Circular functions

Definitions

  • Webster's Revised Unabridged Dictionary
    • Circular functions See Inverse trigonometrical functions (below). -- Continuous function, a quantity that has no interruption in the continuity of its real values, as the variable changes between any specified limits.
    • Circular functions (Math) See under Function.
    • Circular functions the lengths of arcs relative to the sines, tangents, etc. Thus, AB is the arc whose sine is BD, and (if the length of BD is x) is written sin -1x, and so of the other lines. See Trigonometrical functionbelow). Other transcendental functions are the exponential functions, the elliptic functions, the gamma functions, the theta functions, etc.
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Usage

In literature:

There are three circular rooms in Sun Temple which from their form may be identified as ceremonial in function, technically called kivas.
"Mesa Verde National Park, Colorado" by Anonymous
There is nothing arbitrary in the use of a circular function to represent the waves.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 6" by Various
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In news:

The pleasing circularity of Gus Van Sant 's masterful Paranoid Park is not only a function of the film's narrative structure but reflects the arc of its maker's career.
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In science:

Satellite number as a function of circular velocity for the Galaxy and the Virgo cluster as observed (dots) and as predicted by hierarchical models (dashed and solid lines, for the Galaxy and Virgo respectively).
Understanding dwarf galaxies as galactic building blocks
It seems that this problem may have gone away: the number of ob jects predicted is a steep function of the sub-halo’s peak circular speed.
Dark Matter in Galaxies: Conference Summary
FIG. 1: Variation, as a function of the parameter r/R0 , of the tangential velocity vtg of a test particle in a stable circular orbit in a conformally symmetric vacuum space-time on the brane, for B = 1.00001 and different values of k: k = 0.9999 (solid curve), k = 0.99985 (dotted curve) and k = 0.9998 (dashed curve).
Can the galactic rotation curves be explained in brane world models?
Efforts to mine the CMB deeper pose data analysis challenges in particular to account for finer syste matic effects in observations, such as accounting for the non-circularity of the experimental beam response function presented in the meeting. 3.
Summary of ICGC04 Cosmology Workshop
Let us finally consider the case of a geodesic circular motion, as described by the “physical” observers, i.e., by our local observers (even if we find it convenient to express everything as a function of the old Schwarzshild-deSitter coordinates).
Multi-verses, Micro-universes and Elementary Particles (Hadrons)
FIGURE 6. (a) Cumulative number of Milky Way satellite galaxies as a function of halo circular velocity, assuming Poisson errors on the number count of satellites in each bin.
Dark Matter and Galaxy Formation
The observations are done at many position angles (which are a function of time of observation) leading to a more uniform, circularized, final point spread function (PSF).
The IRAC Dark Field; Far- Infrared to X-ray Data
The function F includes the use of four S-boxes, each of size 8 x 32, the left circular rotation operation and four operation functions that vary depending on the round number.
Encryption Quality Analysis and Security Evaluation of CAST-128 Algorithm and its Modified Version using Digital Images
We use I to refer to the intermediate 32-bit value after the left circular rotation function and the labels Ia, Ib, Ic and Id to refer to the 4 bytes of I where Ia is the most significant and Id is the least significant.
Encryption Quality Analysis and Security Evaluation of CAST-128 Algorithm and its Modified Version using Digital Images
The value of h as a function of radius for the two galaxies in their sample with circular velocity vc > 100 km s−1 is the same, except for the final steep rise just before the end of the H I data.
Outer Galactic Disks and a Quantitative Test of Gravity at Low Accelerations
The equation for N in Houde et al. (2009) is derived assuming a (circular) Gaussian beam and Gaussian turbulent auto-correlation functions.
Magnetic Field Properties in High Mass Star Formation from Large to Small Scales - A Statistical Analysis from Polarization Data
This method of proof is circular, monotone convergence can be applied to the right hand side, since the integral is a normal linear function on L∞ (M ).
Measure Theory in Noncommutative Spaces
Because we use a single product of Slater determinants, given the circular symmetry of the dots considered, the nodes depend only on the set of single-particle functions used.
Ab initio computation of circular quantum dots
This density function is symmetric around y = θ , which is the mode and the circular mean of the distribution.
Local power of the LR, Wald, score and gradient tests in dispersion models
Radius of (left) the ISCO and of (right) the circular photon orbit as a function of the spin a for several values of the parameter ǫ3 .
Testing the No-Hair Theorem with Sgr A*
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