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Dead or Alive 5 Last Round: Core Fighters (also called as “Dead or Alive 5: Last Round Core Fighters”) is a fighting game created by Team Ninja with its characters from the…
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Orthogonal projection in $R^n$
Let $R^n$ be the vector space of all $n$-tuples of real numbers.
Define an inner product in $R^n$ by:
$$ = \sum_{i=1}^na_ib_i$$
Let $e_1 = (1,0,\dots,0)$ and $e_2 = (0,1,\dots,0),\dots,e_n = (0,\dots,0,1)$.
So, $e_i$ is orthogonal to $e_j$ whenever $i
eq j$.
I want to prove that if $a_1,\dots,a_n$ is orthogonal to $e_1,\dots,e_n$, then $a_1^2+\dots+a_n^2 \leq n.$
I tried to do this as follows:
We have
$$ = \sum_{i=1}^na_ib_i = \sum_{i=1}^na_i^2 + \sum_{i=1}^nb_i^2$$
It’s obvious that $$\sum_{i=1}^na_i^2 \leq \sum_{i=1}^na_i = n\cdot a_1$$
Also,
$$\sum_{i=1}^nb_i^2 = \sum_{i=1}^nb_i = \sum_{i=1}^n(-b_i)
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This is a freeware side scrolling RPG, with a focus on action rather than exploration or item collecting.
The story begins once upon a time in the mythical land of Ancient Egypt. The Queen and the King have been gone for thousands of years but the world is still ruled by the mysterious Anubis. The people are afraid to say the word Anubis for fear of angering the god. In the calm kingdom of the Fayru people secretly worship the god Anubis and the days of his rule. But only during the night.
One evening the villagers pass a comment about a piece of dark metal. The metal is not something they have seen before. The villagers are afraid to go into the dark and witness the unknown. The next day the villagers quietly remove the dark metal from their village. They begin to hide the metal in secret places to protect the people of the Fayru from the King’s anger.
The metal is stolen by the College to prove that the gods in the ancient mythology were real.
This is no ordinary college!
The residents are the students of Ancient Egypt College. They enjoy a night of freedom while the students of History, Archeology and Anthropology sleep. The teachers keep a close watch on these daring students.
Mysterious and supernatural happenings have begun to happen at night and all the students from History, Archeology and Anthropology have been assigned as observers.
The College’s students are with out a break wandering through the ancient Egyptian ruins and an ancient temple that has long since been forgotten.
The students are terrified by the monsters from the dark and refuse to enter the temple, but they have to. If they want to be accepted into History, Archeology or Anthropology.
Through the ages the temple has watched the students of History, Archeology and Anthropology. The students are trying to find Anubis’ final resting place.
The students are close to the end of their journey. They are not sure if they will be accepted as they enter the final battle with Anubis!
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An Egyptian temple has recently been discovered deep in the Kaylo desert. It seems like the temple is the final resting place of an Egyptian God. You have been sent to explore the temple and find the location of Anubis’ final resting place.
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Climbtime is an off the chart jazz-fusion, neo soul, pop, inspirational, chill-hop, hip-hop, new jack swing (NJS), old school hip hop, old school funk, Electro soul, gospel, future soul & trip hop DJ from New York City; born and raised in the Bronx.Career
Climbtime’s career has began in the gospel music industry and as a DJ at a radio station. He began his career spinning gospel music by the request of the deejay and b-boy that was the mixtape of the year. For four years he continued to remix, remix and to spin until he began to fly solo as a disc jockey in late 1996.
He then went on to play over 350 gigs a year. In the year 2000 he slowly but surely began to ascend the the NY underground with his first official album release, “the Future”, a tribute to funk legends, The New York Funk group Funkadelic (Fred Wesley & Rick Gardner) eventually he followed up with a remixed version on Century Records. His hard hitting selling single, “the Future” has been gaining traction nationally.Climbtime is an off the chart DJ, Los Angeles, Miami & Chicago base. He opened up for R&B/hip-hop soul singer Avery Jordan “Swingators”. He has been known to spin at The Love Shack
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“The Future – Greatest cover of the year” Cover by a White Artist, selected by Graffity of AfroTrapup with five other covers.
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Over the last couple of years, Kavalier & Clay have written and illustrated three graphic novels based on their award-winning comic book series, “Punisher,” set in the years after the Marvel Universe’s original “Punisher” took a vacation. Punisher: The Slavers is Kavalier & Clay’s second comics-based game.
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