text:
Grants and fundraising/Funding

Funding: sufficient income to cover costs, diversion of person-hours from a day job, and as an incentive to perform the research or exploration to overcome specified risks (hopefully).

Costs: intellectual effort, computer use time and resources, possible publication costs, a trip to a conference in a neat location.

The higher the risk of success, the closer to a gift the resource becomes. The lower the risk of success, the closer to an investment or loan usually with interest, the resource is.

 * Challenges - of those unexpired with valid links, none are applicable to dominant group exploratory research.
 * Grants - It seems that no one has utilized a grant on behalf of Wikiversity.
 * Grant proposals
 * Research funding - Wikipedia

Agency funding per year
This search is conducted using Google scholar with keywords "agency abbreviation" + "dominant group", e.g., NASA "dominant group", since 1999. For several of the funding agencies the key words used had to be the agency general title rather than the abbreviation: the Max Planck Institute - "Max Planck Institute" (MPI), "National Endowment for the Humanities" (NEH), "Office of Naval Research" (ONR), and "Canadian Space Agency" (CSA). "Satlantic" funded one paper in 2002 and may be a company. Notation such as "33 p 3" indicates 33 articles so far from pages 1-3 of the search.

Abbreviations used stand for
 * 1) NASA - National Aeronautics and Space Administration, USA,
 * 2) NSF - National Science Foundation, USA,
 * 3) MPI - Max Planck Institute, Germany,
 * 4) NIH - National Institutes of Health, USA,
 * 5) NEH - National Endowment for the Humanities, USA,
 * 6) ONR - Office of Naval Research, USA,
 * 7) CSA - Canadian Space Agency, Canada,
 * 8) NSERC - Natural Sciences and Engineering Research Council, Canada,
 * 9) NOAA - National Oceanic and Atmospheric Administration, USA,
 * 10) ESA - European Space Agency, European Union, and
 * 11) USGS - US Geological Survey, USA.

Additional funding agencies are, for example, the Boreskov Institute of Catalysis, the Getty Research Institute for the History of Art and the Humanities, the Social Sciences and Humanities Research Council of Canada, Max-Planck Institute for Evolutionary Anthropology, the Swiss Society for Humanities, the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Arts and Humanities Research Council (UK), and the Max Planck Institute for Social Anthropology.

European Space Agency
"Through this Call the Director of Science solicits from the broad scientific community proposals for the competitive selection of new "Science Ideas", to be investigated in terms of feasibility and needed technology developments."

"Prospective proposers must submit a mandatory Letter of Intent (LoI) by the deadline indicated in the table reported above. Proposals not preceded by a corresponding LoI will not be considered. LoI submissions are accepted exclusively in electronic form, in PDF format, using the online submission form that can be accessed below or from the left-hand menu."

Max Planck Institute for the History of Science
This institute as a possible funder is being studied. Another may be the Max Planck Institute for Psycholinguistics.

National Aeronautics and Space Administration
This may be a possibility. Current press releases include 20 uses of "dominant group".

National Endowment for the Humanities

 * National Endowment for the humanities - The Division of Research Programs 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. http://www.neh.gov/whoweare/divisions/Research/index.html. NEH has extensive interest in Darwin, Origin of species, and their influence. The Darwin interest does not appear in the listed grant programs offered.
 * Apply for a Grant, http://www.neh.gov/grants/index.html.
 * Still featured at the website is "Darwin the Young Adventurer" . "Janet Browne is Aramont Professor of the History of Science at Harvard University and the author of the two-volume biography Charles Darwin: Voyaging (1995) and Charles Darwin: The Power of Place (2002), which received the National Book Critics Award and the Pfizer Prize for Biography from the British History of Science Society. From 1983 to 1991, Browne was associate editor of the Correspondence of Charles Darwin, where she studied more than 14,000 letters."
 * Correspondence after 1859 have been searched, a definition of "dominant group" has been found.
 * Potential for help from Janet Browns has diminished due to discovery of term in work of Kirby in 1826 and unresponsiveness of Browne to email communication - possibly associated with then and upcoming holidays, plus university endeavors.
 * Although most grantees are associated with a university, there are "Independent Scholar"s and science museum and library employees. Being associated with Wikiversity may not be a drawback if expressed as a novel and open access approach to research and the research process.

 * The Division of Research Programs staff probably contains at least one potential program manager to be sent a letter of interest:
 * 1) Jane Aikin, Director of the Division of Research Programs, jaikin@neh.gov, attending 128th Convention of the Modern Language Association,
 * 2) Russell Wyland, Deputy Director, rwyland@neh.gov,
 * 3) Jason Boffetti, Senior Program Officer (SPO), jboffetti@neh.gov, attending the American Political Science Association Annual Meeting,
 * 4) John Cox, SPO, jcox@neh.gov,
 * 5) Claudia Kinkela, SPO, ckinkela@neh.gov, attending the American Political Science Association Annual Meeting,
 * 6) Mary Macklem, SPO, mmacklem@neh.gov,
 * 7) Ann Meyer, SPO, ameyer@neh.gov,
 * 8) Daniel Sack, SPO, dsack@neh.gov, attending joint Annual Meeting of the American Historical Association/American Society of Church History,
 * 9) Mark Silver, SPO, msilver@neh.gov,
 * 10) Stefanie Walker, SPO, swalker@neh.gov, attending College Art Association conference (CAA), no written differentiation with respect to program areas is given.

The department "In the Field: Research Programs" contains a list of SPOs attending conferences that suggests areas of interest or expertise.

"All applicants to National Endowment for the Humanities are required to use Grants.gov."

"The [US] federal government has mandated that all federal government grant-making agencies use Grants.gov as their primary way of receiving grant applications."

Prior to a successful registration on Grants.gov, an individual or organization/company/insitution must register with the US federal government's System for Award Management (SAM) at SAM.

A successful registration at SAM is in turn predicated upon appropriate recognition by the US Internal Revenue Service (IRS) within SAM. This process may take up to a week and is fraught with conceptual potholes, although each website seeks improvement through user surveys.

If you register as an organization, sole proprietorship, or company (profit-making or not-for-profit) you likely need a DUNS number. Registering only as an individual may limit your grant-seeking opportunities.

If you already have a DUNS number but your input into SAM keeps coming back with an error message, words to the effect, that you inputted the DUNS number correctly but the name, address, and additional information does not match the Dun & Bradstreet, Inc., record, try checking their listing using iUpdate.

National Institutes of Health

 * National Institutes of Health - Wikipedia. One limitation on funding from NIH is that usually at least one principal investigator must be an MD. Basic scientific research is usually redirected to NSF.

National Science Foundation

 * National Science Foundation - Wikipedia
 * NSF Home url=http://www.nsf.gov/index.jsp.
 * Search of NSF website produced the following results:

 * 1) "But between the latest Devonian Period and the subsequent Carboniferous period, placoderms disappeared and ray-finned fishes rapidly replaced lobe-finned fishes as the dominant group, a demographic shift that persists to today." This usage is in research efforts of Geosciences and Biology (Paleontology).
 * 2) "The dominant group is using a subordinate group’s ethnicity for their own entertainment.", under the heading "Problem with Mascots" . This is in Ethnicity.
 * 3) "The next society will be a knowledge society. Knowledge will be its key resource, and knowledge workers will be the dominant group in its workforce." Sociology and society are the focus.

 * Applicants proposing research in the social or behavioral sciences, linguistics, or economics are encouraged to consider the funding programs of the National Science Foundation’s Directorate for Social, Behavioral, and Economic Sciences at http://nsf.gov/dir/index.jsp?org=sbe.

Linguistics Program
"The program supports research on the syntactic, semantic, morphological, phonetic, and phonological properties of individual languages and of language in general. The Linguistics Program ... encourages investigation of linguistic questions that are interdisciplinary in nature ... social and cultural factors in language use, variation, and change".

With respect to "dominant group" and possibly its relative synonyms, paraphrasing the NSF program statement: "[t]he program [may] support research on the syntactic [and] semantic ... investigation of linguistic questions that are interdisciplinary in nature ... [including] social and cultural factors in [dominant group] use, variation, and change."

From an apparent origin in William Kirby's book with William Spence: An introduction to Entomology: or Elements of the Natural History of Insects, Volume IV of 1826, as an expression of Hutchinsonian natural creation theory, the technical term "dominant group", has traveled forward in time. Charles Darwin incorporated it into his On the origin of the species by means of natural selection: or, The Preservation of Favoured Races in the Struggle for Life in 1859. Thomas Henry Huxley coined the term Darwinism, and Joseph Fisher, among others included social darwinism as a part of evolutionary progressivism (eugenics) in the 1870s. Having survived these theories of evolution, it is now part of George Gaylord Simpson's modern evolutionary synthesis from the 1940s to present.

The term seems to have radiated out of the entomology of 1826 into political science as part of Alexis de Tocqueville's The Old Regime and the Revolution: Notes on the French Revolution and Napoleon between 1853-1857. And, has since diversified into nearly every professional scientific, cultural, social, and linguistic niche, including high energy physics.

It is a technical term that may have origins in religion even before Kirby's use. It seems to have either a rigorous definition in sociology or a general, somewhat vague metadefinition, allowing its use almost ubiquitously in professional scholarly literature.

 * 1) Intellectual Merit: "How important is the proposed activity to advancing knowledge and understanding within its own field or across different fields? How well qualified is the proposer (individual or team) to conduct the project? (If appropriate, the reviewer will comment on the quality of prior work.) To what extent does the proposed activity suggest and explore creative, original, or potentially transformative concepts? How well conceived and organized is the proposed activity? Is there sufficient access to resources?"
 * 2) Broader Impacts: "How well does the activity advance discovery and understanding while promoting teaching, training, and learning? How well does the proposed activity broaden the participation of underrepresented groups (e.g., gender, ethnicity, disability, geographic, etc.)? To what extent will it enhance the infrastructure for research and education, such as facilities, instrumentation, networks, and partnerships? Will the results be disseminated broadly to enhance scientific and technological understanding? What may be the benefits of the proposed activity to society?"

