Sample records for harmonic analysis mathematics

  1. Harmonic Analysis : special program at the Nankai Institute of Mathematics

    Deng, Dong-Gao; Zhou, Xing-Wei


    All papers in this volume are original (fully refereed) research reports by participants of the special program on Harmonic Analysis held in the Nankai Institute of Mathematics. The main themes include: Wavelets, Singular Integral Operators, Extemal Functions, H Spaces, Harmonic Analysis on Local Domains and Lie Groups, and so on. See also :G. David "Wavelets and Singular Integrals on Curves and Surfaces", LNM 1465,1991. FROM THE CONTENTS: D.C. Chang: Nankai Lecture in -Neumann Problem.- T.P. Chen, D.Z. Zhang: Oscillary Integral with Polynomial Phase.- D.G. Deng, Y.S. Han: On a Generalized Paraproduct Defined by Non-Convolution.- Y.S. Han: H Boundedness of Calderon-Zygmund Operators for Product Domains.- Z.X. Liu, S.Z. Lu: Applications of H|rmander Multiplier Theorem to Approximation in Real Hardy Spaces.- R.L. Long, F.S. Nie: Weighted Sobolev Inequality and Eigenvalue Estimates of Schr|dinger Operator.- A. McIntosh, Q. Tao: Convolution Singular Integral Operators on Lipschitz Curves.- Z.Y. Wen, L.M.Wu, Y.P. ...

  2. Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics

    Chill, Ralph; Tomilov, Yuri


    This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern...

  3. Spherical harmonics in texture analysis

    Schaeben, Helmut; van den Boogaart, K. Gerald


    The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.

  4. Measurement and Analysis Harmonics Using DSP

    Lee, Sang Ik; Yoo, Jae Geun; Jeon, Jonog Chay [Korea Electrical Safety Corporation (Korea)


    Limitation countermeasure on harmonics occurred by power conversion installation. motor speed control equipment, and so on of power system is very important problem, and first of all, accuracy harmonics analysis in system is required for appropriate limitation counterplan. Analysis and judgement on power system harmonic by measurement are needed because analysis by mathematical model generally used for these harmonic analysis, if nonlinear ingredient is included in system, is not relatively correct. So, in this paper, system to measure and analyze harmonic by installing it in a power system, using DSP(Digital Signal Processor), is designed and developed, Also, it's performance is verified by installing it in the system that harmonics occurred. (author). 5 refs., 10 figs.

  5. Building Mathematical Models of Simple Harmonic and Damped Motion.

    Edwards, Thomas


    By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

  6. Principles of harmonic analysis

    Deitmar, Anton


    This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

  7. Harmonic and geometric analysis

    Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao


    This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights.  The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...

  8. Mathematical analysis fundamentals

    Bashirov, Agamirza


    The author's goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric o

  9. Morrey spaces in harmonic analysis

    David R. Adams; Xiao, Jie


    Through a geometric capacitary analysis based on space dualities, this paper addresses several fundamental aspects of functional analysis and potential theory for the Morrey spaces in harmonic analysis over the Euclidean spaces.

  10. Morrey spaces in harmonic analysis

    Adams, David R.; Xiao, Jie


    Through a geometric capacitary analysis based on space dualities, this paper addresses several fundamental aspects of functional analysis and potential theory for the Morrey spaces in harmonic analysis over the Euclidean spaces.

  11. Introduction to abstract harmonic analysis

    Loomis, Lynn H


    Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.

  12. Automatic Functional Harmonic Analysis

    de Haas, W.B.; Magalhães, J.P.; Wiering, F.; Veltkamp, R.C.


    Music scholars have been studying tonal harmony intensively for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of W

  13. Elements of abstract harmonic analysis

    Bachman, George


    Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give

  14. Prony Analysis for Power System Transient Harmonics

    Qi Li


    Full Text Available Proliferation of nonlinear loads in power systems has increased harmonic pollution and deteriorated power quality. Not required to have prior knowledge of existing harmonics, Prony analysis detects frequencies, magnitudes, phases, and especially damping factors of exponential decaying or growing transient harmonics. In this paper, Prony analysis is implemented to supervise power system transient harmonics, or time-varying harmonics. Further, to improve power quality when transient harmonics appear, the dominant harmonics identified from Prony analysis are used as the harmonic reference for harmonic selective active filters. Simulation results of two test systems during transformer energizing and induction motor starting confirm the effectiveness of the Prony analysis in supervising and canceling power system transient harmonics.

  15. Mathematical Development and Computational Analysis of Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) Based on Bloch Nuclear Magnetic Resonance (NMR) Diffusion Model for Myocardial Motion.

    Dada, Michael O; Jayeoba, Babatunde; Awojoyogbe, Bamidele O; Uno, Uno E; Awe, Oluseyi E


    Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) is a tagged image analysis method that can measure myocardial motion and strain in near real-time and is considered a potential candidate to make magnetic resonance tagging clinically viable. However, analytical expressions of radially tagged transverse magnetization in polar coordinates (which is required to appropriately describe the shape of the heart) have not been explored because the physics required to directly connect myocardial deformation of tagged Nuclear Magnetic Resonance (NMR) transverse magnetization in polar geometry and the appropriate harmonic phase parameters are not yet available. The analytical solution of Bloch NMR diffusion equation in spherical geometry with appropriate spherical wave tagging function is important for proper analysis and monitoring of heart systolic and diastolic deformation with relevant boundary conditions. In this study, we applied Harmonic Phase MRI method to compute the difference between tagged and untagged NMR transverse magnetization based on the Bloch NMR diffusion equation and obtained radial wave tagging function for analysis of myocardial motion. The analytical solution of the Bloch NMR equations and the computational simulation of myocardial motion as developed in this study are intended to significantly improve healthcare for accurate diagnosis, prognosis and treatment of cardiovascular related deceases at the lowest cost because MRI scan is still one of the most expensive anywhere. The analysis is fundamental and significant because all Magnetic Resonance Imaging techniques are based on the Bloch NMR flow equations.

  16. Representation Discovery using Harmonic Analysis

    Mahadevan, Sridhar


    Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu

  17. Harmonic oscillator: an analysis via Fourier series

    de Castro, A S


    The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.

  18. Pairwise harmonics for shape analysis

    Zheng, Youyi


    This paper introduces a simple yet effective shape analysis mechanism for geometry processing. Unlike traditional shape analysis techniques which compute descriptors per surface point up to certain neighborhoods, we introduce a shape analysis framework in which the descriptors are based on pairs of surface points. Such a pairwise analysis approach leads to a new class of shape descriptors that are more global, discriminative, and can effectively capture the variations in the underlying geometry. Specifically, we introduce new shape descriptors based on the isocurves of harmonic functions whose global maximum and minimum occur at the point pair. We show that these shape descriptors can infer shape structures and consistently lead to simpler and more efficient algorithms than the state-of-the-art methods for three applications: intrinsic reflectional symmetry axis computation, matching shape extremities, and simultaneous surface segmentation and skeletonization. © 2012 IEEE.

  19. Mathematical analysis

    Donaldson, J. A.


    Simple continuum models used in the design, analysis, and control of large space structures are examined. Particular emphasis is placed on boundary value problems associated with the Load Correction Method and control problems involving partial differential equations for the large space structure models. Partial differential equations will be used to model a large space structure, base the design of an optimal controller on this model, approximate the resulting optimal control model, and compare the results with data from other methods.

  20. Mathematical analysis

    Donaldson, J. A.


    Simple continuum models used in the design, analysis, and control of large space structures are examined. Particular emphasis is placed on boundary value problems associated with the Load Correction Method and control problems involving partial differential equations for the large space structure models. Partial differential equations will be used to model a large space structure, base the design of an optimal controller on this model, approximate the resulting optimal control model, and compare the results with data from other methods.

  1. Mathematical and statistical analysis

    Houston, A. Glen


    The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.

  2. Harmonic and applied analysis from groups to signals

    Mari, Filippo; Grohs, Philipp; Labate, Demetrio


    This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction ...

  3. Harmonic Analysis of Currents and Voltages Obtained in the Result of Computational Experiment

    I. V. Novash


    Full Text Available The paper considers a methodology for execution of a harmonic analysis of current and voltage numerical values obtained in the result of a computational experiment and saved in an external data file. The harmonic analysis has been carried out in the Mathcad mathematical packet environment.

  4. Harmonic analysis on symmetric spaces

    Terras, Audrey

    This text explores the geometry and analysis of higher rank analogues of the symmetric spaces introduced in volume one. To illuminate both the parallels and differences of the higher rank theory, the space of positive matrices is treated in a manner mirroring that of the upper-half space in volume one. This concrete example furnishes motivation for the general theory of noncompact symmetric spaces, which is outlined in the final chapter. The book emphasizes motivation and comprehensibility, concrete examples and explicit computations (by pen and paper, and by computer), history, and, above all, applications in mathematics, statistics, physics, and engineering. The second edition includes new sections on Donald St. P. Richards’s central limit theorem for O(n)-invariant random variables on the symmetric space of GL(n, R), on random  matrix theory, and on advances in the theory of automorphic forms on arithmetic groups.

  5. Input Harmonic Analysis on the Slim DC-Link Drive Using Harmonic State Space Model

    Yang, Feng; Kwon, Jun Bum; Wang, Xiongfei


    the shortcomings of the present harmonic analysis methods, such as the time-domain simulation, or the Fourier analysis, this paper proposes a Harmonic State Space model to study the harmonics performance for this type of drive. In this study, this model is utilized to describe the behavior of the harmonic...... variation according to the switching instant, the harmonics at the steady-state condition, as well as the coupling between the multiple harmonic impedances. By using this model, the impaction on the harmonics performance by the film capacitor and the grid inductance is derived. Simulation and experimental...

  6. Harmonic analysis of a cruise ship network

    Guerin, P.; Miegeville, L. [GE44, France (France); Sahnouni, K. [Chantiers de l' Atlantique (France)


    The number and the power rating of equipment using power electronics have been increasing on board of the ships for many years. At present, the harmonic disturbance must be taken into account from the design stage in order to ensure the smooth running of the installation. This paper presents a harmonic analysis of the electrical distribution system of a cruise ship. The comparison between the evaluated and the real harmonic levels allows us to discuss about the interest and the limits of the estimates. (authors)

  7. Harmonic and complex analysis in several variables

    Krantz, Steven G


    Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and...

  8. New trends in applied harmonic analysis sparse representations, compressed sensing, and multifractal analysis

    Cabrelli, Carlos; Jaffard, Stephane; Molter, Ursula


    This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and covers both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

  9. Hecke algebras and harmonic analysis

    Opdam, E.M.; Sanz-Solé, M.; Soria, J.; Varona, J.L.; Verdera, J.


    The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outs

  10. Mathematical analysis II

    Canuto, Claudio


    The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, ...

  11. Harmonic analysis and the theory of probability

    Bochner, Salomon


    Nineteenth-century studies of harmonic analysis were closely linked with the work of Joseph Fourier on the theory of heat and with that of P. S. Laplace on probability. During the 1920s, the Fourier transform developed into one of the most effective tools of modern probabilistic research; conversely, the demands of the probability theory stimulated further research into harmonic analysis.Mathematician Salomon Bochner wrote a pair of landmark books on the subject in the 1930s and 40s. In this volume, originally published in 1955, he adopts a more probabilistic view and emphasizes stochastic pro

  12. Special Functions, Partial Differential Equations and Harmonic Analysis : Conference in Honor of Calixto P. Calderon

    Stokolos, Alexander; Urbina, Wilfredo


    This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.

  13. Mathematical analysis I

    Zorich, Vladimir A


    VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences . This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems...

  14. The Harmonic Theory; A mathematical framework to build intelligent contextual and adaptive computing, cognition and sensory system

    Loghmani, Nick Mehrdad


    Harmonic theory provides a mathematical framework to describe the structure, behavior, evolution and emergence of harmonic systems. A harmonic system is context aware, contains elements that manifest characteristics either collaboratively or independently according to system's expression and can interact with its environment. This theory provides a fresh way to analyze emergence and collaboration of "ad-hoc" and complex systems.

  15. Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

    Mei, Liang; Svanberg, Sune


    This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

  16. Fischer decomposition in symplectic harmonic analysis

    Brackx, Fred; De Schepper, Hennie; Eelbode, David; Lávička, Roman; Soucek, Vladimir


    In the framework of quaternionic Clifford analysis in Euclidean space , which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is obtained in terms of spaces of so-called (adjoint) symplectic spherical harmonics, which are irreducible modules for the symplectic group Sp. Its Howe dual partner is determined to be sl(2, C) circle plus sl(2, C) = so(4, C).

  17. Foundations of mathematical analysis

    Johnsonbaugh, Richard


    This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis. A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss

  18. Harmonic Analysis and Group Representation

    Figa-Talamanca, Alessandro


    This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.

  19. Harmonic analysis on triple spaces

    Danielsen, Thomas Hjortgaard

    In this thesis we study examples of triple spaces, both their structure theory, their invariant differential operators as well as analysis on them. The first major results provide us with some examples of triple spaces which are strongly spherical, i.e. satisfy some conditions reminiscent...... of properties of symmetric spaces. The algebras of invariant differential operators for these spaces are studied and the conclusion is that most of them are non-commutative. Finally, we restrict our attention to a single triple space, giving a specific polar decomposition and corresponding integration formula......, and studying the relations between open orbits of parabolic subgroups, multiplicities and distribution vectors....

  20. Unitary representations and harmonic analysis an introduction

    Sugiura, M


    The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou''s theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.

  1. Harmonic Vibrational Analysis in Delocalized Internal Coordinates.

    Jensen, Frank; Palmer, David S


    It is shown that a principal component analysis of a large set of internal coordinates can be used to define a nonredundant set of delocalized internal coordinates suitable for the calculation of harmonic vibrational normal modes. The selection of internal coordinates and the principal component analysis provide large degrees of freedom in extracting a nonredundant set of coordinates, and thus influence how the vibrational normal modes are described. It is shown that long-range coordinates may be especially suitable for describing low-frequency global deformation modes in proteins.

  2. Analysis of the impact of harmonic interference circuit Costas

    B.I. Shakhtarin


    Full Text Available The analysis of influence of harmonic interference on the phase error in the Costas circuit is carried out. Differential equations of the circuit are obtained. Are obtained in the zero and first approximation the equations of the phase error for the Costas circuit. The simulation in MatLab environment of phase error introduced by the Costas circuit in the first approximation and the graphs of this error is carried out. On the basis of mathematical model, by the phase error counts were obtained graphs of probability density functions of the signal errors introduced by the model. A simulation model of the Costas circuit in the Simulink environment is given. In the simulation model, by the phase error counts in MatLab, were obtained graphs of probability density functions of the signal error due to the simulation model. The comparison of the obtained results of the Costas circuit analysis obtained by mathematical modeling of the phase error equation in the first approximation with simulation results in Simulink environment shows that the results of mathematical modeling rather accurately coincide with the simulation results. On the basis of simulation were obtained the graphs of the average time before mistracking for various values of the interference to signal ratio

  3. Real mathematical analysis

    Pugh, Charles C


    Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the un...

  4. Harmonic Interaction Analysis in Grid Connected Converter using Harmonic State Space (HSS) Modeling

    Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth


    An increasing number of power electronics based Distributed Generation (DG) systems and loads generate coupled harmonic as well as non-characteristic harmonic with each other. Several methods like impedance based analysis, which is derived from conventional small signal- and average-model, are in...... behavior interaction and dynamic transfer procedure. Frequency domain as well as time domain simulation results are represented by means of HSS modeling to verify the theoretical analysis. Experimental results are also included to validate the method....... during the modeling process. This paper investigates grid connected converter by means of Harmonic State Space (HSS) small signal model, which is modeled from Linear Time varying Periodically (LTP) system. Further, a grid connected converter harmonic matrix is investigated to analyze the harmonic...

  5. The fundamentals of mathematical analysis

    Fikhtengol'ts, G M


    The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, i

  6. Harmonic analysis on exponential solvable Lie groups

    Fujiwara, Hidenori


    This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...

  7. Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis

    Hod, Shahar


    The spheroidal harmonics Slm (θ ; c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm (c) } of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m → ∞ with a fixed value of c, or to the complementary regime | c | → ∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m → ∞ and | c | → ∞ with a fixed m / c ratio.

  8. Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis

    Hod, Shahar


    The spheroidal harmonics $S_{lm}(\\theta;c)$ have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues $\\{A_{lm}(c)\\}$ of these functions have been determined by many authors. However, it should be emphasized that all previous asymptotic analyzes were restricted either to the regime $m\\to\\infty$ with a fixed value of $c$, or to the complementary regime $|c|\\to\\infty$ with a fixed value of $m$. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both $m$ and $c$. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit $m\\to\\infty$ and $|c|\\to\\infty$ with a fixed $m/c$ ratio.

  9. Mathematical analysis II

    Zorich, Vladimir A


    This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different go...

  10. Analysis IV integration and spectral theory, harmonic analysis, the garden of modular delights

    Godement, Roger


    Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be modern and classical, is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.

  11. Field measurement and analysis of harmonic levels

    Karunakara, K.; Muthu Kumar, E.; Rajesh Kumar, O.; Nambudiri, P.V.V.; Srinivasan, K.N. [Central Power Research Institute, Bangalore (India)


    The level of harmonics on the transmission and distribution network is rising over the years, due to the rapid development and usage of electronic and semiconductor devices in the industries, as these devices produce harmonic currents. As the harmonic currents produced by these devices are unproductive and affect the ideal sinusoidal waveshapes, these have to be limited to a tolerable limit at the Point of Common Coupling (PCC). Before setting a tolerable limit on harmonics it is necessary to know the level of harmonics already present in the system, so that the limits suggested are comprehensive and practicable. To have a fair idea about the current and voltage harmonics on the Indian system, Central Power Research Institute (CPRI) has carried out a lot of measurements both on the distribution network and transmission network over the past 13 years. This paper discusses the harmonic measurements carried out by CPRI on different loads and voltage levels on the Indian network. The methodology adopted for measurement and results are also discussed in this paper. (author)

  12. Error Analysis in Mathematics Education.

    Rittner, Max


    The article reviews the development of mathematics error analysis as a means of diagnosing students' cognitive reasoning. Errors specific to addition, subtraction, multiplication, and division are described, and suggestions for remediation are provided. (CL)

  13. Mathematical analysis differentiation and integration

    Aramanovich, IG; Lyusternik, LA; Sneddon, I N


    Mathematical Analysis: Differentiation and Integration is devoted to two basic operations of mathematical analysis, differentiation and integration. The problems directly connected with the operations of differentiation and integration of functions of one or several variables are discussed, together with elementary generalizations of these operations. This volume is comprised of seven chapters and begins by considering the differentiation of functions of one variable and of n variables, paying particular attention to derivatives and differentials as well as their properties. The next chapter d

  14. Mathematical analysis I

    Canuto, Claudio


    The purpose of the volume is to provide a support for a first course in Mathematics. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level requires the additional study of ...

  15. Aerodynamic analysis of cup anemometers performance: the stationary harmonic response.

    Pindado, Santiago; Cubas, Javier; Sanz-Andrés, Angel


    The effect of cup anemometer shape parameters, such as the cups' shape, their size, and their center rotation radius, was experimentally analyzed. This analysis was based on both the calibration constants of the transfer function and the most important harmonic term of the rotor's movement, which due to the cup anemometer design is the third one. This harmonic analysis represents a new approach to study cup anemometer performances. The results clearly showed a good correlation between the average rotational speed of the anemometer's rotor and the mentioned third harmonic term of its movement.

  16. Aerodynamic Analysis of Cup Anemometers Performance: The Stationary Harmonic Response

    Santiago Pindado


    Full Text Available The effect of cup anemometer shape parameters, such as the cups’ shape, their size, and their center rotation radius, was experimentally analyzed. This analysis was based on both the calibration constants of the transfer function and the most important harmonic term of the rotor’s movement, which due to the cup anemometer design is the third one. This harmonic analysis represents a new approach to study cup anemometer performances. The results clearly showed a good correlation between the average rotational speed of the anemometer’s rotor and the mentioned third harmonic term of its movement.

  17. Aerodynamic Analysis of Cup Anemometers Performance: The Stationary Harmonic Response

    Santiago Pindado; Javier Cubas; Ángel Sanz-Andrés


    The effect of cup anemometer shape parameters, such as the cups’ shape, their size, and their center rotation radius, was experimentally analyzed. This analysis was based on both the calibration constants of the transfer function and the most important harmonic term of the rotor’s movement, which due to the cup anemometer design is the third one. This harmonic analysis represents a new approach to study cup anemometer performances. The results clearly showed a good correlation between the ave...

  18. Mathematical analysis of deception.

    Rogers, Deanna Tamae Koike (University of California at Davis, Davis, CA); Durgin, Nancy Ann


    This report describes the results of a three year research project about the use of deception in information protection. The work involved a collaboration between Sandia employees and students in the Center for Cyber Defenders (CCD) and at the University of California at Davis. This report includes a review of the history of deception, a discussion of some cognitive issues, an overview of previous work in deception, the results of experiments on the effects of deception on an attacker, and a mathematical model of error types associated with deception in computer systems.

  19. Operational modal analysis in the presence of harmonic excitation

    Mohanty, P.; Rixen, D. J.


    Modal operational analysis methods are procedures to identify modal parameters of structures from the response to unknown random excitations existing on buildings and in machines during operation. In many practical cases, in addition to the random loads, harmonic excitations are also present due for instance to rotating components. If the frequency of the harmonic component of the input is close to an eigenfrequency of the system, operational modal analysis procedures fail to identify the modal parameters accurately. Therefore, we propose a modification of the least-square complex exponential identification procedure to include explicitly the harmonic component. In that way, the modal parameters can be identified properly. We illustrate the efficiency of the proposed approach on the example of a beam structure excited by multi-harmonic loads superposed on random excitation.

  20. Harmonic analysis of Doubly Fed Induction Generators

    Lindholm, Morten; Rasmussen, Tonny Wederberg


    This paper gives an overview of the frequency spectrum of the stator and rotor currents in a doubly fed induction generator (DFIG) used in wind power applications. The paper also presents a method to eliminate higher harmonics and interharmonics in the DFIG stator current. The method is implemented...... on a 40 kW laboratory model connected to the utility-grid, where the DFIG is supplied by a back-to-back 3-level NPC-converter....

  1. Fundamentals of mathematical analysis

    Paul J Sally, Jr


    This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in "AP Calculus", possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread

  2. Recent applications of harmonic analysis to function spaces, differential equations, and data science novel methods in harmonic analysis

    Gia, Quoc; Mayeli, Azita; Mhaskar, Hrushikesh; Zhou, Ding-Xuan


    The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such a...

  3. Mathematical theory of sedimentation analysis

    Fujita, Hiroshi; Van Rysselberghe, P


    Mathematical Theory of Sedimentation Analysis presents the flow equations for the ultracentrifuge. This book is organized into two parts encompassing six chapters that evaluate the systems of reacting components, the differential equations for the ultracentrifuge, and the case of negligible diffusion. The first chapters consider the Archibald method for molecular weight determination; pressure-dependent sedimentation; expressions for the refractive index and its gradient; relation between refractive index and concentration; and the analysis of Gaussian distribution. Other chapters deal with th

  4. Abstract harmonic analysis of continuous wavelet transforms

    Führ, Hartmut


    This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the book can also be read as a problem-driven introduction to the Plancherel formula.

  5. Harmonic pollution produced by low power nonlinear loads: mathematical model and practical cases; Contaminacion armonica producida por cargas no lineales de baja potencia: modelo matematico y casos practicos

    Mora Barajas, M.A.; Banuelos Sanchez, P. [Universidad de las Americas Puebla (Mexico)]. E-mail:;


    Many household electrical appliances like televisions, video recorders and computers are sources of voltage and current harmonics, which increase power losses and contaminate the AC power line. These harmonics can cause serious problems in both, utilities and electrical equipment connected to the same AC line. This paper shows a mathematical analysis of harmonics content on the electrical current for a circuit representing a non linear residential load. A comparative harmonic distortion study produced by the residential loads on the electrical power lines, measured experimentally, is also shown. [Spanish] Muchos de los aparatos electricos que tenemos en casa como televisores, videograbadoras y computadoras, generan armonicos de voltaje y de corriente que incrementan las perdidas de potencia y contaminan las lineas de suministro electrico, pudiendo ocasionar severos danos tanto a las redes de energia como a los equipos que de ellas se alimentan. En este articulo se muestra un analisis matematico del contenido armonico en la corriente de un circuito que representa a una carga residencial no lineal. Ademas, a partir de mediciones electricas realizadas de manera experimental, se presente un estudio comparativo de la contaminacion armonica que este tipo de cargas introduce a las lineas de suministro electrico.

  6. [A New HAC Unsupervised Classifier Based on Spectral Harmonic Analysis].

    Yang, Ke-ming; Wei, Hua-feng; Shi, Gang-qiang; Sun, Yang-yang; Liu, Fei


    Hyperspectral images classification is one of the important methods to identify image information, which has great significance for feature identification, dynamic monitoring and thematic information extraction, etc. Unsupervised classification without prior knowledge is widely used in hyperspectral image classification. This article proposes a new hyperspectral images unsupervised classification algorithm based on harmonic analysis(HA), which is called the harmonic analysis classifer (HAC). First, the HAC algorithm counts the first harmonic component and draws the histogram, so it can determine the initial feature categories and the pixel of cluster centers according to the number and location of the peak. Then, the algorithm is to map the waveform information of pixels to be classified spectrum into the feature space made up of harmonic decomposition times, amplitude and phase, and the similar features can be gotten together in the feature space, these pixels will be classified according to the principle of minimum distance. Finally, the algorithm computes the Euclidean distance of these pixels between cluster center, and merges the initial classification by setting the distance threshold. so the HAC can achieve the purpose of hyperspectral images classification. The paper collects spectral curves of two feature categories, and obtains harmonic decomposition times, amplitude and phase after harmonic analysis, the distribution of HA components in the feature space verified the correctness of the HAC. While the HAC algorithm is applied to EO-1 satellite Hyperion hyperspectral image and obtains the results of classification. Comparing with the hyperspectral image classifying results of K-MEANS, ISODATA and HAC classifiers, the HAC, as a unsupervised classification method, is confirmed to have better application on hyperspectral image classification.

  7. Harmonic component detection: Optimized Spectral Kurtosis for operational modal analysis

    Dion, J.-L.; Tawfiq, I.; Chevallier, G.


    This work is a contribution in the field of Operational Modal Analysis to identify the modal parameters of mechanical structures using only measured responses. The study deals with structural responses coupled with harmonic components amplitude and frequency modulated in a short range, a common combination for mechanical systems with engines and other rotating machines in operation. These harmonic components generate misleading data interpreted erroneously by the classical methods used in OMA. The present work attempts to differentiate maxima in spectra stemming from harmonic components and structural modes. The detection method proposed is based on the so-called Optimized Spectral Kurtosis and compared with others definitions of Spectral Kurtosis described in the literature. After a parametric study of the method, a critical study is performed on numerical simulations and then on an experimental structure in operation in order to assess the method's performance.

  8. Development of a virtual metrology method using plasma harmonics analysis

    Jun, H.; Shin, J.; Kim, S.; Choi, H.


    A virtual metrology technique based on plasma harmonics is developed for predicting semiconductor processes. From a plasma process performed by 300 mm photoresist stripper equipment, a strong correlation is found between optical plasma harmonics intensities and the process results, such as the photoresist strip rate and strip non-uniformity. Based on this finding, a general process prediction model is developed. The developed virtual metrology model shows that the R-squared (R2) values between the measured and predicted process results are 95% and 64% for the photoresist strip rate and photoresist strip non-uniformity, respectively. This is the first research on process prediction based on optical plasma harmonics analysis, and the results can be applied to semiconductor processes such as dry etching and plasma enhanced chemical vapor deposition.

  9. Harmonic Analysis Associated with the Generalized q-Bessel Operator

    Ahmed Abouelaz


    Full Text Available In this article, we give a new harmonic analysis associated with the generalized q-Bessel operator. We introduce the generalized $q$-Bessel transform, the generalized q-Bessel translation and the generalized $q$-Bessel convolution product.


    Néji Bettaibi; Kamel Mezlini; Moufida El Guénichi


    In this paper,a new formulation of the Rubin's q-translation is given,which leads to a reliable q-harmonic analysis.Next,related q-positive definite functions are introduced and studied,and a Bochner's theorem is proved.

  11. The harmonic oscillator, dimensional analysis and inflationary solutions

    San Costa, S


    In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional harmonic oscillator.

  12. Ratio Analysis: Where Investments Meet Mathematics.

    Barton, Susan D.; Woodbury, Denise


    Discusses ratio analysis by which investments may be evaluated. Requires the use of fundamental mathematics, problem solving, and a comparison of the mathematical results within the framework of industry. (Author/NB)


    Amer M. Kado


    Full Text Available This paper presents a computer analysis of the eddy current brake in electric machines. It presents a formula for the braking force when the actual width of the pole is considered. This formula is suitable for both thin and thick discs and may be employed for a wide range of working speed. For this purpose, a mathematical analysis of the problem is presented together with the formula achieved for the braking force. The brake is first represented by a mathematical model based on certain assumptions and then the braking force is obtained as a result of solving a field problem. The problem is simplified to a one-dimensional problem, where a solution for the magnetic vector potential is obtained, and by employing Lorentz force equation, a formula for the braking force of the nth harmonic order is obtained.

  14. Harmonic analysis of precipitation climatology in Saudi Arabia

    Tarawneh, Qassem


    Annual rainfall records of 20 stations for 30 years are used in order to detect rainfall regimes and climatic features of Saudi Arabia using harmonic analysis techniques. In this study, the percentages of variance, amplitudes, and phase angles are calculated in order to depict the spatial and temporal characteristics of the country's rainfall. The first harmonic explains 42 % of rainfall variation in the western (W) region. This percentage increases toward east (E) and north (N) with 69 and 67 %, respectively. In the southwest (SW) region, the percentages explain 43 % of rainfall variation. The percentages of variance in W and SW are lower than in the E, NW, and central (C) regions. This implies significant contributions of the second harmonic in W and SW regions with 26 and 16 %, respectively. The high percentages of the second and third harmonics in W and SW regions suggest that these two regions are affected by different weather systems at different times. The SW region has the highest amplitudes of the first, second, and third harmonics. The amplitude of the first harmonic reaches to 21 mm in SW and 9 mm in both C and E regions. The time of maximum rainfall is calculated using phase angle; the result reflects that maximum rainfall is shifted forward on the time axis toward the spring season in SW and C regions, January in E and NW regions, and October and November in the W region. This reveals that the SW region is a completely different climatic region, though some of what affects this region also affects the central region. Conditions in the E and NW regions are mainly affected by Mediterranean weather systems, while the W region is affected by unstable conditions caused by the active Red Sea Trough (RST) in October and November.

  15. Analysis on h-harmonics and Dunkl transforms


    As a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a...

  16. submitter Generalized Harmonic Analysis of Computed and Measured Magnetic Fields

    Auchmann, B; Petrone, C; Russenschuck, S


    In this paper, we present a generalized approach for the harmonic analysis of the magnetic field in accelerator magnets. This analysis is based on the covariant components of the computed or measured magnetic flux density. The multipole coefficients obtained in this way can be used for magnet optimization and field reconstruction in the interior of circular and elliptical boundaries in the bore of straight magnets.

  17. Harmonic analysis with respect to heat kernel measure

    Hall, B C


    I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main constructions are group analogs of the Hermite expansion, the Segal-Bargmann transform, and the Taylor expansion. The results are related to geometric quantization, to stochastic analysis, and to the quantization of 1+1-dimensional Yang-Mills theory.

  18. Harmonic Instability Analysis of Single-Phase Grid Connected Converter using Harmonic State Space (HSS) modeling method

    Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth;


    and impedance from other renewable energy sources are not taken carefully into account in the installation and design. However, this may bring an unknown harmonic instability into the multiple power sourced system and also make the analysis difficult due to the complexity of the grid network. This paper......The increasing number of renewable energy sources at the distribution grid is becoming a major issue for utility companies, since the grid connected converters are operating at different operating points due to the probabilistic characteristics of renewable energy. Besides, typically, the harmonics...... proposes a new model of a single phase grid connected renewable energy source using the Harmonic State Space modeling approach, which is able to identify such problems and the model can be extended to be applied in the multiple connected converter analysis. The modeling results show the different harmonic...

  19. Harmonic Instability Analysis of Single-Phase Grid-Connected Converter using Harmonic State-space (HSS) modeling method

    Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede;


    and impedance from other renewable energy sources are not taken carefully into account in the installation and design of the systems. It can bring an unknown harmonic instability into a multiple power sourced system and makes the analysis difficult due to the complexity of the grid network. This paper proposes......The increasing number of renewable energy sources in the distribution grid is becoming a major issue for utility companies since grid-connected converters are operating at different operating points due to the probabilistic characteristics of the renewable energy. Usually, the harmonics...... a new model of a single-phase grid-connected renewable energy source by using the Harmonic State-space Modeling approach, which can identify such problems. The model can be extended to a multiple connected converter analysis. The modeling results show the harmonic impedance matrixes, which represent...

  20. Topology of Platonic Spherical Manifolds: From Homotopy to Harmonic Analysis

    Kramer, Peter


    We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology, the three-sphere is tiled into copies of a fundamental domain under the corresponding deck group. We employ the point symmetry of each Platonic manifold to construct its fundamental domain as a spherical orbifold. While the three-sphere supports an~orthonormal complete basis for harmonic analysis formed by Wigner polynomials, a given spherical orbifold leads to a selection of a specific subbasis. The resulting selection rules find applications in cosmic topology, probed by the cosmic microwave background.

  1. An introduction to mathematical analysis

    Shirali, Satish


    This book is an elementary text on the theory of functions of one real variable and is intended for students with a good understanding of calculus. It is supposed to replace traditional and outmoded courses in mathematical analysis. The book begins with material on the real number system as a Dedekind complete ordered field, continuous functions, sequences and series of constant terms as well as of functions. Pointwise and uniform convergence of series of functions, power series, treatment of trigonometric and exponential functions in terms of series are discussed. A detailed treatment of differentiation, including differentiation of uniform limits of sequences is provided. Also included is an example of a continuous nowhere differentiable function. There is an exhaustive treatment of both Riemann integration and Riemann-Stieltjes integration. Some features of this work, such as why Dedekind completeness is necessary for ensuring that nonconstant functions cannot have derivative zero everywhere on an interval...

  2. Caring in Professional Development Projects for Mathematics Teachers: An Example of Stimulation and Harmonizing

    McCloskey, Andrea


    In this article, I build on the work of mathematics education researchers (Hackenberg, 2005; Sztajn, 2008) who have used Noddings's (1984) notion of caring to lend insights to the teaching of mathematics. In particular, I retrospectively analyze my actions when I was serving as a mathematics teacher educator seeking to provide professional…


    Mehmet YUMURTACI


    Full Text Available Space Vector Modulation (SVM technique is a popular and an important PWM technique for three phases voltage source inverter in the control of Induction Motor. In this study harmonic analysis of Space Vector PWM (SVPWM is investigated using multiple-pulses method. Multiple-Pulses method calculates the Fourier coefficients of individual positive and negative pulses of the output PWM waveform and adds them together using the principle of superposition to calculate the Fourier coefficients of the all PWM output signal. Harmonic magnitudes can be calculated directly by this method without linearization, using look-up tables or Bessel functions. In this study, the results obtained in the application of SVPWM for values of variable parameters are compared with the results obtained with the multiple-pulses method.

  4. An Ecological Analysis of Mathematics Teachers' Noticing

    Jazby, Dan


    Most studies which investigate mathematics teacher noticing cast perception into a passive role. This study develops an ecological analysis of mathematics teachers' noticing in order to investigate how teachers actively look for information in classroom environments. This method of analysis is applied to data collected as an experienced primary…

  5. Photonic Crystals Mathematical Analysis and Numerical Approximation

    Dörfler, Willy; Plum, Michael; Schneider, Guido; Wieners, Christian


    This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers. In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of contin

  6. Analysis of Harmonic Coupling and Stability in Back-to-Back Converter Systems for Wind Turbines using Harmonic State Space (HSS)

    Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth;


    Understanding about harmonic propagation in wind turbine converter is fundamental to research the influence of these on a large network harmonic distortion. Therefore, the analysis of wind turbine converter harmonic spectrum as well as the influence of converter operating point into the network i...

  7. Topics in mathematical analysis and applications

    Tóth, László


    This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.

  8. Harmonic Analysis Associated with the Generalized Weinstein Operator

    Ahmed Abouelaz


    Full Text Available In this paper we consider a generalized Weinstein operator ∆d,α,n on Rd−1×]0,∞[, which generalizes the Weinstein operator ∆d,α, we define the generalized Weinstein intertwining operator Rα,n which turn out to be transmutation operator between ∆d,α,n and the Laplacian operator ∆d. We build the dual of the generalized Weinstein intertwining operatortRα,n, another hand we prove the formula related Rα,n andtRα,n . We exploit these transmutation operators to develop a new harmonic analysis corresponding to ∆d,α,n.

  9. Eliminating the Influence of Harmonic Components in Operational Modal Analysis

    Jacobsen, Niels-Jørgen; Andersen, Palle; Brincker, Rune


    on the well-known Enhanced Frequency Domain Decomposition (EFDD) technique for eliminating these harmonic components in the modal parameter extraction process. For assessing the quality of the method, various experiments were carried out where the results were compared with those obtained with pure stochastic......Operational modal analysis is used for determining the modal parameters of structures for which the input forces cannot be measured. However, the algorithms used assume that the input forces are stochastic in nature. While this is often the case for civil engineering structures, mechanical...

  10. Impedance Based Analysis and Design of Harmonic Resonant Controller for a Wide Range of Grid Impedance

    Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede


    in the closed-loop output admittance of converter. Such negative resistances may interact with the grid impedance resulting in steady state error or unstable harmonic compensation. To deal with this problem, a design guideline for harmonic resonant controllers under a wide range of grid impedance is proposed......This paper investigates the effect of grid impedance variation on harmonic resonant current controllers for gridconnected voltage source converters by means of impedance-based analysis. It reveals that the negative harmonic resistances tend to be derived from harmonic resonant controllers...

  11. International Conference on Recent Trends in Mathematical Analysis and its Applications 2014

    Mohapatra, R; Singh, Uaday; Srivastava, H


    This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical an...

  12. Infinitesimal methods of mathematical analysis

    Pinto, J S


    This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmon

  13. Mathematical analysis, approximation theory and their applications

    Gupta, Vijay


    Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

  14. Harmonic inversion analysis of exceptional points in resonance spectra

    Fuchs, Jacob; Cartarius, Holger; Wunner, Günter


    The spectra of, e.g. open quantum systems are typically given as the superposition of resonances with a Lorentzian line shape, where each resonance is related to a simple pole in the complex energy domain. However, at exceptional points two or more resonances are degenerate and the resulting non-Lorentzian line shapes are related to higher order poles in the complex energy domain. In the Fourier-transform time domain an $n$-th order exceptional point is characterised by a non-exponentially decaying time signal given as the product of an exponential function and a polynomial of degree $n-1$. The complex positions and amplitudes of the non-degenerate resonances can be determined with high accuracy by application of the nonlinear harmonic inversion method to the real-valued resonance spectra. We extend the harmonic inversion method to include the analysis of exceptional points. The technique yields, in the energy domain, the amplitudes of the higher order poles contributing to the spectra, and, in the time domai...

