Showing papers on "Inverse trigonometric functions published in 2006"
01 Jan 2006
TL;DR: In this article, a novel space vector PWM algorithm for three-phase voltage fed inverter is proposed, it has only normal arithmetic operations and the whole algorithm becomes very simple and the calculation results become more accurate.
Abstract: The algorithm of conventional space vector PWM needs complex co-ordinate transformations, trigonometric function and inverse trigonometric function calculations, and this leads more calculation operations and low calculation precision A Novel algorithm of space vector PWM for three-phase voltage fed inverter is proposed, it hasn’t any co-ordinate transformations, trigonometric function and inverse trigonometric function calculation, and has only normal arithmetic operations The whole algorithm becomes very simple and the calculation results become more accurate The relationships between SVPWM, SPWM and the algebraic solution of PWM converter’s control equation are discussed in detail, and the essence of SVPWM is pointed out to be an optimum solution of PWM converter’s control equation, the result of SPWM is equal to the special solution of PWM converter’s control equation assuming that there exists a fictional-ground-wire And the essential relationship between SVPWM and SPWM is that they all are the special solutions of PWM converter’s control equation under different supplementary conditions The experiment results of three-phase three-wire DC/AC PWM converter under the proposed algorithm are given and the control performance is analyzed The experiment results show the validity and feasibility
30 citations
04 Sep 2006
TL;DR: A bearings-only tracking problem is simulated to present the proposed low-power implementation of the particle filter algorithm.
Abstract: We propose a low-power, analog and mixed-mode, implementation of particle filters. Low-power analog implementation of nonlinear functions such as exponential and arctangent functions is done using multiple-input translinear element (MITE) networks. These nonlinear functions are used to calculate the probability densities in the particle filter. A bearings-only tracking problem is simulated to present the proposed low-power implementation of the particle filter algorithm.
13 citations
TL;DR: In this article, a series of dieren tiation identities involving the secant and cosecant functions and specic combinations of special functions including trigonometric, exponential and logarithmic functions are proved.
Abstract: Summary. In this article, we prove a series of dieren tiation identities [3] involving the secant and cosecant functions and specic combinations of special functions including trigonometric, exponential and logarithmic functions.
12 citations
8 citations
Book•
01 Jan 2006
TL;DR: In this article, the authors define the concept of a function as a graph of the graph of a real number and define a set of relations between the graph and the real number.
Abstract: 1. FUNDAMENTALS. Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles. 2. EQUATIONS AND INEQUALITIES. Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS. The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Function. Iteration. Inverse Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO OPTIMIZATION. Linear Functions. Quadratic Functions. Using Iteration to Model Population Growth (Optional Section). Setting up Equations That Define Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay. 6. THE TRIGONOMETRIC FUNCTIONS. Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry. 7. GRAPHS OF THE TRIGONOMETRIC FUNCTIONS. Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions. 8. ANALYTICAL TRIGONOMETRY. The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions. 9. ADDITIONAL TOPICS IN TRIGONOMETRY. Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates. 10. SYSTEMS OF EQUATIONS. Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer"s Rule. Nonlinear Systems of Equations. Systems of Inequalities. 11. ANALYTIC GEOMETRY. The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes. 12. ROOTS OF POLYNOMIAL EQUATIONS. The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes" Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions. 13. ADDITIONAL TOPICS. Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre"s Theorem. Appendix 1: Using a Graphing Utility. Appendix 2: Significant Digits and Calculators. Tables. Answers to Selected Exercises. Index.
8 citations
Journal Article•
TL;DR: In this article, the estimates on the n coefficients in the Maclaurin series expansion of the inverse of functions in the class Sδ(α), (0 ≤ δ < ∞, 0 ≤ α < 1), consisting of analytic functions f(z) = z + ∑ ∞ n=2 anz n in the open unit disc and satisfying ∑∞ n = 2 n δ (n−α 1−α ) |an| ≤ 1.
Abstract: In the present paper we find the estimates on the n coefficients in the Maclaurin’s series expansion of the inverse of functions in the class Sδ(α), (0 ≤ δ < ∞, 0 ≤ α < 1), consisting of analytic functions f(z) = z + ∑∞ n=2 anz n in the open unit disc and satisfying ∑∞ n=2 n δ ( n−α 1−α ) |an| ≤ 1. For eachn these estimates are sharp when α is close tozero or one andδ is close tozero. Further for the second, third and fourth coefficients the estimates are sharp for every admissible values of α andδ.
6 citations
TL;DR: In this paper, the authors prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions, and derive closed forms for most of these integrals.
5 citations
TL;DR: By choosing appropriate parameters in the five-parameter exponential-type potential model, this article showed that the energy spectra of some well-known exactly solvable trigonometric potentials can be obtained from a general energy spectrum formula.
