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Journal articles on the topic 'TRIGONOMETRIC FUNCTION'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Putranti, Sri Rejeki Dwi. "Relationship between Trigonometry Functions with Hyperbolic Function." Aloha International Journal of Multidisciplinary Advancement (AIJMU) 1, no. 4 (April 30, 2019): 82. http://dx.doi.org/10.33846/aijmu10402.

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Many engineering problems can be solved by methods involving complex numbers and complex functions. In the definitions below we will prove the relationship between trigonometric functions and hyperbolic functions, where the hyperbolic function is an extension of the trigonometric function. Keywords: trigonometric functions; hyperbolic functions

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2

Saregar, Antomi. "Analisis Spektrum Energi dan Fungsi Gelombang Potensial Non-Centra Menggunakan Supersimetri Mekanika Kuantum." Jurnal Ilmiah Pendidikan Fisika Al-Biruni 4, no. 2 (October 27, 2015): 193. http://dx.doi.org/10.24042/jpifalbiruni.v4i2.92.

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The objectives of this study were: 1) to describe the results of wave and energy function of the Non-central potential system of potential combinations of trigonometric Poschl-Teller plus Rosen Morse, Coloumb and OH 3D potential, and Rosen Morse trigonometric potential plus Pochl-Teller analyzed using Supersymmetry quantum mechanics (SUSY QM); 2) to know the visualization of wave function and energy level at point 1. This study is a literature study conducted from July 2013 to December 2015. Non-central potential of potential combinations of trigonometric Poschl-Teller potency plus Rosen Morse, Coloumb and OH 3D potential and potential Rosen Morse trigonometry plus Pochl-Teller is a potential that has a shape invariance properties. Recent developments, the SUSY method has been successfully used to create complete and precise mathematical analysis of the resolution of some non-central potentials in a closed system. By applying a lowering operator to a basic level wave function, a basic level wave function is obtained, while a top-level wave function is obtained by using a rising operator operated at a ground-level wave function and so on. While the value of energy in a closed system obtained by using the nature of the invariant shape. Tujuan Penelitian ini adalah: 1) mendeskripsikan hasil fungsi gelombang dan energi dari sistem potensial Non sentral hasil kombinasi potensial Poschl-Teller trigonometri plus potensial Rosen Morse, Coloumb, dan OH 3D, serta potensial Rosen Morse trigonometri plus Pochl-Teller yang dianalisis menggunakan metode Supersymmetry mekanika kuantum (SUSY QM); 2) mengetahui visualisasidari fungsi gelombangdan tingkat energy pada poin 1. Penelitian ini merupakan studi literatur yang dilakukan mulai bulan Juli 2013 s.d. Desember 2015. Potensial non sentral hasil kombinasi potensial Poschl-Teller trigonometri plus potensial Rosen Morse, Coloumb, dan OH 3D serta potensial Rosen Morse trigonometri plus Pochl-Teller merupakan potensial yang mempunyai sifat shape invariance.Perkembangan terakhir, metode SUSY telah berhasil digunakan untuk membuat analisis matematis secara lengkap dan tepat penyelesaian beberapa potensial non sentral dalam sistem tertutup. Dengan mengaplikasikan operator penurun pada fungsi gelombang tingkat dasar diperoleh fungsi gelombang tingkat dasar, sedangkan fungsi gelombang tingkat atas satu diperoleh dengan menggunakan operator penaik yang dioperasikan pada fungsi gelombang tingkat dasar dan seterusnya. Sedangkan nilai energinya dalam sistem tertutup diperoleh dengan menggunakan sifat shape invariant.

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3

Titaley, Jullia, Tohap Manurung, and Henriette D. Titaley. "CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTION." JURNAL ILMIAH SAINS 18, no. 2 (November 12, 2018): 103. http://dx.doi.org/10.35799/jis.18.2.2018.21555.

