Idiot Cube

Scumbag Cube



But, seriously...I think all the big ones have been covered already.

Welcome to our humble batcave, weary Goggle travelers!

I see you are hard at work defiling our home page, but I hope you will take a moment out of your busy schedule to join in our discussion of ponies, furries, and higher mathematics.

Today I will be discussing Laplace transforms.

The Laplace transform is a widely used integral transform with many applications in physics and engineering. Denoted , it is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms it to a function F(s) with a complex argument s. This transformation is essentially bijective for the majority of practical uses; the respective pairs of f(t) and F(s) are matched in tables. The Laplace transform has the useful property that many relationships and operations over the originals f(t) correspond to simpler relationships and operations over the images F(s). It is named after Pierre-Simon Laplace, who introduced the transform in his work on probability theory.

The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.


The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace, who used a similar transform (now called z transform) in his work on probability theory. The current widespread use of the transform came about soon after World War II although it had been used in the 19th century by Abel, Lerch, Heaviside and Bromwich. The older history of similar transforms is as follows. From 1744, Leonhard Euler investigated integrals of the form


as solutions of differential equations but did not pursue the matter very far. Joseph Louis Lagrange was an admirer of Euler and, in his work on integrating probability density functions, investigated expressions of the form



which some modern historians have interpreted within modern Laplace transform theory.

These types of integrals seem first to have attracted Laplace's attention in 1782 where he was following in the spirit of Euler in using the integrals themselves as solutions of equations. However, in 1785, Laplace took the critical step forward when, rather than just looking for a solution in the form of an integral, he started to apply the transforms in the sense that was later to become popular. He used an integral of the form:



akin to a Mellin transform, to transform the whole of a difference equation, in order to look for solutions of the transformed equation. He then went on to apply the Laplace transform in the same way and started to derive some of its properties, beginning to appreciate its potential power.

Laplace also recognised that Joseph Fourier's method of Fourier series for solving the diffusion equation could only apply to a limited region of space as the solutions were periodic. In 1809, Laplace applied his transform to find solutions that diffused indefinitely in space.



The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), defined by:


The parameter s is a complex number:


with real numbers σ and ω. The meaning of the integral depends on types of functions of interest. A necessary condition for existence of the integral is that ƒ must be locally integrable on [0,∞). For locally integrable functions that decay at infinity or are of exponential type, the integral can be understood as a (proper) Lebesgue integral. However, for many applications it is necessary to regard it as a conditionally convergent improper integral at ∞. Still more generally, the integral can be understood in a weak sense, and this is dealt with below.
One can define the Laplace transform of a finite Borel measure μ by the Lebesgue integral



An important special case is where μ is a probability measure or, even more specifically, the Dirac delta function. In operational calculus, the Laplace transform of a measure is often treated as though the measure came from a distribution function ƒ. In that case, to avoid potential confusion, one often writes

[stolen word-for-word from the Wikipedia page.]

At this time I will open the thread to discussion. As always, your input on the subject is greatly appreciated. If you do not wish to discuss Laplace transforms, I suggest you leave SPUFpowered immediately, and never return.

Welcome to our humble batcave, weary Goggle travelers!

I see you are hard at work defiling our home page, but I hope you will take a moment out of your busy schedule to join in our discussion of ponies, furries, and higher mathematics.

Today I will be discussing Laplace transforms.

The Laplace transform is a widely used integral transform with many applications in physics and engineering. Denoted , it is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms it to a function F(s) with a complex argument s. This transformation is essentially bijective for the majority of practical uses; the respective pairs of f(t) and F(s) are matched in tables. The Laplace transform has the useful property that many relationships and operations over the originals f(t) correspond to simpler relationships and operations over the images F(s). It is named after Pierre-Simon Laplace, who introduced the transform in his work on probability theory.

The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.


The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace, who used a similar transform (now called z transform) in his work on probability theory. The current widespread use of the transform came about soon after World War II although it had been used in the 19th century by Abel, Lerch, Heaviside and Bromwich. The older history of similar transforms is as follows. From 1744, Leonhard Euler investigated integrals of the form


as solutions of differential equations but did not pursue the matter very far. Joseph Louis Lagrange was an admirer of Euler and, in his work on integrating probability density functions, investigated expressions of the form



which some modern historians have interpreted within modern Laplace transform theory.

These types of integrals seem first to have attracted Laplace's attention in 1782 where he was following in the spirit of Euler in using the integrals themselves as solutions of equations. However, in 1785, Laplace took the critical step forward when, rather than just looking for a solution in the form of an integral, he started to apply the transforms in the sense that was later to become popular. He used an integral of the form:



akin to a Mellin transform, to transform the whole of a difference equation, in order to look for solutions of the transformed equation. He then went on to apply the Laplace transform in the same way and started to derive some of its properties, beginning to appreciate its potential power.

Laplace also recognised that Joseph Fourier's method of Fourier series for solving the diffusion equation could only apply to a limited region of space as the solutions were periodic. In 1809, Laplace applied his transform to find solutions that diffused indefinitely in space.



The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), defined by:


The parameter s is a complex number:


with real numbers σ and ω. The meaning of the integral depends on types of functions of interest. A necessary condition for existence of the integral is that ƒ must be locally integrable on [0,∞). For locally integrable functions that decay at infinity or are of exponential type, the integral can be understood as a (proper) Lebesgue integral. However, for many applications it is necessary to regard it as a conditionally convergent improper integral at ∞. Still more generally, the integral can be understood in a weak sense, and this is dealt with below.
One can define the Laplace transform of a finite Borel measure μ by the Lebesgue integral



An important special case is where μ is a probability measure or, even more specifically, the Dirac delta function. In operational calculus, the Laplace transform of a measure is often treated as though the measure came from a distribution function ƒ. In that case, to avoid potential confusion, one often writes

[stolen word-for-word from the Wikipedia page.]