  15. Research of second harmonic generation images based on texture analysis

    Liu, Yao; Li, Yan; Gong, Haiming; Zhu, Xiaoqin; Huang, Zufang; Chen, Guannan


    Texture analysis plays a crucial role in identifying objects or regions of interest in an image. It has been applied to a variety of medical image processing, ranging from the detection of disease and the segmentation of specific anatomical structures, to differentiation between healthy and pathological tissues. Second harmonic generation (SHG) microscopy as a potential noninvasive tool for imaging biological tissues has been widely used in medicine, with reduced phototoxicity and photobleaching. In this paper, we clarified the principles of texture analysis including statistical, transform, structural and model-based methods and gave examples of its applications, reviewing studies of the technique. Moreover, we tried to apply texture analysis to the SHG images for the differentiation of human skin scar tissues. Texture analysis method based on local binary pattern (LBP) and wavelet transform was used to extract texture features of SHG images from collagen in normal and abnormal scars, and then the scar SHG images were classified into normal or abnormal ones. Compared with other texture analysis methods with respect to the receiver operating characteristic analysis, LBP combined with wavelet transform was demonstrated to achieve higher accuracy. It can provide a new way for clinical diagnosis of scar types. At last, future development of texture analysis in SHG images were discussed.

  16. Comparative Analysis of Instruments Measuring Time Varying Harmonics

    Belchior, Fernando Nunes; Ribeiro, Paulo Fernando; Carvalho, Frederico Marques


    This paper aims to evaluate the performance of commercial class A and class S power quality (PQ) instruments when measuring time-varying harmonics. By using a high precision programmable voltage and current source, two meters from different manufacturers are analyzed and compared. Three-phase voltage signals are applied to PQ instruments, considering 3 situations of time-varying harmonic distortions, whose harmonic distortion values are in accordance with typical values found in power systems. This work is relevant considering that international standardization documents do not pay much attention to this aspect of harmonic distortion.

  17. A modified Ibrahim time domain algorithm for operational modal analysis including harmonic excitation

    Mohanty, P.; Rixen, D. J.


    Operational modal analysis procedures are efficient techniques to identify modal properties of structures excited through unknown random noise produced during operation. In many practical cases, harmonic excitations are often present in addition to the white-noise and, if the harmonic frequency is close to structural frequencies, standard identification techniques fail. Here, a method is presented to take into account the harmonic excitations while doing modal parameter identification for operational modal analysis (OMA). The proposed technique is based on the Ibrahim Time Domain method and explicitly includes the harmonic frequencies known a priori. Therefore, the modified technique allows proper identification of eigenfrequencies and modal damping even when harmonic excitation frequencies are close to the natural frequencies of the structures. Experimental results are shown in the presence of multi-harmonic loads for a steel plate to validate the method.

  18. Harmonic analysis in a distribution system with wind generation using DFIG

    Mirzaei, J. [Monenco Consulting Engineering Co., Tehran (Iran, Islamic Republic of). Dept. of Distributed Generation


    This paper presents the harmonic analysis of wind farm models with DFIG represented as harmonic sources and measurement data on the point of common coupling (PCC) during normal operation. The model describes a wind farm (WF) with converters connected to a public network with a long MV overhead line. The way of propagation and effects of harmonics are presented for different study cases. Modeling strategies of harmonic sources for harmonic analysis are described and compared. Different results dependent on applied harmonic models are shown and discussed in this paper. Simulation results are compared with representative measurement data obtained from measurement campaign done in a typical WF. The problems and limitations related to present standards and practice will be discussed based on measurements from wind farm. (orig.)

  19. Recent Developments in Real and Harmonic Analysis In Honor of Carlos Segovia

    Cabrelli, Carlos A


    Featuring a collection of invited chapters dedicated to Carlos Segovia, this volume examines the developments in real and harmonic analysis. It includes topics such as: Vector-valued singular integral equations; Harmonic analysis related to Hermite expansions; Gas flow in porous media; and, Global well-posedness of the KPI Equation

  20. Generalized functions, volume 4 applications of harmonic analysis

    Gel′fand, I M; Vilenkin, N Ya


    The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The main

  1. Mathematics

    Eringen, A Cemal


    Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th

  2. Mathematical Analysis of Evolution, Information, and Complexity

    Arendt, Wolfgang


    Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.

  3. Harmonic analysis utilizing a Phonodeik and an Henrici analyzer

    Fickinger, William J.; Hanson, Roger J.; Hoekje, Peter L.


    Dayton C. Miller of the Case School of Applied Science assembled a series of instruments for accurate analysis of sound [D. C. Miller, J. Franklin Inst. 182, 285-322 (1916)]. He created the Phonodeik to display and record sound waveforms of musical instruments, voices, fog horns, and so on. Waveforms were analyzed with the Henrici harmonic analyzer, built in Switzerland by G. Coradi. In this device, the motion of a stylus along the curve to be analyzed causes a series of spheres to rotate; two moveable rollers in contact with the nth sphere record the contributions of the sine(nx) and cosine(nx) components of the wave. Corrections for the measured spectra are calculated from analysis of the response of the Phonodeik. Finally, the original waveform could be reconstructed from the corrected spectral amplitudes and phases by a waveform synthesizer, also built at Case. Videos will be presented that show the motion of the gears, spheres, and dials of a working Henrici analyzer, housed at the Department of Speech Pathology and Audiology at the University of Iowa. Operation of the Henrici analyzer and the waveform synthesizer will be explained.

  4. Harmonic analysis of total electron contents time series: methodology and results

    Amiri-Simkooei, A.R.; Asgari, J.


    In an attempt to model regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of the total electron contents (TEC) provided by the JPL analysis center. Multivariate and modulated harmonic estimation spectra are introduced and estimated for the serie

  5. Statistical Analysis and Comparison of Harmonics Measured in Offshore Wind Farms

    Kocewiak, Lukasz Hubert; Hjerrild, Jesper; Bak, Claus Leth


    and shows sophisticated analysis on representative harmonic measurements from Avedøre Holme, Gunfleet Sands and Burbo Bank wind farms. The nature of generation and behavior of harmonic components in offshore wind farms clearly presented and explained based on probabilistic approach. Some issues regarding...

  6. Harmonic-Resonance Analysis in a Maglev Feeding System

    Shigeeda, Hidenori; Okui, Akinobu; Akagi, Hirofumi

    A feeding circuit for a superconducting magnetic levitation train system, or the so-called “maglev” consists of feeder cables and armature coils which show characteristics of a distributed-parameter line. Electric power is supplied to the cables and coils by PWM inverters whose output voltage contains a large amount of harmonics. As a result, a harmonic resonance may occur in the feeding circuit. Besides the above characteristics, the connecting point of sections (groups of armature coils) or the feeder cables length changes according to the movement of a maglev train, thus causing changes in the harmonic-resonance characteristics of the feeding circuit. This paper describes analytical results of the harmonic resonance in the feeding circuit for the maglev, with the focus on changes in the connecting point of sections and the feeder cables length.

  7. In-Depth Mathematical Analysis of Ordinary High School Problems

    Stanley, Dick; Walukiewicz, Jolanta


    The mathematical depth that is potentially present, even in simple problems is illustrated. An extended analysis of a problem that is an analysis from a mature mathematical perspective with careful attention paid to mathematical reasoning and to using good mathematical habits of mind is used.

  8. In-Depth Mathematical Analysis of Ordinary High School Problems

    Stanley, Dick; Walukiewicz, Jolanta


    The mathematical depth that is potentially present, even in simple problems is illustrated. An extended analysis of a problem that is an analysis from a mature mathematical perspective with careful attention paid to mathematical reasoning and to using good mathematical habits of mind is used.

  9. Mathematics without boundaries surveys in pure mathematics

    Pardalos, Panos


    The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the  latest information.

  10. Error Analysis in Mathematics. Technical Report #1012

    Lai, Cheng-Fei


    Error analysis is a method commonly used to identify the cause of student errors when they make consistent mistakes. It is a process of reviewing a student's work and then looking for patterns of misunderstanding. Errors in mathematics can be factual, procedural, or conceptual, and may occur for a number of reasons. Reasons why students make…

  11. Continuous-time operational modal analysis in the presence of harmonic disturbances—The multivariate case

    Pintelon, R.; Peeters, B.; Guillaume, P.


    Recently [R. Pintelon, B. Peeters, P. Guillaume, Continuous-time operational modal analysis in the presence of harmonic disturbances, Mechanical Systems and Signal Processing 22 (5) (2008) 1017-1035] a single-output algorithm for continuous-time operational modal analysis in the presence of harmonic disturbances with time-varying frequency has been developed. This paper extends the results of Pintelon, et al. [Continuous-time operational modal analysis in the presence of harmonic disturbances, Mechanical Systems and Signal Processing 22 (5) (2008) 1017-1035] to multi-output signals. The statistical performance of the proposed maximum likelihood estimator is illustrated on simulations and real helicopter data.

  12. Dynamic companion harmonic circuit models for analysis of power systems with embedded power electronics devices

    Garcia, H.; Madrigal, M. [Programa de Graduados e Investigacion en Ingenieria Electrica, Instituto Tecnologico de Morelia, Morelia (Mexico); Vyakaranam, B.; Rarick, R.; Villaseca, F.E. [Department of Electrical and Computer Engineering, Cleveland State University, OH (United States)


    In this paper a methodology that extends the dynamic harmonic domain (DHD) analysis of large networks is presented. The method combines DHD analysis and discrete companion circuit modeling resulting in a powerful analytic technique called dynamic companion harmonic circuit modeling. It provides for a complete dynamic harmonic analysis of the system while preserving the advantages of discrete companion circuit models. The methodology is illustrated by its application to a three-node power system, where reactive power compensation is achieved using a fixed-capacitor, thyristor-controlled reactor (FC-TCR) and its control system. (author)

  13. Mathematical analysis of complex cellular activity

    Bertram, Richard; Teka, Wondimu; Vo, Theodore; Wechselberger, Martin; Kirk, Vivien; Sneyd, James


    This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Burst...

  14. Harmonics elimination algorithm for operational modal analysis using random decrement technique

    Modak, S. V.; Rawal, Chetan; Kundra, T. K.


    Operational modal analysis (OMA) extracts modal parameters of a structure using their output response, during operation in general. OMA, when applied to mechanical engineering structures is often faced with the problem of harmonics present in the output response, and can cause erroneous modal extraction. This paper demonstrates for the first time that the random decrement (RD) method can be efficiently employed to eliminate the harmonics from the randomdec signatures. Further, the research work shows effective elimination of large amplitude harmonics also by proposing inclusion of additional random excitation. This obviously need not be recorded for analysis, as is the case with any other OMA method. The free decays obtained from RD have been used for system modal identification using eigen-system realization algorithm (ERA). The proposed harmonic elimination method has an advantage over previous methods in that it does not require the harmonic frequencies to be known and can be used for multiple harmonics, including periodic signals. The theory behind harmonic elimination is first developed and validated. The effectiveness of the method is demonstrated through a simulated study and then by experimental studies on a beam and a more complex F-shape structure, which resembles in shape to the skeleton of a drilling or milling machine tool. Cases with presence of single and multiple harmonics in the response are considered.

  15. Design Practices in Harmonic Analysis Studies Applied to Industrial Electrical Power Systems

    S. F. Mekhamer


    Full Text Available Power system harmonics may cause several problems, such as malfunctions of electrical equipment, premature equipment failures and plant shutdowns. Accordingly, mitigation of these harmonics is considered an important target especially for industrial applications where any short downtime period may lead to great economic losses. Harmonic analysis studies are necessary to analyze the current and voltage harmonic levels and check if these levels comply with the contractual or international standard limits. If the studies reveal that the preset limits are exceeded, then a suitable harmonic mitigation technique should be installed. Harmonic analysis studies in the industrial electrical systems are discussed in many references. However, a comprehensive procedure for the steps required to perform a harmonic study is rarely found in the literature even though it is strongly needed for design engineers. This paper provides a comprehensive procedure for the steps required to perform a harmonic study in the form of a flowchart, based on industrial research and experience. Hence, this paper may be considered as a helpful guide for design engineers and consultants of the industrial sector.

  16. Power Transformer Differential Protection Based on Neural Network Principal Component Analysis, Harmonic Restraint and Park's Plots

    Manoj Tripathy


    Full Text Available This paper describes a new approach for power transformer differential protection which is based on the wave-shape recognition technique. An algorithm based on neural network principal component analysis (NNPCA with back-propagation learning is proposed for digital differential protection of power transformer. The principal component analysis is used to preprocess the data from power system in order to eliminate redundant information and enhance hidden pattern of differential current to discriminate between internal faults from inrush and overexcitation conditions. This algorithm has been developed by considering optimal number of neurons in hidden layer and optimal number of neurons at output layer. The proposed algorithm makes use of ratio of voltage to frequency and amplitude of differential current for transformer operating condition detection. This paper presents a comparative study of power transformer differential protection algorithms based on harmonic restraint method, NNPCA, feed forward back propagation neural network (FFBPNN, space vector analysis of the differential signal, and their time characteristic shapes in Park’s plane. The algorithms are compared as to their speed of response, computational burden, and the capability to distinguish between a magnetizing inrush and power transformer internal fault. The mathematical basis for each algorithm is briefly described. All the algorithms are evaluated using simulation performed with PSCAD/EMTDC and MATLAB.

  17. Analysis of higher order harmonics with holographic reflection gratings

    Mas-Abellan, P.; Madrigal, R.; Fimia, A.


    Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.


    Andes Safarandes Asmara


    Full Text Available This research was conducted to determine the literacy skills students of class X on their math skill. This study used a qualitative approach, the approach that drives meaningful results. To determine the ability of mathematical literacy class X, there were study subjects of 3 people who were selected based on their level of math skills. The determination was based on the categories of low, medium and high. Each subject was given a test and interview questions to determine the literacy skills. The results revealed that subjects with low category were in the second level of mathematics literacy, and subjects with high category were in the third level of mathematical literacy skills. Based on these results, it is necessary to seek strategies in the learning process of mathematics, which allows the improvement of mathematics literacy skills.

  19. Power Quality and Harmonic Analysis of End User Devices

    Sonia Leva


    Full Text Available Among the non-linear loads used in household, Compact Fluorescent Lamps (CFLs and LED lamps are becoming more widespread, while incandescent lamps are intended to be replaced by these types of lighting devices. LEDs and CFLs are significantly more efficient and economical than incandescent lamps, and are expected to be used in 100% of residential lighting in the future. As nonlinear loads, LEDs and CFLs produce highly distorted currents. A large number of customers using LEDs or CFLs for domestic, commercial and industrial lighting could determine important Power Quality problems. The paper reports experimental measurement results regarding Power Quality in indoor lighting systems. The harmonic absorptions of several types of luminaries are analyzed, highlighting the impact behavior of different lamps function of used luminaries’ technologies. The recorded harmonic absorption allows characterizing the harmonic spectrum variability of the investigated lamps.

  20. Dynamic Analysis of Wind Turbine Planetary Gears Using an Extended Harmonic Balance Approach: Preprint

    Guo, Y.; Keller, J.; Parker, R. G.


    The dynamics of wind turbine planetary gears with gravity effects are investigated using an extended harmonic balance method that extends established harmonic balance formulations to include simultaneous internal and external excitations. The extended harmonic balance method with arc-length continuation and Floquet theory is applied to a lumped-parameter planetary gear model including gravity, fluctuating mesh stiffness, bearing clearance, and nonlinear tooth contact to obtain the planetary gear dynamic response. The calculated responses compare well with time domain integrated mathematical models and experimental results. Gravity is a fundamental vibration source in wind turbine planetary gears and plays an important role in system dynamics, causing hardening effects induced by tooth wedging and bearing-raceway contacts. Bearing clearance significantly reduces the lowest resonant frequencies of translational modes. Gravity and bearing clearance together lowers the speed at which tooth wedging occurs lower than the resonant frequency.

  1. Modified ERA method for operational modal analysis in the presence of harmonic excitations

    Mohanty, Prasenjit; Rixen, Daniel J.


    Operational modal analysis (OMA) is a procedure which allows to extract modal parameters of structures from measured responses to unknown excitation arising in operation. It is based on the assumption that the input to the structure is stationary white noise. In practice, however, structural vibration observed in operation cannot always be considered as pure white-noise excitation. In many practical cases, vibrations are induced by a combination of white-noise and harmonic excitations. Harmonic excitations in addition to random inputs can occur due to rotating components or fluctuating forces in electric actuators for instance. The usual way to compute modal parameters in the presence of harmonic excitations is to consider harmonically excited frequencies as being virtual eigenfrequencies of the structure. However, if the frequencies of the harmonic inputs are close to an eigenfrequency of the system, OMA procedures fail to identify the modal parameters properly. In this paper a modified ERA method is proposed, which can be applied as an identification procedure to include the effect of purely harmonic vibrations, assuming the harmonic frequencies are known a priori. The efficiency of the proposed approach is evaluated for an experimental example of a pinned-pinned beam structure excited by multi-harmonic loads superposed on random excitation.

  2. The evolution of applied harmonic analysis models of the real world

    Prestini, Elena


    A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "…can be thoroughly recommended to any reader who is curious about the ...

  3. Harmonic analysis of the Euclidean group in three-space. II

    Rno, Jung Sik


    We develop the harmonic analysis for spinor functions which are defined by the matrix elements of the unitary irreducible representations of E(3) with the representation space on the translation subgroup.

  4. Vedic Mathematics: 'Vedic' or 'Mathematics' -- A Fuzzy and Neutrosophic Analysis


    In this book the authors probe into Vedic Mathematics (a concept that gained renown in the period of the religious fanatic and revivalist Hindutva rule in India): and explore whether it is really 'Vedic' in origin or 'Mathematics' in content. We analyzed this problem using fuzzy models like Fuzzy Cognitive Maps (FCM), Fuzzy Relational Maps (FRM) and the newly constructed fuzzy dynamical system (and its Neutrosophic analogue) that can analyze multi-experts opinion at a time using a single mode...

  5. Nonlinear analysis of a cross-coupled quadrature harmonic oscillator

    Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;


    The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...

  6. Mathematical Creativity and Mathematical Aptitude: A Cross-Lagged Panel Analysis

    Tyagi, Tarun Kumar


    Cross-lagged panel correlation (CLPC) analysis has been used to identify causal relationships between mathematical creativity and mathematical aptitude. For this study, 480 8th standard students were selected through a random cluster technique from 9 intermediate and high schools of Varanasi, India. Mathematical creativity and mathematical…

  7. Mathematical Creativity and Mathematical Aptitude: A Cross-Lagged Panel Analysis

    Tyagi, Tarun Kumar


    Cross-lagged panel correlation (CLPC) analysis has been used to identify causal relationships between mathematical creativity and mathematical aptitude. For this study, 480 8th standard students were selected through a random cluster technique from 9 intermediate and high schools of Varanasi, India. Mathematical creativity and mathematical…

  8. A Role for Language Analysis in Mathematics Textbook Analysis

    O'Keeffe, Lisa; O'Donoghue, John


    In current textbook analysis research, there is a strong focus on the content, structure and expectation presented by the textbook as elements for analysis. This research moves beyond such foci and proposes a framework for textbook language analysis which is intended to be integrated into an overall framework for mathematics textbook analysis. The…

  9. Analysis of Harmonics Suppression by Active Damping Control on Multi Slim DC-link Drives

    Yang, Feng; Máthé, Lászlo; Lu, Kaiyuan;


    Compared with conventional dc-link drive, slim dc-link drive is expected to achieve lower cost and longer life time. However, harmonics distortion problem may occur in such drive systems. This paper proposes to use an active damping control method to suppress the harmonic distortion...... with the benefit of low cost and also low loss. A new analysis method, based on the frequency domain impedance model, is presented to explore the mechanism of harmonics suppression. Also, a general method is presented to build the impedance model of a PMSM drive system using Field Oriented Control (FOC) method....... Some design issues, including power levels, current control bandwidth and harmonic interaction, are discussed when the drive system is fed by a weak grid. Case studies on a two-drive system composed by two slim dc-link drive units are provided to verify the proposed analysis method....

  10. Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data

    Gurgiolo, Chris; Vinas, Adolfo F.


    This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.

  11. Comparative analysis of harmonized forest area stimates for European countries

    Seebach, Lucia Maria; Strobl, P.; Miguel-Ayanz, J. San


    contain uncertainties, which must be quantified and included in the error budget. This is a prerequisite for combining and comparing data. The purpose of this study is to compare, taking into account uncertainties, forest area estimates for year 2000 derived from four different harmonized satellite...... the best accordance with official statistics due to its focus on land use. The other maps overestimated the forest area in mountainous countries and showed underestimation in countries with large forest area or open forest formations....

  12. Analysis of higher harmonic contamination with a modified approach using a grating analyser

    Gupta, Rajkumar, E-mail:; Modi, Mohammed H.; Lodha, G. S. [X-ray Optics Section, Indus Synchrotrons Utilization Division, Raja Ramanna Centre for Advanced Technology, Indore 452 013 (India); Kumar, M.; Chakera, J. A. [Laser Plasma Division, Raja Ramanna Centre for Advanced Technology, Indore 452 013 (India)


    Soft x-ray spectra of the toroidal grating monochromator (TGM) at the reflectivity beamline of Indus-1 synchrotron source are analyzed for higher harmonic contribution. A diffraction grating of central line spacing 1200 l/mm is used to disperse the monochromatic beam received from TGM to quantify the harmonic contents in the 50–360 Å wavelength range. In order to calculate the harmonic contamination, conventionally the intensity of higher order peak is divided by first order peak intensity of the desired wavelength. This approach is found to give wrong estimate as first order peak itself is overlapped by higher order peaks. In the present study, a modified approach has been proposed to calculate harmonic contamination where the intensity contributions of overlapping orders have been removed from the first order diffraction peak of the desired wavelength. It is found that the order contamination in the TGM spectra is less than 15% in the wavelength range of 90–180 Å. The total harmonic contribution increases from 6%–60% in the wavelength range of 150–260 Å. The critical wavelength of Indus-1 is 61 Å hence the harmonic contamination below 90 Å is significantly low. The results obtained with modified approach match well with those obtained by quantitative analysis of multilayer reflectivity data. The obtained higher harmonics data are used to fit the transmission of aluminum edge filter in the 120–360 Å wavelength range.

  13. Mathematics

    Stein, Sherman K


    Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi

  14. Mathematics for electronic technology

    Howson, D P


    Mathematics for Electronic Technology is a nine-chapter book that begins with the elucidation of the introductory concepts related to use of mathematics in electronic engineering, including differentiation, integration, partial differentiation, infinite series, vectors, vector algebra, and surface, volume and line integrals. Subsequent chapters explore the determinants, differential equations, matrix analysis, complex variable, topography, graph theory, and numerical analysis used in this field. The use of Fourier method for harmonic analysis and the Laplace transform is also described. The ma

  15. Continuous-time operational modal analysis in the presence of harmonic disturbances

    Pintelon, R.; Peeters, B.; Guillaume, P.


    Operational modal analysis (OMA) allows to identify the modal parameters from the measured response to unknown random perturbations of a mechanical structure in operation. However, in all applications with rotating components (e.g. helicopters, turbines, diesel motors,…,) the structural vibration in operation is a combination of the response to the random perturbation and the harmonic excitation due to the rotating components. Classical OMA methods fail if the harmonic disturbance is close to, or coincides with a resonance frequency of the structure. Therefore, these methods have been extended to deal with harmonic disturbances with a known, fixed frequency. However, in many applications (e.g. helicopters, wind turbines, diesel motors,…) the frequencies of the harmonic disturbances vary in time. This paper presents three methods for suppressing the influence of harmonic disturbances with unknown varying frequencies in operational modal analysis. Two of these methods can handle the case where the peak of the harmonic disturbance and the resonance peak completely overlap. The performance of the three methods is illustrated on simulations and real helicopter data. The present paper handles the single output case only.

  16. Deep Performance Analysis of Refined HarmonicBin Packing Algorithm

    顾晓东; 陈国良; 许胤龙


    Refined Harmonic (RH) is one of the best on-line bin packing algorithms.The algorithm was first proposed by Lee&Lee in 1985 and the upper bound of the worst-case performance ratio has been proved to be 1.63596…… In this paper, it is proved that also the lower bound. The average performance of RH is also studied for the first time.It is shown that the average-case performance ratio of RH is 1.28243... under the uniform distribution.

  17. Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

    Wingeier, B M; Silberstein, R B; Wingeier, Brett M.; Nunez, Paul L.; Silberstein, Richard B.


    We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.

  18. Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

    Wingeier, Brett M.; Nunez, Paul L.; Silberstein, Richard B.


    We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.

  19. The Development of Mathematical Knowledge for Teaching of Mathematics Teachers in Lesson Analysis Process

    Baki, Mujgan


    This study aims to explore the role of lesson analysis in the development of mathematical knowledge for teaching. For this purpose, a graduate course based on lesson analysis was designed for novice mathematics teachers. Throughout the course the teachers watched videos of group-mates and discussed the issues they identified in terms of…

  20. Analysis of magnetic nanoparticles using second harmonic responses

    Tanaka, Saburo; Suzuki, Toshifumi; Kobayashi, Kazuya; Liao, Shu-Hsien; Horng, Herng-Er; Yang, Hong-Chang


    Magnetic particle imaging (MPI) is a new medical imaging technology with a number of potential applications. It is based on utilizing the non-linear magnetization response for magnetic nanoparticles (MNPs). We have proposed a method to improve the detection sensitivity for the magnetization of MNPs, and their imaging technique, based on the detection of a second harmonic of the response using a high Tc SQUID. The advantage of using the second harmonic is that the response can be measured even with small amplitudes. In this paper, superparamagnetic MNPs with different diameters and different compositions of materials were analyzed by this method. In the MNPs, Resovist was found to be almost one order of magnitude larger than that of the other MNPs tested. The magnetic moments of the MNPs were estimated by fitting with the Langevin function to obtain the magnetic moments m of Resovist of 3.62×10-18 [J/T]. The magnetic moment m of Resovist was 7.4 times larger than the other MNPs.

  1. Separation of structural modes and harmonic frequencies in Operational Modal Analysis using random decrement

    Modak, S. V.


    Operational Modal Analysis (OMA) is used to extract modal parameters of a structure on the basis of their output response measured during operation. OMA, when applied to mechanical engineering structures is often faced with the problem of harmonics present in the output response. A complex structure may have many dominant frequency components in its response frequency spectrum. These may contain frequency components associated with resonant frequencies of the structure, which and the associated mode shapes and the damping factors represent the data of interest, but may also contain frequencies or harmonics associated with the excitation sources. Since in OMA the characteristics of the excitation sources are not known, one of the problems lies in separating the resonant frequencies from the harmonic excitation frequencies. Any error in this regard may lead to an error in modal identification with the consequence that a harmonic may be construed as a structural mode and vice versa. This issue is addressed in this paper and a method is presented for separating resonant frequencies from harmonic excitation frequencies using random decrement of the response. The principle of the method is presented using an analytical study on a single degree of freedom system. The effectiveness of the method is then demonstrated through numerical studies on a lumped parameter multi-degree of freedom system and a simulated plate structure. Detection of single and multiple harmonics in the response that are well separated as well as close to resonant frequencies are considered.

  2. The Effect of Plug-in Electric Vehicles on Harmonic Analysis of Smart Grid

    Heidarian, T.; Joorabian, M.; Reza, A.


    In this paper, the effect of plug-in electric vehicles is studied on the smart distribution system with a standard IEEE 30-bus network. At first, harmonic power flow analysis is performed by Newton-Raphson method and by considering distorted substation voltage. Afterward, proper sizes of capacitors is selected by cuckoo optimization algorithm to reduce the power losses and cost and by imposing acceptable limit for total harmonic distortion and RMS voltages. It is proposed that the impact of generated current harmonics by electric vehicle battery chargers should be factored into overall load control strategies of smart appliances. This study is generalized to the different hours of a day by using daily load curve, and then optimum time for charging of electric vehicles batteries in the parking lots are determined by cuckoo optimization algorithm. The results show that injecting harmonic currents of plug-in electric vehicles causes a drop in the voltage profile and increases power loss. Moreover, charging the vehicle batteries has more impact on increasing the power losses rather than the harmonic currents effect. Also, the findings showed that the current harmonics has a great influence on increasing of THD. Finally, optimum working times of all parking lots was obtained for the utilization cost reduction.

  3. Fundaments of Quaternionic Clifford Analysis III: Fischer Decomposition in Symplectic Harmonic Analysis

    Brackx, Fred; De Schepper, Hennie; Eelbode, David; Lavicka, Roman; Soucek, Vladimir


    In the framework of quaternionic Clifford analysis in Euclidean space $\\mathbb{R}^{4p}$, which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is obtained in terms of spaces of so--called (adjoint) symplectic spherical harmonics, which are irreducible modules for the symplectic group Sp$(p)$. Its Howe dual partner is determined to be $\\mathfrak{sl}(2,\\mathbb{C}) \\oplus \\mathfrak{sl}(2,\\mathbb{C}) = \\ma...

  4. Extensions of positive definite functions applications and their harmonic analysis

    Jorgensen, Palle E T; Tian, Feng


    This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data. While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.

  5. Automated cardiac sarcomere analysis from second harmonic generation images

    Garcia-Canadilla, Patricia; Gonzalez-Tendero, Anna; Iruretagoyena, Igor; Crispi, Fatima; Torre, Iratxe; Amat-Roldan, Ivan; Bijnens, Bart H.; Gratacos, Eduard


    Automatic quantification of cardiac muscle properties in tissue sections might provide important information related to different types of diseases. Second harmonic generation (SHG) imaging provides a stain-free microscopy approach to image cardiac fibers that, combined with our methodology of the automated measurement of the ultrastructure of muscle fibers, computes a reliable set of quantitative image features (sarcomere length, A-band length, thick-thin interaction length, and fiber orientation). We evaluated the performance of our methodology in computer-generated muscle fibers modeling some artifacts that are present during the image acquisition. Then, we also evaluated it by comparing it to manual measurements in SHG images from cardiac tissue of fetal and adult rabbits. The results showed a good performance of our methodology at high signal-to-noise ratio of 20 dB. We conclude that our automated measurements enable reliable characterization of cardiac fiber tissues to systematically study cardiac tissue in a wide range of conditions.

  6. Harmonic space analysis of pulsar timing array redshift maps

    Roebber, Elinore


    In this paper, we propose a new framework for treating the angular information in the pulsar timing array response to a gravitational wave background based on standard cosmic microwave background techniques. We calculate the angular power spectrum of the all-sky gravitational redshift pattern induced at the earth for both a single bright source of gravitational radiation and a statistically isotropic, unpolarized Gaussian random gravitational wave background. The angular power spectrum is the harmonic transform of the Hellings & Downs curve. We use the power spectrum to examine the expected variance in the Hellings & Downs curve in both cases. Finally, we discuss the extent to which pulsar timing arrays are sensitive to the angular power spectrum and find that the power spectrum sensitivity is dominated by the quadrupole anisotropy of the gravitational redshift map.

  7. Precise Model Analysis for 3-phase High Power Converter using the Harmonic State Space Modeling

    Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede


    This paper presents about the generalized multi-frequency modeling and analysis methodology, which can be used in control loop design and stability analysis. In terms of the switching frequency of high power converter, there can be harmonics interruption if the voltage source converter has a low...

  8. Comparative Evaluation of Modeling Methods for Harmonic Stability Analysis of Three-Phase Voltage Source Converters

    Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth;


    As the increasing of power electronics based systems, not only the component-based analysis but also a systematic interaction analysis with each other systems are being important. Especially studies about the stability and the harmonics interaction are critical in order to establish the required ...

  9. Mathematical analysis of aircraft intercooler design

    Joyner, Upshur T


    A mathematical analysis has been made to show the method of obtaining the dimensions of the intercooler that will use the least total power for a given set of design conditions. The results of this analysis have been used in a sample calculation and, on the basis of this calculation, a new inter cooler arrangement is suggested. Because the length of the two air passages of the new arrangement is short in comparison with the third dimension, the height of the intercooler, this intercooler arrangement has unusual dimensions. These dimensions give the proposed intercooler arrangement an advantage over one of usual dimensions because less total power will be consumed by the intercooler, the weight and volume of the intercooler will be smaller, and the pressure drop of both the engine air and the cooling air in passing through the intercooler will be lower.

  10. Analysis of the third harmonic for class-F power amplifiers with an I-V knee effect

    Zhao, Bo-Chao; Lu, Yang; Wei, Jia-Xing; Dong, Liang; Wang, Yi; Cao, Meng-Yi; Ma, Xiao-Hua; Hao, Yue


    The appearance of third-generation semiconductors represented by gallium nitride (GaN) material greatly improves the output power of a power amplifier (PA), but the efficiency of the PA needs to be further improved. The Class-F PA reduces the overlap of drain voltage and current by tuning harmonic impedance so that high efficiency is achieved. This paper begins with the principle of class-F PA, regards the third harmonic voltage as an independent variable, analyzes the influence of the third harmonic on fundamental, and points out how drain efficiency and output power vary with the third harmonic voltage with an I-V knee effect. Finally, the best third harmonic impedance is found mathematically. We compare our results with the Loadpull technique in advanced design system environment and conclude that an optimized third harmonic impedance is open in an ideal case, while it is not at an open point with the I-V knee effect, and the drain efficiency with optimized third harmonic impedance is 4% higher than that with the third harmonic open.

  11. Spatio-spectral analysis of ionization times in high-harmonic generation

    Soifer, Hadas, E-mail: [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel); Dagan, Michal; Shafir, Dror; Bruner, Barry D. [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel); Ivanov, Misha Yu. [Department of Physics, Imperial College London, South Kensington Campus, SW7 2AZ London (United Kingdom); Max-Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Strasse 2A, D-12489 Berlin (Germany); Serbinenko, Valeria; Barth, Ingo; Smirnova, Olga [Max-Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Strasse 2A, D-12489 Berlin (Germany); Dudovich, Nirit [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel)


    Graphical abstract: A spatio-spectral analysis of the two-color oscillation phase allows us to accurately separate short and long trajectories and reconstruct their ionization times. Highlights: ► We perform a complete spatio-spectral analysis of the high harmonic generation process. ► We analyze the ionization times across the entire spatio-spectral plane of the harmonics. ► We apply this analysis to reconstruct the ionization times of both short and long trajectories. - Abstract: Recollision experiments have been very successful in resolving attosecond scale dynamics. However, such schemes rely on the single atom response, neglecting the macroscopic properties of the interaction and the effects of using multi-cycle laser fields. In this paper we perform a complete spatio-spectral analysis of the high harmonic generation process and resolve the distribution of the subcycle dynamics of the recolliding electron. Specifically, we focus on the measurement of ionization times. Recently, we have demonstrated that the addition of a weak, crossed polarized second harmonic field allows us to resolve the moment of ionization (Shafir, 2012) [1]. In this paper we extend this measurement and perform a complete spatio-spectral analysis. We apply this analysis to reconstruct the ionization times of both short and long trajectories showing good agreement with the quantum path analysis.

  12. Mathematical analysis of a muscle architecture model.

    Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio


    Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.

  13. The Design of Lessons Using Mathematics Analysis Software to Support Multiple Representations in Secondary School Mathematics

    Pierce, Robyn; Stacey, Kaye; Wander, Roger; Ball, Lynda


    Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students' learning requires carefully designed lessons. This paper reports on design…

  14. The Design of Lessons Using Mathematics Analysis Software to Support Multiple Representations in Secondary School Mathematics

    Pierce, Robyn; Stacey, Kaye; Wander, Roger; Ball, Lynda


    Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students' learning requires carefully designed lessons. This paper reports on design…

  15. Mathematics Teaching Anxiety and Self-Efficacy Beliefs toward Mathematics Teaching: A Path Analysis

    Peker, Murat


    The purpose of this study was to investigate the relationship between pre-service primary school teachers' mathematics teaching anxiety and their self-efficacy beliefs toward mathematics teaching through path analysis. There were a total of 250 pre-service primary school teachers involved in this study. Of the total, 202 were female and 48 were…

  16. Discoursing Mathematically: Using Discourse Analysis to Develop a Sociocritical Perspective of Mathematics Education

    Razfar, Aria


    This article explores how the concepts of discourse and its methodological extension discourse analysis can help mathematics educators re-conceptualize their practices using a sociocultural view of learning. It provides conceptual and methodological tools as well as activities that can be helpful in mathematics methods courses and professional…

  17. Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis

    Hamburg, Maryanna P.


    This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…

  18. Full vector spherical harmonic analysis of the Holocene geomagnetic field

    Richardson, Marcia

    High-quality time-series paleomagnetic measurements have been used to derive spherical harmonic models of Earth's magnetic field for the past 2,000 years. A newly-developed data compilation, PSVMOD2.0 consists of time-series directional and intensity records that significantly improve the data quality and global distribution used to develop previous spherical harmonic models. PSVMOD2.0 consists of 185 paleomagnetic time series records from 85 global sites, including 30 full-vector records (inclination, declination and intensity). It includes data from additional sites in the Southern Hemisphere and Arctic and includes globally distributed sediment relative paleointensity records, significantly improving global coverage over previous models. PSVMOD2.0 records have been assessed in a series of 7 regional intercomparison studies, four in the Northern Hemisphere and 3 in the southern hemisphere. Comparisons on a regional basis have improved the quality and chronology of the data and allowed investigation of spatial coherence and the scale length associated with paleomagnetic secular variation (PSV) features. We have developed a modeling methodology based on nonlinear inversion of the PSVMOD2.0 directional and intensity records. Models of the geomagnetic field in 100-year snapshots have been derived for the past 2,000 with the ultimate goal of developing models spanning the past 8,000 years. We validate the models and the methodology by comparing with the GUFM1 historical models during the 400-year period of overlap. We find that the spatial distribution of sites and quality of data are sufficient to derive models that agree with GUFM1 in the large-scale characteristics of the field. We use the the models derived in this study to downward continue the field to the core-mantle boundary and examine characteristics of the large-scale structure of the magnetic field at the source region. The derived models are temporally consistent from one epoch to the next and exhibit

  19. A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference

    Muir, J. B.; Tkalčić, H.


    The problem of decomposing irregular data on the sphere into a set of spherical harmonics is common in many fields of geosciences where it is necessary to build a quantitative understanding of a globally varying field. For example, in global seismology, a compressional or shear wave speed that emerges from tomographic images is used to interpret current state and composition of the mantle, and in geomagnetism, secular variation of magnetic field intensity measured at the surface is studied to better understand the changes in the Earth's core. Optimization methods are widely used for spherical harmonic analysis of irregular data, but they typically do not treat the dependence of the uncertainty estimates on the imposed regularization. This can cause significant difficulties in interpretation, especially when the best-fit model requires more variables as a result of underestimating data noise. Here, with the above limitations in mind, the problem of spherical harmonic expansion of irregular data is treated within the hierarchical Bayesian framework. The hierarchical approach significantly simplifies the problem by removing the need for regularization terms and user-supplied noise estimates. The use of the corrected Akaike Information Criterion for picking the optimal maximum degree of spherical harmonic expansion and the resulting spherical harmonic analyses are first illustrated on a noisy synthetic data set. Subsequently, the method is applied to two global data sets sensitive to the Earth's inner core and lowermost mantle, consisting of PKPab-df and PcP-P differential traveltime residuals relative to a spherically symmetric Earth model. The posterior probability distributions for each spherical harmonic coefficient are calculated via Markov Chain Monte Carlo sampling; the uncertainty obtained for the coefficients thus reflects the noise present in the real data and the imperfections in the spherical harmonic expansion.

