Journal articles: 'Inverse trigonometric functions'

1

Barrera, Azael. "Unit Circles and Inverse Trigonometric Functions." Mathematics Teacher 108, no. 2 (September 2014): 114–19. http://dx.doi.org/10.5951/mathteacher.108.2.0114.

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Mesa, Vilma, and Bradley Goldstein. "Conceptions of Angles, Trigonometric Functions, and Inverse Trigonometric Functions in College Textbooks." International Journal of Research in Undergraduate Mathematics Education 3, no. 2 (October 20, 2016): 338–54. http://dx.doi.org/10.1007/s40753-016-0042-1.

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Wallace, Edward C. "Investigations Involving Involutions." Mathematics Teacher 81, no. 7 (October 1988): 578–79. http://dx.doi.org/10.5951/mt.81.7.0578.

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Many second-year algebra textbooks include a discussion of functions and their inverses prior to introducing logarithms and the inverse trigonometric functions. Since these functions and some others can be approached neatly as inverses of more familiar functions, a good understanding of the notion of inverse allows students to understand these topics better.

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Neel, Matthew. "Transcendental Functions and Tangent Circles." Mathematics Teacher 112, no. 1 (September 2018): 71–74. http://dx.doi.org/10.5951/mathteacher.112.1.0071.

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These are functions that are not algebraic. The set of transcendental functions includes the trigonometric, inverse trigonometric, exponential and logarithmic functions, but it also includes a vast number of other functions that have never been named…. (Stewart 1999, p. 35)

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Chen, Chao-Ping, and József Sándor. "Inequality chains related to trigonometric and hyperbolic functions and inverse trigonometric and hyperbolic functions." Journal of Mathematical Inequalities, no. 4 (2013): 569–75. http://dx.doi.org/10.7153/jmi-07-53.

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Aprahamian, Mary, and Nicholas J. Higham. "Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms." SIAM Journal on Matrix Analysis and Applications 37, no. 4 (January 2016): 1453–77. http://dx.doi.org/10.1137/16m1057577.

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Li, Bo, Yan Zhang, and Xiquan Liang. "Several Differentiation Formulas of Special Functions. Part III." Formalized Mathematics 14, no. 1 (January 1, 2006): 37–45. http://dx.doi.org/10.2478/v10037-006-0006-z.

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Several Differentiation Formulas of Special Functions. Part III In this article, we give several differentiation formulas of special and composite functions including trigonometric function, inverse trigonometric function, polynomial function and logarithmic function.

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Zhang, Bo, and Chao-Ping Chen. "Sharp Wilker and Huygens type inequalities for trigonometric and inverse trigonometric functions." Journal of Mathematical Inequalities, no. 3 (2020): 673–84. http://dx.doi.org/10.7153/jmi-2020-14-43.

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Wells, Cacey. "Exploring Accessibility: An Application of Inverse Trigonometric Functions." Mathematics Teacher 112, no. 6 (April 2019): 480. http://dx.doi.org/10.5951/mathteacher.112.6.0480.

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Each school year, students enter our classrooms with unique experiences and perspectives that ought to be shared. One year, I noticed a student in our school who used a wheelchair. When I saw how difficult it was for that student to navigate the ramps in our school, I began to think about a trigonometry lesson focused on accessibility. I wanted to use mathematics to explore what life was like—albeit to a minor degree—for those with disabilities. The lesson objective was to explore angles of incline in wheelchair ramps to determine whether such ramps truly offer accessibility.

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Baricz, Árpád, Ali Bhayo, and Matti Vuorinen. "Turán type inequalities for generalized inverse trigonometric functions." Filomat 29, no. 2 (2015): 303–13. http://dx.doi.org/10.2298/fil1502303b.

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In this paper we study the inverse of the eigenfunction sinp of the one-dimensional p-Laplace operator and its dependence on the parameter p, and we present a Tur?n type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur?n type inequality for a series considered by Ramanujan, involving the digamma function.

