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Dear Students,
Please go through the link to learn Numerical Differentiation.

Dear Students,
Please go through the link to learn Newtons Backward Interpolation method.

Dear Students,
Please go through the link to learn Newtons Forward Interpolation method.

Dear Students,
Please go through the link to learn Interpolation by Lagrange's Polynomial

Dear Students,
Please go through the link to learn Fixed Point Iteration Method

Dear Students,
Please go through the link to learn Newton Raphson Method

Dear Students,
Please go through the link to learn False Position Method

Dear Students,
Please go through the link to learn Bisection Method

History / The Ottoman Empire: Part II
« on: November 14, 2016, 08:44:23 PM »
Attached is the link of the famous documentary of BBC on Ottoman Empire.
Among all the renowned video documentaries, this one is highly recommended.

History / The Ottoman Empire: Part I
« on: November 14, 2016, 08:42:36 PM »
(Adapted from BBC)

The Ottoman Empire was the one of the largest and longest lasting Empires in history.

It was an empire inspired and sustained by Islam, and Islamic institutions.

It replaced the Byzantine Empire as the major power in the Eastern Mediterranean.

The Ottoman Empire reached its height under Suleiman the Magnificent (reigned 1520-66), when it expanded to cover the Balkans and Hungary, and reached the gates of Vienna.

The Empire began to decline after being defeated at the Battle of Lepanto (1571) and losing almost its entire navy. It declined further during the next centuries, and was effectively finished off by the First World War and the Balkan Wars.

One legacy of the Islamic Ottoman Empire is the robust secularism of modern Turkey.

At its peak it included:

    Parts of Arabia
    Much of the coastal strip of North Africa

The Ottoman Empire reached the peak of its power during the rule of Selim's son, Suleiman the Magnificent (ruled 1520 -66) and his grandson Selim II (1566 - 74).

Suleiman came to the throne as one of the wealthiest rulers in the world. His strength owed much to the work his father Selim had done in stabilising government, removing opposition, frightening (but not succesfully conquering) the Safavid Empire of Iran into adopting a non-aggression policy, and conquering the Mamluk empire of Egypt and Syria.

These conquests, which united the lands of Eastern Europe and the Eastern Mediterranean under a single ruler, brought a time of peace and stability, under which the Empire flourished.

Suleiman had no internal rivals for power. His father had seen to that by executing his own brothers and their sons, and all 4 of Suleiman's brothers.

The Ottoman Empire now included so much of the territory where Islam was practiced, and so many of the Islamic holy places, that Suleiman was widely regarded as the religious leader of Islam, as well as the earthly ruler of most Muslims.
Ornate mosaic tiles on building walls The Empire attracted Muslim artists and craftsmen ©

The wealth and stability of the Empire at this time attracted the top Muslim brains of the period, and craftsmen, artists, intellectuals and writers were eager to move to Istanbul.

Suleiman was named 'The Magnificent' by the Europeans, but his own people called him 'The Lawgiver'.

History / The History of Shinsengumi : Part 2
« on: November 14, 2016, 08:32:48 PM »
The Shinsengumi submitted a letter to the Aizu clan, another powerful group who supported the Tokugawa regime, requesting their permission to police Kyoto. The request was granted.

On September 30, 1865 (lunar calendar August 18), the Chōshū (anti-Tokugawa) clan were forced from the imperial court by the Tokugawa, Aizu and Satsuma clans. The Shinsengumi were sent to aid the Aizu and guard the gates of the imperial court. The new name "Shinsengumi" may have been coined by Matsudaira Katamori (the daimyō of the Aizu clan) around this time.[8] The opposition forces included the Mori clan of the Chōshū and the Shimazu clan of Satsuma.