Abstract: By choosing appropriate parameters in the five-parameter exponential-type potential model, we generate systematic exactly solvable trigonometric potentials. We show that the energy spectra of some well-known exactly solvable trigonometric potentials can be obtained from a general energy spectrum formula. It is also shown that the five-parameter exponential-type potential model contains all the second class of shape-invariant trigonometric potentials with eigenfunctions corresponding to hypergeometric functions.
5 citations
Journal Article•
TL;DR: The inverse log-polar transformation based on sub-pixel interpolation is presented, which solves the problems of logarithmic and arctangent function of the transformation.
Abstract: Log-polar transformation is not only a mathematical description of the retino-cortical mapping of human vision system,but also an important algorithm of space-variant theory.The log-polar coordinates of an image is decimal fraction and the range is quite narrow because of the logarithmic and arctangent function of the transformation.Aiming at solving these problems,the inverse log-polar transformation based on sub-pixel interpolation is presented.The acquired log-polar image of the new algorithm has a few of mosaic phenomenon,meanwhile the image is continuous.
4 citations
01 Dec 2006
TL;DR: In this paper, a sliding mode approach is developed to control a three phase three wire voltage source inverter operating as a shunt active power filter, where the sliding mode switching functions are chosen in such a way that the multivariable coupled system is controlled as a whole.
Abstract: A sliding mode approach is developed to control a three phase three wire voltage source inverter operating as a shunt active power filter. The novelty of the proposed approach is that the sliding mode switching functions are chosen in such a way that the multivariable coupled system is controlled as a whole. Hence, no need to divide the system model developed in the synchronous dasiadqpsila reference frame into two separate loops. Furthermore, the proposed control strategy allows a better stability and robustness over a wide range of operation. When sine PWM is used for generation of pulses for the switches, a variable switching nature is exhibited. The pulses for the active filter are fed by a Space Vector Modulation in order to have a constant switching of converter switches. But, the conventional space vector modulation, if implemented practically, needs a complicated algorithm which uses the trigonometric functions such as arctan, sine and cosine functions which in turn needs look up tables to store the pre-calculated trigonometric values. In this paper, a very simplified algorithm is proposed for generating Space vector modulated pulse for all six switches without the use of look up tables and only by sensing the voltages and currents of the voltage source inverter acting as shunt active filter. The simulation using PSIM software verifies the results very well.
4 citations
Patent•
23 Aug 2006
TL;DR: In this paper, a total phase inverse cosine double orthogonal transformation method was proposed to simplify the quantification list and increase the quality of re-built images and coding compression ratio.
Abstract: This invention relates to a total phase inverse cosine double orthogonal transformation method, which defines the transformation as [F]=[V][f][V ] and the inverse transformation as [f]=[V ][F][(V ) ] and uses the improved total phase inverse cosine double orthogonal transformation to replace 2-D scatter cosine transformation to simplify the quantification list so as to save computing time and increase quality of re-built images and coding compression ratio including the following steps: inputting an original image and a bit ratio to be divided into 8x8 pixel blocks and processed by total phase inverse cosine double orthogonal transformation to determine the quantification intervals based on the bit ratio to average the transformation coefficients, carrying out forecast coding to the DC coefficient and AC coefficient scan, variable-length coding, Harfmann entropy coding and outputting the bit sequence of a compressed image.
Book•
26 Jul 2006
TL;DR: In this article, the authors introduce the concept of limits and continuity of a function, and define an approach for computing limits at infinity end behavior of the function and define the definition of area as a limit.
Abstract: Chapter 0 Before Calculus 0.1 Functions 0.2 New Functions from Old 0.4 Families of Functions 0.5 Inverse Functions Inverse Trigonometric Functions 0.6 Exponential and Logarithmic Functions Chapter 1 Limits and Continuity 1.1 Limits (An Intuitive Approach) 1.2 Computing Limits 1.3 Limits at Infinity End Behavior of a Function 1.4 Limits (Discussed More Rigorously) 1.5 Continuity 1.6 Continuity of Trigonometric, Exponential, and Inverse Functions Chapter 2 The Derivative 2.1 Tangent Lines and Rates of Change 2.2 The Derivative Function 2.3 Introduction to Techniques of Differentiation 2.4 The Product and Quotient Rules 2.5 Derivatives of Trigonometric Functions 2.6 The Chain Rule Chapter 3 Topics in Differentiation 3.1 Implicit Differentiation 3.2 Derivatives of Logarithmic Functions 3.3 Derivatives of Exponential and Inverse Trigonometric Functions 3.4 Related Rates 3.5 Local Linear Approximation Differentials 3.6 L'Hopital's Rule Indeterminate Forms Chapter 4 The Derivative in Graphing and Applications 4.1 Analysis of Functions I: Increase, Decrease, and Concavity 4.2 Analysis of Functions II: Relative Extrema Graphing Polynomials 4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 4.4 Absolute Maxima