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Bannon, Thomas J. "The Ambiguity of the Inverse Secant." Mathematics Teacher 111, no. 6 (April 2018): 470–75. http://dx.doi.org/10.5951/mathteacher.111.6.0470.

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Defining inverse trigonometric functions involves choosing ranges for the functions. The choices made for the inverse sine, cosine, tangent, and cotangent functions follow generally accepted conventions. However, different authors make different choices when defining y = arcsec x and y = arccsc x for negative x. I first discovered that the definitions of these functions were not a settled convention when I found an alternate definition in Schaum's (Ayers and Mendelson 2012) and Anton's (1995) books. The more commonly used definition is simpler and results in a function more easily evaluated and for that reason is preferable when introducing the inverse trigonometric functions in an algebra or precalculus course. As we shall see, though, the alternate definition of the inverse secant function has many advantages when we move on to calculus. Since we have a choice in our definitions, we should choose what makes the most sense in context.

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Neuman, Edward. "On thep-Version of the Schwab-Borchardt Mean." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/697643.

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This paper deals with a one-parameter generalization of the Schwab-Borchardt mean. The new mean is defined in terms of the inverse functions of the generalized trigonometric and generalized hyperbolic functions. The four new bivariate means are introduced as particular cases of thep-version of the Schwab-Borchardt mean. For the particular value of the parameterp, these means become either the classical logarithmic mean or the Seiffert means or the Neuman-Sándor mean. Wilker- and Huygens-type inequalities involving inverse functions of the generalized trigonometric and the generalized hyperbolic functions are also established.

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Baricz, Árpád, Barkat Ali Bhayo, and Tibor K. Pogány. "Functional inequalities for generalized inverse trigonometric and hyperbolic functions." Journal of Mathematical Analysis and Applications 417, no. 1 (September 2014): 244–59. http://dx.doi.org/10.1016/j.jmaa.2014.03.039.

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Sofo, Anthony. "Families of Integrals of Polylogarithmic Functions." Mathematics 7, no. 2 (February 3, 2019): 143. http://dx.doi.org/10.3390/math7020143.

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We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing new results and further reinforcing the well-known connection between Euler sums and polylogarithmic functions. Many examples of integrals of products of polylogarithmic functions in terms of Riemann zeta values and Dirichlet values will be given. Suggestions for further research are also suggested, including a study of polylogarithmic functions with inverse trigonometric functions.

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LIU, ZHI-GUO. "SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES." International Journal of Number Theory 08, no. 08 (September 19, 2012): 1977–2002. http://dx.doi.org/10.1142/s1793042112501126.

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Two pairs of inverse relations for elliptic theta functions are established with the method of Fourier series expansion, which allow us to recover many classical results in theta functions. Many nontrivial new theta function identities are discovered. Some curious trigonometric identities are derived.

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Sun, Wei, and Jun She An. "Design of High Performance Fixed Point CORDIC Processor." Advanced Materials Research 998-999 (July 2014): 597–601. http://dx.doi.org/10.4028/www.scientific.net/amr.998-999.597.

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To meet the demand for aerospace applications, high-speed computing transcendental functions such as trigonometric functions, we design a high-speed full-parallel CORDIC processor. On this basis,combining the optimized algorithm of simplifing pathway and adding-bits high-precision method , the original design has been improved. The experimental results show that improved design reduces hardware overhead compared to adding-bits high-precision design,and improves accuracy compared to fully parallel design. This high-speed fixed-point CORDIC has high precision and is suitable for high-speed applications in computing trigonometric and inverse trigonometric functions.

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Gustavsson, Jan, and Mikael P. Sundqvist. "Defining trigonometric functions via complex sequences." Mathematical Gazette 100, no. 547 (March 2016): 9–23. http://dx.doi.org/10.1017/mag.2016.4.

