every thing in our uni

every thing in our uni

همه چیز در دانشگاه ما

دختران روستا به شهر فکر می کنند دختران شهر در آرزوی روستا میمیرند !

مردان کوچک به آسایش مردان بزرگ فکر می کنند !

مردان بزرگ در آرزوی آسایش مردان کوچک میمیرند !

پروردگارا کدامین پل ؟ در کجای جهان شکسته است که هیچ کس به خانه اش

نمیرسد ؟

+نوشته شده در شنبه بیست و هفتم مهر 1387ساعت11:32توسط 666 | |

Quaternion

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This page describes quaternions in mathematics. For other uses of this word, see quaternion (disambiguation).

Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = −k, ij = −ji

Quaternions, in mathematics, are a non-commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations, such as in 3D computer graphics, although they have been superseded in many applications by vectors and matrices.

In modern language, quaternions form a 4-dimensional normed division algebra over the real numbers. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by $\mathbb{H}$ (Unicode ℍ). It can also be given by the Clifford algebra classifications Cℓ_0,2(R) = Cℓ⁰_3,0(R). The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only three finite-dimensional division rings containing the real numbers as a subring.

Hamilton product

For two elements a₁ + b₁i + c₁j + d₁k and a₂ + b₂i + c₂j + d₂k, their Hamilton product (a₁ + b₁i + c₁j + d₁k)(a₂ + b₂i + c₂j + d₂k) is determined by the products of the basis elements and the distributive law. The distributive law makes it possible to expand the product so that it is a sum of products of basis elements. This gives the following expression:

a₁a₂ + a₁b₂i + a₁c₂j + a₁d₂k + b₁a₂i + b₁b₂i² + b₁c₂ij + b₁d₂ik + c₁a₁j + c₁b₂ji + c₁c₂j² + c₁d₂jk + d₁a₁k + d₁b₂ki + d₁c₂kj + d₁d₂k².

Now the basis elements can be multiplied using the rules given above to get:

(a₁a₂ − b₁b₂ − c₁c₂ − d₁d₂) + (a₁b₂ + b₁a₂ + c₁d₂ − d₁c₂)i + (a₁c₂ − b₁d₂ + c₁a₂ + d₁b₂)j + (a₁d₂ + b₁c₂ − c₁b₂ + d₁a₂)k.

Ordered list form

Using the basis 1, i, j, k of H makes it possible to write H as a set of quadruples:

Then the basis elements are:

1 = (1,0,0,0),

i = (0,1,0,0),

j = (0,0,1,0),

k = (0,0,0,1),

and the formulas for addition and multiplication are:

(a₁,b₁,c₁,d₁) + (a₂,b₂,c₂,d₂) = (a₁ + a₂,b₁ + b₂,c₁ + c₂,d₁ + d₂).

(a₁,b₁,c₁,d₁)(a₂,b₂,c₂,d₂) = (a₁a₂ − b₁b₂ − c₁c₂ − d₁d₂,a₁b₂ + b₁a₂ + c₁d₂ − d₁c₂,a₁c₂ − b₁d₂ + c₁a₂ + d₁b₂,a₁d₂ + b₁c₂ − c₁b₂ + d₁a₂).

countiniue

+نوشته شده در شنبه بیستم مهر 1387ساعت10:2توسط 666 | |

سلام به همه کاربرهای گل(یاس/پریسا/گل آرا/پروانه/سپیده/مدیریت/و...)

از اونجائیکه این اواخرنتونستم زیاد مطالب به دردبخور بذارم معذرت ... باید بگم بخاطر اینکه جواب تک تک ایمیل های منو میدین دستتون واقعا درد نکنه ...زحمت میکشین...شرمنده کردین...مخصوصا دوستانیکه... بگذریم!!

شاد شاد شاد باشید

+نوشته شده در شنبه سیزدهم مهر 1387ساعت11:36توسط 666 | |

'Brilliant' minds honored

'Brilliant' minds honored

By Marissa Newhall, USA TODAY

Examining ancient trees, probing black holes and observing cannibalistic spiders are all part of the job for young researchers honored in Popular Science's fourth annual "Brilliant 10" feature.

The list recognizes young minds who have pushed their fields in innovative directions but remain virtually unknown to the public. The final 10 were selected based on recommendations from award-dispensing organizations, university department heads and editors of scientific publications.

From computer graphics and math to biophysics and robotics, these scientists from research institutions throughout North America have broken ground while testing the boundaries of the known universe. The honorees:

Amy Barger, 34

Barger used data from multiple telescopes to study black holes, becoming a pioneer in studies of light wavelength. A cosmologist at the University of Wisconsin-Madison, she is now studying how the activity of black holes relates to star formation and possible origins of the universe.

Sebastian Thrun, 38

As director of the Artificial Intelligence Laboratory at Stanford University, Thrun is no stranger to how robotics can make human life easier. He hopes his latest project will become the world's first fully autonomous car, boasting lasers, radar, cameras and software geared toward taking driving out of human hands and reducing fatalities from traffic accidents.

Doug James, 33

Computer graphics animations of colliding objects used to take months to construct. Thanks to James' software tools and research at Carnegie Mellon University, it now takes hours. Paid for in part by animated film company Pixar, James' work makes animated collisions look more realistic, meaning better special effects in movies and video games. Real-time "virtual" surgery is a future application.

Nathan Wolfe, 35

In tracing the roots of outbreaks of infectious diseases, Wolfe takes his work from the labs of Johns Hopkins University to the field, running alongside hunters in Cameroon and collecting blood samples from both tribespeople and their prey. His studies of transmission risks in African primate-hunter populations aim to predict outbreaks and eliminate new diseases before they become epidemics.

Alexis Templeton, 34

Templeton, a geologist and microbial biologist at the University of Colorado-Boulder, has discovered more than 40 new species of metal- and mineral-ingesting bacteria while studying the ocean's depths in tiny submarines. In documenting microscopic organisms that can survive without light in extreme temperatures, her studies have challenged traditional ideas about where life can and cannot exist.

Hope Jahren, 36

By studying the inner chemical composition of plant fossils at Johns Hopkins University, Jahren has unearthed clues about a global heat wave that melted much of Earth's ice cover more than 36 million years ago. Her work earned her the American Geophysical Union's Macelwane Medal, making her the only woman to win both this and the Donath Medal for young Earth scientists.

Maryam Mirzakhani, 28

Mathematicians have long struggled to find a practical way to calculate the volume of possible variants of hyperbolic geometric forms. Iranian-born Mirzakhani of Princeton University showed that mathematics may be her best language by making headway toward a solution: calculating the length of loops drawn on hyperbolic surfaces.

Maydianne Andrade, 35

Andrade has logged her research hours while sitting beneath webs of nocturnal, poisonous Australian redback spiders, observing their bizarre mating rituals in which the female spider eats the male. Now at the University of Toronto-Scarborough, she hopes to advance her studies of mate choice and genetic control by constructing a DNA library for the redback with the intent to explain its cannibalistic sexual behavior.

Kevin Eggan, 31

After cloning mice and manipulating cells, Eggan turned to human embryonic stem-cell research at Harvard University. His work has earned both harsh criticism and glowing praise, and he now plans to create human embryos from cells donated by people with Parkinson's disease to advance research about the condition.

John Crocker, 37

As a biophysicist at the University of Pennsylvania, Crocker uses precise measurements and video cameras to observe the sensory capabilities of cells. His discoveries about how cells deconstruct under stress could pave the way for advancements in cancer detection and tissue engineering.

+نوشته شده در چهارشنبه سوم مهر 1387ساعت11:19توسط 666 | |