Showing papers on "Inverse trigonometric functions published in 2014"
TL;DR: In this paper, a generalised version of Sklyanin's Boundary Quantum Inverse Scattering Method applied to the spin-1/2, trigonometric sl (2 ) case is discussed.
27 citations
TL;DR: In this article, a control point form of quadratic trigonometric functions is developed which obeys all the properties of Bezier curve, and constraints are derived on these free parameters to interpolate positive, monotone and convex data.
Abstract: A control point form of quadratic trigonometric function is developed which obeys all the properties of Bezier curve. To preserve the shape of data, the quadratic trigonometric functions are transformed into $$GC^1$$
-interpolating functions. The $$GC^1$$
-interpolating functions have two free parameters in each subinterval to control the magnitude and direction of the tangent at the end points interval. Constraints are derived on these free parameters to interpolate positive, monotone and convex data. The order of approximation of developed interpolant is investigated as $$O( {h_{i}^{3}})$$
.
25 citations
TL;DR: In this paper, the authors extended the T-spline approach to trigonometric generalized B-splines, a particularly relevant case of non-polynomial splines.
22 citations
TL;DR: The hypergeometric series was introduced by Euler as discussed by the authors, where a, b, c are rational parameters, where b = c = 1 gives Newton's binomial series for (1 − z)−a and c = 3/2 gives arcsin( √z)/√z.
Abstract: where a, b, c are rational parameters. By specialization of the parameters, Euler obtained the various classical functions that were around at that time. For example, taking b = c = 1 gives us Newton’s binomial series for (1 − z)−a and taking a = b = 1/2, c = 3/2 gives us arcsin(√z)/√z. Finally, taking all parameters equal to 1 recovers the ordinary geometric series, which more or less explains the name hypergeometric series that was given by Euler to his series. Hypergeometric functions also include functions that were entirely new in Euler’s time. For example, taking a = b = 1/2, c = 1, one obtains the function
16 citations
TL;DR: In this article, the basis properties of generalized trigonometric functions cos p, q are investigated in the context of Lebesgue spaces L r ( 0, 1 ) for general trigonometrical functions.
15 citations
TL;DR: It is found that the proposed modified inverse tangent (MIT) based adaptive algorithm for a second-order constrained adaptive IIR notch filter (ANF) provides not only high speed of convergence but also high impulsive noise robustness.
14 citations
TL;DR: In this article, the Jordan, Adamovic-Mitrinovic, and Cusa inequalities were improved and several new Shafer-Fink type inequalities for inverse sine function and bivariate means inequalities were established.
Abstract: We improve the Jordan, Adamovic-Mitrinovic, and Cusa inequalities. As applications, several new Shafer-Fink type inequalities for inverse sine function and bivariate means inequalities are established, and a new estimate for sine integral is given.
13 citations
Posted Content•
TL;DR: In this article, the convexity/concavity properties of generalized p- trigonometric functions in the sense of P. Lindqvist with respect to the power means were studied.
Abstract: We study the convexity/concavity properties of the generalized p- trigonometric functions in the sense of P. Lindqvist with respect to the power means.
11 citations
Posted Content•
TL;DR: In this article, various miscellaneous functional inequalities for generalized inverse trigonometric and hyperbolic functions are derived for sums, difference, and quotient functions, as well as Grunbaum inequalities with the aid of Bernoulli inequalities.
Abstract: Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.
11 citations
TL;DR: The class of irreducible functions as discussed by the authors includes all open maps on [ 0, 1 ] which are not homeomorphisms, and these functions can be used to obtain an indecomposable continuum as an inverse limit, and sufficient conditions for two such inverse limits to be homeomorphic.
10 citations
25 Jun 2014
TL;DR: In this article, the problem of finding all algebraic values of α ∈ [−1; 1] when arccos α arcsin α and arctan α are rational multiples of π is solved.
Abstract: The problem of finding all algebraic values of α ∈ [−1; 1] when arccos α arcsin α and arctan α are rational multiples of π is solved. The values of such α of degree less than five are explicitly determined.
01 Sep 2014
TL;DR: In this paper, the authors considered the Carlson inequalities for inverse cosine functions and the Shafer inequalities for the inverse tangent function, and showed that they are equivalent for both functions.
Abstract: In this paper the authors re ne the Carlson"s inequalities for inverse cosine function, and the Shafer"s inequalities for inverse tangent function.
TL;DR: A new representation of A"T","S^(^2^,^3^) of A having prescribed range space T and null space S is derived and the well known generalized inverses such as the Moore-Penrose inverse, the group inverse, and the Drazin inverse are computed.
TL;DR: In this paper, a new PD-based compensation technique based on the inverse model of the loudspeaker nonlinearity is proposed, which is represented by an approximated memory-less inverse tangent hyperbolic function (ITHF).
