text:
Numerical Analysis/LU decomposition exercises

=LU Decomposition exercises and quiz=

Exercise 1
Problem Given the 3x3 matrix:
 * $$ A = \begin{bmatrix} 2&-1&3\\4&2&1\\-6&-1&2\end{bmatrix}$$

Find LU decomposition of A

Solution

''The procedure of LU decomposition runs similar to the process of Gaussian Elimination. Firstly A is reduced to upper triangular form, which is U, using just the third elementary row operation, namely: add to one row of matrix a scalar time another row of that same matrix. Those scalar used during this process are co-efficient in the L matrix.''

The final result will look like this: $$ A = \begin{bmatrix} 2&-1&3\\4&2&1\\-6&-1&2\end{bmatrix}= \begin{bmatrix} 1&0&0\\l_{21}&1&0\\l_{31}&l_{32}&1\end{bmatrix} \times \begin{bmatrix} u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{bmatrix}$$.

Here are the solution for this problem:

According to Gaussian Elimination, the first number in row 2 must be zero-out by adding the first row of matrix a scalar times second row. This scalar, fortunately, is $$- l_{21}$$.

Therefore:

{
 * type="{}"}

$$ \displaystyle \ l_{21} = $$ { 2 }.

And $$ A \rightarrow A1 = \begin{bmatrix} 2&-1&3\\0&4&-5\\-6&-1&2\end{bmatrix} $$.

In the similar manner we have:

$$ \displaystyle \ l_{31} = $$ { -3 }.

And $$ A1 \rightarrow A2 = \begin{bmatrix} 2&-1&3\\0&4&-5\\0&-4&11\end{bmatrix} $$

$$ \displaystyle \ l_{32} = $$ { -1 }.

And $$ A2 \rightarrow A3 = U = \begin{bmatrix} 2&-1&3\\0&4&-5\\0&0&6\end{bmatrix} $$.

Eventually, A has been factorized to LU:

$$ A = \begin{bmatrix} 2&-1&3\\4&2&1\\-6&-1&2\end{bmatrix}= \begin{bmatrix} 1&0&0\\**&1&0\\**&*&1\end{bmatrix}\times \begin{bmatrix} 2&-1&3\\0&4&-5\\0&0&6\end{bmatrix}$$.

Exercise 2
Use exercise 1's result to solve the system:

$$\begin{bmatrix} 2x_1-x_2+3x_3=4\\4x_1+2x_2+x_3=7\\-6x_1-x_2+2x_3=-5 \end{bmatrix} $$

Solution:

''The idea of using LU decomposition to solve systems of simultaneous linear equations Ax=b is rewriting the systems as L(Ux)=b. To solve x, we first solve the systems Ly=b for y, and then, once y is determined, we solve the systems: Ux=y for x. Both systems are easy to solve, the first by forward substitution and the second by backward substitution.''

Here is the solution for this exercise:

This system has the matrix form:

$$ A = \begin{bmatrix} 2&-1&3\\4&2&1\\-6&-1&2\end{bmatrix} \times \begin{bmatrix} x_1\\x_2\\x_3\end{bmatrix} $$ = $$\begin{bmatrix} 4\\7\\-5\end{bmatrix}. $$

Since A = LU, by Exercise 1 we have:

$$ \begin{bmatrix} 1&0&0\\**&1&0\\**&*&1\end{bmatrix} \times \begin{bmatrix} 2&-1&3\\0&4&-5\\0&0&6\end{bmatrix}\times \begin{bmatrix} x_1\\x_2\\x_3\end{bmatrix} = \begin{bmatrix} 4\\7\\-5\end{bmatrix}. $$

Lets $$y = U\times x$$, we have:

$$\begin{bmatrix} 1&0&0\\**&1&0\\**&*&1\end{bmatrix} \times \begin{bmatrix} y_1\\y_2\\y_3\end{bmatrix} = \begin{bmatrix} 4\\7\\-5\end{bmatrix} $$.

Use forward substitution we have:

{
 * type="{}"}

$$ \displaystyle \ y_1 = $$ { 4 } $$ \displaystyle \ y_2 = $$ { -1 } $$ \displaystyle \ y_3 = $$ { 6 }

Next, since $$ Ux = y$$, we have

$$ \begin{bmatrix} 2&-1&3\\0&4&-5\\0&0&6\end{bmatrix} \times \begin{bmatrix} x_1\\x_2\\x_3\end{bmatrix} = \begin{bmatrix} y_1\\y_2\\y_3\end{bmatrix} $$.

Use backward substitution we have:

$$ \displaystyle \ x_1 = $$ { 1 } $$ \displaystyle \ x_2 = $$ { 1 } $$ \displaystyle \ x_3 = $$ { 1 }


text:
User:Markmorris182

I am currently studying electrical installation including the 17th edition wiring regulations in the UK and hope to use this as a platform to study electrical engineering to a higher level, I have had experience with electronics and worked as a technician for a few years mainly on microprocessor based equipment but I would say this was to an intermediate level and not to an advanced one, so I do have some electrical background.

My aim on the Wikiversity is to at first study and improve my knowledge of electrical engineering but I would like to contribute to the school in the future, when I feel that my level of knowledge is sufficient to make a valued contribution to the school.

I feel that the Wikiversity is an excellent project and would really like to get involved with it, and I am always open to people getting in touch with me to discuss any subjects relating to electrical engineering as I feel that discussion with like minded individuals is just as useful a learning tool as text books and lecture’s. Thank you for taking the time to read my page and I hope to hear from other students at this school really soon.

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title: User:Markmorris182


text:
American Revolution/Chapter 1: The English Colonies in 1750/Lesson 1

In Lesson 1, we will review the manner in which each individual colony came into existence. The first few years of the colony's history and major activities will be studied, but the 150 years of colonial history prior to the American Revolution are not the subject of this course. Chapters 2 and 3 will provide overviews of this time period and explain the situation of the American colonies at the outset of the French & Indian War.

Pay careful attention to the Key Terms listed below. Links for additional reading will be provided throughout, but these terms are those that may appear on the section quiz.

Key Terms

 * Anne Hutchinson
 * Congregationalism
 * Elizabeth I
 * Elizabethan Settlement
 * enclosure movement
 * Fundamental Orders of Connecticut
 * James I
 * Jamestown
 * John Smith
 * Mayflower
 * Mayflower Compact
 * Pilgrims
 * Puritans
 * Roanoke Colony
 * Roger Williams
 * Richard Hakluyt
 * Sir Walter Raleigh
 * Spanish Armada
 * starving time
 * Virginia Company

English Colonization
The story of English colonial ventures begins in the 1500s. Unlike England's southern neighbors, religious, economic, and political upheaval prevented the British monarchy from expanding westward. After excommunication from the Roman Catholic Church, Henry VIII founded the Church of England and named himself as its Head. His heirs, Edward VI, Mary I, and Elizabeth I struggled over which religious doctrine, Catholic or Protestant, would dominate England. Edward was a devout Protestant and favored his father's Church of England. Mary was the complete opposite: a devout Catholic who returned papal dominance to the British isles. After Mary's death in 1558, Elizabeth assumed the throne. Knowing that the continual religious upheaval was likely to destroy England, Elizabeth instituted a compromise to restore order within the realm. The Elizabethan Settlement provided England with a Protestant theology dominated by Catholic ritual. Elizabeth also secured the English economic position. The enclosure movement transitioned land from agricultural production to livestock grazing. Landlords found it more profitable to raise sheep for wool than grow wheat; however, this market flooded with supply in the 1550s and collapsed. She instituted several reforms following the collapse of the wool market that expanded the authority of England's merchant class, removed competition, and encouraged agricultural variation. Elizabeth's final contribution to the pre-colonization era was the defeat of the Spanish Armada in 1588. Philip II of Spain, former husband of Elizabeth's sister, Mary, sent his armada (Spanish, for fleet) against England when Elizabeth executed her cousin Mary, Queen of Scots, for offering abdication in favor of Philip. (Elizabeth knew he would surely return England to Catholic domination.)

With stability in England, Elizabeth encouraged the foundation of colonies in North America. Richard Hakluyt, an Oxford clergyman, proposed in a 1584 essay titled Discourse Of Western Planting three reasons why England should establish New World colonies. These colonies would:
 * Create new markets for English goods,
 * Siphon off the excess population and alleviate poverty and unemployment, and
 * Provide raw materials not available in England.

In the early 1580s, Elizabeth authorized Sir Walter Raleigh to send an expedition to the New World in search of a suitable site for colonization. In 1584, the expedition, under Philip Amadas and Arthur Barlowe, landed in what would become North Carolina. They returned home after staying two months. A second expedition, under Sir Richard Grenville, was sent the following year to found a colony in the newly christened Virginia named Roanoke. After only a year, the 100 occupants wanted to return home. A second attempt was tried in 1588. When reinforcements came three years later, the colonists were nowhere to be found. The only clue to their whereabouts was the word Croatoan carved into a tree. (The "Lost Colony of Roanoke" remains one of the greatest unsolved mysteries of history.)

