text:
User:Kaihsu/IMlawA3

European internal market.

Section A: The scope of the four freedoms.

Chapter 3: Material scope – notion of economic activity.

Notes by Kaihsu Tai, 2011-12-22.

Goods
Objects shipped across a frontier for the purposes of commercial transactions are goods: Case C-2/90 Belgian waste, confirmed in Case C-221/06 Frohnleiten.

If a measure concerns two freedoms, but one is ancillary to the other, only the principal freedom is considered. So, lottery tickets and fishing licences fall under services: Case C-275/92 Schindler, Case C-97/98 Jägerskiöld. But internet-based sale of contact lenses falls under goods: Case C-108/09 Ker-Optika.

Coins no longer legal tender are goods; otherwise they fall within payments: Case 7/78 Thompson.

Persons
Union citizens enjoy equal treatment: Article 18 TFEU; Article 24, Directive 2004/38. EU provisions may result in “reverse discrimination” of own nationals.

Further, workers who is a national of a Member State enjoy the same social and tax advantages as national workers: Article 7(2), Regulation 492/2011. These are defined widely as “all those which, whether or not linked to a contract of employment, are generally granted to national workers primarily because of their objective status as workers or by virtue of the mere fact of their residence on the national territory and the extension of which to workers who are nationals of other member states therefore seems suitable to facilitate their mobility within the [EU]”: Case 207/78 Even (war pension). For example: Case 65/81 Reina (childbirth grant), Case C-237/94 O’Flynn (funeral expenses). They do not need to flow directly from the employment: Case 63/76 Inzirillo (handicap allowance).

But distinguish from social security benefits, governed by Regulation 1408/71 with the same equality of treatment (Article 3) and defined at Article 4.

Neither covers war benefits: Even, Case C-315/94 de Vos, Case C-386/02 Baldinger. But restrictions should not impinge on the freedom of movement: Case C-192/05 Tas-Hagen and Tas, Case C-499/06 Nerkowska, Case C-221/07 Zablocka-Weyhermüller.

A child of an EU migrant worker, along with its carer, can remain in the host state to receive education: Case C-413/99 Baumbast and R, Case C-310/08 Ibrahim, Case C-480/08 Teixeira. See more widely Case C-34/09 Ruiz Zambrano.

Services and establishment
Services (defined residually in Article 57 TFEU) “are normally provided for remuneration”; see also Directive 2006/123 (Services Directive). Payment is not necessarily by the recipient: Case 352/85 Bond van Adverteerders. An activity without payment is beyond the scope: Case C-159/90 SPUC v Grogan; but expense allowance for teaching falls within: Case C-281/06 Jundt. Despite the authorization requirement provided in Regulation 883/2004), “health tourism” such as those by UK NHS patients fall within the scope of services, but reimbursement only up to objective treatment cost: earlier cases such as Case C-157/99 Smits and Peerbooms confirmed in Case C-372/04 Watts.

Establishment and services are mutually exclusive: Case C-55/94 Gebhard, Case C-456/02 Trojani. Establishment is distinguished by permanent presence: Case 205/84 German insurance services, confirmed in Gebhard as “stable and continuous participation in the economic life of the host Member State”.

Capital
ECJ often relies on Directive 88/361 for the distinction between capital and other freedoms: Case C-98/01 Commission v UK (BAA special shares). Current payments do not fall within free movement of capital: Case 286/82 Luisi and Carbone.

The distinction is often blurred and effects cumulative with movement of persons (services, establishment). In Case C-118/96 Safir on taxation of life insurance premiums, services rules were applied despite its residual nature instead of capital rules; likewise Case C-356/08 Austrian doctor bank accounts. Rules on capital and on services can apply to the same economic activity: Case C-484/93 Svensson and Gustavsson, Case C-279/00 Italian temporary labour. National rules affecting primarily services does not require consideration of consequential effects on capital: Case C-452/04 Fidium Finanz; and vice versa: Case C-233/09 Dijkman and Dijkman-Lavaleije.

Capital rules do not have to be examined if it is a corollary of establishment by shareholding: Case C-196/04 Cadbury Schweppes, Case C-524/04 Thin Cap Group. The distinction is in whether there the shareholdings “enable the holder to have a definite influence on a company’s decisions and to determine its activities”: Case C-157/05 Holböck. In Case C-531/06 Italian pharmacies, both capital and establishment rules were examined.

Economic activity
The freedoms cannot be relied upon to object municipal restrictions prohibiting non-residents from cannabis shops, but the consequential loss in sales of non-alcoholic beverages and food can be challenged using services rules; such restriction of services freedom is “justified by the objective of combating drug tourism and the accompanying public nuisance”: C-137/09 Josemans.

Services “are normally provided for remuneration”. This is widely interpreted to include e.g. lottery and gambling: Schindler, C-338/04 Placanica. Grant of right to hunt in return for payment is an economic activity: Case C-70/09 Hengartner and Gasser.

Publicly-funded secondary technical education is excluded thence: Case 263/86 Humbel. “Conversely, courses given in an establishment of higher education which seeks to make an economic profit and which is financed essentially out of private funds, particularly out of payments made by students or their parents, do constitute services”: Case C-109/92 Wirth; see also Case C-76/05 Schwarz and Gootjes-Schwarz, Case C-318/05 German school fees.

Sport “is subject to [EU] law in so far as it constitutes an economic activity”: Case C-415/93 Bosman. But national selection does not in itself “constitute a restriction on the freedom to provide services”: C-191/97 Deliège.

Establishment “involves the actual pursuit of an economic activity through a fixed establishment in another Member State for an indefinite period”: Case C-221/89 Factortame II.

title: User:Kaihsu/IMlawA3


text:
User talk:Esmith1993/enes100/bridges

0/0/0 .. nothing to grade

10/5/0 ... no reference to where the graphic came from, do not want truss bridge built, want bridge to win a competition built that your team has been working on 1sfoerster 14:58, 5 December 2011 (UTC)

10/0 ... nothing to push the project forward .. saw the links to competitions 1sfoerster 15:14, 14 December 2011 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Esmith1993/enes100/bridges


text:
Talk:Engineering Projects/Bridges/Howard Community College/fall2011/501 DAS 3

90/100 points .. team poster is not original, source is not sited and has nothing to do with the project. 1sfoerster 15:26, 14 December 2011 (UTC)


text:
User talk:Cdiffendal7527/enes100/Rubberband gun

0/0/0 .. nothing to grade 1sfoerster 15:43, 21 November 2011 (UTC)

Very nice, seemed to properly outline what you decided to do  64.134.68.136 21:38, 25 November 2011 (UTC)

nice drawings man... keep up the good work, fahad68.84.0.28 05:04, 30 November 2011 (UTC)

10/5/30 ... I changed your week 1 to week 2 ... otherwise no points 1sfoerster 13:50, 28 November 2011 (UTC)

Nice page... could use a little more detail though ...  Mderrick4950 21:00, 4 December 2011 (UTC)

looks like you will be building another piece, judging from that pic. cant wait to see the full design. Fissbusta 07:04, 5 December 2011 (UTC)

0/0/0 ... don't see corey writing anything on the page .. see some links to pictures of drawings on wood and comment on personal page by another team member 1sfoerster 15:16, 5 December 2011 (UTC)

0/0/0 ... nothing to grade 1sfoerster 16:05, 14 December 2011 (UTC)


text:
User talk:Dkromer1996/enes100/drones

I had commented on this discussion page on Saturday but it was erased. The page looks good, so are you doing something similar to what Andy is doing? Dcaldero8983 17:22, 20 Novemeber 2011

10/10/10 ... 1sfoerster 19:46, 21 November 2011 (UTC)

have ordered deans ultra connectors for batteries .. and tamiya female large to tamiya small so the drone batteries can be charged on the fancy charger

Try to add your documentation for this week so i can be involved with what you are doing so far. Dcaldero8983 17:22, 27 Novemeber 2011

10/10/50 ... 1sfoerster 13:40, 28 November 2011 (UTC)

Try to get week 3 documentated Andyn6361 03:23, 5 December 2011 (UTC)

0/0/0 ... nothing to grade 1sfoerster 15:08, 5 December 2011 (UTC)

10/10/10 ... 1sfoerster 15:47, 14 December 2011 (UTC)

title: User talk:Dkromer1996/enes100/drones


text:
TESOL/Conversation strategies

Conversation strategies in ESL

 * Debate: Any type of discussion where partners have opposing views.
 * Speculation: Discuss a situation where the outcome is unknown.
 * Consensus: Partners must reach the same view.
 * Information gap: One partner must ask questions to discover some secret information, e.g. 20 questions.
 * Ranking or Rating: Arranging in some order (ranking) or assigning a value on some scale (rating).
 * Simulation or Role play: Acting out a situation as oneself (simulation) or as an imaginary character (role play).

These methods are especially useful for a broad range of mid-level students but can often be used for beginners or advanced students.

As always, key techniques to use with these are to:

 * scaffold
 * model
 * personalize
 * start with examples
 * introduce kick-start phrases if necessary

title: TESOL/Conversation strategies


text:
Dominant group/Origin

The origin of the term dominant group may have been from William Kirby in his book with William Spence: An Introduction to Entomology: or Elements of the Natural History of Insects, Volume IV published in 1826. But, an examination of relative synonyms has discovered an earlier date of 1820 for "dominant party". This suggests that "dominant group" is firmly established much before Darwin, perhaps as part of "natural theology", and that Darwin incorporated "dominant groups" into his theory of evolution by natural selection to replace a creationist approach to evolution of "dominant groups".

The relative synonyms of "dominant group" appear to date from earlier times suggesting that the concept behind "dominant group" has been around longer and represents perhaps an artifact in human evolution.

Searching alternative fields may reveal the two-word term in completely different contexts.

Research questions
Def. "a social group that controls the value system and rewards in a particular society" is called a dominant group.

 * What is the origin and first use of the term or its primordial concept and usage?

Dominant group
Examples from primary sources are to be used to prove or disprove each hypothesis. These can be collected per subject or in general.

 * 1) Accident hypothesis: dominant group is an accident of whatever processes are operating.
 * 2) Artifact hypothesis: dominant group may be an artifact of human endeavor or may have preceded humanity.
 * 3) Association hypothesis: dominant group is associated in some way with the original research.
 * 4) Bad group hypothesis: dominant group is the group that engages in discrimination, abuse, punishment, and additional criminal activity against other groups. It often has an unfair advantage and uses it to express monopolistic practices.
 * 5) Control group hypothesis: there is a control group that can be used to study dominant group.
 * 6) Entity hypothesis: dominant group is an entity within each field where a primary author of original research uses the term.
 * 7) Evolution hypothesis: dominant group is a product of evolutionary processes, such groups are the evolutionary process, produce evolutionary processes, or are independent of evolutionary processes.
 * 8) Identifier hypothesis: dominant group is an identifier used by primary source authors of original research to identify an observation in the process of analysis.
 * 9) Importance hypothesis: dominant group signifies original research results that usually need to be explained by theory and interpretation of experiments.
 * 10) Indicator hypothesis: dominant group may be an indicator of something as yet not understood by the primary author of original research.
 * 11) Influence hypothesis: dominant group is included in a primary source article containing original research to indicate influence or an influential phenomenon.
 * 12) Interest hypothesis: dominant group is a theoretical entity used by scholarly authors of primary sources for phenomena of interest.
 * 13) Metadefinition hypothesis: all uses of dominant group by all primary source authors of original research are included in the metadefinition for dominant group.
 * 14) Null hypothesis: there is no significant or special meaning of dominant group in any sentence or figure caption in any refereed journal article.
 * 15) Object hypothesis: dominant group is an object within each field where a primary author of original research uses the term.
 * 16) Obvious hypothesis: the only meaning of dominant group is the one found in Mosby's Medical Dictionary.
 * 17) Original research hypothesis: dominant group is included in a primary source article by the author to indicate that the article contains original research.
 * 18) Primordial hypothesis: dominant group is a primordial concept inherent to humans such that every language or other form of communication no matter how old or whether extinct, on the verge of extinction, or not, has at least a synonym for dominant group.
 * 19) Purpose hypothesis: dominant group is written into articles by authors for a purpose.
 * 20) Regional hypothesis: dominant group, when it occurs, is only a manifestation of the limitations within a region. Variation of those limitations may result in the loss of a dominant group with the eventual appearance of a new one or none at all.
 * 21) Source hypothesis: dominant group is a source within each field where a primary author of original research uses the term.
 * 22) Term hypothesis: dominant group is a significant term that may require a 'rigorous definition' or application and verification of an empirical definition.

