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Relevant bibliographies by topics / Harmonic function

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Academic literature on the topic 'Harmonic function'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 April 2022

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Journal articles on the topic "Harmonic function"

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Abi-Khuzam, Faruk F. "Meromorphic functions with harmonic ∗-function." Complex Variables, Theory and Application: An International Journal 12, no. 1-4 (October 1989): 261–65. http://dx.doi.org/10.1080/17476938908814370.

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Mustafa, M. T. "Harmonic Morphisms Projecting Harmonic Functions to Harmonic Functions." Abstract and Applied Analysis 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/315757.

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For Riemannian manifoldsMandN, admitting a submersionϕwith compact fibres, we introduce the projection of a function via its decomposition into horizontal and vertical components. By comparing the Laplacians onMandN, we determine conditions under which a harmonic function onU=ϕ−1(V)⊂Mprojects down, via its horizontal component, to a harmonic function onV⊂N.

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Pilipović, Stevan, and Dimitris Scarpalézos. "Harmonic generalized functions in generalized function algebras." Monatshefte für Mathematik 163, no. 1 (December 19, 2009): 81–106. http://dx.doi.org/10.1007/s00605-009-0180-5.

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Choudhary, Masood Ahmed, and ToseefAhmed Malik. "Harmonic Convex function and Harmonic Variational Inequalities." International Journal of Mathematics Trends and Technology 54, no. 4 (February 25, 2018): 320–24. http://dx.doi.org/10.14445/22315373/ijmtt-v54p536.

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Sebbar, Ahmed. "Harmonic numbers, harmonic series and zeta function." Moroccan Journal of Pure and Applied Analysis 4, no. 2 (December 1, 2018): 122–57. http://dx.doi.org/10.1515/mjpaa-2018-0012.

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AbstractThis paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias. The other parts are devoted to the series $\mathcal{M}{i_s}(z) = \sum\limits_{n = 1}^\infty {{{\mu (n)} \over {{n^s}}}{z^n}} $. A significant result is that the real part f of$$\sum {{{\mu (n)} \over n}{e^{2in\pi \theta }}}$$is an example of a non-trivial real-valued continuous function f on the real line which is 1-periodic, is not odd and has the property $\sum\nolimits_{h = 1}^n {f(h/k) = 0}$ for every positive integer k.

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Awan, Muhammad, Muhammad Noor, Marcela Mihai, Khalida Noor, and Nousheen Akhtar. "On approximately harmonic h-convex functions depending on a given function." Filomat 33, no. 12 (2019): 3783–93. http://dx.doi.org/10.2298/fil1912783a.

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A new class of harmonic convex function depending on given functions which is called as ?approximately harmonic h-convex functions? is introduced. With the discussion of special cases it is shown that this class unifies other classes of approximately harmonic h-convex function. Some associated integral inequalities with these new classes of harmonic convexity are also obtained. Several special cases of the main results are also discussed.

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Matsuoka, Osamu. "Molecular integrals over Laguerre Gaussian-type functions of real spherical harmonics." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 388–92. http://dx.doi.org/10.1139/v92-055.

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Molecular integrals are formulated over the Laguerre Gaussian-type functions (LGTF) of real spherical harmonics. They include the overlap integrals and the energy integrals of kinetic, nuclear attraction, and electron repulsion. For the nuclear-attraction integrals the formulations based on the point as well as the Gaussian nuclear charge distribution models are presented. Integral formulas over the LGTFs of real spherical harmonics are found a little more complicated than those of the LGTFs of complex spherical harmonics due to the summations over magnetic quantum numbers. Keywords: molecular integral, Gaussian-type function, spherical harmonic, solid harmonic, Sonine polynomial.

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Xu, Yuan. "Harmonic Polynomials Associated With Reflection Groups." Canadian Mathematical Bulletin 43, no. 4 (December 1, 2000): 496–507. http://dx.doi.org/10.4153/cmb-2000-057-2.

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AbstractWe extend Maxwell’s representation of harmonic polynomials to h-harmonics associated to a reflection invariant weight function hk. Let 𝑫i, 1 ≤ i ≤ d, be Dunkl’s operators associated with a reflection group. For any homogeneous polynomial P of degree n,we prove the polynomial is a h-harmonic polynomial of degree n, where γ = ∑ki and 𝑫 = (𝑫1, … ,𝑫d). The construction yields a basis for h-harmonics. We also discuss self-adjoint operators acting on the space of h-harmonics.

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Schaeben, H. "The de la Vallée Poussin Standard Orientation Density Function." Textures and Microstructures 33, no. 1-4 (January 1, 1999): 365–73. http://dx.doi.org/10.1155/tsm.33.365.