Science, Technology, and Society
"The Science, Technology, and Society (STS) program supports research that uses historical, philosophical, and social scientific methods to investigate the intellectual, material, and social facets of the scientific, technological, engineering and mathematical (STEM) disciplines. It encompasses a broad spectrum of STS topics including interdisciplinary studies of ethics, equity, governance, and policy issues that are closely related to STEM disciplines, including medical science."

"The program’s review process is approximately six months. It includes appraisal of proposals by ad hoc reviewers selected for their expertise and by an advisory panel that meets twice a year. The deadlines for the submission of proposals are February 2nd for proposals to be funded as early as July, and August 3rd for proposals to be funded in or after January."

Current solicitation: 15-506

Who May Submit Proposals:
 * 1) Standard Research Grants and Grants for Collaborative Research: US Academic Institutions and Non-Profit Research Organizations.
 * 2) Scholars Awards: US Academic Institutions and Independent Scholars

"Scholars Awards are normally made to U.S. academic institutions, although an individual who is not affiliated with an appropriate U.S. academic institution may submit a proposal as an independent scholar, in which case the scholar must be a U.S. citizen or national, or have permanent resident status."

"Full proposals submitted via FastLane: Proposals submitted in response to this program solicitation should be prepared and submitted in accordance with the general guidelines contained in the NSF Grant Proposal Guide (GPG). The complete text of the GPG is available electronically on the NSF website at: http://www.nsf.gov/publications/pub_summ.jsp?ods_key=gpg. Paper copies of the GPG may be obtained from the NSF Publications Clearinghouse, telephone (703) 292-7827 or by e-mail from nsfpubs@nsf.gov. Proposers are reminded to identify this program solicitation number in the program solicitation block on the NSF Cover Sheet For Proposal to the National Science Foundation. Compliance with this requirement is critical to determining the relevant proposal processing guidelines. Failure to submit this information may delay processing."

"Full proposals submitted via Grants.gov: Proposals submitted in response to this program solicitation via Grants.gov should be prepared and submitted in accordance with the NSF Grants.gov Application Guide: A Guide for the Preparation and Submission of NSF Applications via Grants.gov. The complete text of the NSF Grants.gov Application Guide is available on the Grants.gov website and on the NSF website at: (http://www.nsf.gov/publications/pub_summ.jsp? ods_key=grantsgovguide). To obtain copies of the Application Guide and Application Forms Package, click on the Apply tab on the Grants.gov site, then click on the Apply Step 1: Download a Grant Application Package and Application Instructions link and enter the funding opportunity number, (the program solicitation number without the NSF prefix) and press the Download Package button. Paper copies of the Grants.gov Application Guide also may be obtained from the NSF Publications Clearinghouse, telephone (703) 292-7827 or by e-mail from nsfpubs@nsf.gov."

"Letters of Intent: Not required, Preliminary Proposal Submission: Not required".

"The Program encourages potential investigators with questions as to whether their proposal fits the goals of the program to contact one of the program officers."

Social Psychology Program
"The Social Psychology Program at NSF supports basic research on human social behavior, including cultural differences and development over the life span.

Among the many research topics supported are: attitude formation and change, social cognition, personality processes, interpersonal relations and group processes, the self, emotion, social comparison and social influence, and the psychophysiological and neurophysiological bases of social behavior.

The scientific merit of a proposal depends on four important factors: (1) The problems investigated must be theoretically grounded. (2) The research should be based on empirical observation or be subject to empirical validation. (3) The research design must be appropriate to the questions asked. (4) The proposed research must advance basic understanding of social behavior." This program is a part of "Psychological and Language Sciences".

Letter of intent
A letter of intent is part of the application process to a funding agency directed to a specific program manager after exchange of initial communication to determine interest of the program manager in the project's subject, goals, and possible significance.

Letter of interest
A letter of interest to a program manager at the United States National Science Foundation (NSF) is written and sent to politely ascertain whether there is sufficient interest in a proposal topic on the part of the program manager to warrant the submission of a formal proposal through the FastLane system.

Points of interest
The concept embodied by the two-word scientific term dominant group may be primordial to human society, culture, and language. Searching context and usage of the term and its relative synonyms in contemporary and extinct languages, and those languages on the verge of extinction may reveal important facts about this concept. It is sometimes the case that a language is on the verge of extinction precisely because of the presence of a dominant group, especially one engaging in monopolistic or oligopolistic practices.

Dominant group may represent a force for extinction in the evolution and application of language, specifically terminology, to the real and imaginary world. A more readable version may be found at [:http://en.wikiversity.org/wiki/Dominant_group/Funding].

Intellectual merit
The current activity is exploratory in nature and is resulting in an advance of knowledge and understanding about the term dominant group and its uses within various fields. The identification of its own field may result; thereby, in allowing differentiation of other fields so as to determine how knowledge is advanced across those different fields. It's like differential equations. Although differential equations is a subject within mathematics, it's spread to other subjects such as physics with ensuing use advances knowledge within physics. Differential equations is a two-word scientific term.

Advancing knowledge and understanding
The proposed activity consists of finding the origin of dominant group or one of its relative synonyms, defining the two-word scientific/technical term perhaps from context (lexical pragmatics) (or perhaps rigorously), determining why scientists outside biology (especially evolution or entomology) use the term, and verifying its divergence and radiance by examples.

The field of dominant group appears to be regions, or the science of regions. Within a region in any science, including the social sciences, there may be a dominant group. Each region is defined by its limits. These limits in turn may allow for a dominant group. Change the limits (characteristics) for any region and the dominant group may go extinct. If a regional genome in biology lacks the potency to take advantage of any change in regional characteristics, there will be no dominant biological group.

In each field of use
Part of the proposed activity is to determine how dominant group advances knowledge and understanding within each field which may be considered its own field or across all these different fields.

Dominant group is already being used as a scientific/technical term to advance knowledge and understanding across a great many fields.

In theory, dominant group in any field may have at least two uses: (1) a group of field-based entities, sources, or objects, or (2) a dominant group in some way associated with that field.

In practice, depending upon the scientist's intent, dominant group may be the bad group that engages in monopolistic practices, or socially negative behavior such as discrimination, abuse, punishment, and additional possible criminal activity against other demographic groups.

It can also serve as an empirical identifier in observations. At one extreme, it is 100 % of the effect or phenomenon under study. At the other, it is a minority group effect that perhaps has some natural or artificial unfair advantage. In a society a dominant group often has an unfair advantage such as numbers, military power, or assets and money. Here's an example of how searching and using the power of the internet can bring about remarkable discoveries.

In an article that appeared in the American Scientist (May-June 2012) issue entitled "Herschel and the Puzzle of Infra-red", "Jack White mentions that it is not known who coined the term "infrared."" "A Google Books search for "infra-red" finds two articles published in April 1874, both of which use the term in the context of Edmond Bacquerel's treatise on light." There is an 1867 work using the French infra-rouge and one in English near the same time using "infra-red", "having translated it from the French."

The author responds that "ultra red" and "infra-red" appear in a paper from 1873, researched in 1960 "in the dark ages before the Internet. Rosenberg's find is a reminder of the Internet's amazing, growing power to search original works in different languages."

Evolution
The term dominant group and perhaps the concept the term represents has been an integral part of nearly every theory of evolution.

Hypothesis: As an evolutionary process, a dominant group may be a force for extinction by driving a number of groups to extinction and a force for speciation when spatial or temporal dispersion creates diversity and isolation which may eventually produce new groups. As a force for extinction a particular dominant group may also through its actions on other groups ultimately produce its own extinction event. This departure from a zone then allows other groups to fill the niche.

Changes in the characteristics or properties of a region may force the dominant group into extinction; thereby, making room for the next dominant group. However, some changes may not allow a dominant group to emerge. Additionally, properties of dominance may be appearance only. No competition for resources may have occurred.

Lexical pragmatics
From a metadefinitional point of view each use of dominant group has a relationship between members of the dominant group, a population from which the dominant group is a subset, a criterion for dominance, and a region, range, distribution or "in their own country". But, each of these four structures may have their meaning in the context within which the author or speaker places the two-word scientific/technical term.

Proposer qualifications
Much of the explorational data for reviewer evaluation sits within the resource structure and substructure of the dominant group research project displayed in the template entitled "Dominant group" near the bottom of this page.

Initial efforts using the scientific method may be found within the effort to demonstrate proof of concept.

Transformative concepts
"[T]wo-word glossary items are the most common technical terms". Dominant group is a likely two-word glossary item captured by data mining algorithms. A first-principle's demonstration that dominant group is a two-word scientific/technical term yields one test standard for data mining algorithms to find.

Dominant group serves as an indicator that original research has been conducted, especially when it appears in a primary source.

As a two-word scientific/technical term, is dominant group a member of the dominant group of two-word scientific/technical terms?

This exploratory investigation into dominant group and its usage has the potential to demonstrate that dominant group
 * 1) when identified is a causative force for change that by its nature requires further investigation,
 * 2) should be no longer used as a scientific/technical term because its meanings are unclear and vague, or
 * 3) identifies an inhibiting or moderating force that works against 'high-risk, high-reward' "research with an inherent high degree of uncertainty and the capability to produce a major impact on important problems in biomedical/behavioral research", or in other scientific/technical fields.

Conception and organization
This exploratory effort uses the template system (the dominant group template is near the bottom of this page) to organize and keep readily available the efforts already begun and those still needed.

Access to resources
Part of the challenge of this type of experimental inquiry is that authors of today or even in the 1800s are likely to use dominant group to describe the past when the term itself was actually not used by an earlier author.