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CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTIONABSTRACTJulia set are defined by iterating a function of a complex number and is generated from the iterated function . We investigate in this paper the complex dynamics of different functions and applied iteration function system to generate an entire new class of julia set. The purpose of this research is to make variation of Cubic and Quadratic polynomial on Julia Set and the two obvious to investigate from julia set are Sine and Cosine function. The results thus obtained are innovative and studies about different behavior of two basic trigonometry.Keywords : Julia Set, trigonometric function, polynomial function POLINOMIAL KUBIK DAN KUADRATIK PADA HIMPUNAN JULIA DENGAN FUNGSI TRIGONOMETRI ABSTRAKHimpunan Julia didefiniskan oleh fungsi iterasi dari bilangan kompleks dan dibangkitkan dari fungsi iterasi . Kami melakukan penelitian dalam penulisan ini tentang sistem dinamik kompleks dari fungsi yang berbeda dengan iterasi yang diterapkan untuk menghasilkan kelas baru dari himpunan Julia. Tujuan dari penelitian ini adalah untuk membuah kelas baru himpunan Julia dengan fungsi polinomial kubik dan kuadratik dengan fungsi sinus dan kosinus. Hasil akhir dari penelitian ini ada menemukan inovatif baru dari himpunan Julia dengan menggunakan dua fungsi trigonometri.Kata kunci: Julia set, fungsi trigonometri, fungsi polinomial

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4

Baric, Mate, David Brčić, Mate Kosor, and Roko Jelic. "An Axiom of True Courses Calculation in Great Circle Navigation." Journal of Marine Science and Engineering 9, no. 6 (May 31, 2021): 603. http://dx.doi.org/10.3390/jmse9060603.

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Based on traditional expressions and spherical trigonometry, at present, great circle navigation is undertaken using various navigational software packages. Recent research has mainly focused on vector algebra. These problems are calculated numerically and are thus suited to computer-aided great circle navigation. However, essential knowledge requires the navigator to be able to calculate navigation parameters without the use of aids. This requirement is met using spherical trigonometry functions and the Napier wheel. In addition, to facilitate calculation, certain axioms have been developed to determine a vessel’s true course. These axioms can lead to misleading results due to the limitations of the trigonometric functions, mathematical errors, and the type of great circle navigation. The aim of this paper is to determine a reliable trigonometric function for calculating a vessel’s course in regular and composite great circle navigation, which can be used with the proposed axioms. This was achieved using analysis of the trigonometric functions, and assessment of their impact on the vessel’s calculated course and established axioms.

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5

AGHELI, BAHRAM. "Approximate Solution of Bratu Differential Equations Using Trigonometric Basic Functions." Kragujevac Journal of Mathematics 45, no. 02 (April 2021): 203–14. http://dx.doi.org/10.46793/kgjmat2102.203a.

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In this paper, I have proposed a method for ﬁnding an approximate function for Bratu diﬀerential equations (BDEs), in which trigonometric basic functions are used. First, by deﬁning trigonometric basic functions, I deﬁne the values of the transformation function in relation to trigonometric basis functions (TBFs). Following that, the approximate function is deﬁned as a linear combination of trigonometric base functions and values of transform function which is named trigonometric transform method (TTM), and the convergence of the method is also presented. To get an approximate solution function with discrete derivatives of the solution function, we have determined the approximate solution function which satisﬁes in the Bratu diﬀerential equations (BDEs). In the end, the algorithm of the method is elaborated with several examples. In one example, I have presented an absolute error comparison of some approximate methods.

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6

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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7

Devine, M. L. "Real time trigonometric function evaluation." Microprocessors and Microsystems 16, no. 8 (January 1992): 417–25. http://dx.doi.org/10.1016/0141-9331(92)90028-r.

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8

CHAND, A. K. B., M. A. NAVASCUÉS, P. VISWANATHAN, and S. K. KATIYAR. "FRACTAL TRIGONOMETRIC POLYNOMIALS FOR RESTRICTED RANGE APPROXIMATION." Fractals 24, no. 02 (June 2016): 1650022. http://dx.doi.org/10.1142/s0218348x16500225.

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One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.

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9

Phan-Yamada, Tuyetdong, and Walter M. Yamada. "Exploroing Polar Curves with GeoGebra." Mathematics Teacher 106, no. 3 (October 2012): 228–33. http://dx.doi.org/10.5951/mathteacher.106.3.0228.

