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Topic: Omega constant

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	Chaitin’s Constant
		Omega is uncomputable and unknowable: we don't know its value for any programming language and we never will.
		Omega'' is equivalent to the probability that, during an infinite computation, a computer will fail to produce an output – for example, get no result from a computation and move on to the next one – and that it will do this only a finite number of times.
		Omega and the Omega hierarchy are revealing to mathematicians an unsettling truth: the problems that we can hope ever to solve form a tiny archipelago in a vast ocean of undecidability.
	www.daviddarling.info /encyclopedia/C/Chaitins_constant.html (527 words)

	Omega (Site not responding. Last check: 2007-11-07)
		Omega is a variable meteorologists use to quantify vertical motions in the atmosphere.
		Omega is commonly displayed on a four panel map for the 700 mb level.
		Since omega values are useful for indicating regions with and lacking precipitation, it is also possible to use omega values to correlate to cloud cover.
	www.personal.psu.edu /students/d/s/dsb175/omega (1140 words)

	omega Comparison Table (Site not responding. Last check: 2007-11-07)
		The ratio of the average density of mass in the universe to the critical mass density, the latter being the density of mass needed to eventually halt the outward expansion of the universe.
		In an open universe, omega is always less than 1; in a closed universe, it is always greater than 1; in a flat universe it is always exactly equal to 1.
		Unless omega is exactly equal to 1, it changes in time, constantly decreasing in an open universe and constantly increasing in a closed universe.
	www.site.uottawa.ca:4321 /astronomy/omega_table.html (196 words)

	The Sound of Mathematics - Constants
		Digits of the constant e was used for this piece, which has four parts.
		The digits 1 to 8 is the E harmonic minor scale, 0 is a quarter pause, 9 means change octave and the 9 itself takes on the same pitch as the previously dtermined tone but in the new octave (the piece oscillates up and down over two octaves).
		The Omega constant W(1) and its inverse 1 / W(1) was used for this piece.
	www.geocities.com /Vienna/9349/constants.html (1250 words)

	Omega - Wikipedia, the free encyclopedia
		Omega (Ω ω) is the 24th and last letter of the Greek alphabet.
		In the Bible, Jesus declares himself to be the "Alpha and Omega, the beginning and the end, the first and the last".
		A lowercase omega is used for the omega mesons.
	en.wikipedia.org /wiki/Omega (699 words)

	Omega - The real meaning from Timesharetalk wikipedia (Site not responding. Last check: 2007-11-07)
		Omega (O ?) is the 24th and last letter of the Greek alphabet.
		The Omega symbol is now to be represented as one on the six numbers that formulate the universe founded by Martin J. Rees.The cosmic number omega measures the amount of material in our Universe - galaxies, diffuse gas, and 'dark matter'.
		Omega is often used to denote the last, the end, or the ultimate limit of a set, in contrast to Alpha, the first letter of the Greek Alphabet.
	www.timesharetalk.co.uk /wiki.asp?k=Omega (650 words)

	Omega Watches - Orolus.com
		For 150 years, the Omega spirit has been behind an impressive series of achievements in fields as varied as technology, design and the human adventure.
		Omega's success today is expressed in the image association of its leading watches with brand ambassadors from the world of fashion, sports and performing arts who reflect the time-honoured vitality of Omega.Get yours here today, at Orolus.com.
		OMEGA continues to make strides in both technology and design with elegant timepieces prized by collectors and aficionados alike.
	www.orolus.com /omega.shtml (222 words)

	NewStandard: 8/18/96
		The Hubble constant is sort of a yardstick for the expanding universe, because it tells astronomers how fast galaxies and other astronomical objects are moving away from one another.
		If omega is 1, that means there's enough mass and energy to gradually slow the big bang expansion, but not enough to reverse it.
		It says that if a cosmological constant is the only way of producing a universe where humans can evolve into thinking beings capable of exploring the cosmos, then the number has to exist or else we wouldn't be here wondering about it.
	www.southcoasttoday.com /daily/08-96/08-18-96/m02wn179.htm (1384 words)