Experimentation
Sampling: Google scholar, Wikipedia, Wikiversity, other Wikimedia sources and offline libraries are sampled for likely valuable examples.

So far the earliest occurrence of "dominant group" in an 1840 monograph on ants and beetles is a discovery using Google scholar with the search concepts: "1840" and "dominant group". The search begins at "1858" and proceeds backwards in time, examining the first two to three hundred returns for the date of publication.

Language searches use dominant group translated usually using Google Translate, plus 1800 or 1700, for example.

Other search engines in use are www.altavista.com, www.lycos.com, and www.yahoo.com.

Searches are conducted in specific subject areas where early publications are included: www.adsabs.harvard.edu, www.jstor.org, www.questia.com, and www.tandfonline.com.

A book or an article may contain a quote from an earlier work that includes dominant group.

Humanities
"The term 'humanities' includes, but is not limited to, the study and interpretation of the following: language, both modern and classical; linguistics; literature; history; jurisprudence; philosophy; archaeology; comparative religion; ethics; the history, criticism and theory of the arts; those aspects of social sciences which have humanistic content and employ humanistic methods; and the study and application of the humanities to the human environment with particular attention to reflecting our diverse heritage, traditions, and history and to the relevance of the humanities to the current conditions of national life." --National Foundation on the Arts and the Humanities Act, 1965, as amended.

The Division of Research Programs for the National Endowment for the Humanities encourages research and writing in all areas of the humanities, including the study of history, literature, philosophy, religion, and foreign cultures. Through grants to individual scholars and institutions, the division fosters work that enables Americans to understand the world.

What aspects of the origin of dominant group are considered to be part of the humanities?

Between 1853 and 1857 (the French Revolution and Napoleon): “The fact that a group is egoistic and dominant proves that it is well formed and that it approaches the make-up of a man.”

1899 (Human Progress): "While the human groups are many and diverse, they are conveniently combined in two categories: first, the natural or consanguineal or kinship group in which the unit is the ethnos; and second, the artificial or essentially social group in which the unit is the demos. The ethnos, or ethnic group, is the homologue of the varietal or specific group of animals; it is the dominant group in lower savagery, but its influence on human life wanes upward, to practically disappear in enlightenment except as retained in the structure of the family. The demos is the product of intelligence applied to the regulation of human affairs; it has no true homologue among animals; its importance waxes as that of the ethnos wanes from savagery through barbarism and civilization and thence into enlightenment."

Dominant and group
The two words "dominant" and "group" have far earlier origins. From JSTOR, url=http://www.jstor.org, the earliest occurrence of each is "dominant" 1672 and "group" ~1739. While earlier origins of both words may exist, "dominant group" is cuurently limited in its origin to ~1739 to present.

"Dominant" as an adjective has its origin in Middle French (MF) or Latin (L), from L dominant-, dominans, present participle (prp.) of dominari. From the Wikipedia article Middle French, Middle French "is a historical division of the French language that covers the period from (roughly) 1340 to 1611."

"Group" is from French groupe, in turn from Italian gruppo, of Germanic (Gmc) origin. From the Wikipedia article History of French: "Following a period of unification, regulation and purification or latinization, the French of the 17th to the 18th centuries is sometimes referred to as Classical French (français classique), although many linguists simply refer to French language from the 17th century to today as Modern French (français moderne)."

Associations
In the following excerpt, the two words are associated by the author toward the same or similar objects.

"[Tien-ti-huih] has been called by the Chinese, the three united, from being composed of the members of a sacred triad; viz. heaven, earth, and man, to whom equal adoration is offered, being all considered of equal dignity and rank; but to man, only after death, under the name of ancestors. Heaven and earth are worshipped as the father and mother of mankind. They are styled the three dominant powers, and supposed to exist in perfect harmony. There appears to be some mystic importance attached to the number three by the Chinese; it is related in the Peach Garden Record, that Chang-Shan afterwards entered the society, and made the fourth brother; still his name is rarely, if ever adduced. Three is the number also of the officials, or elder brethren, of the drops of blood shed during the inaugural rites, of their days of meeting during the month, and of the prescribed prostrations before the idol, viz. pae, kwei, and kow, bowing, kneeling, and placing the forehead in the dust; the last in some ceremonies is thrice repeated. The grand day is the ninth of the moon, equal to three times three. The secret manual signs are made with three fingers. The characters on some of the secret seals are grouped in triads. One of the smaller seals a, is in the form of a triangle. The symbol in the small seal b, appears to have been selected for its triune character, resembling the trisula of the Hindus, and three is generally the number of the personages forming the group in the picture worshiped by almost every Chinese."

Collocation
"In corpus linguistics, collocation defines a sequence of words or terms that co-occur more often than would be expected by chance. In phraseology, collocation is a sub-type of phraseme. An example of a phraseological collocation (from Michael Halliday ) is the expression strong tea. While the same meaning could be conveyed by the roughly equivalent powerful tea, this expression is considered incorrect by English speakers. Conversely, the corresponding expression for computer, powerful computers is preferred over strong computers. Phraseological collocations should not be confused with idioms although both are similar in that there is a degree of meaning present in the collocation or idiom that is not entirely compositional. With idioms, the meaning is completely non-compositional whereas collocations are mostly compositional."

Substitution restrictions
"We can say highly sophisticated, and we can say extremely happy. Both adverbs have the same lexical functions, that is adding the degree, or magnifying the impact of the adjectives (sophisticated, happy), However, they are not interchangeable. Still, other adverbs, such as very can replace both highly and extremely." .

Modified syntaxes
"Unlike the majority of idioms, collocations are subject to syntactic modification. For example, we can say effective writing and write effectively." .

For the term "dominant group", this may be "group dominantly". Another may be "group dominants", which has been shown to be a type of dominant group. See group of dominants.

Compound nouns
"Some words are often found together because they make up a compound noun, for example 'riding boots' or 'motor cyclist'." .

Syntactic relations
"Collocations can be in a syntactic relation".

Lexical relations
The "lexical relation" can be antonymy, or "in no linguistically defined relation." .

Key words
A collocation may be "a Key Word in Context (KWIC)".

Collocation processing
"The processing of collocations involves a number of parameters, the most important of which is the measure of association, which evaluates whether the co-occurrence is purely by chance or statistically significant. Due to the non-random nature of language, most collocations are classed as significant, and the association scores are simply used to rank the results. Commonly used measures of association include mutual information, t scores, and log-likelihood. "

Collocation definitions
"Rather than select a single definition, Gledhill proposes that collocation involves at least three different perspectives: (i) cooccurrence, a statistical view, which sees collocation as the recurrent appearance in a text of a node and its collocates,  (ii) construction, which sees collocation either as a correlation between a lexeme and a lexical-grammatical pattern, or as a relation between a base and its collocative partners and (iii) expression, a pragmatic view of collocation as a conventional unit of expression, regardless of form.  It should be pointed out here that these different perspectives contrast with the usual way of presenting collocation in phraseological studies. Traditionally speaking, collocation is explained in terms of all three perspectives at once, in a continuum:

 * ‘Free Combination’ ↔ ‘Bound Collocation’ ↔ ‘Frozen Idiom’".

Darwin's dominant groups
The term “dominant group” does not appear in Darwin’s 1859 book, “On the Origin of Species by Means of Natural Selection”. But the plural term “dominant groups” appears thirteen times. The earliest use of the phrase is on page 343, “The dominant species of the larger dominant groups tend to leave many modified descendants, and thus new sub-groups and groups are formed.”

"In 1831, ... [Darwin] had just completed his BA degree at Cambridge University in England. ... The voyage [on the Beagle] lasted from December 1831 to October 1836". "Darwin had been much impressed by Paley’s Natural Theology while a student at Cambridge; and his greatest achievement ultimately lay in providing a different explanation for the apparent design of all living beings." "He traveled with a copy of Charles Lyell’s pathbreaking summary of a new way of thinking about geological processes, Principles of Geology, published in 1830–1833. This book influenced Darwin greatly." In Lyell's book is the phrase "dominant influence", but "dominant group" does not appear.

Def. “[u]nder the many conditions of life which this world affords, any group which is numerous in individuals and species and is widely distributed, may properly be called dominant" [a dominant group]. [Letter 110. To W.H. Harvey, August, 1860]

Early dominant groups
"The Ants and the Staphylini have been supposed to represent each other in the tropical and temperate zones. In the temperate zone, and especially in our own country, the Staphylini are a dominant group, and the ants a secondary one."

Kirby's dominant groups
The system established by William Kirby as published in 1826 concerns the "geographical distribution of insects; their stations and haunts; seasons; times of action and repose." "Starting in 1822, Kirby and Spence published their four volumes of An Introduction to Entomology."

"Groups, according to their range, may be denominated either predominant, dominant, sub-dominant, or quiescent."

"M. Latreille has observed, that where the empire of Flora ceases, there also terminates that of Zoology2. Phytiphagous animals can only exist where there are plants; and those that are carnivorous and feed upon the former, must of necessity stop where they stop. Even the gnat, which extends its northern reign so highb, must cease at this limit; while, where vegetation is the richest and most abundant, there the animal productions, especially the insect, must be equally abundant. I call that, therefore, a predominant group, members of which are found in all the countries between these points, or from the limits of animal-depasturing vegetation in the polar regions to the line."

"There are other groups which, though their empire extends to the tropics, fall short of the polar circles: - these I call dominant groups."

"I call those subdominant groups, which either never enter the tropics, or those tropical ones whose range does not exceed 50° of N.L. in the old world, or 43° in the new."

Relative synonyms
The term "dominant group" is used in many subjects by authors to identify entities. The genera differentia for possible definitions of "dominant group" fall into the following set of orderable pairs:

'Orderable' means that any synonym from within the first category can be ordered with any synonym from the second category to form an alternate term (relative synonym) for "dominant group"; for example, "superior class", "influential sect", "master assembly", "most important arrangement", and "governing grouping". Further, any word which has its most or much more common usage within these categories may also form an alternate term, such as "ruling group", where "ruling" has its most common usage in category 739 and "group" is in category 61; or "dominant party", where "dominant" is in 171, and "party" is in 74.

Dominant party

 * 1820

"There was a violent war party, who wished all the resources of the State to be placed at the disposal of the national government; there was a peace party, composed of members of both parties, determined to put every obstacle in the way of the administration; while the Federalists generally regarded the declaration of war as an act of tyranny, and the measures of the dominant party as an infringement of State rights." [Bold added]

Most important interests

 * 1780

"Even the actual promoters of the most important interests of mankind have seldom anticipated, in idea, the progressive consequences of their own plans."

The dominants

 * 1757

“so sind solche entweder tonische Noten, Dominanten, oder Unterdominanren, und die Dominanten können simple oder tonische Dominanten seyn.”

Upper departments

 * 1780

"For the impression of the commercial arts is often conspicuous in the upper departments of life, before it reaches those of inferior condition; but the circle gradually widens."

Bokmål
dominerende gruppe

Český
dominantní skupina

1925: Portion of a text, probably with a few errors: "oznacovani byvají mravenci jako ov1 ádajíсí, dominantní skupina zivocisná, neb ninezenéji jakc dominantní skupina hmyzová, jez za jistych okolností skoro se jaksi stává pánem pfírody, aspoñ v jistém smyslu, v omezeném okruhu."

Dansk
dominerende gruppe

1908: "Den talrigste og absolut dominerende Gruppe er tilstede i et Antal af ca. 90-95 pCt."