University level access, including its medial research center, (both of which are available local to the principal investigator, PI) to much earlier original documents may be required to confirm the term earlier than 1826, its current date of specific use in English by Kirby. Local availability for interlibrary loan of needed resources also exists.

As Google scholar, for example, displays older and older manuscripts or books, especially before 1826, the probability increases of finding the term or eliminating its use by specific authors.

Web-based resources (including e-mail) are available to the PI.

Broader impacts
Exploring modern languages, languages on the verge of extinction, and extinct languages for terms that are either relative or exact synonyms (translations) for dominant group advances discovery and raises awareness of meaning and terminology.

For example: "In January 2008, a coalition of over 40 civil society groups endorsed a statement of principles calling for precautionary action related to nanotechnology." "The group has urged action based on eight principles. They are 1) A Precautionary Foundation 2) Mandatory Nano-specific Regulations 3) Health and Safety of the Public and Workers 4) Environmental Protection 5) Transparency 6) Public Participation 7) Inclusion of Broader Impacts and 8) Manufacturer Liability."

"Nanomedicines are just beginning to enter drug regulatory processes, but within a few decades could comprise a dominant group within the class of innovative pharmaceuticals, the current thinking of government safety and cost-effectiveness regulators appearing to be that these products give rise to few if any nano-specific issues. " Bold added.

Advancing discovery and training
"Ethnocide is when a dominant political group attempts to purposely put an end to a people’s traditional way of life. Linguicide (linguistic genocide) is when such a dominant group tries to extinguish the language of a minority group, say by punishing anyone caught speaking it." Exploring the meaning and use of dominant group in such context increases understanding of the forces at work characterized by the terms inclusion.

Underrepresented group participation
The proposed activity is ongoing at Wikiversity.

"Wikiversity is a Wikimedia Foundation project devoted to learning resources, learning projects, and research for use in all levels, types, and styles of education from pre-school to university, including professional training and informal learning. We invite teachers, students, and researchers to join us in creating open educational resources and collaborative learning communities. To learn more about Wikiversity, try a guided tour or start editing now."

Infrastructure enhancement
Information may be made available in various venues:
 * 1) databases or contributions to other databases of all institutions, agencies, and individuals who manage similar databases,
 * 2) contributions to ongoing network analyses, and
 * 3) information sharing and access.

Wikiversity is the premier online research and education database, facility, network and partnership of the WMF. That the proposed activity is ongoing at Wikiversity makes the information generated available through access and sharing.

"Just as an FYI, Wikiversity has been placed among the 'top picks' for this Google+ education list. It has been shared over 2000 times since its original posting. "

The proposed activity would partner NSF with Wikiversity to enhance the infrastructure for research and education, including where possible, facilities, instrumentation, and networks within Wikiversity and between Wikiversity and NSF.

Broad dissemination
Dominant group is an ongoing original research project that is being open-sourced here at Wikiversity both as a learning resource and to yield the broadest possible dissemination.

Benefits to society
"Dominant group(s)", designated vaguely by the term, and the associated ideologies of exclusion, serve as apparent focused power structures that increase existing disparities in wealth and status, while marginalizing or disenfranchising "Others".

This proposed activity explores the two-word term "dominant group" to increase awareness of what dominant groups are linguistically as well as socially and scientifically. As the original research effort is ongoing at Wikiversity it benefits all audiences that explore learning through Wikiversity. A successful collaboration between NSF and Wikiversity helps to disseminate the societal benefits of NSF to any local community where some access to the internet and computer terminals in various forms exists such as at pre-schools, elementary and secondary schools, high schools and universities.

Dominant group is a two-word term that occurs at least once in some 270 English Wikipedia entries. These usages may be original research, plagiarism, copyright violations, properly cited uses, or simply mistakes in usage by editors and contributors. Or, dominant group because of its long history may have become a commonly used two-word term that crosses the barrier between common language words that are in a dictionary and the scientific/technical vocabulary of specialists, scholars, and experts. On the general web as sampled by Google, dominant group yields about 513,000 results. Many of these relate right back to the ongoing research at Wikiversity or to the earlier dominant group entries on Wikipedia that were deleted as being original research.

As a potential indicator of copyright violation, dominant group may serve to help improve major web-based resources such as Wikipedia. On Wikipedia dominant group occurs in some 270 entries and as a split term such as dominant ethnic group in some 15,700 entries. Overall the English Wikipedia contains some 4,014,000 entries.

Articles or presentations of the research outside Wikiversity will be prepared openly here at Wikiversity as a teaching and training resource. Publication of such resources in open-access journals or scientific society journals benefits multiple audiences.

Before the benefits of the term and its relative synonyms is assessed, there is a need for some form of control group to serve as comparison. It should be noted that the two-word scientific term control group is a synonym of dominant group.

Hypotheses

 * 1) Funding for original research into the origin and radiation of dominant grooup to most fields of research may be difficult to justify because of its minority popularity.

title: Grants and fundraising/Funding


text:
User:EGM6321.f09.team1.Zhichao Gong/Mtg16

Mtg 16: Tue, 29 Sep 09

page16-1

Application: Homog. L2-ODE-VC

$${x}^{2}{y}^{''}-2x{y}^{'}+2y=0 \ {\color{red}(1)}$$

$${\color{blue} \underset{Transf. \ of \ var.}{ \underline {Meth1:}}} \ Let \ {\color{red} \underset{ \overset{\uparrow}{current \ var.}}}={e}^ \ {\color{red}(2)}$$

$${(.)}^{'}:=\frac{d}{dx}(.){\color{blue}={(.)}_{x}} \ {\color{green} Need \ symbol \ to \ designate \ \frac{d}{dt}(.)}$$

$$\overset{0}{(.)}:=\frac{d}{dt}(.){\color{blue}{(.)}_{t}}$$

$${\color{red}(1) \ \Rightarrow} \ {x}^{2}{y}_{xx}-2x{y}_{x}+2y=0 \ {\color{red}(3)}$$

$$Note: \ y(x)=y(x(t)) \ {\color{red}(4)}$$

$${\color{blue} \underset{{y}_{t}}{ \underbrace}}={\color{blue} \underset{{y}_{x}}{ \underbrace}}{\color{black} \underset{{e}^{t}}{ \underbrace}} \ \Rightarrow$$

page16-2

$$\frac{dy}{dx}=\frac{dy}{dt}{\color{blue} \underset{{(\frac{dx}{dt})}^{-1}={e}^{-t}}{ \underbrace}}=(\frac{dt}{dx} \frac{d}{dt})(y)$$

$$\Rightarrow$$

$$\frac{{d}^{2}y}{d{x}^{2}}=\frac{d}{dx}(\frac{d}{dx}y)={\color{red} \underset{ \underbrace}}$$

$$\Rightarrow$$

page16-3

Eq(3) p.16-1 $${y}_{tt}-3{y}_{t}+2y=0 \ {\color{red}(8)}$$

Homog. L2-ODE-CC CC means Const. Coeff.

Meth2: under coeff or

$${\color{red} \underline trial \ soln} \ {\color{blue}y={e}^{rt}} \ {\color{red}(9)}$$

Put(9) into (8) $$\Rightarrow$$ charac. eq. for r (=root)

$${r}^{2}-3r+2=0 \ \Rightarrow \ \begin{cases} & \ {r}_{1}=1 \\ & \ {r}_{2}=2 \end{cases}$$

$$y={\color{blue} \underset{lin. \ combo. \ of \ 2 \ trial \ soln.}{ \underbrace{{\color{black}{C}_{1}{e}^{{r}_{1}t}+{C}_{2}{r}^{2}}t}}}$$

$$={C}_{1}{({\color{blue} \underset{x}{ \underbrace}})}^{{r}_{1}}+{C}_{2}{({\color{blue} \underset{x}{ \underbrace}})}^{{r}_{2}}$$

page16-4

HW: Try solve Eq(1)p.16-1 directly using meth. of trial soln y=erx for b.c. y(1)=3 and y(2)=4 comp. soln w/ Eq(10) p.16-3
Use matlab to plot Soln.

$${\color{blue} \underline Appl:} \ {x}^{3}{y}^{'}-{x}^{2}{y}^{}-2x{y}^{'}-4y=0$$

$$Trial \ Soln: \ y={x}^{r}$$

$$Char. \ eq: \ ({r}^{2}+1)(r-4)=0$$

$$\Rightarrow$$

$$ {r}_{1}=4, \ \begin{cases} & {r}_{2}= +i, \ i=\sqrt{-1} \\ & {r}_{3}= -i \end{cases}$$

$$\ y(x)={C}_{1}{x}^{4}+{C}_{2}cos(logx)+{C}_{3}sin(logx)$$

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


text:
User:Egm4313.s12.team19.Horwitz

My contribution to Report 1

For Report 1, I compiled the report as a Word document and canverted it into a Wikimedia page. Furthermore, I made the user pages uniformly formatted for consistency and turned problem 1.3 into a Word document.