In 1864, in an incident at the Ikedaya Inn, Kyoto, thirty Shinsengumi suppressed a cell of twenty Choshu revolutionaries, possibly preventing the burning of Kyoto. The incident made the squad more famous and led to soldiers enlisting in the squad.

n 1867, when Tokugawa Yoshinobu withdrew from Kyoto, the Shinsengumi left peacefully under the supervision of the wakadoshiyori, Nagai Naoyuki.[6](p172–174) The emperor Meiji had been named the head of a new government (meaning the end of over a century of military rule by the shoguns). This marked the beginning of the Boshin civil war.[5]

Following their departure from Kyoto, the Shinsengumi fought in the Battle of Toba-Fushimi.[6](p177) At Fushimi, Kondo suffered a gunshot wound but went on to fight at the Battle of Kōshū-Katsunuma. He was then captured in Nagareyama. After surrendering to imperial government forces, he was declared guilty of participation in the assassination of Sakamoto Ryōma and was beheaded in Itabashi three weeks later. Kondo was killed near Tokyo.[5]

The Shinsengumi fought in defense of Aizu territory under Saitō Hajime and joined the forces of the Republic of Ezo in the north.[6](p217–230) Shinsengumi numbers grew to over one hundred in this period and they fought on despite the fall of Edo and clear defeat of Tokugawa.[5] For example, Hijikata led a daring but doomed raid to steal the imperial warship, the Kotetsu. Hijikata's death from a gunshot wound on June 20 (lunar calendar May 11), 1869, in Hokkaido, marked the end of the Shinsengumi. Before his death, he wrote of his loyalty to the Tokugawa

    "Though my body may decay on the Island of Ezo,
    My spirit guards my lords in the East."

[9] Even so, another group of survivors, under Sōma Kazue, who had been under Nagai Naoyuki's supervision at Benten Daiba, surrendered separately,[6](p246) and a few core members, such as Nagakura Shinpachi, Saitō Hajime, and Shimada Kai, survived the war. Some members, such as Takagi Teisaku, went on to become prominent figures.[10]


Clements J. "A brief history of the samurai." Constable & Robinson, 2013 ISBN 1472107721, 9781472107725.
"Takagi became a professor of economics at Hitotsubashi University." Kuwana city website.
Turnbull S. "Katana: the samurai sword." Osprey Publishing, 2011 ISBN 1849086583, 9781849086585.
Zwier L. and Cunnungham M. "The End of the Shoguns and the birth of modern Japan (Pivotal moments in history series)." Twenty-First Century Books, revised edition, 2013 p63 ISBN 146770377X, 9781467703772.
新選組! NHK website.
"Shinsengumi: Assassins of Honour IMDB website.
"When the last sword is drawn." IMDB website
Kapell M. and Elliot A. (ed.)"Playing with the past: digital games and the simulation of history." A&C Black, 2013 p140 ISBN 1623563879, 9781623563875.
"Home | Best Japanese Restaurant Los Angeles - Shin-Sen-Gumi". Retrieved 2016-06-24.

History / The History of Shinsengumi : Part 1
« on: November 14, 2016, 08:30:26 PM »
The Shinsengumi (新選組 or 新撰組, meaning "the new squad") was a special police force organized by the Bakufu (military government) during Japan's Bakumatsu period (late shogun) in 1864. It was active until 1869. It was founded to protect the Shogunate representatives in Kyoto at a time when a controversial imperial edict to exclude foreign trade from Japan had been made and the Choshu clan had been forced from the imperial court. The men were drawn from the sword schools of Edo. Although the Shinsengumi are lauded as brave and determined heroes in popular culture, they have been described by historians as a "ruthless murdering death squad".