Deutsch
dominante Gruppe

Ελληνικά
κυρίαρχη ομάδα

Español
Grupo dominante

Euskara
dominante talde

Français
groupe dominant

1899: "Il est différent dans une société purement familiale, dans une société fondée sur la conquête avec un groupe dominant et un groupe dominé, et dans une société établie sous le régime de castes."

1847: "L'individu dominant de tout groupe, ou le groupe dominant, pivotal de toute série, à pour place naturelle le centre."

Italiano
Gruppo dominante

日本語
支配的なグループ

支配集団

Nederlands
dominante groep

Polski
grupą dominującą

Pусский
доминирующей группы

Suomi
hallitseva ryhmä

Türkçe
Baskın grubu

Hypotheses

 * 1) Dominant group has an origin, probably much earlier than patrician class.

Such proof of concept has been demonstrated for dominant group, but not necessarily for its many relative synonyms.

title: Dominant group/Origin


text: File:IMG 066143.JPG

title: File:IMG 066143.JPG


text: File:Pea1.f11.circle.area.approximated.svg


text:
User:Egm6321.f11.team1/report7

=R*7.1 Infinitesimal Length in Spherical Coordinates= Question from 39-1: Given: A infinitesimal length in spherical coordinates. Find: Show that the infinitesimal length ds in (2) p. 38-6 can be written in spherical coordinates as follows. $$ds^2 = 1 \cdot dr^2 + r^2 d\theta^2 + r^2(\cos\theta)^2\, d \varphi^2$$ $$\displaystyle (Equation\;7.1.1)$$

From lecture notes [[media:pea1.f11.mtg39.djvu|Mtg 39]]

Solution
=

The key is to start with equation (1) on 38-5

 $$\mathbf{ds} = dx_i \mathbf{e}_i \Rightarrow \ ds^2= \mathbf{ds} \cdot \mathbf{ds} = (dx_i \mathbf{e}_i) \cdot (dx_j \mathbf{e}_j) = dx_i\, dx_j(\mathbf{e}_i \cdot \mathbf{e}_j)$$ $$\displaystyle (Equation\;7.1.2)$$

Next, note the following expressions.

$$\mathbf{e}_i \cdot \mathbf{e}_j = \delta_{ij}$$ $$\delta_{ij} := \begin{cases}1, & \text{for} i = j \\ 0, & \text{for} i \ne j \end{cases}$$

The form of the infinitesimal length ds is expressed in Cartesian coordinates. $$ds^2 = dx_i dx_i = \sum_{i=1}^3(dx_i)^2$$ This can be rewritten in the following form, which is the key for derivation steps, which are rigorous with trigonometric identities. $$ds^2 = dx_1^2 + dx_2^2 + dx_3^2$$ $$\displaystyle (Equation\;7.1.3)$$ The spherical coordinates can be utilized. Simply identify the appropriate identities. Recall that we are using the "astronomical" coordinate system. $$x = r\cos {\theta} \cos {\phi} = \xi_1 \cos{\xi_2}\cos{\xi_3}$$ $$y = r\cos {\theta} \sin {\phi} = \xi_1 \cos{\xi_2} \sin{\xi_3}$$ $$z = r\sin {\theta} = \xi_1 \sin{\xi_2}$$ Now, make the trigonometric substitutions for each term in 7.1.3.

$$ds^2 = (dr\cos{\theta} \cos{\phi} - (r\sin{\theta} \cos{\phi} d\theta + r\cos{\theta} \sin{\phi} d\phi))^2 +(dr\cos{\theta} \sin{\phi} - (r\sin{\theta} \sin{\phi} d\theta - r\cos{\theta} \cos{\phi} d\phi))^2 + (dr\sin{\theta} + r\cos{\theta} d\theta)^2$$ In such long math equations, simple variable substitutions allow easier management of squared terms (FOIL). $$\alpha = (r\sin{\theta} \cos{\phi} d\theta + r\cos{\theta} \sin{\phi} d\phi)$$ $$\beta = (r\sin{\theta} \sin{\phi} d\theta - r\cos{\theta} \cos{\phi} d\phi)$$ The substitutions then give the shortened form, which allows derivation of the squared terms. $$ds^2 = (dr\cos{\theta} \cos{\phi} - \alpha)^2 +(dr\cos{\theta} \sin{\phi} - \beta)^2 + (dr\sin{\theta} + r\cos{\theta} d\theta)^2$$ Simply apply algebraic FOIL method to the equation above and get the terms below.
$$ds^2 = (dr\cos{\theta} cos{\phi})^2 - 2\alpha dr\cos{\theta} \cos{\phi} + \alpha^2 + (dr\cos{\theta} \sin{\phi})^2 - 2\beta dr\cos{\theta} \sin{\phi} + \beta^2$$ The algebraic manipulation is long, but proper addition and subtraction eliminate unnecessary terms. The key is to appply trigonometric identities and grouping with the identity of $$\sin^2{x} + \cos^2{x} = 1$$.
$$ds^2 = (dr^2\cos^2{\theta}(cos^2{\phi} + \sin^2{\phi}) - 2\alpha dr \cos{\theta} \cos{\phi} + \alpha^2 - 2\beta dr\cos{\theta} \sin{\phi} + \beta^2 + dr^2 \sin{\theta}^2 + 2rdr \sin{\theta} \cos{\theta}d\theta + r^2 \cos^2{\theta} d{\theta}^2$$
$$ds^2 = dr^2\cos^2{\theta} + dr^2\sin^2{theta} - 2\alpha dr\cos{\theta} \cos{\phi} + \alpha^2 - 2\beta dr\cos{\theta} \sin{\phi} + \beta^2 + 2rdr\sin{\theta} \cos{\theta}d\theta + r^2\cos^2{\theta} d{\theta}^2$$
$$ds^2 = dr^2 - 2\alpha dr\cos{\theta} \cos{\phi} + \alpha^2 - 2\beta dr\cos{\theta} \sin{\phi} + \beta^2 + 2rdr\sin{\theta} \cos{\theta}d\theta + r^2\cos^2{\theta} d{\theta}^2 $$
$$\displaystyle (Equation\;7.1.4)$$ The next set of steps involves solutions utilizing our substitutions of $$\alpha$$ and $$\beta$$. Recall the "inner" and "outer" terms from the FOIL multiplications. Each of those terms must now be expanded and simplified.

$$A = - 2\alpha dr\cos{\theta} \cos{\phi}$$
$$A = - 2rdr(\sin{\theta}\cos{\theta}\cos^2{\phi}d\theta + \cos^2{\theta} \cos{\phi} \sin{\phi}d{\phi})$$

$$B = - 2\beta dr\cos{\theta} \sin{\phi}$$
$$B = - 2rdr(\sin{\theta} \cos{\theta} \sin^2{\phi} d\phi - \cos^2{\theta} \cos{\phi} \sin{\phi} d\phi)$$
$$A + B = -2rdr \sin{\theta}\cos{\theta}(\cos{\phi}^2 + \sin^2{\phi})d\theta = -2rdr \sin{\theta} \cos{\theta}d\theta$$

Recall equation 7.1.4. The terms A and B can be put back into the equation to get the simplification.
$$ds^2 = dr^2 + A + \alpha^2 + B + \beta^2 + 2rdr\sin{\theta} \cos{\theta}d\theta + r^2\cos^2{\theta} d{\theta}^2 $$
$$ds^2 = dr^2 - 2rdr \sin{\theta} \cos{\theta} d\theta + \alpha^2 + \beta^2 + 2rdr\sin{\theta} \cos{\theta}d\theta + r^2\cos^2{\theta} d{\theta}^2 $$ Next, the terms for $${\alpha}^2 + {\beta}^2$$ must be expanded.
$${\alpha}^2 = r^2 \sin^2{\theta} \cos^2{\phi} d{\theta}^2 + 2r^2 \sin{\theta} \cos{\theta} \cos{\phi} \sin{\phi} d\theta d\phi r^2 \cos^2{\theta} \sin^2{\phi} d{\phi}^2$$
$${\beta}^2 = r^2 \sin^2{\theta} \sin^2{\phi} d{\theta}^2 - 2r^2 \sin{\theta} \cos{\theta} \cos{\phi} \sin{\phi} d\theta d\phi r^2 \cos^2{\theta} \cos^2{\phi} d{\phi}^2$$
$${\alpha}^2 + {\beta}^2 = r^2\sin^2{\theta} d{\theta}^2 (\cos^2{\phi} + \sin^2{\phi}) + r^2 \cos^2{\theta}(\sin^2{\phi} + \cos^2{\phi})d{\phi}^2$$
$${\alpha}^2 + {\beta}^2 = r^2\sin^2{\theta} d{\theta}^2 + r^2 \cos^2{\theta} d{\phi}^2$$ Moving along, all inner and outer terms from the FOIL calculation are added and simplified below.

$$ds^2 = dr^2 - rdr \sin{\theta} \cos{\theta} d\theta + r^2 \cos^2{\theta} d{\theta}^2 + r^2 \sin^2{\theta} d{\theta}^2 + r^2 \cos^2{\theta} d{\phi}^2 + 2rdr \sin{\theta} \cos{\phi} d\theta - 2rdr \sin{\theta} \cos{\theta} d\theta$$ Finally, after addition and subtracting terms above, the solution is derived in the desired form to solve the problem.
$$ds^2 = dr^2 + r^2 d{\theta}^2 + r^2 \cos^2{\theta} d{\phi}^2$$ Each coordinate line has a tangent vector with a magnitude of h.
$$dr^2 = 1 * dr^2 = {h_1}^2{\xi_1}^2$$
$${h_1}^2 = 1$$
$${h_1} = 1$$ Similarly, the other h parameters can be found for each variable.
$$r^2 d{\theta}^2 = {h_2}^2{\xi_2}^2$$
$${h_2}^2 = r^2$$
$${h_2} = r$$
$$r^2 \cos^2{\theta} d{\phi}^2 = {h_3}^2{\xi_3}^2$$
$${h_3}^2 = r^2 \cos^2{\theta}$$
$${h_3} = r\cos{\theta}$$

=R*7.2- Laplacian in Cylindrical Coordinate System=

Given
$$\begin{align} & {{x}_{1}}=x=r\cos \phi ={{\xi }_{1}}\cos {{\xi }_{2}} \\ & {{x}_{2}}=y=r\sin \phi ={{\xi }_{1}}\sin {{\xi }_{2}} \\ & {{x}_{3}}=z={{\xi }_{3}} \\ \end{align}$$

Find
$$\begin{align} & \text{(1) Express }\left\{ d{{x}_{i}} \right\} \text{ in terms of } \left\{ d{{\xi }_{i}} \right\} \text{ and }\left\{ {{\xi }_{i}} \right\} \\ & \text{(2) Find } d{{s}^{2}}=\sum\limits_{i=1}^{3}{dx_{i}^{2}}=\sum\limits_{i=1}^{3}{h_{i}^{2}\cdot d\xi _{i}^{2}} \text{ and express } \left\{ {{h}_{i}} \right\}\text{ in terms of } \left\{ {{\xi }_{i}} \right\} \\ & \text{(3) Find Laplacian } \Delta u \\ & \text{(4) Obtain Bessel Equation by solving }\Delta u =0 \\ \end{align}$$

Solution
$$\displaystyle ds^2=\sum_{k=1}^3(h_k)^2(d\xi_k)^2= \sum_{i=1}^{3}(dx_i)^2 $$ $$\displaystyle dx_i=\frac{\partial x_i}{\partial \xi_1} d\xi_1+\frac{\partial x_i}{\partial \xi_2} d\xi_2+\frac{\partial x_i}{\partial \xi_3} d\xi_3 $$ $$\displaystyle dx_1 =\cos \xi_2 d\xi_1-\xi_1 \sin \xi_2 d\xi_2+(0) d\xi_3 $$ $$\displaystyle dx_2 =\sin \xi_2 d\xi_1+\xi_1 \cos \xi_2 d\xi_2+(0) d\xi_3 $$ $$\displaystyle dx_3 =(0) d\xi_1+(0) d\xi_2+(1) d\xi_3 $$