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Most trigonometry textbooks teach the graphing of polar equations as a two-step process: (1) plot the points corresponding to values of θ such as π, π/2, π/3, π/4, π/6, and so on; and then (2) connect these points with a curve that follows the behavior of the trigonometric function in the Cartesian plane. Many students have difficulty using this method to graph general polar curves. The difficulty seems to stem from an inability to convert changes in the value of the trigonometric equation as a function of angle (abscissa vs. ordinate in Cartesian coordinates) to changes of the radius as a function of angle (r[θ] in polar coordinates). GeoGebra provides a tool to help students visualize this relationship, thus significantly improving students' ability

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10

HE, WEN-YU, and WEI-XIN REN. "ADAPTIVE TRIGONOMETRIC HERMITE WAVELET FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS." International Journal of Structural Stability and Dynamics 13, no. 01 (February 2013): 1350007. http://dx.doi.org/10.1142/s0219455413500077.

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Owing to its good approximation characteristics of trigonometric functions and the multi-resolution local characteristics of wavelet, the trigonometric Hermite wavelet function is used as the element interpolation function. The corresponding trigonometric wavelet beam element is formulated based on the principle of minimum potential energy. As the order of wavelet can be enhanced easily and the multi-resolution can be achieved by the multi-scale of wavelet, the hierarchical and multi-resolution trigonometric wavelet beam element methods are proposed for the adaptive analysis. Numerical examples have demonstrated that the aforementioned two methods are effective in improving the computational accuracy. The trigonometric wavelet finite element method (WFEM) proposed herein provides an alternative approach for improving the computational accuracy, which can be tailored for the problem considered.

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11

Zayed, E. M. E., and Khaled A. Gepreel. "A series of complexiton soliton solutions for nonlinear Jaulent—Miodek PDEs using the Riccati equations method." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 5 (September 26, 2011): 1001–15. http://dx.doi.org/10.1017/s0308210510000405.

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We use the extended multiple Riccati equations expansion method to construct a series of double-soliton-like solutions, double triangular function solutions and complexiton soliton solutions for nonlinear Jaulent-Miodek PDEs. With the help of symbolic computation using Maple and Mathematica, we obtain many new types of complexiton soliton solutions, i.e. various combinations of trigonometric periodic functions and hyperbolic function solutions, various combinations of trigonometric periodic functions and rational function solutions, and various combinations of hyperbolic functions and rational function solutions.

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12

Omer, Faruk CETIN. "Students perceptions and development of conceptual understanding regarding trigonometry and trigonometric function." Educational Research and Reviews 10, no. 3 (February 10, 2015): 338–50. http://dx.doi.org/10.5897/err2014.2017.

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13

Chorlton, Frank. "71.44 Outpourings from a Trigonometric Function." Mathematical Gazette 71, no. 458 (December 1987): 305. http://dx.doi.org/10.2307/3617057.

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14

Chu, Wenchang. "Jordan's totient function and trigonometric sums." Studia Scientiarum Mathematicarum Hungarica 57, no. 1 (March 2020): 40–53. http://dx.doi.org/10.1556/012.2020.57.1.1452.

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15

Ibraheem, Farheen, Maria Hussain, Malik Zawwar Hussain, and Akhlaq Ahmad Bhatti. "Positive Data Visualization Using Trigonometric Function." Journal of Applied Mathematics 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/247120.

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16

Chen, Hongwei. "On some trigonometric power sums." International Journal of Mathematics and Mathematical Sciences 30, no. 3 (2002): 185–91. http://dx.doi.org/10.1155/s0161171202007731.

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Using the generating function method, the closed formulas for various power sums of trigonometric functions are established. The computer algebra system Maple is used to carry out the complex calculations.

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17

Zhengrong, Liu, Jiang Tianpei, Qin Peng, and Xu Qinfeng. "Trigonometric Function Periodic Wave Solutions and Their Limit Forms for the KdV-Like and the PC-Like Equations." Mathematical Problems in Engineering 2011 (2011): 1–23. http://dx.doi.org/10.1155/2011/810217.