Japan's forced opening to the west in 1854 (the choice to open her shores for trade or enter military conflict), exacerbated internal political instability. One long-standing line of political opinion was sonnō jōi (meaning, "revere the emperor, expel the barbarians").[4] Loyalists (particularly the Choshu clan) in Kyoto began to rebel. In response, the Tokugawa shogunate formed the Rōshigumi (浪士組?, meaning "the rōnin squad") on October 19, 1863. The Roshigumi was a squad of 234 rōnin (Samurai without master) drawn from the sword schools of Edo.[5](p168)

The squad's nominal commander was the hatamoto Matsudaira Tadatoshi, and their leader was Kiyokawa Hachirō (a rōnin from Shonai Domain). The Roshigumi's mission was to protect Tokugawa Iemochi, the 14th shogun, during an important trip to Kyoto to meet with the Emperor Kōmei.[6](p65) There had not been such a meeting since the third shogun of the Tokugawa Bakufu, Tokugawa Iemitsu, had visited Kyoto in the 17th century. Tokugawa Iemochi, the head of the military government, the Bakufu, had been invited to discuss how Japan should enact the recent imperial edict calling for the expulsion of foreigners.[3](p186)

Although the Rōshigumi was funded by the Tokugawa government, the leader, Kiyokawa Hachirō and others had strong loyalties to the emperor and planned to gather other rōnin in Kyoto to police the city from insurgents. When Kiyokawa's scheme was revealed in Kyoto, they were forced to go back to Edo (Tokyo). But thirteen Rōshigumi members mainly from Mito clan remained and formed the Shinsengumi. The remaining members disbanded and then returned to Edo to form the Shinchōgumi (新徴組?) under the patronage of the Shōnai domain.

Initially, the Shinsengumi were called Miburō (壬生浪?), meaning "rōnin of Mibu". At the time, Mibu was a village south west of Kyoto, and was the place where the Shinsengumi were stationed. The Shinsengumi were led by Serizawa Kamo (b. 1830, Mino province), Kondō Isami (b. 1834, Musashi province – he came from a small dojo in Edo called Shieikan[7]) and Niimi Nishiki and initially formed three factions under Serizawa (the Mito group), Kondō (the Shieikan group) and Tonouchi. There were disagreements and tensions in the group: Kondo and Tonouchi killed Serizawa[5] and then Kondo killed Tonouchi on Yojou bridge. Serizawa had also ordered another member, Iesato Tsuguo, to commit seppuku for deserting. All this infighting left Kondo as leader.

#Watsuki, N. "Glossary of the Restoration." Rurouni Kenshin Volume 3. Viz Media p190.
#Hurst G. and Hurst I. "Armed martial arts of Japan: swordsmanship and archery." Yale University Press 1998 p95. ISBN 9780300116748.
#Turnbull S. "The Samurai swordsman – master of war." Tuttle Publishing, 2013 ISBN 1462908349, 9781462908349.
#Wakabayashi B. T. Anti-foreignism and Western learning in early-modern Japan: the new theses of 1825. Harvard University Press, Cambridge 1986.
#Dougill J. "Kyoto: a cultural history." Oxford University Press, 2006 p171. ISBN 0195301374, 9780195301373.
#Oishi M. Shinsengumi: Saigo no Bushi no Jitsuzō. Shin Jinbutsu Oraisha, Tokyo, 2004.
#Tokeshi J. "Kendo: rules and philosophy." University of Hawaii Press, 2003 p227 ISBN 0824825985, 9780824825980.

EEE / The God Particle: Part VII
« on: November 14, 2016, 08:21:45 PM »
“That won’t happen,” he said fiercely. “That’s the worst thing imaginable.” I realized that I was treading on delicate territory whenever I asked what kinds of things could go wrong with the LHC. No, the collider can’t blow up the world, but this is high-energy physics. When those magnets are turned on, scientist Richard Jacobsson pointed out, a person swinging a hammer in the vicinity would do well to wear a helmet.

When the LHC starts smashing particles, Europe will suddenly become the dominant location for particle physics, and the United States will find itself struggling to figure out how to stay relevant. Perhaps that’s a petty concern given the magnitude of what the LHC might turn up, but it’s something people talk about. Since the Manhattan Project there’s been a general notion that the U.S. dominates the world of physics. Until now, the energy frontier has been at Fermilab, home of the Tevatron. That collider has found some important particles, but it might not have quite enough juice to nail the Higgs.