Part 2

$$\displaystyle ds^2=(\cos \xi_2 d\xi_1-\xi_1 \sin \xi_2 d\xi_2)^2 + (\sin \xi_2 d\xi_1+\xi_1 \cos \xi_2 d\xi_2)^2 + (d\xi_3)^2=(d\xi_1)^2+\xi_1^2 (d \xi_2)^2+(d\xi_3)^2 = (h_1)^2(d\xi_1)^2 + (h_2)^2(d\xi_2)^2 + (h_3)^2(d\xi_3)^2 $$ $$\displaystyle ds^2=dr^2+r^2d \theta^2 + dz^2 $$ Thus, $$\displaystyle h_1(\xi)=1 $$ $$\displaystyle h_2(\xi)=r=\xi_1 $$ $$\displaystyle h_3(\xi)=1 $$

Part 3 $$\displaystyle \Delta u = \frac{1}{h_1h_2h_3}\sum_{i=1}^{3} \frac{\partial}{\partial \xi_i}\left [ \frac{h_1h_2h_3}{h_i^2}\frac{\partial u }{\partial \xi_i} \right] $$ Where $$\displaystyle h_1h_2h_3=\xi_1=r $$ So, $$\displaystyle \Delta u = \frac{1}{\xi_1} \left [\frac{\partial}{\partial \xi_1} \left (\frac{\xi_1}{1^2} \frac{\partial u }{\partial \xi_1}\right ) +\frac{\partial}{\partial \xi_2} \left (\frac{\xi_1}{\xi_1^2}\frac{\partial u }{\partial \xi_2}\right )+\frac{\partial}{\partial \xi_3} \left ( \frac{\xi_1}{1^2}\frac{\partial u }{\partial \xi_3} \right ) \right ] =\frac{1}{\xi_1} \frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial u }{\partial \xi_1}\right ) +\frac{1}{\xi_1^2}\frac{\partial^2 u }{\partial \xi_2^2}+\frac{\partial^2 u }{\partial \xi_3^2} $$

part 4

$$\displaystyle \Delta u = \frac{1}{\xi_1} \frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial u }{\partial \xi_1}\right ) +\frac{1}{\xi_1^2}\frac{\partial^2 u }{\partial \xi_2^2}+\frac{\partial^2 u }{\partial \xi_3^2}=0 $$ $$\displaystyle u = X(\xi_1)Y(\xi_2)Z(\xi_3) $$ $$\displaystyle \frac{Y Z}{\xi_1} \frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial X }{\partial \xi_1}\right ) +\frac{X Z }{\xi_1^2}\frac{\partial^2 Y }{\partial \xi_2^2}+X Y \frac{\partial^2 Z }{\partial \xi_3^2}=0 $$ divide through by  $$\displaystyle XYZ $$ $$\displaystyle \frac{1}{X \xi_1} \frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial X }{\partial \xi_1}\right ) +\frac{1}{Y\xi_1^2}\frac{\partial^2 Y }{\partial \xi_2^2}+\frac{1}{Z} \frac{\partial^2 Z }{\partial \xi_3^2}=0 $$ Assuming that $$\displaystyle \frac{1}{Z} \frac{\partial^2 Z }{\partial \xi_3^2}=A $$ $$\displaystyle \frac{1}{X \xi_1} \frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial X }{\partial \xi_1}\right ) +\frac{1}{Y\xi_1^2}\frac{\partial^2 Y }{\partial \xi_2^2}+A=0 $$ multiplying through by $$\displaystyle \xi_1^2 $$ $$\displaystyle \frac{\xi_1}{X } \frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial X }{\partial \xi_1}\right ) +\frac{1}{Y}\frac{\partial^2 Y }{\partial \xi_2^2}+A \xi_1^2 =0 $$

assumeing for second term $$\displaystyle \frac{1}{Y}\frac{\partial^2 Y }{\partial \xi_2^2}=-B $$ $$\displaystyle \frac{\xi_1}{X } \frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial X }{\partial \xi_1}\right ) -B+A \xi_1^2 =0 $$ multiplying through by $$\displaystyle X $$ $$\displaystyle \xi_1\frac{\partial}{\partial \xi_1} \left (\xi_1 \frac{\partial X }{\partial \xi_1}\right ) +(A \xi_1^2-B)X =0 $$ The Original equation is following that $$\displaystyle \xi_1^2 \frac{\partial^2 X }{\partial \xi_1^2}+\xi_1 \frac{\partial X }{\partial \xi_1}+(A \xi_1^2-B)X =0 $$

Lets define $$\displaystyle \xi_1 =x, \,\,\,\,\, X =y $$ Thus, the above equations is following that $$\displaystyle x^2 y''+xy'+(A x^2-B)y =0 $$

=R*7.3- Laplacian in Spherical Coordinate System with Math/Phy Convention=

Given
The Laplacian Equation is given in general form - $$\Delta u$$.

Find
The expression of Laplacian in spherical coordinates for math/physics convention. From lecture notes [[media:pea1.f11.mtg41.djvu|Mtg 41]]

Solution
The approach is to derive the Laplacian in spherical coordinates with the astronomical convention.
$$(\xi_1, \xi_2, \xi_3) = (r, \theta, \phi)$$ Then we will convert the final form to the math/physics equation using the standard transformation identity. From meeting 39, the general equation for the Laplacian in curvilinear coordinates is given.
$$\Delta{u} = \frac{1}{h_1 h_2 h_3} \sum^3_{i=1} \frac{\partial}{\partial \xi_i} \left[\frac{h_1 h_2 h_3}{(h_i)^2} \frac{\partial u}{\partial \xi_i} \right]$$
$$\displaystyle (Equation\;7.3.1)$$

The spherical coordinates from R*7.1 can be utilized. Recall the appropriate identities using the "astronomical" coordinate system.
$$x = r\cos {\theta} \cos {\phi} = \xi_1 \cos{\xi_2}\cos{\xi_3}$$
$$y = r\cos {\theta} \sin {\phi} = \xi_1 \cos{\xi_2} \sin{\xi_3}$$
$$z = r\sin {\theta} = \xi_1 \sin{\xi_2}$$ We derived the solution in R*7.1 that can be reapplied to R*7.3.
$$ds^2 = dr^2 + r^2 d{\theta}^2 + r^2 \cos^2{\theta} d{\phi}^2$$ Each coordinate line has a tangent vector with a magnitude of h.
$$dr^2 = 1 * dr^2 = {h_1}^2{\xi_1}^2$$
$${h_1}^2 = 1$$
$${h_1} = 1$$
$$r^2 d{\theta}^2 = {h_2}^2{\xi_2}^2$$
$${h_2}^2 = r^2$$
$${h_2} = r$$
$$r^2 \cos^2{\theta} d{\phi}^2 = {h_3}^2{\xi_3}^2$$
$${h_3}^2 = r^2 \cos^2{\theta}$$
$${h_3} = r\cos{\theta}$$ Based on the identities derived in R*7.1, the following expression can be utilized for the Laplacian equation.
$${h_1}*{h_2}*{h_3} = 1 * r * r\cos{\theta}$$
$${h_1}{h_2}{h_3} = r^2\cos{\theta}$$ The Laplacian has three terms for the summation in sigma notation i= 1, 2, 3. Each must be derived separately and summed based on the identities derived from R*7.1. The total is multiplied by $$({h_1}{h_2}{h_3})^-1$$. Before the latter is applied, let us derive each term for i = 1, 2, and 3 below.
$${h_1} = 1$$
$$d\xi_1 = dr$$
$$\partial {\xi_1} = \partial r$$
$$\frac{\partial}{\partial \xi_1} \left[\frac{h_1 h_2 h_3}{(h_1)^2} \frac{\partial u}{\partial \xi_1} \right] = \frac{\partial}{\partial r} \left[\frac{r^2 \cos \theta}{(1)^2} \frac{\partial u}{\partial r} \right]$$ Next, we derive the 2nd term.
$${h_2} = r$$
$$d\xi_2 = d\theta$$
$$\partial {\xi_2} = \partial {\theta}$$
$$\frac{\partial u}{\partial \xi_2} \left[\frac{h_1 h_2 h_3}{(h_2)^2} \frac{\partial u}{\partial \xi_2} \right] = \frac{\partial}{\partial \theta} \left[\frac{r^2 \cos \theta}{(r)^2} \frac{\partial u}{\partial \theta} \right]$$

Moving along, we derive the 3rd term.
$${h_3} = r\cos{\theta}$$
$$d\xi_3 = d\phi$$
$$\partial {\xi_3} = \partial {\phi}$$
$$\frac{\partial u}{\partial \xi_3} \left[\frac{h_1 h_2 h_3}{(h_3)^2} \frac{\partial u}{\partial \xi_3} \right] = \frac{\partial}{\partial \phi} \left[\frac{r^2 \cos \theta}{(r \cos{\theta})^2} \frac{\partial u}{\partial \phi} \right]$$ Finally, sum all three terms and multiply each by $$({h_1}{h_2}{h_3})^{-1}$$. Equation 7.3.1 is repeated again for clarity.
$$\Delta{u} = \frac{1}{h_1 h_2 h_3} \sum^3_{i=1} \frac{\partial}{\partial \xi_i} \left[\frac{h_1 h_2 h_3}{(h_i)^2} \frac{\partial u}{\partial \xi_i} \right]$$ Simply sum and multiply appropriate terms for the Laplacian.
$$\Delta{u} = \frac{1}{r^2 \cos{\theta}}[\frac{\partial}{\partial r} \left[\frac{r^2 \cos{\theta}}{(1)^2} \frac{\partial u}{\partial r} \right] + \frac{\partial}{\partial \theta} \left[\frac{r^2 \cos \theta}{(r)^2} \frac{\partial u}{\partial \theta} \right] + \frac{\partial}{\partial \phi} \left[\frac{r^2 \cos \theta}{(r \cos{\theta})^2} \frac{\partial u}{\partial \phi} \right]]$$ From analysis, the equation can be factored with the following terms: $$r$$ and $$\cos{\theta}$$.
$$\Delta u = \frac{1}{r^2}\frac{\partial}{\partial r} \left(r^2 \frac{\partial u}{\partial r}\right) + \frac{1}{r^2 \cos^2\theta} \frac{\partial^2 u}{\partial \phi^2} + \frac{1}{r^2 \cos \theta} \frac{\partial}{\partial \theta} \left(\cos \theta \frac{\partial u}{\partial \theta} \right)$$ Now, this equation must be converted to the math/physics convention. The following identities can be utilized.
$$(\xi_1, \xi_2, \xi_3) = (r, \bar \theta, \phi)$$
$$\bar \theta := \frac{\pi}{2} - \theta$$ In order to solve the Laplacian for the math/physics convention, the following two identities are utilized.
$$\partial \theta = \partial {\bar \theta}$$
$$\cos{\theta} = \cos{\frac{\pi}{2} - {\bar \theta}} = \cos{\frac{\pi}{2}} \cos{\bar \theta} + \sin{\frac{\pi}{2}} \sin{\bar \theta} = \sin{\bar \theta}$$ Therefore, simply make the appropriate substitutions of $$\partial \theta = \partial \bar \theta$$ and $$\cos{\theta} = \sin{\bar \theta}$$.
$$\Delta u = \frac{1}{r^2}\frac{\partial}{\partial r} \left(r^2 \frac{\partial u}{\partial r}\right) + \frac{1}{r^2 \sin^2{\bar \theta}} \frac{\partial^2 u}{\partial \phi^2} + \frac{1}{r^2 \sin {\bar \theta}} \frac{\partial}{\partial {\bar \theta}} \left(\sin{\bar \theta} \frac{\partial u}{\partial {\bar \theta}} \right)$$

= R*7.4 Laplacian In Elliptic Coordinates =

Given
See wikipedia reference of ellipitic coordinates.