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In the literature we find several different ways of introducing elementary functions. For the exponential function, we mention the following ways of characterising the exponential function:(a) (b) , also for complex values of x;(c) x → exp (x) is the unique solution to the initial value problem [4](d) x → exp (x) is the inverse of (e)x → exp (x) is the unique continuous function satisfying thefunctional equation f (x + y) = f (x) f (y) and f(0) = 1 [6]; the corresponding definition is done for the logarithm in [7];(f) Define dr for rational r, and then use a continuity/density argument [8].All of them have their advantages and disadvantages. We like (a) and (c), mostly because they have natural interpretations, (a) in the setting of compound interest and (c) being a simple model of many processes in physics and other sciences, but also because they are related to methods and ideas that are (usually) introduced rather early to the students.

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Chen, Chao-Ping. "Sharp Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions." Integral Transforms and Special Functions 23, no. 12 (December 2012): 865–73. http://dx.doi.org/10.1080/10652469.2011.644851.

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XU, FEI, PEI YU, and XIAOXIN LIAO. "SYNCHRONIZATION AND STABILIZATION OF MULTI-SCROLL INTEGER AND FRACTIONAL ORDER CHAOTIC ATTRACTORS GENERATED USING TRIGONOMETRIC FUNCTIONS." International Journal of Bifurcation and Chaos 23, no. 08 (August 2013): 1350145. http://dx.doi.org/10.1142/s0218127413501459.

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Sigmoidal functions are usually used to characterize the behavior of dynamical systems, in particular, for neural networks. Recently, multilevel piecewise linear functions have been employed in cellular neural networks (CNN). In this paper, we first use the inverse trigonometric function, tan -1(x), to generate a series of trigonometric functions to obtain one-, two- and three-directional multi-scroll integer and fractional order chaotic attractors. Then, based upon the properties of the chaotic systems, simple feedback control laws are designed to stabilize or synchronize the integer and fractional order chaotic systems. Numerical simulations are presented to demonstrate the applicability of theoretical predictions.

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Shinohara, Kazunori. "Addition formulas of leaf functions according to integral root of polynomial based on analogies of inverse trigonometric functions and inverse lemniscate functions." Applied Mathematical Sciences 11 (2017): 2561–77. http://dx.doi.org/10.12988/ams.2017.78265.

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Apelblat, Alexander, and Francesco Mainardi. "Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)." Symmetry 13, no. 2 (February 22, 2021): 354. http://dx.doi.org/10.3390/sym13020354.

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Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

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Pradhan, Karan K., and S. Chakraverty. "Natural frequencies of shear deformed functionally graded beams using inverse trigonometric functions." Journal of the Brazilian Society of Mechanical Sciences and Engineering 39, no. 9 (January 6, 2017): 3295–313. http://dx.doi.org/10.1007/s40430-016-0701-9.

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23

Ghany, Hossam A., and M. Zakarya. "Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation." Physics Research International 2014 (December 15, 2014): 1–9. http://dx.doi.org/10.1155/2014/937345.

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F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. By means of Hermite transform, inverse Hermite transform, and white noise analysis, the variable coefficients and Wick-type stochastic Schamel KdV equations are completely described. Abundant exact traveling wave solutions for variable coefficients Schamel KdV equations are given. These solutions include exact stochastic Jacobi elliptic functions, trigonometric functions, and hyperbolic functions solutions.

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Iakovlev, Serguei. "On the Singular Behavior of the Inverse Laplace Transforms of the Functions." Canadian Mathematical Bulletin 45, no. 3 (September 1, 2002): 399–416. http://dx.doi.org/10.4153/cmb-2002-042-0.

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AbstractExact analytical expressions for the inverse Laplace transforms of the functions are obtained in the form of trigonometric series. The convergence of the series is analyzed theoretically, and it is proven that those diverge on an infinite denumerable set of points. Therefore it is shown that the inverse transforms have an infinite number of singular points. This result, to the best of the author’s knowledge, is new, as the inverse transforms of have previously been considered to be piecewise smooth and continuous. It is also found that the inverse transforms have an infinite number of points of finite discontinuity with different left- and right-side limits. The points of singularity and points of finite discontinuity alternate, and the sign of the infinity at the singular points also alternates depending on the order n. The behavior of the inverse transforms in the proximity of the singular points and the points of finite discontinuity is addressed as well.