Virginia
Though it had settlements only in the Florida peninsula, Gulf of Mexico, and far west, Spain maintained a blanket claim over all North America. This did not prevent James I from granting a settlement charter to the Virginia Company, a group of merchants, knights, and gentlemen, in 1606. Even though there was only one charter, the group was divided into two parts, one based in London called itself the London Company and the other based in Plymouth called itself the Plymouth Company. Their charters overlapped in the center but housed a provision stating one could not establish a colony within one hundred miles of an existing colony.

The Plymouth Company's first endeavour, the Popham Colony lasted only one winter. In August 1607, an expedition of men built a fort at the mouth of the Kennebec River in present-day Maine named St. George. The next spring, the fort was abandoned and the Plymouth Company waned. The London Company was far more successful. After a harrowing voyage across the Atlantic, just over one hundred men landed on a small peninsula about thirty-two miles up the James River from its mouth in the Chesapeake Bay. With the exception of the large, swampy marsh nearby, the site was perfect for the first settlement. There was plenty of nearby anchorage for the mooring of boats. Located on a peninsula, the colony was easy to defend against both water and land attacks. They named it Jamestown after the king.

The Virginia colony struggled to gain a sure foothold in the tender wilderness of North America. Strict rules and labor requirements imposed by colonial governor John Smith assured survival in the first years. When Smith returned to England, Jamestown suffered its "starving time," a period during which most colonists died from hunger and disease. When John Rolfe discovered a smoother-tasting variety of tobacco in 1616, Virginia finally began to prosper. Rolfe also married the native princess Pocahontas, ensuring calmer relations with the local tribe. Two years later, London officials instituted new rules governing how individuals earned land in the new colony. They also established the first representative assembly; it met one year later in the Jamestown church on July 30, 1619. That year also saw the development of two other firsts for the colony: a ship arrived with 90 women as potential wives for the colonists and another with the first African Americans. Despite these prosperous years, tensions with the natives over land and trade led to back-and-forth struggles between 1622 and 1624. When the British government assumed authority over the colony in 1624, only a mere 1,132 people (of over 14,000 emigrants) were still alive.

At first, Virginia had revealed to be an unhealthy and hazardous place and when tobacco became an important crop, it helped to create an economic boom for the colony. To increase the supply of labor, the Virginia Company enacted in 1618 a new system of land grants : each settlers was to receive a parcel of lands and another 50 acres for each additional person (in order to encourage settlers to grow tobacco and make the colony survive.) The following year, the company sanctioned the formation of the House of Burgesses, the first legislative assembly in the new world. Then, when Virginia became a royal colony in 1624 because the London Company failed to protect its inhabitants from Indian raids that killed around 350 settlers. As a royal colony, Virginia expanded and grew to the detriment of natives on the frontier. In the meantime, the House of Burgesses became a powerful club of landowners at the expense of the electorate, increasingly restricted. Royal authory was challenged in 1676 when Governor Berkeley failed to respond to Indian attacks by force. The settlers, many facing poverty, took the matter in their own hands and led by Nathaniel Bacon, they burned the colonial capital of Jamestown.

Maryland
Sir George Calvert served as the principal secretary of state under James I. After declaring his Catholic faith, he resigned his position with the king but became enstated as the first Baron of Baltimore in the peerage of Ireland. In 1632, James' son, Charles I, granted Lord Baltimore a land charter in the Chesapeake. Lord Baltimore died before he could assume control of the charter and it passed to his son, Cecilius Calvert. According to the land grant, the Calverts received an area between the Potomac River and the 40th Parallel. Charles named this land after his wife, Henrietta Maria of France. In addition to the land, the king granted large governmental powers provided they be in accordance with the laws of England and gain the approval of the men of the colony.

The colony of Maryland prospered from its start. Cecil Calvert selected his brother, Leonard Calvert, to serve as governor of the colony and found the first settlement. In 1634, they built a town near the mouth of St. George's River and named it St. Mary's. Unlike Jamestown, St. Mary's was "found to be [in] a very commodious situation for a town, in regard the land is good, the air wholesome and pleasant, the river affords a safe harbor for ships of any burden, and very bold shore; fresh water and wood there is in great plenty, and the place so naturally fortified, as with little difficulty, it will be defended from any enemy." Also unlike Jamestown, the first settlers in Maryland had the benefit of Jamestown's mistakes in the founding of their colony. The proportion of laborers to gentlemen was higher and there were greater incentives to work.

Instead of quarreling with the local Indians, the colonists feared most an attack from neighboring Virginia. Under the Virginia Company's original charter, the land granted to Lord Baltimore was a part of Virginia. When the charter was absolved and Virginia became a royal colony, technically distribution of the land became the prerogative of the crown; however, many Virginians did not agree. They established a trading settlement on Kent Island in 1631 (predating St. Mary's) and argued that it belonged under the governance of Virginia. Maryland's governor knew the territory lay within the boundaries of Baltimore's grant and petitioned the king to address the issue. A royal proclamation declared the territory to be a part of Maryland and alleviated a potential war between the two colonies.

New England
By the end of the reign of Elizabeth I in 1603, Protestantism was the dominant religion in England. The Anglican communion was accepted as the state church and all other forms of worship were prohibited; however, there were some who believed that Anglicans were too conservative in ritual and doctrine and that Anglicanism too closely resembled Catholicism. Those who desired the abolition of popish customs and errors in doctrine called themselves Puritans. Puritans believed in the personal obligation to seek God and find grace. They sought to reform the evils of society by reinforcing the values of thrift, diligence, and delayed gratification. Puritans denounced the acquisition of wealth and insisted that the purpose of human life was to prepare for salvation in the next world.

Two prominant groups of Puritans existed. There were those who believed that their dissatisfaction with the Anglican church could be ameliorated via specific reforms. They desired to fight the church from within and make changes to bring its doctrine into harmony with their beliefs. Today they are known as the Nonconformists. The other group advocated complete separation with the Church of England as the only means by which religious purity could be achieved. They believed that each congregation should manage its own religious affairs and choose its own minister (a movement later known as congregationalism). This second group is known as the Separatists.

In the founding of New England, the settlers at Plymouth (the Pilgrims) were Separatists while those landing in Massachusetts Bay were Nonconformists. Eventually, however, the Massachusetts Bay settlers did adopt the congregationalist view of religion.

Massachusetts Bay, Plymouth, & Maine
Settlement at Popham, in the current state of Maine, predated the lower colonies around the Massachusetts Bay, by 17 years. The Popham Colony was a short-lived adventure; by the time of the American Revolution, only a few towns of any significant size existed. As a consequence, the Province of Maine was absorbed by the larger Massachusetts Bay in 1664 by grant of Charles II.

After a two month journey that began in September 1620, 41 men signed a declaration of self-governance and alliance aboard the Mayflower. The Mayflower Compact, as the declaration became known, provided a promise of cooperation among the settlers to found a colony "unto which [they] promise[d] all due Submission and Obedience." It appeared early on that the New England environment matched the spirit of the Puritans that had landed on her shores. With harsh winters and rocky soil, the cultivation of New England required diligent, manual labor. Despite this, the first inhabitants of the Massachusetts colony, the Pilgrims, landed at Plymouth Rock and occupied an abandoned native village with already cleared fields. They named their settlement Plymouth. After a rough first winter, good crops and annual emigration stabilized the population such that 1,500 English lived there only 10 years later. The Colony of New Plymouth (so named to distinguish it from the town) was short-lived. It was located poorly for cultivation of land or the fur trade. It had a very shallow port and could not compete with more northerly fishing posts. Finally, the type of Separatism practiced by the Pilgrims quickly lost muster in England and failed to contribue annual immigrants for the colony's expansion. In 1691, a new charter was issued by the crown to the Massachusetts Bay colony that consumed the land grant of Plymouth and absolved its charter.

In 1630, under the leadership of John Winthrop, a much larger Puritan contingent obtained a charter from the king as the Massachusetts Bay Company. They quickly moved their charter, colonists, and capital funds to the New World and settled north of Plymouth at a site they named Boston. As emigration increased throughout the 1630s and 1640s, the new colonists spread further inland, establishing towns with churches and schools. Early disagreement over local government influenced the spread of these settlements; as individuals found they disagreed with the established order, they simply moved with their like-minded peers further inland and set up their own town government. The Crown revoked the colony's independent charter in 1684 and sent a royal governor two years later.

Rhode Island & Providence Plantations
Roger Williams established the town of Providence (so-named because he believed divine providence had led him to the site) in 1636. Establishment Puritans exiled Williams (first to Salem, and then later out of the colony's boundaries) because he preached against congregationalism in favor of the separation of church and state. A year later, another exile, Anne Hutchinson founded Portsmouth nearby. Together, the two towns grew in size.

As settlers from Massachusetts Bay moved westward and southwestward, they clashed with the Pequot Indians of the Connecticut Valley. The Pequots refused to pay tribute to the settlers and rebelled. The Naragansetts, the tribe surrounding the newly-formed colony of Providence Plantations allied with the English to drive the Pequot out of the valley, an era known as the Pequot War. The indiscriminate slaughter of the Pequot tribe appalled the Naragansett. They became subsequent victims of the Massachusetts Bay when a decade later the colonists attempted to destroy their power by convincing the Pequot to take revenge.

