February 6th, 2010

One day I shall hear the thunder....Down under...6 foot 4 and full of muscle

I enjoy the watch....As it ticks and stops....I watch as friends tick and then stop...I enjoy learning about the people of this Earth...They tempt me, this world of plenty and plunder....We Loot and Plunder, Luther Plunder....Go PLANET!~ The Power is Yours!  On a hopeful note...I hope the Saints destroy the Colts/Omega Horse Shoes!

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Omega

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Search Wiktionary Look up Ω or ω in Wiktionary, the free dictionary.
Omega uc lc.svg
Greek alphabet
Αα Alpha Νν Nu
Ββ Beta Ξξ Xi
Γγ Gamma Οο Omicron
Δδ Delta Ππ Pi
Εε Epsilon Ρρ Rho
Ζζ Zeta Σσς Sigma
Ηη Eta Ττ Tau
Θθ Theta Υυ Upsilon
Ιι Iota Φφ Phi
Κκ Kappa Χχ Chi
Λλ Lambda Ψψ Psi
Μμ Mu Ωω Omega
Obsolete letters
Digamma uc lc.svg Digamma Qoppa uc lc.svg Qoppa
San uc lc.svg San Sampi uc lc.svg Sampi
Other characters
Stigma uc lc.svg Stigma Sho uc lc.svg Sho
Heta uc lc.svg Heta

Greek diacritics
For other uses, see Omega (disambiguation).

Omega (majuscule: Ω, minuscule: ω; Greek Ωμέγα) is the 24th and last letter of the Greek alphabet. In the Greek numeric system, it has a value of 800. The word literally means "great O" (ō mega, mega meaning 'great'), as opposed to Omicron, which means "little O" (o mikron, micron meaning "little").[1] This name is Byzantine; in Classical Greek, the letter was called ō (), whereas the Omicron was called ou (οὖ).[2] The form of the lowercase letter derives from a double omicron, which came to be written open at the top.

Phonetically, the Ancient Greek Ω is a long open-mid o [ɔː], similar to the vowel of English raw as pronounced in New York. In Modern Greek Ω represents the same sound as omicron. The letter omega is transcribed ō or simply o.

Omega (the last letter of the Greek alphabet) 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. In the New Testament book of Revelation, Christ is declared to be the "alpha and omega, the beginning and the end, the first and the last".[3]

As the symbol of the Sumerian goddess Ninhursag, the omega has been depicted in art from around 3000 BC, though more generally from the early second millennium. It appears on some boundary stones on the upper tier, which indicates her importance.

Omega was also adopted into the early Cyrillic alphabet. See Cyrillic omega (Ѡ, ѡ). A Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark .

  • In fictional worlds:
    • In the fictional world of Star Trek, the Omega symbol is used in conjunction with the Omega Directive.
    • As the logo of the popular PlayStation franchise God of War.
    • In the fictional universe Warhammer 40,000, the symbol for the Sons of Orar Chapter and, if turned upside down, the symbol for the Ultramarine Chapter of the Space Marines (Warhammer 40,000).
    • In the popular web series Red vs Blue the Blood Gulch Chronicles Omega (or o'mally) is freelancer Tex's AI implant and the main antagonist of the Blood Gulch Chronicles

[edit] The symbol ω (lower case letter)

The minuscule letter ω is used as a symbol:

 

[edit] Notes

  1. ^ The Greek Alphabet
  2. ^ Herbert Weir Smyth. A Greek Grammar for Colleges. §1
  3. ^ Revelation 22:13, KJV, and see also 1:8, Greek ἐγὼ τὸ ἄλφα καὶ τὸ ὦ, ὁ πρῶτος καὶ ὁ ἔσχατος, ἡ ἀρχὴ καὶ τὸ τέλος. Or in Revelation 1:8 as seen in the Latin Vulgate Bible, the Greek is shown, surrounded by Latin: "ego sum α et ω principium et finis dicit Dominus Deus qui est et qui erat et qui venturus est Omnipotens"
  4. ^ Excerpts from the The Unicode Standard, Version 4.0, accessed 11 October 2006



It’s the song of the redeemed
Rising from the African plain
It’s the song of the forgiven
Drowning out the Amazon rain
The song of Asian believers
Filled with God’s holy fire
It’s every tribe, every tongue, every nation
A love song born of a grateful choir

It’s all God’s children singing
Glory, glory, hallelujah
He reigns, He reigns
It’s all God’s children singing
Glory, glory, hallelujah
He reigns, He reigns