Some U.S. money has gone into the LHC, which will cost billions of dollars: five, maybe ten—the exact number is elusive (the science will be precise, but the accounting apparently follows the Uncertainty Principle). But most of the engineering is being done by European firms. Jürgen Schukraft, who supervises an LHC experiment named ALICE (which will re-create conditions the same as those just after the big bang), said, “The brain drain that used to go from Europe to the States definitely has reversed.”

The cynic might say that there’s no practical use for any of this, that there might be other uses for all the money and brainpower going into these particle guns. But we live in a civilization shaped by physics. We know that the forces within an atom are so powerful that, unleashed and directed against humanity, they can obliterate cities in an instant. The laptop computer on which I’m writing uses microprocessors that would not exist had we not discovered quantum physics and the quirky behavior of electrons. This story will be posted on the World Wide Web—invented, in case you hadn’t heard, at CERN, by computer scientist Tim Berners-Lee. Maybe you’re reading it while listening to your iPod, which wouldn’t exist but for something called “giant magnetoresistance.” Two physicists discovered it independently in the late 1980s, with not much thought of how it might eventually be used. It became crucial to making tiny consumer electronics that used magnetized hard disks. The physicists won a Nobel Prize in 2007, and you got a nifty sound system that’s smaller than a Hershey bar.

When I asked Peter Jenni why the LHC is important, he said, “Humankind differs from a collection of ants. We have intellectual curiosity; we need to understand the mechanisms of life and the universe.”

And anyone who thinks these big machines are soulless contraptions should listen to Richard Jacobsson. The LHC is replacing a particle detector he worked with for a decade. He came to know every inch of that instrument. He understood its moods and idiosyncrasies. The day the engineers came to rip it out, Jacobsson was overcome with emotion. “I had tears in my eyes,” he said. “When they cut the cables, I thought blood would flow out.” Now entire lives are wrapped up in the new machine, which physicists have been dreaming about since the 1980s.

Many people at CERN are hoping they’ll get more than just answers: They’d like to uncover some new mysteries. John Ellis confided that he wouldn’t even mind if the LHC failed to find a Higgs. “Many of us theorists would find that failure much more interesting than if we just find another boring old particle that some theorists predicted 45 years ago.”

New puzzles seem a sure bet. After all, the universe doesn't seem to be constructed for our investigative convenience. We’re big, sloppy meat-creatures who haven’t even taken a good census of the species of bacteria that live in our bodies. One day I asked George Smoot, a Nobel laureate physicist, if he thinks our most basic questions will ever be answered.

“It depends on how I’m feeling on any particular day,” he said. “But every day I go to work I’m making a bet that the universe is simple, symmetric, and aesthetically pleasing—a universe that we humans, with our limited perspective, will someday understand.”

(Written by - Joel Achenbach, a Washington Post staff writer. He has written columns and features for National Geographic since 1998.)

EEE / The God Particle: Part VI
« on: November 14, 2016, 08:20:14 PM »
You can take an elevator down into the LHC tunnel if you wear a hard hat and carry an emergency oxygen mask. When I visited, I found a major construction project still under way, with all the usual sounds of blowtorches and metal saws. Workers were installing magnets. They’ve since completed the process, having installed more than 1,600 magnets, most half the length of a basketball court and weighing more than 30 tons.

Oddly enough, none of those magnets will accelerate particles. The acceleration will come from electrical waves in a separate apparatus that boosts particles around the ring. The job of the magnets is to nudge the beams of particles to bend ever so slightly around the ring. Lots of particles moving at nearly the speed of light have only one desire in life: to keep moving straight ahead. So the bend needs to be gradual—thus the 17-mile circumference of the ring.