Williams received a charter in 1647 that permitted the merger of the four plantations around Naragansett Bay. A separate "colony" appeared in the southern portion centered around an island in the bay. This island, Rhode, along with the town of Portsmouth, formed the separate colony of Rhode Island. Oliver Cromwell supported the separation of the two areas, but after the restoration of the monarchy, Charles II combined the two areas into one colony.

New Haven & Connecticut

The area of Connecticut was originally contested with the Dutch; by the late 1630s, however, it was firmly in the hands of the British. Like many of the other New England colonies, Connecticut was the result of a merger between smaller settlement areas: New Haven, Connecticut, and Saybrook. The major boost in settlement occurred in 1636 when Thomas Hooker led a group of 100 unhappy settlers from Massachusetts Bay into the Connecticut River Valley to found Wethersfield. Along with the settlements at Hartford and Windsor, leaders from the three towns constructed the Fundamental Orders of Connecticut in 1638. Though a small document, the Fundamental Orders established the role of government and the rights of citizens in the colony. The three separate areas were combined by royal decree in 1662 as the Colony of Connecticut. Under this charter, King Charles II granted Connecticut's governor, John Winthrop, Jr., all the land south of Massachusetts to the Atlantic and west of the Naragansett River to the Pacific, ignoring the land claims of the settlement at New Haven as well as the claim of New Netherlands.

New Hampshire
In 1629, the land between the Merrimack and Piscataqua Rivers was named New Hampshire. Several settlements comprised the area but the towns were unable to confederate given their religious differences. Portsmouth was Anglican while Dover was both Anglican and Puritan. Exeter and Hampton were both Puritan, but of the orthodox variety. Massachusetts used the regional weakness to assert its interpretation of its charter as rationale for sovereignty over the territory. According the Massachusetts charter, anything above three miles north of the Merrimack River belonged to her; Massachusetts calculated its territory using a line three miles from the northernmost reach of the river. This included the New Hampshire settlements. The New Hampshire towns accepted this control until the territory brought a case before the Lords Chief Justices of the King's Bench and Common Pleas in 1677. Two years later, the King granted a royal charter to the colony.

Middle Colonies
New York

Pennsylvania & Delaware

New Jersey

Southern Colonies
The Carolinas

Georgia

Important Dates

 * 1558 -- Elizabeth I ascends English throne
 * 1588 -- Defeat of Spanish Armada; Attempt to colonize Roanoke Island
 * 1607 -- Foundation of colony at Jamestown
 * 1620 -- Foundation of colony at Plymouth
 * 1632 -- Charles I grants land to Lord Baltimore
 * 1634 -- Foundation of St. Mary's in Maryland
 * 1636 -- Exile of Roger Williams/Anne Hutchinson; settlement of Providence Plantations
 * 1662 -- Merger of New Haven, Saybrook, and Connecticut under one royal charter

Additional Resources

 * The Avalon Project: This site contains many primary sources relating to legal issues in colonial America. There is also a nice selection of primary sources for modern times. The site is divided into centuries.
 * Virtual Jamestown: This site has searchable databases of first-hand records concerning the foundation of Virginia and its early years.

Section Questions

 * Read the wikipedia entries for Henry VIII, Edward VI, Mary I, and Elizabeth I. Describe the religious, social, and political climate Elizabeth I inherited when she assumed the throne in 1558.

 * Read the wikipedia entries for Supply and Demand Economics and the enclosure movement. Provide an economic argument Elizabeth I might have used to convince landlords to renounce sheepherding and return to wheat farming.

 * How are the sciences of archaeology, genetics, and climatology helping to solve the mystery of the Lost Colony of Roanoke?

 * How did the English Civil War impact the early history of the colonies, specifically that of Maryland? Check the wikipedia entry for the Battle of the Severn for more information.

 * The English settlers routinely played the natives against one another. How did the encouragement of inter-tribal fighting, like the Pequot War in Rhode Island and Connecticut, benefit the English colonists?

Section Quiz
 Which of the following statements is true of the Chesapeake colonies? The Maryland charter to Lord Baltimore included the territory where the Virginia Company founded Jamestown.The profitability of tobacco allowed the Virginia colony to grow and prosper.Both Maryland and Virginia were granted charters that included clauses relating to religious tolerance.St. Mary's and Jamestown became centers of significant trade in the British triangular trade routes.Relations with other colonies were mediated through peaceful congresses of leaders in both colonies.

Which of the following statements is not true of the New England colonies?</li> <ol><li>The geographic boundaries of the colonies on the eve of revolution had changed since their foundation.</li><li>Religious disagreements, specifically related to the separation of church and state, formed significant rationale for the foundation of the grouping of colonies in the southern area of New England.</li><li>The Popham Colony pre-dated English settlement in every other American colony but is not remembered because it failed after a few years.</li><li>Boston emerged as the capital of a unified Confederation of New England after the defeat of the Connecticut Valley Pequot Indians in 1664</li><li>Leaders of the several New England colonies drafted governing documents that contained many of the freedoms later espoused in the Constitution.</ol>

</ol>


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Unidirectional propagation antenna

A unidirectional propagation antenna is an antenna that's propagation pattern is in one direction. Unidirectional propagation antenna are good for communicating with someone when you know where they are The following are examples of these.

Radar antennas
Radar antennas are type of unidirectional propagation antenna.

Yagi-Uda antennas
this kind of antenna is also a unidirectional propagation antenna.

Satellite dishes
A satellite dish is a unidirectional propagation antenna that we see a lot. They are usually used to communicate with satellites hence the name "satellite dish"

Also see

 * Amateur radio

title: Unidirectional propagation antenna


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User:CarrieBerg/The Bet

Down in fiery hell, where demons like to play

There were to low level devils that made a bet one day.

Mephistopheles said “I bet you can’t convert the holiest man of all

for how can the likes of you convince anyone to fall?”

To that Beelzebub replied “I am the very best!

If you doubt my powers, then put me to the test!

I will convert this holy man, and just to show you

I’ll do it only in a month or at most two!”

“Very well” Mephistopheles said, “But don’t forget the cost

If you fail it’s more that just you pride you’ll have lost

For if you lose then I’ll will get your powers too

And you’ll be left powerless, on Earth, with nothing else to do.”

Beelzebub just scoffed and laughed, she knew she always won.

And so she left for the mortal plane, it was time her work begun!

In a tiny village, three miles north of Rome

There lived the holiest man the world had ever known.

Little did the village, or for that matter the Earth

Know he was the world’s best liar and had been so since his birth.

Now this Roberto wanted money, and above all else fame

And so that was how he started his little game.

In a tavern in Rome, while talking to his friends

They suggested a way to have both money and fame in the end.

All he’d have to do, they said, was be holy

And he’d have both fame and money.

“I’ll do it” Roberto cried joyously out

But his friends just sat shaking their heads with doubt.

“Alright”, Roberto said, “you doubt me but you’re wrong

I’ll start a new life somewhere, you’ll have to come along

And see how I fool the people into thinking that I’m pure

As soon as they believe, I’m a winner for sure

For they’ll throw money at me, so absolve them of their sins

And you can take the money, so everybody wins.”

His friends like the idea, and so they headed out that night

Roberto dressed in rags, was not a pretty sight.

That had been half a year ago

That Roberto had started up his little show

And now the world believed that he

Was the purest of men, the most holy.

Up in heaven were the angels when the word got out

Of Beelzebub’s bet, and what it was about.

“Someone must save that poor man from

The tricks of Beelzebub that are sure to come!”

And so the angels conversed and chose a mighty angel to protect

The holiest of men, whom they did respect.

And so Raphael set up a hut not far from Roberto

To wait for the time when Beelzebub would show.

He made his looks similar to the holy one

And that was how Beelzebub saw him when he did come.

“Hello there!” called out Beelzebub, now a lovely maid

With long brown hair and eyes a deep rich brown shade.

“Hello” replied Raphael, unsure of what to do.

So far he had thought ten others had been Beelzebub too.

He had treated them poorly, only to find them to be

Regular humans, so he doubted himself, you see.

“I’m lost good sir,” the maid stated, with sad downcast eyes

Raphael was taken in, hooked by her lies

“Don’t fret, I will help you find your way”

He was hoping to undo some of the bad he did that day.

And so he helped the maiden and led her back to the village

She thanked him heartily and said she would visit his cottage.

Everyday for a month she returned to visit him

To bring him food in thanks, or sometimes on a whim.

Raphael grew to love her visits, and forget why he was there

Thinking more of the fair maid and her luscious brown hair.

At first Beelzebub cared so much of winning her bet

But after time, she too, started to forget.

And she began to think more of what clothes to wear

Or food that would please Raphael, when she went their.

Mephistopheles just smiled, watching it all play out

He had won from the start, he knew without a doubt.

For he had fooled Beelzebub into thinking that she

Was wooing Roberto, when in fact she

Was converting an angel. Oh what would heaven do

When they found out, what she was up too?

The Angel Gabriel had known Mephistopheles plan.

And knew what would happen, when this all began.

And so he’d chosen Raphael carefully

To be the angel that loses his divinity.

But he would not be lost without a fight

For Raphael would bring Beelzebub to the light.

And so after two months, the happy couple wed.

The thoughts of their old lives were throughly dead.

Raphael did not remember that he had been an angel,

Nor did Beelzebub remember she had been a devil.