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Akgün, Ramazan. "Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth." gmj 18, no. 2 (May 2, 2011): 203–35. http://dx.doi.org/10.1515/gmj.2011.0022.

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Abstract This work deals with basic approximation problems such as direct, inverse and simultaneous theorems of trigonometric approximation of functions of weighted Lebesgue spaces with a variable exponent on weights satisfying a variable Muckenhoupt A p(·) type condition. Several applications of these results help us transfer the approximation results for weighted variable Smirnov spaces of functions defined on sufficiently smooth finite domains of complex plane ℂ.

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Malešević, Branko J., Bojan Banjac, and Ivana Jovović. "A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions." Journal of Mathematical Inequalities, no. 1 (2017): 151–62. http://dx.doi.org/10.7153/jmi-11-15.

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Juhas, Anamarija, and Ladislav A. Novak. "Maximally Flat Waveforms with Finite Number of Harmonics in Class-FPower Amplifiers." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/169590.

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In this paper general solution to the problem of finding maximally flat waveforms with finite number of harmonics (maximally flat trigonometric polynomials) is provided. Waveform coefficients are expressed in closed form as functions of harmonic orders. Two special cases of maximally flat waveforms (so-called maximally flat even harmonic and maximally flat odd harmonic waveforms), which proved to play an important role in class-Fand inverse class-Fpower amplifier (PA) operations, are also considered. For these two special types of waveforms, coefficients are expressed as functions of two parameters only. Closed form expressions for efficiency and power output capability of class-Fand inverse class-FPA operations with maximally flat waveforms are also provided as explicit functions of number of a harmonics.

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Shimizu, Toshimi, and Haruhisa Kawasaki. "An Analysis of Inverse Kinematics of Robot Manipulators using Grobner Basis." Journal of Robotics and Mechatronics 9, no. 5 (October 20, 1997): 324–31. http://dx.doi.org/10.20965/jrm.1997.p0324.

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This paper presents a new method for solving the inverse kinematics of robot manipulators symbolically using computer algebra. The kinematics equations, including the trigonometric functions of joint displacements, are expressed as multivariate polynomial equations by transforming these functions into variables. The multivariate polynomial equations can be solved by evaluating their reduced Grobner basis. The properties for efficient evaluation of the reduced Grobner basis and the inverse kinematics of a robot, whose last three joint axes intersect at a point, are shown. This procedure is implemented using Maple V and built into ROSAM (Robot Symbolic Analysis, by Maple) that is a robot analysis library made by our group. An analysis example of a structurechanged PUMA type robot is given.

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Khan, Nida, and Muhammad Aslam. "Statistical Analysis of Location Parameter of Inverse Gaussian Distribution Under Noninformative Priors." Journal of Quantitative Methods 3, no. 2 (August 31, 2019): 62–76. http://dx.doi.org/10.29145/2019/jqm/030204.

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Bayesian estimation for location parameter of the inverse Gaussian distribution is presented in this paper. Noninformative priors (Uniform and Jeffreys) are assumed to be the prior distributions for the location parameter as the shape parameter of the distribution is considered to be known. Four loss functions: Squared error, Trigonometric, Squared logarithmic and Linex are used for estimation. Bayes risks are obtained to find the best Bayes estimator through simulation study and real life data

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Qian, Wei-Mao, and Yu-Ming Chu. "Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/8901258.

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We prove that the double inequalityLp(a,b)<U(a,b)<Lq(a,b)holds for alla,b>0witha≠bif and only ifp≤p0andq≥2and find several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions, wherep0=0.5451⋯is the unique solution of the equation(p+1)1/p=2π/2on the interval(0,∞),U(a,b)=(a-b)/[2arctan⁡((a-b)/2ab)], andLp(a,b)=[(ap+1-bp+1)/((p+1)(a-b))]1/p (p≠-1,0),L-1(a,b)=(a-b)/(log⁡a-log⁡b)andL0(a,b)=(aa/bb)1/(a-b)/eare the Yang, andpth generalized logarithmic means ofaandb, respectively.