R2 Code test page

title: User:Egm4313.s12.team19.Horwitz


text:
User:EGM6321.f09.team1.Zhichao Gong/Mtg18

Mtg 18: Thu, 1 Oct 09

page18-1

HW: Develop reduct. of order meth using diff algebraic eqs:

$${\color{blue}1)} \ y(x)=U(x) \underset{-}{+} {u}_{1}(x)$$

$${\color{blue}2)} \ y(x)=U(x)/{u}_{1}(x)$$

$${\color{blue}3)} \ y(x)={u}_{1}(x)/U(x)$$

Application: $$(1-{x}^{2}){y}^{''}-2x{y}^{'}+2y=0 \ {\color{red}(1)}$$

homog. L2-ODE-VC

Given: $${u}_{1}=x{\color{blue}={x}^{+1}} \ {\color{blue}(2)}$$

Ans: $${u}_{2}(x)=\frac{x}{2}log(\frac{1+x}{1-x})-1 \ {\color{red}(3)}$$

$${u}_{2}(x){\color{blue}\neq {x}^{-1}}$$

$${a}_{1}=\frac{-2x}{1-{x}^{2}} \ {\color{red}(4)}$$

Rem: Comp.(1) to Legendre L2-ODE-VC $$\leftarrow$$ Eq(1) p.1402

page18-2

$$ \overset{-}{{a}_{1}}(t)=\int^{}_{t}{a}_{1}(s)ds=log(1-{t}^{2})$$

Eq.(2 ) p.17-4:                            K.p.6

$${u}_{2}=x \int^{}_{x}\frac{dt}{{t}^{2}(1-{t}^{2})}$$

$$=x \int^{}_{x} \left\{\frac{1}{{t}^{2}}+\frac{1}{2(1+t)}+\frac{1}{2(1-t)} \right\}dt$$

$${\color{red}=Eq.(3)} \ {\color{blue}p.18-1}$$

HW: Find u1(x) and u2(x) of Eq.(1)

p.18-1 using 2 trial solns:

$${\color{blue}1)} \ y=a{x}^{b}$$

$${\color{blue}2)} \ y={e}^{rx}$$

Comp the 2 solns using b.c.'s

y(0)=1, y(1)=2: and comp. to

soln by reduct. of order

method2. Plot solns with matlab

page18-3

Particular soln: non-homog. L2-ODE-VC

2 methods:

- trial soln(undet. coeff) = not dep. on knowledge of u1 and u2

- var. of parameters: (dep. on knowledge of u1 and u2)

u1 and u2 are homog. solns.

Assume full soln y of non-homog L2-ODE-VC Eq(1)p.3-1

$${\color{red}(1)} \ y(x)={c}_{1}{\color{red}(x)}{u}_{1}(x)+{c}_{2}{\color{red}(x)}{u}_{2}(x)$$

Find c1(x) and c2(x) unkown

Given u1(x) and u2(x) known

$${\color{red}(2)} \ {y}^{'}=({c}^{'}_{1}{u}_{1}+{c}_{1}{u}^{'}_{1})+({c}^{'}_{2}{u}_{2}+{c}_{2}{u}^{'}_{2})$$

If c1 and c2 were const, then

$${c}^{'}_{1}={c}^{'}_{2}=0$$

page18-4

Break thru assump:

$${\color{blue} \underset{ \overset{\neq}{0}}}{u}_{1}+{\color{blue} \underset{ \overset{\neq}{0}}}{u}_{2}=0 \ {\color{red}(1)}$$

$${\color{red}(2)} \ \underset{\Rightarrow} \ {y}^{'}={c}_{1}{u}^{'}_{1}+{c}_{2}{u}^{'}_{2} \ {\color{red}(2)}$$

$${\color{blue}Q:} \ why \ not \ {c}^{'}_{1}{u}^{'}_{1}+{c}^{'}_{2}{u}^{'}_{2}=0$$

$${y}^{}=[{c}^{'}_{1}{u}^{'}_{1}+{c}_{1}{u}^{}_{1}]+[{c}^{'}_{2}{u}^{'}_{2}+{c}_{2}{u}^{''}_{2}]$$


text:
User:Egm4313.s12.team7.d'amico

User:egm4313.s12.team7.d'amico/R1.1

User:egm4313.s12.team7.d'amico/R1.2

User:egm4313.s12.team7.d'amico/R1.3

User:egm4313.s12.team7.d'amico/R1.4

User:egm4313.s12.team7.d'amico/R1.5

title: User:Egm4313.s12.team7.d'amico


text:
User:Egm4313.s12.team7.d'amico/Lecture 1

hello


text:
User:EGM6321.f09.team1.Zhichao Gong/Mtg20

Mtg 20: Thu, 8 Oct 09

page20-1

(3) & (4) p.19-3 : c1(x), c2(x) in (1)p.18-3

$$y(x)={\color{blue} \underset{{y}^{(x)}_{H}}{ \underbrace}}+{\color{blue} \underset{{y}^{(x)}_{H}}{ \underbrace}}+{\color{blue} \underset{{y}^{(x)}_{P}}{ \underbrace}}$$

Application: $${y}^{''}+y=xsinx=f(x)$$

Homog. soln: $$ \begin{cases} & {u}_{1}(x)=cosx \\ & {u}_{2}(x)=sinx \end{cases}$$

Note:trial soln $${y}_{H}={e}^{x}$$

$${r}^{2}+1=0 \ \Rightarrow \ r=+i, \ -i \ i=\sqrt{-1}$$

de Moivre $${e}^{i{\color{red}x}}=cosx+isinx$$

$$ \underset{-}{W}= \begin{bmatrix} \ cosx & sinx \\ -sinx & cosx \end{bmatrix} \Rightarrow W=det \underset{-}{W}=1$$

page20-2

$${d}^{(x)}_{1}=-\int^{}_{x}\frac{(sins)(ssins)}{1}ds$$

$${d}^{(x)}_{2}=-\int^{}_{x}\frac{(coss)(scoss)}{1}ds$$

$$y(x)=Acosx+Bsinx-\frac{1}{4}{x}^{2}cosx+\frac{1}{4}xsinx$$

K. p. 8

Trial solns for non-homog L2-ODE-CC(const coeff)

(for part. soln yp)

$${a}_{2}{y}^{''}+{a}_{1}{y}^{'}+{a}_{0}y=f(x)$$

$${a}_{1}, \ {a}_{2}, \ {a}_{3}=const.$$

$${\color{red}\underline{f(x)}} \ \ {\color{blue}|} \  \ {\color{red}\underline{Trial \ Soln \ y(x)}}$$ $${P}_{n}(x)=\sum_{i=0}^{n}{\color{blue} \underset{ \overset{\uparrow}{known \ coeff}}}{x}^{i} \ \ {\color{blue}|} \  \ y(x)={x}^{m}\sum_{i=0}^{n}{\color{blue} \underset{ \overset{\uparrow}{unknown \ coeff. \ to \ be \ determined}}}{x}^{i}$$

page20-3

$${p}_{n}(x){e}^{{\color{blue} \underset{ \overset{\uparrow}{known}}{{\color{black}\alpha}}}x} \ \  {\color{blue}|} \  \ {x}^{m}(\sum_{n}^{i=0}{c}_{i}{x}^{i}){e}^{\alpha x}$$ $${p}_{n}{e}^{\alpha x} \begin{cases} & sin \beta x \\ & cos \beta x \end{cases} \ \ {\color{blue}|} \ {x}^{m}{e}^{\alpha x} \left[(\sum_{i=0}^{n}{c}_{i}{x}^{i})sin\beta x +(\sum_{i=0}^{n}{d}_{i}{x}^{i}cos \beta x) \right]$$

Trial soln for non-homog. L2-ODE-VC

(Note: Trial soln meth. also applicable to Nn-ODE)('Guess')

Application:

$${y}^{''}-\frac{2}{{x}^{2}}y=7{x}^{4}+3{x}^{3}$$

Note: Homog. ODE

$${\color{blue} \underset{Euler \ eq. \ p.15-4}{ \underbrace}}=0$$

Trial soln:

$$y(x)={\color{blue}a}{x}^$$

a, b areunknow coeff.

page20-4

$${\color{red} \underset{ \underbrace}}=7{x}^{4}+3{x}^{3} \ {\color{red}(1)}$$

$${\color{blue}1)} \ b=-1 \ \Rightarrow \ {b}^{2}-b-2=0$$


text:
User talk:Egm4313.s12.team16.brandonw

My name is Brandon Wright

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title: User talk:Egm4313.s12.team16.brandonw


text:
Dominant group/Journals

The two-word term dominant group appears to occur most often in articles within periodicals (or journals), conference proceedings, and least often in books. Although the earliest occurrence so far is within a book published in 1826. Relative synonyms for the term have been discovered as far back as 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." Bold added. And, another, “die Dominanten Religionen von ganz Europa” occurs in 1726. Bold added.

This learning resource focuses on those most recent periodicals that include the term in an article, possibly discuss the term in some way, or directly focus research on the term. Initially, discovering at least one use of the term places the journal on the list, but including those that do not, perhaps versus impact factor, may be important.

The objective is to determine through research the category of periodicals most likely to publish or desire to publish an article about the term dominant group.

As the answer to the search is unknown, this learning resource is an exploratory research effort. It is conceded from the beginning that there is in all likelihood at least one expert somewhere who probably knows from experience the best journal within which to publish such an article on dominant group and in fact the funding agency most able to provide publication costs, at the minimum.

Ultimately, interviews with authors who have used and continue to use the term dominant group in their articles may be necessary.

Synonyms
The term patrician class seems to be the earliest relative synonym for dominant group.

"According to Livy, the first 100 men appointed as senators by Romulus were referred to as "fathers" (patres), and the descendants of those men became the Patrician class. The patricians were distinct from the plebeians because they had wider political influence, at least in the times of the Republic."

Romulus may not have been a human, but something in the sky used by a group of humans to make themselves into a ruling class, or by using religion to reinforce their dominance over others.

Onomantics
That dominant group occurs in at least one journal has been demonstrated. That dominant group occurs at least once in almost every journal is possible with about 71,550 occurrences of the two-word term in the scholarly literature. Although its frequency in any subject is low (usually less than 3 % of the articles), its frequency across subjects is not a constant, and it may be picked up by data mining search engines looking for relevant terms.

Def. "the science and practice of term evaluation" is called onometrics.

"Since onometrics adds rationality to the evaluation of terms, we can eliminate much of the same subjectivity (in the form of personal taste, personal connotations, ego, etc.) which all science seeks to avoid."

"In formal metrics, as in any scientific approach, clear and precise definitions are crucial."

"The ... field ... is the scientific or technological field of the object. ... [F]or onometrics it is terminology science' and ultimately language science or linguistics."