Unseen by them at the wedding, were two other guests

They had not been invited, but they were impressed.

To see the two so happy, Gabriel couldn’t help by smile,

And Mephistopheles frowned after waiting for a while

“Alright,” he said angrily, “You win, you always do...”

“For once, dear Mephistopheles, you say something true...”

Mephistopheles and Gabriel had made a bet

To see which one could do the most powerful transformation yet.

Mephistopheles had transformed Roberto into a saint most holy

Through pretending and lies and sly trickery.

However Gabriel had bested him yet again

By turning an angel and a devil into human!

Gabriel transformed two hated enemies into lovers.

And it was good that Mephistopheles gained Beelzebub’s powers,

For when Mephistopheles groaned and paid the price agreed on

All his old powers were gone.

Gabriel smiled, and fly away

While Mephistopheles sulked for the rest of the day.

.:.:.:.:.:.

Why did I chose to make this tale? Simple really. I thought, “what tales are missing from the Canterbury Tales.” It seems to me that religious tales are few and far too dry. It would be right to add a humorous tale where heaven wins in the end. Since Chaucer never got around to writing the return tales, I decided to write one. This tale would have been told in the middle of the way back, halfway between the crude tavern and the religious experience that the pilgrims just had. They would still be reverent, and would perhaps have more faith, believing that God did know all, and that it was all part of His (or one of his angel’s) plan.

My inspiration for this tale came from several places. One source would be Bring Me the Head of Prince Charming by Roger Zelazny. The book centers on a Millennial competition between Heaven and Hell. Though my tale is more of a personal bet, there are touches of the book. A tiny taste of Faust can also be seen. After all, Mephistopheles does make two bets in this tale. So, like Chaucer I drew on other tales and gave them a new twist. Sadly, Modern English just doesn’t have the Rhyming capabilities that Middle English had, so I had to reuse rhyming words, which I don’t particularly like doing when writing poems. However, this was a long poem, so I guess some repetition is expected.

I did not have a set pilgrim in mind to read this tale. I figured that one of the pilgrims that Chaucer “forgot” to place in the Capricorn/Aquarius slot would read it. Of the existing pilgrims, someone from the Cook’s party (the Haberdasshere, Carpenter, Webbe, Dyere, or Tapycer) would work fine. After all, they are all the “forgotten” members of Capricorn. I hope you enjoyed the tale.

Should I explain the Capricorn comment? Ah, each group of characters on the pilgrimage takes after one of the astrological signs. The stories they tell reflect the humors/traits of that sign. I forget if the order is astrological based on the order they are introduced or the order they speak the tales... one of them does put them in order of the twelve signs. I could go into more detail here, but it would take far too long... and I'd have to dig out my copious piles of notes on the subject.

title: User:CarrieBerg/The Bet


text:
American Revolution/Chapter 2: The Colonists in 1750/Lesson 1

 * 1619 -- First blacks brought on Dutch ship to Jamestown.
 * 1620 -- First pilgrims find Plymouth.
 * 1622 -- The Indian Massacre of 1622 in Virginia


text:
Index:Novial/Novial Lexike/y

Back to the Novial front page

Back to Novial Lexike 1930 main page

Back to the Novial front page

Back to Novial Lexike 1930 main page

title: Index:Novial/Novial Lexike/y


text:
User:Mynameinc

Hello. See me at wikipedia:user:mynameinc. I will mostly help with math–related articles. Mynameinc 19:01, 31 May 2009 (UTC)

title: User:Mynameinc


text:
User:CarrieBerg/The Marriage Debate

The Marriage Debate

Act VI, Scene III

Setting: In the tavern where the pilgrims started from. It is after the dinner to the winner of the Best Tale has been finished. Several of the pilgrims sit together nursing a few pints of ale. These are the Wife of Bath, the Franklin, the Clerk, and the Merchant. The Miller and a few other pilgrims are around, but most have retired for the night.

Wife of Bath: So, as I was saying over dinner, we all just want to be heard. That is what a woman really wants. We’re people too...

Miller: *drunk* You just want to talk our bloody ears off!

Other men in tavern: Here, here!

Wife of Bath: Oh, shut up!

Miller: *still drunk, winces from his alcohol induced headache* See? Bloody ‘arpy.

Clerk: Your tale did state that “Wommen desiren to have sovereynetee As wel over hir housbond as hir love, And for to been in maistrie hym above.”

Wife of Bath: Yes, but my tale also states that after he allowed her to choose “she obeyed hym in every thyng That myghte doon hym plesance or likyng.” Women don’t want to actually control men, they just don’t want to be taken for granted. We just want to have a say about our own lives, and to be treated fairly, not like some thrice damned possession.

Merchant: Well that is one way to manipulate a man. *high pitched voice mimicking wife* I’m an ugly hag when I don’t get my way then I’m all nice and pretty until the next time I don’t get what I want.

Wife of Bath: *glares darkly at Merchant* That’s not what I meant.

Franklin: *dryly* Oh, and you don’t manipulate men daily with your job, Merchant?

Merchant: Not as well as my wife does daily! Why are you taking her side? It’s not like your tale paints women in such a wonderful light. *takes a long swig of ale*

Franklin: I’d say my tale paints women in a much better light than yours. The woman in mine at least stays faithful to her husband. While in your tale, how do you so delicately put it, ah yes, Damyan “swyved” her in a tree.

Merchant: *sputters into cup*

Clerk: *blushes*

Wife of Bath: *raises and eyebrow and takes a drink*

Merchant: My tale shows the true power that women have over words. They can twist any phrase to suit themselves, not caring about others at all. Your tale shows that too.

Franklin: Oh?

Merchant: Just look at your tale! Women use words to their advantage all the time. *glares at Wife of Bath*

Franklin: Actually, I’d say your tale is the only tale that does that. After all, May talks her way out of trouble by convincing Januarie “a man that waketh out of his sleep, He may sodeynly wel taken keep Upon a thyng, ne seen it parfitly, Til that he be adawed verraily.” The Wife of Bath’s Tale has the woman telling the man the answer to the riddle, which, might I remind you, saves his life. She doesn’t outright lie at all. Also the Clerk’s Tale has the faithful Grisilde not saying a word against her husband the entire time.

Merchant: Remember when Dorigen says to Aurelie that “Ye remoeve alle the rokkes, stoon by stoon, That they ne lette ship ne boot to goon – I seye, whan ye han maad the coost so clene Of rokkes that ther nys no stoon ysene, Thanne I wol love yow best of any man.” And then when he does that, she still doesn’t love him! That is using words to manipulate a man.

Wife of Bath: *slams down cup* You can’t use that! She kept her promise to her husband at the end. And that promise overrides some silly phrase said to turn away an unwanted suitor.

Merchant: But she still made a promise and broke it!

Franklin: You know, she never realized that he would remove all the rocks so she would have to keep it.

Wife of Bath: Technically she didn’t have to keep it.

Franklin: *takes a sip to hide his growing smile, his eyes dance merrily*

Clerk: *confused* How so? He removed the rocks. He fulfilled his obligations.

Wife of Bath: Aurelie didn’t fulfill three of the qualifications. First, he hires a magician. Second, the magician “thurgh his magik, for a wyke or tweye, It seemed that alle the rooks were aweye” this means the rocks were still there! He didn’t get rid of them. And finally, Aurelie was supposed to remove then one by one and not all at once.

Merchant: *scowls* Yes, well, you just proved how sneaky and conniving women really are. Franklin: *raises an eyebrow* And I suppose your twisting of my words proves you aren’t just as sneaky?

Wife of Bath: *throws up hands in exasperation* Gentlemen! This is not about the sneakiness of anyone, but of marriage!

Clerk: I agree. Let us return to the topic at hand. *dreamy look in eyes* That blessed arrangement where the woman gives herself to a man.

Wife of Bath: *glares at Clerk* Where a man and woman join equally.

Clerk: In my tale Grisilde willingly gives up everything for her wonderful husband, and they live many happy years together because of it.

Wife of Bath: What are you? A sadist? Look at what Grisilde’s husband put her through!

Clerk: *blushes* I... she wasn’t...

Franklin: *whispered to person next to him* It’s always the quiet types, isn’t it...

Clerk: No... I...

Wife of Bath: So you want a woman to go sit back and take all the abuse you throw at her?

Clerk: That’s not...

Merchant: Hey, lighten up. Leave a man his “fantasyes’. If he wants someone to control completely, who are we to stop him. It’s the only way Januarie could live with such a wife as May.

Wife of Bath: *tartly* Well, since you are no help, I’ll just have to drag the Clerk from his world of books into the real world that we all live in. He is not Pygmalion and his mental virgin bride will not turn into a reality.

Franklin: Ladies! Really, do you have to bicker? *looks pointedly at Wife of Bath* Remember, you were the one who wanted to get back on topic about marriage.

Wife of Bath: *actually manages to look sheepish and mutters* I still think he’s deluded... A man can’t do all those things to a woman and expect her to take it willingly!

Clerk: *blushes* I am not a lady.

Franklin: Obviously we will be getting nowhere tonight. So on that note, I bid you all a goodnight. *leaves the table*

Wife of Bath: *yawns* Well, I must be getting my beauty sleep. Perhaps we could continue this some other time? *follows the Franklin out*

Clerk: *stiffly stands up from table and leaves in opposite direction of the other two mumbling* Am not a lady...