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The de la Vallée Poussin standard orientation density function νκ(ω)=C(κ)cos⁡2κ(ω/2) is discussed with emphasis on the finiteness of its harmonic series expansion which, advantageously distinguishes it from other known standard functions. Given its halfwidth, the de la Vallée Poussin standard orientation density function allows, for example, to tabulate the degree of series expansion into harmonics required for its exact representation.

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STEVIĆ, Stevo. "On harmonic function spaces." Journal of the Mathematical Society of Japan 57, no. 3 (July 2005): 781–802. http://dx.doi.org/10.2969/jmsj/1158241935.

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Dissertations / Theses on the topic "Harmonic function"

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Alhwaitiy, Hebah Sulaiman. "POTENTIAL THEORY AND HARMONIC FUNCTIONS." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1448671803.

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Abrahamson, Krista. "History, Implementation, and Pedagogical Implications of an Updated System of Functional Analysis." Thesis, University of Oregon, 2016. http://hdl.handle.net/1794/20480.

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This dissertation follows the history of functional ideas and their pedagogy, illuminates with many examples the implementation of my updated system of Functional Analysis, and discusses the pedagogical implications that this updated system implies. The main goal is to update a system of labeling to be as pedagogically friendly as possible, in order to assist students and teachers of harmony to more easily and enjoyably learn, teach, and engage with common-practice tonal harmonic practice. Example syllabi, assignments, classroom demonstrations, and long projects are also included, and each aspect of the labeling is carefully discussed as it is presented. By surveying the history of functional thinking in music theory, we find that desire to analyze for function is not a new idea, and has been a goal of many theorists and harmony teachers for centuries. However, the current methods for instructing in function still leave students confused or baffled, as they struggle to match functional concepts to labels that do not exemplify their analysis goals and methods that insist on starting from tiny detail instead of coming from a more complete musical perspective. The elaboration of each detail of my Functional Analysis system shows how each part of Functional Analysis has been designed to help make harmonic analysis quicker, easier, more intuitive, and more personalized. The greater pedagogical implications on a larger scale involving courses and curricula are also covered, informed by my experience both as a teacher of today’s standard system and from teaching Functional Analysis in the classroom.

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Nie, Guangqi. "Quasi-Harmonic Function Approach to Human-Following Robots." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31465.

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In this thesis, an approach for robot motion control with collision avoidance and human-following is investigated. Using velocity potential fields approach in a modified, quasi-harmonic, solution, the navigation controller is developed. A quasi-harmonic function based controller uses harmonic solutions for collision avoidance and smoothly changes toward a non-harmonic solution which tends toward a zero velocity command only when approaching the goal. After the motion controller was created, human-following strategy was designed to let a non-holonomic robot have the ability to follow a human in an unknown environment with obstacles. The approach is based on velocity potential fields that permit to generate velocity vector commands that drive the robot at a safe distance with regard to the human while avoiding obstacles. The quasi-harmonic approach is investigated analytically using symbolic math solutions of MAPLETM as well as in simulations using MATLABTM. Motion simulations of both holonomic and non-holonomic robot motion illustrate how the proposed approach operates. Experiments are also made with LEGO MINDSTROMS NXT robot to test the algorithm in environment with simple and complex obstacles.

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Petersen, Willis L. "The Lie Symmetries of a Few Classes of Harmonic Functions." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd837.pdf.

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Candy, Timothy Lars. "A study of Besov-Lipschitz and Triebel-Lizorkin spaces using non-smooth kernels." Thesis, University of Canterbury. Mathematics and Statistics, 2008. http://hdl.handle.net/10092/2854.

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We consider the problem of characterising Besov-Lipshitz and Triebel-Lizorkin spaces using kernels with limited smoothness and decay. This extends the work of H.-Q. Bui et al in [4] and [5] from kernels in S to more general kernels, including the Poisson kernel. We overcome the difficulty of defining the convolution of a general kernel with a distribution by using the concept of a bounded distribution introduced by E. Stein [12]. The characterisations we obtain are valid for the full range of indices.

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Iakovlev, Alexander. "On estimates of constants for maximal functions." Doctoral thesis, KTH, Matematik (Avd.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-145704.

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In this work we will study Hardy-Littlewood maximal function and maximal operator, basing on both classical and most up to date works. In the first chapter we will give definitions for different types of those objects and consider some of their most important properties. The second chapter is entirely devoted to an overview of the fundamental properties of Hardy-Littlewood maximal function, which are strong (p, p) and weak (1, 1) inequalities. Here we list the most actual results on this inequalities in correspondence to the way the maximal func-tion is defined. The third chapter presents the theorem on asymptotic behavior of the lower bound of the constant in the weak-type (1, 1) inequality for the maximal function associated with cubes of Rd, then the dimension d tends to infinity. In the last chapter a method forcomputing constant c, appearing in the main theorem of chapter 3, is given.