Def. "a terminological approach in which first a concept is given and then its name or names are sought" is called onomantics.

Def. "anything artificially produced (by man), including not only tangible objects and substances but intangibles such as services, procedures, programs, plans, and ideas" is called an artifact.

Here is the key question: Is dominant group in context "selecting and using good terminology."

Term-evaluating criteria:
 * 1) Accuracy
 * 2) Precision - Semantics
 * 3) Descriptiveness
 * 4) Unequivocalness
 * 5) Mononymy
 * 6) Appropriate Register - Vocality
 * 7) Precedent
 * 8) Conciseness - Efficiency
 * 9) Appropriate Simplicity
 * 10) Form Correctness - Morphology
 * 11) Etymological Purity
 * 12) Derivability
 * 13) Inflectability - Uniformity
 * 14) Series Uniformity
 * 15) Acceptability - Diction
 * 16) Euphony - Phonetics
 * 17) Pronounceability.

"[N]aming often involves finding a satisfactory balance among conflicting criteria."

Communications
Discourse & Society

"Negative emotions in the dominant group, such as anger and guilt, were neither central nor salient in justifying the apology."

"Racist assaults characteristically involve members of a dominant group speaking or acting against members of ethnic or religious minority groups."

"The first form of stigmatization is poverty, which occurs when the dominant group is able to monopolize the highest social positions in terms of power, social prestige and material advantage."

"The majority population was the dominant group, responsible for the process of doing and saying as actors and sayers."

Technical Communication Quarterly

Culture
International Journal of Intercultural Relations

"This strategy attempts to achieve the goals of empowering of members of the minority group and helping the dominant group develop new insights into their ambivalence and power orientation (Maoz & Bar-On, 2000)."

Sexuality & Culture

Citizenship Studies

"The same pattern also persisted in Rome from its founding until the sixth century BC (753-510 BC), when the king was overthrown and driven out of the city. This upheaval was apparently related to the rise of a patrician class which owned the means of warfare."

The Slavonic and East European Review

"The dervish sees the treatment of his brother as an insult to his honour and position and manages to topple the local officialdom, but he cannot overcome the solidarity of the patrician class. First he is disgraced by a campaign of rumours and then he is crushed."

Ecology
Applied Soil Ecology

Aquatic Toxicology

Biochemical Systematics and Ecology

Deep Sea Research Part I: Oceanographic Research Papers

Desalination

Ecological Modelling

Environmental Pollution

Estuarine, Coastal and Shelf Science

Journal of Environmental Management

Journal of Environmental Radioactivity

Journal of Experimental Marine Biology and Ecology

Journal of Great Lakes Research

Journal of Marine Systems

Journal of Microbiological Methods

Limnologica - Ecology and Management of Inland Waters

Marine Pollution Bulletin

Nematology

"All nematode trophic groups were present in the investigated birch forests, with bacteriovores being the dominant group, followed by plant-parasitic nematodes, fungal feeders, root-fungal feeders, omnivores and predators."

Pedobiologia

Remote Sensing of Environment

Research in Microbiology

Soil Biology and Biochemistry

Water Research

Economics
International Business Review

Journal of Banking & Finance

Journal of Economic Behavior & Organization

Journal of Macroeconomics

Journal of Public Economics

Labour Economics

Education
International Journal of Educational Development

The Journal of Negro Education

Journal of Teacher Education

Teaching and Teacher Education

"Today's “mugwumps” are not defending a declining patrician class, but are pushing an orthodoxy that is fundamentally anti-intellectual, in the name, of course, of educational improvement."

Ethnicity
Ethnicities

Journal of Asian and African Studies

Journal of Black Studies

Evolution
Archives of Biochemistry and Biophysics

Human Development

Food
Acta Agrophysica

"All the species were in the eudominant group and the most numerously collected was Dalopius marginatus (D = 50.0%)."

Anaerobe

Food Chemistry

Food Control

Scientia Horticulturae

Geography
Journal of Transport Geography

Geology
Chemical Geology

Geomorphology

Journal of Volcanology and Geothermal Research

Marine Geology

Palaeogeography, Palaeoclimatology, Palaeoecology

Health care
Alimentary Pharmacology & Therapeutics

Biochimica et Biophysica Acta

Biochimica et Biophysica Acta (BBA) - Molecular Basis of Disease

European Journal of Radiology

FEMS Immunology & Medical Microbiology

Journal de Mycologie Médicale / Journal of Medical Mycology

Seminars in Fetal and Neonatal Medicine

Social Science & Medicine

History
The American Historical Review

"This allows him to address the culture of these two institutions, which for him represent the competing approaches to medicine in the period. As with his earlier work, Lawrence asserts the influence of elite hospital physicians—or a patrician class—on the faculty and hospital."

Humanities
Computers and the Humanities

"However, for reasons not clear to me, they are not uncomfortable sharing the company of people who have yet to publish a grand synthesis or to edit an important text, or otherwise establish themselves in the dominant group."

Human Development

"Berry and his colleagues suggest that the assimilation strategy occurs when the individual decides not to maintain his or her cultural identity by seeking contact in his/her daily interaction with the dominant group."

International Critical Thought

"The effect of this structure was that executive power in Rome was always held by a member of the slave-owning patrician class."

Journal of Medical Humanities

"It is often the group that is being assailed through medical categorization that makes the point that they are oppressed, subjected to the violence of the dominant group."

Medical Humanities

"But more often, difference is identified as a negative deviation from the norms of a dominant group."

Language
Applied Psycholinguistics

Brain and Language

Clinical linguistics & phonetics

International Journal of Bilingualism

Journal of Language Contact

Journal of Speech, Language, and Hearing Research

Journal of Sociolinguistics

Philosophical Perspectives

Materials science
International Journal of Multiphase Flow

Materials Chemistry and Physics

Metagenome
Journal of Proteomics

Paleontology
Cretaceous Research

Gondwana Research

Quaternary International

Philosophy
Philosophical Perspectives

Political science
Political Studies (2012)

Scandinavian Political Studies

Psychology
The psychology of groups as well as meaning often includes discussions of a dominant group.

Acta Psychologica (1997)

Adolescence

Advances in Experimental Social Psychology (2005)

American Behavioral Scientist (1984)

American Journal of Community Psychology

American Journal of Orthopsychiatry

American Psychologist (2001)

Animal Behaviour (2012)

Antipode (2012)

Applied Animal Behaviour Science

Applied and Preventive Psychology (1994)

Asian Journal of Social Psychology (2012)

"[T]he dominant group of Malay had higher in-group indispensability, more strongly endorsed an inclusive national representation, had stronger ethnic and national identification, and a stronger association between both identifications."

Australian Journal of Psychology (1986)

Brain and Language (1978)

British Journal of Management (2012)

British Journal of Social Psychology (2006)

Children and Youth Services Review (2007)

Cognitive Psychology (1992)

Culture & Psychology

Current Directions in Psychological Science (2007)

European Economic Review (2011)

European Journal of Social Psychology (2005)

Group Processes & Intergroup Relations (2003)

International Journal of Intercultural Relations (2011)

International Journal of Psychology (2000)

International Migration

Journal of Abnormal Psychology

Journal of Abnormal and Social Psychology

Journal of Applied Social Psychology (2012)

Journal of Business and Psychology

Journal of Community and Applied Social Psychology

Journal of Consumer Psychology (1995)

Journal of Cross-Cultural Psychology

Journal of Economic Behavior & Organization

Journal of Experimental Social Psychology (2012)

Journal of Humanistic Psychology (1989)

"When an illiterate peasant claims to be powerless, Freire wants to know how this was learned and whether it is really true or merely an untested myth promoted by the dominant group, which the peasant has incorporated."

Journal of Organizational Behavior (2012)

Journal of Personality and Social Psychology (2008)

Journal of Research in Personality

Journal of Social Psychology (2002)

Journal of Vocational Behavior (2012)

Mis Quarterly (1996)

Negotiation Journal (2002)

Nursing Inquiry (2012)

Organizational Behavior and Human Decision Processes

Personality and Individual Differences (2005)

Personality and Social Psychology Bulletin (2004)

Political Psychology (2012)

Psychological Review (2008)

Psychological Science (2000)

Social Psychology of Education (2001)

Social Psychology Quarterly (1980)

Social Science & Medicine (2011)

Socio-Economic Planning Sciences (2010)

Theory and Psychology (1999)

Trends in Cognitive Sciences (2008)

Women's Studies International Forum (2007)

Regions
Journal of Rural Studies

Semantics
Journals and periodicals are included under semantics when an article is published dealing with semantics and dominant group. These include possible publication of an article about the term dominant group.

Aphasiology

Brain

Cognition

Cognitive Brain Research

Cognitive psychology

European Journal of International Relations

History and Memory

International Journal of Qualitative Studies in Education

Journal of Semantics: according to a Google scholar search this journal has never published any article containing the term dominant group.

Journal of Web Semantics: none.

Linguistics and Philosophy

Natural Language Semantics: none.

Nature

Qualitative Inquiry

The Journal of Nervous and Mental Disease

Sociology
American Journal of Economics and Sociology (2012)

American Journal of Sociology

Analyses of Social Issues and Public Policy (2012)

Children and Youth Services Review

Disability, Handicap & Society

European Journal of Political Research

International Sociology

Journal of Health and Social Behavior

Journal of Social Issues (2012)

Journal of Urban Affairs (2012)

Law and Social Inquiry (2012)

Peace Review

Social Identities

Society

Sociological Perspectives

Sociology Compass (2012)

Tourism Management

Transforming Anthropology (2012)

Technology
Information Sciences

New Biotechnology

Telecommunications Policy

Telematics and Informatics

Terminology
Terminology - zero articles contain the two-word term dominant group.