Merchant: *sits at table still nursing his ale* Bastards. The lot of them. What do they know?

Miller: *passed out on the next table over*

The Host: *comes around to clear away the tankards, tsks at the Miller and avoids the Merchant*

End Act VI, Scene III

.:.:.:.:.:.

Act VI, Scene IV

Setting: The next morning at breakfast before the party finally goes their separate ways. All the pilgrims are there. The Miller is still passed out on a table. The Host is busy bringing breakfast orders around. The Merchant continues the debate with the Wife of Bath, drawing everyone in to a large argument. Chaucer sits off to the side, seemingly writing and occasionally refereeing the increasingly heated debate. Just when all Hell is about to break loose, the people the Miller swindled come in to nab him. All chaos ensues.

title: User:CarrieBerg/The Marriage Debate


text:
Amateur radio/Unidirectional propagation antenna

A unidirectional propagation antenna is an antenna that has a propagation pattern in only one direction. Unidirectional propagation antenna are good for communicating with someone or something when you know where the station is. The following are examples of these.

Radar antennas
Radar antennas are type of unidirectional propagation antenna.

Yagi-Uda antennas
This kind of antenna is also a unidirectional propagation antenna.

Satellite dishes
A satellite dish is a unidirectional propagation antenna that we see a lot. They are usually used to communicate with satellites hence the name "satellite dish"


text:
Numerical Analysis/LU decomposition concept quiz

Choose the best answer for each question:

{The LU decomposition is - The name of an algorithm to solve a linear system. + A matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix. - The same as a QR decomposition. - None of those
 * type=""}

{Is it true that any matrix can be factorized to LU form without pivoting? - Yes + No
 * type=""}

{If A = LU then, det(a) equals: - -det(L)*det(U) + $$ (l_{11}*l_{22}*...*l_{nn})*(u_{11}*u_{22}*...*u_{nn})$$ - Cannot say anything - None of those
 * type=""}

{The computational cost of the LU decomposition of an $$n\times n$$ matrix is: -O($$ n^2$$) -O($$ n^3$$) +O($$ n^3/3$$) -O($$ n^{1/2}$$)
 * type=""}

{The number of operations to solve Ax=b when we know L, U is +O($$ 2n^2$$) -O($$ n^3$$) -O($$ n$$) -O($$ n^{1/2}$$)
 * type=""}


text:
User:Srmeier

Hi I am a student at the University of North Carolina Greensboro. I am majoring in Physics and I really enjoy Mathematics. I am making this brief because I am still getting to know the site and its many functions.

Thank you for viewing my page.

Visit my blog for more info.

title: User:Srmeier


text:
User talk:Srmeier

Problems

 * Please take the time to evaluate the questions before continuing on to the solutions.
 * There are only a few questions up at this time. I plan on add on to this list in the coming days.
 * If you have any questions please contact me.
 * (scroll past the problems to get the answers)

Problem #1:Find the Limit of the function.

$$\lim_{x \to \frac{\pi}{4}}\frac{\tan(x)-1}{x-\frac{\pi}{4}}$$

Problem #2:Find the derivative of the tangent function using the quotient rule.

$$\frac{d}{dx}\tan(x)= \frac{\sin(x)}{\cos(x)}$$

Problem #3:Find the slope of the tangent line at point P(4,.5).

$$f(x)= \frac{1}{\sqrt{x}}$$

Problem #4:Find the limit.
 * current problem (hint: think substitution and the limits of "e")

$$\lim_{x \to 0}\frac{\ln(1+2x)}{x}$$

Answers
Problem #1:This tests your knowledge of trig identities.

$$\lim_{x \to \frac{\pi}{4}}\frac{\tan(x)-\tan(\frac{\pi}{4})}{x-\frac{\pi}{4}}$$

$$\lim_{x \to \frac{\pi}{4}}\frac{\frac{\sin(x)}{\cos(x)}-\frac{\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{4})}}{x-\frac{\pi}{4}}$$

$$\lim_{x \to \frac{\pi}{4}}\frac{\sin(x-\frac{\pi}{4})}{(x-\frac{\pi}{4})\cos(\frac{\pi}{4})\cos(x)} = \frac{1}{(\frac{\sqrt{2}}{2})(\frac{\sqrt{2}}{2})}= 2$$

Problem #2: This is very basic.

$$\frac{d}{dx}\tan(x)= \frac{\cos(x)\frac{d}{dx}\sin(x)-\sin(x)\frac{d}{dx}\cos(x)}{\cos^2(x)}$$

$$\frac{d}{dx}\tan(x)= \frac{\cos^2(x)+\sin^2(x)}{\cos^2(x)}$$

$$\frac{d}{dx}\tan(x)= \sec^2(x)$$

Problem #3:This is quite basic.

$$f ' (x) = \frac{ \sqrt{x} - \sqrt{x+h} }{ h \sqrt{x} \sqrt{x+h} }$$

$$f'(x)= \frac{ -1 }{ 2 \sqrt{x^3} }$$

title: User talk:Srmeier


text:
User:Spuckie

Just learning my way around wikiverisity. I hope to participate in the School:Anthropology.

(and my first lesson will be how to make that a direct link to the anthro school page ;-)

title: User:Spuckie


text:
Publication bias

Publication bias arises from the tendency for researchers, editors, and companies to handle the reporting of experimental results that are positive (i.e., they show a significant finding) differently from results that are negative (i.e. supported the null hypothesis) or inconclusive.

This page provides an undergraduate-level introduction to the problem of publication bias.

Two counter-acting biases

 * Low Power: under-estimation of real effects
 * Publication Bias or File-drawer effect: over-estimation of real effects

What is publication bias?

 * Publication of results depends on their nature and direction.
 * Studies that show significant effects are more likely to be published.
 * Type I publication errors are underestimated to the extent that they are: “frightening, even calling into question the scientific basis for much published literature.” (Greenwald, 1975, p. 15)

Funnel plots

 * A scatterplot of treatment effect against study size.
 * Precision in estimating the true treatment effect increases as N increases.
 * Small studies scatter more widely at the bottom of the graph.
 * As studies become less precise, results should be more variable, scattered to both sides of the more precise larger studies … unless there is publication bias.
 * In the absence of bias the plot should resemble a symmetrical inverted funnel.
 * If there is publication bias this will cause meta-analysis to overestimate effects.
 * The more pronounced the funnel plot asymmetry, the more likely it is that the amount of bias will be substantial.

File drawer effects

 * 1) Tendency for non-sig. results to be ‘filed away’ (hidden) and not published.
 * 2) of null studies which would have to ‘filed away’ in order for a body of significant published effects to be considered doubtful.

Countering the bias

 * 1) Journal Articles in Support of the Null Hypothesis

title: Publication bias


text:
User:RekonDog

 * Military Science (Wikiversity)
 * Military Science (Wikipedia)

title: User:RekonDog


text:
School talk:Engineering and Technology/Help Desk

put in the mainspace! :)


text:
Scientific integrity

"Integrity is doing the right thing, especially when no one is watching." (Wikipedia)

Scientific integrity refers to honest and transparent methods and reporting of research. In other words, there is no cooking the books or even subtly influences of bias to privilege some lines of investigation or results over others. There is no falsification or fabrication or plagiarism.

What are some examples of compromised scientific integrity?
 * 1) Witholding of politically unwanted results

title: Scientific integrity


text: File:4428 85285993796 603638796 1956984 3448101 n.jpg


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User talk:SnoozingInTheLemonGrove

Snoozing In The Lemon Grove

Thank you for your visit. Though I am an active user of Wikiversity, the project to which I mostly contribute to is Wikipedia which is therefore the location of my primary user account. Please be sure to visit there for updated information or to leave me any messages.