and Minima 4.5 Applied Maximum and Minimum Problems 4.6 Rectilinear Motion 4.7 Newton's Method 4.8 Rolle's Theorem Mean-Value Theorem Chapter 5 Integration 5.1 An Overview of the Area Problem 5.2 The Indefinite Integral 5.3 Integration by Substitution 5.4 The Definition of Area as a Limit Sigma Notation 5.5 The Definite Integral 5.6 The Fundamental Theorem of Calculus 5.7 Rectilinear Motion Revisited Using Integration 5.8 Average Value of a Function and its Applications 5.9 Evaluating Definite Integrals by Substitution 5.10 Logarithmic and Other Functions Defined by Integrals Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering 6.1 Area Between Two Curves 6.2 Volumes by Slicing Disks and Washers 6.3 Volumes by Cylindrical Shells 6.4 Length of a Plane Curve 6.5 Area of a Surface of Revolution 6.6 Work 6.7 Moments, Centers of Gravity, and Centroids 6.8 Fluid Pressure and Force 6.9 Hyperbolic Functions and Hanging Cables Ch 7 Principles of Integral Evaluation 7.1 An Overview of Integration Methods 7.2 Integration by Parts 7.3 Integrating Trigonometric Functions 7.4 Trigonometric Substitutions 7.5 Integrating Rational Functions by Partial Fractions 7.6 Using Computer Algebra Systems and Tables of Integrals 7.7 Numerical Integration Simpson's Rule 7.8 Improper Integrals Ch 8 Mathematical Modeling with Differential Equations 8.1 Modeling with Differential Equations 8,2 Separation of Variables 8.3 Slope Fields Euler's Method 8.4 First-Order Differential Equations and Applications Ch 9 Infinite Series 9.1 Sequences 9.2 Monotone Sequences 9.3 Infinite Series 9.4 Convergence Tests 9.5 The Comparison, Ratio, and Root Tests 9.6 Alternating Series Absolute and Conditional Convergence 9.7 Maclaurin and Taylor Polynomials 9.8 Maclaurin and Taylor Series Power Series 9.9 Convergence of Taylor Series 9.10 Differentiating and Integrating Power Series Modeling with Taylor Series Ch 10 Parametric and Polar Curves Conic Sections 10.1 Parametric Equations Tangent Lines and Arc Length for Parametric Curves 10.2 Polar Coordinates 10.3 Tangent Lines, Arc Length, and Area for Polar Curves 10.4 Conic Sections 10.5 Rotation of Axes Second-Degree Equations 10.6 Conic Sections in Polar Coordinates
Posted Content•
TL;DR: In this paper, the authors proved several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions and derived closed forms for most of these integrals.
Abstract: We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler measures. Several of these results generalize formulas due to Condon and Lalin. As a corollary, we also obtain three $q$-series expansions for the dilogarithm.
01 Dec 2006
TL;DR: The inverse tangent based second-order adaptive IIR notch filter (ITANF) is presented and it is found that the proposed algorithm provides not only high speed convergence but also high impulse noise robustness.
Abstract: The inverse tangent based second-order adaptive IIR notch filter (ITANF) is presented in this paper. It is well known that the gradient-based adaptive IIR notch filter (ANF) has inherent low convergence speed due to the flattened error function. Moreover, the magnitude of error function depends on magnitude of sinusoid which implies that the speed of convergence of the gradient-based adaptive algorithm also depends on the magnitude of an input signal. To improve such drawback, the new inverse tangent based adaptive algorithm for a second order IIR notch filter is therefore proposed. The proposed algorithm employs the ratio of output to input signals as an error criterion where the inverse tangent value of the ratio is employed to adapt the filter parameter. It is found that the proposed algorithm provides not only high speed convergence but also high impulse noise robustness. The simulation results confirm that the performance of the proposed algorithm has been improved over the conventional ANF.
TL;DR: In this article, the authors used phase plane analysis to study the compactons of the nonlinear equation and obtained four new implicit expressions of the compactions by inverse tangent functions.
Abstract: In this paper, we use phase plane analysis to study the compactons of the nonlinear equation. Four new implicit expressions of the compactons are obtained. These new implicit expressions are given by inverse tangent functions. Our work extends previous results. For two sets of the data, the graphs of the implicit functions are drawn and numerical simulations are given to test the correctness of our theoretical results.
01 Nov 2006
TL;DR: The new inverse tangent based adaptive algorithm for a second-order constrained adaptive IIR notch filter is presented and it is found that the proposed algorithm provides not only high speed convergence but also high impulse noise robustness.
Abstract: The new inverse tangent based adaptive algorithm for a second-order constrained adaptive IIR notch filter is presented in this paper. The proposed algorithm employs the ratio of output to input signals as an error criterion where the inverse tangent value of the ratio is used to adapt the filter parameter. It is found that the proposed algorithm provides not only high speed convergence but also high impulse noise robustness. The simulation results confirm that the performance of the proposed algorithm has been improved over the conventional gradient based technique.
TL;DR: In this paper, the authors apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x] and evaluate a generalization of Riemann's zeta function in terms of the period of a function which generalizes the function sin z.
Abstract: We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x] This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic