Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
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TL;DR: In this article , a least square approach is used to solve simultaneously for the illumination background and the introduced phase shift in a local window, which allows to calculate the interferogram phase of the pixel at the center of the window with the standard arc-tangent formula.
Abstract: Abstract A procedure to recover the phase from two interferograms with unknown phase step is proposed. A least-square approach is used to solve simultaneously for the illumination background and the introduced phase shift in a local window. This allows to calculate the interferogram phase of the pixel at the center of the window with the standard arc-tangent formula. This process is carried out sequentially across the interferogram field until all pixels are recovered. The proposed scheme is fast and robust, and unlike others methods eliminates the need to implement prior steps of background suppression or interferogram normalization. The developed procedure may be used in problematic environments where vibrations or other disturbances difficult to acquire a full set of phase shifted interferograms with constants phase shifts. The developed procedure is validated in real and simulated data with good results.
09 May 2022
TL;DR: In this article , a cyclic function is determined to correspond as the equivalent of the classic sine formula to isosceles triangles, which is called isn^-1(x) sine equivalent.
Abstract: Abstract This paper discusses a new formula to solve for the angle of isosceles triangles given proportion of differentiated unequivalent edge length versus the always-equivalent edges. The equation is equal to the arcsine of (X/2) multiplied by two. This formula is to be called ‘isn^-1(x)’, short for inverse isosceles sine equivalent. Also discussed is the non-inverse ‘isn(x)’ which is the cyclic function which is determined to correspond as the equivalent of the classic sine formula to isosceles triangles. The formula set is clearly superior and powerful at calculating the angle and measure of any given obtuse or acute triangle of an unclassified type, as well as unifying a simplest-fit formula across all types of triangle. Also discussed are two transform approximation formulas, which help to analyze graphs and samples.
19 Aug 2022
TL;DR: In this paper , a variant of multiple zeta values (MZVs) of level four, called alternating multiple mixed values or alternating multiple $M$-values (AMMVs), which form a subspace of the space of colored MZVs of level 4 as ${\mathbb Q}[i]$-vector spaces, was defined and studied.
Abstract: In this paper, we define and study a variant of multiple zeta values (MZVs) of level four, called alternating multiple mixed values or alternating multiple $M$-values (AMMVs), which forms a subspace of the space of colored MZVs of level four as ${\mathbb Q}[i]$-vector spaces. This variant includes the alternating version of Hoffman's multiple $t$-values, Kaneko-Tsumura's multiple $T$-values, and the multiple $S$-values studied by the authors previously as special cases. We exhibit nice properties similar to the ordinary MZVs such as the duality, integral shuffle and series stuffle relations. After setting up the algebraic framework we derive the regularized double shuffle relations of the AMMVs. We also investigate several alternating multiple $T$- and $S$-values by establishing some explicit relations of integrals involving arctangent function. In the end, we discuss the explicit evaluations of a kind of AMMVs at depth three and compute the dimensions of a few interesting subspaces of AMMVs for weight less than 7.
TL;DR: In this article , the trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps, and they are shown how the angle sum formula for tangent can be realized by equating two different conformal mapping from an infinite strip to a disk.
Abstract: SummaryThe trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps. In particular, we show how the angle-sum formula for tangent can be realized by equating two different conformal maps from an infinite strip to a disk, and the formulas for sine and cosine by similarly equating conformal maps from an infinite strip to a certain slit domain.
Patent•
27 Aug 1999
TL;DR: In this article, the authors proposed a method to reduce the calculation time required for decoding an image while keeping a high image quality by correcting processes of inverse cosine transform and inverse weighting so as to process only image information used for display.
Abstract: PROBLEM TO BE SOLVED: To reduce a calculation time required for decoding an image while keeping a high image quality by correcting processes of inverse cosine transform and inverse weighting so as to process only image information used for display SOLUTION: Applications of an inverse weighting(IW) 135 and an inverse cosine transform (IDCT) 140 are combined to obtain one function As a means of decoding an image of 1/4 size, a horizontal 4-point IW/ICDT processing is applied to coefficients up to a 4th column from a side of a first 4 rows corresponding to lower coefficients in a 8×8 matrix of transformation coefficients being part of a video frame A vertical 8-point IW/IDCT processing is applied to all coefficients of first 4 columns where the coefficients up to a 4th row from a side of each column corresponding to a high frequency are set to zero In the case that an input block consists of two 4×8 matrices consisting of sum and difference coefficients, the horizontal 4-point processing is applied to each row of each matrix and the vertical 4-point processing is applies to the sum of sum coefficients and difference coefficients