  20. Harmonic analysis of wrist mechanism of robot manipulator

    Akbar, Shaik; Navuri, Karteek; Eswara Kumar, A.; Prakash, D.


    Wrist mechanism is a part of robot manipulator which is used to provide the pitch and yaw motions to the end effectors for orienting the loads carried by the end effectors. The wrist mechanism is subjected to different types of vibrations because of the various working conditions. Due to these vibrations wrist mechanism experience higher deformations and stresses; this causes failure of wrist mechanism. It is important to study the dynamic behaviour of the wrist mechanism under different loads before adopting in the application. The structure of the wrist mechanism is modelled in the ANSYS Workbench software and analysed for harmonic loads. Proper boundary conditions, mesh and connections between links& pins are assigned to the wrist mechanism assembly. From the present work, peak deformations of links and pins are occurred at 569.83Hz. Further, the link are analysed with 3D composites those are carbon epoxy and E-glass epoxy. It is observed that carbon epoxy shows better stiffness than E-Glass epoxy and it has weight reduction of 13.76% compared with metals.

  1. Mathematical Analysis and Optimization of Infiltration Processes

    Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W.


    A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants.

  2. Limitations in Using Multiple Imputation to Harmonize Individual Participant Data for Meta-Analysis.

    Siddique, Juned; de Chavez, Peter J; Howe, George; Cruden, Gracelyn; Brown, C Hendricks


    Individual participant data (IPD) meta-analysis is a meta-analysis in which the individual-level data for each study are obtained and used for synthesis. A common challenge in IPD meta-analysis is when variables of interest are measured differently in different studies. The term harmonization has been coined to describe the procedure of placing variables on the same scale in order to permit pooling of data from a large number of studies. Using data from an IPD meta-analysis of 19 adolescent depression trials, we describe a multiple imputation approach for harmonizing 10 depression measures across the 19 trials by treating those depression measures that were not used in a study as missing data. We then apply diagnostics to address the fit of our imputation model. Even after reducing the scale of our application, we were still unable to produce accurate imputations of the missing values. We describe those features of the data that made it difficult to harmonize the depression measures and provide some guidelines for using multiple imputation for harmonization in IPD meta-analysis.

  3. Contributions to the Structural Analysis of the Double Gear Harmonic Transmission

    DraghiŃa Ianici


    Full Text Available In this paper, we present the construction and functioning of a new constructive variant of harmonic drive called double gear harmonic transmission (DGHT. In the second part of the paper, we present the desmodromy analysis of the DGHT considering the planar approach of the respective mechanism. At establishing the mobility, class and order of the DGHT we have used the procedure of instantaneous– isokinetic transformation wich followed the identifica-tion of the kinematic groups of the mechanism and the replacement of the higher kinematic pairs by links and by lower kinematic pairs.

  4. Harmonic Analysis of Offshore Wind Farms with Full Converter Wind Turbines

    Kocewiak, Lukasz Hubert; Hjerrild, Jesper; Bak, Claus Leth


    This paper presents the harmonic analysis of offshore wind farm (OWF) models with full converters represented as harmonic sources and measurement data on the point of common coupling (PCC) during normal operation. The model describes a wind farm (WF) with full rated converters installed connected....... Simulation results are compared with representative measurement data obtained from measurement campaign done in an OWF situated in United Kingdom. The problems and limitations related to present standards and practice will be discussed based on measurements from offshore wind farm....

  5. Theoretical analysis of harmonic suppression in multi-step error separation technique

    Gu, Wei; Tan, Jiubin; Huang, Jingzhi


    Multi-step error separation technique is one of the most widely used roundness separation technique. It can improve the precision of the roundness measuring instrument. By analyzing the model of multi-step, we can find that it has harmonic suppression and cannot be completely separate the roundness error of the tested parts from the rotation error of the spindle. When we use the M-steps, the km times harmonic in tested parts is lost and is mixed 1:1 with the rotation error of the spindle. In this paper, theoretical provement and simulation analysis of harmonic suppression of multi-step error separation technique are carried out: 1) using a group circular standards to separate the same spindle; and 2) using different steps to separate the same spindle.

  6. Quantum-orbit analysis of high-order harmonic generation by resonant plasmon field enhancement

    Shaaran, T; Lewenstein, M


    We perform a detailed analysis of high-order harmonic generation (HHG) in atoms within the strong field approximation (SFA) by considering spatially inhomogeneous monochromatic laser fields. We investigate how the individual pairs of quantum orbits contribute to the harmonic spectra. We show that in the case of inhomogeneous fields, the electron tunnels with two different canonical momenta. One of them leads to a higher cutoff and the other one develops a lower cutoff. Furthermore, we demonstrate that the quantum orbits have a very different behavior in comparison to the homogeneous field. We also conclude that in the case of the inhomogeneous fields, both odd and even harmonics are present in the HHG spectra. Within our model, we show that the HHG cutoff extends far beyond the semiclassical cutoff as a function of inhomogeneity strength. Our findings are in good agreement both with quantum mechanical and classical models.

  7. Analysis of Second-Harmonic Generation from CuttbPc LB Film/Metal Interface

    程晓曼; 姚素薇; 李成全; 间中孝彰; 岩本光正


    Second-harmonic generation signals from a CuttbPc LB film deposited on metal (Al or Au)-glass substrates were investigated. It was observed that there were two second-harmonic peaks at the wavelength of 1060 and 1250nm in the CuttbPc/A1 film, but only one peak at 1050nm in the CuttbPc/Au film. Meanwhile the surface electric potentials (SEP) at the interfaces of LB film/metals were also measured using a Kelvin probe. The SEP in the CuttbPc/Al decreases and eventually approaches a saturated value of -1.0 V as the film thickness increases,while the SEP in the CuttbPc/Au is nearly zero. Based on the experimental results and theoretical analysis, it was considered that the space-charge-induced electric field makes a main contribution to the second-harmonic generation at 1250nm in the CuttbPc/Al film.

  8. Evaluation of Harmonic Analysis of Time Series (HANTS): impact of gaps on time series reconstruction

    Zhou, J.Y.; Jia, L.; Hu, G.; Menenti, M.


    In recent decades, researchers have developed methods and models to reconstruct time series of irregularly spaced observations from satellite remote sensing, among which the widely used Harmonic Analysis of Time Series (HANTS) method. Many studies based on time series reconstructed with HANTS docume

  9. Harmonic tidal analysis at a few stations using the least squares method

    Fernandes, A.A; Das, V.K.; Bahulayan, N.

    Using the least squares method, harmonic analysis has been performed on hourly water level records of 29 days at several stations depicting different types of non-tidal noise. For a tidal record at Mormugao, which was free from storm surges (low...

  10. Harmonic Analysis on semisimple symmetric spaces. A survey of some general results.

    Ban, E.P. van den; Flensted-Jensen, M.; Schlichtkrull, H.


    We give a survey of the status of some of the fundamental problems in harmonic analysis on semisimple symmetric spaces, including the description of the discrete series, the denition of the Fourier transform, the inversion formula, the Plancherel formula and the Paley{ Wiener theorem.

  11. Evaluation of Harmonic Analysis of Time Series (HANTS): impact of gaps on time series reconstruction

    Zhou, J.Y.; Jia, L.; Hu, G.; Menenti, M.


    In recent decades, researchers have developed methods and models to reconstruct time series of irregularly spaced observations from satellite remote sensing, among which the widely used Harmonic Analysis of Time Series (HANTS) method. Many studies based on time series reconstructed with HANTS docume

  12. Eigenvalue-based harmonic stability analysis method in inverter-fed power systems

    Wang, Yanbo; Wang, Xiongfei; Blaabjerg, Frede


    This paper presents an eigenvalue-based harmonic stability analysis method for inverter-fed power systems. A full-order small-signal model for a droop-controlled Distributed Generation (DG) inverter is built first, including the time delay of digital control system, inner current and voltage cont...

  13. Harmonic Stability Analysis of Inverter-Fed Power Systems Using Component Connection Method

    Wang, Yanbo; Wang, Xiongfei; Blaabjerg, Frede


    This paper presents a Component Connection Method (CCM)-based harmonic stability analysis for ac power-electronic-fed power systems. In the approach, the system is partitioned as individual components, including the controllers of DG units, LC filters, network impedances, and power loads. They ar...

  14. State-space-based harmonic stability analysis for paralleled grid-connected inverters

    Wang, Yanbo; Wang, Xiongfei; Chen, Zhe


    This paper addresses a state-space-based harmonic stability analysis of paralleled grid-connected inverters system. A small signal model of individual inverter is developed, where LCL filter, the equivalent delay of control system, and current controller are modeled. Then, the overall small signa...

  15. Evaluation of Harmonic Analysis of Time Series (HANTS): impact of gaps on time series reconstruction

    Zhou, J.Y.; Jia, L.; Hu, G.; Menenti, M.


    In recent decades, researchers have developed methods and models to reconstruct time series of irregularly spaced observations from satellite remote sensing, among which the widely used Harmonic Analysis of Time Series (HANTS) method. Many studies based on time series reconstructed with HANTS

  16. Development of a Standard Protocol for the Harmonic Analysis of Radial Pulse Wave and Assessing Its Reliability in Healthy Humans



    This study was aimed to establish a standard protocol and to quantitatively assess the reliability of harmonic analysis of the radial pulse wave measured by a harmonic wave analyzer (TD01C system). Both intraobserver and interobserver assessments were conducted to investigate whether the values of harmonics are stable in successive measurements. An intraclass correlation coefficient (ICC) and a Bland–Altman plot were used for this purpose. For the reliability assessments of the intraobserver ...

  17. Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software

    Pierce, Robyn; Stacey, Kaye


    This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its…

  18. Analysis of Research in the Teaching of Mathematics.

    Brown, Kenneth E.; Abell, Theodore L.

    This is the sixth in a series of publications prepared by the U.S. Office of Education which are concerned with an analysis of research in mathematics education. This publication presents a summary analysis of research in mathematics education and includes reports of Cooperative Research Projects supported by the Cooperative Research Program of…

  19. Mathematics analysis of polymerase chain reaction kinetic curves.

    Sochivko, D G; Fedorov, A A; Varlamov, D A; Kurochkin, V E; Petrov, R V


    The paper reviews different approaches to the mathematical analysis of polymerase chain reaction (PCR) kinetic curves. The basic principles of PCR mathematical analysis are presented. Approximation of PCR kinetic curves and PCR efficiency curves by various functions is described. Several PCR models based on chemical kinetics equations are suggested. Decision criteria for an optimal function to describe PCR efficiency are proposed.

  20. Frames and other bases in abstract and function spaces novel methods in harmonic analysis

    Gia, Quoc; Mayeli, Azita; Mhaskar, Hrushikesh; Zhou, Ding-Xuan


    The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including ...

  1. Mathematical Problem Solving through Sequential Process Analysis

    Codina, A.; Cañadas, M. C.; Castro, E.


    Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

  2. Talking Mathematically: An Analysis of Discourse Communities

    Imm, Kara; Stylianou, Despina A.


    Discourse has always been at the heart of teaching. In more recent years, the mathematics education community has also turned its attention towards understanding the role of discourse in mathematics teaching and learning. Using earlier classifications of discourse, in this paper, we looked at three types of classrooms: classrooms that engage in…

  3. Mathematical theory of compressible viscous fluids analysis and numerics

    Feireisl, Eduard; Pokorný, Milan


    This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...

  4. [Representation and mathematical analysis of human corneal surface].

    Tălu, Stefan; Tălu, Mihai; Giovanzana, Stefano


    In the description and analysis of human corneal surface are used various mathematical models based on parametric representations, used in biomechanical studies and 3D solid modeling of the cornea. Mathematical models are important into the biomechanics of the cornea to model the corneal behavior. Corneal biomechanics also has the potential to improve outcomes in refractive surgery. The objective of this paper is to present the most representative mathematical models currently used for modeling of human corneal in optics and biomechanics fields.

  5. Some Opinions on Normal College Mathematical Analysis Teaching

    LUO Dong-sheng; WANG Chang-chun; TAN Xiao-yan


    Basing on the nature and special characters of normal college, talk about mathematical analysis teaching in several aspects.First, mathematical analysis should be taught as a foundation course because it will be used as one of the basic tools for further mathematics’study, and in the succeed course.The second, it being strictly relative with the primary mathematic course, so it should be taught as a guidance to pre-middle school mathematics teachers.The third, as any subject, getting the general structure of it is useful to let the students get the whole sensation, and help them to stimulate them to explore. Especially,for the future teacher, the course should build research interest and make the students know how to excite creation emotion from any subject as we do in mathematical analysis.

  6. Mathematics Education Research in Turkey: A Content Analysis Study

    Ciltas, Alper; Guler, Gursel; Sozbilir, Mustafa


    In this study, a content analysis of research is aimed in the field of mathematics education of Turkish researchers. To this aim, the investigation of 359 article were made which were accessed from web in full text between 1987 and 2009 years and which were published in the field of mathematics education from 32 different journals. 27 of these…

  7. Mathematical Modelling Research in Turkey: A Content Analysis Study

    Çelik, H. Coskun


    The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

  8. Operational modal analysis in the presence of harmonic excitations by the use of transmissibility measurements

    Devriendt, Christof; De Sitter, Gert; Vanlanduit, Steve; Guillaume, Patrick


    Operational modal analysis (OMA) is based on the assumption that the forces on the structure are the result of a stochastic process, so being white noise. In practice, however, structural vibrations observed in operation cannot always be considered as pure white-noise excitation. In many mechanical structures the loading forces are often more complex and even harmonic components can be present in the response. This is especially true, when measuring on mechanical structures containing rotating parts (e.g. cars, turbines, windmills), but also civil engineering structures may have responses superimposed by harmonic components. OMA procedures are, strictly speaking, not applicable in these situations. Current techniques may encounter difficulties to correctly identify the modal parameters, especially for modes with eigenfrequencies close to the harmonic frequencies. In this paper a recently proposed OMA technique based on transmissibility measurements will be applied. This method reduces the risk to wrongly identify the modal parameters due to the presence of harmonics. The unknown operational forces can be arbitrary (coloured noise, swept sine, impact, etc.) as long as they are persistently exciting in the frequency band of interest.

  9. An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics, with applications to problems in mathematical

    Byerly, William Elwood


    Originally published over a century ago, this work remains among the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. The subsequent growth of science into a diverse range of specialties has enhanced the value of this classic, whose thorough, basic treatment presents material that is assumed in many other studies but seldom available in such concise form. The development of functions, series, and their differential equations receives detailed explanations, and throughout the text, theory is applied to practical problems, with the

  10. Selected papers on harmonic analysis, groups, and invariants

    Nomizu, Katsumi


    This volume contains papers that originally appeared in Japanese in the journal Sūgaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including representation theory, differential geometry, invariant theory, and complex analysis.

  11. Mathematical Modeling for Simulation of Nuclear Reactor Analysis

    Salah Ud-Din Khan; Shahab Ud-Din Khan


    In this paper, we have developed a mathematical model for the nuclear reactor analysis to be implemented in the nuclear reactor code. THEATRe is nuclear reactor analysis code which can only work for the cylindrical type fuel reactor and cannot applicable for the plate type fuel nuclear reactor. Therefore, the current studies encompasses on the modification of THEATRe code for the plate type fuel element. This mathematical model is applicable to the thermal analysis of the reactor which is ver...

  12. Numerical Analysis vs. Mathematics: Modern mathematics often does not deal with the practical problems which face numerical analysis.

    Hamming, R W


    I hope I have shown not that mathematicians are incompetent or wrong, but why I believe that their interests, tastes, and objectives are frequently different from those of practicing numerical analysts, and why activity in numerical analysis should be evaluated by its own standards and not by those of pure mathematics. I hope I have also shown you that much of the "art form" of mathematics consists of delicate, "noise-free" results, while many areas of applied mathematics, especially numerical analysis, are dominated by noise. Again, in computing the process is fundamental, and rigorous mathematical proofs are often meaningless in computing situations. Finally, in numerical analysis, as in engineering, choosing the right model is more important than choosing the model with the elegant mathematics.

  13. Global and Stochastic Analysis with Applications to Mathematical Physics

    Gliklikh, Yuri E


    Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces ...

  14. Quantitative Analysis of the Interdisciplinarity of Applied Mathematics.

    Xie, Zheng; Duan, Xiaojun; Ouyang, Zhenzheng; Zhang, Pengyuan


    The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999-2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.

  15. A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities

    Kononenko, O. [SLAC National Accelerator Lab., Menlo Park, CA (United States)


    ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)

  16. Reimagining a Riemannian symbology for the structural harmonic analysis of 19th-century tonal music.

    Marcus Alessi Bittencourt


    Full Text Available In the context of a preview of central topics taken from a larger research work, this article presents and explains a proposition of a functional analytical symbology which is currently being developed as a tool for the structural harmonic analysis of tonal music. This symbology constitutes a key component for a proposal of an analytical methodology for 19th century extended tonality, which is the core of the aforementioned larger research work. Based on a critical revision of the history of music theory and analysis, this methodology is mainly the result of the recasting and the amplification of thoughts and concepts developed by 19th century theorists such as Hugo Riemann and Arthur von Oettingen. The article introduces the proposed analytical symbology through a comparison to its historical counterparts, and it also highlights the ability of the proposed symbols to graph the harmonic language of 19th century extended tonality by means of a few analytical examples.

  17. Mathematical analysis of epidemiological models with heterogeneity

    Van Ark, J.W.


    For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.

  18. Harmonic Analysis of Boolean Networks: Determinative Power and Perturbations

    Heckel, Reinhard; Bossert, Martin


    Consider a large Boolean network with a feed forward structure. Given a probability distribution for the inputs, can one find-possibly small-collections of input nodes that determine the states of most other nodes in the network? To identify these nodes, a notion that quantifies the determinative power of an input over states in the network is needed. We argue that the mutual information (MI) between a subset of the inputs X = {X_1, ..., X_n} of node i and the function f_i(X)$ associated with node i quantifies the determinative power of this subset of inputs over node i. To study the relation of determinative power to sensitivity to perturbations, we relate the MI to measures of perturbations, such as the influence of a variable, in terms of inequalities. The result shows that, maybe surprisingly, an input that has large influence does not necessarily have large determinative power. The main tool for the analysis is Fourier analysis of Boolean functions. Whether a function is sensitive to perturbations or not...

  19. Mathematical Metaphors: Problem Reformulation and Analysis Strategies

    Thompson, David E.


    This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

  20. Modelling of Nonlinear Devices for Power Harmonic Analysis%非线性装置的谐波分析模型



    提出了一种采用多项式逼近非线性装置稳态特性的谐波分析新模型——时域稳态模型。阐明了建立时域稳态模型的一般数学方法,并在此基础上提出了一种工程适用的谐波分析模型——受控源综合模型,这类模型适用于电力网络的时域非线性稳态分析。%A new model of nonlinear devices for power harmonic analysis is derived rigorously first. The model representing the time-domain steady-state characteristics of nonlinear devices is presented on the basis of polynomial fits to the time-domain waveform of the output current versus system supply voltage. This mathematical model can be straightforwardly transfered to an equivalent circuit model composed of a linear capacitance (inductance) and a multidimension controlled suorce. The paremeters of the equivalent circuit model are random variables obtained from the statistic properties of the data acquisition of the output current. This model is useful for analysts to perform harmonic studies both in linear and nonlinear power systems by the use of general purpose simulators. As examples, the plots showing harmonic analysis are drawn by the commonly-used softwares MATLAB and MathCAD.

  1. Plasma harmonics

    Ganeev, Rashid A


    Preface; Why plasma harmonics? A very brief introduction Early stage of plasma harmonic studies - hopes and frustrations New developments in plasma harmonics studies: first successes Improvements of plasma harmonics; Theoretical basics of plasma harmonics; Basics of HHG Harmonic generation in fullerenes using few-cycle pulsesVarious approaches for description of observed peculiarities of resonant enhancement of a single harmonic in laser plasmaTwo-colour pump resonance-induced enhancement of odd and even harmonics from a tin plasmaCalculations of single harmonic generation from Mn plasma;Low-o

  2. Error and Symmetry Analysis of Misner's Algorithm for Spherical Harmonic Decomposition on a Cubic Grid

    Fiske, David R.


    In an earlier paper, Misner (2004, Class. Quant. Grav., 21, S243) presented a novel algorithm for computing the spherical harmonic components of data represented on a cubic grid. I extend Misner s original analysis by making detailed error estimates of the numerical errors accrued by the algorithm, by using symmetry arguments to suggest a more efficient implementation scheme, and by explaining how the algorithm can be applied efficiently on data with explicit reflection symmetries.

  3. An overview of the Normal Ogive Harmonic Analysis Robust Method (NOHARM approach to item response theory

    Lee, J. J.


    Full Text Available Here we provide a description of the IRT estimation method known as Normal Ogive Harmonic Analysis Robust Method (NOHARM. Although in some ways this method has been superseded by new computer programs that also adopt a specifically factor-analytic approach, its fundamental principles remain useful in certain applications, which include calculating the residual covariance matrix and rescaling the distribution of the common factor (latent trait. These principles can be applied to parameter estimates obtained by any method.

  4. Mathematical methods of analysis of biopolymer sequences

    Gindikin, S G


    This collection contains papers by participants in the seminar on mathematical methods in molecular biology who worked for several years at the Laboratory of Molecular Biology and Bioorganic Chemistry (now the Institute of Physical and Chemical Problems in Biology) at Moscow State University. The seminar united mathematicians and biologists around the problems of biological sequences. The collection includes original results as well as expository material and spans a range of perspectives, from purely mathematical problems to algorithms and their computer realizations. For this reason, the book is of interest to mathematicians, statisticians, biologists, and computational scientists who work with biopolymer sequences.

  5. Mathematical principles of signal processing Fourier and wavelet analysis

    Brémaud, Pierre


    Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...


    郭定和; 吴学谋; 冯向军; 李永礼


    Based on new analysis modes and new definitions with relative mathematization and simplification or strengthening forms for concepts of generalized systems,panderivatives , pansymmetry , panbox principle, pansystems relativity, etc. , the framework and related principles of pansystems methodology and pansystems relativity are developed. Related contents include: pansystems with relatively universal mathematizing forns, 200 types of dualities, duality transformation, pansymmetry transformation,pansystems dialectics, the 8-domain method, pansystems mathematical methods,generalized quantification, the principles of approximation-transforming, pan-equivalence theorems , supply-demand analysis, thinking experiment, generalized gray systems, etc.

  7. Harmonic analysis of AC/DC systems based on phase-domain multi-port network approach

    Gutierrez, O.; Fuerte-Esquivel, C.R. [Universidad Michoacana de San Nicolas de Hidalgo, Facultad de Ingenieria Electrica, Division de Estudios de Posgrado, Cuidad Universitaria, 58030 Morelia, Michoacan (Mexico); Rubio, J.A.; Guardado, J.L. [Instituto Tecnologico de Morelia, Av. Tecnologico 1500, 58120 Morelia, Michoacan (Mexico)


    This paper describes a phase-domain frequency domain technique to the harmonic analysis of a three-phase AC/DC system. The methodology is based on the harmonic multi-port network concept, expressed in terms of an ABCD parameter matrix which links voltage and current harmonics of different orders on both sides of the converter. Since the commutation angles are unknown, the harmonic interactions are computed by a sequential solution of the AC/DC system state variables, related by the ABCD matrix, and the updating of the commutation periods. A set of analytical equations has been derived to compute commutation times taking place in the converter. Test results are presented which demonstrate the effectiveness of the proposed methodology to assess harmonic interactions on both balanced and unbalanced operating conditions. The results are validated to those obtained by a time domain simulation. (author)

  8. Mathematical modeling models, analysis and applications

    Banerjee, Sandip


    ""…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses.""-Svitlana P. Rogovchenko, Zentralblatt MATH 1298

  9. Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems

    Khajah, Tahsin; Bordas, Stéphane P A


    We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical results performed with high-order basis functions (third or fourth orders) showed no visible pollution error even for very high frequencies. This property combined with exact geometrical representation makes isogeometric analysis a very promising platform to solve high-frequency acoustic problems.

  10. Topics in algebra and analysis preparing for the mathematical olympiad

    Bulajich Manfrino, Radmila; Valdez Delgado, Rogelio


    The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world. In the first four chapters the authors cover material for competitions at high school level. The level advances with the chapters. The topics explored include polynomials, functional equations, sequences and an elementary treatment of complex numbers. The final chapters provide a comprehensive list of problems posed at national and international contests in recent years, and solutions to all exercises and problems presented in the book. It helps students in preparing for national and international mathematical contests form high school level to more advanced competitions and will also be useful for their first year of mathematical studies at the university. It will be of interest to teachers in college and university level, and trainers of the mathematical Olympiads.

  11. Harmonic d-tensors

    Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)


    Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

  12. A method for the harmonic removal in operational modal analysis of rotating blades

    Agneni, Alessandro; Coppotelli, Giuliano; Grappasonni, Chiara


    The operational modal analysis, OMA, allows estimating the dynamic properties of a structure, natural frequencies, damping ratios, and mode shapes, without measuring the input forces. According to the main hypothesis concerning the input excitation, i.e., stochastic with frequency independent spectra (at least in the frequency band of interest), it is not theoretically possible to apply the OMA procedures in structures characterized by the presence of harmonic components in the excitation loading. In this paper, an approach capable to identify the presence of harmonic excitations, acting together with a broad band stochastic loading, and then to remove their effects in the modal parameter estimate is presented. The approach is based on the joint use of the statistical parameter called "entropy" and the already developed output-only procedure based on the application of the Hilbert transform properties to the output response signals. The capability to improve the OMA procedures is investigated numerically and through whirl tower experimental tests of a rotating blade in which both stochastic and harmonic contributions to the dynamic excitations have been provided by the perturbations arising from the operative conditions. A sensitivity analysis has been also performed to evaluate the effects of the filtered responses, in the time domain, on the statistical characterization, required to distinguish the operational frequencies from the natural ones.

  13. The Modeling and Harmonic Coupling Analysis of Multiple-Parallel Connected Inverter Using Harmonic State Space (HSS)

    Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth;


    be difficult in terms of complex multi-parallel connected systems, especially in the case of renewable energy, where possibilities for intermittent operation due to the weather conditions exist. Hence, it can bring many different operating points to the power converter, and the impedance characteristics can...... change compared to the conventional operation. In this paper, a Harmonic State Space modeling method, which is based on the Linear Time varying theory, is used to analyze different operating points of the parallel connected converters. The analyzed results show that the HSS modeling approach explicitly...

  14. Inter-annual variation of NDVI over Korea Peninsula using harmonic analysis

    Kim, In-hwan; Han, Kyung-Soo; Pi, Kyoung-Jin; Park, Soo-Jae; Kim, Sang-Il


    Global warming and climatic changes due to human activities impact on marine and terrestrial ecosystems, which feedbacks to climate system. These negative feedbacks amplify or accelerate again global climate change. In particular, life cycle of vegetation sensitively vary according to global climate change. This study attempts to analyze quantitatively vegetation change in Korea peninsula using harmonic analysis. Satellite data was extracted from SPOT/VEGETATION S10 MVC (Maximum Value Composite) NDVI (Normalized Difference Vegetation Index) products during 10 years (1999 to 2008) around Korea peninsula. This NDVI data set was pre-processed to correct noise pixels cause by cloud and ground wetness. Variation of vegetation life cycle was analyzed through amplitudes and phases of annual harmonic components (first harmonic components) per year for two land cover types (cropland and forest). The results clearly show that the peak of vegetation life cycle in Korea peninsula is brought forward to early. Especially, it represents that the phases over low latitudes area between 32.8°N and 38°N steadily decrease every year both forest and cropland. The study estimated that phase values moved up approximately 0.5 day per year in cropland and 0.8 day per year in forest.

  15. Tax harmonization in the European Union and the eurozone: a multilateral analysis of tax systems

    Sonja Engeli Pippin


    Full Text Available This exploratory study takes a new look at the tax systems of countries in the Organisation of Economic Co-operation and Development (OECD. We measure a country’s tax system using time-series cross-sectional data on tax collection variables as well as a cross-sectional metric assessing tax administration and enforcement. More specifically, we examine the countries’ (i overall tax burden, (ii income tax reliance, and (iii fiscal decentralization as well as some “non-rate” variables related to tax administration and enforcement. The purpose is to compare European Union (EU member states and those countries in the eurozone with other OECD countries and over time in order to test (1 whether EU member states and eurozone countries have tax systems that are more similar to each other than to other countries, and (2 whether some tax harmonization is taking place - within the EU (eurozone and other countries. The descriptive analysis and graphical representation, as well as first empirical tests, show that the tax systems of EU member states and eurozone countries are significantly different from other countries’tax systems. Yet, we do not find much tax harmonization in the EU (eurozone countries over time. Future research might delve more into the question what drives harmonization with the intention of eventually formulating policy strategies.

  16. Geometry, analysis, and computation in mathematics and applied sciences. Final report

    Kusner, R.B.; Hoffman, D.A.; Norman, P.; Pedit, F.; Whitaker, N.; Oliver, D.


    Since 1993, the GANG laboratory has been co-directed by David Hoffman, Rob Kusner and Peter Norman. A great deal of mathematical research has been carried out here by them and by GANG faculty members Franz Pedit and Nate Whitaker. Also new communication tools, such as the GANG Webserver have been developed. GANG has trained and supported nearly a dozen graduate students, and at least half as many undergrads in REU projects.The GANG Seminar continues to thrive, making Amherst a site for short and long term visitors to come to work with the GANG. Some of the highlights of recent or ongoing research at GANG include: CMC surfaces, minimal surfaces, fluid dynamics, harmonic maps, isometric immersions, knot energies, foam structures, high dimensional soap film singularities, elastic curves and surfaces, self-similar curvature evolution, integrable systems and theta functions, fully nonlinear geometric PDE, geometric chemistry and biology. This report is divided into the following sections: (1) geometric variational problems; (2) soliton geometry; (3) embedded minimal surfaces; (4) numerical fluid dynamics and mathematical modeling; (5) GANG graphics and mathematical software; (6) description of the computational and visual analysis facility; and (7) research by undergraduates and GANG graduate seminar.

  17. Harmonic function theory

    Axler, Sheldon; Ramey, Wade


    This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.

  18. Harmonic analysis of DC capacitor current in sinusoidal and space-vector modulated neutral-point-clamped inverters

    Gopalakrishnan K S; G Narayanan


    The voltage ripple and power loss in the DC-capacitor of a voltage source inverter depend on the harmonic currents flowing through the capacitor. This paper presents a double Fourier series based analysis of the harmonic contents of the DC capacitor current in a three-level neutral-point clamped (NPC) inverter, modulated with sine-triangle pulse-width modulation (SPWM) or conventional space vector pulse-width modulation (CSVPWM) schemes. The analytical results are validated experimentally on a 3-kVA three-level inverter prototype. The capacitor current in an NPC inverter has a periodicity of 120º at the fundamental or modulation frequency. Hence, this current contains third-harmonic and triplen-frequency components, apart from switching frequency components. The harmonic components vary with modulation index and power factor for both PWM schemes. The third harmonic current decreases with increase in modulation index and also decreases with increase in power factor in case of both PWM methods. In general, the third harmonic content is higher with SPWM than with CSVPWM at a given operating condition. Also, power loss and voltage ripple in the DC capacitor are estimated for both the schemes using the current harmonic spectrum and equivalent series resistance (ESR) of the capacitor.

  19. Functional analysis in modern applied mathematics

    Curtain, Ruth F


    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

  20. Mathematical analysis of multi-antibiotic resistance.

    Zhao, Bin; Zhang, Xiaoying


    Multi-antibiotic resistance in bacterial infections is a growing threat to public health. Some experiments were carried out to study the multi-antibiotic resistance. The changes of the multi-antibiotic resistance with time were achieved by numerical simulations and the mathematical models, with the calculated temperature field, velocity field, and the antibiotic concentration field. The computed results and experimental results are compared. Both numerical simulations and the analytic models suggest that minor low concentrations of antibiotics could induce antibiotic resistance in bacteria. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

  1. Mathematical Analysis of the BIBEE Approximation for Molecular Solvation: Exact Results for Spherical Inclusions

    Bardhan, Jaydeep P


    We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to Generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GB$\\epsilon$ theory suggests a modified BI...

  2. Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

    Alama, Jesse; Tsivtsivadze, Evgeni; Urban, Josef; Heskes, Tom


    Smart premise selection is essential when using automated reasoning as a tool for large-theory formal verification, formal proof development, and experimental reverse mathematics. A strong method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing new precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a new benchmark consisting of 2078 large-theory mathematical problems is constructed, extending the older MPTP Challenge benchmark. The combined effect of the both techniques developed shows 40% improvement on t...

  3. Multiple harmonic ULF waves in the plasma sheet boundary layer: Instability analysis

    Denton, R. E.; Engebretson, M. J.; Keiling, A.; Walsh, A. P.; Gary, S. P.; DéCréAu, P. M. E.; Cattell, C. A.; RèMe, H.


    Multiple-harmonic electromagnetic waves in the ULF band have occasionally been observed in Earth's magnetosphere, both near the magnetic equator in the outer plasmasphere and in the plasma sheet boundary layer (PSBL) in Earth's magnetotail. Observations by the Cluster spacecraft of multiple-harmonic electromagnetic waves with fundamental frequency near the local proton cyclotron frequency, Ωcp, were recently reported in the plasma sheet boundary layer by Broughton et al. (2008). A companion paper surveys the entire magnetotail passage of Cluster during 2003, and reports 35 such events, all in the PSBL, and all associated with elevated fluxes of counterstreaming ions and electrons. In this study we use observed pitch angle distributions of ions and electrons during a wave event observed by Cluster on 9 September 2003 to perform an instability analysis. We use a semiautomatic procedure for developing model distributions composed of bi-Maxwellian components that minimizes the difference between modeled and observed distribution functions. Analysis of wave instability using the WHAMP electromagnetic plasma wave dispersion code and these model distributions reveals an instability near Ωcp and its harmonics. The observed and model ion distributions exhibit both beam-like and ring-like features which might lead to instability. Further instability analysis with simple beam-like and ring-like model distribution functions indicates that the instability is due to the ring-like feature. Our analysis indicates that this instability persists over an enormous range in the effective ion beta (based on a best fit for the observed distribution function using a single Maxwellian distribution), β', but that the character of the instability changes with β'. For β' of order unity (for instance, the observed case with β' ˜ 0.4), the instability is predominantly electromagnetic; the fluctuating magnetic field has components in both the perpendicular and parallel directions, but the

  4. Pythagorean Triples from Harmonic Sequences.

    DiDomenico, Angelo S.; Tanner, Randy J.


    Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)

  5. Analysis of mathematical modelling on potentiometric biosensors.

    Mehala, N; Rajendran, L


    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

  6. Bladed wheels damage detection through Non-Harmonic Fourier Analysis improved algorithm

    Neri, P.


    Recent papers introduced the Non-Harmonic Fourier Analysis for bladed wheels damage detection. This technique showed its potential in estimating the frequency of sinusoidal signals even when the acquisition time is short with respect to the vibration period, provided that some hypothesis are fulfilled. Anyway, previously proposed algorithms showed severe limitations in cracks detection at their early stage. The present paper proposes an improved algorithm which allows to detect a blade vibration frequency shift due to a crack whose size is really small compared to the blade width. Such a technique could be implemented for condition-based maintenance, allowing to use non-contact methods for vibration measurements. A stator-fixed laser sensor could monitor all the blades as they pass in front of the spot, giving precious information about the wheel health. This configuration determines an acquisition time for each blade which become shorter as the machine rotational speed increases. In this situation, traditional Discrete Fourier Transform analysis results in poor frequency resolution, being not suitable for small frequency shift detection. Non-Harmonic Fourier Analysis instead showed high reliability in vibration frequency estimation even with data samples collected in a short time range. A description of the improved algorithm is provided in the paper, along with a comparison with the previous one. Finally, a validation of the method is presented, based on finite element simulations results.

  7. Second order harmonic guided wave mutual interactions in plate: Vector analysis, numerical simulation, and experimental results

    Hasanian, Mostafa; Lissenden, Cliff J.


    The extraordinary sensitivity of nonlinear ultrasonic waves to the early stages of material degradation makes them excellent candidates for nondestructive material characterization. However, distinguishing weak material nonlinearity from instrumentation nonlinearity remains problematic for second harmonic generation approaches. A solution to this problem is to mix waves having different frequencies and to let their mutual interaction generate sum and difference harmonics at frequencies far from those of the instrumentation. Mixing of bulk waves and surface waves has been researched for some time, but mixing of guided waves has not yet been investigated in depth. A unique aspect of guided waves is their dispersive nature, which means we need to assure that a wave can propagate at the sum or difference frequency. A wave vector analysis is conducted that enables selection of primary waves traveling in any direction that generate phase matched secondary waves. We have tabulated many sets of primary waves and phase matched sum and difference harmonics. An example wave mode triplet of two counter-propagating collinear shear horizontal waves that interact to generate a symmetric Lamb wave at the sum frequency is simulated using finite element analysis and then laboratory experiments are conducted. The finite element simulation eliminates issues associated with instrumentation nonlinearities and signal-to-noise ratio. A straightforward subtraction method is used in the experiments to identify the material nonlinearity induced mutual interaction and show that the generated Lamb wave propagates on its own and is large enough to measure. Since the Lamb wave has different polarity than the shear horizontal waves the material nonlinearity is clearly identifiable. Thus, the mutual interactions of shear horizontal waves in plates could enable volumetric characterization of material in remote regions from transducers mounted on just one side of the plate.

  8. Frequency Response Analysis of Current Controllers for Selective Harmonic Compensation in Active Power Filters

    Lascu, C.; Asiminoaei, L.; Boldea, I.;


    This paper compares four current control structures for selective harmonic compensation in active power filters. All controllers under scrutiny perform the harmonic compensation by using arrays of resonant controllers, one for the fundamental and one for each harmonic of interest, in order to ach...

  9. Numerical and experimental analysis of harmonic distortion in a moving-coil loudspeaker

    Chang, Chun; Wang, Chi-Chang; Shiah, Y. C.; Huang, Jin H.


    The nonlinear effect of a moving-coil loudspeaker, originating from its magnetic coupling factor and the system's stiffness, presents a significant impact on the sound quality. For improving the sound quality, this article proposes an approach to reduce the total harmonic distortion (THD) by adjusting the initial position of its voice-coil. First, a mathematical model involving the nonlinearities of force factor, mechanical stiffness, and inductance of voice coil is constructed and then solved using a novel algorithm called the parameter spline difference method (PSD). In the course of pursuing reduction of the corresponding THD of a typical moving-coil loudspeaker, the model was used to analyze the nonlinearity of the THD, revealing itself as a nonlinear function of force factor, the system's stiffness and inductance of voice coil. For various initial positions of the voice-coil, the coupled nonlinear differential equations were solved using the PSD to yield corresponding sound pressure level and THD. To our satisfaction, the loudspeaker driver with its voice-coil optimally tuned for the initial position turns out to have a THD reduction of 10%, which is also consistent with our experimental observations.