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We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limit forms for the KdV-like equationut+a(1+bu)uux+uxxx=0, and PC-like equationvtt- vttxx- (a1v+a2v2+a3v3)xx=0, respectively. Via some special phase orbits, we obtain some new explicit periodic wave solutions which are called trigonometric function periodic wave solutions because they are expressed in terms of trigonometric functions. We also show that the trigonometric function periodic wave solutions can be obtained from the limits of elliptic function periodic wave solutions. It is very interesting that the two equations have similar periodic wave solutions. Our work extend previous some results.

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18

Tričković, Slobodan B., Mirjana V. Vidanović, and Miomir S. Stanković. "Series involving the product of a trigonometric integral and a trigonometric function." Integral Transforms and Special Functions 18, no. 10 (October 2007): 751–63. http://dx.doi.org/10.1080/10652460701446458.

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19

Goodman, T. N. T., and A. Sharma. "Trigonometric interpolation." Proceedings of the Edinburgh Mathematical Society 35, no. 3 (October 1992): 457–72. http://dx.doi.org/10.1017/s0013091500005745.

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We consider interpolation at 2n equidistant nodes in [0,π) from the space ℱN spanned by sines and cosines of odd multiples of x. This interpolation problem is shown to be correct for an arbitrary sequence of derivatives specified at all the nodes. Explicit expressions for the fundamental polynomials are obtained and it is shown that under mild smoothness assumptions on the function f interpolant from ℱN converges uniformly to f as the node spacing goes to zero.

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20

Stavek, Jiri. "On the Hidden Beauty of Trigonometric Functions." Applied Physics Research 9, no. 2 (March 17, 2017): 57. http://dx.doi.org/10.5539/apr.v9n2p57.

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In the unit circle with radius R = E0 = mc2 = 1 we have defined the trigonometric function cos(Theta) = v/c. The known trigonometric functions revealed the hidden relationships between sensible energy, latent energy, sensible momentum and latent momentum of the moving object, and the absorbed momentum from outside and the available momentum in the outside of the moving object. We present the trigonometric concept inspired by the old Babylonian clay tablet IM 55357 and based on the knowledge of the School of Athens (the fresco of Raphael) and the work of many generations of the Masters of trigonometry. The concept of the Divided Line of Plato can be now quantitatively tested. For the experimental analysis of this concept we propose to study in details the very well known beta decay of RaE to determine the sensible and latent energy (heat) of those beta particles and the sensible and latent energy of the remaining nucleus. The longitudinal momentum and the transverse (latent) momentum can be studied on the effects of the slow neutrons. The longitudinal momentum and the transverse momentum of photons can be manipulated in a convenient medium in order to prepare slow photons. The photoormi effect might improve the efficiency of the light-to-electricity conversion and the efficiency of the light-to-heat conversion.

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21

Kong, Sixiao, Chunbiao Li, Haibo Jiang, Yibo Zhao, and Yanling Wang. "Asymmetry Evolvement and Controllability of a Symmetric Hyperchaotic Map." Symmetry 13, no. 6 (June 9, 2021): 1039. http://dx.doi.org/10.3390/sym13061039.

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Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation.

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22

Yang, Yun Jie, and Yun Mei Zhao. "Derivation of Exact Solutions for the (3+1)-Dimensional KP Equation with (G'/G²)-Expansion Method." Advanced Materials Research 1044-1045 (October 2014): 1110–12. http://dx.doi.org/10.4028/www.scientific.net/amr.1044-1045.1110.

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Using the-expansion method proposed recently the exact solutions of the (3+1)-dimensional KP equation are found out. The exact solutions are expressed by two types of functions which are the trigonometric functions and the rational functions. When the parameters are taken as special values the trigonometric function solutions can be expressed as periodic wave solutions.

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23

Li, Bo, and Peng Wang. "Several Differentiation Formulas of Special Functions. Part IV." Formalized Mathematics 14, no. 3 (January 1, 2006): 109–14. http://dx.doi.org/10.2478/v10037-006-0013-0.