	Omega and why maths has no TOEs (Site not responding. Last check: 2007-11-07)
		Also, when defining Omega, you have to make certain restrictions on which types of programs are valid, to avoid counting things twice, and to make sure that Omega does not become infinitely large.
		Even though Omega has a very precise mathematical definition, its infinitely many bits cannot be captured in a finite program — they are just as "bad" as a string of infinitely many bits chosen at random.
		Omega tells us that there are in fact infinitely many such statements: whether any one of the infinitely many bits of Omega is a 0 or a 1 is something we cannot deduce from any mathematical theory.
	plus.maths.org /issue37/features/omega (3317 words)

	Omega
		Omega Ω phonetically represents a long "O" in the English language, such as the pronunciation in the word "close".
		Jesus declares himself to be the "Alpha and Omega, the beginning and the end, the first and the last." (Revelation 22:13, KJV, and see also 1:8).
		Omega is a sci-fi novel by Robert Sheckley about a penal colony planet Omega.
	www.mlahanas.de /Greeks/LX/Omega.html (568 words)

	Formulas for Physics (Site not responding. Last check: 2007-11-07)
		The force (F) by an ideal spring on an object is proportional to the displacement (x) from the equilibrium position of the moving end of the spring.
		The constant of proportionality is negative so that the spring always acts to force the object back towards the equilibrium position.
		The gravitational torque on the pendulum is the mgL in magnitude, where m is the mass of the pendulum, g is the gravitational field strength (9.8 m/sec^2), and L is the distance from the pivot point to the center of mass of the pendulum.
	members.aol.com /jwdooley/eqns/SHM/XMPLS/XMPLS.HTM (228 words)

	Method of sensing excessive slip in a wheel slip control system - Patent 5315519
		The term C.sub..omega.du may in one embodiment be a calibration constant stored in read only memory or in another embodiment may be computed as a function of various vehicle parameters including vehicle speed (which may be represented by the average of the undriven wheel speeds.omega..sub.lu and.omega..sub.ru) and the steering angle.alpha..
		In one embodiment, the commanded wheel speed.omega..sub.com may be a constant speed added to the vehicle speed which in turn is the average of the undriven wheel speeds.
		In one embodiment, the slip index threshold may be the sum of one component that decreases with increasing vehicle speed and another component that increases from zero with vehicle acceleration from a certain level.
	www.freepatentsonline.com /5315519.html (5909 words)

	[No title]
		The constant K is called the spring constant or stiffness of the spring (expressed in N / m).
		If the ratio of omega sub 2 to omega sub 1 (or omega sub 1 to omega sub 2) is a rational number, the motion is periodic with an angular frequency given by the largest common divisor of omega sub 2 and omega sub 1.
		Nevertheless, the time between zero crossings in the same direction remains constant and equal to T sub d = 1/f sub d = 2 * pi / omegad, which is defined as the period of the oscillation.
	www.afn.org /~afn49304/rfatt.htm (2580 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		In the hydrogen atom, {\bf A} is a constant of the motion, the property responsible for the well-known accidental degeneracy, both classical and quantal.
		We note that \({\omega }\) may also be thought of as a function of \(\rm \theta \), but writing it in terms of \(\ell \) is more convenient for this derivation.
		According to the correspondence principle this frequency must be the precessional frequency \({\omega }_{c}\) caused by the polarizability of the core.
	newton.umsl.edu /~atomic/ajp3/ajp3.tex.txt (2474 words)

	New Scientist: The Omega Man
		The Omega strain of incalculable numbers reveals that mathematics is not simply moth-eaten, it is mostly made of gaping holes.
		Chaitin discovered Omega and its astonishing properties while wrestling with two of the most influential mathematical discoveries of the 20th century.
		Going further, they showed that Omega'' is equivalent to the probability that, during an infinite computation, a computer will fail to produce an output--for example, get no result from a computation and move on to the next one--and that it will do this only a finite number of times.
	www.dc.uba.ar /people/profesores/becher/ns.html (2388 words)