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Homa, Agostinho Iaqchan Ryokiti. "Robotics Simulators in STEM education." Acta Scientiae 21, no. 5 (October 7, 2019): 178–91. http://dx.doi.org/10.17648/acta.scientiae.5417.

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This article discusses STEM (Science, Technology, Engineering and Mathematics) education as an initiative from various countries around the world to address young people's lack of interest in careers in Science, Mathematics, Technology and Engineering. Understanding that STEM education must explore two or more of STEM themes, using transdisciplinarity, engaging the student in activities with this approach, we present the studies of an activity proposal integrating Engineering, Technology and Mathematics with the objective of learning Mathematics. In this activity students work with situations involving robotics and, for solution, use robotic arm simulators, developed in GeoGebra software, that simplify the real environment in which the robotic arm manipulates an object positioned in the plane, taking to organize strategies by identifying and applying mathematics, such as trigonometry with right triangle, trigonometric identities, inverse trigonometric functions, to solve the problem. An experiment was conducted to validate the simulators with undergraduate mathematics students from Universidade Luterana do Brasil (ULBRA) in the city of Canoas in Rio Grande do Sul. The results indicate that it is possible to integrate the STEM areas with the developed simulators, being indicated for activities with high school students (10th or 11th grade).

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Ciccariello, Salvino. "The chord-length probability density of the regular octahedron." Journal of Applied Crystallography 47, no. 4 (June 25, 2014): 1216–27. http://dx.doi.org/10.1107/s1600576714011121.

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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.

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Borwein, Jonathan M., and Roland Girgensohn. "Addition Theorems and Binary Expansions." Canadian Journal of Mathematics 47, no. 2 (April 1, 1995): 262–73. http://dx.doi.org/10.4153/cjm-1995-013-4.

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AbstractLet an interval I ⊂ ℝ and subsets D0, D1 ⊂ I with D0 ∪ D1 = I and D0 ∩ D1 = Ø be given, as well as functions r0: D0 → I, r1: D1 → I. We investigate the system (S) of two functional equations for an unknown function f: I → [0, 1]: We derive conditions for the existence, continuity and monotonicity of a solution. It turns out that the binary expansion of a solution can be computed in a simple recursive way. This recursion is algebraic for, e.g., inverse trigonometric functions, but also for the elliptic integral of the first kind. Moreover, we use (S) to construct two kinds of peculiar functions: surjective functions whose intervals of constancy are residual in I, and strictly increasing functions whose derivative is 0 almost everywhere.

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Plonka, Gerlind, Kilian Stampfer, and Ingeborg Keller. "Reconstruction of stationary and non-stationary signals by the generalized Prony method." Analysis and Applications 17, no. 02 (March 2019): 179–210. http://dx.doi.org/10.1142/s0219530518500240.

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We employ the generalized Prony method in [T. Peter and G. Plonka, A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators, Inverse Problems 29 (2013) 025001] to derive new reconstruction schemes for a variety of sparse signal models using only a small number of signal measurements. By introducing generalized shift operators, we study the recovery of sparse trigonometric and hyperbolic functions as well as sparse expansions into Gaussians chirps and modulated Gaussian windows. Furthermore, we show how to reconstruct sparse polynomial expansions and sparse non-stationary signals with structured phase functions.

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Ishkhanyan, Tigran A., Vladimir P. Krainov, and Artur M. Ishkhanyan. "A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms." Zeitschrift für Naturforschung A 73, no. 5 (May 24, 2018): 407–14. http://dx.doi.org/10.1515/zna-2017-0314.

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AbstractWe present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term ~x−1/2 with arbitrary strength and a repulsive centrifugal barrier core ~x−2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrödinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels.