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

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24

BORESKOV, K. G., A. V. TURBINER, J. C. LÓPEZ VIEYRA, and M. A. G. GARCÍA. "SUTHERLAND-TYPE TRIGONOMETRIC MODELS, TRIGONOMETRIC INVARIANTS AND MULTIVARIATE POLYNOMIALS III: E8 CASE." International Journal of Modern Physics A 26, no. 07n08 (March 30, 2011): 1399–437. http://dx.doi.org/10.1142/s0217751x11053018.

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It is shown that the E8 trigonometric Olshanetsky–Perelomov Hamiltonian, when written in terms of the fundamental trigonometric invariants, is in algebraic form, i.e. it has polynomial coefficients, and preserves two infinite flags of polynomial spaces marked by the Weyl (co)-vector and E8 highest root (both in the basis of simple roots) as characteristic vectors. The explicit form of the Hamiltonian in new variables has been obtained both by direct calculation and by means of the orbit function technique. It is shown the triangularity of the Hamiltonian in the bases of orbit functions and of algebraic monomials ordered through Weyl heights. Examples of first eigenfunctions are presented.

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25

Malallah, Fahad Layth, Zaid Ahmed Aljawaryy, Baraa Tariq Sharef, Asem Khmag, and Lway Faisal A. Razak. "Irreversible Biometric Template Protection by Trigonometric Function." International Review on Computers and Software (IRECOS) 11, no. 12 (December 31, 2016): 1138. http://dx.doi.org/10.15866/irecos.v11i12.11003.

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26

Gisuthan, Bimal, and Thambipillai Srikanthan. "Pipelining flat CORDIC based trigonometric function generators." Microelectronics Journal 33, no. 1-2 (January 2002): 77–89. http://dx.doi.org/10.1016/s0026-2692(01)00107-0.

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27

Sworowska, Tat'yana A. "Recovering a function from its trigonometric integral." Sbornik: Mathematics 201, no. 7 (September 2, 2010): 1053–68. http://dx.doi.org/10.1070/sm2010v201n07abeh004102.

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28

Bazarkhanov, D. B. "Nonlinear trigonometric approximations of multivariate function classes." Proceedings of the Steklov Institute of Mathematics 293, no. 1 (May 2016): 2–36. http://dx.doi.org/10.1134/s0081543816040027.

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29

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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30

Saffari, H., and R. Tabatabaei. "A Finite Circular Arch Element Based on Trigonometric Shape Functions." Mathematical Problems in Engineering 2007 (2007): 1–19. http://dx.doi.org/10.1155/2007/78507.

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The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordinates. The element with three nodal parameters is chosen on curvature. Then, curvature field in the element is interpolated as the conventional trigonometric functions. Shape functions are obtained as usual by matrix operations. To consider the boundary conditions, a transformation matrix between nodal curvature and nodal displacement vectors is introduced. The equilibrium equation is written by minimizing the total potential energy in terms of the displacement components. In such equilibrium equation, the locking phenomenon is eliminated. The interesting point in this method is that for most problems, it is sufficient to use only one element to obtain the solution. Four examples are presented in order to verify the element formulation and to show the accuracy and efficiency of the method. The results are compared with those of other concepts.

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Li, Bo, Na Ma, and Xiquan Liang. "Integrability Formulas. Part II." Formalized Mathematics 18, no. 2 (January 1, 2010): 129–41. http://dx.doi.org/10.2478/v10037-010-0016-8.

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Integrability Formulas. Part II In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.

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You, Minghui, Wei Song, and Xiaoyu Wang. "On a new generalization of some Hilbert-type inequalities." Open Mathematics 19, no. 1 (January 1, 2021): 569–82. http://dx.doi.org/10.1515/math-2021-0034.

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Abstract In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.

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33

Cai, X. Z., G. Q. Wang, M. El Ghami, and Y. J. Yue. "Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/710158.

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We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for linear optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods,O(n2/3log⁡(n/ε)), and small-update methods,O(nlog⁡(n/ε)). These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.

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34

SAIGO, MEGUMI, and R. K. RAINA. "EVALUATION OF CERTAIN INTEGRALS IN TERMS OF GENERALIZED KAMPE DE FERIET FUNCTION AND LAURICELLA FUNCTION $F_D^{(n)}$." Tamkang Journal of Mathematics 26, no. 1 (March 1, 1995): 41–47. http://dx.doi.org/10.5556/j.tkjm.26.1995.4377.