Laplacian operator:

 * $$\Delta u=\frac{1}{h_1h_2h_3}\sum^3_{i=3}\frac{\partial}{\partial\xi_i}\left[\frac{h_1h_2h_3}{(h_i)^2}\frac{\partial u}{\partial\xi_i}\right]$$

== Find ==

Verify the Laplacian in elliptic coordinates:

 * $$\nabla^2u=\frac{1}{a^2(\sinh^2\mu+\sin^2\nu)}\left(\frac{\partial^2u}{\partial\mu^2}+\frac{\partial^2u}{\partial\nu^2}\right)$$

Solution
Using the reference listed above, we find that

$$\displaystyle \xi_1=\mu$$

$$\displaystyle\xi_2=\nu$$

$$\displaystyle h_1=h_2=a\sqrt{\sinh^2\mu+\sin^2\nu}$$

The reference does not give a derivation for each magnitude h of the tangential vector to the coordinate line. However, team 1 provides a derivation here based on class principles. The key is to define each variable with its 2nd and 3rd derivatives for the infinitesimal summation of ds.
$$x_1 = x = a\cosh{\mu} \cos{\nu}$$
$$dx_1 = a(\sinh{\mu} \cos{\nu}d\mu - \cosh{\mu} \sin{\nu}d\nu$$
$${dx_1}^2 = a^2 \sinh^2{\mu} \cos^2{\nu}du^2 - 2a^2 \sinh{\mu} \cos{\nu} \cosh{\mu} \sin{\nu} d\mu d\nu + a^2 \sinh^2{\mu} ]cos^2{\nu}d{\nu}^2$$
$$x_2 = x = a\sinh{\mu} \sin{\nu}$$
$$dx_2 = a(\cosh{\mu} \sin{\nu}d\mu + \sinh{\mu} \cos{\nu}d\nu$$
$${dx_2}^2 = a^2 \cosh^2{\mu} \sin^2{\nu} du^2 + 2a^2 \sinh{\mu} \cos{\nu} \cosh{\mu} \sin{\nu} d\mu d\nu + a^2 \sinh^2{\mu} ]cos^2{\nu}d{\nu}^2$$ Sum all terms to get ds squared.
$$ds^2 = {dx_1}^2 + {dx_2}^2$$
$$ds^2 = a^2 \sinh^2{\mu} \cos^2{\nu} du^2 - 2a^2 \sinh{\mu} \cos{\nu} \cosh{\mu} \sin{\nu} d\mu d\nu + a^2 \sinh^2{\mu}]cos^2{\nu}d{\nu}^2 + a^2 \cosh^2{\mu} \sin^2{\nu} du^2 + 2a^2 \sinh{\mu} \cos{\nu} \cosh{\mu} \sin{\nu} d\mu d\nu + a^2 \sinh^2{\mu} ]cos{\nu}^2d{\nu}^2$$ Add all terms to simplify - note +/- signs. Then group by similar variables.
$$ds^2 = a^2[( \sinh^2{\mu} \cos^2{\nu} + \cosh^2{\mu} \sin^2{\nu})d{\mu}^2 + (\cosh^2{\mu} \sin^2{\nu} + \sinh^2{\mu} \cos^2{\nu})d{\nu}^2]$$ Substitute the following hyperbolic identity: $$\cosh^2{\mu} = 1 + \sinh^2{\mu}$$. The simplification progresses below.
$$ds^2 = a^2[( \sinh^2{\mu} \cos^2{\nu} + \sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu})d{\mu}^2 + (\sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu} + \sinh^2{\mu} \cos^2{\nu})d{\nu}^2]$$ Next, the standard trigonometric subsitution can be applied: $$\cos^2{x} = 1 - \sin^2{x}$$. This leads to the next simplification.
$$ds^2 = a^2[( \sinh^2{\mu} ( 1 - \sin^2{\nu}) + \sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu})d{\mu}^2 + (\sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu} + \sinh^2{\mu} (1 - \sin^2{\nu}))d{\nu}^2]$$
$$ds^2 = a^2[( \sinh^2{\mu} ( 1 - \sin^2{\nu}) + \sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu})d{\mu}^2 + (\sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu} + \sinh^2{\mu} (1 - \sin^2{\nu}))d{\nu}^2]$$
$$ds^2 = a^2[( \sinh^2{\mu} ( 1 - \sin^2{\nu}) + \sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu})d{\mu}^2 + (\sin^2{\nu} + \sinh^2{\mu} \sin^2{\nu} + \sinh^2{\mu} (1 - \sin^2{\nu}))d{\nu}^2]$$
$$ds^2 = a^2[( \sinh^2{\mu} + \sin^2{\nu})d{\mu}^2 + (\sin^2{\nu} + \sinh^2{\mu})d{\nu}^2]$$
$$ds^2 = {h_1}^2{\xi_1}^ + {h_2}^2{\xi_2}^2 = a^2[( \sinh^2{\mu} + \sin^2{\nu})d{\mu}^2 + (\sin^2{\nu} + \sinh^2{\mu})d{\nu}^2]$$ Therefore, the h parameters are derived below.
$${h_1}^2 = {h_2}^2 = a^2(\sinh^2{\mu} + \sin^2{\nu})$$
$$h_1 = h_2 = a\sqrt{(\sinh^2{\mu} + \sin^2{\nu})}$$

Therefore, using the definition of Laplacian operator in the above section,

$$\nabla^2u=\Delta u=\frac{1}{h_1h_2}\left[\frac{\partial}{\partial\xi_1}\left(\frac{h_1h_2}{(h_1)^2}\frac{\partial u}{\partial\xi_1}\right)+\frac{\partial}{\partial\xi_2}\left(\frac{h_1h_2}{(h_2)^2}\frac{\partial u}{\partial\xi_2}\right)\right]$$

$$\nabla^2u=\frac{1}{a^2(\sinh^2\mu+\sin^2\nu)}\left[\frac{\partial}{\partial\mu}\left((1)\frac{\partial u}{\partial\mu}\right)+\frac{\partial}{\partial\nu}\left((1)\frac{\partial u}{\partial\nu}\right)\right]$$

Therefore we arrive at our solution.

= R7.5 Laplacian In Parabolic Coordinates =

Given
See wikipdia reference of parabolic coordinates.

Laplacian operator:

 * $$\Delta u=\frac{1}{h_1h_2h_3}\sum^3_{i=3}\frac{\partial}{\partial\xi_i}\left[\frac{h_1h_2h_3}{(h_i)^2}\frac{\partial u}{\partial\xi_i}\right]$$

== Find ==

Verify the Laplacian in parabolic coordinates:

 * $$\nabla^2u=\frac{1}{\mu^2+\nu^2}\left(\frac{\partial^2u}{\partial\mu^2}+\frac{\partial^2u}{\partial\nu^2}\right)$$

Solution
Using the reference listed above, we find that

$$\displaystyle \xi_1=\sigma$$

$$\displaystyle\xi_2=\tau$$

$$\displaystyle h_1=h_2=\sqrt{\sigma^2+\tau^2}$$

The reference did not give a derivation for each value of h. However, our team 1 will give a brief derivation here. The form of the infinitesimal length ds is expressed in parabolic coordinates.
$$ds^2 = dx_i dx_i = \sum_{i=1}^3(dx_i)^2$$ This can be rewritten in the following form, which is the key for derivation steps with parabolic coordinates in two dimensions.
$$ds^2 = dx_1^2 + dx_2^2$$
$$\displaystyle (Equation\;7.5.1)$$ The key is to identify the proper partial derivatives for 7.5.1. There are two variables for parabolic coordinates, so ds must include partial deriviates for each: $$\sigma$$ and $$\tau$$.
$$ x_1 = \sigma*\tau$$
$$ dx_1 = d\sigma*\tau + d\tau*\sigma$$
$$ x_2 = {\frac{1}{2}}({\tau}^2 - {\sigma}^2)$$
$$ dx_2 = \tau*d\tau - \sigma*d\sigma$$ Now, square each term and add below.
$$ {dx_1}^2 + {dx_2}^2 = {d\sigma*\tau}^2 + 2\tau \sigma d\sigma d\tau + {\sigma*d\tau}^2 + {\tau*d\tau}^2 - 2\tau \sigma d\sigma d\tau + {\sigma*d\sigma}^2$$ By rearranging the terms above, the values of each h can be determined.
$$ {dx_1}^2 + {dx_2}^2 = ({\tau}^2 + {\sigma}^2){d\sigma}^2 + ({\tau}^2 + {\sigma}^2){d\tau}^2 = {h_1}^2{d\sigma}^2 + {h_2}^2{d\tau}^2$$ This gives the identity we need to derive each value of h.
$$ {h_1}^2 = {h_2}^2 = ({\tau}^2 + {\sigma}^2)$$
$$ h_1 = h_2 = \sqrt{{\tau}^2 + {\sigma}^2}$$

I will use the following definitions to match the syntax given in the problem.

$$\displaystyle \mu:=\sigma$$

$$\displaystyle \nu:=\tau$$

Therefore, using the definition of Laplacian operator in the above section,

$$\nabla^2u=\Delta u=\frac{1}{h_1h_2}\left[\frac{\partial}{\partial\xi_1}\left(\frac{h_1h_2}{(h_1)^2}\frac{\partial u}{\partial\xi_1}\right)+\frac{\partial}{\partial\xi_2}\left(\frac{h_1h_2}{(h_2)^2}\frac{\partial u}{\partial\xi_2}\right)\right]$$

$$\nabla^2u=\frac{1}{\mu^2+\nu^2}\left[\frac{\partial}{\partial\mu}\left((1)\frac{\partial u}{\partial\mu}\right)+\frac{\partial}{\partial\nu}\left((1)\frac{\partial u}{\partial\nu}\right)\right]$$

Therefore we arrive at our solution.

=R*7.6 - Verify Legendre Polynomials 0 through 4 =

Find
Verify that the first five Legendre Polynomials

= R*7.7 Find the separated equation for the Laplace Equation in Parabolic coordinates= == Given == The Laplacian in parabolic coordinates given by
 * {| style="width:100%" border="0" align="left"

$$
 * $$\displaystyle \nabla^2 u=\frac{1}{\mu^2+\nu^2}\left(\frac{\partial^2 u}{\partial \mu^2}+\frac{\partial^2 u}{\partial \nu^2}\right)$$
 *
$$\displaystyle (Equation\;7.7.1)
 *
$$\displaystyle (Equation\;7.7.1)
 * }
 * }

Find
Find the separated equation for the Laplace equation in Pararbolic coordinates.

Solution
Separation of variables: $$\displaystyle u(\mu,\nu)=U(\mu)V(\nu)$$ Substituting it into Equation (7.7.1), $$\displaystyle \Delta u=0=\frac{1}{\mu^2+\nu^2}\left(V \frac{\partial^2 U}{\partial \mu^2}+ U \frac{\partial^2 V}{\partial \nu^2}\right)$$ Cancel $$\displaystyle \frac{1}{\mu^2+\nu^2} $$ and $$\displaystyle UV$$, $$\displaystyle \frac{1}{U}\,\frac{\partial^2 U}{\partial \mu^2}+ \frac{1}{V}\,\frac{\partial^2 V}{\partial \nu^2}=0$$ Rearranging it, we can obtain that $$\displaystyle \frac{1}{U}\,\frac{\partial^2 U}{\partial \mu^2} = - \frac{1}{V}\,\frac{\partial^2 V}{\partial \nu^2}=k(const.)$$ Therefore, the separated equations are:

= R*7.8 - Plot Legendre Functions for $$n=0 \text{ to } 3$$ =

Given
From [[media:pea1.f11.mtg42.djvu|Mtg 42]] Pg 42-2

Legendre polynomials

$$\begin{align} & {{P}_{0}}(x)=1 \\ & {{P}_{1}}(x)=x \\ & {{P}_{2}}(x)=\frac{1}{2}(3{{x}^{2}}-1) \\ & {{P}_{3}}(x)=\frac{1}{2}(5{{x}^{3}}-3x) \\ \end{align}$$

Legendre functions

$$\begin{align} & {{Q}_{0}}(x)=\frac{1}{2}\log \left( \frac{1+x}{1-x} \right) \\ & {{Q}_{1}}(x)=\frac{1}{2}x\log \left( \frac{1+x}{1-x} \right)-1 \\ & {{Q}_{2}}(x)=\frac{1}{4}(3{{x}^{2}}-1)\log \left( \frac{1+x}{1-x} \right)-\frac{3}{2}x \\ & {{Q}_{3}}(x)=\frac{1}{4}(5{{x}^{3}}-3x)\log \left( \frac{1+x}{1-x} \right)-\frac{5}{2}{{x}^{2}}+\frac{2}{3} \\ \end{align}$$

Find
The plot of the Legendre polynomials (figure 1) and functions (figure 2) together:

Show that for $$ n = 0 $$: $$\scriptstyle \mu \to \pm 1 \Rightarrow \left|Q_0 (\mu) \right| \to + \infty$$

Observe the limits of $$P_n(\mu)$$ and $$Q_n(\mu)$$ as $$\scriptstyle \mu \rightarrow \pm 1$$.