N.B. Please state which project to which you refer when leaving a message.

title: User talk:SnoozingInTheLemonGrove


text:
User:Graeme E. Smith/GreySmith Allocortical Tissue Protocol 1

{{User:Graeme_E._Smith/GreySmith Article Framework| Heading = GreySmith Allocortical Tissue Protocol 1| Subheading = Testing Allocotical Tissue for Implicit/Explicit Access| Author=Graeme E. Smith| Abstract = Cortex Tissue can be separated according to micro-architecture, into areas that have 6 layers and are called Isocortical, or Granular, areas that have 5 layers because their 4th layer is attenuated or missing and are called AGranular, and areas that have 4 or less layers which are called Allocortical. Although the Allocortex is probably the largest area of Allocortical tissues, There are many places throughout the brain where Allocortical tissue can be found. While working on a Neuro-Psycho-Architectural theory of memory, I hypothesised that Allocortical Tissue was implicit memory with no explicit access, and that Isocortical Tissue had both Implicit and explicit access. In this article I describe a protocol that might be used to indicate with greater certainty whether in fact this is the case. I call it the GreySmith Allocortical Tissue Protocol 1 or GSATP1 for short. Body= {{indent|8}}To test the theory that Allocortical Tissue is Implicit memory with no Explicit Access, we need to test both Allocortical tissue and Isocortical Tissue so that we can dissociate between them, and we need to test for implicit and explicit memory so that we can dissociate between them. This creates essentially a 4 box 2 dimensional array where the results of the tests should indicate the access potential of both Isocortical and Allocortical memory.{{indent|9}}What we are looking for is the condition where the Isocortical line of the array shows both implicit and explicit access, and the Allocortical line of the array shows only implicit access. Any other solution can be seen to be a disproof of the hypothesis.{{indent|8}}To be able to support or disprove the hypothesis, we need to do sufficient controls to assure ourselves that we can dissociate between Isocortical and Allocortical Tissues and between implicit and explicit memories. To create a control for Isocortical and Allocortical tissues we must pick tissues that are known to be one or the other, and test for cross contamination of our results. A signal thought to be handled by an Allocortical tissue, must not impact on the action of a test for an Isocortical Tissue and visa versa. We can do this by isolating the test stimuli, by sensory modality. For instance for our Isocortical Test we could use the Visual System, and for our Allocortical Test we could use the Olfactory Bulb. We could then test some of the subjects by giving them the test for an olfactory stimulus with only a visual stimulus, and test some of the subjects by giving them the test for a visual stimulus with only an olfactory stimulus, and thus prove that the two routes through the memory were discrete. Care must be taken to manage the population of controls so that they have a statistical significance.{{indent|8}}The next problem is how to Dissociate the implicit from explicit memory. The job here is to take advice of the fact that implicit memory responds to priming, while explicit memory doesn't, and Explicit memory responds despite delays between stimulus and response, and implicit memory doesn't. The test factors are speed of response which indicates priming, and delay length which eliminates priming as a factor. So in order to test our experiment we need to do controls which test the speed of response after a delay, and controls that test speed of response for different delay lengths to show when priming is no longer a factor. Those tests then determine the minimum delay length we can use to eliminate priming in tests of explicit memory By judicious choice of a longer delay length than the minimum indicated we can virtually eliminate priming as a factor in explicit memory tests. Now that we have proven our test as dissociating the four factors in tuples, we need to test for cross contamination between the diagonal arrangements of the tests. This should be possible with statistical means. We can test our output results for all four lobes, by eliminating two lobes and testing the other two lobes for statistical cross-over.{{indent|8}}once we have our control system in place, the next problem is how to test for the experimental conditions. Up until now I have glossed over what the actual tests are in order to point out how to control them. We need 4 tests, One visual priming test, one Visual delayed response test, hopefully similar enough that we are testing the same area of the brain, one Olfactory priming test, and one Olfactory delayed response test, with a similar provisio. A Statistically significant number of mice should be run through the test a statistically significant number of times, and then the results tabulated and statistically analyzed, and projected onto the 4 area 2 dimensional graph suggested above to indicate the accuracy of the hypothesis. I leave the choice of the particular tests to the individual researcher, since this test should hold true with multiple test conditions as long as the tests do what they are supposed to do.

Conclusion
While I haven't declared any specific olfactory and visual tests for this protocol, as long as the tests can be clearly seen to dissociate priming from delayed response with different periods of response delays that are long enough to eliminate priming and compare the speed of response between the immediate response tests and the delayed response tests, and as long as the controls are managed properly this test should clearly show whether or not the hypothesis that Allocortical Tissues are Tissues without explicit access and Isocortical Tissue have both implicit and explicit access, which are the conditions required for my hypothesis to be supported. The 2 dimensional graph with the results tabulated in it, would indicate the success of the experiment. category=GreySmith/Psychology|}}


text:
User:Bennó

See me here

title: User:Bennó


text:
User talk:Bennó

Find me here

title: User talk:Bennó


text:
The Hundred Years War and its Aftermath

The Hundred Years War and its Aftermath The Hundred Years War was an era of war laying the stepping stones for the further development of France and England. The war, which was a series of successive battles and truces, lasted for 116 years or even more, depending which dates one uses as start and stop time.

Prelude to the War

Research offers 3 dates in an attempt to pinpoint the reasons of the war. The earliest date is 1066 and is linked with William the Conqueror, sometimes also called William the Bastard (before the battle of Hastings). Due to his victory William linked England and France under one crown and by this lay the "founding stone" of the conflict. The second more common date is 1154. The third most renowned date is 1337, which was also used in order to give the Hundred Years War its name.

title: The Hundred Years War and its Aftermath


text:
Talk:Stem cells

I was not familiar with stem cells being found in menstrual blood. Are you sure about this?

title: Talk:Stem cells


text: User:Graeme E. Smith/GreySmith Isocortical Tissue Protocol 1


text:
Numerical Analysis/Matrix norm exercises

Consider the general $$3\times 3$$ matrix $$ A=     \begin{bmatrix} a_{11}&a_{12}&a_{13} \\ a_{21}&a_{22}&a_{23} \\ a_{31}&a_{32}&a_{33} \\ \end{bmatrix} $$ and the specific example $$ B=     \begin{bmatrix} 1 & 2 & 3 \\          4 & 5 & 6 \\           7 & 8 & 9 \\      \end{bmatrix} $$.

Find $$\left \| A \right \| _1 $$ Solution: given: $$ \left \| A \right \| _1 = \max \limits _{1 \leq j \leq n} \sum _{i=1} ^n | a_{ij} | $$

Solve for column 1: $$\sum _{i=1}^3|a_{i1}| = |a_{11}|+|a_{21}|+|a_{31}|$$

Solve for column 2: $$\sum _{i=1}^3|a_{i2}| = |a_{12}|+|a_{22}|+|a_{32}|$$

Solve for column 3: $$\sum _{i=1}^3|a_{i3}| = |a_{13}|+|a_{23}|+|a_{33}|$$

$$ \left \| A \right \| _1$$ = the maximum absolute column sum of the matrix

Find $$\left \| B \right \| _1$$ Solution: Solve for column 1: $$\sum _{i=1}^3|b_{i1}| = |1|+|4|+|7| = 12 $$

Solve for column 2: $$\sum _{i=1}^3|b_{i2}| = |2|+|5|+|8| = 15 $$

Solve for column 3: $$\sum _{i=1}^3|b_{i3}| = |3|+|6|+|9| = 18 $$

$$ \left \| B \right \| _1 = \max[12,15,18] = 18 $$

Find the infinite norm, $$\left \| A \right \| _\infty$$ Solution: given: $$ \left \| A \right \| _\infty = \max \limits _{1 \leq i \leq n} \sum _{j=1} ^n | a_{ij} | $$

Solve for row 1: $$\sum _{j=1}^3|a_{1j}| = |a_{11}|+|a_{12}|+|a_{13}|$$

Solve for row 2: $$\sum _{j=1}^3|a_{2j}| = |a_{21}|+|a_{22}|+|a_{23}|$$

Solve for row 3: $$\sum _{j=1}^3|a_{3j}| = |a_{31}|+|a_{32}|+|a_{33}|$$

$$ \left \| A \right \| _\infty$$ = the maximum absolute row sum of the matrix

Find the infinite norm, $$\left \| B \right \| _\infty$$ Solution: Solve for row 1: $$\sum _{j=1}^3|b_{1j}| = |1|+|2|+|3| = 6 $$

Solve for row 2: $$\sum _{j=1}^3|b_{2j}| = |4|+|5|+|6| = 15 $$

Solve for row 3: $$\sum _{j=1}^3|b_{3j}| = |7|+|8|+|9| = 24 $$

$$ \left \| B \right \| _\infty = \max[6,15,24] = 24 $$

Find the Frobenius norm, $$\left \| A \right \| _F$$ Solution: given: $$\|A\|_F=\sqrt{\sum_{i=1}^3\sum_{j=1}^3 |a_{ij}|^2}$$

$$\|A\|_F=\sqrt{|a_{11}|^2+|a_{12}|^2+|a_{13}|^2+|a_{21}|^2+|a_{22}|^2+|a_{23}|^2+|a_{31}|^2+|a_{32}|^2+|a_{33}|^2}$$

Find the Frobenius norm, $$\left \| B \right \| _F$$ Solution: $$\|B\|_F=\sqrt{|1|^2+|2|^2+|3|^2+|4|^2+|5|^2+|6|^2+|7|^2+|8|^2+|9|^2} = \sqrt{285} \approx 16.9 $$


text:
KOIIA/The Complexity of Identity

KOIIA 2, 7,5 hp vt -09 Örebro University Catarina Schmidt

The Complexity of Identity
This paper discusses the conditions for identity; what it is, how it is created and developed. I will argue that there is a strong connection between identity and learning and also claim that there is crucial link between confidence in the written language and identity development.

In the Swedish National Encyclopedia the word identity is defined as ”self image, awareness of oneself as a unique individual” and as “individuals or groups own identification of belonging to a certain culture, ethnical group or nation” (www.ne.se). Consequently dentity is about who I am, my sense of belonging to other groups, my relations, how I think of myself and how others understand me. We do not always reflect upon the term identity – it can be difficult to describe your own identity and even more difficult to take someone else’s perspective and be able to understand the conditions which creates another person’s identity.”My identity is”, writes Feinberg (1998),”as common to me as it may be uncommon to you” (p. 3). Our thoughts, feelings and ideas are inside us while the surrounding world is outside us, we can here talk about an inner and an outer world. Wenger (1998) means that identity ”narrows the focus onto the person, but from a social perspective” (s. 145). The concept of identity focuses the individual, the self and the subject. At the same time every individual needs the interaction with others to develop identity. To become a subject, to become someone, can therefore be seen as a double process (Nordin-Hultman, 2004). We construct our own identity at the same time as we are constructed. What does this really mean; how and on what conditions does identity develop? What does identity mean for the conditions of learning and, more specifically, for the credence and confidence in the written language?