  10. Scaling of mode shapes from operational modal analysis using harmonic forces

    Brandt, A.; Berardengo, M.; Manzoni, S.; Cigada, A.


    This paper presents a new method for scaling mode shapes obtained by means of operational modal analysis. The method is capable of scaling mode shapes on any structure, also structures with closely coupled modes, and the method can be used in the presence of ambient vibration from traffic or wind loads, etc. Harmonic excitation can be relatively easily accomplished by using general-purpose actuators, also for force levels necessary for driving large structures such as bridges and highrise buildings. The signal processing necessary for mode shape scaling by the proposed method is simple and the method can easily be implemented in most measurement systems capable of generating a sine wave output. The tests necessary to scale the modes are short compared to typical operational modal analysis test time. The proposed method is thus easy to apply and inexpensive relative to some other methods for scaling mode shapes that are available in literature. Although it is not necessary per se, we propose to excite the structure at, or close to, the eigenfrequencies of the modes to be scaled, since this provides better signal-to-noise ratio in the response sensors, thus permitting the use of smaller actuators. An extensive experimental activity on a real structure was carried out and the results reported demonstrate the feasibility and accuracy of the proposed method. Since the method utilizes harmonic excitation for the mode shape scaling, we propose to call the method OMAH.

  11. Electrical Rhythms Revealed by Harmonic Analysis of a High-Resolution Cardiogram.

    Revenko, S V; Selector, L Ya; Gavrilov, I Yu; Nesterov, A V; Limonov, E V; Mudraya, I S; Kirpatovskii, V I


    The front-end low-noise electronic amplifiers and high-throughput computing systems made it possible to record ECG with a high resolution in the low-frequency range including the respiration and Mayer frequencies and to analyze ECG with digital filtering technique and harmonic analysis. These tools yielded ECG spectra of narcotized rats, which contained the characteristic pulsatile triplets and pentaplets with splitting constant equal to respiration rate, as well as the peaks at respiration and Mayer frequencies. The harmonic analysis of ECG determined the frequency parameters employed to tune the software bandpass filters, which revealed the respiratory (R) and Mayer (M) waves in the time domain with the amplitudes of 20-30 μV amounting to 5% ECG amplitude. The depolarizing myorelaxant succinylcholine chloride capable to trigger various types of arrhythmias, transiently increased R-wave, inhibited M-wave, and provoked a negative U-wave within a heartbeat ECG cycle synchronously with inspiration. It is hypothesized that M-, R-, and U-waves in ECG reflect cardiotropic activity of autonomic nervous system. The respective spectral peaks in ECG can be employed to assess intensity of sympathetic and parasympathetic cardiotropic influences, their balance, and the risk of arrhythmias.

  12. Functional Analysis in Applied Mathematics and Engineering

    Pedersen, Michael


    Lecture notes for the course 01245 Functional Analysis. Consists of the first part of amonograph with the same title.......Lecture notes for the course 01245 Functional Analysis. Consists of the first part of amonograph with the same title....

  13. General Mission Analysis Tool (GMAT) Mathematical Specifications

    Hughes, Steve


    The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development.

  14. Mathematical methods in time series analysis and digital image processing

    Kurths, J; Maass, P; Timmer, J


    The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences. In particular, mathematically justified algorithms and methods, the mathematical analysis of these algorithms, and methods as well as the investigation of connections between methods from time series analysis and image processing are reviewed. An interdisciplinary comparison of these methods, drawing upon common sets of test problems from medicine and geophysical/enviromental sciences, is also addressed. This volume coherently summarizes work carried out in the field of theoretical signal and image processing. It focuses on non-linear and non-parametric models for time series as well as on adaptive methods in image processing.

  15. A Mathematical Analysis of Conflict Prevention Information

    Maddalon, Jeffrey M.; Butler, Ricky W.; Munoz, Cesar A.; Dowek, Gilles


    In air traffic management, conflict prevention information refers to the guidance maneuvers, which if taken, ensure that an aircraft's path is conflict-free. These guidance maneuvers take the form of changes to track angle or ground speed. Conflict prevention information may be assembled into prevention bands that advise the crew on maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for any maneuver, giving the pilot confidence that if a maneuver is made, then no near-term conflicts will result. Because near-term conflicts can lead to safety concerns, strong verification of information correctness is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information incorporating an arbitrary number of traffic aircraft and with both a near-term and intermediate-term lookahead times. The framework is illustrated with a formally verified algorithm for 2-dimensional track angle prevention bands.

  16. Aeroelastic analysis for helicopter rotors with blade appended pendulum vibration absorbers. Mathematical derivations and program user's manual

    Bielawa, R. L.


    Mathematical development is presented for the expanded capabilities of the United Technologies Research Center (UTRC) G400 Rotor Aeroelastic Analysis. This expanded analysis, G400PA, simulates the dynamics of teetered rotors, blade pendulum vibration absorbers and the higher harmonic excitations resulting from prescribed vibratory hub motions and higher harmonic blade pitch control. Formulations are also presented for calculating the rotor impedance matrix appropriate to these higher harmonic blade excitations. This impedance matrix and the associated vibratory hub loads are intended as the rotor blade characteristics elements for use in the Simplified Coupled Rotor/Fuselage Vibration Analysis (SIMVIB). Sections are included presenting updates to the development of the original G400 theory, and material appropriate to the user of the G400PA computer program. This material includes: (1) a general descriptionof the tructuring of the G400PA FORTRAN coding, (2) a detaild description of the required input data and other useful information for successfully running the program, and (3) a detailed description of the output results.

  17. A Comparative Analysis of Elementary Mathematics Teachers’ Examination Questions And SBS Mathematics Questions According To Bloom’s Taxonomy


    This study has been planned for the purpose of comparative analysis of examination questions of elementary mathematics teachers and mathematics questions of Placement Examination (SBS) for 6th, 7th and 8th grades in 2010 in terms of Bloom’s Taxonomy. Document analysis method was used in this study. Accordingly, 715 examination questions mathematics teachers working in 12 different primary schools asked in 2009-2010 academic year and 54 mathematics questions for 6th, 7th and 8th grades in SBS ...

  18. Gaussian-Schell analysis of the transverse spatial properties of high-harmonic beams

    Lloyd, David T; Anderson, Patrick N; Hooker, Simon M


    High harmonic generation (HHG) is an established means of producing coherent, short wavelength, ultrafast pulses from a compact set-up. Table-top high-harmonic sources are increasingly being used to image physical and biological systems using emerging techniques such as coherent diffraction imaging and ptychography. These novel imaging methods require coherent illumination, and it is therefore important to both characterize the spatial coherence of high-harmonic beams and understand the processes which limit this property. Here we investigate the near- and far-field spatial properties of high-harmonic radiation generated in a gas cell. The variation with harmonic order of the intensity profile, wavefront curvature, and complex coherence factor is measured in the far-field by the SCIMITAR technique. Using the Gaussian-Schell model, the properties of the harmonic beam in the plane of generation are deduced. Our results show that the order-dependence of the harmonic spatial coherence is consistent with partial c...

  19. STEM: Science Technology Engineering Mathematics. State-Level Analysis

    Carnevale, Anthony P.; Smith, Nicole; Melton, Michelle


    The science, technology, engineering, and mathematics (STEM) state-level analysis provides policymakers, educators, state government officials, and others with details on the projections of STEM jobs through 2018. This report delivers a state-by-state snapshot of the demand for STEM jobs, including: (1) The number of forecast net new and…

  20. Professional Development for Mathematics Teachers: Using Task Design and Analysis

    Lee, Hea-Jin; Özgün-Koca, S. Asli


    This study is based on a Task Design and Analysis activity from a year-long professional development program. The activity was designed to increase teacher growth in several areas, including knowledge of mathematics, understanding of students' cognitive activity, knowledge of good questions, and ability to develop and improve high quality tasks.…

  1. Tension between Intuitive Infinitesimals and Formal Mathematical Analysis

    Katz, Mikhail G


    We discuss the repercussions of the development of infinitesimal calculus into modern analysis, beginning with viewpoints expressed in the nineteenth and twentieth centuries and relating them to the natural cognitive development of mathematical thinking and imaginative visual interpretations of axiomatic proof.

  2. Making Culturally Responsive Mathematics Teaching Explicit: A Lesson Analysis Tool

    Aguirre, Julia M.; Zavala, Maria del Rosario


    In the United States, there is a need for pedagogical tools that help teachers develop essential pedagogical content knowledge and practices to meet the mathematical education needs of a growing culturally and linguistically diverse student population. In this article, we introduce an innovative lesson analysis tool that focuses on integrating…

  3. Making Culturally Responsive Mathematics Teaching Explicit: A Lesson Analysis Tool

    Aguirre, Julia M.; Zavala, Maria del Rosario


    In the United States, there is a need for pedagogical tools that help teachers develop essential pedagogical content knowledge and practices to meet the mathematical education needs of a growing culturally and linguistically diverse student population. In this article, we introduce an innovative lesson analysis tool that focuses on integrating…

  4. [Mathematics - astronomy - astrology special library].

    Gluch, Sibylle


    About 1560 Elector August of Saxony created an unusual library--one distinguished within its period by both its specialization and location. Situated within the Kunstkammer this library was mostly dedicated to the mathematical sciences and related disciplines. It contained works by the most important authors on mathematics, astronomy, and astrology from the classical, medieval, and early modern periods. This essay traces the formation and composition of August's library, and examines its function: What kind of relationship existed between the library and the Kunstkammer? In what way did the library mirror the interests of the Elector, and to what extend does it permit inferences regarding the Elector's knowledge of mathematics? From the analysis August emerges not as a specialist with a deep understanding of mathematics, but as a particular aficionado of mathematical applications. As a practitioner and general follower of the mathematical arts he took part in a far-reaching intellectual network the center of which lay in the University of Wittenberg. Here, Melanchthon had effectively strengthened the importance of the mathematical disciplines within the university curriculum. He regarded mathematics as the foremost science, arguing that before all other disciplines its method enabled man to recognize the harmonic order of the world, and to discern divine providence. Thus, mathematics offered consoling stability and support in an often seemingly chaotic world torn by religious controversies. This kind of esteem for the mathematical sciences did not presuppose expert knowledge. Hence, the fact that August does not appear to have read the mathematical books he collected does not come as a contradiction. On the contrary, for August it sufficed to recognize the potential of the mathematical sciences, which he brought into life through the creation of a specialized library that developed a rhetoric of its own. The collection of his Kunstkammer library spoke of a

  5. Resolution-Enhanced Harmonic and Interharmonic Measurement for Power Quality Analysis in Cyber-Physical Energy System.

    Liu, Yanchi; Wang, Xue; Liu, Youda; Cui, Sujin


    Power quality analysis issues, especially the measurement of harmonic and interharmonic in cyber-physical energy systems, are addressed in this paper. As new situations are introduced to the power system, the impact of electric vehicles, distributed generation and renewable energy has introduced extra demands to distributed sensors, waveform-level information and power quality data analytics. Harmonics and interharmonics, as the most significant disturbances, require carefully designed detection methods for an accurate measurement of electric loads whose information is crucial to subsequent analyzing and control. This paper gives a detailed description of the power quality analysis framework in networked environment and presents a fast and resolution-enhanced method for harmonic and interharmonic measurement. The proposed method first extracts harmonic and interharmonic components efficiently using the single-channel version of Robust Independent Component Analysis (RobustICA), then estimates the high-resolution frequency from three discrete Fourier transform (DFT) samples with little additional computation, and finally computes the amplitudes and phases with the adaptive linear neuron network. The experiments show that the proposed method is time-efficient and leads to a better accuracy of the simulated and experimental signals in the presence of noise and fundamental frequency deviation, thus providing a deeper insight into the (inter)harmonic sources or even the whole system.

  6. Ten mathematical essays on approximation in analysis and topology

    López-Gómez, J; Ruiz del Portal, F R


    This book collects 10 mathematical essays on approximation in Analysis and Topology by some of the most influent mathematicians of the last third of the 20th Century. Besides the papers contain the very ultimate results in each of their respective fields, many of them also include a series of historical remarks about the state of mathematics at the time they found their most celebrated results, as well as some of their personal circumstances originating them, which makes particularly attractive the book for all scientist interested in these fields, from beginners to experts. These gem pieces

  7. Mathematical analysis of a Vuilleumier refrigerator.

    Sherman, A.


    A comprehensive analysis of the Vuilleumier refrigerator was conducted. This analysis includes the effects of nonisothermal gas heat addition and rejection, hot and cold regenerator inefficiencies, conduction losses, and gas leakage losses. A computer program was written which solves the equations resulting from the analysis. The program calculates internal pressures, temperatures, and gas flow rates as functions of refrigerator crank angle, as well as overall refrigerator cooling load and power input. Comparisons between the program results and available data show good agreement, with a marked improvement over the predictions of the ideal model.

  8. Mathematics for the analysis of algorithms

    Greene, Daniel H


    This monograph, derived from an advanced computer science course at Stanford University, builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions. The authors cover recurrence relations, operator methods, and asymptotic analysis in a format that is terse enough for easy reference yet detailed enough for those with little background. Approximately half the book is devoted to original problems and solutions from examinations given at Stanford.

  9. Mathematical analysis of a Vuilleumier refrigerator.

    Sherman, A.


    A comprehensive analysis of the Vuilleumier refrigerator was conducted. This analysis includes the effects of nonisothermal gas heat addition and rejection, hot and cold regenerator inefficiencies, conduction losses, and gas leakage losses. A computer program was written which solves the equations resulting from the analysis. The program calculates internal pressures, temperatures, and gas flow rates as functions of refrigerator crank angle, as well as overall refrigerator cooling load and power input. Comparisons between the program results and available data show good agreement, with a marked improvement over the predictions of the ideal model.

  10. Harmonic Instability Assessment Using State-Space Modeling and Participation Analysis in Inverter-Fed Power Systems

    Wang, Yanbo; Wang, Xiongfei; Blaabjerg, Frede


    This paper presents a harmonic instability analysis method using state-space modeling and participation analysis in the inverter-fed ac power systems. A full-order state-space model for the droop-controlled Distributed Generation (DG) inverter is built first, including the time delay of the digit...

  11. Nonlinear circuit analysis of harmonic currents in a floating Langmuir probe with a capacitive load

    Kim, Kyung-Hyun; Kim, Dong-Hwan; Chung, Chin-Wook


    Plasma diagnostics using the floating harmonic technique were first used to obtain the electron temperature in a tokamak plasma. In this technique, the electron temperature depends on the ratio of the harmonic currents in a resistive sheath. Because these harmonic currents are determined by a modulated sheath voltage, calculation of the exact modulated voltage across the sheath is important; in general, the voltage is calculated using a phase of the first harmonic current. However, when a series load capacitance is present, the second harmonic currents are abnormally reduced compared to those expected by the conventional floating harmonic model, resulting in an unreliable measurement of the electron temperature. To describe this phenomenon, we used a modified floating harmonic model by applying the harmonic balance technique, a method that analyzes nonlinear circuits. Theoretical prediction of the harmonic current obtained from the modified model was compared with the experimental results, and they are in good agreement. In addition, the degrees of sheath nonlinearity, defined as the ratio of the second harmonic current (or voltage) to the fundamental current (or voltage), are discussed.

  12. Quantitative analysis for harmonic responsibility proration among multiple harmonic sources%多谐波源用户的谐波责任分摊的定量分析

    许加柱; 庞丽忠; 张志文; 罗隆福; 曾进辉; 曹志煌; 周冠东


    A method of harmonic responsibility proration among multiple harmonic sources (users) is proposed, which apportions the voltage and current harmonics step by step and takes different factors into account,such as filters,initial phase angle and harmonic source amount. Its principle is analyzed,its general mathematical model is established,and the detailed implementation steps are given. A simulation system model with three harmonic sources is established in PSCAD and the impact of filter operation on harmonic responsibility proportion is analyzed. Results indicate that,the proposed method apportions well the harmonic responsibility among multiple users,with greatly improved accuracy.%提出了一种分步分摊电压电流的谐波责任分摊方法.在考虑滤波器、谐波电压和谐波电流初相角、谐波源用户数目等因素的基础上,对该方法的分摊原理进行了分析,建立了多谐波源用户的谐波电压和电流责任分摊的通用数学模型,并给出了详细的实施步骤;最后,以某3谐波源用户系统为例,建立了PSCAD仿真模型,仿真分析了滤波器投入对谐波责任分摊的影响;结果表明所提方法可很好地分摊多谐波源用户间的谐波责任,大幅提高了谐波责任分摊的精确性.

  13. Phase-shifting algorithms for a finite number of harmonics: first-order analysis by solving linear systems.

    Téllez-Quiñones, Alejandro; Malacara-Doblado, Daniel; García-Márquez, Jorge


    From generalized phase-shifting equations, we propose a simple linear system analysis for algorithms with equally and nonequally spaced phase shifts. The presence of a finite number of harmonic components in the fringes of the intensity patterns is taken into account to obtain algorithms insensitive to these harmonics. The insensitivity to detuning for the fundamental frequency is also considered as part of the description of this study. Linear systems are employed to recover the desired insensitivity properties that can compensate linear phase shift errors. The analysis of the wrapped phase equation is carried out in the Fourier frequency domain.

  14. The Harmonic Response Analysis with Acoustic-vibration Coupling of the Combustion Chamber under Different Combustion Conditions

    Zheng Min


    Full Text Available In this paper, numerical calculations of harmonic response with acoustic-vibration coupling of the combustion chamber under different combustion conditions has been performed by combining CFD and FEM methods. Temperature and sound pressure fields created by the flame in the combustion chamber are calculated first. And then the results of the CFD are exported to the FEM analysis for the interaction between acoustic waves and wall vibrations. The possible acoustic-vibration coupled eigenfrequencies at given combustion conditions are predicted by the harmonic response analysis.

  15. Wavelet methods in mathematical analysis and engineering

    Damlamian, Alain


    This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a stateoftheart in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective. The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented.

  16. Attitude Determination Error Analysis System (ADEAS) mathematical specifications document

    Nicholson, Mark; Markley, F.; Seidewitz, E.


    The mathematical specifications of Release 4.0 of the Attitude Determination Error Analysis System (ADEAS), which provides a general-purpose linear error analysis capability for various spacecraft attitude geometries and determination processes, are presented. The analytical basis of the system is presented. The analytical basis of the system is presented, and detailed equations are provided for both three-axis-stabilized and spin-stabilized attitude sensor models.

  17. Higher harmonic control analysis for vibration reduction of helicopter rotor systems

    Nguyen, Khanh Q.


    An advanced higher harmonic control (HHC) analysis has been developed and applied to investigate its effect on vibration reduction levels, blade and control system fatigue loads, rotor performance, and power requirements of servo-actuators. The analysis is based on a finite element method in space and time. A nonlinear time domain unsteady aerodynamic model, based on the indicial response formulation, is used to calculate the airloads. The rotor induced inflow is computed using a free wake model. The vehicle trim controls and blade steady responses are solved as one coupled solution using a modified Newton method. A linear frequency-domain quasi-steady transfer matrix is used to relate the harmonics of the vibratory hub loads to the harmonics of the HHC inputs. Optimal HHC is calculated from the minimization of the vibratory hub loads expressed in term of a quadratic performance index. Predicted vibratory hub shears are correlated with wind tunnel data. The fixed-gain HHC controller suppresses completely the vibratory hub shears for most of steady or quasi-steady flight conditions. HHC actuator amplitudes and power increase significantly at high forward speeds (above 100 knots). Due to the applied HHC, the blade torsional stresses and control loads are increased substantially. For flight conditions where the blades are stalled considerably, the HHC input-output model is quite nonlinear. For such cases, the adaptive-gain controller is effective in suppressing vibratory hub loads, even though HHC may actually increase stall areas on the rotor disk. The fixed-gain controller performs poorly for such flight conditions. Comparison study of different rotor systems indicates that a soft-inplane hingeless rotor requires less actuator power at high speeds (above 130 knots) than an articulated rotor, and a stiff-inplane hingeless rotor generally requires more actuator power than an articulated or a soft-inplane hingeless rotor. Parametric studies for a hingeless rotor

  18. Mathematical Model For Engineering Analysis And Optimization

    Sobieski, Jaroslaw


    Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.

  19. Mathematical Model For Engineering Analysis And Optimization

    Sobieski, Jaroslaw


    Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.

  20. Neighborhood structure effects on the Dynamic response of soil-structure interaction by harmonic analysis

    Pan Dan-guang


    Full Text Available For realizing the variation of structural dynamic characteristics due to neighbor structure in buildings group, the surface structure is idealized as an equivalent single degree of freedom system with rigid base whose site consists of a single homogeneous layer. Based on the model, a equivalent method on the equivalent seismic excitation is proposed. Then, the differences of seismic response and equivalent seismic input between soil - structure interaction (SSI system and structure -soil-structure interaction (SSSI system are investigated by harmonic analysis. The numerical results show that dynamic responses would be underestimated in SSSI system when the forcing frequencies are close to the Natural frequency if the effects of neighborhood structure were ignored. Neighborhood structure would make the translational displacement increase and rocking vibration decrease. When establishing an effective seismic input, it is necessary to consider the impact of inertia interaction.

  1. Analysis of stationary displacement patterns in rotating machinery subject to local harmonic excitation

    Österlind, Tomas; Kari, Leif; Nicolescu, Cornel Mihai


    Rotor vibration and stationary displacement patterns observed in rotating machineries subject to local harmonic excitation are analysed for improved understanding and dynamic characterization. The analysis stresses the importance of coordinate transformation between rotating and stationary frame of reference for accurate results and estimation of dynamic properties. A generic method which can be used for various rotor applications such as machine tool spindle and turbo machinery vibration is presented. The phenomenon shares similarities with stationary waves in rotating disks though focuses on vibration in shafts. The paper further proposes a graphical tool, the displacement map, which can be used for selection of stable rotational speed for rotating machinery. The results are validated through simulation of dynamic response of a milling cutter, which is a typical example of a variable speed rotor operating under different load conditions.

  2. Modal and harmonic response analysis of cutter head of juice extractor

    Li, Jinkuan; Liu, Zaixin; Zhou, Dingli; Li, Zhao


    A cutter head is one of the most important parts in juice extractor, because whether the juice extractor is reliable or secure enough is directly to the cutter head natural frequency as well as its mode shape size. Cutter head is took as an example in this paper. By establishing the vibration dynamics equations and using finite element method, the 6 modal of the cutter head is analyzed. The range of the rotate speed to keep safety is obtained when it is working. The result shows that the highest rotate speed of the cutter head is far lower than its first order critical speed which avoids the sympathetic vibration efficiently, and the cutter head is designed relatively rational. The harmonic response of the cutter head is analyzed based on the result of modal analysis. The resonant frequency and amplitude of cutter head are obtained. They can provide a theoretical basis for the further design optimization of the cutter head.

  3. Meta-analysis and Harmonization of Life Cycle Assessment Studies for Algae Biofuels.

    Tu, Qingshi; Eckelman, Matthew; Zimmerman, Julie


    Algae biodiesel (BioD) and renewable diesel (RD) have been recognized as potential solutions to mitigating fossil-fuel consumption and the associated environmental issues. Life cycle assessment (LCA) has been used by many researchers to evaluate the potential environmental impacts of these algae-derived fuels, yielding a wide range of results and, in some cases, even differing on indicating whether these fuels are preferred to petroleum-derived fuels or not. This meta-analysis reviews the methodological preferences and results for energy consumption, greenhouse gas emissions, and water consumption for 54 LCA studies that considered algae BioD and RD. The significant variation in reported results can be primarily attributed to the difference in scope, assumptions, and data sources. To minimize the variation in life cycle inventory calculations, a harmonized inventory data set including both nominal and uncertainty data is calculated for each stage of the algae-derived fuel life cycle.

  4. Symmetries and Laplacians introduction to harmonic analysis, group representations and applications

    Gurarie, D


    Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete...

  5. Symmetry Analysis of ZnSe(100) Surface in Air By Second Harmonic Generation

    Song, X; Maripuu, R; Siegbahn, Kai; Song, Xiangyang; Neumann, Arnold; Maripuu, Rein; Siegbahn, Kai


    Polarized and azimuthal dependencies of optical second harmonics generation (SHG) at the surface of noncentrosymmetric semiconductor crystals have been measured on polished surfaces of ZnSe(100), using a fundamental wavelength of 1.06$\\mu m$. The SHG intensity patterns were analyzed for all four combination of p- and s-polarized incidence and output, considering both the bulk and surface optical nonlinearities in the electric dipole approximation. We found that the measurement using $S_{in}-S_{out}$ is particularly useful in determining the symmetry of the oxdized layer interface, which would lower the effective symmetry of the surface from $C_{4v}$ to $C_{2v}.$ We also have shown that the [011] and [0$\\bar{1}$1] directions can be distinguished through the analysis of p-incident and p-output confugration.

  6. Numerical analysis of dynamic force spectroscopy using the torsional harmonic cantilever

    Solares, Santiago D [Department of Mechanical Engineering, University of Maryland, 2181 Glenn L. Martin Hall, College Park, MD 20742 (United States); Hoelscher, Hendrik, E-mail: [Karlsruhe Institute for Technology (KIT), Institute for Microstructure Technology (IMT), Hermann-von Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany)


    A spectral analysis method has been recently introduced by Stark et al (2002 Proc. Natl Acad. Sci. USA 99 8473-8) and implemented by Sahin et al (2007 Nat. Nanotechnol. 2 507-14) using a T-shaped cantilever design, the torsional harmonic cantilever (THC), which is capable of performing simultaneous tapping-mode atomic force microscopy imaging and force spectroscopy. Here we report on numerical simulations of the THC system using a simple dual-mass flexural-torsional model, which is applied in combination with Fourier data processing software to illustrate the spectroscopy process for quality factors corresponding to liquid, air and vacuum environments. We also illustrate the acquisition of enhanced topographical images and deformed surface contours under the application of uniform forces, and compare the results to those obtained with a previously reported linear dual-spring-mass model.

  7. Polarized Light in Random media: a formalism based on non commutative harmonic analysis

    Said, Salem


    This is a note containing the most recent results we have arrived at in our work on polarized light in random media. After an introduction fixing the problem we are dealing with, we start by pointing out the connection between the Poincare sphere formalism and noncommutative harmonic analysis. This leads us to the main equations of our formalism. We use these equation to generalize the notions of Stokes vector, degree of polarization (DOP) and Mueller matrix to higher order statistics of the electric field. We also use them to give a formalism for the propagation of a state of polarisation (SOP) in a random medium. We show how a more detailed description of this propagation is then made possible.

  8. Harmonic Analysis of Seven and Nine Level Cascade Multilevel Inverter using Multi-Carrier PWM Technique

    Chetanya Gupta


    Full Text Available The use of multilevel inverters has become popular in recent years for high-power applications. Multilevel Inverters are power converter systems composed by an array of power semiconductor sources that when properly connected and controlled can generate a multistep voltage waveform with variable and controllable frequency, phase and amplitude. This study deals with the comparison of a 7-level inverter with a 9-level inverter system; the voltage source inverters (VSI are modelled and simulated using MATLAB Simulink and the results are presented. The test results verify the effectiveness of the proposed strategy in terms of computational efficiency as well as the capability of the inverter to produce very low distorted voltage with low-switching losses. This research aims to extend the knowledge about the performance of different clamped multilevel inverter through harmonic analysis. Simulations results validate up to the mark performance of the mentioned topologies.

  9. Analysis of space harmonic selectivity of period-varying folded waveguide

    Xu Ao; Wang Wen-Xiang; Wei Yan-Yu; Gong Yu-Bin


    A period-varying folded waveguide is formed by varying the period of a folded waveguide. It has the advantages of the space harmonic selectivity and the wide bandwidth. However, the regularities of the variety of these period-varying folded waveguides are unavailable from the published papers. In order to solve this problem, the principle of the space harmonic selectivity of a period-varying folded waveguide is analysed, and the conditions to select the space harmonic for this slow wave system are obtained. In addition, the space harmonic selectivities for a linear period-varying folded waveguide and a hyperbolic sine-varying period folded waveguide are also analysed as examples.

  10. Mathematical models of ABE fermentation: review and analysis.

    Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S


    Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.

  11. A Statistical Analysis of the Relationship between Harmonic Surprise and Preference in Popular Music.

    Miles, Scott A; Rosen, David S; Grzywacz, Norberto M


    Studies have shown that some musical pieces may preferentially activate reward centers in the brain. Less is known, however, about the structural aspects of music that are associated with this activation. Based on the music cognition literature, we propose two hypotheses for why some musical pieces are preferred over others. The first, the Absolute-Surprise Hypothesis, states that unexpected events in music directly lead to pleasure. The second, the Contrastive-Surprise Hypothesis, proposes that the juxtaposition of unexpected events and subsequent expected events leads to an overall rewarding response. We tested these hypotheses within the framework of information theory, using the measure of "surprise." This information-theoretic variable mathematically describes how improbable an event is given a known distribution. We performed a statistical investigation of surprise in the harmonic structure of songs within a representative corpus of Western popular music, namely, the McGill Billboard Project corpus. We found that chords of songs in the top quartile of the Billboard chart showed greater average surprise than those in the bottom quartile. We also found that the different sections within top-quartile songs varied more in their average surprise than the sections within bottom-quartile songs. The results of this study are consistent with both the Absolute- and Contrastive-Surprise Hypotheses. Although these hypotheses seem contradictory to one another, we cannot yet discard the possibility that both absolute and contrastive types of surprise play roles in the enjoyment of popular music. We call this possibility the Hybrid-Surprise Hypothesis. The results of this statistical investigation have implications for both music cognition and the human neural mechanisms of esthetic judgments.

  12. Mathematical Analysis of Urban Spatial Networks

    Blanchard, Philippe


    Cities can be considered to be among the largest and most complex artificial networks created by human beings. Due to the numerous and diverse human-driven activities, urban network topology and dynamics can differ quite substantially from that of natural networks and so call for an alternative method of analysis. The intent of the present monograph is to lay down the theoretical foundations for studying the topology of compact urban patterns, using methods from spectral graph theory and statistical physics. These methods are demonstrated as tools to investigate the structure of a number of real cities with widely differing properties: medieval German cities, the webs of city canals in Amsterdam and Venice, and a modern urban structure such as found in Manhattan. Last but not least, the book concludes by providing a brief overview of possible applications that will eventually lead to a useful body of knowledge for architects, urban planners and civil engineers.

  13. A comparative analysis of the density of the SNOMED CT conceptual content for semantic harmonization.

    He, Zhe; Geller, James; Chen, Yan


    found that intermediate concepts could be imported into SNOMED CT or into the reference terminology, respectively, to enhance their conceptual content, if approved by a human curator. Other cases included synonymy and errors in one of the terminologies. These results show that structure-based algorithmic methods can be used to identify potential concepts to enrich SNOMED CT and the four reference terminologies. The comparative analysis has the future potential of supporting terminology authoring by suggesting new content to improve content coverage and semantic harmonization between terminologies. Copyright © 2015 Elsevier B.V. All rights reserved.

  14. [Harmonic imaging analysis for assessment of morphological changes in mini-pig alveolar bone by normal and increased functional load].

    Guseva, I E; Zhitkov, M Iu; Loginova, N K; Mokhov, A V


    The aim of the study was to reveal the mastication forces effect on the microstructure of mandible bone tissue of mini-pigs by Fouirier harmonic imaging analysis of bone sections images of back scattered electrons and assessment of calcium and phosphorous distribution maps obtained by roentgenofluorescence technique. The results showed that by higher functional loads not only the total content of mineral elements in the bone matrix increased but also the of the low-frequency harmonics in the image spectrum indicating structural heterogeneity decrease in bone mineralization.

  15. Second harmonic generation analysis of early Achilles tendinosis in response to in vivo mechanical loading


    Background Tenocytes have been implicated in the development of tendinosis, a chronic condition commonly seen in musculoskeletal overuse syndromes. However, the relation between abnormal tenocyte morphology and early changes in the fibrillar collagen matrix has not been closely examined in vivo. Second harmonic generation (SHG) microscopy is a recently developed technique which allows examination of fibrillar collagen structures with a high degree of specificity and resolution. The goal of this study was to examine the potential utility of SHG and multiphoton excitation fluorescence (MPEF) microscopy in understanding the relation between tenocytes and their surrounding collagenous matrix in early tendon overuse lesions. Methods Histological preparations of tendon were prepared from adult male Sprague-Dawley rats subjected to an Achilles tendon loading protocol for 12 weeks (Rat-A-PED), or from sedentary age-matched cage controls. Second harmonic generation and multiphoton excitation fluorescence were performed simultaneously on these tissue sections in at least three different areas. Results SHG microscopy revealed an association between abnormal tenocyte morphology and morphological changes in the fibrillar collagen matrix of mechanically loaded Achilles tendons. Collagen density and organization was significantly reduced in focal micro-regions of mechanically loaded tendons. These pathological changes occurred specifically in association with altered tenocyte morphology. Normal tendons displayed a regular distribution of fibre bundles, and the average size of these bundles as determined by Gaussian analysis was 0.47 μm ± 0.02. In comparison, fibre bundle measures from tendon regions in the vicinity of abnormal tenocytes could not be quantified due to a reduction in their regularity of distribution and orientation. Conclusions SHG microscopy allowed high resolution detection of focal tendon abnormalities affecting the fibrillar collagen matrix. With ongoing

  16. Second harmonic generation analysis of early Achilles tendinosis in response to in vivo mechanical loading

    Fong Gloria


    Full Text Available Abstract Background Tenocytes have been implicated in the development of tendinosis, a chronic condition commonly seen in musculoskeletal overuse syndromes. However, the relation between abnormal tenocyte morphology and early changes in the fibrillar collagen matrix has not been closely examined in vivo. Second harmonic generation (SHG microscopy is a recently developed technique which allows examination of fibrillar collagen structures with a high degree of specificity and resolution. The goal of this study was to examine the potential utility of SHG and multiphoton excitation fluorescence (MPEF microscopy in understanding the relation between tenocytes and their surrounding collagenous matrix in early tendon overuse lesions. Methods Histological preparations of tendon were prepared from adult male Sprague-Dawley rats subjected to an Achilles tendon loading protocol for 12 weeks (Rat-A-PED, or from sedentary age-matched cage controls. Second harmonic generation and multiphoton excitation fluorescence were performed simultaneously on these tissue sections in at least three different areas. Results SHG microscopy revealed an association between abnormal tenocyte morphology and morphological changes in the fibrillar collagen matrix of mechanically loaded Achilles tendons. Collagen density and organization was significantly reduced in focal micro-regions of mechanically loaded tendons. These pathological changes occurred specifically in association with altered tenocyte morphology. Normal tendons displayed a regular distribution of fibre bundles, and the average size of these bundles as determined by Gaussian analysis was 0.47 μm ± 0.02. In comparison, fibre bundle measures from tendon regions in the vicinity of abnormal tenocytes could not be quantified due to a reduction in their regularity of distribution and orientation. Conclusions SHG microscopy allowed high resolution detection of focal tendon abnormalities affecting the fibrillar collagen


    Elmas Gun


    Full Text Available This research, which aims to detect the theoric information levels of pre-service music teachers gathered from harmony-counterpoint-accompaniment courses, is considered significant with regards to the necessity of these two courses being educated simultaneously. In the research, 26 students that are studying on second grade have been selected from Mehmet Akif Ersoy University, Education Faculty, Music Education Department as working group. Harmonic analysing has been applied to students selected by researchers in sonatin form for the piano. All points gathered from the test have been judged and correlated with the grades of students in the courses of “piano” and “harmony-counterpoint-accompaniment”. Between the harmony analysis and piano course grade, 0.135 (A low value/dependance has been detected by using pearson correlation analysis. Between the harmony analysis and harmony-counterpoint-accompaniment course grades, 0.669 (A medium value/dependance has been detected by using pearson correlation analysis.

  18. Numerical Analysis of Harmonic Influence for Selected Harmonic Elimination PWM%消谐法SHEPWM的谐波影响数值分析

    王榕生; 吴汉光


    为了研究特定谐波消除脉宽调制技术(SHEPWM)的谐波影响,采用数值法计算了SHEPWM线电压波形特征及全电压范围的谐波分布、THD、转矩脉动。并与不对称规则采样正弦波脉宽调制(SPWM)进行了数值对比。结果表明,相同开关频率下,在M〉0.54区间,SHEPWM的转矩与转速脉动优于SPWM的对应值;而在M〈0.54区间,SHEPWM不具有优势。在M∈[0,1]区间,SPWM的THD优于SHEPWM。因此,不同PWM的转矩脉动比值与相应的THD比值之间不具有对应关系。所得结果为客观评估SHEPWM技术性能及其谐波影响提供了新依据。%In order to study SHEPWM's harmonic influence,the numerical analysis is applied to calculate SHEPWM line-voltage waveform characteristics,harmonics distribution,THD,and torque pulsation over the complete fundamental voltage range.Further,numeric comparisons are performed on above-mentioned parameters but with an asymmetric regular sampled SPWM.The results show that,under the same switching frequency,SHEPWM is superior to SPWM in terms of torque and speed pulsation only if the modulation index M〉0.54;while SHEPWM has no superiority if M〈0.54.The THD of SPWM outperforms that of SHEPWM if M∈.Therefore,a correlation does not exist between the torque pulsation ratio and THD ratio for different PWM.The study results provide a new basis to fairly evaluate the SHEPWM performance and its harmonic influence.

  19. Mathematics Competency for Beginning Chemistry Students Through Dimensional Analysis.

    Pursell, David P; Forlemu, Neville Y; Anagho, Leonard E


    Mathematics competency in nursing education and practice may be addressed by an instructional variation of the traditional dimensional analysis technique typically presented in beginning chemistry courses. The authors studied 73 beginning chemistry students using the typical dimensional analysis technique and the variation technique. Student quantitative problem-solving performance was evaluated. Students using the variation technique scored significantly better (18.3 of 20 points, p chemistry students were more likely to use the variation technique rather than the typical technique. The variation technique may be useful as an alternative instructional approach to enhance beginning chemistry students' mathematics competency and problem-solving ability in both education and practice. [J Nurs Educ. 2017;56(1):22-26.]. Copyright 2017, SLACK Incorporated.

  20. [Simulation and analysis of second-harmonic signal based on tunable diode laser absorption spectroscopy].

    Li, Han; Liu, Jian-Guo; He, Ya-Bai; He, Jun-Feng; Yao, Lu; Xu, Zhen-Yu; Chen, Jiu-Ying; Yuan, Song; Kan, Rui-Feng


    Tunable diode laser absorption spectroscopy (TDLAS) is a new gas detection technique developed recently with high spectral resolution, high sensitivity and fast time response. The second-harmonic signal of wavelength modulation spectroscopy (WMS) is often used as the detection signal for gas concentration inversion. Using Simulink, a visual modeling and simulation platform, the authors simulated the WMS signal based on TDLAS, and got the second-harmonic signal by using lock-in amplifier algorithm. Digital orthogonal algorithm was studied in this paper. The relationship between second-harmonic signals and the modulation indexes was analyzed by comparing changes of second-harmonic under different modulation indexes, in order to find out the optimized parameters for second-harmonic detection.