Hypotheses

 * 1) Finding an appropriate journal for an article about dominant group may be harder than finding out what dominant group is.

title: Dominant group/Journals


text:
User:Egm4313.s12.team4.patel

This is my home page
 * 1) Report 1

 * 1) TEST

title: User:Egm4313.s12.team4.patel


text:
User:Egm4313.s12.team14.kimiagarov

PDF to djvu

Main course wiki

Team14 Page

Help Page

Videos and Notes

HW 1

HW 2

HW 5

title: User:Egm4313.s12.team14.kimiagarov


text:
User:Egm4313.s12.team3.pliskow

Our Official Team Reports
Report 1 [] Report 2 Report 3 Report 4 Report 5 Report 6 Report 7

My Work for Team Reports
My Report 1 Work: [] My Report 2 Work: [] My Report 3 Work: My Report 4 Work: My Report 5 Work: My Report 6 Work: My Report 7 Work:

Course Links
Course Wiki []

Report Table []

Online Lectures/Notes

Good Model Reports []

Displaying in the Mediawiki Environment

Grading Criteria []

My Report 1 Work []

title: User:Egm4313.s12.team3.pliskow


text:
Government-Business Relations/FAQs

Frequently Asked Questions for 6606 Government-Business Relations:

Are lectures video recorded?
Yes. All lectures are video recorded and will be available via links provided on this site.

Am I required to attend lectures and tutorials?
Yes. Although some activities are conducted online, this is designed to be a face-to-face unit. However, all lectures will be video-recorded. Please note that you are required to attend a two-hour Final Exam during the exam period and you MUST attempt all assessment items to pass this unit.

Am I required to attend both lectures?
No. You can attend either lecture, or both, or none. It is up to you. Please note that the content of both lectures is the same, but since this is a large class and many students in the Faculty of Business, Government & Law work full-time, we offer two lecture times. Both lectures are video-recorded.

Do I need to provide a preference for my lecture time?
No. You can attend any lecture and attendance is not recorded at lectures.

There are two different types of tutorials. Do I need to enrol in both?
No. If you want to use your own computer or mobile device, then you should select a "Bring Own Computer To The Class" tutorial. However, if you do not have your own device or you would prefer to use one of the University's computers, then you should enrol in one of the "Computers Supplied in Computer Lab" tutorials.

What does "face-to-face and online (F2FO)" mode mean?
Face-to-face and online (F2FO) mode means that all lectures are video-recorded and some tutorial activities will be conducted online. Please note that you will be required to attend the Final Exam in accordance with the exam timetable.

What are the assessment items for this unit?
This unit is assessed as follows:

''' NOTE: To pass this unit, you MUST submit all assessment items AND obtain a minimum of 40% in the final exam AND obtain a mark of at least 50% overall. '''
 * Assignment 1: Referencing & Researching Activity (Blog, 500 words): 20% (Due 5pm Friday Week 5)
 * Assignment 2: Academic Essay (Blog, 2,000 words): 40% (Due 9am Friday Week 12)
 * Assignment 3: Final Exam 80 multiple choice questions, 2 hours (Exam Period)
 * Total: 100%

What is the textbook for this unit?
The textbook for this an e-text. Please see the unit Moodle site for details.

What if I don't like reading online?
This unit is specifically designed to be paperless (except for the Final Exam). There are two reasons for this: (1) "Paperless" means less impact on the environment in accordance with the University of Canberra's strategy; and (2) Learning to screen-read is an essential skill in today's fast-paced business environment. There are still plenty of opportunities to use paper-based materials (such as library books or in other units) but this unit deliberately requires you to operate in a paperless environment.

How do I count the total number of words in my essay?
Easy. The number of words includes the first word of the first sentence of your assignment to the last word of the last sentence of your assignment. The reference list is not included in the word count but in-text referencing does count. The easiest way to check the number of words in your assignment is to copy and paste your work into http://www.wordcounttool.com/ and click "Submit". This will give you the number of words. In this unit, the number of words is prescribed, but you have a +/-10% leeway. For example, a 2,000 word essay means your word count should be between 1,800 words and 2,200 words.

title: Government-Business Relations/FAQs


text:
User:Egm4313.s12.team8.tclamb

R1.1

R2.8

R3.2

R4.4.1

R5.9

R6.6

R6 Level 2

R7.2

R7 Level 2

title: User:Egm4313.s12.team8.tclamb


title: File:C.Work.Function.1.A.20120117.pdf


title: File:C.Work.Scope.1.A.20120117.pdf


title: File:Cpp.Poly.1.A.20120117.pdf


title: File:Java.Poly.1.A.20120117.pdf


text:
User:Egm4313.s12.team8.tclamb/R1

=R1.1 - Equation of Motion for a Parallel Spring-Dashpot System=

Find
Derive the equation of motion of a spring-dashpot system in parallel, with a mass and applied force $$f(t)$$.

Solution
Solved on my own

Kinematics

 * $$\displaystyle\begin{align}

y = y_k = y_c \end{align}$$

Kinetics

 * $$\displaystyle m y'' + f_k + f_c = f(t)$$

Constitutive Relations

 * $$\displaystyle\begin{align}

f_k &= k y_k \\ f_c &= c y_c' \end{align}$$

Therefore

 * $$\displaystyle m y''(t) + c y'(t) + k y(t) = f(t)$$

The general solution of the above ODE is:

 * $$\displaystyle\begin{align}

y_g (t) &= C_1 \; e^{\frac{-c - \sqrt{c^2 - 4 m k}}{2 m} t} \\ &+ C_2 \; e^{\frac{-c + \sqrt{c^2 - 4 m k}}{2 m} t} \\ &- \frac{\int e^{\frac{\left( c + \sqrt{c^2 + 4 m k} \right) t}{2 m}} f(t) \,dt}{\sqrt{c^2 - 4 m k}} \; e^{\frac{-c - \sqrt{c^2 - 4 m k}}{2 m} t} \\ &+ \frac{\int e^{\frac{\left( c - \sqrt{c^2 + 4 m k} \right) t}{2 m}} f(t) \,dt}{\sqrt{c^2 - 4 m k}} \; e^{\frac{-c + \sqrt{c^2 - 4 m k}}{2 m} t} \end{align}$$

title: User:Egm4313.s12.team8.tclamb/R1


text:
User:Mattski au/Creativity and Mindfulness

Theory
Does Mindfulness help or hinder the process of  Creativity?

Mindfulness is the ability to align one's self with a desired way of life, it provides the ability to be free from social norms and pressures felt from peers.
 * The process of creativity can flourish without fear.
 * Mindfulness can benefit the process of Creativity.
 * Through the Broaden and Build theory, creativity can flourish through the upward spiral of emotions.
 * Mindfulness and creativity are both related to openness and flexibility which allow for the consideration of different and altering perspectives.

Hypothesis

 * Mindfulness will have a positive effect on the creative process and product.
 * Mindfulness will be effective across all domains of the creative process.

Participants
University students enrolled in three units, which assess creativity as part of the major assessment (ie. writing, art, and architecture/design).

Method
A 3x2x2 mixed group design: participants in each unit will be separated into two groups (control and a mindfulness training group). The participant’s will fill out questionnaires, looking at mindfulness (TEST TYPE) and on their creativity (TEST TYPE), at the beginning of the class and after they submit their final assessment. A further written self-report evaluating their creativity process on assessment will be conducted on unit completion.


text:
User talk:Curly5

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Thank you for experimenting with the page I would like to learn tagalog, do you offer free classes? on Wikiversity. Your test worked, and it has been reverted or removed. Please use the sandbox for any other tests you want to do. Take a look at the welcome page if you would like to learn more about contributing. Ruy Pugliesi ◥ 14:18, 17 January 2012 (UTC)

title: User talk:Curly5


text:
User:Egm4313.s12.team2.nicellis44

$$\frac{\partial u }{\partial t}=\kappa\frac{\partial^2 u}{\partial x^2} $$ First, decompose u into its component functions in x and t $$ u(x,t)=F(x)G(t)  $$ Then substitute this expression for u back into the heat equation to yield: $$ F(x)*\dot G(t)=\kappa*(\ddot F(x)*G(t)  $$ Rearrange so that X varying terms are on one side of the equation and T varying terms on the other.   $$\frac {\dot G(t)}{\kappa G(t)}=\frac{\kappa \ddot F(x)}{F(x)}=C (constant) $$ As both equations are equal to the same constant C, they can be separated and both independently set equal to C.    $$\frac {\dot G(t)}{\kappa G(t)}=C $$, $$ \frac{\kappa \ddot F(x)}{F(x)}=C $$ These equations are then rearranged to set them equal to zero.  $$ \dot G(t)-C \kappa G(t)=0 $$  ,  $$ \kappa \ddot F(x)-C F(x)=0 $$ The resulting homogenous differential equations can then be represented in standard ODE notation.   $$ (1)\frac{dG} {dt}-(C \kappa) G=0 $$ $$  (\kappa) \frac{d^2 F}{dx^2}-(C)F=0 $$

title: User:Egm4313.s12.team2.nicellis44


text:
User talk:Mattski au/Creativity and Mindfulness

=How to measure creativity?= A fundamental problem that first hit me when looking at this research proposal was the factor of being able to measure creativity, for example:
 * In an experiment does one use laymen? Or does one use artist?
 * How would you compare between different people?
 * Where does creativity stop and technical ability begin (ie. drawing, painting, drama)?
 * Using Self-Report for creativity: I was thinking about using self-report for people to detail their perception and process of creativity. The reason for this is to embody creativity as a "process" rather then an achievable state; People know their own states of creativity.

=Research Method= For this research proposal I am thinking of using three university courses which involves an aspect of creativity as the main assessment - an architecture, art and writing course - and within each course have a controlled group and a group which will be provided with mindfulness lessons. A pre-test will involve two parts: a self-report of students creative abilities, and a "creativity" test made up of problem-solving, etc. After the course the groups will be tested again using the same methods, plus an extra question asking specifically about the student's creativity for the major assignment in the completed course.