CONDITIONS FOR IDENTITY

Riley (2007) stresses that ”the ability to establish intersubjectivity, to enter into social and meaningfull contact with another, is a necessary condition for the formation of identity” (p. 33). Many researchers stress the fact that identity is a product of social interaction (Wenger, 1998; Caldas-Coulthard & Iedema, 2008; Riley, 2007; ) It is the meeting between the subjects that is necessary for the creation of identity. Caldas-Coulthard & Iedema (2008) explain the notion of identity like representations of personal experiences and feelings that express themselves through organized action. Spoken or signed interaction can be seen as the very foundation of identity construction. To be able to express what simultaneously establishes our identity, we need a language. In a wider sense identity is all we say, express, gesture, wear and possess. The creation of identity commute, according to Lemke (2008) and Wenger (1998), between the individual’s and the minor group’s activities within the major institutional contexts. Wenger (1998) argues that it is not either an individual, nor an institutional or a social perspective. Instead we meet, he argues, them all three together at the same time dialogically “with a human face” (Ibid., p. 145). When we meet institutions we also meet its people, artifacts, discourses, practices and contexts (Lemke, 2008).

Identity craves space and room in order to be created and developed over and over again. ”A society worth living in must make room for people to craft identities”, accentuates Wikan (2002, p. 74). Bhabha (1994) gives us the vision of ”a third space for enunciation (p. 53)” as a possible room where we can talk about ourselves and the other without putting the former aside as less worthy. Except this room with mutual respect for each other where interaction is possible through language we need a variety and a richness of words in order to express our identities. Lemke (2008) refers to Paulo Freire who ”asks us to try to speak an authentic word, to try to name ourselves outside the realm of names given to us by social institutions and the interest of power” (p. 39). Where ever interaction takes place it is put against categories like age, gender, race, ethnicity, religion and class. Those social categories, which identity can be investigated from, are also them pluralistic and changeable (Lemke, 2008; Eriksson-Zetterquist & Styhre, 2007; Feinberg, 1998 .) Eriksson-Zetterquist & Styhre (2007) give us the picture of a human as an aggregate of different identities, coexisting without being syncronised referring to Rosa Baraidotti (2006) :

It is absolutely the case that one is not a Muslim on Tuesday and a European on Wednesday, a woman on Monday, black on Sunday and lesbian on Thursday afternoon. These variables coexist in time. They also intersect, coincide or clash; they are seldom synchronized. (p. 13)

The many possibilities to interaction and language in order to ”name ourselves” are sources to both the individual and the collective identity. The construction of identity is always negotiating with different social categories of society, which can result in both restrictions as well as a legitimizations of the construction of identity.

LEGITIMISATION OF IDENTITY

Identity needs, as earlier mentioned, space. What is then happening when this space is limited, decreased or not existing? Eriksson-Zetterquist & Styhre (2007) claim that ”even if postmodern identity theories describe human identity as flowing and fragmental they will in unclear ways be stabilized into different social categorizations (p. 32). If, for example, only conflicts between gender is focused it can mean a stabilization of only this category which will make us disregard from other kind of oppressions. One such example is, mean de los Reys et.al (2005) immigrated women experiences and problems. If all women are compared with an idealized Swedish womanhood ethnical limits will be created where the Swedishness will be the norm (Ibid.). But, by taking in to consideration other social categoreis like ethnicity/race, age and social class the picture of immigrant women might be widened and the unclear stabilization around only one category might be painted in more colors and shades. The concept of intersectionality contributes to the possibility to see more social categories and the impact of these at the same time. Eriksson-Zetterquist & Styhre (2007) refer to Lycke (2003) and claim that intersectionality has its background in postmodern theories, feminist theories, postcolonial theories, Afro-American theories, theories about ethnicity, theories about class and queer theory. The authors strongly emphasize the importance of seeing “both ethnicity, color of skin, gender, class, sexuality, religion, age and other categories” (Ibid. p. 10) and their conclusion is that different social categories cannot be separated from each other, instead they state that we have to investigate ”how the different analytical categories clutch to each other and co-vary (p. 13) since they exist within a mutual relation with each other. To each one of these social categories values are connected - values that create social hierarchies.

Postcolonial theoretical tools can show u show social hierarchies are being constructed without reflections and/or awareness from us as individuals within the very context. Colonization is not only about the conquering of land and natural assets, it is also about the ideology that justifies the construction of ”the others”. de los Reyes (2007) means that the ethnical hierarchy, existing within the employment- and resident market of today follows the colonial map. By connecting the colonial project to contemporary diversifying varieties, de los Reyes et.al. (2005) argue that there is a way to make social hierarchies visible. One expression for the ideology of colonization  is the eugenic that was developed and got academically established at the University of Uppsala during the beginning of 1900 in Sweden. These thoughts were, according to the authors (Ibid.), the foundation of what they name culture racism. They explain culture racism as defining the typical Swedish; the seeking after a Swedish identity points to the fact that the classification of the population of today is not built upon racial differences in a biological sense – now the concept of culture dominates the rhetoric. Just like Bhabha (1994) the authors (Ibid.) emphasize that binaries like women/men, labour/capital, immigrants/Swedes are taken for granted. An uncritical use might have the effect that some categories are dominated by another and that social hierarchies will be established. Another example of this is, according to de los Reyes et.al. (2005), single mothers, which they mean are put against and compared with a heterogeneous norm of differentiation.

Feinberg (1998) further claims that we are born into a national identity that includes some of us and excludes others and he therefore argues for an including national identity ”that takes seriously the claims of different cultural communities and other identity formations for public recognition” (p. 27). “To be a stranger”, Feinberg writes, “is to be in a social world that does not respond in the way one anticipates” (p. 137) and by that he clearly touches Bhabha (1994) who in his construction of a “third space of enunciation” wants to escape from “we” and “them”. In order to avoid this, cultural pride and cultural respect is crucial, but Feinberg like Wikan (2002) stresses the fact that there are limits for cultural respect. Respecting the fundamental human rights of the individual can mean that culture must be resisted or reduced (Wikan, 2002). Feinberg argues for ”a robust recognition” and means by that that a certain group can have a specific right to have their story told. Also Riley (2007) emphasizes the importance of recognition for identity development to establish, explaining that ”it is otherness which makes interaction both possible and necessary” (p. 176).

IDENTITY AND LEARNING

Interaction and language constitute the conditions for identity. Seen from another angle interaction and language constitute the conditions for learning. Learning is situated, according to Lave & Wenger (1991), within communities of practice where negotiating takes place through participation. Communities of practice is, as I understand the authors, a context where a history of learning is shared. The situated learning has a characteristic process, which Lave & Wenger, call Legitimate Peripheral Participation (LPP). The process is legitimated since the new member from the very beginning is allowed to participate. The participation is first peripheral, but exceeds gradually to become more and more central for the purpose of the shared project; “a newcomer’s task is short and simple, the costs of errors are small, the apprentice has little responsibility for activity as a whole” (Ibid. p. 110). Lave & Wenger stress the importance of identity development and the process of LPP as a necessary condition for learning. Identity and learning are from this view dependent from each other and seen as inseparable:

We have claimed that the development of identity is central to the careers of newcomers in communities of practice, and thus fundamental to the concept of legitimate peripheral participation. This is illustrated most vividly by the experience of newcomers to A.A., but we think that it is true of all learning. In fact, we have argued that, from the perspective we have developed here, learning and a sense of identity are inseparable. They are aspects of the same phenomenon. (Lave & Wenger, 1991, p. 115)

From this theoretical perspective the individual’s participation is strongly connected with the development of identity, the sense of belonging and being a member (Wenger, 1998). A parallel to this is Smith (1998) who talks about membership and socialization in to the association of readers. Lave & Wenger (1991) emphasize strongly the importance of communities of practices in order to develop identity. In the ongoing work with authentic tasks the member becomes ”an old-timer, whose changing knowledge, skill and discourse are part of a developing identity” (p. 122). This means a constant negotiation with the inner self where the story of our life becomes a part of our identity: In the same way that meaning exists in its negotiation, identity exists – not as an object in and of itself – but in the constant work of negotiating the self. It is in this cascading interplay of participation and reification that our experience of life becomes one of identity, and indeed of human existence and consciousness. (Wenger, 1998, p. 151)

Already the little child develops and internalizes in to a culture through dialogue and interaction. The child’s cultural integration do not take place through a passive imitation – the child is itself an actor together with other important actors. This is, according to Sommer (2005), the condition for children’s different childhoods within different historical, social and cultural practices. The concept of culture is by Feinberg (1998) seen ”as the system of meaning, which enables individuals to make sense of their own and other’s experiences” (p. 64). These sociocultural conditions constitute the practice where the child is included and proceeds from in its own learning. This reasoning focuses ”questions that deal with how people will master such knowledge and such skills that distinguish their own society and the time they are living in” (Säljö, 2005, p. 21). At the same time these sociocultural conditions constitute a potential for maximal development, which according to Feinberg (1998), demands a ”robust recognition” of different children’s life stories and identities.

