, James N. Lottes, James W. Argonne Natl Lab Div Math & Comp Sci Argonne IL 60439 USA Univ New S Wales Sch Math Sydney NSW 2052 Australia Univ Oxford Inst Math Oxford OX1 3LB England

We treat finite oscillatory integrals of the form integral(b)(a) F(x)e(ikG(x)) dx in which both F and G are real on the real line, are analytic over the open integration interval, and may have algebraic singularities at either or both interval end points. For many of these, we establish asymptotic expansions in inverse powers of k. No appeal to the theories of stationary phase or steepest descent is involved. We simply apply theory involving inverse functions and expansions for a Fourier coefficient integral(b)(a) phi(t)e(ikt) dt. To this end, we have assembled several results involving inverse functions. Moreover, we have derived a new asymptotic expansion for this integral, valid when phi(t) = Sigma a(j)t(sigma j), -1 < sigma(1) < sigma(2) < center dot center dot center dot.

关键词： Variable phase oscillatory integral inverse functions Series inversion Fourier coefficient asymptotic expansion Fourier integral

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Working with Families of inverse functions 15th

Working with Families of Inverse Functions

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15th International Conference on Intelligent Computer Mathematics (CICM) part of the Computational Logic Autumn Summit (CLAS)

作者： Jeffrey, David J. Watt, Stephen M. Univ Western Ontario Dept Appl Math London ON Canada Univ Waterloo David R Cheriton Sch Comp Sci Waterloo ON Canada

ISBN: (纸本)9783031166815;9783031166808

When evaluating or simplifying mathematical expressions, the question arises of how to handle inverse functions. The problem is that for a non-injective function f: D -> R, the inverse is generally not a function R -> D since there may be multiple pre-images for a given point. The majority of work in this area has fallen into two camps: either the inverse functions, and expressions involving them, are treated as multi-valued objects, or inverse functions are taken to have one principal value. Both these approaches lead to difficulties in evaluation and simplification. It is possible to define the inverse as a function from R to sets of elements of D, but then the algebra of expressions involving the inverse becomes overly complicated. This article extends previous work based on a different approach: instead, the inverse of a function is taken to be a labelled family of functions, with the label specifying the pre-image in the original function's domain. This convention is already used by some authors for logarithms, but it can be applied more generally. In some cases, the branch indices can appear in identities that give more broadly applicable simplification rules. In this paper we survey how this approach can be applied to elementary functions, including the Lambert W.

关键词： inverse functions Simplification Rules Branch Cuts

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Pumping stations: solving algorithm with inverse functions

Pumping stations: solving algorithm with inverse functions

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12th International Conference on Computing-and-Control-for-the-Water-Industry (CCWI)

作者： Anton, A. Aldea, A. Tech Univ Civil Engn Bucharest Romania

The problem of pumps connected in parallel can be easily solved by means of graphical method, but it becomes very time consuming when dealing with multiple scenarios. An analytical approach offers the possibility of implementing a software program that can significantly reduce this time and also adds further features. The mathematical algorithm used is dealing with a non-linear equitation system and with polynomial fitting functions.. Since the presented algorithm assume that every physical measure is expressed in SI units, then the unitless values of flow rates are at least 10(-3) magnitude order compared to other values (pump head for example). This in turn leads to very poor fitting polynomials and the end results are far from the truth. The key for solving this particular issue resides in constructing the inverse functions of H(Q) and at the same time the inverse for the system characteristic. (C) 2013 The Authors. Published by Elsevier Ltd.

关键词： pumping stations inverse functions analytical solver system of equations

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