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The paper is concerned with the evaluation ofthree integrals involving general polynomial systems and a rational function of trigonometric functions. Our new formulas reduce to many known formulas.

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Li, Bo, and Na Ma. "Integrability Formulas. Part I." Formalized Mathematics 18, no. 1 (January 1, 2010): 27–37. http://dx.doi.org/10.2478/v10037-010-0004-z.

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Integrability Formulas. Part I In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, and the polynomial function.

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36

Islam, Saeed, Muhammad Ghaffar Khan, Bakhtiar Ahmad, Muhammad Arif, and Ronnason Chinram. "Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function." Mathematics 8, no. 10 (October 1, 2020): 1676. http://dx.doi.org/10.3390/math8101676.

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The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class.

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37

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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Chu, Wei, S. Sathiya Keerthi, and Chong Jin Ong. "Bayesian Trigonometric Support Vector Classifier." Neural Computation 15, no. 9 (September 1, 2003): 2227–54. http://dx.doi.org/10.1162/089976603322297368.

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This letter describes Bayesian techniques for support vector classification. In particular, we propose a novel differentiable loss function, called the trigonometric loss function, which has the desirable characteristic of natural normalization in the likelihood function, and then follow standard gaussian processes techniques to set up a Bayesian framework. In this framework, Bayesian inference is used to implement model adaptation, while keeping the merits of support vector classifier, such as sparseness and convex programming. This differs from standard gaussian processes for classification. Moreover, we put forward class probability in making predictions. Experimental results on benchmark data sets indicate the usefulness of this approach.

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CHAND, A. K. B., and K. R. TYADA. "PARTIALLY BLENDED CONSTRAINED RATIONAL CUBIC TRIGONOMETRIC FRACTAL INTERPOLATION SURFACES." Fractals 24, no. 03 (August 30, 2016): 1650027. http://dx.doi.org/10.1142/s0218348x16500274.

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Fractal interpolation is an advance technique for visualization of scientific shaped data. In this paper, we present a new family of partially blended rational cubic trigonometric fractal interpolation surfaces (RCTFISs) with a combination of blending functions and univariate rational trigonometric fractal interpolation functions (FIFs) along the grid lines of the interpolation domain. The developed FIFs use rational trigonometric functions [Formula: see text], where [Formula: see text] and [Formula: see text] are cubic trigonometric polynomials with four shape parameters. The convergence analysis of partially blended RCTFIS with the original surface data generating function is discussed. We derive sufficient data-dependent conditions on the scaling factors and shape parameters such that the fractal grid line functions lie above the grid lines of a plane [Formula: see text], and consequently the proposed partially blended RCTFIS lies above the plane [Formula: see text]. Positivity preserving partially blended RCTFIS is a special case of the constrained partially blended RCTFIS. Numerical examples are provided to support the proposed theoretical results.

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Ibraheem, Farheen, Maria Hussain, and Malik Zawwar Hussain. "Monotone Data Visualization Using Rational Trigonometric Spline Interpolation." Scientific World Journal 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/602453.

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Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.

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JENA, M. K. "CONSTRUCTION OF COMPACTLY SUPPORTED WAVELETS FROM TRIGONOMETRIC B-SPLINES." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (September 2011): 843–65. http://dx.doi.org/10.1142/s021969131100433x.

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We construct a class of semiorthogonal wavelets by taking a normalized trigonometric B-spline of any order as the scaling function. The construction is based on generalized Euler–Frobenius polynomial and generalized autocorrelation function. We also show that the odd order normalized trigonometric B-spline satisfies convex hull property as well as partition of unity property. Moreover, we also present a subdivision algorithm for the convolution of normalized trigonometric B-splines. Several examples of wavelet are also provided.

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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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He, Yinghui, Shaolin Li, and Yao Long. "Exact Solutions to the Sharma-Tasso-Olver Equation by Using ImprovedG′/G-Expansion Method." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/247234.

