Showing papers on "Inverse trigonometric functions published in 1996"
TL;DR: A multiresolution analysis of nested subspaces of trigonometric polynomials of Hermite interpolation on a dyadic partition of nodes on the interval [0,2π].
Abstract: The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0,2π]. Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.
34 citations
TL;DR: In this article, the properties of q-exponential and q-trigonometric functions were examined and discussed in the literature, and it was shown that they are related to Jackson's q-analogues of the exponential and trigonometric functions by classical Fourier - Gauss transformations.
Abstract: We examine the properties of q-exponential and q-trigonometric functions, recently introduced and discussed in the literature. It is shown that they are related to Jackson's q-analogues of the exponential and trigonometric functions by classical Fourier - Gauss transformations.
11 citations
TL;DR: In this article, a volume formula for hyperbolic tetrahedra with one vertex at infinity is derived, which yields a new representation of the four-dimensional three-point function of Euclidean quantum field theory.
11 citations
01 Jan 1996
TL;DR: In this paper, the Laguerre polynomials were used to approximate a lognormal density and examined numerically for inverse Gaussian distributions with quadratic variance functions.
Abstract: The univariate natural exponential families with quadratic variance functions have the orthogonal polynomial systems which are generated by differentiating the densities. This method, however, is not applicable to inverse Gaussian distributions because their variance functions are cubic. We will generate non-orthogonal but simple polynomials and orthogonal functions of inverse Gaussian distributions based on Laguerre polynomials. Properties of the polynomials and the functions are obtained by the use of the generating functions. They are applied to approximate a lognormal density and examined numerically.
4 citations
4 citations
13 Mar 1996
TL;DR: Analysis of proposed unitary trigonometric (cosine, sine and combined sine-cosine) transforms is performed, and efficient algorithms for their computation are developed.
Abstract: In this paper, we introduce a new class of discrete parametric trigonometric transforms. We establish the conditions of unitarity of the discrete parametric trigonometric transform matrices, by which we construct a wide range of orthonormal transform matrices. Analysis of proposed unitary trigonometric (cosine, sine and combined sine-cosine) transforms is performed, and efficient algorithms for their computation are developed.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
4 citations
Patent•
16 Oct 1996
TL;DR: In this article, the authors propose a teaching tool for helping study mathematics, comprising a frame whose middle is provided with a round hole, a transparent disc (or a ring) and an opaque disc.
Abstract: The utility model discloses a teaching tool for helping study mathematics, comprising a frame whose middle is provided with a round hole, a transparent disc (or a ring) and an opaque disc. The overall thickness of two discs is identical with the thickness of the frame. After the two discs are superposed and placed in the frame, the two discs can be rotated flexibly without interference. Each part is marked with centimeter scales, or a plurality of kinds of logarithmic linear groups, or trigonometric function linear groups, or 100 or 360 equidistant lattices, or abscissa, or ordinate or mathematic symbols. Various correlations among provided conditions and the rotation of the discs are used. The utility model can be used for calculating positive and inverse trigonometric functions, logarithm, equation and rational number, drawing various geometrical figures and helping remember triangular formulas.
1 citations
Patent•
03 Jan 1996
TL;DR: In this article, a drawing and calculating instrument is composed of a semicircular protractor, a central shaft, and a ruler, which can be used for measuring angles, drawing straight lines, converting and calculating complex number, convert and calculating polar coordinates and rectangular coordinates, solving trigonometric functions, solving right triangles, drawing circles, etc.
Abstract: The utility model relates to a multi-purpose drawing and calculating instrument which belongs to a multi-purpose plotter. The drawing and calculating instrument is composed of a semicircular protractor, a central shaft, and a ruler, wherein, the center of the central shaft, the center of the angle measuring circle of the semicircular protractor, and the middle point of one side with scale of the ruler are coincident and can rotate around the central shaft; the semicircular protractor is provided with coordinate grids which are vertically and horizontally intersecting. The drawing and calculating instrument can be used for measuring angles, drawing straight lines, converting and calculating complex number, converting and calculating polar coordinates and rectangular coordinates, solving trigonometric functions and inverse trigonometric functions, solving right triangles, drawing circles, etc. The drawing and calculating instrument has the advantage of simple structure and the drawing and calculating functions, and is suitable for students and engineering drawing workers.
1 citations
TL;DR: This article established recurrence relations for successive derivates atx = 0 of some trigonometric and hyperbolic functions and constructed an arithmetrical triangle which gives immediately, by recurrence, the derivatives of the desidered order, of the functions sec, tan, cosec, cot, sech and tanh.
Abstract: We establish some recurrence relations for the successive derivates atx=0 of some trigonometric and hyperbolic functions. We also construct an arithmetical triangle which gives immediately, by recurrence, the derivatives of the desidered order, of the functions sec, tan, cosec, cot, sech and tanh.