Artificial intelligent assistant

prolate

answer Answers

ProphetesAI is thinking...

MindMap

Sources

1
prolate
▪ I. prolate, a. (ˈprəʊleɪt) [ad. L. prōlāt-us, pa. pple. of prōferre to bring forward, produce, prolong, f. prō, pro-1 + ferre to carry.] 1. Geom. Lengthened in the direction of the polar diameter: said of a spheroid formed by the revolution of an ellipse about its longer axis. Cf. oblate a. prolat... Oxford English Dictionary
prophetes.ai 0.0 3.0 0.0
2
Prolate rotator galaxy
A prolate rotator galaxy, or spindle galaxy, is an unusual class of galaxy that is cigar-shaped and rotates around its long axis. A prolate rotator galaxy is an elliptical galaxy in prolate rotation, meaning they possess a significant amount of rotation around their major axis. wikipedia.org
en.wikipedia.org 0.0 1.5 0.0
3
Prolate trochoidal mass spectrometer
A prolate trochoidal mass spectrometer is a chemical analysis instrument in which the ions of different mass-to-charge ratio are separated by means of mutually perpendicular electric and magnetic fields so that the ions follow a prolate trochoidal path. wikipedia.org
en.wikipedia.org 0.0 0.90000004 0.0
4
prolating
prolating, vbl. n. (prəʊˈleɪtɪŋ) [f. prolate v. + -ing1.] Increase or extension.1919 Empire Rev. 256 The loss of wealth, high taxation, the dislocation of trade and industry with their attendant evils, labour unrest and the prolating of unemployment. Oxford English Dictionary
prophetes.ai 0.0 0.6 0.0
5
Trochoid
Curtate, common, prolate If lies inside the circle (), on its circumference (), or outside (), the trochoid is described as being curtate ("contracted "), common, or prolate ("extended"), respectively. wikipedia.org
en.wikipedia.org 0.0 0.6 0.0
6
The prolate cycloid A cycloid is given by the parametric equations: $ x = 2 - \pi \cos(t)$ and $ y = 2t - \pi \sin(t)$. The problem asks for the slope of the tangents on the cycloid at a point where the cycloid inter...
At $t$ and $t'$ the coordinates repeat: $x(t)=x(t')\land y(t)=y(t')\implies2t-\pi\sin t=2t'-\pi\sin t'\land\cos t=\cos t'$ $\cos t=\cos t'\implies t'=t+k2\pi;\in\mathbb Z-\\{0\\}\lor (t'=-t+k'2\pi,t\neq n\pi);k,n\in\mathbb Z$ a) $2t-\pi\sin t=2(t+k2\pi)-\pi\sin (t+k2\pi)$ $\sin(t+k2\pi)-\sin t=4k$, ...
prophetes.ai 0.0 0.3 0.0
7
Prolate spheroidal wave function
The prolate spheroidal wave functions are eigenfunctions of the Laplacian in prolate spheroidal coordinates, adapted to boundary conditions on certain Here, is the interfocal distance of the elliptical cross section of the prolate spheroid. wikipedia.org
en.wikipedia.org 0.0 0.3 0.0
8
Fitting a prolate cycloid between two points (to a certain length) I need to draw a prolate cycloid such that it fits a certain length l, and has an integer number of wavelengths. I have these equations for the prolat...
We have: $$ x(0)=h\cos(\phi)\cos(\theta) \quad\hbox{and}\quad x(2\pi n)=h\cos(\phi)\cos(\theta)+2\pi na\sin\theta. $$ We want $x(2\pi n)-x(0)=l$, that is $2\pi na\sin\theta=l$, whence: $$ \sin\theta={l\over 2\pi na}. $$
prophetes.ai 0.0 0.3 0.0
9
Prolate spheroidal coordinates
Definition The most common definition of prolate spheroidal coordinates is where is a nonnegative real number and . Hence, the curves of constant are prolate spheroids, whereas the curves of constant are hyperboloids of revolution. wikipedia.org
en.wikipedia.org 0.0 0.3 0.0
10
Average projected area of an ellipsoid Consider an ellipsoid of semi-axes a, b, c (possibly prolate, b=c). I am interested in the "shadow" of this solid onto a distant plane, in a given direction d=(k,l,m) orthogonal ...
When a surface element $d\omega$ at a point $P$ in three-space is projected orthogonally into all possible directions then the average area of the image is $\rho\thinspace d\omega$ where $\rho$ is a universal constant. To determine the value of $\rho$ we argue as follows: The unit sphere $S^2$ has a...
prophetes.ai 0.0 0.3 0.0
11
Spheroid
A prolate spheroid with has surface area The prolate spheroid is generated by rotation about the -axis of an ellipse with semi-major axis and semi-minor Prolate spheroids The prolate spheroid is the approximate shape of the ball in several sports, such as in the rugby ball. wikipedia.org
en.wikipedia.org 0.0 0.0 0.0
12
Pigskin
Pigskin may refer to: Ball (gridiron football) (also a pigskin), a ball, roughly in the form of a prolate spheroid, used in the context of playing gridiron wikipedia.org
en.wikipedia.org 0.0 0.0 0.0
13
Integration of combination of Bessel Function and Exponential Function I have read "Watson:Treatise Theory of Bessel Function", "Table of Integration, Series and Product", "Handbook of Mathematical Functions, Formulas...
This function is derived by Slepian and Pollak in 1961 and this is also know by Prolate-spheroidal wave function. For more detail read these articles Prolate spheroidal wave functions, Fourier analysis, and uncertainty-I Prolate spheroidal wave functions, Fourier
prophetes.ai 0.0 0.0 0.0
14
Close packing of ellipsoids How can the packing density of a set of congruent ellipsoids be calculated? I'm dealing with prolate spheroids so technically I do not need the general answer for ellipsoids, but my abstrac...
The densest known packing of ellipsoids of any kind, including prolate spheroids, is given in this paper.
prophetes.ai 0.0 0.0 0.0
15
Oblate spheroidal wave function
In applied mathematics, oblate spheroidal wave functions (like also prolate spheroidal wave functions and other related functions) are involved in the These results are based on earlier work on prolate spheroidal wave functions. wikipedia.org
en.wikipedia.org 0.0 0.0 0.0