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Hwu, Chyanbin, Chung-Lei Hsu, and Wei-Ren Chen. "Corrective evaluation of multi-valued complex functions for anisotropic elasticity." Mathematics and Mechanics of Solids 22, no. 10 (September 11, 2017): 2040–62. http://dx.doi.org/10.1177/1081286517728542.

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It is well known that the Stroh formalism is an elegant and powerful complex variable method for anisotropic elasticity. Through this formalism, several analytical solutions for the problems of anisotropic elasticity have been presented in the literature. To evaluate the analytical solutions, some problems may occur on the numerical evaluation of multi-valued complex functions and their related singular integrals. In this paper, to get a correct single-valued solution, proper branch cuts are suggested for several different multi-valued complex functions, such as the logarithmic function, inverse trigonometric function, power function, mapping function, Plemelj function, and the logarithmic function with mapped variables. To get the correct numerical integration for weakly and strongly singular integrals with multi-valued complex variables, based upon the concept of finite part integrals, formulae employing the Gaussian quadrature rules of standard, logarithmic, and inverse type are derived. According to the branch cuts selected for different complex functions and the integration formulae for singular integrals, some remarks on the computer programming are provided. Verification of the remarks is then made by typical examples of anisotropic elasticity such as holes, cracks, punches, and singular integrals used in boundary element formulation.

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Al-Babtain, Abdulhakim A., Ibrahim Elbatal, Christophe Chesneau, and Mohammed Elgarhy. "Sine Topp-Leone-G family of distributions: Theory and applications." Open Physics 18, no. 1 (September 24, 2020): 574–93. http://dx.doi.org/10.1515/phys-2020-0180.

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AbstractRecent studies have highlighted the statistical relevance and applicability of trigonometric distributions for the modeling of various phenomena. This paper contributes to the subject by investigating a new trigonometric family of distributions defined from the alliance of the families known as sine-G and Topp-Leone generated (TL-G), inspiring the name of sine TL-G family. The characteristics of this new family are studied through analytical, graphical and numerical approaches. Stochastic ordering and equivalence results, determination of the mode(s), some expansions of distributional functions, expressions of the quantile function and moments and basics on order statistics are discussed. In addition, we emphasize the fact that the sine TL-G family is able to generate original, simple and pliant trigonometric models for statistical purposes, beyond the capacity of the former sine-G models and other top models of the literature. This fact is revealed with the special three-parameter sine TL-G model based on the inverse Lomax model, through an efficient parametric estimation and the adjustment of two data sets of interest.

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Dharmendra, Kumar Patel, K. Ramachandra, and Singh Sartaj. "Kinematic Modeling and Hardware Development of 5-DoF Robot Manipulator." Applied Mechanics and Materials 612 (August 2014): 51–58. http://dx.doi.org/10.4028/www.scientific.net/amm.612.51.

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This paper presents a 5-DoF articulated robot manipulator and proposes a strategy for solving its inverse kinematics. The Denavit – Hartenberg (D-H) parameterization has been used to model the kinematics of the manipulator. As degree of freedom of manipulator increases, the geometrical solution for inverse kinematics becomes difficult; hence an analytical method for the same is presented. Novelty in the method presented is that no approximations of trigonometric functions are used resulting in a theoretical positional accuracy of 10-10mm of the end-effector. The articulated robotic manipulator developed makes use of integrated actuators and rapid prototyping technology enabling easy replication for educational purposes. The robot arm has been used for manipulation tasks in its workspace successfully.

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Medvedev, Andrei, Andrei Berezhnoi, Aleksei Kudryashov, and Leonid Liokumovich. "Precise digital demodulation for fiber optic interferometer sensors." International Journal of Modern Physics: Conference Series 41 (January 2016): 1660139. http://dx.doi.org/10.1142/s2010194516601393.