Let it rise above the four winds
Caught up in the heavenly sound
Let praises echo from the towers of cathedrals
To the faithful gathered underground
Of all the songs sung from the dawn of creation
Some were meant to persist
Of all the bells rung from a thousand steeples
None rings truer than this

It’s all God’s children singing
Glory, glory, hallelujah
He reigns, He reigns
It’s all God’s children singing
Glory, glory, hallelujah
He reigns, He reigns
It’s all God’s children singing
Glory, glory, hallelujah
He reigns, He reigns
It’s all God’s children singing
Glory, glory, hallelujah
He reigns, He reigns

And all the powers of darkness
Tremble at what they’ve just heard
‘Cause all the powers of darkness
Can’t drown out a single word

When all God’s children sing out
Glory, glory, hallelujah
He reigns, He reigns
All God’s children singing
Glory, glory, hallelujah
He reigns, He reigns

In Numbers...I am Lost and Found...Infinately never alone



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ARTIST: The Carpenters
TITLE: Top of the World
Lyrics and Chords


Such a feelin's coming over me 
There is wonder in most every thing I see 
Not a cloud in the sky, got the sun in my eyes 
And I won't be surprised if it's a dream 

/ C GF C - / Em DmG C - / F G Em A / Dm Fm G Gsus4 / 

Everything I want the world to be 
Is now coming true especially for me 
And the reason is clear, it's because you are here 
You're the nearest thing to heaven that I've seen 

{Refrain}
I'm on the top of the world looking down on creation 
And the only explanation I can find 
Is the love that I've found ever since you've been around 
Your love's put me at the top of the world 

/ C - F - / Em DmG C - / F G C F / C DmG C - /

Something in the wind has learned my name 
And it's telling me that things are not the same 
In the leaves on the trees and the touch of the breeze
There's a pleasin' sense of happiness for me 

There is only one wish on my mind 
When this day is through I hope that I will find 
That tomorrow will be just the same for you and me 
All I need will be mine if you are here 

{Refrain twice}

Devas and avatars

Krishna (left), the eighth incarnation (avatar) of Vishnu or svayam bhagavan, with his consort Radha, worshiped as Radha Krishna across a number of traditions - traditional painting from the 1700s.

The Hindu scriptures refer to celestial entities called Devas (or devī in feminine form; devatā used synonymously for Deva in Hindi), "the shining ones", which may be translated into English as "gods" or "heavenly beings".[47] The devas are an integral part of Hindu culture and are depicted in art, architecture and through icons, and mythological stories about them are related in the scriptures, particularly in Indian epic poetry and the Puranas. They are, however, often distinguished from Ishvara, a supreme personal god, with many Hindus worshiping Ishvara in a particular form as their iṣṭa devatā, or chosen ideal.[48][49] The choice is a matter of individual preference,[50] and of regional and family traditions.[50]

Hindu epics and the Puranas relate several episodes of the descent of God to Earth in corporeal form to restore dharma to society and to guide humans to moksha. Such an incarnation is called an avatar. The most prominent avatars are of Vishnu and include Rama (the protagonist in Ramayana) and Krishna (a central figure in the epic Mahabharata).


From Wikipedia, the free encyclopedia

  (Redirected from Wright Omega Function)
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The Wright Omega function along part of the real axis

In mathematics, the Wright omega function, denoted ω, is defined in terms of the Lambert W function as:

\omega(z) = W_{\big \lceil \frac{\mathrm{Im}(z) - \pi}{2 \pi} \big \rceil}(e^z).

Contents

[hide]

[edit] Uses

One of the main applications of this function is in the resolution of the equation z = ln(z), as the only solution is given by z = e−ω(π i).

y = ω(z) is the unique solution, when z \neq x \pm i \pi for x ≤ −1, of the equation y + ln(y) = z. Except on those two rays, the Wright omega function is continuous, even analytic.

[edit] Properties

The Wright omega function satisfies the relation Wk(z) = ω(ln(z) + 2πik).