The use of the three different classes needs to carefully considered though, although the ease of just looking at one class seems enough to look at the effect of mindfulness on creativity, the question still remains: Does mindfulness work the same on the creative process across different domains? There are variables that need to be considered when/if looking across the three classes though, such as if the marking weight of the assessment varies, how the assessment is marked (i.e. if there is a stronger theoretical basis in one class opposed to design of another) and university level of the courses (ie. an introduction level or third year with perquisites).

Other variables to consider: Students work load (both inside and outside university), the communication of the controlled groups and the mindfulness groups, the student's desire to do the course, and the social factor of the "lecturer" being the judge of the assessment. Blondlox 22:27, 23 January 2012 (UTC)


text:
User talk:Egm4313.s12.team20.calvo

I am new :)

title: User talk:Egm4313.s12.team20.calvo


text:
User:EGM4313.spr12.team5.wallace

Lecture 1

title: User:EGM4313.spr12.team5.wallace


text:
User:Egm4313.s12.team20.calvo

R1.1

title: User:Egm4313.s12.team20.calvo


text:
User:Egm4313.s12.team20.calvo/HW1

I am new to this $$\alpha - \beta = \gamma$$

title: User:Egm4313.s12.team20.calvo/HW1


text:
Big bang/a critique of The cosmological constant is back

(Review Paper) Cited in


text:
User:EGM6321.f09.team1.Zhichao Gong/Mtg22

Mtg 22: Tue, 13 Oct 09

page22-1

- p.12-3 - p.20-3: Trial soln for non-homog. L2-ODE-CC Note on m, \alpha, \beta in table: m=0, 1, 2 = number of times that 0 (zero) is root of char. eq. so to make sure that no terms in trial soln (particular soln) is
a homog.soln.

$$\alpha \ \in \ R \ is \ a \ root. \ of \ char. \ eq.$$

$$\alpha+i \beta \ \in \ {\color{blue} \underset{ \overset{\uparrow}{set \ of \ complex \ numbers \ (black \ board \ font)}}} \ is \ another \ root \ of \ char. \ eq. \ \beta \in \ R$$

HW: K. p.28, pb. 1.3.a.

Application:

$${y}^{''}-2x{y}^{'}+2y=3$$

Non-homog. L2-ODE-VC

$$Homog. \ soln: \ {u}_{1}(x)=x$$

page22-2

(3) p.21-3 $$\Rightarrow \ x{Z}^{'}+2(1-{x}^{2})Z=3$$

Find Z by (4) p.8-2

(4) p.21-3 $$\Rightarrow \ U(x)=\frac{3}{2x}+A \int_{\frac{1}{{s}^{2}}}^{x}exp({s}^{2})ds+B$$

$$y(x)=U(x){\color{blue} \underset{x}{ \underbrace}}$$

HW cf. K. p.28, pb. 1.1 . b

$${\color{blue}b)} \ {\color{blue} \underset{HOW? \ {\color{red}Pretend \ not \ knowing.}}{ \underbrace}}=\frac{sinx}{x} \ homog \ soln \ for$$

$$x{y}^{''}=2{y}^{'}+xy={\color{red} \underset{ \overset{\uparrow}{WORD}}} \ {\color{red}(1)}$$

1) Verify exactness of(1).

Int. fact. meth. 2

2) Trial solns

 2.1) y(x)erx, r=const

  2.2) y(x)=xerx, r=const

page22-3

(3) p.21-3 $$\Rightarrow \ x{Z}^{'}+2(1-{x}^{2})Z=3$$

Find Z by (4) p.8-2

(4) p.21-3 $$\Rightarrow \ U(x)=\frac{3}{2x}+A \int_{\frac{1}{{s}^{2}}}^{x}exp({s}^{2})ds+B$$

$$y(x)=U(x){\color{blue} \underset{x}{ \underbrace}}$$

HW cf. K. p.28, pb. 1.1 . b

$${\color{blue}b)} \ {\color{blue} \underset{HOW? \ {\color{red}Pretend \ not \ knowing.}}{ \underbrace}}=\frac{sinx}{x} \ homog \ soln \ for$$

$$x{y}^{''}=2{y}^{'}+xy={\color{red} \underset{ \overset{\uparrow}{WORD}}} \ {\color{red}(1)}$$

1) Verify exactness of(1).

Int. fact. meth. 2

2) Trial solns

 2.1) y(x)erx, r=const

  2.2) y(x)=xerx, r=const

page22-4

2.3) y(x)=1/x(erx) ,

3) Use undet. fact. meth.

to find u2(x), knowing u1(x),

compare to above results.

HW: Describe in words step-by-step

meth. of attacking similar pbs, given

only homog. and non-homog.L2-ODE-VC


text:
User:EGM6321.f09.team1.Zhichao Gong/Mtg24

Mtg 24: Thu, 15 Oct 09

page24-1

Chladni :

 * PEA1.F09.Mtg24.pg1.fig1.new.svg

p=mass / area T=uniform tension in membr.

$$ \underset{({\color{black} \underset{ \overset{\uparrow}{spatial \ coord.(1-D) \ \psi=ps;}}},{\color{black} \underset{ \overset{\uparrow}{time}}})} \ {\color{blue} \underset{ \overset{\uparrow}{generic \ dep. \ var.}}} \equiv {\color{blue} \underset{ \overset{\uparrow}{trans. \ disp \ membr.}}}$$

$${\color{red}(2)} \ \frac{{\partial}^{2}\psi}{\partial {x}^{2}}=\frac{1}{{c}^{2}}\frac{{\partial}^{2}\psi}{\partial {t}^{2}}$$

page24-2

$$Sep. \ of \ var: \ {\color{red} \underset{ \overset{\uparrow}{{\color{blue}Ansatz}(guess) \ (trial \ soln)}}}=X(x){\color{blue} \underset{T(t)}{ \underbrace}} \ {\color{red}(3)}$$

$$i=\sqrt{-1}$$

(3) in (2): $${\color{blue} \underset{ \overset{||}{0}}}{\color{blue} \underset{\neq 0}{ \underbrace}}=0$$

1.D Helmholtz eq.

$${\color{red}\underset{separeted \ ed. \ for \ X}{\underline{{X}^{''}+{k}^{2}X=0, \ {k}^{2}=\frac{{\omega}^{2}}{{c}^{2}}}}}$$

Trial solns$$\Rightarrow$$ coskx, sinkx

Note:

$$\ast \ \frac{{\partial}^{2}\psi}{\partial {t}^{2}}=X{{\color{red} \underset{-}{+}}i\omega}^{2}{e}^{{\color{red} \underset{-}{+}}i\omega t}$$

$$\ast \ Add \ \underset{-}{+}2\pi \ in \ exp({\color{red} \underset{-}{+}}i\omega t \underset{-}{+}{\color{blue} \underset{\psi}{ \underbrace}})$$

$$\psi(x, \ t)=X(x)exp({\color{red} \underset{-}{+}}i\omega t \ + \ \psi)$$

$$X(x)={e}^{ikx}$$

$$\psi(x, \ t)={\color{red} \underset{ \overset{\uparrow}{Amplitude(Const)}}}{e}^{ikx}{e}^{\underset{-}{+}i\omega t}$$

page24-3

$$\psi(x, \ t)=A{e}^{i(kx \underset{-}{+}\omega t)}$$

$$=A{e}^{ik(x \underset{-}{+}ct)}$$

$$\omega \ = \ freq. \ in \ time$$

$$k \ = \ freq. \ in \ space{\color{blue}(ware \ number)}$$

More gen. soln:

$$\psi(x, \ t)=G(x{\color{red}\underset{-}{+}}ct) \ {\color{blue}K. \ p. \ 82}$$

 * PEA1.F09.Mtg24.pg3.fig1.new.svg

Wave eq. in 1-D is shape preserving. c>0 speed. + out going wave (+ x direction) - incoming wave (- x direction) Wave eq in 2-D more complex
                    3-D even more complex

      curv. coordinate (even more complex)2


text:
User:Areil314/sandbox/new page

(Review Paper) Cited in

title: User:Areil314/sandbox/new page


text:
User:EGM6321.f09.team1.Zhichao Gong/Mtg28

Mtg 28: Tue, 27 Oct 09

page28-1

(Mtgs 26+27 : Exam 1, Thu, 22 Oct)

 * PEA1.F09.Mtg28.pg1.fig1.svg :PEA1.F09.Mtg28.pg1.fig2.svg
 * PEA1.F09.Mtg28.pg1.fig3.svg

Gen. to 3-D: polar (2D) $$\rightarrow$$ spherical (3D)

Elliptic (2D) $$\rightarrow$$ Elliseidal coord. (3D)

Ellipse $$\rightarrow$$ Ellipseisl (around x axis)

Hyperbole $$\rightarrow$$ Hyperboloid with one sheet(y axis)

" $$\rightarrow$$ " with 2 sheet along z axis

page28-2

3-D Wave equation(2-D, 1-D, ..., n-D): $$ \triangle \phi=\frac{1}{{c}^{2}}\frac{{\partial}^{2}\phi}{\partial {t}^{2}} \ {\color{red}(1)}$$