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Different methods are used in the interferometer sensors for target signal extraction. Digital technologies provide new opportunities for precise signal detection. We have developed the principle of signal demodulation using an additional harmonic phase modulation and digital signal processing. The principle allows implementation of processing algorithms using different ratios between modulation and discretization frequencies. The expressions allowing calculation of the phase difference using the inverse trigonometric functions were derived. The method was realized in LabVIEW programming environment and was demonstrated for various signal shapes.

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Sofo, Anthony, and Amrik Singh Nimbran. "Euler Sums and Integral Connections." Mathematics 7, no. 9 (September 9, 2019): 833. http://dx.doi.org/10.3390/math7090833.

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In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler’s work on the subject followed by notations used in the body of the paper. After discussing some alternating Euler sums, we investigate the connection of integrals of inverse trigonometric and hyperbolic type functions to generate many new Euler sum identities. We also give some new identities for Catalan’s constant, Apery’s constant and a fast converging identity for the famous ζ ( 2 ) constant.

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Carricato, Marco, Vincenzo Parenti-Castelli, and Joseph Duffy. "Inverse Static Analysis of a Planar System With Flexural Pivots." Journal of Mechanical Design 123, no. 1 (January 1, 2000): 43–50. http://dx.doi.org/10.1115/1.1338483.

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This article presents the inverse static analysis of a two degrees of freedom planar mechanism with flexural pivots. Such analysis aims to detect the entire set of equilibrium configurations of the system once the external load is assigned. The presence of flexural pivots represents a novelty, although it remarkably complicates the problem since it causes the two state variables to appear in the solving equations as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention is paid to the analysis of the reliability of the final equations: critical situations, in which the solving equations may hide solutions or yield false ones, are studied. Finally, a numerical example is provided and, in the Appendix, a special design that offers computational advantages is proposed.

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Mojtaba, Hatami, and Alamatsaz Hossein. "Transformation of circular random variables based on circular distribution functions." Filomat 32, no. 17 (2018): 5931–47. http://dx.doi.org/10.2298/fil1817931m.

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In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

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Voloshko, Valeriy A., and Egor V. Vecherko. "New upper bounds for noncentral chi-square cdf." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (March 31, 2020): 70–74. http://dx.doi.org/10.33581/2520-6508-2020-1-70-74.

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Some new upper bounds for noncentral chi-square cumulative density function are derived from the basic symmetries of the multidimensional standard Gaussian distribution: unitary invariance, components independence in both polar and Cartesian coordinate systems. The proposed new bounds have analytically simple form compared to analogues available in the literature: they are based on combination of exponents, direct and inverse trigonometric functions, including hyperbolic ones, and the cdf of the one dimensional standard Gaussian law. These new bounds may be useful both in theory and in applications: for proving inequalities related to noncentral chi-square cumulative density function, and for bounding powers of Pearson’s chi-squared tests.

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Steen, Marie. "Measuring Price–Quantity Relationships in the Dutch Flower Market." Journal of Agricultural and Applied Economics 46, no. 2 (May 2014): 299–308. http://dx.doi.org/10.1017/s1074070800000808.

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This research applies an inverse, almost ideal demand model with seasonal adjustments to estimate price–quantity relationships among major cut flower species traded at the Dutch flower auctions. Trigonometric functions are used as a flexible and efficient alternative to standard seasonal dummies. The estimated price and scale flexibilities were all found to be statistically significant with signs as expected. The demand for all flower groups is inflexible, and most of them are quantity substitutes. Based on the estimated values for price and scale flexibilities, a potential for market timing seems to exist, i.e., flower producers may use easily available calendar information to predict prices and quantities.

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Wern, H., and L. Suominen. "Selfconsistent Evaluation of Non-Uniform Stress Profiles and X-Ray Elastic Constants from X-ray Diffraction Experiments." Advances in X-ray Analysis 39 (1995): 339–52. http://dx.doi.org/10.1154/s0376030800022758.