At this time I will open the thread to discussion. As always, your input on the subject is greatly appreciated. If you do not wish to discuss Laplace transforms, I suggest you leave SPUFpowered immediately, and never return.

"I don't know who you are. I don't know what you want. If you're looking for ransom, I can tell you I don't have money... but what I do have are a very particular set of skills. Skills I have acquired over a very long career. Skills that make me a nightmare for people like you. If you let my daughter go now, that will be the end of it - I will not look for you, I will not pursue you... but if you don't, I will look for you, I will find you... and I will kill you."-Bryan Mills

I used to think Runescape was a good game.

Item and Enemy Ideas (Since everyone and their Robot kajigger wants to be a character)-Silent's Rep Cannon-Some kind of rocket launcher-Demoknight-Melee Enemy (Damage by touch)Has ability to Charge in a straight line toward the player (Think Syrian werebull or Kleer)Above average durability-Flame Shield-Provides Damage ResistanceCould be Equipped item or Time limit based powerup-Spycicle-Provides more damage resistance than the Flame Shield, but recharges after every hit (Or breaks after 3 hits or something)Could be Equipped item or durability based powerup-Fire Axe-Swings in a close range arc, similar to Link's Sword from Top down Zelda Games.-Trade Forum-Could be shopping Zone-Misplaced Trade Topic-Find and redirect these to unlock new items in the Trade Forum-New Users forum-Tutorial Zone-Cructo-Recurring miniboss that reappears under different names-Demopan-Elite Demoknight UnitSame as Demoknight, but with Stout Shako ProjectileAlternatively Shopkeeper-Spycrab-Peaceful until attackedSummons more spycrabs to help it (Think LoZ Chickens)Could conceivably spawn spycrabs from itself ala blob enemy to reduce spawn shenanigans-Spygineer-Erects Dispensers to heal itself and AlliesCould be ally/playable character or medictype enemy-Troll-Generic Melee EnemyImage Macros appear on screen when hit by them-Level 3 Minisentry-Deployable pewpew turretWould presumably be bonus item/easter egg-Necroposter-Revives old Topics to fight for itRevived topic acts as a portal that spawns ghosts or something, I don't know.-Powerups called Buffs--Debuffs called Nerfs-Hats could be collectables, or one form of currency, or the plot device.IE: Gaben has removed all hats from TF2, Fight to unite the Spuf and restore hats to their previous glory.IE2: Collect all *Number* hats to unlock no reward what so everIE3: Trade Hat A to NPC for Item B-Golden Machine Gun-Unobtainable item put in plain sight to taunt the player

Meanwhile on Rainbow Road.

I call that the "Nothing to see here" gif.

Fret not, Hertz old boy. I shall use my expertise in gentlemanly facial hair to provide you with a moustache, free of charge.
Let's see now...for someone of your rather...unique complexion...I believe a classic handlebar moustache would be most suitable. I shall affix it to your face, like so...oh, for goodness sake, please do try to hold still, mister Hertz! We're nearly finished.

And now the final touch: A simple, but dignified, top hat.

All done, mister Hertz! Behold your new, gentlemannly image!





What do you say, Hertz? Does this not capture the refined gentle mann you see inside yourself? Wear this avatar with pride, old chap.

We should also only post in this font.

Hm, yes.

I have achieved ultimate handsomeness.

This is now my new avatar.

Having a TV like that is most of how I got into PC gaming

http://mustachified.com/
Oh god

It's right at the top of the Settings page.

Make their melee weapons swing 20% slower.Balanced.
 

11/15

So I wrote this...thing...ages ago and I never got around to posting it on SPUF, but this seems like a sort of acceptable place.
So:

If you, as a SPUFer, were in this game, what would your character look like? What would your signature hat and weapon be? What would your FINAL REP SMASH be?

Who would be the final boss of this game, and who would the level bosses be?

What in the ♥♥♥♥ possessed me to even imagine this?

Seems like it might turn out nice.WHY it's on the Wizardry forums, I dunno.http://www.wizard101central.com/forums/showthread.php?t=267016

I drew a weird bird-thing when I was young, and I asked my dad what I should call it. He said Grobag.

Sonic the Hedgehog.I could beat Green Hill Zone before I could read.

Super Mario Bros Deluxe. Basically the original Mario bros, but ported for the the Game Boy Color with a few fancy minigames and such.I was 4 or 5 at the time. My dad bought a Game Boy Advance and that all in one fell swoop and I complained it wouldnt work because I didn't have the reflexes to jump over the very first goomba.I still never finished it. Gave it to my cousins all the way in california, along with the GBA. Christ, I wish I had it back.EDIT:
WHOA HOLY CRAPBROFIST ME RIGHT THE ♥♥♥♥ NOW.

Behold my writing prowess

I'm writing a sequel too.

Read it or Saxton Hale will perform a NON PAINFUL FLEX and explode your hippie brain.

I keep posting semi-witty comments for easy rep, but nothing happens!

Done. :tin:

Here's his profile. Somebody add him and invite him here. And give him a subforum where he can post his brilliant ideas.