  1. Harmonic statistics

    Eliazar, Iddo


    The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their 'public relations' for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford's law, and 1/f noise.

  2. Mathematical analysis techniques for modeling the space network activities

    Foster, Lisa M.


    The objective of the present work was to explore and identify mathematical analysis techniques, and in particular, the use of linear programming. This topic was then applied to the Tracking and Data Relay Satellite System (TDRSS) in order to understand the space network better. Finally, a small scale version of the system was modeled, variables were identified, data was gathered, and comparisons were made between actual and theoretical data.

  3. An analysis of the mathematics school examination test quality

    Hadi Sutrisno


    Full Text Available This research aims to describe: (1 the quality of mathematics school examination test of the Junior High School for the academic year 2015/2016 in Kabupaten Bangkalan based on qualitative analysis of tests item, (2 the quality of mathematics school examination test of Junior High School for the academic year 2015/2016 in Kabupaten Bangkalan based on quantitative analysis of test items, and (3 the test equating on mathematics school examination test for the academic year of 2015/2016 of Junior High School in Kabupaten Bangkalan. A test is said to be quality if it fulfills validity, reliability, and it has good characteristic. A test is said to be equivalent to another if the test scores of one test can be exchanged with the scores of another test. The data is taken from school examination script accompanied with the answer sheets of students. Qualitative data analysis was conducted with the help of experts judgement. Quantitative data analysis was conducted with Classical Test Theory by Iteman and Item Response Theory by BilogMG. These programs are used to find out the test quality quantitatively. In order to analyze the equivalence between series of tests, item-characteristic curves were used. These curves were drawn by Geogebra. The research result shows: (1 qualitatively, the test plan quality of mathematics school examination test is quite good. Meanwhile, the school exam quality is quite good and not so good, (2 quantitatively, the school examination test quality is good, and (3 equating, based on the item-characteristic curves, the school examination tests is equal.

  4. [Relations between biomedical variables: mathematical analysis or linear algebra?].

    Hucher, M; Berlie, J; Brunet, M


    The authors, after a short reminder of one pattern's structure, stress on the possible double approach of relations uniting the variables of this pattern: use of fonctions, what is within the mathematical analysis sphere, use of linear algebra profiting by matricial calculation's development and automatiosation. They precise the respective interests on these methods, their bounds and the imperatives for utilization, according to the kind of variables, of data, and the objective for work, understanding phenomenons or helping towards decision.

  5. Research in applied mathematics, numerical analysis, and computer science


    Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

  6. Full-Band Quasi-Harmonic Analysis and Synthesis of Musical Instrument Sounds with Adaptive Sinusoids

    Marcelo Caetano


    Full Text Available Sinusoids are widely used to represent the oscillatory modes of musical instrument sounds in both analysis and synthesis. However, musical instrument sounds feature transients and instrumental noise that are poorly modeled with quasi-stationary sinusoids, requiring spectral decomposition and further dedicated modeling. In this work, we propose a full-band representation that fits sinusoids across the entire spectrum. We use the extended adaptive Quasi-Harmonic Model (eaQHM to iteratively estimate amplitude- and frequency-modulated (AM–FM sinusoids able to capture challenging features such as sharp attacks, transients, and instrumental noise. We use the signal-to-reconstruction-error ratio (SRER as the objective measure for the analysis and synthesis of 89 musical instrument sounds from different instrumental families. We compare against quasi-stationary sinusoids and exponentially damped sinusoids. First, we show that the SRER increases with adaptation in eaQHM. Then, we show that full-band modeling with eaQHM captures partials at the higher frequency end of the spectrum that are neglected by spectral decomposition. Finally, we demonstrate that a frame size equal to three periods of the fundamental frequency results in the highest SRER with AM–FM sinusoids from eaQHM. A listening test confirmed that the musical instrument sounds resynthesized from full-band analysis with eaQHM are virtually perceptually indistinguishable from the original recordings.

  7. Analysis of human knee osteoarthritic cartilage using polarization sensitive second harmonic generation microscopy

    Kumar, Rajesh; Grønhaug, Kirsten M.; Romijn, Elisabeth I.; Drogset, Jon O.; Lilledahl, Magnus B.


    Osteoarthritis is one of the most prevalent joint diseases in the world. Although the cause of osteoarthritis is not exactly clear, the disease results in a degradation of the quality of the articular cartilage including collagen and other extracellular matrix components. We have investigated alterations in the structure of collagen fibers in the cartilage tissue of the human knee using mulitphoton microscopy. Due to inherent high nonlinear susceptibility, ordered collagen fibers present in the cartilage tissue matrix produces strong second harmonic generation (SHG) signals. Significant morphological differences are found in different Osteoarthritic grades of cartilage by SHG microscopy. Based on the polarization analysis of the SHG signal, we find that a few locations of hyaline cartilage (mainly type II collagen) is being replaced by fibrocartilage (mainly type I cartilage), in agreement with earlier literature. To locate the different types and quantify the alteration in the structure of collagen fiber, we employ polarization-SHG microscopic analysis, also referred to as _-tensor imaging. The image analysis of p-SHG image obtained by excitation polarization measurements would represent different tissue constituents with different numerical values at pixel level resolution.

  8. Applying an Alternative Mathematics Pedagogy for Students with Weak Mathematics: Meta-Analysis of Alternative Pedagogies

    Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William


    Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was…

  9. Applying an Alternative Mathematics Pedagogy for Students with Weak Mathematics: Meta-Analysis of Alternative Pedagogies

    Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William


    Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was…

  10. Probabilistic Harmonic Analysis on Distributed Photovoltaic Integration Considering Typical Weather Scenarios

    Bin, Che; Ruoying, Yu; Dongsheng, Dang; Xiangyan, Wang


    Distributed Generation (DG) integrating to the network would cause the harmonic pollution which would cause damages on electrical devices and affect the normal operation of power system. On the other hand, due to the randomness of the wind and solar irradiation, the output of DG is random, too, which leads to an uncertainty of the harmonic generated by the DG. Thus, probabilistic methods are needed to analyse the impacts of the DG integration. In this work we studied the harmonic voltage probabilistic distribution and the harmonic distortion in distributed network after the distributed photovoltaic (DPV) system integrating in different weather conditions, mainly the sunny day, cloudy day, rainy day and the snowy day. The probabilistic distribution function of the DPV output power in different typical weather conditions could be acquired via the parameter identification method of maximum likelihood estimation. The Monte-Carlo simulation method was adopted to calculate the probabilistic distribution of harmonic voltage content at different frequency orders as well as the harmonic distortion (THD) in typical weather conditions. The case study was based on the IEEE33 system and the results of harmonic voltage content probabilistic distribution as well as THD in typical weather conditions were compared.

  11. Surface second-harmonic generation from coupled spherical plasmonic nanoparticles: Eigenmode analysis and symmetry properties

    Butet, Jérémy; Dutta-Gupta, Shourya; Martin, Olivier J. F.


    The surface second-harmonic generation from interacting spherical plasmonic nanoparticles building different clusters (symmetric and asymmetric dimers, trimers) is theoretically investigated. The plasmonic eigenmodes of the nanoparticle clusters are first determined using an ab initio approach based on the Green's functions method. This method provides the properties, such as the resonant wavelengths, of the modes sustained by a given cluster. The fundamental and second-harmonic responses of the corresponding clusters are then calculated using a surface integral method. The symmetry of both the linear and nonlinear responses is investigated, as well as their relationship. It is shown that the second-harmonic generation can be significantly enhanced when the fundamental field is such that its second harmonic matches modes with suitable symmetry. The role played by the nanogaps in second-harmonic generation is also underlined. The results presented in this article demonstrate that the properties of the second-harmonic generation from coupled metallic nanoparticles cannot be fully predicted from their linear response only, while, on the other hand, a detailed knowledge of the underlying modal structure can be used to optimize the generation of the second harmonic.

  12. Mathematical competencies and the role of mathematics in physics education: A trend analysis of TIMSS Advanced 1995 and 2008

    Trude Nilsen


    Full Text Available As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal on the application of mathematics in physics education compared with the research related to the conceptual knowledge of physics. In order to clarify the nature of mathematics in physics education, we developed a theoretical framework for mathematical competencies pertinent to various physics tasks based on theoretical frameworks from mathematics and physics education. We used this synthesis of frameworks as a basis to create a model for physics competence. The framework also served as a tool for analyzing and categorizing trend items from the international large-scale survey, TIMSS Advanced 1995 and 2008. TIMSS Advanced assessed students in upper secondary school with special preparation in advanced physics and mathematics. We then investigated the changes in achievements on these categorized items across time for nations who participated in both surveys. The results from our analysis indicate that students whose overall physics achievement declined struggled the most with items requiring mathematics, especially items requiring them to handle symbols, such as manipulating equations. This finding suggests the importance of collaboration between mathematics and physics education as well as the importance of traditional algebra for physics education.

  13. Calculation and analysis of the harmonic vibrational frequencies in molecules at extreme pressure: methodology and diborane as a test case.

    Cammi, R; Cappelli, C; Mennucci, B; Tomasi, J


    We present a new quantum chemical method for the calculation of the equilibrium geometry and the harmonic vibrational frequencies of molecular systems in dense medium at high pressures (of the order of GPa). The new computational method, named PCM-XP, is based on the polarizable continuum model (PCM), amply used for the study of the solvent effects at standard condition of pressure, and it is accompanied by a new method of analysis for the interpretation of the mechanisms underpinning the effects of pressure on the molecular geometries and the harmonic vibrational frequencies. The PCM-XP has been applied at the density functional theory level to diborane as a molecular system under high pressure. The computed harmonic vibrational frequencies as a function of the pressure have shown a satisfactory agreement with the corresponding experimental results, and the parallel application of the method of analysis has reveled that the effects of the pressure on the equilibrium geometry can be interpreted in terms of direct effects on the electronic charge distribution of the molecular solutes, and that the effects on the harmonic vibrational frequencies can be described in terms of two physically distinct effects of the pressure (curvature and relaxation) on the potential energy for the motion of the nuclei.

  14. Methods of Approximation Theory in Complex Analysis and Mathematical Physics

    Saff, Edward


    The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...

  15. Mathematical modeling of isotope labeling experiments for metabolic flux analysis.

    Nargund, Shilpa; Sriram, Ganesh


    Isotope labeling experiments (ILEs) offer a powerful methodology to perform metabolic flux analysis. However, the task of interpreting data from these experiments to evaluate flux values requires significant mathematical modeling skills. Toward this, this chapter provides background information and examples to enable the reader to (1) model metabolic networks, (2) simulate ILEs, and (3) understand the optimization and statistical methods commonly used for flux evaluation. A compartmentalized model of plant glycolysis and pentose phosphate pathway illustrates the reconstruction of a typical metabolic network, whereas a simpler example network illustrates the underlying metabolite and isotopomer balancing techniques. We also discuss the salient features of commonly used flux estimation software 13CFLUX2, Metran, NMR2Flux+, FiatFlux, and OpenFLUX. Furthermore, we briefly discuss methods to improve flux estimates. A graphical checklist at the end of the chapter provides a reader a quick reference to the mathematical modeling concepts and resources.

  16. Analysis of the Reactive Power Compensation in Contaminated Systems with Harmonics

    Secundino Marrero


    Full Text Available The article is given the evaluation obtained of an industrial network with the presence of harmonic contamination, where the non lineal loads correspond fundamentally to rectifiers and variators of speed. Where the typical harmonic generated by these loads settled down and allowed it to determine the levels of harmonic distortion of tension and current to analyze their influence in the selection of the bank of condensers during the compensation of the power it reactivates assisting to the behavior of thesystem before different load states.

  17. [Multi-harmonic analysis of quasi-continuous-wave laser modulation absorption spectroscopy].

    Qi, Ru-bin; Du, Zhen-hui; Meng, Fan-li; Li, Jin-yi; Gao, Dong-yu; Xu, Xiao-bin; Chen, Wen-liang; Xu, Ke-xin


    Numerous harmonic components such as multiple frequency, sum frequency and difference frequency of multiple modulation signals were found in quasi-continuous-wave (QCW) diode laser modulation absorption spectroscopy. Then, the authors analyzed these harmonic components' existence in terms of non-linear interactions of laser and gas absorption line. And the signals' characteristics were studied experimentally. The results shows that there are some sum frequency and difference frequency components that have larger amplitudes compared to the second harmonic wavelength modulation spectroscopy signal (2f-WMS) commonly used in tunable diode laser spectroscopy (TDLAS), and it may improve the detection sensitivity of QCW modulation spectroscopy.

  18. Harmonics and voltage stability analysis in power systems including thyristor-controlled reactor

    M Uzunoglu


    In this study, non-sinusoidal quantities and voltage stability, both known as power quality criteria, are examined together in detail. The widespread use of power electronics elements cause the existence of significant non-sinusoidal quantities in the system. These non-sinusoidal quantities can create serious harmonic distortions in transmission and distribution systems. In this paper, harmonic generation of a static VAR compensator with thyristor-controlled reactor and effects of the harmonics on steady-state voltage stability are examined for various operational conditions.

  19. Stochastic finite element method for random harmonic analysis of composite plates with uncertain modal damping parameters

    Sepahvand, K.


    Damping parameters of fiber-reinforced composite possess significant uncertainty due to the structural complexity of such materials. Considering the parameters as random variables, this paper uses the generalized polynomial chaos (gPC) expansion to capture the uncertainty in the damping and frequency response function of composite plate structures. A spectral stochastic finite element formulation for damped vibration analysis of laminate plates is employed. Experimental modal data for samples of plates is used to identify and realize the range and probability distributions of uncertain damping parameters. The constructed gPC expansions for the uncertain parameters are used as inputs to a deterministic finite element model to realize random frequency responses on a few numbers of collocation points generated in random space. The realizations then are employed to estimate the unknown deterministic functions of the gPC expansion approximating the responses. Employing modal superposition method to solve harmonic analysis problem yields an efficient sparse gPC expansion representing the responses. The results show while the responses are influenced by the damping uncertainties at the mid and high frequency ranges, the impact in low frequency modes can be safely ignored. Utilizing a few random collocation points, the method indicates also a very good agreement compared to the sampling-based Monte Carlo simulations with large number of realizations. As the deterministic finite element model serves as black-box solver, the procedure can be efficiently adopted to complex structural systems with uncertain parameters in terms of computational time.

  20. 3D texture analysis for classification of second harmonic generation images of human ovarian cancer

    Wen, Bruce; Campbell, Kirby R.; Tilbury, Karissa; Nadiarnykh, Oleg; Brewer, Molly A.; Patankar, Manish; Singh, Vikas; Eliceiri, Kevin. W.; Campagnola, Paul J.


    Remodeling of the collagen architecture in the extracellular matrix (ECM) has been implicated in ovarian cancer. To quantify these alterations we implemented a form of 3D texture analysis to delineate the fibrillar morphology observed in 3D Second Harmonic Generation (SHG) microscopy image data of normal (1) and high risk (2) ovarian stroma, benign ovarian tumors (3), low grade (4) and high grade (5) serous tumors, and endometrioid tumors (6). We developed a tailored set of 3D filters which extract textural features in the 3D image sets to build (or learn) statistical models of each tissue class. By applying k-nearest neighbor classification using these learned models, we achieved 83-91% accuracies for the six classes. The 3D method outperformed the analogous 2D classification on the same tissues, where we suggest this is due the increased information content. This classification based on ECM structural changes will complement conventional classification based on genetic profiles and can serve as an additional biomarker. Moreover, the texture analysis algorithm is quite general, as it does not rely on single morphological metrics such as fiber alignment, length, and width but their combined convolution with a customizable basis set.

  1. Quantitative analysis of biological tissues using Fourier transform-second-harmonic generation imaging

    Ambekar Ramachandra Rao, Raghu; Mehta, Monal R.; Toussaint, Kimani C., Jr.


    We demonstrate the use of Fourier transform-second-harmonic generation (FT-SHG) imaging of collagen fibers as a means of performing quantitative analysis of obtained images of selected spatial regions in porcine trachea, ear, and cornea. Two quantitative markers, preferred orientation and maximum spatial frequency are proposed for differentiating structural information between various spatial regions of interest in the specimens. The ear shows consistent maximum spatial frequency and orientation as also observed in its real-space image. However, there are observable changes in the orientation and minimum feature size of fibers in the trachea indicating a more random organization. Finally, the analysis is applied to a 3D image stack of the cornea. It is shown that the standard deviation of the orientation is sensitive to the randomness in fiber orientation. Regions with variations in the maximum spatial frequency, but with relatively constant orientation, suggest that maximum spatial frequency is useful as an independent quantitative marker. We emphasize that FT-SHG is a simple, yet powerful, tool for extracting information from images that is not obvious in real space. This technique can be used as a quantitative biomarker to assess the structure of collagen fibers that may change due to damage from disease or physical injury.

  2. Practical results from a mathematical analysis of guard patrols

    Indusi, Joseph P.


    Using guard patrols as a primary detection mechanism is not generally viewed as a highly efficient detection method when compared to electronic means. Many factors such as visibility, alertness, and the space-time coincidence of guard and adversary presence all have an effect on the probability of detection. Mathematical analysis of the guard patrol detection problem is related to that of classical search theory originally developed for naval search operations. The results of this analysis tend to support the current practice of using guard forces to assess and respond to previously detected intrusions and not as the primary detection mechanism. 6 refs.

  3. RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers

    Figueroa-Vinas, Adolfo


    programmable gate arrays), and DSP (digital signal processing) elements. The fundamental computational algorithm de constructs 3D velocity distributions in terms of spherical harmonic spectral coefficients (which are analogous to a Fourier sine-cosine decomposition), but uses instead spherical harmonics Legendre polynomial orthogonal functions as a basis for the expansion, portraying each 2D angular distribution at every energy or, geometrically, spherical speed-shell swept by the particle spectrometer. Optionally, these spherical harmonic spectral coefficients may be telemetered to the ground. These will provide a smoothed description of the velocity distribution function whose quality will depend on the number of coefficients determined. Successfully implemented on the GSFC-developed processor, the capability to integrate the proposed methodology with both heritage and anticipated future plasma particle spectrometer designs is demonstrated (with sufficiently detailed design analysis to advance TRL) to show specific science relevancy with future HSD (Heliophysics Science Division) solar-interplanetary, planetary missions, sounding rockets and/or CubeSat missions.

  4. Nanoantenna harmonic sensor: theoretical analysis of contactless detection of molecules with light

    Farhat, Mohamed


    The nonlinear harmonic sensor is a popular wireless sensor and radiofrequency identification (RFID) technique, which allows high-performance sensing in a severe interference/clutter background by transmitting a radio wave and detecting its modulated higher-order harmonics. Here we introduce the concept and design of optical harmonic tags based on nonlinear nanoantennas that can contactlessly detect electronic (e.g. electron affinity) and optical (e.g. relative permittivity) characteristics of molecules. By using a dual-resonance gold-molecule–silver nanodipole antenna within the quantum mechanical realm, the spectral form of the second-harmonic scattering can sensitively reveal the physical properties of molecules, paving a new route towards optical molecular sensors and optical identification (OPID) of biological, genetic, and medical events for the \\'Internet of Nano-Things\\'.

  5. Three dimensional mathematical model of tooth for finite element analysis

    Puškar Tatjana


    Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

  6. [Three dimensional mathematical model of tooth for finite element analysis].

    Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka


    The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

  7. Mathematical Modeling and Analysis of Multirobot Cooperative Hunting Behaviors

    Yong Song


    Full Text Available This paper presents a mathematical model of multirobot cooperative hunting behavior. Multiple robots try to search for and surround a prey. When a robot detects a prey it forms a following team. When another “searching” robot detects the same prey, the robots form a new following team. Until four robots have detected the same prey, the prey disappears from the simulation and the robots return to searching for other prey. If a following team fails to be joined by another robot within a certain time limit the team is disbanded and the robots return to searching state. The mathematical model is formulated by a set of rate equations. The evolution of robot collective hunting behaviors represents the transition between different states of robots. The complex collective hunting behavior emerges through local interaction. The paper presents numerical solutions to normalized versions of the model equations and provides both a steady state and a collaboration ratio analysis. The value of the delay time is shown through mathematical modeling to be a strong factor in the performance of the system as well as the relative numbers of the searching robots and the prey.

  8. Mathematical analysis of intermittent gas injection model in oil production

    Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.


    Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.

  9. Design-Oriented Analysis of Resonance Damping and Harmonic Compensation for LCL-Filtered Voltage Source Converters

    Wang, Xiongfei; Blaabjerg, Frede; Loh, Poh Chiang


    This paper addresses the interaction between harmonic resonant controllers and active damping of LCL resonance in voltage source converters. A virtual series R-C damper in parallel with the filter capacitor is proposed with the capacitor current feedback loop. The phase lag resulting from the dig...... crossover frequency defined by the proportional gain of current controller. This is of particular interest for high-performance active harmonic filtering applications and low-pulse-ratio converters. Case studies in experiments validate the theoretical analysis.......This paper addresses the interaction between harmonic resonant controllers and active damping of LCL resonance in voltage source converters. A virtual series R-C damper in parallel with the filter capacitor is proposed with the capacitor current feedback loop. The phase lag resulting from...... the digital computation and modulation delays is thus compensated by the virtual capacitor. The frequency region that allows using resonant controllers is then identified with the virtual damper. It reveals that the upper frequency limit of harmonic resonant controllers can be increased above the gain...

  10. Toward an Analysis of Video Games for Mathematics Education

    Offenholley, Kathleen


    Video games have tremendous potential in mathematics education, yet there is a push to simply add mathematics to a video game without regard to whether the game structure suits the mathematics, and without regard to the level of mathematical thought being learned in the game. Are students practicing facts, or are they problem-solving? This paper…

  11. Latent Variable Graphical Model Selection using Harmonic Analysis: Applications to the Human Connectome Project (HCP).

    Kim, Won Hwa; Kim, Hyunwoo J; Adluru, Nagesh; Singh, Vikas


    A major goal of imaging studies such as the (ongoing) Human Connectome Project (HCP) is to characterize the structural network map of the human brain and identify its associations with covariates such as genotype, risk factors, and so on that correspond to an individual. But the set of image derived measures and the set of covariates are both large, so we must first estimate a 'parsimonious' set of relations between the measurements. For instance, a Gaussian graphical model will show conditional independences between the random variables, which can then be used to setup specific downstream analyses. But most such data involve a large list of 'latent' variables that remain unobserved, yet affect the 'observed' variables sustantially. Accounting for such latent variables is not directly addressed by standard precision matrix estimation, and is tackled via highly specialized optimization methods. This paper offers a unique harmonic analysis view of this problem. By casting the estimation of the precision matrix in terms of a composition of low-frequency latent variables and high-frequency sparse terms, we show how the problem can be formulated using a new wavelet-type expansion in non-Euclidean spaces. Our formulation poses the estimation problem in the frequency space and shows how it can be solved by a simple sub-gradient scheme. We provide a set of scientific results on ~500 scans from the recently released HCP data where our algorithm recovers highly interpretable and sparse conditional dependencies between brain connectivity pathways and well-known covariates.

  12. Interference harmonics and rigorous EM spectrum analysis method for low-k1 CD Bossung tilt correction

    Chou, Shuo-Yen; Ng, Hoi-Tou; Chen, Yi-Yin; Lee, Chien-Fu; Liu, Ru-Gun; Gau, Tsai-Sheng


    This paper discusses the CD Bossung tilt phenomena in low-k1 lithography using interference harmonics and rigorous EM spectrum analysis. Interference harmonics analysis is introduced to explain the interaction of diffraction orders in the focal region leading to this abnormal CD behavior. This method decomposes the vector image formula into a superposition of cosine components to describe the interference of diffraction orders. The symmetry properties of components of an optical projection system were investigated to find out three potential sources for the asymmetric Bossung behavior, namely mask 3D (M3D) effect, lens aberration, and wafer reflectivity. Under good lens aberration and substrate reflectivity controls, the M3D effect accounts for most of the CD Bossung tilt. A rigorous EM mask spectral analysis was performed to reveal the impact of mask topography on the near-field intensity of mask transmission and the far-field image formation. From the analysis, the asymmetric phase distribution in the mask spectrum is the root cause for CD Bossung tilt. Using both the interference harmonics and the rigorous EM spectrum analysis, the effect of various resolution enhancement techniques (RET) to the Bossung tilt is also studied to find the best RET combination for M3D immunity. In addition, a pupil optimization algorithm based on these two analyses is proposed to generate the phase compensation map for M3D effect counteraction.

  13. Harmonic statistics

    Eliazar, Iddo, E-mail:


    The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

  14. Background and Mathematical Analysis of Diffusion MRI Methods.

    Ozcan, Alpay; Wong, Kenneth H; Larson-Prior, Linda; Cho, Zang-Hee; Mun, Seong K


    The addition of a pair of magnetic field gradient pulses had initially provided the measurement of spin motion with nuclear magnetic resonance (NMR) techniques. In the adaptation of DW-NMR techniques to magnetic resonance imaging (MRI), the taxonomy of mathematical models is divided in two categories: model matching and spectral methods. In this review, the methods are summarized starting from early diffusion weighted (DW) NMR models followed up with their adaptation to DW MRI. Finally, a newly introduced Fourier analysis based unifying theory, so-called Complete Fourier Direct MRI, is included to explain the mechanisms of existing methods.

  15. Stator Current Harmonic Control with Resonant Controller for Doubly Fed Induction Generator

    Liu, Changjin; Blaabjerg, Frede; Chen, Wenjie;


    Voltage harmonics in the grid can introduce stator current harmonics in a doubly fed induction generator (DFIG) wind turbine system, which may potentially impact the generated power quality. Therefore, wind turbine current controllers need to be designed to eliminate the impact of grid voltage...... rotor current control loop for harmonic suppression. The overall control scheme is implemented in dq frame. Based on a mathematical model of the DFIG control system, the effects on system stability using the resonant controller, an analysis of the steady-state error, and the dynamic performance...

  16. Harmonic scalpel versus flexible CO2 laser for tongue resection: A histopathological analysis of thermal damage in human cadavers

    Wolf Tamir


    Full Text Available Abstract Background Monopolar cautery is the most commonly used surgical cutting and hemostatic tool for head and neck surgery. There are newer technologies that are being utilized with the goal of precise cutting, decreasing blood loss, reducing thermal damage, and allowing faster wound healing. Our study compares thermal damage caused by Harmonic scalpel and CO2 laser to cadaveric tongue. Methods Two fresh human cadaver heads were enrolled for the study. Oral tongue was exposed and incisions were made in the tongue akin to a tongue tumor resection using the harmonic scalpel and flexible C02 laser fiber at various settings recommended for surgery. The margins of resection were sampled, labeled, and sent for pathological analysis to assess depth of thermal damage calculated in millimeters. The pathologist was blinded to the surgical tool used. Control tongue tissue was also sent for comparison as a baseline for comparison. Results Three tongue samples were studied to assess depth of thermal damage by harmonic scalpel. The mean depth of thermal damage was 0.69 (range, 0.51 - 0.82. Five tongue samples were studied to assess depth of thermal damage by CO2 laser. The mean depth of thermal damage was 0.3 (range, 0.22 to 0.43. As expected, control samples showed 0 mm of thermal damage. There was a statistically significant difference between the depth of thermal injury to tongue resection margins by harmonic scalpel as compared to CO2 laser, (p = 0.003. Conclusion In a cadaveric model, flexible CO2 laser fiber causes less depth of thermal damage when compared with harmonic scalpel at settings utilized in our study. However, the relevance of this information in terms of wound healing, hemostasis, safety, cost-effectiveness, and surgical outcomes needs to be further studied in clinical settings.

  17. A Meta-Analysis of Mathematics and Working Memory: Moderating Effects of Working Memory Domain, Type of Mathematics Skill, and Sample Characteristics

    Peng, Peng; Namkung, Jessica; Barnes, Marcia; Sun, Congying


    The purpose of this meta-analysis was to determine the relation between mathematics and working memory (WM) and to identify possible moderators of this relation including domains of WM, types of mathematics skills, and sample type. A meta-analysis of 110 studies with 829 effect sizes found a significant medium correlation of mathematics and WM, r…

  18. A Meta-Analysis of Mathematics and Working Memory: Moderating Effects of Working Memory Domain, Type of Mathematics Skill, and Sample Characteristics

    Peng, Peng; Namkung, Jessica; Barnes, Marcia; Sun, Congying


    The purpose of this meta-analysis was to determine the relation between mathematics and working memory (WM) and to identify possible moderators of this relation including domains of WM, types of mathematics skills, and sample type. A meta-analysis of 110 studies with 829 effect sizes found a significant medium correlation of mathematics and WM, r…

  19. The runoff characteristics and harmonic analysis of the soil moisture dynamics in Robinia pseudoacacia stand

    GAOPeng; LIUZuo-xin; CHENFu-sheng


    Robinia pseudoacacia stands act as a typical ecorogicar protection forest in hirly semi-arid area of China. Two fierds of surface runoff were separately set up in R. pseudoacacia stand and its crearcut area in the western Liaoning Province (18°50′-122°25′E, 40°24′-42°34′N) for measuring the characteristics of runoff and sediment as werl as soir moisture dynamics.Contractive analysis of the two land types showed that there existed a significant difference in vorumes of runoff and sediment between the sites of R. pseudoacacia stand and its crearcut area. The runoff vorume and sediment vorume in crearcut area were much bigger than those in R. pseudoacacia stand, with an increase amount of 40%-177% for runoff and 180%-400% for sediment. Hydrograph of surface runoff of typical rainfall showed that the peak value of runoff in R. pseudoacacia stand was decreased by 1.0-2.5x10-3m3·s-1 compared with that in its crearcut area, and the occurring time of peak varue of runoff in R.pseudoacacia stand was 10-20 rain later than that in its crearcut area. Harmonic analysis of soir moisture dynamics indicated that the soir moisture in R. pseudoacacia stand was 2.3 % higher than that in clearcut area, and the soir moisture both in R. pseudoacacia stand and its clearcut area courd be divided into dry season and humid season and varied periodicarly with annual rainfall precipitation. It was concruded that R. pseudoacacia stand plays a very important rote in storing water, increasing soil moisture, and reducing surface runoff and soil erosion.

  20. Aeroelastic analysis for propellers - mathematical formulations and program user's manual

    Bielawa, R. L.; Johnson, S. A.; Chi, R. M.; Gangwani, S. T.


    Mathematical development is presented for a specialized propeller dedicated version of the G400 rotor aeroelastic analysis. The G400PROP analysis simulates aeroelastic characteristics particular to propellers such as structural sweep, aerodynamic sweep and high subsonic unsteady airloads (both stalled and unstalled). Formulations are presented for these expanded propeller related methodologies. Results of limited application of the analysis to realistic blade configurations and operating conditions which include stable and unstable stall flutter test conditions are given. Sections included for enhanced program user efficiency and expanded utilization include descriptions of: (1) the structuring of the G400PROP FORTRAN coding; (2) the required input data; and (3) the output results. General information to facilitate operation and improve efficiency is also provided.

  1. Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

    Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie


    The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity

  2. The mediation of mathematical learning through the use of pedagogical tools: a sociocultural analysis

    Jones, Keith


    A sociocultural analysis suggests that pedagogical artifacts employed in the teaching and learning of mathematics both enable and constrain learning. This paper summarises three classroom studies of mathematics learning that have utilised a sociocultural approach. Each of the studies indicates how insight can be gained into the ways in which students attempt to make sense of the mathematics they encounter.

  3. Trend Analysis on Mathematics Achievements: A Comparative Study Using TIMSS Data

    Ker, H. W.


    Research addressed the importance of mathematics education for the students' preparation to enter scientific and technological workforce. This paper utilized Trends in International Mathematics and Science Study (TIMSS) 2011 data to conduct a global comparative analysis on mathematics performance at varied International Benchmark levels. The…

  4. Non-Traditional Socio-Mathematical Norms in Undergraduate Real Analysis

    Dawkins, Paul Christian


    This study builds upon the framework of classroom norms (Cobb, Wood, & Yackel, 1993) and socio-mathematical norms (Cobb & Yackel, 1996) to understand how non-traditional socio-mathematical norms influence student reasoning and transitions to advanced mathematical thinking in undergraduate real analysis. The research involves a qualitative…

  5. The Use of Video Analysis and the Knowledge Quartet in Mathematics Teacher Education Programmes

    Liston, Miriam


    This study investigates the potential of video analysis and a mathematical knowledge for teaching framework, the Knowledge Quartet (KQ), in mathematics teacher education programmes. It reports on the effectiveness of these tools in analysing and supporting secondary level pre-service mathematics teachers' subject matter knowledge and pedagogical…

  6. An introduction to lymphocyte and viral dynamics: the power and limitations of mathematical analysis.

    Asquith, Becca; Bangham, Charles R M


    Mathematics is a useful tool in the analysis and understanding of population dynamic aspects of the immune response. However, the power of mathematical modelling in immunology is frequently limited by the shortage of experimental data. Here, we review the contribution of mathematics to two areas of immunology. We highlight the problem caused by lack of knowledge of the system, which can greatly restrict the use of mathematics and lead to errors caused by model-specific results.

  7. Stability Analysis of an Inverted Pendulum Subjected to Combined High Frequency Harmonics and Stochastic Excitations

    HUANG Zhi-Long; JIN Xiao-Ling; ZHU Zi-Qi


    Stability of vertical upright position of an inverted pendulum with its suspension point subjected to high frequency harmonics and stochastic excitations is investigated. Two classes of excitations, i.e., combined high frequency harmonic excitation and Gaussian white noise excitation, and high frequency bounded noise excitation, respectively,are considered. Firstly, the terms of high frequency harmonic excitations in the equation of motion of the system can be set equivalent to nonlinear stiffness terms by using the method of direct separation of motions. Then the stochastic averaging method of energy envelope is used to derive the averaged It(o) stochastic differential equation for system energy. Finally, the stability with probability 1 of the system is studied by using the largest Lyapunov exponent obtained from the averaged It(o) stochastic differential equation. The effects of system parameters on the stability of the system are discussed, and some examples are given to illustrate the efficiency of the proposed procedure.

  8. High-order harmonic generation from polyatomic molecules including nuclear motion and a nuclear modes analysis

    Madsen, Christian Bruun; Abu-Samha, Mahmoud; Madsen, Lars Bojer


    We present a generic approach for treating the effect of nuclear motion in high-order harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters...... as a nuclear correlation function. We express the nuclear correlation function in terms of Franck-Condon factors, which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the high-order harmonic generation process. We show results for the isotopes CH4 and CD4...... and thereby provide direct theoretical support for a recent experiment [S. Baker et al., Science 312, 424 (2006)] that uses high-order harmonic generation to probe the ultrafast structural nuclear rearrangement of ionized methane....

  9. Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM.

    Kuchuk, Kfir; Sivan, Uri


    The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic amplitudes generally require simultaneous measurements of multiple harmonics to achieve satisfactory accuracy. In the present letter we address the mathematical challenge and derive accurate, explicit formulae for both conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM) each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range.

  10. Realization of interpolated FFT algorithm on DSP for accurate harmonic analysis

    Wu, R.C.; Chen, H.M.; Huang, C.C.; Chiang, C.T. [I-Shou Univ., Kaohsiung, Taiwan (China). Dept. of Electrical Engineering


    A study was conducted in which an analog-to-digital converter chip AD7822 was used to estimate harmonic parameters by the interpolated Fast Fourier Transformation (FFT) method. A digital signal processor (DSP) displayed the results via a liquid crystal displayer (LCD). The harmonics parameters included frequencies, amplitudes, and phases that can be found by the interpolated FFT. This paper showed that the newly presented digital meter can obtain results that are more accurate than an oscilloscope. 15 refs., 2 tabs., 5 figs.

  11. Towards harmonized seismic analysis across Europe using supervised machine learning approaches

    Zaccarelli, Riccardo; Bindi, Dino; Cotton, Fabrice; Strollo, Angelo


    . These classes might be a simply binary case (e.g., "good for analysis" vs "bad") or more complex one (e.g., "good for analysis" vs "low SNR", "multi-event", "bad coda envelope"). It is important to stress the fact that our approach can be generalized to any use case providing, as in any supervised approach, an adequate training set of labelled data, a feature-set, a statistical classifier, and finally model validation and evaluation. Examples of use cases considered to develop the system prototype are the characterization of the ground motion in low seismic areas; harmonized spectral analysis across Europe for source and attenuation studies; magnitude calibration; coda analysis for attenuation studies.

  12. Experimental Analysis of a Piezoelectric Energy Harvesting System for Harmonic, Random, and Sine on Random Vibration

    Cryns, Jackson W.; Hatchell, Brian K.; Santiago-Rojas, Emiliano; Silvers, Kurt L.


    Formal journal article Experimental analysis of a piezoelectric energy harvesting system for harmonic, random, and sine on random vibration Abstract: Harvesting power with a piezoelectric vibration powered generator using a full-wave rectifier conditioning circuit is experimentally compared for varying sinusoidal, random and sine on random (SOR) input vibration scenarios. Additionally, the implications of source vibration characteristics on harvester design are discussed. Studies in vibration harvesting have yielded numerous alternatives for harvesting electrical energy from vibrations but piezoceramics arose as the most compact, energy dense means of energy transduction. The rise in popularity of harvesting energy from ambient vibrations has made piezoelectric generators commercially available. Much of the available literature focuses on maximizing harvested power through nonlinear processing circuits that require accurate knowledge of generator internal mechanical and electrical characteristics and idealization of the input vibration source, which cannot be assumed in general application. In this manuscript, variations in source vibration and load resistance are explored for a commercially available piezoelectric generator. We characterize the source vibration by its acceleration response for repeatability and transcription to general application. The results agree with numerical and theoretical predictions for in previous literature that load optimal resistance varies with transducer natural frequency and source type, and the findings demonstrate that significant gains are seen with lower tuned transducer natural frequencies for similar source amplitudes. Going beyond idealized steady state sinusoidal and simplified random vibration input, SOR testing allows for more accurate representation of real world ambient vibration. It is shown that characteristic interactions from more complex vibrational sources significantly alter power generation and power processing

  13. Numerical analysis of near and far field patterns of second-harmonic generation with tiling nonlinear optical crystals

    Harimoto, T [Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, 4-3-11 Kofu, Yamanashi 400-8511 (Japan); Shiraga, H [Institute of Laser Engineering, Osaka University, Suita, Osaka (Japan)], E-mail:


    We report numerical analysis of near- and far-field patterns of the second-harmonic wave in a large-scale high-power laser used in the laser fusion with type I KDP crystals arranged in a tiling style. The thickness and phase-matching angle of the tiling crystals are designed based on the near-field pattern of the second-harmonic wave. The tilting angle error and thickness difference of the tiling crystals are evaluated by the energy distribution included in the Airy spot of the far-field pattern at the focal point. The parallelism and flatness of the tiling crystals can also be estimated with the same method.