QC 20140527

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Byrne, David A. "The Harmonic Theories of Sigfrid Karg-Elert: Acoustics, Function, Transformation, Perception." University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1522417315389199.

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Cavina, Michelangelo. "Bellman functions and their method in harmonic analysis." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19214/.

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This work uses the method of the Bellman function to show a new proof of Hardy's inequality for Carleson measures. Bellman functions come from the theory of stochastic optimal control and there is a method to prove theorems about inequalities over dyadic trees (which have applications in harmonic analysis) that takes inspiration from concepts from the theory of the Bellman functions. The work will display the important concepts of the theory of Bellman functions in stochastic analysis, will show how to use the method of the Bellman function to prove the estimate over dyadic trees for Carleson measures for Hardy spaces (while also showing the connections between the stochastic theory and the harmonic analysis) and will give a new proof of Hardy's inequality for dyadic trees (which is related to the characterization of Carleson measures in Besov spaces) using the Bellman function method.

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Rehding, Alexander. "Nature and nationhood in Hugo Riemann's dualistic theory of harmony." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343248.

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Hoffmann, Mark. "Topics in complex analysis and function spaces /." free to MU campus, to others for purchase, 2003. http://wwwlib.umi.com/cr/mo/fullcit?p3091931.

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Books on the topic "Harmonic function"

1

Axler, Sheldon Jay. Harmonic function theory. New York: Springer-Verlag, 1992.

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Axler, Sheldon Jay. Harmonic function theory. New York: Springer-Verlag, 1992.

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Axler, Sheldon Jay. Harmonic function theory. 2nd ed. New York: Springer, 2001.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. Harmonic Function Theory. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/b97238.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. Harmonic Function Theory. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-8137-3.

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Simon, Barry. Harmonic analysis. Providence, Rhode Island: American Mathematical Society, 2015.

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Vakhtang, Paatashvili, ed. Boundary value problems for analytic and harmonic functions in nonstandard Banach function spaces. Hauppauge, N.Y: Nova Science Publishers, 2011.

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Krantz, Steven G. Explorations in harmonic analysis: With applications to complex function theory and the Heisenberg group. Boston: Birkhäuser, 2009.

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1976-, Lee Lina, ed. Explorations in harmonic analysis: With applications to complex function theory and the Heisenberg group. Boston: Birkhäuser, 2009.

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Invariant function spaces on homogeneous manifolds of Lie groups and applications. Providence, R.I: American Mathematical Society, 1993.

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Book chapters on the topic "Harmonic function"

1

Terefenko, Dariusz. "Harmonic Function." In Jazz Theory Workbook, 11–13. New York ; London : Routledge, 2019.: Routledge, 2019. http://dx.doi.org/10.4324/9780429445477-3.

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Weik, Martin H. "harmonic function." In Computer Science and Communications Dictionary, 713. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_8242.

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Terefenko, Dariusz. "Harmonic Function." In Jazz Theory, 23–32. Second edition. | New York ; London : Routledge, 2017.: Routledge, 2017. http://dx.doi.org/10.4324/9781315305394-3.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Harmonic Polynomials." In Harmonic Function Theory, 73–109. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-8137-3_5.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Bounded Harmonic Functions." In Harmonic Function Theory, 31–44. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/0-387-21527-1_2.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Positive Harmonic Functions." In Harmonic Function Theory, 45–58. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/0-387-21527-1_3.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Harmonic Hardy Spaces." In Harmonic Function Theory, 97–124. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/0-387-21527-1_6.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Harmonic Bergman Spaces." In Harmonic Function Theory, 151–68. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/0-387-21527-1_8.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Bounded Harmonic Functions." In Harmonic Function Theory, 31–44. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-8137-3_2.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Positive Harmonic Functions." In Harmonic Function Theory, 45–57. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-8137-3_3.

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Conference papers on the topic "Harmonic function"

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Wray, Kyle Hollins, Dirk Ruiken, Roderic A. Grupen, and Shlomo Zilberstein. "Log-space harmonic function path planning." In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2016. http://dx.doi.org/10.1109/iros.2016.7759245.

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Pray, Carl M., and Stephen A. Hambric. "Finite Element Study of Harmonic Forcing Function Scattering Mechanisms for Cylindrical Structures." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32686.