Solution
See the requested solutions plotted below.

What has been shown

Clearly with $$ n = 0 $$ for $$\scriptstyle \mu \to \pm 1 $$ the value of $$ \left|Q_0 (\mu) \right|$$ goes to $$ + \infty$$ as can be seen in the plot for $$Q_0$$ above

The limits of $$P_n(\mu)$$ and $$Q_n(\mu)$$ as $$\scriptstyle \mu \rightarrow \pm 1$$ are as follows:

$$P_0(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+1$$

$$P_0(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$+1$$

$$P_1(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+1$$

$$P_1(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$-1$$

$$P_2(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+1$$

$$P_2(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$+1$$

$$P_3(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+1$$

$$P_3(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$-1$$

$$Q_0(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+ \infty$$

$$Q_0(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$- \infty$$

$$Q_1(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+ \infty$$

$$Q_1(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$+ \infty$$

$$Q_2(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+ \infty$$

$$Q_2(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$- \infty$$

$$Q_3(\mu)$$ as $$\scriptstyle \mu \rightarrow + 1$$ = $$+ \infty$$

$$Q_3(\mu)$$ as $$\scriptstyle \mu \rightarrow - 1$$ = $$+ \infty$$

So the limits depend on whether $$ n $$ is odd or even

= R7.9 Express Vector As Linear Combination of Basis Vectors =

Given
Non-orthonormal basis:

 * $$\displaystyle{\mathbf b_1,\mathbf b_2,\mathbf b_3}$$

Orthonormal basis:

 * $$\displaystyle{\mathbf e_1,\mathbf e_2,\mathbf e_3}$$

Expressing the non-orthonormal in the orthonormal basis:

 * $$\displaystyle\mathbf b_i=A_{ij}\mathbf e_j$$

 * where

 * $$\mathbf A=[A_{ij}]=\left[\begin{matrix}5&2&3\\4&5&6\\7&8&5\end{matrix}\right]$$

Vector $$\displaystyle\mathbf v$$ in $$\displaystyle\mathbb{R}^3$$:

 * $$\displaystyle-2\mathbf e_1+4\mathbf e_2-5\mathbf e_3$$

Definition of Gram Matrix:

 * $$\boldsymbol\Gamma=[\Gamma_{ij}]=[(\mathbf b_i\cdot\mathbf b_j)]\in\mathbb R^{n\times n}$$

Finding components of $$\displaystyle\mathbf v$$

 * $$\displaystyle{v_j}=\mathbf\Gamma^{-1}\{\mathbf b_i\mathbf v\}$$

== Find ==

 * $$\displaystyle{\mathbf v_i}\in\mathbb{R}^{3\times 1}$$ such that $$\displaystyle\mathbf=v_i\mathbf b_i$$

Solution
To begin, find each entry of the Gram Matrix:

$$\Gamma_{11}=\mathbf b_1\cdot\mathbf b_1=25+4+9=38$$

$$\Gamma_{12}=\mathbf b_1\cdot\mathbf b_2=20+10+18=48$$

$$\Gamma_{13}=\mathbf b_1\cdot\mathbf b_3=35+16+25=76$$

$$\Gamma_{21}=\mathbf b_2\cdot\mathbf b_1=48$$

$$\Gamma_{22}=\mathbf b_2\cdot\mathbf b_2=16+25+36=77$$

$$\Gamma_{23}=\mathbf b_2\cdot\mathbf b_3=28+40+30=98$$

$$\Gamma_{31}=\mathbf b_3\cdot\mathbf b_1=76$$

$$\Gamma_{32}=\mathbf b_3\cdot\mathbf b_2=98$$

$$\Gamma_{33}=\mathbf b_2\cdot\mathbf b_3=49+64+25=128$$

Thus

$$\boldsymbol\Gamma=\left[\begin{matrix}38&48&76\\48&77&98\\76&98&128\end{matrix}\right]$$

And

$$\boldsymbol\Gamma^{-1}=\left[\begin{matrix}-0.017&-0.086&0.076\\-0.086&0.060&0.005\\0.076&0.005&0.041\end{matrix}\right]$$

Also we can see that

$$\displaystyle\mathbf b_1\cdot\mathbf v=-10+8-15=-17$$

$$\displaystyle\mathbf b_2\cdot\mathbf v=-8+20-30=-18$$

$$\displaystyle\mathbf b_3\cdot\mathbf v=-14+32-25=-7$$

So then

$$\displaystyle\mathbf b_i\cdot\mathbf v=\left[\begin{matrix}-17\\-18\\-7\end{matrix}\right]$$

Therefore by matrix multiplication

$$\displaystyle\Gamma^{-1}\{\mathbf b_i\cdot\mathbf v\}=\left[\begin{matrix}1.305\\0.347\\-1.095\end{matrix}\right]$$

This implies our solution is

= References for Report 7 = Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 38) [[media:pea1.f11.mtg38.djvu|Mtg 38]] 10 Nov 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 39) [[media:pea1.f11.mtg39.djvu|Mtg 39]] 15 Nov 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 40) [[media:pea1.f11.mtg40.djvu|Mtg 40]] 17 Nov 2011. Vu-Quoc, L. Class Lecture: Principles of Engineering Analysis. University of Florida, Gainesville, FL, (Meeting 41) [[media:pea1.f11.mtg41.djvu|Mtg 41]] 17 Nov 2011. http://en.wikipedia.org/wiki/Elliptic_coordinates http://en.wikipedia.org/wiki/Parabolic_coordinates http://en.wikipedia.org/wiki/Spherical_coordinates http://math.arizona.edu/~goriely/M322/PDE_Handout_1x2.pdf Stevens, David E, and Masoud Olia. "Fundamentals of Engineering Exam, 2nd Ed." Hauppauge, NY: Barron's Educational Series, Inc., 2008, p. 27. Print.

= Team Work Distribution =

{| cellpadding="10" cellspacing="5" style="width: 95%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="width: 20%; background-color: wit; border: 1px solid wit; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

 * style="width: 80%; background-color: wit; border: 1px solid wit; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" |

=Book Derivation of Quadratic Shape Functions (p. 82-83)= The book derives the quadratic shape functions with an inverse manipulation of the matrix of polynomials. $$ \mathbf{d^e} = \begin{bmatrix} \theta_1^e \\ \theta_2^e \\ \theta_3^e \end{bmatrix} $$ $$ \mathbf{M^e} = \begin{bmatrix} 1 & x_1^e & x_1^{e^2} \\ 1 & x_2^e & x_2^{e^2} \\ 1 & x_3^e & x_3^{e^2} \end{bmatrix} $$ $$ \mathbf{\alpha^e} = \begin{bmatrix} \alpha_0^e \\ \alpha_1^e \\ \alpha_2^e \end{bmatrix} $$ $$\theta^e = \mathbf{p}(\mathbf{M^e}^{-1} = \mathbf{N^e}\mathbf{d^e} = \sum_{I=1}^{n_{en}} N_I^e(x)\theta_I^e$$ The derivation of the quadratic shape function leads to this initial solution. $$\mathbf{N^e} = \frac{2} \begin{bmatrix} (x-x_2^e)(x-x_3^e) -2(x-x_1^e)(x-x_3^e) (x-x_1^e)(x-x_2^e) \end{bmatrix} $$ In order for the 1st shape function to vanish at nodes 2 and 3 but have a value of 1 at node 1, then the following derivation applies. $$N_1^e(x) = \frac{(x-x_2^e)(x-x_3^e)}{(x_1^e-x_2^e)(x_1^e-x_3^e)}$$ Similarly, the 2nd and 3rd shape functions follow similar derivations. $$N_2^e(x) = \frac{(x-x_1^e)(x-x_3^e)}{(x_2^e-x_1^e)(x_2^e-x_3^e)}$$ $$N_3^e(x) = \frac{(x-x_1^e)(x-x_2^e)}{(x_3^e-x_1^e)(x_3^e-x_2^e)}$$

=EML 5526 In-Class Derivation - Lecture 8=

title: User:Egm6321.f11.team1/report7


text:
Talk:Helicopter/Howard Community College/Fall2011/501 Drones

90/100 .. no poster 1sfoerster 15:48, 14 December 2011 (UTC)


text:
User talk:Tfalak/enes100/Illuminate clothing

10/10/0 ... do something ... you should have all the parts 1sfoerster 20:07, 21 November 2011 (UTC)

0/0/0 ... nothing to grade 1sfoerster 14:21, 28 November 2011 (UTC)

0/0/0 ... nothing to grade1sfoerster 19:37, 5 December 2011 (UTC)

0/0/0 ... nothing to grade 1sfoerster 17:18, 14 December 2011 (UTC)


text: File:EGM6341.s11.TEAM1.WILKS Extra Credit 45 3.vql.svg


text:
Talk:Engineering Projects/Rubberband gun/Howard Community College/fall2011/550 JK

10/10/80 .... keep up the work 1sfoerster 20:13, 21 November 2011 (UTC)

100/100 ... 1sfoerster 17:32, 14 December 2011 (UTC)


text:
User talk:Muzzlbock/enes100/Synthcontrol

10/10/30 ... good ... 1sfoerster 21:11, 21 November 2011 (UTC)


text: File:Probability Discussion left continuity 2.svg


text:
Talk:Engineering Projects/Model boat/Howard Community College/fall2011/502 AHZ

Team Points:100/100


text: User talk:Stewart.boyd/Business, Politics and Sport – The expansion of the Australian Football League


text:
Category:User de-AT

Users in this category indicate they have knowledge of language Austrian German.

title: Category:User de-AT


text:
Category:User de-AT-N

Users in this category indicate they have skill level N for language Austrian German.

title: Category:User de-AT-N


text:
User:AleXXw

Me@de-WP

title: User:AleXXw


text:
User:Der Buckesfelder

w:de:   :Der Buckesfelder

title: User:Der Buckesfelder


text: User talk:Toddjdavey/Cricket, the gentleman's sport?


text:
User talk:Der Buckesfelder

w:de:   :Der Buckesfelder

title: User talk:Der Buckesfelder


text: User talk:Downie/Limited News Involvement is the Best Thing for Rugby League Presentation


text: User talk:SDunk/Corruption; Sport's skeleton in the closet


title: File:CommercialisationInSport2-1.ogg


text: User talk:Granado23/The Future of Extreme Sport


text: User talk:NGrant/The Decline of Test Cricket?


text: User talk:Trent hop/Revival of Australia Cricket


text: File:EGM6341.s11.TEAM1.WILKS EC45 1.vql.svg


title: File:DLTI.zTrans.1.A.20111122.pdf


title: File:DLTI.FreqRsp.1.A.20111122.pdf


text:
User:PeterSymonds/common.js

mw.loader.load('//meta.wikimedia.org/w/index.php?title=User:PeterSymonds/global.js&action=raw&ctype=text/javascript');

title: User:PeterSymonds/common.js


text:
User talk:Magnolia28

 Hello Magnolia28, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 18:40, 22 November 2011 (UTC) - Ottava Rima (talk) 18:40, 22 November 2011 (UTC)

 Hello , we are the Baah and Bahh twins and we'd both like to welcome you to Wikiversity. While you sit back and explore Wikiversity, enjoy some of our fresh goat milk. You can help us learn by creating new learning resources or help us by improving the guided tours and other exploration tools. We look forward to seeing you around. Baaaahbye for now.

Motivation and emotion
Hi. Welcome to the unit and to Wikiversity! I look forward to learning with you and I hope you find the topic and the unit rewarding. Please feel free to let me know if you have any suggestions or would like help at any point along the way. Sincerely, James Neill, -- Jtneill - Talk - c 04:34, 23 November 2011 (UTC) Thanks James - I've really got the gist now of editing on the Wikiversity - what a great tool.

title: User talk:Magnolia28


text:
User talk:Narohi

 Hello Narohi, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 18:40, 22 November 2011 (UTC) - Ottava Rima (talk) 18:40, 22 November 2011 (UTC)

title: User talk:Narohi


text: User:Johnmoor

title: User:Johnmoor


text:
User talk:Johnmoor

 Hello Johnmoor, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Ottava Rima (talk) 19:47, 22 November 2011 (UTC)

title: User talk:Johnmoor


text:
Template:Bot

Documentation

 * Replace "Example" with your bot's username.

title: Template:Bot


text: File:INSPIRE-map.jpg

title: File:INSPIRE-map.jpg


text:
Draft:Original research/Serpens X-1

Serpens X-1 is a more recent designation for an astronomical X-ray source (Serpens XR-1, 'XR' for X-ray) in the constellation Serpens Cauda. It is designated as the first X-ray source discovered overall in the constellation Serpens.

This learning resource is exploratory and experimental, in part, because many subsequent sounding rocket launches, balloon flights, and satellite X-ray scans have apparently found several locations for this early X-ray source.

The question is "Are any of these subsequent X-ray sources the original Serpens XR-1?"

The number of nearby X-ray sources detected as Serpens X-1 over time suggests that different X-ray sources are being detected by different probes and X-ray observatories. Depending upon the accuracy of location, strength of X-ray signal and possible variation over spectral, temporal, or spatial distributions, the original astronomical X-ray source appears to be missing. This search effort is ongoing so that anyone may enjoy contributing and discussing.

Notations
The astronomical X-number notation (X-#) for an astronomical X-ray source in a constellation has its start from the initial discoverers of an extrasolar X-ray source at the American Science and Engineering Company (ASE)-Massachusetts Institute of Technology (MIT). "[T]he constellation genitive (or an abbreviation) followed by X and a digit, such as SCO X-1 [is applied]." Researchers at the US Naval Research Laboratory suggested "XR" (for X-Ray) rather than "X". This would be SCO XR-1 for the first X-ray source discovered in the constellation Scorpius. "[I]t seems more logical to use this in the standard astronomical notation where the identification precedes the constellation, i.e., X-1 Scorpii." Among the first 17 catalogued astronomical X-ray sources are X1 Scorpii to X3 Scorpii, X1 and X2 Sagittarii, and X1 to X4 Cygni. X1 Serpentis is listed at RA 18h 45m Dec +5° 18'.

Later, the sources became simply the constellation (or an abbreviation) followed by X-#, e.g., Scorpius X-1 (Sco X-1).

Proof of concept for sources
"In some cases, source locations are suspect unless confirmed by two or more separate experimenters."

Theoretical Serpens XR-1
Here's a theoretical definition:

Def. source 'C', located at B 1950.0 RA 18h 45m Dec 05.3° with flux of 1.5 x 10-8 erg/cm2.s for a computed black body source with temperature of 2 x 107 K for the range in wavelength 0.15-0.8 nm, or 0.3 x 10-8 erg/cm2.s for a computed black body source with temperature of 5 x 106 K for the same wavelength range, from 16 June 1964, and 25 April 1965, is called Serpens XR-1.

Entities
Serpens is split into two non-contiguous parts, Serpens Caput (Serpent's Head) to the west and Serpens Cauda (Serpent's Tail) to the east. Between these two halves lies the constellation of Ophiuchus, the "Serpent-Bearer". ... Stars in the tail include [Zeta Serpentis] ζ, [Eta Serpentis] η, [Theta Serpentis] θ, [Nu Serpentis] ν, [Xi Serpentis] ξ, and [Omicron Serpentis] ο Serpentis.

The image at the left is of Serpens Cauda.

The image at the right is of Serpens Caput.

In the center is a combined image with Serpens Cauda on the left, skyward West, and Serpens Caput on the right.

Objects
TYC 460-624-1 is a rotationally variable star. It is X-ray source 1RXS J184510.6+062016.

Astronomical X-ray sources
On March 31, and April 2, 1966, two separate balloon flights detected an X-ray source at approximately B 1950.0 RA 19h ±30m Dec +5° ±10°, with a flux of about 5 x 10-8 ergs cm-2 sec-1, in the energy range from 20 to 180 keV.

"Possible fittings of our distribution, together with the evaluation of the NRL group for ... Ser X1, give an index of 1.6 for a power law and a temperature of 2 x 109 °K for an exponential law ... Independently of the mechanism invoked, a black-body source would appear to be excluded: the high energies involved will demand extraordinary conditions in the [source], such as strong magnetic fields and high electron energies or hot dense plasmas at quite unusual temperatures."

The "[b]alloon measurements ... observed ... [a flux] (20 to 180 kev) from Ser XR-1 [of] about 8 x 10-8 erg/cm2ˑsec".

On May 15, 1967, a balloon flight, designated 296-P, observed X-ray counts in the direction for Serpens XR-1 using the NRL coordinates. The flight used the same gondola and detector, a 56.3-cm2 NaI crystal and a collimator with 8.4° full-width-at-half-maximum (FWHM) field of view, as used in earlier and later balloon flights. In the energy range of 16.6 to 23.4 keV the detector registered < 0.075 counts/second source rate for Serpens XR-1. In the range 23.4-46.7 keV, the count rate was 0.124±0.130. For the same ranges the detector also observed Scorpius X-1 at 0.243 and 0.098 counts/second (cts/s), suggesting that the source emission ratios were < 0.309 and 1.27 of Scorpius X-1, respectively.

"A Hydra-Iris rocket was launched from the open ocean 500 miles off the coast of Baja California [on November 3, 1968, at 18h00m UTC], at latitude 27.4 N and longitude 125 W." Ser XR-1 was observed at a galactic longitude of 36.0°. Ser XR-2 was at 16.5° in galactic longitude. The galactic longitude for Ser XR-1 (NRL) is 37° 15' 05.7". The source observed on November 3, 1968, is just short of 2° from Ser XR-1.

"The strength of these sources [Ser XR-1 at 0.8 photons cm-2 sec-1 and Ser XR-2 at 2.1 photons cm-2 sec-1] is about the same as that observed by NRL on 1965 April 25 (Friedman et al. 1967). Ser XR-1 seems to be strongest at low energies and has a shape similar to that of the Crab Nebula. The background subtraction for Ser XR-2 is a bit uncertain because of the nearness of other sources. Nevertheless, our result is reasonably close to that of the 1965 October 11 experiment of Gorenstein et al. (1967). The 1965 September 30 experiment of Fisher et al. (1967) is similar in shape but lower in intensity."

Uhuru X-ray sources
The Uhuru satellite detected an X-ray source at 2U 1836+05. The exact position was listed as B 1950.0 RA 18 36 29 Dec +05 02 24. In an error box with corners: RA 18 36 51 Dec +05 02 24, RA 18 35 34 Dec +05 05 06, RA 18 35 34 Dec +05 03 00, and RA 18 36 48 Dec +04 59 24. The authors designated the 2U 1836+05 source as Ser XR-1. But this did not include the final position for this source at 4U 1837+04.

By December 5, 1977, at least five other positions, in epoch 1950.0 coordinates, for Serpens XR-1 are indicated
 * 1) RA 18h 37m 29.8s Dec +04° 59' 23",
 * 2) GX +36.3,
 * 3) 4U 1837+04,
 * 4) MXB 1837+049, and
 * 5) 2S 1837+049.

These have been observed by sounding rocket on
 * 1) November 25, 1964, over the range 0.15-0.8 nm,
 * 2) April 25, 1965, over the range 0.15-0.8 nm,
 * 3) September 30, 1965, over the range 0.4-0.8 nm,
 * 4) October 11, 1966, over the range 0.2-0.5 nm,
 * 5) September 24, 1970, over the range 0.12-1.6 nm, and
 * 6) May 25, 1971, over the range 0.2-0.6 nm.

Subsequent satellite observations are
 * 1) Uhuru, 1971-73, over the range 0.2-0.6 nm,
 * 2) Ariel, in November 1974, over the range 0.2-1.8 nm,
 * 3) SAS 3, October 4-7, 1975, over the range 0.2-2.4 nm,
 * 4) SAS 3, August 22-28, 1976, over the range 0.2-1.1 nm, and
 * 5) SAS 3, 1975-77, over the range 0.2-1.1 nm.

The SIMBAD astronomical database has Serpens XR-1 located at epoch 2000.0 RA 18h 39m 57.56s Dec +05° 02' 09.6".

The image at right is a celestial map of the astronomical sources within the 1.5° radius error circle around Serpens X-1, not Serpens XR-1. The other sources, or astronomical objects, within this error circle are stars (*), additional X-ray sources (X), a gamma-ray burst source (gammaBurst), and a dark nebula (DkNeb).

XMM-Newton sources
The image at the top right is a graph of the XMM-Newton spectral signature from superheated iron atoms at the inner edge of the accretion disk orbiting the neutron star in Serpens X-1. Normally, the line would be a symmetrical peak, but it exhibits the classic features of distortion due to relativistic effects. The extremely fast motion of the iron-rich gas causes the line to spread out. The entire line has been shifted to longer wavelengths (left, red) because of the neutron star's powerful gravity. The line is brighter toward shorter wavelengths (right, blue) because Einstein's special theory of relativity predicts that a high-speed source beamed toward Earth will appear brighter than the same source moving away from Earth.

As of August 27, 2007 discoveries concerning asymmetric iron line broadening and their implications for relativity have been a topic of much excitement. With respect to the asymmetric iron line broadening, "We're seeing the gas whipping around just outside the neutron star's surface. And since the inner part of the disk obviously can't orbit any closer than the neutron star's surface, these measurements give us a maximum size of the neutron star's diameter. The neutron stars can be no larger than 18 to 20.5 miles across, results that agree with other types of measurements."

"We've seen these asymmetric lines from many black holes, but this is the first confirmation that neutron stars can produce them as well. It shows that the way neutron stars accrete matter is not very different from that of black holes, and it gives us a new tool to probe Einstein's theory."

"This is fundamental physics. There could be exotic kinds of particles or states of matter, such as quark matter, in the centers of neutron stars, but it's impossible to create them in the lab. The only way to find out is to understand neutron stars."

Serpens X-1, which contains a neutron star and a stellar companion, was observed using XMM-Newton and Suzaku's superb spectral capabilities to survey Serpens X-1. The Suzaku data confirmed the XMM-Newton result regarding the iron line in Serpens X-1.

The observations of the iron line asymmetric broadening using XMM-Newton of a Serpens X-1 (the LMXB) as reported in 2007 do not contain coordinates for the X-ray source.

MM Serpentis
B1950 coordinates are RA 18 37 29.55 Dec +04 59 21.0. Other designations: 3A 1837+049, GPS 1838+047, 1H 1837+049, INTEGRAL1 98, 1M 1837+049, 1RXS J183956.9+050203, 2S 1837+049, SWIFT J1840.0+0501, 2U 1836+05, 	3U 1837+04, 4U 1837+04, XB 1837+049, [BM83] X1837+049, and [KRL2007b] 331.

J2000 coordinates are RA 18 39 57.56 Dec +05 02 09.6.