  14. Sunspots and Their Simple Harmonic Motion

    Ribeiro, C. I.


    In this paper an example of a simple harmonic motion, the apparent motion of sunspots due to the Sun's rotation, is described, which can be used to teach this subject to high-school students. Using real images of the Sun, students can calculate the star's rotation period with the simple harmonic motion mathematical expression.

  15. Harmonic Analysis of AC-DC Topologies and their Impacts on Power Systems

    Mukhtiar Ahmed Mahar


    Full Text Available Power Electronic Converters are commonly used in different applications because of high efficiency and low cost. Due to latest advancement in semiconductor devices it is difficult to draw the boundaries for applications of power electronic topologies. These topologies are variable structure systems and generate harmonics during the operation which will affect the power quality when are connected to system network. Rectifier is a big family of converters and used when ac-dc conversion is needed. These converters are widely used in distribution system. Therefore, it is necessary to predict the harmonic levels of these converters and also observe their impacts on system network. Pakistan now days facing serious energy crises specially, in power sector due to increase in load demand. To bridge the gap between load demand and generation of electricity, various steps are taken by power companies and government. The steps include the up gradation of existing power plants, generation of power from rental power plants, installation of renewable power sources, taking different steps of demand side management etc. But efforts of power companies on power quality is still lacking. This research work focuses on power quality of the system network. In this work, harmonics of single phase and three phase full bridge diode rectifiers are analyzed by using the fast fourier transform method of MATLAB. The effects of harmonics on the system network are also discussed.

  16. Modeling and analysis of harmonic resonance in a power electronics based AC power system

    Wang, Xiongfei; Blaabjerg, Frede; Chen, Zhe


    The dynamic interactions among the interconnected power converters may bring in harmonic resonance in a power electronics based power system. This paper addresses this issue in a power system dominated by multiple current- and voltage-controlled inverters with LCL- and LC-filters. The impedance-b...

  17. Comparative Analysis on Romanian Taxation in the European Context, as a Prerequisite for Tax Harmonization

    Georgeta Dragomir


    Full Text Available The issue of tax harmonization at EU level is becoming more present in the global crisis context, as it is both accepted and disputed by the European officials that manifest their preference for either coordination or tax competition. The crisis has generated, among other things, large budget deficits and a dangerous crisis of debts in the euro area, a situation that has attracted many followers in terms of tax harmonization. There is a European regulated Area, a unique European market, European unique currency and common monetary policy which regard the criteria relating to public finances (budget deficits, public debt. We ask ourselves to what extent it is necessary to achieve coordination or even tax unification and how does that help. This paper examines, according to the statistical database, the level and type of taxation, on categories of taxes and as a share of GDP, in Romania compared to EU countries, in order to clarify the current situation, the existing differences, the prospect of good European practice. If we speak of tax harmonization in terms of being acquired by Romania, the conclusion is that we can not report only to the technical or quantifiable aspects, as compared with the best results in European area, because they do not represent a guarantee of similar results. The fiscal policy must be both a prerequisite and a consequence of sustainable economic and financial policies, and the tax harmonization can only help insofar as it relates to the relationships between states and not at the tax level.

  18. Modeling and Analysis of Harmonic Stability in an AC Power-Electronics-Based Power System

    Wang, Xiongfei; Blaabjerg, Frede; Wu, Weimin


    This paper addresses the harmonic stability caused by the interactions among the wideband control of power converters and passive components in an AC power-electronicsbased power system. The impedance-based analytical approach is employed and expanded to a meshed and balanced threephase network...

  19. Using Enhanced Frequency Domain Decomposition as a Robust Technique to Harmonic Excitation in Operational Modal Analysis

    Jacobsen, Niels-Jørgen; Andersen, Palle; Brincker, Rune


    Enhanced Frequency Domain Decomposition technique for eliminating the influence of these harmonic components in the modal parameter extraction process. For various experiments, the quality of the method is assessed and compared to the results obtained using broadband stochastic excitation forces. Good...

  20. Mathematical analysis of mammary ducts in lactating human breast.

    Mortazavi, S Negin; Geddes, Donna; Hassiotou, Foteini; Hassanipour, Fatemeh


    This work studies a simple model for milk transport through lactating human breast ducts, and describes mathematically the mass transfer from alveolar sacs through the mammary ducts to the nipple. In this model both the phenomena of diffusion in the sacs and conventional flow in ducts have been considered. The ensuing analysis reveals that there is an optimal range of bifurcation numbers leading to the easiest milk flow based on the minimum flow resistance. This model formulates certain difficult-to-measure values like diameter of the alveolar sacs, and the total length of the milk path as a function of easy-to-measure properties such as milk fluid properties and macroscopic measurements of the breast. Alveolar dimensions from breast tissues of six lactating women are measured and reported in this paper. The theoretically calculated alveoli diameters for optimum milk flow (as a function of bifurcation numbers) show excellent match with our biological data on alveolar dimensions. Also, the mathematical model indicates that for minimum milk flow resistance the glandular tissue must be within a short distance from the base of the nipple, an observation that matches well with the latest anatomical and physiological research.

  1. Life Cycle Inventory Analysis of Recycling: Mathematical and Graphical Frameworks

    Jun Nakatani


    Full Text Available A mathematical framework of the life cycle inventory (LCI analysis in life cycle assessment (LCA of recycling is systematically reviewed with the aid of graphical interpretation. First, the zero burden approach, which has been applied to LCI analyses of waste management systems, is theoretically justified in terms of relative comparison of waste management options. As recycling is a multi-functional system including the dual functions of waste management and secondary material production, the allocation issue needs to be handled in LCIs of recycling, and two forms of system expansion, i.e., the avoided burden and product basket approaches, have dominated to avoid the allocation problem. Then, it is demonstrated that conclusions derived from both approaches should mathematically be identical as far as system boundaries are correctly defined. A criticism against system expansion is also reviewed from the viewpoint of ambiguity of what-if scenarios. As an approach to this issue, market-based consequential LCA is discussed in the context of LCI analyses of open-loop recycling.

  2. Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation.

    Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P; Chaplain, Mark A J


    The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.

  3. Modeling and Interpreting CHAMP Magnetic Anomaly Field over China Continent Using Spherical Cap Harmonic Analysis

    Fu Yuanyuan; Liu Qingsheng; Yang Tao


    Based on the CHAMP Magsat data set, spherical cap harmonic analysis was used to model the magnetic fields over China continent. The data set used in the analysis includes the 15′×15′ gridded values of the CHAMP anomaly fields (latitude φ=25°N to 50°N and longitude λ=78°E to 135°E). The pole of the cap is located at φ=35°N and λ=110°E with half-angle of 30°. The maximum index (Kmax) of the model is 30 and the total number of model coefficients is 961, which corresponds to the minimum wavelength at the earth's surface about 400 km. The root mean square (RMS) deviations between the calculated and observed values are ~ 4 nT for ΔX, ~ 3 nT for ΔY and ~ 3.5 nT for ΔZ, respectively. Results show that positive anomalies are found mainly at the Tarim basin with ~6- 8 nT, the Yangtze platform and North China platform with ~4 nT, and the Songliao basin with ~4-6 nT. In contrast, negative anomaly is mainly located in the Tibet orogenic belt with the amplitude ~ (-6)-(-8) nT. Upward continuation of magnetic anomalies was used to semi-quantitatively separate the magnetic anomalies in different depths of crust. The magnetic anomalies at the earth's surface are from -6 to 10 nT for upper crust, middle crust -27 to 42 nT and lower crust -12 to 18 nT, respectively. The strikes of the magnetic anomalies for the upper crust are consistent with those for the middle crust, but not for the lower crust. The high positive magnetic anomalies mainly result from the old continental nucleus and diastrophic block (e.g. middle Sichuan continental nucleus, middle Tarim basin continental nucleus, Junggar diastrophic block and Qaidam diastrophic block). The amplitudes of the magnetic anomalies of the old continental nucleus and diastrophic block are related to evolution of deep crust. These results improve our understanding of the crustal structure over China continent.

  4. A Framework for Examining Mathematics Teacher Knowledge as Used in Error Analysis

    Peng, Aihui; Luo, Zengru


    Error analysis is a basic and important task for mathematics teachers. Unfortunately, in the present literature there is a lack of detailed understanding about teacher knowledge as used in it. Based on a synthesis of the literature in error analysis, a framework for prescribing and assessing mathematics teacher knowledge in error analysis was…

  5. International seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications

    Rancic, Milica


    This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The book consists of contributed chapters covering research developed as a result of a focused interna...

  6. Comparative analysis of fourth-harmonic multiplying gyrotron traveling-wave amplifiers operating at different frequency multiplications

    Yeh, Y. S.; Kao, W. J.; Li, L. J.; Guo, Y. W.


    The harmonic multiplying operation in a gyrotron traveling-wave amplifier (gyro-TWA) permits magnetic field reduction and frequency multiplication. This study presents a comparative analysis of fourth-harmonic multiplying gyro-TWAs with three schemes of operation. An improved mode-selective circuit using circular waveguides with various radii provides the rejection points within the range of operating frequencies to suppress the competing modes of gyro-TWAs. The simulated results reveal that gyro-TWAs are the most susceptible to the fundamental-harmonic TE11 competing mode, regardless of the operating scheme, and that the mode-selective circuit can provide an attenuation of more than 20 dB to suppress the competing modes. The amplification of the waves in a gyro-TWA depends on the lengths of the sections, and the simulated results show that the gain increases for all schemes, as the length of the lossy section or the length of the copper section increases. All schemes exhibit nearly the same saturated output powers and bandwidths; however, the saturated gain of the scheme at a high frequency multiplication ratio is less than that of the scheme at a low frequency multiplication ratio. Extensive numerical calculations of power and gain scaling are conducted for all schemes.

  7. Harmonic Current Predictors for Wind Turbines

    Shun-Yu Chan


    Full Text Available The harmonic impact caused by wind turbines should be carefully investigated before wind turbines are interconnected. However, the harmonic currents of wind turbines are not easily predicted due to the variations of wind speed. If the harmonic current outputs can be predicted accurately, the harmonic impact of wind turbines and wind farms for power grids can be analyzed efficiently. Therefore, this paper analyzes the harmonic current characteristics of wind turbines and investigates the feasibility of developing harmonic current predictors. Field measurement, data sorting, and analysis are conducted for wind turbines. Two harmonic current predictors are proposed based on the measured harmonic data. One is the Auto-Regressive and Moving Average (ARMA-based harmonic current predictor, which can be used for real-time prediction. The other is the stochastic harmonic current predictor considering the probability density distributions of harmonic currents. It uses the measured harmonic data to establish the probability density distributions of harmonic currents at different wind speeds, and then uses them to implement a long-term harmonic current prediction. Test results use the measured data to validate the forecast ability of these two harmonic current predictors. The ARMA-based predictor obtains poor performance on some harmonic orders due to the stochastic characteristics of harmonic current caused by the variations of wind speed. Relatively, the prediction results of stochastic harmonic current predictor show that the harmonic currents of a wind turbine in long-term operation can be effectively analyzed by the established probability density distributions. Therefore, the proposed stochastic harmonic current predictor is helpful in predicting and analyzing the possible harmonic problems during the operation of wind turbines and wind farms.

  8. Computational mathematics models, methods, and analysis with Matlab and MPI

    White, Robert E


    Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses the ensuing results. These chapters include an abundance of MATLAB code. By studying the code instead of using it as a "black box, " you take the first step toward more sophisticated numerical modeling. The last four chapters focus on multiprocessing algorithms implemented using message passing interface (MPI). These chapters include Fortran 9x codes that illustrate the basic MPI subroutines and revisit the applications of the previous chapters from a parallel implementation perspective. All of the codes are available for download from book is not just about math, not just about computing, and not just about applications, but about all three--in other words, computational science. Whether us...

  9. Mathematical analysis of a cholera model with public health interventions.

    Mwasa, A; Tchuenche, J M


    Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. We formulate a mathematical model that captures some essential dynamics of cholera transmission to study the impact of public health educational campaigns, vaccination and treatment as control strategies in curtailing the disease. The education-induced, vaccination-induced and treatment-induced reproductive numbers R(E), R(V), R(T) respectively and the combined reproductive number R(C) are compared with the basic reproduction number R(0) to assess the possible community benefits of these control measures. A Lyapunov functional approach is also used to analyse the stability of the equilibrium points. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Graphical representations are provided to qualitatively support the analytical results.

  10. Mathematical analysis of dynamic spread of Pine Wilt disease.

    Dimitrijevic, D D; Bacic, J


    Since its detection in Portugal in 1999, the pinewood nematode Bursaphelenchus xylophilus (Steiner and Buhrer), a causal agent of Pine Wilt Disease, represents a threat to European forestry. Significant amount of money has been spent on its monitoring and eradication. This paper presents mathematical analysis of spread of pine wilt disease using a set of partial differential equations with space (longitude and latitude) and time as parameters of estimated spread of disease. This methodology can be used to evaluate risk of various assumed entry points of disease and make defense plans in advance. In case of an already existing outbreak, it can be used to draw optimal line of defense and plan removal of trees. Optimization constraints are economic loss of removal of susceptible trees as well as budgetary constraints of workforce cost.

  11. Mathematical analysis of a nutrient-plankton system with delay.

    Rehim, Mehbuba; Zhang, Zhenzhen; Muhammadhaji, Ahmadjan


    A mathematical model describing the interaction of nutrient-plankton is investigated in this paper. In order to account for the time needed by the phytoplankton to mature after which they can release toxins, a discrete time delay is incorporated into the system. Moreover, it is also taken into account discrete time delays which indicates the partially recycled nutrient decomposed by bacteria after the death of biomass. In the first part of our analysis the sufficient conditions ensuring local and global asymptotic stability of the model are obtained. Next, the existence of the Hopf bifurcation as time delay crosses a threshold value is established and, meanwhile, the phenomenon of stability switches is found under certain conditions. Numerical simulations are presented to illustrate the analytical results.

  12. Mathematical modeling of spinning elastic bodies for modal analysis.

    Likins, P. W.; Barbera, F. J.; Baddeley, V.


    The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

  13. Analysis of quantitative pore features based on mathematical morphology

    QI Heng-nian; CHEN Feng-nong; WANG Hang-jun


    Wood identification is a basic technique of wood science and industry. Pore features are among the most important identification features for hardwoods. We have used a method based on an analysis of quantitative pore feature, which differs from traditional qualitative methods. We applies mathematical morphology methods such as dilation and erosion, open and close transformation of wood cross-sections, image repairing, noise filtering and edge detection to segment the pores from their background. Then the mean square errors (MSE) of pores were computed to describe the distribution of pores. Our experiment shows that it is easy to classift the pore features into three basic types, just as in traditional qualitative methods, but with the use of MSE of pores. This quantitative method improves wood identification considerably.

  14. A new mathematical approach to the Stirling engine analysis

    de Cicco, A.

    A new approach to the theoretical analysis of Stirling machine is presented. The mathematical model takes into account the phenomena occurring into the all main parts of the engine such as the expansion space, the heater, the regenerator, the cooler and the compression space as well. Energy, mass and momentum conservation differential equations are applied to each control volume, with the assumption the working fluid being regarded as a perfect, compressible gas, while the flow is unsteady, one dimensional, with friction and heat transfer. A set of algebraic equations is introduced, in order to consider the boundary conditions which express the constancy of total enthalpy and mass flow, and total pressure drop of the fluid flowing through the boundary sections of the control volumes.

  15. Interrelation of GDP and pension capital: Mathematical and econometrical analysis

    Nepp, A. N.; Dolgodvorov, A. D.


    This article is a mathematicalanalysis of the relationship between GDP and the development of funded pension systems. For this purpose, a mathematical formula was derived from the macro-economic GDP, proportional to the level of income and consumption for the dependence of GDP on the level of pension payments, the value of pension savings and the structure of compulsory contributions to the pension fund allocated to the distribution and accumulative pension system. A derivation of the equation proves the linear relationship of GDP and the share of pension contributions channeled to the funded pension system. Thus, the macroeconomic indicator with the larger negative impact on GDP was proven to be the elimination of the compulsory funded pension system. Based on the econometric analysis, the positive effect of the distributive pension system was proven on macroeconomic parameters.

  16. Reading Grade Levels and Mathematics Assessment: An Analysis of Texas Mathematics Assessment Items and Their Reading Difficulty

    Lamb, John H.


    Increased reading difficulty of mathematics assessment items has been shown to negatively affect student performance. The advent of high-stakes testing, which has serious ramifications for students' futures and teachers' careers, necessitates analysis of reading difficulty on state assessment items and student performance on those items. Using…

  17. Texture analysis applied to second harmonic generation image data for disease classification and development of a multi-view second harmonic generation imaging platform

    Wen, Lianggong

    Many diseases, e.g. ovarian cancer, breast cancer and pulmonary fibrosis, are commonly associated with drastic alterations in surrounding connective tissue, and changes in the extracellular matrix (ECM) are associated with the vast majority of cellular processes in disease progression and carcinogenesis: cell differentiation, proliferation, biosynthetic ability, polarity, and motility. We use second harmonic generation (SHG) microscopy for imaging the ECM because it is a non-invasive, non-linear laser scanning technique with high sensitivity and specificity for visualizing fibrillar collagen. In this thesis, we are interested in developing imaging techniques to understand how the ECM, especially the collagen architecture, is remodeled in diseases. To quantitate remodeling, we implement a 3D texture analysis to delineate the collagen fibrillar morphology observed in SHG microscopy images of human normal and high grade malignant ovarian tissues. In the learning stage, a dictionary of "textons"---frequently occurring texture features that are identified by measuring the image response to a filter bank of various shapes, sizes, and orientations---is created. By calculating a representative model based on the texton distribution for each tissue type using a training set of respective mages, we then perform classification between normal and high grade malignant ovarian tissues classification based on the area under receiver operating characteristic curves (true positives versus false positives). The local analysis algorithm is a more general method to probe rapidly changing fibrillar morphologies than global analyses such as FFT. It is also more versatile than other texture approaches as the filter bank can be highly tailored to specific applications (e.g., different disease states) by creating customized libraries based on common image features. Further, we describe the development of a multi-view 3D SHG imaging platform. Unlike fluorescence microscopy, SHG excites

  18. Dealing with periodical loads and harmonics in operational modal analysis using time-varying transmissibility functions

    Weijtjens, Wout; Lataire, John; Devriendt, Christof; Guillaume, Patrick


    Periodical loads, such as waves and rotating machinery, form a problem for operational modal analysis (OMA). In OMA only the vibrations of a structure of interest are measured and little to nothing is known about the loads causing these vibrations. Therefore, it is often assumed that all dynamics in the measured data are linked to the system of interest. Periodical loads defy this assumption as their periodical behavior is often visible within the measured vibrations. As a consequence most OMA techniques falsely associate the dynamics of the periodical load with the system of interest. Without additional information about the load, one is not able to correctly differentiate between structural dynamics and the dynamics of the load. In several applications, e.g. turbines and helicopters, it was observed that because of periodical loads one was unable to correctly identify one or multiple modes. Transmissibility based OMA (TOMA) is a completely different approach to OMA. By using transmissibility functions to estimate the structural dynamics of the system of interest, all influence of the load-spectrum can be eliminated. TOMA therefore allows to identify the modal parameters without being influenced by the presence of periodical loads, such as harmonics. One of the difficulties of TOMA is that the analyst is required to find two independent datasets, each associated with a different loading condition of the system of interest. This poses a dilemma for TOMA; how can an analyst identify two different loading conditions when little is known about the loads on the system? This paper tackles that problem by assuming that the loading conditions vary continuously over time, e.g. the changing wind directions. From this assumption TOMA is developed into a time-varying framework. This development allows TOMA to not only cope with the continuously changing loading conditions. The time-varying framework also enables the identification of the modal parameters from a single dataset

  19. Theoretical and computational analysis of second- and third-harmonic generation in periodically patterned graphene and transition-metal dichalcogenide monolayers

    Weismann, Martin; Panoiu, Nicolae C.


    Remarkable optical and electrical properties of two-dimensional (2D) materials, such as graphene and transition-metal dichalcogenide (TMDC) monolayers, offer vast technological potential for novel and improved optoelectronic nanodevices, many of which rely on nonlinear optical effects in these 2D materials. This paper introduces a highly effective numerical method for efficient and accurate description of linear and nonlinear optical effects in nanostructured 2D materials embedded in periodic photonic structures containing regular three-dimensional (3D) optical materials, such as diffraction gratings and periodic metamaterials. The proposed method builds upon the rigorous coupled-wave analysis and incorporates the nonlinear optical response of 2D materials by means of modified electromagnetic boundary conditions. This allows one to reduce the mathematical framework of the numerical method to an inhomogeneous scattering matrix formalism, which makes it more accurate and efficient than previously used approaches. An overview of linear and nonlinear optical properties of graphene and TMDC monolayers is given and the various features of the corresponding optical spectra are explored numerically and discussed. To illustrate the versatility of our numerical method, we use it to investigate the linear and nonlinear multiresonant optical response of 2D-3D heteromaterials for enhanced and tunable second- and third-harmonic generation. In particular, by employing a structured 2D material optically coupled to a patterned slab waveguide, we study the interplay between geometric resonances associated to guiding modes of periodically patterned slab waveguides and plasmon or exciton resonances of 2D materials.

  20. A Time-Distinguished Analysis of the Harmonic Structure from a Model Molecular Ion

    杨玉军; 陈高; 陈基根; 朱颀人


    We present high-order harmonic generation spectra resulted from a single-electron model molecular ion exposed to intense laser fields by numerically solving a one-dimensional time-dependent Schrodinger equation. There are three plateaus in the spectra and the maximal cutoff energy is Ip + 8.5Up, when the inter-nuclear distance R equals πα0/2. Here Ip is the ionization potential and Up = E02/(4ω2) is the ponderomotive potential with E0 and ω being the laser electric field amplitude and the central frequency. The harmonic structures are well interpreted by a modified three-step model in which the effects of the electron reflected by the non-parent ion are stressed.

  1. Response Analysis of Frame Supporting Structure of Slope under Harmonic Vibration

    Jian Duan


    Full Text Available Based on certain assumptions, the dynamic mechanical model for frame supporting structure of slope is established, the dynamic equilibrium governing equation for vertical beam under forced vibration is derived, and hence its analytical solutions to harmonic forced vibration are obtained. What is more, the finite difference format and corresponding calculation procedure for vertical beam under forced vibration are given and programmed by using MATLAB language. In the case studies, comparative analyses have been performed to the response of vertical beam under horizontal harmonic forced vibration by using different calculating methods and with anchoring system damping effect neglected or considered. As a result, the feasibility, correctness, and characteristics of different methods can be revealed and the horizontal forced vibration law of vertical beam can be unveiled as well.


    Anass BAYAGA


    Full Text Available The objective of this second part of a two-phased study was to explorethe predictive power of quantitative risk analysis (QRA method andprocess within Higher Education Institution (HEI. The method and process investigated the use impact analysis via Nicholas risk model and Bayesian analysis, with a sample of hundred (100 risk analysts in a historically black South African University in the greater Eastern Cape Province.The first findings supported and confirmed previous literature (KingIII report, 2009: Nicholas and Steyn, 2008: Stoney, 2007: COSA, 2004 that there was a direct relationship between risk factor, its likelihood and impact, certiris paribus. The second finding in relation to either controlling the likelihood or the impact of occurrence of risk (Nicholas risk model was that to have a brighter risk reward, it was important to control the likelihood ofoccurrence of risks as compared with its impact so to have a direct effect on entire University. On the Bayesian analysis, thus third finding, the impact of risk should be predicted along three aspects. These aspects included the human impact (decisions made, the property impact (students and infrastructural based and the business impact. Lastly, the study revealed that although in most business cases, where as business cycles considerably vary dependingon the industry and or the institution, this study revealed that, most impacts in HEI (University was within the period of one academic.The recommendation was that application of quantitative risk analysisshould be related to current legislative framework that affects HEI.

  3. Operational modal analysis of a ship model in the presence of harmonic excitation

    Xu, Junchen; Hong, Ming; Liu, Xiaobing


    A ship is operated under an extremely complex environment, and waves and winds are assumed to be the stochastic excitations. Moreover, the propeller, host and mechanical equipment can also induce the harmonic responses. In order to reduce structural vibration, it is important to obtain the modal parameters information of a ship. However, the traditional modal parameter identification methods are not suitable since the excitation information is difficult to obtain. Natural excitation technique-eigensystem realization algorithm (NExT-ERA) is an operational modal identification method which abstracts modal parameters only from the response signals, and it is based on the assumption that the input to the structure is pure white noise. Hence, it is necessary to study the influence of harmonic excitations while applying the NExT-ERA method to a ship structure. The results of this research paper indicate the practical experiences under ambient excitation, ship model experiments were successfully done in the modal parameters identification only when the harmonic frequencies were not too close to the modal frequencies.

  4. Response analysis of dielectric elastomer spherical membrane to harmonic voltage and random pressure

    Jin, Xiaoling; Wang, Yong; Chen, Michael Z. Q.; Huang, Zhilong


    Spherical membranes consisting of dielectric elastomer play important roles in flexible and stretchable devices, such as flexible actuators, sensors and loudspeakers. Executing various functions of devices depends on the dynamical behaviors of dielectric elastomer spherical membranes to external electrical and/or mechanical excitations. This manuscript concentrates on the random aspect of dielectric elastomer spherical membranes, i.e., the random response to combined excitations of harmonic voltage and random pressure. To analytically evaluate the response statistics of the stretch ratio, a specific transformation and stochastic averaging technique are successively adopted to solve the strongly nonlinear equation with respect to the stretch ratio. The stochastic differential equations for the system first integral and the phase difference between harmonic excitation and response are first derived through this transformation. The Fokker-Planck-Kolmogorov equation with respect to the stationary probability density of the system first integral and the phase difference is obtained. The stationary probability densities and the response statistics of the stretch ratio and its rate of change are then subsequently calculated. The phenomenon of stochastic jumps is found and the stochastic jump bifurcates with the variations of the frequency and the amplitude of the harmonic voltage and the intensity of the random pressure. The efficacy and accuracy of the analytical results are verified by comparing with the results from Monte Carlo simulation. Besides, the reliability of the dielectric elastomer spherical membrane is discussed briefly. The obtained results could provide options in implementing and designing dielectric elastomer structures for dynamic applications.

  5. International Conference on Recent Advances in Mathematical Biology, Analysis and Applications

    Saleem, M; Srivastava, H; Khan, Mumtaz; Merajuddin, M


    The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and ...

  6. A Theoretical Analysis of Sideband Harmonics on the Inverter DC-link Current for an Electric Railcar

    Ogawa, Tomoyuki; Wakao, Shinji; Taufiq, Jat; Kondo, Keiichiro; Terauchi, Nobuo

    The harmonics of the return current may interfere with the signaling current along with the rails. In this paper, we present the theoretical studies of the return current harmonics in the inverter-controlled DC electric railcar, aiming at contributing future work to improve the compatibility with the signaling current. We theoretically derive sideband harmonics of the DC-link current. Then, in order to verify the theoretical study, we experimentally measure the harmonics and numerically simulate the harmonics. As a result, we concluded the theoretical DC-link current is enough accurate to be utilized for the future improvement of the inverter harmonics current.

  7. Infinite dimensional spherical analysis and harmonic analysis for groups acting on homogeneous trees

    Axelgaard, Emil

    of the groups, the so-called irreducible tame representations. We prove the existence of irreducible non-tame representations by constructing a compactification of the boundary of the tree - an object which until now has not played any role in the analysis of automorphism groups for trees which are not locally......In this thesis, we study groups of automorphisms for homogeneous trees of countable degree by using an inductive limit approach. The main focus is the thourough discussion of two Olshanski spherical pairs consisting of automorphism groups for a homogeneous tree and a homogeneous rooted tree...... finite. Finally, we discuss conditionally positive definite functions on the groups and use the generalized Bochner-Godement theorem for Olshanski spherical pairs to prove Levy-Khinchine formulas for both of the considered pairs....

  8. Harmonics mitigation on industrial loads using series and parallel ...

    This work compared the use of series and parallel resonant harmonic filters in suppressing harmonics using Simulink ... From the analysis, series resonant filter mitigated the total harmonic distortion from 30.080% to 3.460%. ... Article Metrics.

  9. Tides and tidal harmonics at Umbharat, Gujarat

    Suryanarayana, A.; Swamy, G.N.

    A part of the data on tides recorded at Machiwada near Umbharat, Gulf of Cambay during April 1978 was subjected to harmonic analysis following the Admiralty procedure. The general tidal characteristics and the value of four major harmonic...

  10. Contact analysis and mathematical modeling of traveling wave ultrasonic motors.

    Zhu, Meiling


    An analysis of the contact layer and a mathematical modeling of traveling wave ultrasonic motors (TWUM) are presented for the guidance of the design of contact layer and the analyses of the influence of the compressive force and contact layer on motor performance. The proposed model starts from a model previously studied but differs from that model in that it adds the analysis of the contact layer and derives the steady-state solutions of the nonlinear equations in the frequency domain, rather than in the time domain, for the analyses of vibrational responses of the stator and operational characteristics of the motor. The maximum permissible compressive force of the motor, the influences of the contact layer material, the thickness of the contact layer, and the compressive force on motor performance have been discussed. The results show that by using the model, one can understand the influence of the compressive force and contact layer material on motor performance, guide the choice of proper contact layer material, and calculate the maximum permissible compressive force and starting voltage.

  11. Mathematical analysis and numerical methods for science and technology

    Dautray, Robert

    These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which ...

  12. Local modes analysis of a rotating marine ship propeller with higher order harmonic elements

    Feng, Chen; Yong, Chen; Hongxing, Hua


    An annular harmonic finite element for the computation of the local modes of a pretwisted ship propeller is developed. The elements take into account both the gyroscopic effect and centrifugal stiffening of the propeller blades. The displacement field is expressed by a truncated Fourier series along the angle and by polynomial shape functions in the radial direction. As an example, the dynamic behaviour, i.e. the nature frequency and local modes, of a ship propeller is studied, and compared with ANSYS, both of which have good consistency.

  13. Quantitative and Qualitative Analysis of Bose-Einstein Condensation in Harmonic Traps

    HU Guang-Xi; YE Ji-Ping; DAI Xian-Xi; DAI Ji-Xin; William E. Evenson


    A simple and direct approach to handle summation is presented. With this approach, we analytically investigate Bose-Einstein condensation of ideal Bose gas trapped in an isotropic harmonic oscillator potential. We get the accurate expression of Tc which is very close to (0.43% larger than) the experimental data. We find the curve of internal energy of the system vs. temperature has a turning point which marks the beginning of a condensation. We also find that there exists specific heat jump at the transition temperature, no matter whether the system is macroscopic or finite. This phenomenon could be a manifestation of a phase transition in finite systems.

  14. Harmonic engine

    Bennett, Charles L.


    A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.

  15. Second harmonic generation imaging


    Second-harmonic generation (SHG) microscopy has shown great promise for imaging live cells and tissues, with applications in basic science, medical research, and tissue engineering. Second Harmonic Generation Imaging offers a complete guide to this optical modality, from basic principles, instrumentation, methods, and image analysis to biomedical applications. The book features contributions by experts in second-harmonic imaging, including many pioneering researchers in the field. Written for researchers at all levels, it takes an in-depth look at the current state of the art and possibilities of SHG microscopy. Organized into three sections, the book: Provides an introduction to the physics of the process, step-by-step instructions on how to build an SHG microscope, and comparisons with related imaging techniques Gives an overview of the capabilities of SHG microscopy for imaging tissues and cells—including cell membranes, muscle, collagen in tissues, and microtubules in live cells—by summarizing experi...


    T. N. Mikulik


    Full Text Available The paper considers a mathematical model of local «driver-seat» system and an algorithm for vibratory loading formation at external actions. Results of the investigations on the system vibration according to minimum vibration acceleration depending on transfer force factor acting on the seat and a vibration isolation factor are presented in the paper.

  17. An Analysis of Students’ Communication during Group Work in Mathematics

    Pinelopi D. Vasileiadou


    Full Text Available Utilizing observation grid and interview study methologies, this research examines the ways in which students communicate with each other while working in a team during problem solving in mathematics. The study focuses primarily on the language used for communication. Results suggest that participants make assumptions to solve mathematical problems and justify their individual opinions, and cooperate and help each other, rarely asking for their teacher’s help, while using both the ordinary, and the mathematical spoken and written language. The interview indicates that students, although not experienced in undertaking group work, are able to readily identify its benefits and positive aspects.

  18. [Representation and mathematical analysis of human crystalline lens].

    Tălu, Stefan; Giovanzana, Stefano; Tălu, Mihai


    The surface of human crystalline lens can be described and analyzed using mathematical models based on parametric representations, used in biomechanical studies and 3D solid modeling of the lens. The mathematical models used in lens biomechanics allow the study and the behavior of crystalline lens on variables and complex dynamic loads. Also, the lens biomechanics has the potential to improve the results in the development of intraocular lenses and cataract surgery. The paper presents the most representative mathematical models currently used for the modeling of human crystalline lens, both optically and biomechanically.

  19. Coherent Harmonic Generation using the Elettra Storage-Ring Optical Klystron A Numerical Analysis

    Curbis, F


    Coherent harmonic generation can be obtained by means of frequency up-conversion of a high-power external laser focused into the first undulator of an optical klystron. The standard configuration is based on a single-pass device, where the seed laser is synchronized with an electron beam entering the first undulator of the optical klystron after being accelerated using a linear accelerator. As an alternative, the optical klystron may be installed on a storage ring, where it is normally used as interaction region for an oscillator free-electron laser. In this case, removing the optical cavity and using an external seed, one obtains a configuration which is similar to the standard one but also presents some peculiar characteristics. In this paper we investigate the possibility of harmonic generation using the Elettra storage-ring optical klystron. We explore different experimental set-ups varying the beam energy, the seed characteristics and the strength of the optical-klystron dispersive section. We also study...

  20. Harmonic Analysis and Design of Embedded Z-Source Inverter for Induction Motor Drives



    Full Text Available This Project deals with an Embedded Z-source inverter to control the three phase induction motor. The Z-source inverters are recent topological options for buck–boost energy conversion with a number of possible voltage and current-type circuitries. The common advantage of Z-source inverter and Embedded Z-source inverter is the inclusion of an LC impedance network, placed between the dc input source and inverter bridge. The drawbacks of the conventional Z-source inverters are more harmonic, less reliable, more diode blocking voltage and capacitor size also high. By introducing Embedded Z-source inverters, the drawbacks of the conventional Z-source inverter can be eliminated and also gain produced is same as that of Z-source inverter. It can produce smoother and smaller current or voltage maintained across the dc input source without using any additional passive filter, less cost and low harmonic distortion. The project is further carried to control the induction motor drive which is used in paper mills, textile mills and cement industries etc.

  1. Optimal analysis on the performance of an irreversible harmonic quantum Brayton refrigeration cycle.

    Lin, Bihong; Chen, Jincan


    An irreversible model of a quantum refrigeration cycle working with many noninteracting harmonic oscillators is established. The refrigeration cycle consists of two adiabatic and two constant-frequency processes. The general performance characteristics of the cycle are investigated, based on the quantum master equation and the semigroup approach. The expressions for several important performance parameters such as the coefficient of performance, cooling rate, power input, and rate of entropy production are derived. By using numerical solutions, the cooling rate of the refrigeration cycle subject to finite cycle duration is optimized. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal region of the coefficient of performance and the optimal ranges of temperatures of the working substance and times spent on the two constant-frequency processes are determined. Moreover, the optimal performance of the cycle in the high-temperature limit is compared with that of a classical Brayton refrigerator working with an ideal gas. The results obtained here show that in the high-temperature limit a harmonic quantum Brayton cycle may be equivalent to a classical Brayton cycle.

  2. Analysis of third harmonic generation and four wave mixing in gold nanostructures by nonlinear finite difference time domain.

    Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan


    Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.

  3. Dynamic Geometry Software Improves Mathematical Achievement: Systematic Review and Meta-Analysis

    Chan, Kan Kan; Leung, Siu Wai


    Dynamic geometry software (DGS) aims to enhance mathematics education. This systematic review and meta-analysis evaluated the quasi-experimental studies on the effectiveness of DGS-based instruction in improving students' mathematical achievement. Research articles published between 1990 and 2013 were identified from major databases according to a…

  4. An Error Analysis in Division Problems in Fractions Posed by Pre-Service Elementary Mathematics Teachers

    Isik, Cemalettin; Kar, Tugrul


    The present study aimed to make an error analysis in the problems posed by pre-service elementary mathematics teachers about fractional division operation. It was carried out with 64 pre-service teachers studying in their final year in the Department of Mathematics Teaching in an eastern university during the spring semester of academic year…

  5. Research in progress in applied mathematics, numerical analysis, and computer science


    Research conducted at the Institute in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized. The Institute conducts unclassified basic research in applied mathematics in order to extend and improve problem solving capabilities in science and engineering, particularly in aeronautics and space.

  6. Proceedings: Workshop on Advanced Mathematics and Computer Science for Power Systems Analysis



    EPRI's Office of Exploratory Research sponsors a series of workshops that explore how to apply recent advances in mathematics and computer science to the problems of the electric utility industry. In this workshop, participants identified research objectives that may significantly improve the mathematical methods and computer architecture currently used for power system analysis.

  7. Mathematical Analysis of Piaget's Grouping Concept. Papy's Minicomputer as a Grouping

    Steiner, H. G.


    Through a mathematical analysis, Piaget's grouping concept can be formally interpreted as being a hybrid between the mathematical concepts of a group and a lattice. Some relevant pedagogical models are presented. Activities with Cuisenaire Rods, Dienes Blocks, and Papy's Minicomputer are shown to take place in groupings. (LS)

  8. Parameter analysis for a high-gain harmonic generation FEL using a recently developed 3D polychromatic code

    Biedron, S G; Yu, L H


    One possible design for a fourth-generation light source is the high-gain harmonic generation (HGHG) free-electron laser (FEL). Here, a coherent seed with a wavelength at a subharmonic of the desired output radiation interacts with the electron beam in an energy-modulating section. This energy modulation is then converted into spatial bunching while traversing a dispersive section (a three-dipole chicane). The final step is passage through an undulator tuned to the desired higher harmonic output wavelength. The coherent seed serves to suppress and can be at a much lower subharmonic of the output radiation. Recently, a 3D code that includes multiple frequencies, multiple undulators (both in quantity and/or type), quadrupole magnets, and dipole magnets was developed to easily simulate HGHG. Here, a brief review of the HGHG theory, the code development, the Accelerator Test Facility's (ATF) HGHG FEL experimental parameters, and the parameter analysis from simulations of this specific experiment will be discussed...

  9. An overview of the mathematical and statistical analysis component of RICIS

    Hallum, Cecil R.


    Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.

  10. Analysis of second-harmonic generation microscopy under refractive index mismatch

    Wang Xiang-Hui; Lin Lie; Zhang Yang


    On the basis of the vector diffraction theory and Green's function method, this paper investigates the effects of refractive index mismatch on second-harmonic generation (SHG) microscopy. The polarization distribution and SHG intensity are calculated as functions of the sample radius and probe depth. The numerical results show that refractive index mismatch can result in peak intensity degradation, increase secondary lobes and extension of secondharmonic polarization distribution. Because of the attenuation of polarization intensity, the detected SHG intensity significantly decreases with increasing probe depth, which can limit the imaging depth of SHG microcopy inside thick samples. Forward SHG intensity decays slowly than backward SHG, due to the combination of extension secondharmonic polarization distribution and strong dependency of forward SHG on sample radius.