It also satisfies the differential equation

 \frac{d\omega}{dz} = \frac{\omega}{1 + \omega}

wherever ω is analytic (as can be seen by performing separation of variables and recovering the equation ln(ω) + ω = z), and as a consequence its integral can be expressed as:

\int w^n \, dz = <br />\begin{cases} <br />  \frac{\omega^{n+1} -1 }{n+1} + \frac{\omega^n}{n}  & \mbox{if } n \neq -1, \\<br />  \ln(\omega) - \frac{1}{\omega} & \mbox{if } n = -1.<br />\end{cases}

Its Taylor series around the point a = ωa + ln(ωa) takes the form :

\omega(z) = \sum_{n=0}^{+\infty} \frac{q_n(\omega_a)}{(1+\omega_a)^{2n-1}}\frac{(z-a)^n}{n!}

where

q_n(w) = \sum_{k=0}^{n-1} \bigg \langle \! \! \bigg \langle <br />\begin{matrix}<br />  n+1 \\<br />  k<br />\end{matrix} <br />\bigg \rangle \! \! \bigg \rangle (-1)^k w^{k+1}

in which

\bigg \langle \! \! \bigg \langle <br />\begin{matrix}<br />  n \\<br />  k<br />\end{matrix} <br />\bigg \rangle \! \! \bigg \rangle

is a second-order Eulerian number.

[edit] Values

\begin{array}{lll}<br />\omega(0) &= W_0(1) &\approx 0.56714 \\<br />\omega(1) &= 1 & \\<br />\omega(-1 \pm i \pi) &= -1 & \\<br />\omega(-\frac{1}{3} + \ln \left ( \frac{1}{3} \right ) + i \pi ) &= -\frac{1}{3} & \\<br />\omega(-\frac{1}{3} + \ln \left ( \frac{1}{3} \right ) - i \pi ) &= W_{-1} \left ( -\frac{1}{3} e^{-\frac{1}{3}} \right ) &\approx -2.237147028 \\<br />\end{array}

[edit] Plots

Plots of the Wright Omega function on the complex plane

z = Re(ω(x + i y))

z = Im(ω(x + i y))

z = |ω(x + i y)|

[edit] References

Ohm's law

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This article is about the law related to electricity. For other uses, see Ohm's acoustic law.
V, I, and R, the parameters of Ohm's law.

In electrical circuits, Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them[, provided that the temperature remains constant].[1]

The mathematical equation that describes this relationship is:[2]

I = \frac{V}{R}

where V is the potential difference measured across the resistance in units of volts; I is the current through the resistance in units of amperes and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.[3]

The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above (see History section below) to explain his experimental results. The above equation is the modern form of Ohm's law.

In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

\boldsymbol{J} = \sigma \boldsymbol{E},

From Wikipedia, the free encyclopedia

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This article is about the SI (Omega) derived unit. For other meanings, see Ohm (disambiguation).
A multimeter can be used to measure resistance in ohms. It can also be used to measure capacitance, voltage, current, and other electrical characteristics.
Several resistors. Their resistance, in ohms, is marked using a color code.

The ohm (symbol: Ω) is the SI unit of electrical impedance or, in the direct current case, electrical resistance, named after Georg Simon Ohm.

Contents

[hide]

[edit] Definition

The ohm is defined as a resistance between 2 points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force.[1]

\Omega = \dfrac{\mbox{V}}{\mbox{A}} = \dfrac{\mbox{m}^2 \cdot \mbox{kg}}{\mbox{s} \cdot \mbox{C}^2} = \dfrac{\mbox{J}}{\mbox{s} \cdot \mbox{A}^2}=\dfrac{\mbox{kg}\cdot\mbox{m}^2}{\mbox{s}^3 \cdot \mbox{A}^2} =\dfrac{\mbox{HP}}{745.69 \cdot \mbox{A}^2}

In many cases the resistance of a conductor in ohms is approximately constant within a certain range of voltages, temperatures, and other parameters; one speaks of linear resistors. In other cases resistance varies (e.g., thermistors).

Commonly used multiples and submultiples in electrical and electronic usage are the milliohm, ohm, kilohm, and megohm.[2]

[edit] Conversions

[edit] Power as a function of resistance

The power dissipated by a linear resistor may be calculated from its resistance, and voltage or current. The formula is a combination of Ohm's law and Joule's laws:

P=V\cdot I =\frac{V^2}{R} = I^2\cdot R

where P is the power in watts, R the resistance in ohms, V the voltage across the resistor, and I the current through it.

This formula is applicable to devices whose resistance varies with current.

[edit] Use of the Ω symbol in electronic documents

Care should be taken when preparing documents (including HTML documents) which make use of the symbol Ω. Some document editing software will attempt to use the symbol typeface to render the character. Where the font is not supported, a W is displayed instead. As this represents the SI unit of power, not resistance, this can lead to confusion.

Unicode encodes an ohm symbol distinct from Greek omega among Letterlike Symbols