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Functional Equations Related to Sine Type Functions
Complex Analysis and Operator Theory, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manfred Möller, Vyacheslav Pivovarchik
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form, 2003
This paper is an English version of a part of some lecture notes by N. Kurokawa from 1991, the notes having been taken by S. Koyama. In the paper, a theory of multiple sine functions is constructed which generalizes the usual sine function. The double sine function was introduced by Hölder in 1886, and the authors introduce the triple and higher sine ...
Kurokawa Nobushige, Koyama Shin-ya
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This paper is an English version of a part of some lecture notes by N. Kurokawa from 1991, the notes having been taken by S. Koyama. In the paper, a theory of multiple sine functions is constructed which generalizes the usual sine function. The double sine function was introduced by Hölder in 1886, and the authors introduce the triple and higher sine ...
Kurokawa Nobushige, Koyama Shin-ya
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A fast approximation to the sine function
Software: Practice and Experience, 1977AbstractA function approximating the sine function is given which was designed for high speed when coded into a computer routine. The domain is divided into a small number of intervals and in each of these a straight line approximation is used. The slopes of the straight line segments have denominators which are powers of 2, and so an implementation ...
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Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, 1955
This paper describes a sine function resistor of rather unusual design. A linear resistance card bent to circular shape about an eccentric frame of very simple construction is employed to obtain a resistance variation that is within very close limits of true sine values.
K. L. Nielsen, E. H. Roland
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This paper describes a sine function resistor of rather unusual design. A linear resistance card bent to circular shape about an eccentric frame of very simple construction is employed to obtain a resistance variation that is within very close limits of true sine values.
K. L. Nielsen, E. H. Roland
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2014 IEEE International Symposium on Bioelectronics and Bioinformatics (IEEE ISBB 2014), 2014
This paper proposes the class of the translinear (TL) circuits implementing a wide range of static nonlinear relationships in the current signal domain to computational such as generating products, quotients, vector magnitude and rational functions, which are implemented in a standard 0.35-µm SiGe technology.
null Jun-Hong Weng, null Di-Yu Lin
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This paper proposes the class of the translinear (TL) circuits implementing a wide range of static nonlinear relationships in the current signal domain to computational such as generating products, quotients, vector magnitude and rational functions, which are implemented in a standard 0.35-µm SiGe technology.
null Jun-Hong Weng, null Di-Yu Lin
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Differential Algebraicity of Multiple Sine Functions
Letters in Mathematical Physics, 2005Let \(w_1,\dots, w_r> 0\). The multiple sine function of period \(\underline w= (w_1,\dots, w_r)\) is defined by \[ S_r(x,\underline w)= \Gamma_r(x,\underline w)^{-1} \Gamma_r(|\underline w|- x,\underline w)^{-1)^r}, \] where \(|\underline w|= w_1+\cdots+ w_r\), and \(\Gamma_r(x,\underline w)\) is the multiple gamma function originally studied by ...
Kurokawa, Nobushige, Wakayama, Masato
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On the cosine-sine functional equation on groups
aequationes mathematicae, 2002The authors find the solutions \(f,g\in C(G)\) of each of the functional equations \[ \frac{f(x+y)\pm f(x+\sigma y)}{2}=f(x)g(y)+g(x)f(y)+h(x)h(y), \;\forall x,y\in G \] where \(G\) is a topological Abelian group, \(\sigma :G\longrightarrow G\) is a continuous involutive automorphism of \(G\), and where \(C(G)\) denotes the algebra of continuous ...
Friis, P. de Place, Stetkær, H.
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A smoothness indicator constant for sine functions
Journal of Computational Physics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Conghai Wu, Ling Wu, Shuhai Zhang
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On Functional Versions of the Arc-Sine Law
Journal of Theoretical Probability, 2008Suppose \(R(t)\) and \(R_n(t)\), \(n\geq 1\), are random processes in \(D(0,1)\) such that \(R_n(t)\) converges weakly to \(R(t)\) in \(D(0,1)\). For \(z\in(-\infty,\infty)\) define \(\Lambda_n(z)= \int^1_0\mathbf{1}\{R_n(t)\leq z\}\,dt\) and similarly \(\Lambda(z)\) for the process \(R(t)\).
Berkes, István +2 more
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A characterization of the sine function
Mathematical Proceedings of the Cambridge Philosophical Society, 1980AbstractIf a function and all its derivatives and integrals are absolutely uniformly bounded, then the function is a sine function with period 2π.
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