  11. In pixel analysis of molecular structure with Stokes vector resolved second harmonic generation microscopy

    Mazumder, Nirmal; Xiang, Lu Yun; Qiu, Jianjun; Kao, Fu-Jen


    We report on measurements and characterization of polarization properties of Second Harmonic (SH) signals using a four-channel photon counting based Stokes polarimeter from type I collagen and starch granules. In this way, the critical polarization parameters including the degree of polarization (DOP), the degree of linear polarization (DOLP), and the degree of circular polarization (DOCP), are extracted from the reconstructed Stokes vector based SH images in a pixel-by-pixel manner. The measurements are further extended to determine the molecular structure and orientation of the samples by varying the polarization states of the incident light and recording the resulting Stokes parameters of the SH signal. The combination of SHG microscopy and Stokes polarimeter hence makes a powerful tool to investigate the structural order of starch granules under water and heating environment.

  12. Vibration analysis of nonlinear systems with the bilinear hysteretic oscillator by using incremental harmonic balance method

    Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo


    This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.

  13. Quantitative analysis of thermally-induced alterations of corneal stroma by second-harmonic generation imaging

    Matteini, P.; Rossi, F.; Ratto, F.; Cicchi, R.; Kapsokalyvas, D.; Pavone, F. S.; Pini, R.


    Thermal modifications induced in the corneal stroma were investigated by means of second harmonic generation (SHG) imaging. Whole fresh cornea samples were heated in a water bath at temperatures in the 35-80 °C range for a 4-min time. SHG images of the structural modifications induced at each temperature were acquired from different areas of cross-sectioned corneal stroma by using an 880 nm linearly- and circularly-polarized excitation light emitted by a mode-locked Ti:Sapphire laser. The SHG images were then analyzed by means of both an empirical approach and a 2D-theoretical model. The proposed analyses provide a detailed description of the changes occurring in the structural architecture of the cornea during the thermal treatment. Our results allow us to depict a temperature-dependent biochemical model for the progressive destructuration occurring to collagen fibrils and nonfibrillar components of the stroma.

  14. Harmonic analysis and field quality improvement of an HTS quadrupole magnet for a heavy ion accelerator

    Zhang, Zhan; Wei, Shaoqing; Lee, Sang Jin [Uiduk University, Gyeongju (Korea, Republic of); Jo, Hyun Chul; Kim, Do Gyun; Kim, Jong Won [Rare Isotope Science Project, Institute for Basic Science, Daejeon (Korea, Republic of)


    In recent years, the iron-dominated high-temperature superconductor (HTS) quadrupole magnets are being developed for heavy ion accelerators. Field analyses for iron-dominated quadrupole magnets were based on the normal-conducting (NC) quadrupole magnet early in the development for accelerators. Some conclusions are still in use today. However, the magnetic field of iron-dominated HTS quadrupole magnets cannot fully follow these conclusions. This study established an HTS quadrupole magnet model and an NC quadrupole magnet model, respectively. The harmonic characteristics of two magnets were analyzed and compared. According to the comparison, the conventional iron-dominated quadrupole magnets can be designed for maximum field gradient; the HTS quadrupole magnet, however, should be considered with varying field gradient. Finally, the HTS quadrupole magnet was designed for the changing field gradient. The field quality of the design was improved comparing with the result of the previous study. The new design for the HTS quadrupole magnet has been suggested.

  15. Analysis of collagen fiber domain organization by Fourier second harmonic generation microscopy

    Ghazaryan, Ara; Tsai, Halley F.; Hayrapetyan, Gor; Chen, Wei-Liang; Chen, Yang-Fang; Jeong, Myung Yung; Kim, Chang-Seok; Chen, Shean-Jen; Dong, Chen-Yuan


    We present an automated and systematic two-dimensional discrete Fourier transform (2D-FFT) approach to analyze collagen fiber organization through the use of second harmonic generation (SHG) microscopy. Average orientations of individual domains and Ising-like order parameters introduced to characterize the correlation between orientations of adjacent domains may be used to quantitatively characterize fibrous tissues. Our approach was applied to analyze tissues including rat tail tendon, mouse skin, bovine corneas, and human corneas. We also show that collagen fiber organization in normal and keratokonus human corneas may be distinguished. The current approach may be used for the quantitative differentiation of SHG collagen fiber morphology in different tissues and may be applied for diagnostic purposes.

  16. Harmonic analysis, partial differential equations and applications in honor of Richard L. Wheeden

    Franchi, Bruno; Lu, Guozhen; Perez, Carlos; Sawyer, Eric


    This is a collection of contributed papers by many eminent Harmonic Analysts and specialists of Partial Differential equations. The papers focus on weighted norm equalities for singular integrals, focusing wave equations, degenerate elliptic equations, Navier-Stokes flow in two dimensions and Poincare-Sobolev inequalities in the setting of metric spaces equipped with measures among others. Many topics considered in this volume stem from the interests of Richard L. Wheeden whose contributions to Potential Theory, singular integral theory and degenerate elliptic PDE theory this volume honors. Luis Caffarelli, Sagun Chanillo, Bruno Franchi, Cristian Guttierez, Xiaojun Huang, Carlos Kenig, Ermanno Lanconelli, Eric Sawyer and Alexander Volberg, are some of the many contributors to this volume. .

  17. A Note on the Analysis of Electrodynamic Fields Radiated by Time-Harmonic Sources Within Non-Birefringent Anisotropic Media

    Sainath, Kamalesh


    We address a challenge concerning the spectral-domain-based analysis of electromagnetic fields produced by time-harmonic current sources within planar-layered media, which arises specifically when sources are embedded inside non-birefringent anisotropic medium (NBAM) layers. In NBAM, the highly symmetric permeability and permittivity tensors can induce directionally-dependent, but polarization independent, propagation properties supporting "degenerate" characteristic polarizations. That is to say, the considered NBAM support four linearly independent field polarization eigenvectors associated with only two (rather than four) unique, non-defective eigenvalues. We explain problems that can arise when the source(s) specifically reside within NBAM planar layers when using canonical field expressions as well as obtain alternative expressions, immune to such problems, that form the foundation for a robust eigenfunction-based analysis of electromagnetic radiation and scattering within planar-layered media.

  18. Critical comparison of three modal methods: bidirectional eigenmode expansion propagation method, aperiodic rigorous coupled mode analysis, and harmonic expansion method

    Ctyroký, Jirí; Richter, Ivan; Kwiecien, Pavel


    The performance of three bidirectional modal methods the "classical" bidirectional eigenmode expansion propagation method, the aperiodic rigorous coupled wave analysis (known also as the Fourier modal method), and the mode expansion method based on harmonic expansion are mutually compared using modeling tasks that include eigenmode calculation of a relatively high-contrast planar waveguide, spectral transmittance of a one-dimensional "photonic crystal" filter in a photonic wire, spectral transmittance of a surface plasmon based optical sensor, and a reflectance from a double-groove structure in a high-contrast waveguide. All methods exhibit generally comparable performance, as follows from good mutual agreement of the results and generally comparable computational time. Although all methods use perfectly matched layers as absorbing boundary conditions, their implementation in the aperiodic rigorous coupled wave analysis exhibits significantly stronger attenuation than that used in the other two methods. Thus, significant improvement of the latter methods seems possible.

  19. Tidal harmonic analysis of TOPEX/POSEIDON data in the Northwest Pacific by introducing difference-ratio relations

    刘克修; 马继瑞; 韩桂军; 范振华; 许崇金


    The difference-ratio relations are introduced to separate tidal constituents that are aliased due to the sampling interval and sampling span of the TOPEX/POSEIDON altimeter. It is found that some tidal constituents such as K1 and SSA, though aliased at along track points, are not aliased at crossover points because the data at crossover points are double those at along track points. So the harmonic analysis method can be employed directly for the analysis of time series at crossover points. Then the difference-ratio relations from crossover points are introduced to analyze the time series at along track points. The TOPEX/POSEIDON data in the Northwest Pacific are analyzed with this method. The results from this method agree well with tidal constants from tidal gauges.

  20. Numerical Analysis of Induced Current in Human Head Exposed to Nonuniform Magnetic Field Including Harmonics

    Tarao, Hiroo; Hayashi, Noriyuki; Isaka, Katsuo

    In this paper, induced currents in an anatomical head model exposed to a non-uniform ELF magnetic field (B-field) including harmonics are numerically calculated, and are discussed based on the basic restriction established by International Commission on Non-Ionizing Radiation Protection (ICNIRP). A casual hair dryer of 100V and 1.2kW is chosen as a typical source of the non-uniform B-field including both the fundamental and second harmonic components. The B-field distribution around the hair dryer is estimated by using the 3-orthogonal magnetic dipole moments, which are derived from a couple of measured values around it. The high-resolution human head model used is constructed based on the MRI images of a real human, and consists of six kinds of tissues (bone, brain, eyeballs, muscle, skin and blood). So-called impedance method is used for the numerical calculation of the induced current. The numerical results show that the maximum values of the induced current of 17µA/m2, for the 60Hz component, which is about 1/120 of the ICNIRP basic restriction appear in the muscle near the eyeball when the hair dryer is used from the side of the head model, and the averaged current in the eyeballs that have the highest conductivity is the highest among the six tissues. It is also demonstrated that the induced current due to the 120Hz B-field becomes comparable to the 60Hz current although the magnitude of the 120Hz B-field is much smaller than that of the 60Hz B-field.

  1. Mathematical tasks, study approaches, and course grades in undergraduate mathematics: a year-by-year analysis

    Maciejewski, Wes; Merchant, Sandra


    Students approach learning in different ways, depending on the experienced learning situation. A deep approach is geared toward long-term retention and conceptual change while a surface approach focuses on quickly acquiring knowledge for immediate use. These approaches ultimately affect the students' academic outcomes. This study takes a cross-sectional look at the approaches to learning used by students from courses across all four years of undergraduate mathematics and analyses how these relate to the students' grades. We find that deep learning correlates with grade in the first year and not in the upper years. Surficial learning has no correlation with grades in the first year and a strong negative correlation with grades in the upper years. Using Bloom's taxonomy, we argue that the nature of the tasks given to students is fundamentally different in lower and upper year courses. We find that first-year courses emphasize tasks that require only low-level cognitive processes. Upper year courses require higher level processes but, surprisingly, have a simultaneous greater emphasis on recall and understanding. These observations explain the differences in correlations between approaches to learning and course grades. We conclude with some concerns about the disconnect between first year and upper year mathematics courses and the effect this may have on students.

  2. Mathematical bridges

    Andreescu, Titu; Tetiva, Marian


    Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

  3. Mathematical modelling methodologies in predictive food microbiology: a SWOT analysis.

    Ferrer, Jordi; Prats, Clara; López, Daniel; Vives-Rego, Josep


    Predictive microbiology is the area of food microbiology that attempts to forecast the quantitative evolution of microbial populations over time. This is achieved to a great extent through models that include the mechanisms governing population dynamics. Traditionally, the models used in predictive microbiology are whole-system continuous models that describe population dynamics by means of equations applied to extensive or averaged variables of the whole system. Many existing models can be classified by specific criteria. We can distinguish between survival and growth models by seeing whether they tackle mortality or cell duplication. We can distinguish between empirical (phenomenological) models, which mathematically describe specific behaviour, and theoretical (mechanistic) models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. We can also distinguish between primary, secondary and tertiary models, by examining their treatment of the effects of external factors and constraints on the microbial community. Recently, the use of spatially explicit Individual-based Models (IbMs) has spread through predictive microbiology, due to the current technological capacity of performing measurements on single individual cells and thanks to the consolidation of computational modelling. Spatially explicit IbMs are bottom-up approaches to microbial communities that build bridges between the description of micro-organisms at the cell level and macroscopic observations at the population level. They provide greater insight into the mesoscale phenomena that link unicellular and population levels. Every model is built in response to a particular question and with different aims. Even so, in this research we conducted a SWOT (Strength, Weaknesses, Opportunities and Threats) analysis of the different approaches (population continuous modelling and Individual-based Modelling), which we hope will be helpful for current and future

  4. Analysis of anatomic variability in children with low mathematical skills

    Han, Zhaoying; Fuchs, Lynn; Davis, Nikki; Cannistraci, Christopher J.; Anderson, Adam W.; Gore, John C.; Dawant, Benoit M.


    Mathematical difficulty affects approximately 5-9% of the population. Studies on individuals with dyscalculia, a neurologically based math disorder, provide important insight into the neural correlates of mathematical ability. For example, cognitive theories, neuropsychological studies, and functional neuroimaging studies in individuals with dyscalculia suggest that the bilateral parietal lobes and intraparietal sulcus are central to mathematical performance. The purpose of the present study was to investigate morphological differences in a group of third grade children with poor math skills. We compare population averages of children with low math skill (MD) to gender and age matched controls with average math ability. Anatomical data were gathered with high resolution MRI and four different population averaging methods were used to study the effect of the normalization technique on the results. Statistical results based on the deformation fields between the two groups show anatomical differences in the bilateral parietal lobes, right frontal lobe, and left occipital/parietal lobe.

  5. A mathematical analysis of multiple-target SELEX.

    Seo, Yeon-Jung; Chen, Shiliang; Nilsen-Hamilton, Marit; Levine, Howard A


    SELEX (Systematic Evolution of Ligands by Exponential Enrichment) is a procedure by which a mixture of nucleic acids can be fractionated with the goal of identifying those with specific biochemical activities. One combines the mixture with a specific target molecule and then separates the target-NA complex from the resulting reactions. The target-NA complex is separated from the unbound NA by mechanical means (such as by filtration), the NA is eluted from the complex, amplified by PCR (polymerase chain reaction), and the process repeated. After several rounds, one should be left with the nucleic acids that best bind to the target. The problem was first formulated mathematically in Irvine et al. (J. Mol. Biol. 222:739-761, 1991). In Levine and Nilsen-Hamilton (Comput. Biol. Chem. 31:11-25, 2007), a mathematical analysis of the process was given. In Vant-Hull et al. (J. Mol. Biol. 278:579-597, 1998), multiple target SELEX was considered. It was assumed that each target has a single nucleic acid binding site that permits occupation by no more than one nucleic acid. Here, we revisit Vant-Hull et al. (J. Mol. Biol. 278:579-597, 1998) using the same assumptions. The iteration scheme is shown to be convergent and a simplified algorithm is given. Our interest here is in the behavior of the multiple target SELEX process as a discrete "time" dynamical system. Our goal is to characterize the limiting states and their dependence on the initial distribution of nucleic acid and target fraction components. (In multiple target SELEX, we vary the target component fractions, but not their concentrations, as fixed and the initial pool of nucleic acids as a variable starting condition). Given N nucleic acids and a target consisting of M subtarget component species, there is an M × N matrix of affinities, the (i,j) entry corresponding to the affinity of the jth nucleic acid for the ith subtarget. We give a structure condition on this matrix that is equivalent to the following

  6. Analysis of mathematical model for micromechanical vibratory wheel gyroscope

    LUO Yue-sheng; FAN Chong-jin; TAN Zhen-fan


    By the sketch of structure of MVWG,the working laws of this kind of gyroscope were explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.

  7. Harmonic analysis approach to the 'TunneLadder' - A modified Karp circuit for millimeter-wave TWTA's

    Kosmahl, H. G.; Palmer, R. W.


    A field approach to the summed harmonic analysis of the TunneLadder structure, or modified forward-wave Karp circuit, is developed by combining TM(01) and TE(11) modes. Results suggest the suitability of this structure as a high-impedance, about 1-% bandwidth circuit, millimeter-wave forward-wave-type amplifier that is voltage tunable over about a 5-% frequency range and has excellent power handling ability. Theory gives good agreement with experimental results obtained by Karp in omega-beta dispersion and predicts qualitatively the appearances of the antisymmetric mode discussed and of the so called Hightron mode that was discussed earlier in White, Enderby and Birdsall (1964), and Enderby (1964), in addition to the desired symmetric mode.

  8. Harmonic analysis approach to the 'TunneLadder' - A modified Karp circuit for millimeter-wave TWTA's

    Kosmahl, H. G.; Palmer, R. W.


    A field approach to the summed harmonic analysis of the TunneLadder structure, or modified forward-wave Karp circuit, is developed by combining TM(01) and TE(11) modes. Results suggest the suitability of this structure as a high-impedance, about 1-% bandwidth circuit, millimeter-wave forward-wave-type amplifier that is voltage tunable over about a 5-% frequency range and has excellent power handling ability. Theory gives good agreement with experimental results obtained by Karp in omega-beta dispersion and predicts qualitatively the appearances of the antisymmetric mode discussed and of the so called Hightron mode that was discussed earlier in White, Enderby and Birdsall (1964), and Enderby (1964), in addition to the desired symmetric mode.

  9. Analysis of Harmonic Vibration of Cable-Stayed Footbridge under the Influence of Changes of the Cables Tension

    Pakos Wojciech


    Full Text Available The paper presents numerical analysis of harmonically excited vibration of a cable-stayed footbridge caused by a load function simulating crouching (squats while changing the static tension in chosen cables. The intentional synchronized motion (e.g., squats of a single person or group of persons on the footbridge with a frequency close to the natural frequency of the structure may lead to the resonant vibrations with large amplitudes. The appropriate tension changes in some cables cause detuning of resonance on account of stiffness changes of structures and hence detuning in the natural frequency that is close to the excitation frequency. The research was carried out on a 3D computer model of a real structure - a cable-stayed steel footbridge in Leśnica, a quarter of Wrocław, Poland, with the help of standard computer software based on FEM COSMOS/M System.

  10. Analysis of Harmonic Vibration of Cable-Stayed Footbridge under the Influence of Changes of the Cables Tension

    Pakos, Wojciech


    The paper presents numerical analysis of harmonically excited vibration of a cable-stayed footbridge caused by a load function simulating crouching (squats) while changing the static tension in chosen cables. The intentional synchronized motion (e.g., squats) of a single person or group of persons on the footbridge with a frequency close to the natural frequency of the structure may lead to the resonant vibrations with large amplitudes. The appropriate tension changes in some cables cause detuning of resonance on account of stiffness changes of structures and hence detuning in the natural frequency that is close to the excitation frequency. The research was carried out on a 3D computer model of a real structure - a cable-stayed steel footbridge in Leśnica, a quarter of Wrocław, Poland, with the help of standard computer software based on FEM COSMOS/M System.

  11. Philosophy of Mathematics, Mathematics Education and Philosophy of Mathematics Education.

    Zheng, Yuxin


    Uses the modern development of mathematics education in the United States as background for the analysis of the influence of mathematics philosophy on mathematics education. Discusses the problem of how to develop the subject of philosophy of mathematics education, regarded as an impetus from mathematics education, to the further development of…

  12. Harmonic analysis of irradiation asymmetry for cylindrical implosions driven by high-frequency rotating ion beams

    Bret, Antoine; Tahir, Naeem


    Cylindrical implosions driven by intense heavy ions beams should be instrumental in a near future to study High Energy Density Matter. By rotating the beam by means of a high frequency wobbler, it should be possible to deposit energy in the outer layers of a cylinder, compressing the material deposited in its core. The beam temporal profile should however generate an inevitable irradiation asymmetry likely to feed the Rayleigh-Taylor instability (RTI) during the implosion phase. In this paper, we compute the Fourier components of the target irradiation in order to make the junction with previous works on RTI performed in this setting. Implementing a 1D and 2D beam models, we find these components can be expressed exactly in terms of the Fourier transform of the temporal beam profile. If $T$ is the beam duration and $\\Omega$ its rotation frequency, "magic products" $\\Omega T$ can be identified which cancel the first harmonic of the deposited density, resulting in an improved irradiation symmetry.

  13. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    Bogdan, V. M.; Bond, V. B.


    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  14. Analysis of second-harmonic-generation microscopy in a mouse model of ovarian carcinoma.

    Watson, Jennifer M; Rice, Photini F; Marion, Samuel L; Brewer, Molly A; Davis, John R; Rodriguez, Jeffrey J; Utzinger, Urs; Hoyer, Patricia B; Barton, Jennifer K


    Second-harmonic-generation (SHG) imaging of mouse ovaries ex vivo was used to detect collagen structure changes accompanying ovarian cancer development. Dosing with 4-vinylcyclohexene diepoxide and 7,12-dimethylbenz[a]anthracene resulted in histologically confirmed cases of normal, benign abnormality, dysplasia, and carcinoma. Parameters for each SHG image were calculated using the Fourier transform matrix and gray-level co-occurrence matrix (GLCM). Cancer versus normal and cancer versus all other diagnoses showed the greatest separation using the parameters derived from power in the highest-frequency region and GLCM energy. Mixed effects models showed that these parameters were significantly different between cancer and normal (P<0.008). Images were classified with a support vector machine, using 25% of the data for training and 75% for testing. Utilizing all images with signal greater than the noise level, cancer versus not-cancer specimens were classified with 81.2% sensitivity and 80.0% specificity, and cancer versus normal specimens were classified with 77.8% sensitivity and 79.3% specificity. Utilizing only images with greater than of 75% of the field of view containing signal improved sensitivity and specificity for cancer versus normal to 81.5% and 81.1%. These results suggest that using SHG to visualize collagen structure in ovaries could help with early cancer detection.

  15. Thermodynamical analysis of a quantum heat engine based on harmonic oscillators

    Insinga, Andrea; Andresen, Bjarne; Salamon, Peter


    Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

  16. Harmonic Differential Quadrature Analysis of Soft-Core Sandwich Panels under Locally Distributed Loads

    Xinwei Wang


    Full Text Available Sandwich structures are widely used in practice and thus various engineering theories adopting simplifying assumptions are available. However, most engineering theories of beams, plates and shells cannot recover all stresses accurately through their constitutive equations. Therefore, the soft-core is directly modeled by two-dimensional (2D elasticity theory without any pre-assumption on the displacement field. The top and bottom faces act like the elastic supports on the top and bottom edges of the core. The differential equations of the 2D core are then solved by the harmonic differential quadrature method (HDQM. To circumvent the difficulties in dealing with the locally distributed load by point discrete methods such as the HDQM, a general and rigorous way is proposed to treat the locally distributed load. Detailed formulations are provided. The static behavior of sandwich panels under different locally distributed loads is investigated. For verification, results are compared with data obtained by ABAQUS with very fine meshes. A high degree of accuracy on both displacement and stress has been observed.

  17. Technical and harmonic analysis of Carl Czerny op. 299 number 34 etude

    Mehmet Serkan Umuzdas


    Full Text Available In this study, the 34th etude of the book Czerny Op. 299 that is one of the commonly employed books in the piano training was analysed in terms of technique and harmony. The etude was examined in terms of its technical features and contributions to technical development. If an etude is analysed before it is played, time and effort can be amanged much more efficiently. In turn, it may contribute to play the etude or work in accordance with its objectives and to produce outcomes. The aims of this study are to make the students aware of the goals and methods of etudes and to provide them with the suggestions for studying. It is suggested that any etude written with the 2/4 rhythm pattern should be played very vividly and energytically. Any etude written in the octave width of 5.5 is made up of 43 scales in two section. The etude is composed of two sections, each with four sentences and two periods. It also involves 43 scales. Of them, 16 scales are in the first section and the remaining 27 scales are in the second section. The etude has very regular system in terms of harmonic continuity and motives. It has a homogenious pattern in terms of the order of the sentences with half-decsion and those with full-decision.

  18. Mathematical Modelling and Experimental Analysis of Early Age Concrete

    Hauggaard-Nielsen, Anders Boe


    The report deals with mathematical models for concrete at early age. In the hardening process chemical reactions take place and the concrete skeleton is created. The processes changes the moisture content and produces heat. The associated temperature rise gives expansion of the material which may...

  19. Analysis of rear end impact using mathematical human modelling

    Happee, R.; Meijer, R.; Horst, M.J. van der; Ono, K.; Yamazaki, K.


    At TNO an omni-directional mathematical human body model has been developed. Until now this human model has been validated for frontal and lateral loading using response data of volunteer and post mortem human subject (PMHS) sled tests. For rearward loading it has been validated for high speed impac

  20. Classroom Data Analysis with the Five Strands of Mathematical Proficiency

    Groth, Randall E.


    Qualitative classroom data from video recordings and students' written work can play important roles in improving mathematics instruction. In order to take full advantage of these data sources, it is helpful to have a strong analytic lens to orient one's reflections on the data. One promising analytic lens is the National Research Council's five…

  1. Phononic High Harmonic Generation

    Ganesan, Adarsh; Seshia, Ashwin A


    This paper reports the first experimental evidence for phononic low-order to high-order harmonic conversion leading to high harmonic generation. Similar to parametric resonance, phononic high harmonic generation is also mediated by a threshold dependent instability of a driven phonon mode. Once the threshold for instability is met, a cascade of harmonic generation processes is triggered. Firstly, the up-conversion of first harmonic phonons into second harmonic phonons is established. Subsequently, the down-conversion of second harmonic phonons into first harmonic phonons and conversion of first and second harmonic phonons into third harmonic phonons occur. On the similar lines, an eventual conversion of third harmonic phonons to high orders is also observed to commence. This surprising physical pathway for phononic low-order to high-order harmonic conversion may find general relevance to other physical systems.

  2. Modal test and analysis: Multiple tests concept for improved validation of large space structure mathematical models

    Wada, B. K.; Kuo, C-P.; Glaser, R. J.


    For the structural dynamic analysis of large space structures, the technology in structural synthesis and the development of structural analysis software have increased the capability to predict the dynamic characteristics of the structural system. The various subsystems which comprise the system are represented by various displacement functions; the displacement functions are then combined to represent the total structure. Experience has indicated that even when subsystem mathematical models are verified by test, the mathematical representations of the total system are often in error because the mathematical model of the structural elements which are significant when loads are applied at the interconnection points are not adequately verified by test. A multiple test concept, based upon the Multiple Boundary Condition Test (MBCT), is presented which will increase the accuracy of the system mathematical model by improving the subsystem test and test/analysis correlation procedure.

  3. Engineering Mathematical Analysis Method for Productivity Rate in Linear Arrangement Serial Structure Automated Flow Assembly Line

    Tan Chan Sin


    Full Text Available Productivity rate (Q or production rate is one of the important indicator criteria for industrial engineer to improve the system and finish good output in production or assembly line. Mathematical and statistical analysis method is required to be applied for productivity rate in industry visual overviews of the failure factors and further improvement within the production line especially for automated flow line since it is complicated. Mathematical model of productivity rate in linear arrangement serial structure automated flow line with different failure rate and bottleneck machining time parameters becomes the basic model for this productivity analysis. This paper presents the engineering mathematical analysis method which is applied in an automotive company which possesses automated flow assembly line in final assembly line to produce motorcycle in Malaysia. DCAS engineering and mathematical analysis method that consists of four stages known as data collection, calculation and comparison, analysis, and sustainable improvement is used to analyze productivity in automated flow assembly line based on particular mathematical model. Variety of failure rate that causes loss of productivity and bottleneck machining time is shown specifically in mathematic figure and presents the sustainable solution for productivity improvement for this final assembly automated flow line.

  4. Linear analysis of the 4-step Carr\\'e phase shifting algorithm: spectrum, signal-to-noise ratio, and harmonics response

    Servin, Manuel


    We analyze the nonlinear Carr\\'e 4-steps algorithm including its frequency response, signal-to-noise ratio, and harmonics rejection using linear systems theory. At first sight the previous statement as well as the title of this paper seems paradoxical. How can we analyze the 4-step non-linear Carr\\'e Phase Shifting Algorithm (PSA) using linear system theory? The short answer is that the non-linear Carr\\'e algorithm may be decomposed into two building blocks. The first block is a tunable linear 4-step PSA, and the second one is a non-linear phase-step estimator. Although this fact is well known from the derivation of the Carr\\'e algorithm, nobody has properly exploited it. In other words, to this day, we do not have explicit mathematical formulae for a) the spectrum, b) the harmonics rejection, and c) the signal-to-noise ratio of the non-linear Carr\\'e algorithm. These are the properties of the Carr\\'e's PSA that we show here with novel and explicit mathematical formulae.

  5. 基于 ADA MS 谐波减速器的模态分析%Modal Analysis of Harmonic Reducer Based on ADAMS

    王晓伟; 郝长中


    In order to study the harmonic reducer vibra-tion in the working process and to avoid the resonance ,first-ly ,this paper sets up three dimensional rigid body model of harmonic gear reducer in Pro/E according to the calculated parameters of main components .Then it makes the modal a-nalysis for flexible wheel of harmonic reducer in ANSYS ,fi-nally it builds the harmonic reducer of Rigid -Flex Hybrid Modeling in ADAMS and makes the modal analysis for the whole machine modal .According to the analyses in this pa-per ,the harmonic reducer reasonable design does not pro-duce resonance phenomenon , to ensure that the design of harmonic gear reducer has good dynamic performance .%为了研究谐波减速器在工作过程中的振动情况,避免共振,首先根据计算得到的主要零部件参数,在Pro/E中建立谐波减速器的刚体三维模型;然后利用 A N-SYS对谐波减速器的柔轮进行模态分析;最后在 ADAMS中建立谐波减速器刚-柔混合虚拟样机,并进行整机模态分析。分析得知,该谐波减速器设计合理,不会产生共振现象,具有良好的动力学性能。

  6. Mathematical analysis and numerical simulation of a model of morphogenesis.

    Muñoz, Ana I; Tello, José Ignacio


    We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.

  7. Mathematical analysis of dermal absorption rate of heavy metals.

    Batkin, Izmail; Bolic, Miodrag


    Presently 90 - 95% of children in the US wear disposable diapers before completing their toilet training at average age of 30 months. The diaper absorbs urine and liquid component from feces contaminated with excreted toxicants. In this initial study, we posit that the long contact between the diaper and the skin leads to increased dermal reabsorption of excreted body toxicants, mainly heavy metals, which are statistically associated with autism and neurodevelopmental disorder. We developed a mathematical model to analyse the increase of the level of toxicants due to dermal reabsorption after excretion. This simple kinetic model gives us the average reabsorbtion factor in the range of 1.6 to 5. The limitation of this work is that only mathematical model has been considered and it has not been verified experimentally.

  8. Experimental and Mathematical Analysis of Multilayer Insulation below 80 K

    Chorowski, M; Parente, C; Riddone, G


    The Large Hadron Collider [1], presently under construction at CERN, will make an extensive use of multilayer insulation system (MLI). The total surface to be insulated will be of about 80000 m2. A mathematical model has been developed to describe the heat flux through MLI from 80 K to 4.2 K. The total heat flux between the layers is the result of three distinct heat transfer modes: radiation, residual gas conduction and solid conduction. The mathematical model enables prediction of MLI behavior with regard to different MLI parameters, such as gas insulation pressure, number of layers and boundary temperatures. The calculated values have been compared to the experimental measurements carried out at CERN. Theoretical and experimental results revealed to be in good agreement, especially for insulation vacuum between 10-5 Pa and 10-3 Pa.



    Gradual faults and abrupt faults of mechanical systems are differentiated by variation patterns of state var ibles.After the reasons of abrupt faults are analyzed by nonlinear dynamics,two methods establishing the mathematical models for abrupt faults are presented.As an example,a cusp catastrophe model of the vibration amplitudes of a Jeffcott rotor with nonlinear stiffness and its parameter condition of the vibration state catastrophe are obtained.

  10. A Mathematical and Sociological Analysis of Google Search Algorithm


    it is the most used computational algorithm in the world. More and more websites such as Facebook, Amazon, Netflix , and etc.. use similar search...matrix completion is a research topic in mathematics which is recently actively studied. It starts from the well-known Netflix problem. Indeed... Netflix (cf. [36]) made available publicly such a set of data with about 105 known entries of its movie rating matrix of size about 5 × 105 times 2 × 105

  11. Mathematical Theory of Compressible Viscous Fluids: Analysis and Numerics

    Feireisl, E. (Eduard); Karper, T.; Pokorný, M.


    This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring...

  12. Variational analysis and aerospace engineering mathematical challenges for the aerospace of the future

    Mohammadi, Bijan; Pironneau, Olivier; Cipolla, Vittorio


    This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics methods, optimization methods in aerodynamics, optimum controls, dynamic systems, the theory of structures, space missions, flight mechanics, control theory, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful as it illustrates current collaborative research projects in applied mathematics and aerospace engineering.

  13. Analysis of Science and Mathematics Education Articles Published In Turkey-I: Keywords

    Enver TATAR


    Full Text Available In this study, a descriptive analysis of science and mathematics education articlespublished in Turkey was purposed. The study was carried out based on the keywords ofa total of 680 articles which were published in 26 refereed journals during 2000-2006.As a result of the analysis of the data obtained from the study, the following werefound: (a there were keywords including up to eight words, almost in the form of asentence (b The frequencies of nearly all keywords related to topics in the curriculumof science and mathematics were low c Science and mathematics topics in thecurriculum of primary school were studied less than topics in secondary and universitylevel (d Studies related to the misconceptions in the science education and related toattitude the mathematics education were mostly studied by researchers.

  14. Data Analysis in the K-12 Mathematics Curriculum: Teaching the Teachers.

    Scheaffer, Richard L.


    Provides an overview of the structure of data analysis, the interrelationship between data analysis and probability, and the connection between data analysis and other components of the mathematics curriculum. Presents a possible order for topics being consistent with modern statistical practice and allows the topics to grow as students moves…

  15. Harmonic structures and intrinsic torsion

    Conti, Diego; Madsen, Thomas Bruun

    We discuss the construction of 8-manifolds with harmonic Sp(2)Sp(1)-structures. In particular, we find 10 new examples of nilmanifolds that admit a closed 4-form Omega whose stabiliser is Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough inv...... investigation of the intrinsic torsion of such structures; in addition to the construction of harmonic structures, this analysis leads to explicit Lie group examples with invariant intrinsic torsion....

  16. An analysis method for harmonic resonance and stability of multi-paralleled LCL-filtered inverters

    Lu, Minghui; Wang, Xiongfei; Blaabjerg, Frede;


    the resonance characteristic and stability analysis in multi-paralleled grid-connected inverters with LCL-filters. An intuitive analytical method based on equivalent grid impedance has been proposed. The analysis clearly describes the open loop resonance characteristic and provides a relatively easy method...... to define the stable region of multi-inverters system. Experimental results are provided for verifying the theoretical analysis....

  17. Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

    Bardhan, Jaydeep P; Knepley, Matthew G


    We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements.

  18. A Critical Discourse Analysis of a Real-World Problem in Mathematics: Looking for Signs of Change

    Le Roux, Kate


    The concepts of "access" and "relevance" feature prominently in the discourse of change in mathematics education in South Africa. One way in which these concepts have been played out in mathematics classrooms is in the use of mathematical problems with real-world contexts. This paper presents a Critical Discourse Analysis of…

  19. A Critical Discourse Analysis of a Real-World Problem in Mathematics: Looking for Signs of Change

    Le Roux, Kate


    The concepts of "access" and "relevance" feature prominently in the discourse of change in mathematics education in South Africa. One way in which these concepts have been played out in mathematics classrooms is in the use of mathematical problems with real-world contexts. This paper presents a Critical Discourse Analysis of…

  20. Harmonic analysis and FPGA implementation of SHE controlled three phase CHB 11-level inverter in MV drives using deterministic and stochastic optimization techniques.

    Vesapogu, Joshi Manohar; Peddakotla, Sujatha; Kuppa, Seetha Rama Anjaneyulu


    With the advancements in semiconductor technology, high power medium voltage (MV) Drives are extensively used in numerous industrial applications. Challenging technical requirements of MV Drives is to control multilevel inverter (MLI) with less Total harmonic distortion (%THD) which satisfies IEEE standard 519-1992 harmonic guidelines and less switching losses. Among all modulation control strategies for MLI, Selective harmonic elimination (SHE) technique is one of the traditionally preferred modulation control technique at fundamental switching frequency with better harmonic profile. On the other hand, the equations which are formed by SHE technique are highly non-linear in nature, may exist multiple, single or even no solution at particular modulation index (MI). However, in some MV Drive applications, it is required to operate over a range of MI. Providing analytical solutions for SHE equations during the whole range of MI from 0 to 1, has been a challenging task for researchers. In this paper, an attempt is made to solve SHE equations by using deterministic and stochastic optimization methods and comparative harmonic analysis has been carried out. An effective algorithm which minimizes %THD with less computational effort among all optimization algorithms has been presented. To validate the effectiveness of proposed MPSO technique, an experiment is carried out on a low power proto type of three phase CHB 11- level Inverter using FPGA based Xilinx's Spartan -3A DSP Controller. The experimental results proved that MPSO technique has successfully solved SHE equations over all range of MI from 0 to 1, the %THD obtained over major range of MI also satisfies IEEE 519-1992 harmonic guidelines too.

  1. Optimal Selective Harmonic Control for Power Harmonics Mitigation

    Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede


    the cost, the complexity and the performance: high accuracy, fast transient response, easy-implementation, cost-effective, and also easy-to-design. The analysis and synthesis of the optimal SHC system are addressed. The proposed SHC offers power convert-ers a tailor-made optimal control solution......This paper proposes an Internal Model Principle (IMP) based optimal Selective Harmonic Controller (SHC) for power converters to mitigate power harmonics. According to the harmonics distribution caused by power converters, a universal recursive SHC module is developed to deal with a featured group...... of power harmonics. The proposed optimal SHC is of hybrid structure: all recursive SHC modules with weighted gains are connected in parallel. It bridges the real “nk+-m order RC” and the complex “parallel structure RC”. Compared to other IMP based control solutions, it offers an optimal trade-off among...

  2. Investigating Pre-Service Candidates' Images of Mathematical Reasoning: An In-Depth Online Analysis of Common Core Mathematics Standards

    Davis, C. E.; Osler, James E.


    This paper details the outcomes of a qualitative in-depth investigation into teacher education mathematics preparation. This research is grounded in the notion that mathematics teacher education students (as "degree seeking candidates") need to develop strong foundations of mathematical practice as defined by the Common Core State…

  3. Unique Signal mathematical analysis task group FY03 status report.

    Baty, Roy Stuart (Los Alamos National Laboratory, Los Alamos, NM); Johnston, Anna Marie; Hart, Elizabeth (Utah State University, Logan, UT); White, Allan (NASA, Langley Research Center, Hampton, VA); Cooper, James Arlin


    The Unique Signal is a key constituent of Enhanced Nuclear Detonation Safety (ENDS). Although the Unique Signal approach is well prescribed and mathematically assured, there are numerous unsolved mathematical problems that could help assess the risk of deviations from the ideal approach. Some of the mathematics-based results shown in this report are: 1. The risk that two patterns with poor characteristics (easily generated by inadvertent processes) could be combined through exclusive-or mixing to generate an actual Unique Signal pattern has been investigated and found to be minimal (not significant when compared to the incompatibility metric of actual Unique Signal patterns used in nuclear weapons). 2. The risk of generating actual Unique Signal patterns with linear feedback shift registers is minimal, but the patterns in use are not as invulnerable to inadvertent generation by dependent processes as previously thought. 3. New methods of testing pair-wise incompatibility threats have resulted in no significant problems found for the set of Unique Signal patterns currently used. Any new patterns introduced would have to be carefully assessed for compatibility with existing patterns, since some new patterns under consideration were found to be deficient when associated with other patterns in use. 4. Markov models were shown to correspond to some of the engineered properties of Unique Signal sequences. This gives new support for the original design objectives. 5. Potential dependence among events (caused by a variety of communication protocols) has been studied. New evidence has been derived of the risk associated with combined communication of multiple events, and of the improvement in abnormal-environment safety that can be achieved through separate-event communication.