When the particles collide, they’ll produce showers of debris as their energy gets transformed into mass. The physicists won’t see the Higgs itself in that shower, but two of the four major experiments that the LHC will perform are capable of recording the detritus of the disintegrating Higgs—the telltale signal that a Higgs is decaying. And the assumption is that only the rare collision—one among many trillions—will produce a Higgs. Most collisions won’t result in anything terribly interesting. The particle—or rather its debris—will show up in a detector’s computers, found by sorting through massive amounts of data measured in petabytes—thousands of trillions of bits.

A major issue for CERN is how to decide that they’ve found the Higgs. How much proof do you need? They’ve got two experiments competing to find the same particle. Do they announce the discovery by one experiment even if the other hasn’t confirmed it yet?

The relationship between the ATLAS and CMS experiments is like Coke versus Pepsi. They’re working the same side of the street, but with different techniques. And they’re highly competitive. The day I went to see ATLAS, the man in charge, Peter Jenni, found out that I’d already seen the CMS experiment. “Now you’ll see something bigger,” he said. His voice carried a slight my-detector-is-better-than-yours tone.

CMS was built at the surface and will be lowered in several large chunks down through a shaft into a cavern along the tunnel. Tactlessly, I asked Dave Barney, one of the CMS scientists, what would happen if something went wrong and a part was dropped. You know, splat.

EEE / The God Particle: Part V
« on: November 14, 2016, 08:17:40 PM »
By smashing pieces of matter together, creating energies and temperatures not seen since the universe's earliest moments, the LHC could reveal the particles and forces that wrote the rules for everything that followed. It could help answer one of the most basic questions for any sentient being in our universe: What is this place?

There’s one puzzle piece in particular that physicists hope to pick out of the debris from the LHC's high-energy collisions. Some call it the God particle.

The first thing you learn when you ask scientists about the God particle is that it’s bad form to call it that. The particle was named a few years back by Nobel Prize-winning physicist Leon Lederman, who has a knack for turning a phrase. Naturally the moniker took root among journalists, who know a good name for a particle when they hear one (it beats the heck out of the muon or the Z-boson).

The preferred name for the God particle among physicists is the Higgs boson, or the Higgs particle, or simply the Higgs, in honor of the University of Edinburgh physicist Peter Higgs, who proposed its existence more than 40 years ago. Most physicists believe that there must be a Higgs field that pervades all space; the Higgs particle would be the carrier of the field and would interact with other particles, sort of the way a Jedi knight in Star Wars is the carrier of the “force.” The Higgs is a crucial part of the standard model of particle physics—but no one’s ever found it.

Theoretical physicist John Ellis is one of the CERN scientists searching for the Higgs. He works amid totemic stacks of scientific papers that seem to defy the normal laws of gravity. He has long, gray hair and a long, white beard and, with all due respect, looks as if he belongs on a mountaintop in Tibet. Ellis explains that the Higgs field, in theory, is what gives fundamental particles mass. He offers an analogy: Different fundamental particles, he says, are like a crowd of people running through mud. Some particles, like quarks, have big boots that get covered with lots of mud; others, like electrons, have little shoes that barely gather any mud at all. Photons don’t wear shoes—they just glide over the top of the mud without picking any up. And the Higgs field is the mud.

The Higgs boson is presumed to be massive compared with most subatomic particles. It might have 100 to 200 times the mass of a proton. That’s why you need a huge collider to produce a Higgs—the more energy in the collision, the more massive the particles in the debris. But a jumbo particle like the Higgs would also be, like all oversize particles, unstable. It’s not the kind of particle that sticks around in a manner that we can detect—in a fraction of a fraction of a fraction of a second it will decay into other particles. What the LHC can do is create a tiny, compact wad of energy from which a Higgs might spark into existence long enough and vivaciously enough to be recognized. Building a contraption like the LHC to find the Higgs is a bit like embarking on a career as a stand-up comic with the hope that at some point in your career you’ll happen to blurt out a joke that’s not only side-splittingly funny but also a palindrome.

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