Lasith (lasith) wrote,

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

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 

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).



[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!}


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

[edit] References

Ohm's law

From Wikipedia, the free encyclopedia

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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},

Tags: 2010, buddhism, religion

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