  4. Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications

    Marilyn E. Noz


    Full Text Available Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac’s light-cone coordinate system, Lorentz boosts are squeeze transformations. Thus the squeeze transformation is one of the fundamental transformations in Einstein’s Lorentz-covariant world. It is possible to define a complete set of orthonormal functions defined for one Lorentz frame. It is shown that the same set can be used for other Lorentz frames. Transformation properties are discussed. Physical applications are discussed in both optics and high-energy physics. It is shown that the Lorentz harmonics provide the mathematical basis for squeezed states of light. It is shown also that the same set of harmonics can be used for understanding Lorentz-boosted hadrons in high-energy physics. It is thus possible to transmit physics from one branch of physics to the other branch using the mathematical basis common to them.

  5. Analysis of a mathematical model describing necrotic tumor growth

    Escher, Joachim; Matioc, Bogdan-Vasile


    In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical formulation is a moving boundary problem where both boundaries delimiting the nonnecrotic shell are allowed to evolve in time.We determine all radially symmetric stationary solutions of the problem and reduce the moving boundary problem into a nonlinear evolution. Parabolic theory provides us the perfect context in order to show local well-posed of the problem for small initial data.

  6. Analysis of central venous pressure (CVP) signals using mathematical methods.

    Atefvahid, Parham; Hassani, Kamran; Jafarian, Kamal; Doyle, D John; Ahmadi, Hessam


    Central venous pressure (CVP) is an important clinical parameter for physicians but only the absolute CVP value is typically monitored in the intensive care unit (ICU). In this study, we propose a novel mathematical method to present and analyze CVP signals. A total of 44 suitable samples were chosen from a total of 65 collected in an ICU. Pre-processing of the samples included rate reduction and digital filtering. The statistical features of time and frequency domain, wavelet, and empirical mode decomposition of these signals were extracted. We found no significant difference among the CVP signals regarding sex, smoking, coronary disease, and respiration mode of the samples.

  7. Mathematical analysis of partial differential equations modeling electrostatic MEMS

    Esposito, Pierpaolo; Guo, Yujin


    Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed

  8. Molecular structure, Normal Coordinate Analysis, harmonic vibrational frequencies, Natural Bond Orbital, TD-DFT calculations and biological activity analysis of antioxidant drug 7-hydroxycoumarin

    Sebastian, S.; Sylvestre, S.; Jayarajan, D.; Amalanathan, M.; Oudayakumar, K.; Gnanapoongothai, T.; Jayavarthanan, T.


    In this work, we report harmonic vibrational frequencies, molecular structure, NBO and HOMO, LUMO analysis of Umbelliferone also known as 7-hydroxycoumarin (7HC). The optimized geometric bond lengths and bond angles obtained by computation (monomer and dimmer) shows good agreement with experimental XRD data. Harmonic frequencies of 7HC were determined and analyzed by DFT utilizing 6-311+G(d,p) as basis set. The assignments of the vibrational spectra have been carried out with the help of Normal Coordinate Analysis (NCA) following the Scaled Quantum Mechanical Force Field Methodology (SQMFF). The change in electron density (ED) in the σ* and π* antibonding orbitals and stabilization energies E(2) have been calculated by Natural Bond Orbital (NBO) analysis to give clear evidence of stabilization originating in the hyperconjugation of hydrogen-bonded interaction. The energy and oscillator strength calculated by Time-Dependent Density Functional Theory (TD-DFT) complements with the experimental findings. The simulated spectra satisfactorily coincides with the experimental spectra. Microbial activity of studied compounds was tested against Staphylococcus aureus, Streptococcus pyogenes, Bacillus subtilis, Escherichia coli, Psuedomonas aeruginosa, Klebsiella pneumoniae, Proteus mirabilis, Shigella flexneri, Salmonella typhi and Enterococcus faecalis.

  9. Mathematics of uncertainty modeling in the analysis of engineering and science problems

    Chakraverty, S


    For various scientific and engineering problems, how to deal with variables and parameters of uncertain value is an important issue. Full analysis of the specific errors in measurement, observations, experiments, and applications are vital in dealing with the parameters taken to simplify the problem. Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems aims to provide the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications. This book is an essential reference work for students, scholars, practitioners and researchers in the assorted fields of engineering and applied mathematics interested in a model for uncertain physical problems.

  10. Discrete Mathematics

    Sørensen, John Aasted


    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  11. Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.

    Zhang, Elizabeth R; Wu, Lani F; Altschuler, Steven J


    The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. Copyright © 2013 Elsevier Ltd. All rights reserved.

  12. The use of video analysis and the Knowledge Quartet in mathematics teacher education programmes

    Liston, Miriam


    This study investigates the potential of video analysis and a mathematical knowledge for teaching framework, the Knowledge Quartet (KQ), in mathematics teacher education programmes. It reports on the effectiveness of these tools in analysing and supporting secondary level pre-service mathematics teachers' subject matter knowledge and pedagogical content knowledge. This paper describes how a videotaped lesson of one pre-service teacher, teaching a class of mature students, was analysed and makes comparisons between the teacher educators' and the pre-service teacher's observations. Inter-rater reliability was investigated and a Kappa coefficient of .72 indicated substantial agreement between both coders. Findings are presented and implications of the use of video and the KQ for mathematics teacher education are drawn.

  13. Mathematical adventures in performance analysis from storage systems, through airplane boarding, to express line queues

    Bachmat, Eitan


    This monograph describes problems in the field of performance analysis, primarily the study of storage systems and the diverse mathematical techniques that are required for solving such problems. Topics covered include best practices for scheduling I/O requests to a disk drive, how this problem is related to airplane boarding, and how both problems can be modeled using space-time geometry. The author also explains how Riemann's proof of the analytic continuation and functional equation of the Riemann zeta function can be used to analyze express-line queues in a minimarket. Overall, the book reveals the surprising applicability of abstract mathematical ideas that are not usually associated with applied topics. Advanced undergraduate students or graduate students with an interest in the applications of mathematics will find this book a useful resource. It will also be of interest to professional mathematicians who want exposure to the surprising ways that theoretical mathematics may be applied to engineering pr...


    Piotr FOLĘGA


    Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.

  15. Random harmonic analysis program, L221 (TEV156). Volume 1: Engineering and usage

    Miller, R. D.; Graham, M. L.


    A digital computer program capable of calculating steady state solutions for linear second order differential equations due to sinusoidal forcing functions is described. The field of application of the program, the analysis of airplane response and loads due to continuous random air turbulence, is discussed. Optional capabilities including frequency dependent input matrices, feedback damping, gradual gust penetration, multiple excitation forcing functions, and a static elastic solution are described. Program usage and a description of the analysis used are presented.

  16. A Mathematical Analysis of Semantic Maps, with Theoretical and Applied Implications for Blended Learning Software

    Tang, Michael; David, Hyerle; Byrne, Roxanne; Tran, John


    This paper is a mathematical (Boolean) analysis a set of cognitive maps called Thinking Maps[R], based on Albert Upton's semantic principles developed in his seminal works, Design for Thinking (1961) and Creative Analysis (1961). Albert Upton can be seen as a brilliant thinker who was before his time or after his time depending on the future of…

  17. Using Online Error Analysis Items to Support Preservice Teachers' Pedagogical Content Knowledge in Mathematics

    McGuire, Patrick


    This article describes how a free, web-based intelligent tutoring system, (ASSISTment), was used to create online error analysis items for preservice elementary and secondary mathematics teachers. The online error analysis items challenged preservice teachers to analyze, diagnose, and provide targeted instructional remediation intended to help…

  18. A Mathematical Analysis of Semantic Maps, with Theoretical and Applied Implications for Blended Learning Software

    Tang, Michael; David, Hyerle; Byrne, Roxanne; Tran, John


    This paper is a mathematical (Boolean) analysis a set of cognitive maps called Thinking Maps[R], based on Albert Upton's semantic principles developed in his seminal works, Design for Thinking (1961) and Creative Analysis (1961). Albert Upton can be seen as a brilliant thinker who was before his time or after his time depending on the future of…

  19. A Historical Analysis of Primary Mathematics Curricula in Terms of Teaching Principles

    Ozmantar, Mehmet Fatih


    This study carries out a comparative analysis of primary mathematics curricula put into practice during Turkish Republican period. The data for this study are composed of official curricula documents which are examined in terms of teaching principles. The study adopts a qualitative approach and employs document analysis method. The official…

  20. Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

    Deng Ming-Xi; Xiang Yan-Xun


    Within the second-order perturbation approximation,this paper investigates the physical process of generation of the time-domain second harmonic by a primary Lamb wave waveform in an elastic plate.The present work is performed based on the preconditions that the phase velocity matching is satisfied and that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero.It investigates the influences of the difference between the group velocities of the primary Lamb wave and the double frequency Lamb wave,the propagation distance and the duration of the primary Lamb wave waveform on the envelope shape of the time-domain second harmonic.It finds that the maximum magnitude of the envelope of the second-harmonic waveform can grow within some propagation distance even if the condition of group velocity matching is not satisfied.Our analyses also indicate that the maximum magnitude of the envelope of the second-harmonic waveform is kept constant beyond a specific propagation distance.Furthermore,it concludes that the integration amplitude of the time-domain second-harmonic waveform always grows with propagation distance within the second-order perturbation.The present research yields new physical insight not previously available into the effect of generation of the time-domain second harmonic by propagation of a primary Lamb wave waveform.

  1. A Mathematical Analysis of Air Traffic Priority Rules

    Nakawicz, Anthony J.; Munoz, Cesar A.; Maddalon, Jeffrey M.


    This paper analyzes priority rules, such as those in Part 91.113 of the Federal Aviation Regulations. Such rules determine which of two aircraft should maneuver in a given conflict scenario. While the rules in 91.113 are well accepted, other concepts of operation for NextGen, such as self separation, may allow for different priority rules. A mathematical framework is presented that can be used to analyze a general set of priority rules and enables proofs of important properties. Specific properties considered in this paper include safety, effectiveness, and stability. A set of rules is said to be safe if it ensures that it is never the case that both aircraft have priority. They are effective if exactly one aircraft has priority in every situation. Finally, a set of rules is called stable if it produces compatible results even under small changes to input data.

  2. The Mathematical Statistics Theory Application on the Price Fluctuation Analysis

    Jintao Meng


    Full Text Available Grain price and output fluctuation are the normal state of market economy. It is one of the most important economic researches to understand grain price and output fluctuation law, which provides theory basis for the macroeconomic regulation and control. According to the cobweb model theory, the relationship between citrus production and price is accord with the divergence type of cobweb model .This means that simply relying on market regulation can make fluctuation between production and price bigger, go against citrus production and cultivation, thus, affecting the interests of farmers. It is well-known most farmers are concerned about the future price trend and the probability of price fluctuation. This paper uses mathematical statistics theory to study the citrus price changes, and the corresponding change trend, providing a theoretical basis for majority of farmers to better estimate citrus price change trend.

  3. Introduction to mathematical biology modeling, analysis, and simulations

    Chou, Ching Shan


    This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies. The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations. In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience. The second set of case studies were adapted from recent and current research papers to the level of the students. Topics have been selected based on public health interest. This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis. Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research. Considered to be the undergraduate companion to t...

  4. Analysis of a Mathematical Model of Ischemic Cutaneous wounds

    Friedman, Avner; Xue, Chuan


    Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia represents a serious complicating factor in wound healing. In this paper we analyze a recently developed mathematical model of ischemic dermal wounds. The model consists of a coupled system of partial differential equations in the partially healed region, with the wound boundary as a free boundary. The extracellular matrix (ECM) is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary of the open wound. The model equations involve the concentrations of oxygen, cytokines, and the densities of several types of cells. The ischemic level is represented by a parameter which appears in the boundary conditions, 0 <= gamma < 1; gamma near 1 corresponds to extreme ischemia and gamma = 0 corresponds to normal non-ischemic conditions. We establish global existence and uniqueness of the free boundary problem and study the dependence of the free boundary on...

  5. Verification of temporal-causal network models by mathematical analysis

    Jan Treur


    Full Text Available Abstract Usually dynamic properties of models can be analysed by conducting simulation experiments. But sometimes, as a kind of prediction properties can also be found by calculations in a mathematical manner, without performing simulations. Examples of properties that can be explored in such a manner are: whether some values for the variables exist for which no change occurs (stationary points or equilibria, and how such values may depend on the values of the parameters of the model and/or the initial values for the variables whether certain variables in the model converge to some limit value (equilibria and how this may depend on the values of the parameters of the model and/or the initial values for the variables whether or not certain variables will show monotonically increasing or decreasing values over time (monotonicity how fast a convergence to a limit value takes place (convergence speed whether situations occur in which no convergence takes place but in the end a specific sequence of values is repeated all the time (limit cycle Such properties found in an analytic mathematical manner can be used for verification of the model by checking them for the values observed in simulation experiments. If one of these properties is not fulfilled, then there will be some error in the implementation of the model. In this paper some methods to analyse such properties of dynamical models will be described and illustrated for the Hebbian learning model, and for dynamic connection strengths in social networks. The properties analysed by the methods discussed cover equilibria, increasing or decreasing trends, recurring patterns (limit cycles, and speed of convergence to equilibria.

  6. Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

    Coifman, R R; Lafon, S; Lee, A B; Maggioni, M; Nadler, B; Warner, F; Zucker, S W


    We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scales. The process of iterating or diffusing the Markov matrix is seen as a generalization of some aspects of the Newtonian paradigm, in which local infinitesimal transitions of a system lead to global macroscopic descriptions by integration. We provide a unified view of ideas from data analysis, machine learning, and numerical analysis.

  7. The Analysis of Harmonized Common Structure Rules%共同结构规范(HCSR)浅析



    The HCSR is harmonized common structure rule for bulk carrier an d oil tanker. Its many content are different from CSR,especially load cases,yield strength criteria,finite element analysis,fatigue strength, etc. So the paper narrates the background of HCSR,also analyzes and studies that the HCSR’s new rules and requirements for the above content in order to provide technical support for HCSR applying.%IACS新开发的适用散货船和油船的共同结构规范( HCSR)相比CSR,许多内容都有了新规定或新要求,尤其是载荷工况、强度衡准、有限元分析以及疲劳强度等几方面。本文对以上几方面内容在HCSR中的主要变化点进行了分析研究,为以后HCSR的实际应用提供支持。

  8. Analysis and quantification of collagen organization with the structure tensor in second harmonic microscopy images of ocular tissues.

    Ávila, Francisco J; Bueno, Juan M


    The important biological role of collagen-based tissues and the changes produced in the fiber distribution under particular situations (surgery, pathology, external damage, etc.) require tools for the analysis of the collagen organization that might potentially help in early diagnoses. Since collagen structures provide efficient second harmonic generation (SHG) signals, SHG microscopy has emerged as a powerful technique to visualize collagen fibers and qualitatively discriminate normal from abnormal tissues. Here we propose a quantitative method based on the structure tensor to quantify the different organization of collagen patterns in SHG images of ocular tissues. Results show that well-organized collagen distributions present a high degree of isotropy (DoI), a dominant orientation (PO), and a low structural dispersion (SD). On the other hand, the PO vanishes when the collagen tissue is not organized as a consequence of an increase in the SD and a decrease in the DoI. The proposed method is also able to discriminate partially organized samples. The combination of SHG microscopy and the structure tensor is a useful method to objectively classify collagen distributions. Clinical applications of this technique could help in the diagnosis and tracking of pathologies related to collagen disorders in connective tissue.

  9. New matrix method for response analysis of circumferentially stiffened non-circular cylindrical shells under harmonic pressure


    Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order, a new matrix method is presented for steady-state vibration analysis of a noncircular cylindrical shell simply supported at two ends and circumferentially stiffened by rings under harmonic pressure. Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration approach other than the Runge-Kutta-Gill integration method. The transfer matrix can easily be determined by a high precision integration scheme. In addition, besides the normal interacting forces, which were commonly adopted by researchers earlier, the tangential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δ function. The effects of the exciting frequencies on displacements and stresses responses have been investigated. Numerical results show that the proposed method is more efficient than the aforementioned method.

  10. Spectral harmonic analysis and synthesis of Earth’s crust gravity field

    Tenzer, R.; Novák, P.; Vajda, P.; Gladkikh, V.; Hamayun, K.


    We developed and applied a novel numerical scheme for a gravimetric forward modelling of the Earth’s crustal density structures based entirely on methods for a spherical analysis and synthesis of the gravitational field. This numerical scheme utilises expressions for the gravitational potentials and

  11. Harmonic analysis of dense time series of landsat imagery for modeling change in forest conditions

    Barry Tyler. Wilson


    This study examined the utility of dense time series of Landsat imagery for small area estimation and mapping of change in forest conditions over time. The study area was a region in north central Wisconsin for which Landsat 7 ETM+ imagery and field measurements from the Forest Inventory and Analysis program are available for the decade of 2003 to 2012. For the periods...

  12. [Development of New Mathematical Methodology in Air Traffic Control for the Analysis of Hybrid Systems

    Hermann, Robert


    The aim of this research is to develop new mathematical methodology for the analysis of hybrid systems of the type involved in Air Traffic Control (ATC) problems. Two directions of investigation were initiated. The first used the methodology of nonlinear generalized functions, whose mathematical foundations were initiated by Colombeau and developed further by Oberguggenberger; it has been extended to apply to ordinary differential. Systems of the type encountered in control in joint work with the PI and M. Oberguggenberger. This involved a 'mixture' of 'continuous' and 'discrete' methodology. ATC clearly involves mixtures of two sorts of mathematical problems: (1) The 'continuous' dynamics of a standard control type described by ordinary differential equations (ODE) of the form: {dx/dt = f(x, u)} and (2) the discrete lattice dynamics involved of cellular automata. Most of the CA literature involves a discretization of a partial differential equation system of the type encountered in physics problems (e.g. fluid and gas problems). Both of these directions requires much thinking and new development of mathematical fundamentals before they may be utilized in the ATC work. Rather than consider CA as 'discretization' of PDE systems, I believe that the ATC applications will require a completely different and new mathematical methodology, a sort of discrete analogue of jet bundles and/or the sheaf-theoretic techniques to topologists. Here too, I have begun work on virtually 'virgin' mathematical ground (at least from an 'applied' point of view) which will require considerable preliminary work.

  13. The Harmonic Oscillator–A Simplified Approach

    L. R. Ganesan


    Full Text Available Among the early problems in quantum chemistry, the one dimensional harmonic oscillator problem is an important one, providing a valuable exercise in the study of quantum mechanical methods. There are several approaches to this problem, the time honoured infinite series method, the ladder operator method etc. A method which is much shorter, mathematically simpler is presented here.

  14. Orientation analysis of collagen fibers in healing tendon by using second-harmonic-generation microscopy

    Hase, E.; Minamikawa, T.; Sato, K.; Yonekura, D.; Takahashi, M.; Yasui, T.


    Tendon rupture is a trauma that is difficult to fully recover from. Therefore, non-destructive and non-invasive evaluation method for the tendon healing is strongly required. In this study, we performed the orientation analysis of collagen fiber in healing tendon by two-dimensional Fourier transform (2D-FT) of SHG image. The extracted 2D-FT power spectra imply the correlation with the degree of the tendon healing. These results indicate that SHG microscopy has a unique potential as a non-destructive and non-invasive indicator of tendon healing.

  15. Spatially-explicit matrix models. A mathematical analysis of stage-structured integrodifference equations.

    Lutscher, Frithjof; Lewis, Mark A


    This paper is concerned with mathematical analysis of the 'critical domain-size' problem for structured populations. Space is introduced explicitly into matrix models for stage-structured populations. Movement of individuals is described by means of a dispersal kernel. The mathematical analysis investigates conditions for existence, stability and uniqueness of equilibrium solutions as well as some bifurcation behaviors. These mathematical results are linked to species persistence or extinction in connected habitats of different sizes or fragmented habitats; hence the framework is given for application of such models to ecology. Several approximations which reduce the complexity of integrodifference equations are given. A simple example is worked out to illustrate the analytical results and to compare the behavior of the integrodifference model to that of the approximations.

  16. Critical Analysis of the Mathematical Formalism of Theoretical Physics. IV. Foundations of Trigonometry

    Kalanov, Temur Z.


    Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.

  17. Mathematical analysis of a model for glucose regulation.

    Fessel, Kimberly; Gaither, Jeffrey B; Bower, Julie K; Gaillard, Trudy; Osei, Kwame; Rempala, Grzegorz A


    Diabetes affects millions of Americans, and the correct identification of individuals afflicted with this disease, especially of those in early stages or in progression towards diabetes, remains an active area of research. The minimal model is a simplified mathematical construct for understanding glucose-insulin interactions. Developed by Bergman, Cobelli, and colleagues over three decades ago, this system of coupled ordinary differential equations prevails as an important tool for interpreting data collected during an intravenous glucose tolerance test (IVGTT). In this study we present an explicit solution to the minimal model which allows for separating the glucose and insulin dynamics of the minimal model and for identifying patient-specific parameters of glucose trajectories from IVGTT. As illustrated with patient data, our approach seems to have an edge over more complicated methods currently used. Additionally, we also present an application of our method to prediction of the time to baseline recovery and calculation of insulin sensitivity and glucose effectiveness, two quantities regarded as significant in diabetes diagnostics.

  18. A retrospective mathematical analysis of controlled release design and experimentation.

    Rothstein, Sam N; Kay, Jennifer E; Schopfer, Francisco J; Freeman, Bruce A; Little, Steven R


    The development and performance evaluation of new biodegradable polymer controlled release formulations relies on successful interpretation and evaluation of in vitro release data. However, depending upon the extent of empirical characterization, release data may be open to more than one qualitative interpretation. In this work, a predictive model for release from degradable polymer matrices was applied to a number of published release data in order to extend the characterization of release behavior. Where possible, the model was also used to interpolate and extrapolate upon collected released data to clarify the overall duration of release and also kinetics of release between widely spaced data points. In each case examined, mathematical predictions of release coincide well with experimental results, offering a more definitive description of each formulation's performance than was previously available. This information may prove particularly helpful in the design of future studies, such as when calculating proper dosing levels or determining experimental end points in order to more comprehensively evaluate a controlled release system's performance.

  19. Repressing the effects of variable speed harmonic orders in operational modal analysis

    Randall, R. B.; Coats, M. D.; Smith, W. A.


    Discrete frequency components such as machine shaft orders can disrupt the operation of normal Operational Modal Analysis (OMA) algorithms. With constant speed machines, they have been removed using time synchronous averaging (TSA). This paper compares two approaches for varying speed machines. In one method, signals are transformed into the order domain, and after the removal of shaft speed related components by a cepstral notching method, are transformed back to the time domain to allow normal OMA. In the other simpler approach an exponential shortpass lifter is applied directly in the time domain cepstrum to enhance the modal information at the expense of other disturbances. For simulated gear signals with speed variations of both ±5% and ±15%, the simpler approach was found to give better results The TSA method is shown not to work in either case. The paper compares the results with those obtained using a stationary random excitation.

  20. Harmonic Analysis of Vibrations of 4-Chloro-2-Fluroaniline: A Scaled Quantum Mechanical approach

    G. RAJA


    Full Text Available The FT-IR and Raman spectra of 4-Chloro-2-Fluroaniline (4C2FA were measured. The fundamental vibrational frequencies and intensity of vibrational bands were evaluated using density functional theory (DFT and standard B3LYP/6-311+G** basis set combination. The vibrational spectra were interpreted, with the aid of normal coordinate analysis based on a scaled quantum mechanical (SQM force field. The infrared and Raman spectra were also predicted from the calculated intensities. Comparison of simulated spectra with the experimental spectra provides important information about the ability of the computational method to describe the vibrational modes. Unambiguous vibrational assignment of all the fundamentals was made using the total energy distribution (TED.

  1. Phenopolis: an open platform for harmonization and analysis of genetic and phenotypic data.

    Pontikos, Nikolas; Yu, Jing; Moghul, Ismail; Withington, Lucy; Blanco-Kelly, Fiona; Vulliamy, Tom; Wong, Tsz Lun Ernest; Murphy, Cian; Cipriani, Valentina; Fiorentino, Alessia; Arno, Gavin; Greene, Daniel; Jacobsen, Julius O B; Clark, Tristan; Gregory, David S; Nemeth, Andrea M; Halford, Stephanie; Inglehearn, Chris F; Downes, Susan; Black, Graeme C; Webster, Andrew R; Hardcastle, Alison J; Plagnol, Vincent


    Phenopolis is an open-source web server providing an intuitive interface to genetic and phenotypic databases. It integrates analysis tools such as variant filtering and gene prioritization based on phenotype. The Phenopolis platform will accelerate clinical diagnosis, gene discovery and encourage wider adoption of the Human Phenotype Ontology in the study of rare genetic diseases. A demo of the website is available at . If you wish to install a local copy, source code and installation instruction are available at . The software is implemented using Python, MongoDB, HTML/Javascript and various bash shell scripts. Supplementary data are available at Bioinformatics online.

  2. Design and Error Analysis of a Vehicular AR System with Auto-Harmonization.

    Foxlin, Eric; Calloway, Thomas; Zhang, Hongsheng


    This paper describes the design, development and testing of an AR system that was developed for aerospace and ground vehicles to meet stringent accuracy and robustness requirements. The system uses an optical see-through HMD, and thus requires extremely low latency, high tracking accuracy and precision alignment and calibration of all subsystems in order to avoid mis-registration and "swim". The paper focuses on the optical/inertial hybrid tracking system and describes novel solutions to the challenges with the optics, algorithms, synchronization, and alignment with the vehicle and HMD systems. Tracker accuracy is presented with simulation results to predict the registration accuracy. A car test is used to create a through-the-eyepiece video demonstrating well-registered augmentations of the road and nearby structures while driving. Finally, a detailed covariance analysis of AR registration error is derived.

  3. Next generation data harmonization

    Armstrong, Chandler; Brown, Ryan M.; Chaves, Jillian; Czerniejewski, Adam; Del Vecchio, Justin; Perkins, Timothy K.; Rudnicki, Ron; Tauer, Greg


    Analysts are presented with a never ending stream of data sources. Often, subsets of data sources to solve problems are easily identified but the process to align data sets is time consuming. However, many semantic technologies do allow for fast harmonization of data to overcome these problems. These include ontologies that serve as alignment targets, visual tools and natural language processing that generate semantic graphs in terms of the ontologies, and analytics that leverage these graphs. This research reviews a developed prototype that employs all these approaches to perform analysis across disparate data sources documenting violent, extremist events.

  4. Second harmonic generation microscopy

    Brüggemann, Dagmar Adeline; Brewer, Jonathan R.; Risbo, Jens


    Myofibers and collagen show non-linear optical properties enabling imaging using second harmonic generation (SHG) microscopy. The technique is evaluated for use as a tool for real-time studies of thermally induced changes in thin samples of unfixed and unstained pork. The forward and the backward......-temperature endotherm peak observable in the differential scanning calorimetry (DSC) thermograms. DSC analysis of epimysium, the connective tissue layer that enfold skeletal muscles, produces one large endotherm starting at 57 °C and peaking at 59.5 °C. SHG microscopy of collagen fibers reveals a variability of thermal...

  5. Modelling of BLDCM with a double 3-phase stator winding and back EMF harmonics

    Drozdowski Piotr


    Full Text Available In this paper the mathematical model of the brushless DC motor (BLDCM with a double 3-phase stator winding is analysed. Both the 3-phase windings are mutually displaced by 30 electrical degree. Special care has been sacrificed to influence of higher harmonics of induced electromotive forces (EMF on electromagnetic torque and zero sequence voltages that may be used for sensorless control. The mathematical model has been presented in natural variables and, after transformation to symmetrical components, in a vector form. This allows, from one side, for formulating the equivalent circuit suitable for circuit oriented simulators (e.g.: Spice, SimPowerSystems of Simulink and, from the other point of view, for analysis of higher harmonics influence on control possibilities. These considerations have been illustrated with some results of four quadrant operation obtainded due to simulation at automatic control.

  6. Multiple imputation for harmonizing longitudinal non-commensurate measures in individual participant data meta-analysis.

    Siddique, Juned; Reiter, Jerome P; Brincks, Ahnalee; Gibbons, Robert D; Crespi, Catherine M; Brown, C Hendricks


    There are many advantages to individual participant data meta-analysis for combining data from multiple studies. These advantages include greater power to detect effects, increased sample heterogeneity, and the ability to perform more sophisticated analyses than meta-analyses that rely on published results. However, a fundamental challenge is that it is unlikely that variables of interest are measured the same way in all of the studies to be combined. We propose that this situation can be viewed as a missing data problem in which some outcomes are entirely missing within some trials and use multiple imputation to fill in missing measurements. We apply our method to five longitudinal adolescent depression trials where four studies used one depression measure and the fifth study used a different depression measure. None of the five studies contained both depression measures. We describe a multiple imputation approach for filling in missing depression measures that makes use of external calibration studies in which both depression measures were used. We discuss some practical issues in developing the imputation model including taking into account treatment group and study. We present diagnostics for checking the fit of the imputation model and investigate whether external information is appropriately incorporated into the imputed values.

  7. Mean squared displacement analysis of an-harmonic behaviour in lyophilised proteins

    Telling, Mark T.F., E-mail: [ISIS Facility, Rutherford Appleton Laboratory, Chilton OX11 0QX (United Kingdom); Department of Materials, University of Oxford, Parks Road, Oxford (United Kingdom); Howells, Spencer [ISIS Facility, Rutherford Appleton Laboratory, Chilton OX11 0QX (United Kingdom); Combet, Jérôme, E-mail: [Institut Laue Langevin, Grenoble (France); Clifton, Luke A., E-mail: [ISIS Facility, Rutherford Appleton Laboratory, Chilton OX11 0QX (United Kingdom); García Sakai, Victoria, E-mail: [ISIS Facility, Rutherford Appleton Laboratory, Chilton OX11 0QX (United Kingdom)


    Highlights: • The mean squared displacement, , from three lyophilised proteins is compared. • Measurements were collected using neutron instruments accessing different time regimes. • Pico-second dynamics appear insensitive to the secondary structure of the protein. • The arrangement of the amino acids appears to play a role at nano-second timescales. • Elevated hydration appear to hinder fast ps motion in some proteins below 240 K. - Abstract: The temperature dependence of the mean squared displacement (msd), , determined from three lyophilised proteins (apoferritin, green fluorescent protein and insulin) observed over two different experimental time scales is presented. The analysis of elastic incoherent neutron scattering data. Fast pico-second (ps) dynamics appear insensitive to the secondary structure of the proteins. However, the arrangement of the amino acids appears to play a role at longer nano-second (ns) timescales. The effect of hydration on is also considered. For apoferritin and green fluorescent protein, elevated hydration levels appear to suppress fast ps dynamic modes when T < 240 K rendering the material more rigid than when in its lyophilised state.

  8. Analyses des discours non strictement mathematiques accompagnant des cours de mathematiques (Analysis of Not Strictly Mathematical Discourse in Mathematics Classes).

    Robert, Aline


    Examines discourse, not strictly mathematical, that teachers might adopt in a mathematics class and presents three major functions of such discourse: communication; structuring and labeling; and reflection. Develops lines for further inquiry, notably on the third function, the most likely focus for specific preparation by the teacher. (13…

  9. Mathematical competencies and the role of mathematics in physics education: A trend analysis of TIMSS Advanced 1995 and 2008

    Trude Nilsen; Carl Angell; Liv Sissel Grønmo


    As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal) on the application of mathematics in physics education compared with the research related to the c...

  10. Latent Class Analysis of Students' Mathematics Learning Strategies and the Relationship between Learning Strategy and Mathematical Literacy

    Lin, Su-Wei; Tai, Wen-Chun


    This study investigated how various mathematics learning strategies affect the mathematical literacy of students. The data for this study were obtained from the 2012 Programme for International Student Assessment (PISA) data of Taiwan. The PISA learning strategy survey contains three types of learning strategies: elaboration, control, and…

  11. The effect of trauma on Neanderthal culture: A mathematical analysis.

    Nakahashi, W


    Traumatic lesions are often observed in ancient skeletal remains. Since ancient medical technology was immature, severely traumatized individuals may have frequently lost the physical ability for cultural skills that demand complex body movements. I develop a mathematical model to analyze the effect of trauma on cultural transmission and apply it to Neanderthal culture using Neanderthal fossil data. I estimate from the data that the proportion of adult individuals who suffered traumatic injuries before death was approximately 0.79-0.94, in which 0.37-0.52 were injured severely and 0.13-0.19 were injured before adulthood. Assuming that every severely traumatized individual and a quarter to a half of the other traumatized individuals lost the capacity for a cultural skill that demands complex control of the traumatized body part, I estimate that if an upper limb is associated with a cultural skill, each individual had to communicate closely with at least 1.5-2.6 individuals during adulthood to maintain the skill in Neanderthal society, and if a whole body is associated, at least 3.1-11.5 individuals were necessary. If cultural transmissions between experts and novices were inaccurate, or if low frequency skills easily disappeared from the population due to random drift, more communicable individuals were necessary. Since the community size of Neanderthals was very small, their high risk of injury may have inhibited the spread of technically difficult cultural skills in their society. It may be important to take this inhibition into consideration when we study Neanderthal culture and the replacement of Neanderthals by modern humans.

  12. Quantizing the damped harmonic oscillator

    Latimer, D C [Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 (United States)


    We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that the unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.

  13. Vacuum tube operation analysis under multi-harmonic driving and heavy beam loading effect in J-PARC RCS

    Yamamoto, M.; Nomura, M.; Shimada, T.; Tamura, F.; Hara, K.; Hasegawa, K.; Ohmori, C.; Toda, M.; Yoshii, M.; Schnase, A.


    An rf cavity in the J-PARC RCS not only covers the frequency range of a fundamental acceleration pattern but also generates multi-harmonic rf voltage because it has a broadband impedance. However, analyzing the vacuum tube operation in the case of multi-harmonics is very complicated because many variables must be solved in a self-consistent manner. We developed a method to analyze the vacuum tube operation using a well-known formula and which includes the dependence on anode current for some variables. The calculation method is verified with beam tests, and the results indicate that it is efficient under condition of multi-harmonics with a heavy beam loading effect.

  14. Generation of cumulative second-harmonic ultrasonic guided waves with group velocity mismatching: Numerical analysis and experimental validation

    Xiang, Yanxun; Zhu, Wujun; Deng, Mingxi; Xuan, Fu-Zhen; Liu, Chang-Jun


    The generation of second-harmonic Lamb waves in a homogeneous, isotropic, stress-free elastic plate is analytically and experimentally investigated. The numerical analyses show that whether the matching condition of the group velocity is satisfied or not, the integrated amplitude of a second-harmonic Lamb wave accumulates with the propagation distance when both the finite duration of the primary Lamb wave tone burst and the phase velocity matching are given. The theoretical analyses are validated by experimental measurements of an aluminium plate. Our conclusions are different from those of the previous works that reported that the group velocity matching is required for the generation of the cumulative second-harmonic Lamb waves with the finite duration of tone bursts.

  15. Harmonic Analysis and Fault-Tolerant Capability of a Semi-12-Phase Permanent-Magnet Synchronous Machine Used for EVs

    Haipeng Wang


    Full Text Available This paper deals with a fault-tolerant semi-12-phase permanent-magnet synchronous machine (PMSM used for electric vehicles. High fault-tolerant and low toque ripple features are achieved by employing fractional slot concentrated windings (FSCWs and open windings. Excessive magnetomotive force (MMF harmonic components can lead to thermal demagnetization of rotor magnets as well as high core loss. An improved all-teeth-wound winding disposition that changes the winding factor of each harmonic is applied to suppress harmonics. A relatively large slot leakage inductance that limits the short-circuit current (SCC induced in the short-circuited winding is proposed to deal with short-circuit fault. Fault-tolerant controls up to two phases open circuited are investigated in this paper based on keeping the same torque-producing MMF. The fault-tolerant control strategies corresponding to each faulty mode are studied and compared to ensure high performance operation.

  16. Simulation of Distributed Generation Connected to Distribution Network and Harmonic Analysis%分布式电源接入配电网的仿真与谐波分析

    朱旭; 陈武; 赵波; 窦晓波; 吴在军; 顾伟


    To analyze the harmonic characteristics of distributed generation of high penetration connected to the large distribution network, the mathematical model and simulation model of grid-connected photovoltaic system and grid-connected wind power system are introduced and several photovoltaic cells and wind turbines are taken into the IEEE 30 bus test system to be simulated in PSCAD/EMTDC. Through fast Fourier transformation (FFT) analysis of node voltage and branch current which are measured, the factors which affect total harmonic distortion of voltage and current are found.%为分析高渗透率情况下的分布式电源接入规模较大的配电网的谐波特性,介绍光伏发电并网系统和风力发电并网系统的数学模型和仿真模型,在PSCAD/EMTDC中将多组光伏电池和风力发电机接入IEEE 30节点标准测试系统进行仿真。测量相应的节点电压和支路电流,对测量的节点电压和支路电流进行快速傅里叶变换(fast Fourier transformation,FFT)分析,得出了影响谐波电压畸变率的因素和影响谐波电流畸变率的因素。

  17. A Meta-Analysis of the Effects of Computer Technology on School Students' Mathematics Learning

    Li, Qing; Ma, Xin


    This study examines the impact of computer technology (CT) on mathematics education in K-12 classrooms through a systematic review of existing literature. A meta-analysis of 85 independent effect sizes extracted from 46 primary studies involving a total of 36,793 learners indicated statistically significant positive effects of CT on mathematics…

  18. Technology in Mathematics Classrooms: A Meta-Analysis of the Recent Literature

    Li, Qing; Ma, Xin


    The increasingly use of technology in education does set off a flurry of research studies that focus on the successfulness and effectiveness of technology in elementary and secondary education. In this study, we conducted a comprehensive meta-analysis of research literature on technology in relation to mathematics teaching and learning.…

  19. Social Capital and Adolescents Mathematics Achievement: A Comparative Analysis of Eight European Cities

    Gisladottir, Berglind


    This study examines the impact of social capital on mathematics achievement in eight European cities. The study draws on data from the 2008 Youth in Europe survey, carried out by the Icelandic Center for Social Research and Analysis. The sample contains responses from 17,312 students in 9th and 10th grade of local secondary schools in the…

  20. Using Metaphor Analysis to Explore High School Students' Attitudes towards Learning Mathematics

    Guner, Necdet


    In this study, the attitudes of Anatolian high school and vocational high school students towards learning mathematics were examined by using the metaphor analysis method. The study included 669 12th grade students (317 female, 352 male) of two Anatolian and two vocational high schools located in a city center in the Aegean region of Turkey. The…