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A method to obtain the triaxial depth profiles of strains and stresses as a function of the depth below the surface is described. Instead of using inverse Laplace transforms to extract the z-profiles from the measured τ-profiles, a numerically stable inverse formalism with trigonometric basis functions is used. The formalism has already been applied with great success to the hole-drilling method for the determination of residual stresses. It requires no prior knowledge of the stress state and is suitable even for strongly non-linear stress fields. This is demonstrated by experimental data sets for the conventional Ω-, ѱ- and modified ѱ goniometers. Furthermore this method enables in situ determination of Poisson's ratio as well as the stress free lattice spacing using a selfconsistency criterion for isotropic materials. It is now possible to find a proper normalization of the residual strains and residual stresses. Because of the formulation as an inverse problem, analytical expressions for the beam path integrals could be derived even for curved surfaces. Inverse problems are often extremely ill-conditioned. Therefore the uniqueness of the solution is discussed in terms of a spectral shift of the corresponding eigenvalues.

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Tseng, Wei-Kuo. "An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere." Journal of Navigation 67, no. 5 (April 11, 2014): 825–44. http://dx.doi.org/10.1017/s0373463314000228.

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An innovative algorithm to determine the inverse solution of a geodesic with the vertex or Clairaut constant located between two points on a spheroid is presented. This solution to the inverse problem will be useful for solving problems in navigation as well as geodesy. The algorithm to be described derives from a series expansion that replaces integrals for distance and longitude, while avoiding reliance on trigonometric functions. In addition, these series expansions are economical in terms of computational cost. For end points located at each side of a vertex, certain numerical difficulties arise. A finite difference method together with an innovative method of iteration that approximates Newton's method is presented which overcomes these shortcomings encountered for nearly antipodal regions. The method provided here, which does not involve an auxiliary sphere, was aided by the Computer Algebra System (CAS) that can yield arbitrarily truncated series suitable to the users accuracy objectives and which are limited only by machine precisions.

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Ciccariello, Salvino. "The chord-length distribution of a polyhedron." Acta Crystallographica Section A Foundations and Advances 76, no. 4 (June 1, 2020): 474–88. http://dx.doi.org/10.1107/s2053273320004519.

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The chord-length distribution function [γ′′(r)] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ′′(r) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R[r, Δ1], Δ1 being the square root of a second-degree r polynomial and R[x, y] a rational function. As r approaches δ, one of the two end points of an r subdomain, the derivative of γ′′(r) can only show singularities of the forms |r − δ|−n and |r − δ|−m+1/2, with n and m appropriate positive integers. Finally, the explicit analytic expressions of the primitives are also reported.

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Bhayo, B. A., and J. Sandor. "Inequalities connecting generalized trigonometric functions with their inverses." Issues of Analysis 20, no. 2 (December 2013): 82–90. http://dx.doi.org/10.15393/j3.art.2013.2385.

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Numpanviwat, Nattakarn, and Pearanat Chuchard. "Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities." Computation 9, no. 3 (March 1, 2021): 27. http://dx.doi.org/10.3390/computation9030027.

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The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

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Singh, Sandeep, Jeeoot Singh, and Karunesh Kumar Shula. "Buckling of Laminated Composite and Sandwich Plates Using Radial Basis Function Collocations." International Journal of Structural Stability and Dynamics 15, no. 01 (January 2015): 1540002. http://dx.doi.org/10.1142/s0219455415400027.

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In this paper, buckling analysis of isotropic, orthotropic, laminated composite and sandwich plates utilizing trigonometric shear deformation theory and meshless method based on the finite point formulation using thin plate, polynomial and inverse multiquadric radial basis function is presented. The convergence of the present method is studied for isotropic and laminated composite plates for different radial basis functions with optimal value of shape parameter. Numerical examples of laminated and sandwich plates subjected to various types of in-plane loads are solved to demonstrate accuracy and applicability of present method. Several new results for variety of composite and sandwich plates are presented. The present results are observed to be in good agreement with those available in literature. The effects of orthotropy ratio of material, span to thickness ratio, number of layers, core thickness and lamination scheme on the critical load of plates are also presented.

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Journal articles on the topic 'Inverse trigonometric functions'

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