	United States Patent: 5,311,526 (Site not responding. Last check: 2007-11-07)
		Exemplarily, the pumping rate and the optical gain are coherently varied such that the output radiation is free of chirp, or the output frequency and the effective carrier temperature are coherently varied such that the output radiation has constant amplitude.
		The pumping rate J(t) is proportional to the pump radiation intensity.PHI.(t), and V(t) causes variation in the refractive index of the cladding and therefore in the confinement factor.GAMMA.(t).
		Numeral 48 refers to constant amplitude pump radiation, 47 to carrier heating radiation, exemplarily CO.sub.2 laser radiation, and 49 to the laser output.
	www.ece.sunysb.edu /~serge/pat20.html (4589 words)

	Friedmann Equation
		Besides the density and gravitation constant G, the equation contains the Hubble parameter H, a scaling parameter R, and a factor k which is called the curvature parameter.
		The Friedmann equation which models the expanding universe has a parameter k called the curvature parameter which is indicative of the rate of expansion and whether or not that expansion rate is increasing or decreasing.
		The original motivation for the cosmological constant was to make possible a static universe which was isotropic and homogeneous.
	hyperphysics.phy-astr.gsu.edu /hbase/astro/fried.html (556 words)

	Omega constant - Wikipedia, the free encyclopedia
		The Omega constant is a mathematical constant defined by
		The name is derived from the alternate name for Lambert's W function, the Omega function.
		It has properties that are akin to those of the golden ratio, in that
	en.wikipedia.org /wiki/Omega_constant (180 words)

	[No title]
		The {\it expectation} of the autocorrelation is that it is an impulse at zero lag.
		The {\it expectation} of the spectrum is that it is a constant, namely \begin{equation} \E[\hat S(Z)] \eq S(Z) \eq {\rm const} \end{equation} \subsection{Paradox: $N \rightarrow \infty$ vrs the ensemble average} \par Now for the paradox.
		A contour of constant $z$ is the (hyperbolic) curve $y = a+b/(x+c)$ (where $a$, $b$, and $c$ are different constants on each of the four faces).
	sepwww.stanford.edu /oldreports/sep61/old_src/jon8.txt (5012 words)

	Amazon.com: The Constants of Nature: From Alpha to Omega--the Numbers That Encode the Deepest Secrets of the Universe: ... (Site not responding. Last check: 2007-11-07)
		These constants quantify some of the simplest statements that science makes about the world, but as this fascinating work of popular science demonstrates, they have profound implications for the fate of the universe and our place within it.
		He traces scientists' evolving understanding of the natural constants as they grew to assume a central role in modern relativity theory and quantum mechanics, and outlines ongoing attempts to determine whether they are just inexplicable facts of nature or the logical consequence of some fundamental Theory of Everything.
		The natural constants are delicately balanced to make the universe safe for living organisms: altering them more than a hair would make stars burn out, atoms fly apart, and the world as we know it impossible.
	www.amazon.com /Constants-Nature-Omega-Numbers-Universe/dp/0375422218 (2898 words)

	Age of the Universe Exercise
		The age of the universe depends on two parameters; the current rate of expansion of the universe, also known as the Hubble constant (H), and the rate at which the expansion is slowing down.
		The best current measurement of the Hubble Constant H is due to a Hubble Space Telescope key project to measure the distance to other galaxies, using Cepheid variable stars.
		Because a non-zero cosmological constant will cause the expansion of the universe to speed up with time, measurements of the distances and recession speeds of distant galaxies can be used to try and measure the value of (Omega Lambda).
	www.uh.edu /~vanderse/astronomy/uni_age.html (1031 words)

	Theory Continued page 2
		The normal mechanism for this repulsive element in GR is the so-called universal constant that determines Omega(mass density) This is what Einstein originally proposed in his GR model.
		With this theory Omega is dependent upon which sub-space or sub-space fussion you are referencing.
		The difference is that now the Constant and Omega are dependent upon 4 masses combined and their individual coupling constants combined.
	www.superstringtheory.fanspace.com /custom3.html (623 words)

	Omega-News: Constant Use of Mobiles for sometimes trivial Purposes is pushing up the Demand for more and more Base ... (Site not responding. Last check: 2007-11-07)
		Omega-News: Constant Use of Mobiles for sometimes trivial Purposes is pushing up the Demand for more and more Base Stations
		Constant Use of Mobiles for sometimes trivial Purposes is pushing up the Demand for more and more Base Stations
		So that is what is happening around the country (and around the world) - people are expecting to use their mobile phones, even when there is a landline handy (she took another call on her landline while we were speaking) - but do not want to live by a base station.
	omega.twoday.net /stories/692981 (450 words)