Abstract: In active noise control (ANC), the performance of the filtered-x least mean squares (FXLMS) algorithm is degraded by the saturation of the loudspeaker in the secondary path. Predistortion is a linearization technique commonly used in signal processing applications to compensate for saturation nonlinearity. The design of the predistorter (PD) requires the use of direct measurement from the output of the nonlinear element. However, in ANC applications, direct measurement from the loudspeaker output is not available. Therefore, a conventional PD design approach cannot be directly applied. In this paper, a new PD-based compensation technique based on the inverse model of the loudspeaker nonlinearity is proposed. The PD is represented by an approximated memory-less inverse tangent hyperbolic function (ITHF). The approximated ITHF is scaled by a pre-identified parameter, which represents the loudspeaker nonlinearity strength. This parameter can be obtained by modelling the secondary path using a proposed block-...
TL;DR: In this paper, the authors dealt with Huygens-type and Wilker-type inequalities for generalized trigonometric functions of P Lindqvist and used a generalized version of the Schwab-Borchardt mean introduced recently by the author of this work.
Abstract: This paper deals with Huygens-type and Wilker-type inequalities for the generalized trigonometric functions of P Lindqvist A major mathematical tool used in this work is a generalized version of the Schwab-Borchardt mean introduced recently by the author of this work
TL;DR: The inverse kinematics in robot manipulator have to handle the arctangent and arccosine function are complicated and need much computation time so that it is difficult to be realized in the typical processing system.
Abstract: Purpose – The inverse kinematics in robot manipulator have to handle the arctangent and arccosine function. However, the two functions are complicated and need much computation time so that it is difficult to be realized in the typical processing system. The purpose of this paper is to solve this problem by using Field Programmable Gate Array (FPGA) to speed up the computation power. Design/methodology/approach – The Taylor series expansion method is firstly applied to transfer arctangent and arccosine function to a polynomial form. And Look-Up Table (LUT) is used to store the parameters of the polynomial form. Then the behavior of the computation algorithm is described by Very high-speed IC Hardware Description Language (VHDL) and a co-simulation using ModelSim and Simulink is applied to evaluate the correctness of the VHDL code. Findings – The computation time of arctangent and arccosine function using by FPGA need only 320 and 420 ns, respectively, and the accuracy is <0.01°. Practical implications – F...
TL;DR: In this paper, the Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established, and the first and second inequalities of Huygen and Wilker for classes of functions under discussion are also investigated.
Abstract: The Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established. The first and the second inequalities of Huygens and Wilker, for classes of functions under discussion, are also investigated.
TL;DR: In this article, the chord-length probability density of the regular octahedron is separated into three contributions, relating to the pairs of facets opposite to each other or sharing an edge or a vertex.
Abstract: The chord-length probability density of the regular octahedron is separated into three contributions, relating to the pairs of facets opposite to each other or sharing an edge or a vertex. Each of these contributions is explicitly evaluated throughout the full range of distances and the final expressions only involve inverse trigonometric functions of elementary algebraic functions. Since the chord-length probability density is proportional to the second derivative of the correlation function, knowledge of the chord-length probability density makes the numerical evaluation of the associated small-angle scattering intensity very fast and accurate.
TL;DR: In this paper, a sliding mode control approach is developed to control a three phase three wire voltage source inverter operating as a shunt active power filter, which allows a better stability and robustness over a wide range of operation.
Abstract: The main aim of this study is to control a multivariable coupled system by choosing sliding mode switching function. A Sliding mode control approach is developed to control a three phase three wire voltage source inverter operating as a shunt active power filter. Hence, no need to divide the system model developed in the synchronous 'dq' 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 study, 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 and MATLAB software verifies the results very well.
TL;DR: Based on the k-Mittag-Lefler function and thek-exponential function, this paper introduced families of functions that allow us define new fractional trigonometric functions that contain the classical trigonometrical functions as particular case for some convenient election of parameters.
Abstract: Based on thek-Mittag-Lefler function and thek- -Exponential Function we introduce families of functions that allows us define new fractional trigonometric functions that contain the classical trigonometric functions as particular case for some convenient election of parameters. We study some elementary properties and obtain the Laplace transform of some elements of the families.
DOI•
23 Jan 2014
TL;DR: In this paper, the authors used the mathematical software Maple for the auxiliary tool to study the differential problem of two types of trigonometric functions and obtained the Fourier series expansions of any order derivatives by using binomial theorem and term by term theorem, and hence greatly reduced the difficulty of calculating their higher order derivative values.
Abstract: This article uses the mathematical software Maple for the auxiliary tool to study the differential problem of two types of trigonometric functions. We can obtain the Fourier series expansions of any order derivatives of these two types of functions by using binomial theorem and differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order derivative values. On the other hand, we propose two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple.