Referring to the the Children’s Convention, Hart (1992) stresses the importance of conditions for a real and genuine participation and he sees this as necessary for the construction of both identity and learning; ”programmes should be designed which maximize the opportunity for any child to choose to participate at the highest level of his ability”. According to Qvarsell (2003) a variety of meanings has to be captured and experiences from several actors being included (p. 102). If all children are compared with an idealized Swedish childhood will the same ethnical boarders be created as de los Reyes (2005) stresses considering immigrant women. Children who could not live up to the norm in the Swedish school during the century of 1800 were categorized as lazy and obstinate (Hjörne & Säljö, 2008) and the same authors show how these categorizations still exist and constitute learning conditions for some children but with other words. Time and again the importance of facets and a variety of many identities emerges. Qvarsell (2003) stresses the fact that there is not existing a single right perspective of being a child and Halldén’s (2003) conclusion is to allow and listen to all children’s voices, but also to interpret them as an expression for a certain context. Referring to the Children’s Convention and the Swedish curriculum considering educational learning Hobohm (2003) emphasizes ”the pupil’s right to be seen not only as a pupil, but also as a human that will be given the necessary space to keep his or her own personality” (p. 46). Also according to Feinberg respect is a necessity for democracy- and knowledge development, but yet he claims the urge for  even more measures:

Hence, one of the functions of the common schools is to teach students how to advance their own ideas and to speak and write in an authentic and convincing manner. In other words, the common school has a role in teaching students how to advance their own concerns – including cultural ones – and to express themselves in ways that ring true. (Feinberg, 2, p. 245)

Today we live in a culture that is distinctly built on the written language. It is therefore crucial to become a human being who read and writes. Through language use we make our voice heard, we create meaning, build frames of reference, understanding and identity in the culture we are co-creators of (Kress, 1997). The ability to read and write is always connected with social activities and domains including relations and a life story in a chronological order. Within research about reading and writing the term Literacy is more and more used. Literacy can be seen as the ability in the written language that every person needs in order to live a satisfactorily life. Literacy is seen as social activity where social relations are integrated and where every person has her own literacy story including a variety of literacy events (Barton, 1994). Every individual participates through its family, interests, hobbies and through its surrounding world in different practices where the written language is used and identity creates and is created. Consequently there are many intersection points where learning, identity and the written language meet up in our time. Riley expresses it like ”just as history tells us who we are, identity is made of the stories we tell ourselves” (p. 244). Literacy learning therefore has a strong impact on self image and identity:

Throughout the whole life communication with other people is a Condition for social and personal development and it is through participation in linguistic and cultural communities that the identity of children and young people increase. In a culture distinctly based on the written language becoming a person who reads and writes is therefore one of the most important personal milestones during growing time. Success and failures in this function might have lifelong consequences. There is powerful risk that the confidence to the linguistic ability becomes fragile or completely lacks. (Bergö & Ewald, 2003, p. 32)

LEARNING THE WRITTEN LANGUAGE AND IDENTITY IN OUR TIME

The Swedish curiculum prescribes that ”by providing a wealth of oppurtunities for discussion, reading and writing, all pupils should be able to develop their ability to communicate and thus enhance confidence in their own language abilities” (National Agency for Education, 2006, p. 6). Confidence in one’s own ability in the written language is one important part of children’s and young people’s construction of identity. Learning deals with developing identity through language – first the oral language and then the written language. School has here a specific social mandate, but social and communicative processes do of course occur in many other contexts and are initiated long before the school start. In the early history of education demands on reading and being able to memorize a limited choice of texts were claimed – today an ability of a critical view and the ability to rate and draw conclusions from texts in books, the computer screen and so on are needed. The demands have increased and the surrounding world has in addition become more complex when our writing culture is rapidly changing through digital resources and virtual communities on the Internet. But, it is still in written communities that children’s and young people’s identity take place. It is here and now that we try to understand and live our lives. By observing and studying which processes in socialization and communication that exist and what patterns of interaction that is established I want in my future research to take part of some children’s literacy practices and identity development. Questions I carry with me is what the relation is between identity and learning in different practices of literacy. My future research will deal with different individual’s literacy experiences that take place within different landscapes of language. Will the processes for learning diverge between these different literacies and, if so, in what ways and who are participating in these different practices? These conditions will then be put against conditions for identity construction.

Dahlberg et.al. (2001) claim in addition that from a postmodern perspective we can no longer fall back on knowledge as something universal and static and therefore argue that we all must take responsibility for our own learning and creation of meaning. This means stronger demands on children today since they have to form and shape their own understanding of the world. I therefore argue that it is even more crucial to be seen as a child as well as to be able to see others and to be able, in different mediums, to express oneself ”in a way that rings true” (Feinberg, 1998, p. 245). Literacy classrooms can therefore be seen as places where face-to-face interactions shape literacy practices (McCarty, 2005). In this perspective literacy becomes a part of life, a linguistic resource for identity development and lifelong learning. Together we need to take responsibility for offering a space full of languages and ways of expressions where a variety of identity can create and be created without the expense of someone else. Or like Tatum (1997) expresses it “we may not have polluted the air, but we need to take responsibility, along with others, for cleaning it up” (p. 6).

REFERENCES

Barton, David (1994). Literacy. An Introduction to the Ecology of Written Language. Oxford: Blackwell. Bergö, Kerstin & Ewald, Annette (2003). “Liv, identitet och kultur. Om utredningen Att lämna skolan med rak rygg och svenska som demokratiämne”, i Örebro universitet. Utbildning & Demokrati vol. 12, nr 2. Bhabha, Homi (1994). The Location of Culture. London: Routledge. Caldas-Coulthard, Carmen Rosa & Iedema, Rick (2007). Identity Trouble. Hampshire & New York: Palgrave Macmillan. Dahlberg, Gunilla, Moss, Peter & Pence, Alan (2001). Från kvalitet till meningsskapande. Postmoderna perspektiv – exemplet förskolan. Stockholm: HLS Förlag. de los Reyes, Paulina (2007), ”Intersektionella perspektiv på etniska relationer”, i Etnicitet. Perspektiv på samhället. Malmö: Gleerups. de los Reyes, Paulina, Molina, Irene & Mulinari, Diana (2005). Maktens (o)lika förklädnader. kön, klass & etnicitet i det postkoloniala Sverige. Stockholm: Atlas. Eriksson-Zetterquist, Ulla & Styhre, Alexander (2007). Organisering och intersektionalitet. Malmö: Liber. Feinberg, Walter (1998). Common schools, uncommon identities. National unity & cultural differences. New Haven: Yale University Press. Hart, A. Roger (1992). ”Children’s participation. From tokenism to citizenship”, i Innocenti Essays, no 4. Florence: UNICEF, 1992 (nätpublikation). Hjörne, Eva & Säljö, Roger (2008). Att platsa i en skola för alla. Elevhälsa och förhandling om normalitet i den svenska skolan. Stockholm: Norstedts Akademiska Förlag. Hobohm, Susanne (2003). Barnets rätt, handbook för vuxna. Stockholm: Liber. Kress, Gunther (1997). Before writing. Rehinking the paths to literacy. London & New York: Routledge. Lemke, Jay (2008). “Identity, Development, and Desire: Critical Questions”, i Identity Trouble. Hampshire & New York: Palgrave Macmillan. McCarty, Teresa (red.). (2005). Literacy and power in schooling. Mahwah New Jersey: Lawrence Erlbaum Associates. Nordin-Hultman, Elisabeth (2004). Pedagogiska miljöer och barns subjektsskapande. Malmö: Liber. Peterson, Abby & Hjerm, Mikael (2007). Etnicitet. Perspektiv på samhället. Malmö: Gleerups. Qvarsell, Birgitta (2003). “Barns perspektiv och mänskliga rättigheter. Godhetsmaximering eller kunskapsbildning?”, i Pedagogisk Forskning i Sverige. Nr 1-2, 2003. Riley, Philip (2007). Language, culture and identity. An ethnolinguistic perspective. London: Continuum International Publishing Group Ltd. Sommer, Dion (2005). Barndomspsykologi. Utveckling i en förändrad värld. Tallin: Runa. Tatum, Beverly Daniel (1997). “Why are all the black kids sitting together in the cafeteria?” And Other Conversations About Race. New York: Basic Books. Utbildningsdepartementet (1998). Läroplan för det obligatoriska skolväsendet, förskoleklassen och fritidshemmet. Stockholm: Skolverket. Wenger, Etienne (1998). Communities of Practice. Learning, Meaning, and Identity. Learning in doing: social, cognitive, and computational perspectives. Cambridge: Cambridge University Press. Wikan, Unni (2002). Generous Betrayal. Politics of Culture in the New Europe. Chicago: The University of Chicago Press.

ÖVRIGA KÄLLOR

http://www.ne.se/sok/identitet?type=NE 2009-05-30 (Nationalencyklopedin)

title: KOIIA/The Complexity of Identity