	Omega (Site not responding. Last check: 2007-11-07)
		Definition: A theoretical measure of the execution of an algorithm, usually the time or memory needed, given the problem size n, which is usually the number of items.
		The values of c and k must be fixed for the function f and must not depend on n.
		The traditional definition is f is big omega of g if it is not little o of g.
	www.nist.gov /dads/HTML/omegaCapital.html (239 words)

	Numerical Constants - Mathematics & Physics - Numericana
		The Omega constant: W(1) is the solution of the equation x exp(x) = 1.
		The attribution of this irrational constant to Ramanujan was made by Simon Plouffe, as a monument to a famous 1975 April fools column by Martin Gardner in Scientific American (where it was claimed that the above had been proven to be exactly an integer, as conjectured by Ramanujan in 1914 [sic!]).
		Some other set of independent constants could have been used to define the 7 basic units (for example, a conventional value of the electron's charge could replace the conventional permeability of the vacuum) but the following one was chosen after careful considerations.
	home.att.net /~numericana/answer/constants.htm (5480 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		In this paper we consider a similar question except that the integrals in the definition of the functionals are taken on some set $\Omega$ which is invariant under rotations but not under translations, that is, $\Omega$ is either a ball, an annulus or the exterior of a ball.
		In this paper we consider a similar problem except that the integrals in the definition of the functionals are taken on a set $\Omega$ which is rotation invariant but not translation invariant (that is, $\Omega$ is either a ball or an annulus or the exterior of a ball).
		In the case of a constrained minimization problem with Dirichlet boundary condition, there are examples for which the global minimizer is radially symmetric and examples for which the global minimizer is not radially symmetric.
	ejde.math.unt.edu /Volumes/1996/03/Lopes-tex (1748 words)

	Notable Properties of Specific Numbers at MROB
		This is the Omega constant, which satisfies each of these simple equations (all equivalent):
		It is called Apéry's constant because in 1979 Apéry surprised the mathematical community by showing that it is irrational.
		This is the Glaisher-Kinkelin constant, related to the Barnes G-function and the K-function.
	home.earthlink.net /~mrob/pub/math/numbers.html (2130 words)

	Numbers, Magick & Motion 3
		This is the Omega constant, which satisfies each of these simple equations (all equivalent): ex = 1/x x = ln(1/x) = - ln(x)
		Tomes (3456 24), Divitry (12th century)288 harmoinic studies.....etc...the Viswanath constant* is probably linked to Feigenbaum's constant somehow because of the order to disorder to order to disorder to order to....
		The twelfth dimensional connection to base 10 is connected to the Theory of Everything through the bifurcation of the "collective unconscious" constant..(3718)...as it transforms between the electrical and gravitational constants*.
	www.gnostics.com /numbersIIIb.htm (2110 words)

	Serious Difficulties for Abiogenesis (Site not responding. Last check: 2007-11-07)
		The standard formulation of entropy is S=kln(omega) where k is the boltzman constant* and omega is the number of different ways that the system can be arranged for a given state.
		The requirement of constant stereochemistry for just the simplest hypothetical simple cell of just 300 proteins can be simply determined by assuming that the formation of a left or right handed molecule is 1/2 just like the coin toss analogy in Section 4.
		The constant stereochemistry issue is also a problem for the RNA world hypothesis as Orgel acknowledges in Ref. 14, "Equally disappointing we can induce copying of the original template only when we run our experiments with nucleotides having a right-handed configuration.
	members.aol.com /SHinrichs9/abiopb/abiopb.htm (8232 words)

	Flat universe
		Assume the cosmological condition for the infinite expansion of the flat universe is Lambda (the cosmological constant) + Omega (the ratio of the actual density of matter in the universe to a certain critical density) = 1.
		0-resolution of the gravitation constant is the mean proportional between the consequent of the creation ratio, 1/100, and the "created 100," (1/.01)/.01 = 10000.
		is the radiation density constant, the relation-power of the ratio of the numerical value of the latter to 7.57
	dgleahy.com /dgl/p26.html (1243 words)

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