"NuSTAR observed Serpens X-1 twice on 12 and 13 July, 2013 (Sequence IDs 30001013002 and 30001013004). The data were screened and processed using the NuSTAR Data Analysis Software (NuSTARDAS) version 1.1.1, resulting in a total of 43.4 ks of on-target time. The source is relatively bright, so the net exposure after instrumental deadtime is taken into account is 30.4 ks. Spectra from the FPMA and FPMB detectors were extracted from 120” regions centered on the source position, using the “nuproducts” FTOOL. Corresponding response files appropriate for the pointing type (on-axis), source type (point), and extraction regions were also created. Backgrounds were created using the “nusky-bgd” tool, which self-consistently accounts for background variations across the face of the detector."

"Serpens X-1 is known to exhibit Type-1 X-ray bursts at a rate of approximately 0.1 per hour (Galloway et al. 2008)."

"Owing to the abilities of NuSTAR, an Fe K line in the spectrum is revealed to be skewed at a high level of statistical confidence, and the Compton back-scattering "hump" expected in disk reflection scenarios is detected in a neutron star X-ray binary for the first time. Both findings are robust since the FPMA and FPMB detectors do not suffer from flux distortions due to effects such as photon pile-up. Clearly, broad Fe K lines in at least some neutron star X-ray binaries arise in the inner disk, and can be used to probe the stellar properties and inner accretion flow."

Hypotheses

 * 1) The first source believed to be Serpens X-1 is probably not as exciting as the currently accepted source.

title: Draft:Original research/Serpens X-1


text:
User:TutorJDD/nutrition

Main namespace links @ Wikiversity

 * nutrition

title: User:TutorJDD/nutrition


text:
Panspermia

(from Controversies in Science)

Did life on Earth arise from Panspermia?

Complexity in the dirt
The 1976 Viking's Mission to Mars conducted a labelled release experiment and found that in Mars, microbial life was present. .

Life's building blocks found in a COMET
NASA scientists discover glycine in a comet. Glycine is the fundamental building block for life. It is used to make proteins in living organisms. Since it was found in a comet, it supports the theory that the life's ingredients were formed in space and then delivered to earth by meteorites.

NASA scientist: Evidence of alien life on meteorite
In what seems to be the greatest discovery in recent history, NASA's Richard B. Hoover discovered clear proof of bacteria fossil evidence in meteorites that are rarely spotted entering the Earth's atmosphere. This discovery makes life on comets possible. He also had found that Mars can sustain life because liquid water is present. This supports the fact that before entering the Earth, forms of life on the meteors existed.

Go Panspermia!
Panspermia or abiogenesis? Did life migrate here through space or begin on Earth? Spores were found to be able to withstand high pressure and high temperature, so it is possible for microbes to have come down to the earth from outer space through meteorites.

Comets Bring Microbial Life
The Hoyle-Wickramasinghe panspermia theory proposes that life on earth was originated approximately 4 billion years ago by comets containing microbial life. Some of the microorganisms continue to be found. Nowadays, Panspermia is considered as a serious alternative to life being originated solely on earth. There are many places on Earth where microbial life is present such as, Antarctic soil and ocean floors. Thus, it is evident that it was transferred from the cosmic life cycle to the Earth. During the cosmic life cycle, comets expanded microbial life.

Humans are made from stars
20 different atoms make up all living material which include atoms that are found in steller nucleosynthesis. Steller nucleosynthesis is a nuclear reaction that takes place in the stars, therefore we can make the conclusion that we are made up of atoms from the stars.

Microorganisms are able to survive/thrive in ultraviolet light.

Various planets including Mars and Venus are showing signs of life in water and clouds on the planets surface. . Stratospheric air shows signs of bacteria which is above the atmosphere free from aerosoles from the earth.

Microorganisms Potentially formed from Hot and Cold Stardust
If a microorganism is successful in going through extreme 'mixing', in which dust from both the coldest and hottest regions of the solar nebula is gathered and lands on Earth, then life was already present in the material that it has collected from the celestial bodies.

Space-traveling bacteria wears a protective coat
Scientists believe that Space-traveling bacteria would be susceptible to damage from the ultraviolet (UV) light of stars; however,a thin layer of carbonized material would protect them and block the UV light.

Panspermia is not reproducible
Scientists Wickramasighe and Bhargava conducted a cryosampler experiment to prove or dismay the theory of Panspermia. Sixteen samples were collected from the cryosampler at various altitudes and split between the two scientists to prove the proposed theory. Wickramasighe stated to have detected microorganisms present from the cryosampler samples. However, Bhargava was unable to produce the same results. This is possibly a fluke that Wickramasighe found any living microorganisms. When asked to reproduce the same results, he declined.

Lichens Die After Re-Entry
After attaching the bacteria and lichens wrapped in rock casings to the space shuttle, their growth rate, ability to germinate and their activity were analyzed. The bacteria could not survive the harsh conditions in space while the lichens lived. Upon re-entering the earth's atmosphere, the lichens died and the rock casings had turned to glass. .

Unreliable Information on Interstellar Medium
When scientists searched for organic material in the interstellar medium, they scanned an absorbance range of 3.0 to 3.5 micrometers because that is the range most biological substances absorb at. However, a false result could have occurred because that range of wavelength is not exclusive to organic materials. In fact, water and ammonia also absorb wavelengths of 3.0 to 3.5 micrometers. Another problem with the concept of life in the interstellar medium is that the ratios of certain elements in space are not suitable for compounds like DNA, RNA and bacterial cytoplasm. For example, 100 times more phosphorus than what can be found in the medium is required to form such compounds. Unfortunately, we do not know enough about the interstellar medium right now to make accurate statements about its composition and its nature. For instance, how can we be certain that life on Earth came from space when we are unfamiliar with the conditions these foreign bacteria originated in ?

Panspermia? Nope.
For the theory of panspermia to be true, the organisms must first leap from their hosting planets onto a carrier with a similar environment as the planet of origin. The cells must then reach the earth before the harmful cosmic rays can kill them, which would take approximately two days. Then the cell must survive entering the Earth's atmosphere and the impact of landing. No host that is capable of fitting the above requirements is in existence therefore panspermia is not possible.

Extreme Environments Disprove Panspermia
Regardless of the appropriate conditions, such as water and nutrients and the fact that the dormant spores will grow, creating a potential for panspermia, the environments (threats of vacuums and radition) in which the spores are growing in are too harsh for further development. Therefore, panspermia can not exist.

Panspermia: Progenote or Prokaryotes (Group 6)
Based on the current theory of genetic code progenotes were the ancestors of prokaryotes. Therefore, if panspermia was true progenotes would have come to earth from other planets. Based on scientific analysis progenotes would have not survived the journey to earth as they are not fully evolved complex micro-organism.

Panspermia doesn't account for similar biology
If there were organisms here on earth from outer space they would be simple, standout, and have characteristics easily recognizable. Panspermia was used to view that life on Earth had originated from outer space. There has been a hypothesis formed that space continues to provide the Earth with life. Any microorganism that had come from outer space to Earth would have had to survive extreme weather conditions in space.

Subpages
Expanded discussion of these topic can be found in these subpages:

title: Panspermia


text:
LHC black hole risk

(from Controversies in Science)

Should we turn on the LHC?

Large Hadron Collider Protection Means No Risk
The Large Hadron Collider has been made safe due to the numerous protection measures, such as the Quench Protection Systems, which assures any excess energy is discharged through magnetic coils. The Fast Magnet Current Charge Monitor detects when current levels in the Large Hadron Collider change and thus are able to control them. Finally, the active hardware diagnostics keeps the Large Hadron Collider running smoothly, making the risk levels go down. .

Correcting the Black Hole Theory
Due to black holes being unstable, they are deemed to be safe.

Review of the Safety of Large Hadron Collider Collisions
The LSAG report proves that the utilization of the Large Hadron Collider would be perfectly and 100% safe.

group 5 point
Black holes generated through the LHC are insignificant in size and strength, resulting in them posing no serious threat to humanity.

LHC Produces Stable and Unstable Strangelets
Studies have shown that the LHC produces two different types of strangelets. the two different types of strangelets (Unstable and Stable) will be discussed as well as the precautionary risks it involves.

group 4 point
The Large Hadron Collider has no real evidence that is is safe. The assumptions that scientists have made stating that the black holes are not dangerous has yet to be tested. Also Hawking radiation is used to promote the safety of this experiment even though it has never been tested.

The LHC Isn't Safe
The magnitude of the experimental Large Hadron Collider, and the largely unknown potential outcomes of the experiment could lead to disastrous consequences for humanity and the planet.

title: LHC black hole risk


text:
Controversies in Science/Recycling

(from Controversies in Science)

Should we recycle?

title: Controversies in Science/Recycling


text:
Nuclear power/Greener

(from Controversies in Science)

Is nuclear power green?

Nuclear power is the only viable substitute for coal
Wind and solar power are other green energy solutions but because they are unpredictable and unreliable nuclear power is the only viable substitie for coal. Nuclear power can satisfy high energy demand based on the facilities built rather than depending on unpredictable natural factors.

Nuclear power can keep up with population growth with breeder reactors
Reactors that make more radioactive fuel create an unlimited supply of energy

Nuclear Power, the clear choice!
Not only is Nuclear energy much safer in terms of lives lost in manufacturing, but compared to coal and electricity its carbon foot print is non-existent. Also, the process of generating nuclear power creates very little waste or by-products.

CANDU(Canadian Deuterium Uranium)power plants use cleaner methods to produce energy such as wind, solar, hydro, and biomass which makes them a reliable source of power. Research has also shown that CANDU Nuclear Plants can supply electricity with zero emissions of greenhouse gases. There are studies also stating that these nuclear power plants produce small emissions compared to other power plants. The study also reviews the life cycle of several different types of Power Plants. .

Many people believe that by 2050, greenhouse gas emissions will increase, along with oil demand. To reduce CO2 emissions, nuclear energy plays a very crucial role in doing so.

Clean Energy? Think nuclear power
The world is heavily dependent on fossil fuels that have been proven to be detrimental to the environment. Nuclear power plants produce energy from nuclear fission and are the most clean and environment friendly source of energy among other forms of power sources including coal, oil, gas and hydro power.

No harmful emissions
Compared to other major existing energy sources such as coal and oil, nuclear power emits almost no greenhouse gases or nitrogen oxide and sulfur dioxide, which are the primary components of air pollution

Mining Uranium is Harmful to the Environment
The mining of uranium around the world for nuclear energy purposes is not as regulated nor as guarded as it is recommended to be. Studies suggest that improper procedures of uranium extraction have caused excessive radiation levels and pose a direct threat to its immediate environment. For a change to occur, there must be a global consensus on how to extract uranium in the safest, most environmentally conscious way.

Leukaemia Rates Higher in Children Close to Nuclear Power Plants
Children under the age of 5 that are within a 5km area around nuclear power plants in Germany had higher rates of leukaemia than those in a control group.

NO Radiation is Okay Raditation
The opinions of doctors regarding the nuclear power industry are not well known because they receive little to no attention from congress on the issue. Helen Caldicott focuses on dangers that we are not aware of nor do we see yet from the impacts of nuclear radation. Many physicists advocate for nuclear power because they focus on the external less harmful sources of radatation. Physicists also do not acknowledge that radiation is cummulative and the harmful effects may not surface until later in life or generations later. There are many long term effects that will take generations to appear from incidents such as Chernobyl or Fukushima.

There is no safe method for Disposal of nuclear waste
Isolation is the safest method for disposing of nuclear waste, and there are many environmental implications associated with this disposal method.

Nuclear Power Would Not Stop Climate Change
Problems that arise when planning to build a new nuclear plant are analyzed.

.

Increase in cancer post Three Mile Island disaster
Residents living near the Three Mile Island nuclear plant were evaluated to see if there was an increase within cancer rates. This took place after the disaster in 1979 where the nuclear plant overheated resulting in a nuclear meltdown.

title: Nuclear power/Greener