01 Jan 2014
TL;DR: The main focus of as discussed by the authors is to study the inverses of the quaternion trigonometric and hyperbolic functions, and their properties, and prove the most known facts.
Abstract: The main focus of this chapter is to study the inverses of the quaternion trigonometric and hyperbolic functions, and their properties. Since the quaternion trigonometric and hyperbolic functions are defined in terms of the quaternion exponential function e p , it can be shown that their inverses are necessarily multi-valued and can be computed via the quaternion natural logarithm function ln(p). The s facts we shall see here attest the great interest of these functions in mathematics. Proofs of the most known facts are ommited.
01 Dec 2014
TL;DR: A modified, non-switching type reaching law for quasi-sliding mode control of linear discrete time dynamic systems is proposed and successfully applied to solve the periodic review inventory management problem.
Abstract: In this paper we propose a modified, non-switching type reaching law for quasi-sliding mode control of linear discrete time dynamic systems. The reaching law determines the sliding variable rate of change proportional to the negative value of the inverse tangent of this variable. The approach proposed in this work helps satisfy input and state constraints in the controlled system, and at the same time it does not excessively damp the system convergence rate when the sliding variable is small. In the second part of this paper the proposed reaching law is successfully applied to solve the periodic review inventory management problem, with suppliers' constraints explicitly taken into account.
TL;DR: In this article, a method to determine all the inverse trigonometric functions directly from the unit circle was proposed, and the method was shown to work for all the trigonometrical functions.
Abstract: A method to determine all the inverse trigonometric functions directly from the unit circle.
Patent•
13 Aug 2014
DOI•
23 Jan 2014
TL;DR: In this article, the generalized trigonometric functions are perversely defined by a system of first order nonlinear ordinary differential equations with initial conditions, which is related to the Hamilton system.
Abstract: A new trigonometric functions called generalized trigonometric functions are perversely defined by a system of first order nonlinear ordinary differential equations with initial conditions. This system is related to the Hamilton system. In this paper, we define these functions using the equation , for m>0 We study the graphs, the trigonometric identities and some of common properties of these functions. We find the first derivatives which have different forms when is even and when is odd.
10 Jul 2014
TL;DR: In this article, a cubic trigonometric Bezier curve with two shape parameters on the basis of cubic trigonal Bernstein-like blending functions was constructed and the proposed curve has all geometric properties of the ordinary cubic bezier curves.
Abstract: In this paper, we construct a cubic trigonometric Bezier curve with two shape parameters on the basis of cubic trigonometric Bernstein-like blending functions. The proposed curve has all geometric properties of the ordinary cubic Bezier curve. Later, based on these trigonometric blending functions a C1 rational trigonometric spline with four shape parameters to preserve positivity of positive data is generated. Simple data dependent constraints are developed for these shape parameters to get a graphically smooth and visually pleasant curve.
TL;DR: Generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations are generalized.
Abstract: The proposed method, called probabilistic nodes combination (PNC), is the method of 2D curve interpolation and modeling using the set of key points (knots or nodes). Nodes can be treated as characteristic points of the object for modeling. The model of each individual symbol or data can be built by choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter $$\gamma $$ ? as probability distribution function enables curve parameterization and interpolation for each specific data or handwritten symbol. Two-dimensional curve is modeled and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arccot or power function. The novelty of the paper consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations.
TL;DR: Recently done work on sine and inverse tangent functions is reviewed in Fractal Geometry applications.
Abstract: Complex graphics of dynamical system have been a subject of intense research nowadays. The fractal geometry is the base of these beautiful graphical images. Many researchers and authors have worked to study the complex nature of the two most popular sets in fractal geometry, the Julia set and the Mandelbrot set, and proposed their work in various forms using existing tools and techniques. The generation of fractals and study of the dynamics of transcendental function is one of the emerging and interesting fields of research nowadays. Recently, Ashish Negi, Rajeshri Rana and Yashwant S. Chauhan are among those researchers who have contributed a lot in the area of Fractal Geometry applications. In this paper we review the recently done work on sine and inverse tangent functions.
TL;DR: The Schröder's process is extended to find and improve high-order fixed-point iteration functions (IFs) for solving a nonlinear equation and is illustrated by using them to find better iterative methods to compute the nth root and the logarithm of a strictly positive real number.
Abstract: Based on the Taylor's expansion of an inverse function, we extend the Schroder's process to find and improve high-order fixed-point iteration functions (IFs) for solving a nonlinear equation. We illustrate the extended processes by using them to find better iterative methods to compute the nth root and the logarithm of a strictly positive real number. IFs for inverse trigonometric function evaluations are also considered.