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Low frequency sound radiation from cylindrical structures is generally dominated by radiation from low order (M=0, 1) circumferential harmonic modes. The high order circumferential harmonic modes are inefficient radiators below the coincidence frequency. For cylindrical structures excited by low frequency, high circumferential order (e.g. N=10) forcing functions, the radiated sound will be dominated by radiation from the low order modes if the forcing function is scattered by structural asymmetries into these modes. In this study, cylindrical structures of varying levels of asymmetry are examined using finite element analysis to quantify the scattering of order N harmonic forcing functions into order M structural response harmonics. First, purely axially-symmetric structures are examined to verify the analysis method used. The models examined include a finite cylinder with constant cross-section and a finite cylinder with tapered cross-section. The constant cross-section cylinder is analyzed in vacuo, and the tapered cylinder is analyzed both in vacuo and with water loading. These structures show no harmonic scattering, as would be expected. Next, a finite tapered cylinder with cyclically symmetric impedance discontinuities and a finite tapered cylinder with an asymmetric large impedance discontinuities are analyzed, both with water loading, to determine the impact of structural discontinuity on the harmonic scattering and radiated sound spectra. The periodic and single discontinuities both show significant scattering into low order circumferential modes and corresponding increases in radiated sound.

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Iturra, R. Guzman, M. Cruse, K. Mutze, P. Thiemann, and C. Dresel. "Shunt Active Power Filter for Harmonics Mitigation with Harmonic Energy Recycling Function." In 2018 IEEE 18th International Power Electronics and Motion Control Conference (PEMC). IEEE, 2018. http://dx.doi.org/10.1109/epepemc.2018.8521979.

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Novak, Jonathan I. "Jucys-Murphy elements and the unitary Weingarten function." In Noncommutative Harmonic Analysis with Applications to Probability II. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc89-0-14.

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Cheng-wen, Zhu, Chen Xin-qin, Zheng Yan, Cai Xiao-yan, and Zeng Chui-zhen. "Multi-view dimensionality reduction via harmonic function." In 2015 IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC). IEEE, 2015. http://dx.doi.org/10.1109/iaeac.2015.7428691.

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Farhang, K., A. Midha, and A. K. Bajaj. "Synthesis of Harmonic Motion Generating Linkages: Part I — Function Generation." In ASME 1987 Design Technology Conferences. American Society of Mechanical Engineers, 1987. http://dx.doi.org/10.1115/detc1987-0111.

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Abstract This paper deals with the first- and higher-order function generation problems in the synthesis of linkages with relatively small input cranks. Such linkages tend to produce nearly simple harmonic motions at the output members. Owing to this distinction, the generality of the conventional synthesis techniques is no longer applicable. Thus, in function generation, only harmonic functions of the input motion may be expected to be synthesized for output motions.

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Kazemi, M., and M. Mehrandezh. "Robotic navigation using harmonic function-based probabilistic roadmaps." In IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004. IEEE, 2004. http://dx.doi.org/10.1109/robot.2004.1302471.

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Gismero, Javier, and Jorge Perez. "Harmonic Describing Function: Application to Microwave Oscillator's Design." In 20th European Microwave Conference, 1990. IEEE, 1990. http://dx.doi.org/10.1109/euma.1990.336231.

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Xiao yong, Zhang, Sui Jiang Hua, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Spherical Harmonic–Generalized Laguerre Function Mixed Spectral Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636998.

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Farhang, Kambiz, and Vinay Ghatti. "A Higher Order Synthesis for Harmonic Motion Generating RSSR Mechanisms." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-16110.

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Consideration of a mechanism for high-speed application inevitably poses certain kinematic design requirements that can be cast as a function generation synthesis problem involving the entire motion cycle of the mechanism. This paper addresses such application of RSSR four bar mechanisms for high-speed application. It employs a perturbational kinematic analysis of the mechanism to obtain approximate equations relating the follower and input angular displacements. The follower angular motion is derived, approximately, as a linear combination of two simple harmonic functions, in terms of the first and second harmonics of the crank angle. Albeit the exact mathematical description relating the input and output links exists it is not conducive to a kinematic design for dynamic performance. In contrast the approximate equations derived in this paper enable function generation of RSSR four bar mechanisms in which the higher harmonics of the input link are minimized. This utility of the approximate equations are demonstrated through several mechanism design examples.

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Reports on the topic "Harmonic function"

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Oh, H. G., H. R. Lee, Thomas F. George, and C. I. Um. Exact Wave Functions and Coherent States of a Damped Driven Harmonic Oscillator. Fort Belvoir, VA: Defense Technical Information Center, February 1989. http://dx.doi.org/10.21236/ada205785.

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