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This paper is concerned with a double nonlinear dispersive equation: the Sharma-Tasso-Olver equation. We propose an improvedG′/G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained. When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solutions are derived from the trigonometric function solutions. The improvedG′/G-expansion method is straightforward, concise and effective and can be applied to other nonlinear evolution equations in mathematical physics.

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Mithun, A. T., and M. C. Lineesh. "Standard pairs and existence of symmetric multiscaling functions." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 02 (October 16, 2019): 1950057. http://dx.doi.org/10.1142/s0219691319500577.

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Construction of multiwavelets begins with finding a solution to the multiscaling equation. The solution is known as multiscaling function. Then, a multiwavelet basis is constructed from the multiscaling function. Symmetric multiscaling functions make the wavelet basis symmetric. The existence and properties of the multiscaling function depend on the symbol function. Symbol functions are trigonometric matrix polynomials. A trigonometric matrix polynomial can be constructed from a pair of matrices known as the standard pair. The square matrix in the pair and the matrix polynomial have the same spectrum. Our objective is to find necessary and sufficient conditions on standard pairs for the existence of compactly supported, symmetric multiscaling functions. First, necessary as well as sufficient conditions on the standard pairs for the existence of symbol functions corresponding to compactly supported multiscaling functions are found. Then, the necessary and sufficient conditions on the class of standard pairs, which make the multiscaling function symmetric, are derived. A method to construct symbol function corresponding to a compactly supported, symmetric multiscaling function from an appropriate standard pair is developed.

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Latinčić, Dragan. "Possible principles of mathematical music analysis." New Sound, no. 51 (2018): 153–74. http://dx.doi.org/10.5937/newso1851153l.

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The text is a summary of many years of research in the domains of micro-intervals, metric-rhythmic projection of the spectrum harmonics, and the establishment of a link with mathematics, more precisely, geometry, with a special focus on the application of the Pythagorean Theorem. Mathematical music analysis enables the establishment of methods for constructing right, obtuse, and acute musical triangles as well as projections of their edges (sides), which are recognized in trigonometry as the functions of angles: the sine, cosine, and so on; as well as the establishment of methods for constructing spectral and scalar (intonative-temporal) trigonometric unit circles with their function graphs.

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Chigira, M. "Morpho-densitometry of bone using a trigonometric function." Medical Hypotheses 44, no. 6 (June 1995): 479–82. http://dx.doi.org/10.1016/0306-9877(95)90510-3.

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Awad, Mervat El-Sayed. "Trigonometric series representations of the orbital inclination function." Astrophysics and Space Science 125, no. 2 (1986): 243–58. http://dx.doi.org/10.1007/bf00648025.

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Yu, Wanbo, and Ting Yu. "Analysis of chaotic characteristics of trigonometric function system." Modern Physics Letters B 34, no. 21 (May 9, 2020): 2050210. http://dx.doi.org/10.1142/s0217984920502103.

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Chaos, as an important subject of nonlinear science, plays an important role in solving problems in both natural sciences and social sciences such as the fields of secure communications, fluid motion, particle motion and so on. Aiming at this problem, this paper proposes a nonlinear dynamic system composed of product trigonometric functions and studies its chaotic characteristics. Through the mathematical derivation of the system’s period, the analysis of the necessary conditions at the fixed point, the experimental drawing of the Lyapunov exponential graph and the branch graph of the system, it is proved that the system has larger chaotic interval and stronger chaotic characteristics. The parameters of the proposed dynamic system are generated randomly, and then the chaotic sequence can be generated. The chaotic sequence is used to encrypt the digital image, a good encryption effect is obtained, and there is a large key space. At the same time, the motion of the particles in the space magnetic field is simulated, which further proves that the trigonometric system has strong chaotic characteristics.

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Pickover, C. A. "Halley maps for a trigonometric and rational function." Computers & Mathematics with Applications 17, no. 1-3 (1989): 125–32. http://dx.doi.org/10.1016/0898-1221(89)90153-3.

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Hua, Liu, and Du Jing-yuan. "On convergence for trigonometric interpolation of analytic function." Wuhan University Journal of Natural Sciences 4, no. 3 (September 1999): 275–77. http://dx.doi.org/10.1007/bf02842349.

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