Plane wave: $$\phi(\underset{-}{x}, \ t)=Aexp[i(\underset{-}{k}\underset{-}{x}-\omega t)] \ {\color{red}(2)}$$

$$\underset{-}{x}=({x}_{1}, \ {x}_{2}, \ {x}_{3})={x}_{i}{\underset{-}{e}}_{i}$$

$$\underset{-}{k}={k}_{i}{\underset{-}{e}}_{i}$$

 * PEA1.F09.Mtg28.pg2.fig1.svg

Ansatz: $$\phi({\color{blue} \underset{ \overset{\uparrow}{x=({x}_{1}, \ {x}_{2}, \ {x}_{3})}}}, \ t)=X({\color{blue} \underset{ \overset{\uparrow}{x=({x}_{1}, \ {x}_{2}, \ {x}_{3})}}}){e}^{-i\omega t} \ {\color{red}(3)}$$

$${\color{red}(3) \ and \ (2)}\Rightarrow \ \triangle X+{k}^{2}X=0 \ {\color{red}(4)}$$

$${k}^{2}=\frac{{\omega}^{2}}{{c}^{2}} \ {\color{red}3-D \ Helmhottz \ eq.}$$

Sep. of var. : $$X(x) \underset{=}{X}_{1}({x}_{1}){X}_{2}({x}_{2}){X}_{3}({x}_{3})$$

page28-3

(5) into (4) : $$\frac{{X}^{}_{1}}{{X}_{1}}+\frac{{X}^{}_{2}}{{X}_{2}}+\frac{{X}^{''}_{3}}{{X}_{3}}+{k}^{2}=0 \ {\color{red}(1)}$$

Curv. lin. coord. $$ \xi=({\xi}_{1}, \ {\xi}_{2}, \ {\xi}_{3})$$

$$X(\xi)={X}_{1}({\xi}_{1}){X}_{2}({\xi}_{2}){X}_{3}({\xi}_{3}) \ {\color{red}(2)}$$

Separated eq. :

$${\color{red} \underset{\triangle X}{ \underbrace}}+{\color{blue} \underset{ \overset{\uparrow}{{X}_{i}}}{[{\color{black}\sum_{j=1}^{3}{\phi}_{ij}({\xi}_{i}){{k}_{j}}^{2}}]}} \ {\color{red}(3)}$$

$${\color{red} \underset{{k}^{2}x, \ {\color{black}=0, \ i=1, \ 2, \ 3}}{ \underbrace}}$$

Application Eng: Elliptic, Ellipsoidel coordinate

- Earth : spheroial (ellipsoial of revolution) - Flow with particles : serierse, eng. ash flow (e.g. volcanoes) liquid crystal

 * PEA1.F09.Mtg28.pg3.fig1.svg

Ellipsoial: diverse shapes

disk $$\rightarrow$$ needle microfluidics


text:
User:Wittylama

I'm Liam, this is me.

title: User:Wittylama


text:
User:Egm4313.s12.team1.wyattling

EGM4313 Team 1 USER: Wyatt Ling Team Page

Solutions

My Report 3 problems

My Report 5 Problems

My Report 6 Problem

My Report 7 Problem

Important Links

 * 1) Lecture Plan
 * 2) Lecture Notes
 * 3) Course Website
 * 4) Editing Help
 * 5) Editing Help 2
 * 6) Starting a New Page
 * 7) Helpful Wikiversity Tour
 * 8) Latex Code Website
 * 9) Report Table

SANDBOX

 * {| style="width:100%" border="0"

$$\displaystyle{2Ce^{5x} + 20Cxe^{5x} + 25Cx^2e^{5x} - 2K_2 - 20Cxe^{5x} - 50Cx^2e^{5x} + 20K_2x + 10K_1 + 25Cx^2e^{5x} - 25K_2x^2 - 25K_1x - 25K_0 = 7e^{5x} - 2x^2}$$ (3.0)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Therefore, the general form for the general solution is: :{| style="width:100%" border="1" $$  \displaystyle 2Ce^{5x} + 20Cxe^{5x} +25Cx^2e^{5x} $$
 * style="width:95%" |
 * style="width:95%" |
 * }

$$Q=Cv_{c}\ $$

Statement
For each ODE in Fig.2 in Kreyszig 2011 p.3 (except the last one involving a system of 2 ODEs), determine the order, linearity (or lack of), and show whether the principle of superposition can be applied.

Given

 * {| style="width:100%" border="0"

$$  \displaystyle y''=g=const. $$     (6.0)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle mv'=mg-bv^2 $$     (6.1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle h'=-k\sqrt{h} $$     (6.2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle my''+ky=0 $$     (6.3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle y''+w_{0}^2y=coswt, w_{0}=w $$     (6.4)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle LI''+RI'+\frac{C}I=E' $$     (6.5)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle EIy=f(x) $$     (6.6)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle L\Theta''+gsin\Theta=0 $$     (6.7)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Solution
In order to determine the order of any ODE, one must simply find the highest prime term in each equation.

ROUGH ANSWERS IN CASE ANYONE WANTS TO CHECK: (Okay so I think I got the superposition part, but i really want to run it past you all during our meeting before I latex everything etc.)

(6.0) = 2nd order/linear

(6.1) = 1st order/non-linear

(6.2) = 1st order/non-linear

(6.3) = 2nd order/linear

(6.4) = 2nd order/linear

(6.5) = 2nd order/linear

(6.6) = 4th order/linear

(6.7) = 2nd order/non-linear

Author
Solved and typed by -

Reviewed By -

Statement
Find a general solution for the following two problems.

Given

 * {| style="width:100%" border="0"

$$  \displaystyle y'' + 4y' + (\pi^2 + 4)y = 0 $$     (5.0)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Solution
The characteristic equation of this linear ODE with constant coefficients (L2-ODE-CC) is:

 * {| style="width:100%" border="0"

$$  \displaystyle \lambda^2+4\lambda+(\pi^2+4)=0 $$     (5.1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Note: The discriminant of the characteristic equation is negative.
 * {| style="width:100%" border="0"

$$  \displaystyle \lambda=-\frac{1}{2}a\pm bi $$ (5.2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Which yields a general solution of:

 * {| style="width:100%" border="0"

$$  \displaystyle y(x)=c_1e^{ax}\cos bx+c_2e^{ax}\sin bx $$ (5.3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

By applying the quadratic equation to the characteristic equation, we see that the roots are:
 * {| style="width:100%" border="0"

$$  \displaystyle \lambda =-2\pm (4\pi)i $$     (5.4)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

This yields a general solution of: :{| style="width:100%" border="1" $$  \displaystyle y(x)=c_1e^{-2x}\cos (4\pi*x)+c_2e^{-2x}\sin (4\pi*x) $$     (5.5)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Solved by: Egm4313.s12.team1.durrance 20:23, 25 January 2012 (UTC)

Given

 * {| style="width:100%" border="0"

$$  \displaystyle y''=2\pi*y'+\pi^2y $$     (5.6)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Solution
This ODE is a linear ODE with constant coefficients (L2-ODE-CC).

First equation (5.6) is rearranged into general form:
 * {| style="width:100%" border="0"

$$  \displaystyle y''-(2\pi)y'-(\pi^2)y=0 $$     (5.7)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

The characteristic equation is:
 * {| style="width:100%" border="0"

$$  \displaystyle \lambda^2-2\pi\lambda-\pi^2=0 $$     (5.8)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Substituting the characteristic equation coefficients into the quadratic formula, we find:
 * {| style="width:100%" border="0"

$$  \displaystyle \lambda_1=\lambda_2=\lambda=\pi $$     (5.9)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Therefore, the general form for the general solution is: :{| style="width:100%" border="1" $$  \displaystyle y(x)=c_1e^{\pi*x}+c_2xe^{\pi*x} $$     (5.10)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Solved by Egm4313.s12.team1.durrance 20:30, 25 January 2012 (UTC)

Statement
Using the Circuit equation (4.1) (see Sec2 Notes), derive equations (4.2) and (4.3) from it.

Solution
Given:

Capacitance Equation:

 * {| style="width:100%" border="0"

$$  \displaystyle Q=Cv_{c}\rightarrow \int idt=Cv_{c}\rightarrow i=C\frac{\mathrm{d} v_{c}}{\mathrm{d} t} $$ (4.0)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Circuit Equation:

 * {| style="width:100%" border="0"

$$  \displaystyle V=LC\frac{\mathrm{d^2}v_{c}}{\mathrm{d} t^2}+RC\frac{\mathrm{d} v_{c}}{\mathrm{d} t}+v_{c} $$     (4.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

First Alternate Circuit Equation:

 * {| style="width:100%" border="0"

$$  \displaystyle LI''+RI'+\frac{1}{C}I=V' $$     (4.2)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Second Alternate Circuit Equation:

 * {| style="width:100%" border="0"

$$  \displaystyle LQ''+RQ'+\frac{1}{C}Q=V $$     (4.3)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

First we are asked to derive the alternate circuit equation (4.2) from the original circuit equation (4.1).

 * {| style="width:100%" border="0"

$$  \displaystyle V=LC\frac{\mathrm{d^2}v_{c}}{\mathrm{d} t^2}+RC\frac{\mathrm{d} v_{c}}{\mathrm{d} t}+v_{c}\rightarrow LI''+RI'+\frac{1}{C}I=V' $$     (4.4)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

The first step is to take the derivative of the original equation so there is the V' term on one side:

 * {| style="width:100%" border="0"

$$  \displaystyle V'=LC\frac{\mathrm{d^3}v_{c}}{\mathrm{d} t^3}+RC\frac{\mathrm{d^2} v_{c}}{\mathrm{d} t^2}+\frac{\mathrm{d} v_{c}}{\mathrm{d} t} $$ (4.5)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

L and C are constants and therefore remain unchanged by the derivative.

Next use the capacitance equation which states:
 * {| style="width:100%" border="0"

$$  \displaystyle I=C\frac{\mathrm{d} v_{c}}{\mathrm{d} t} $$ (4.6)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Take both the first and second derivative of this equation.

First Derivative:
 * {| style="width:100%" border="0"

$$  \displaystyle I'=C\frac{\mathrm{d^2} v_{c}}{\mathrm{d} t^2} $$     (4.7)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Second Derivative:
 * {| style="width:100%" border="0"

$$  \displaystyle I''=C\frac{\mathrm{d^3} v_{c}}{\mathrm{d} t^3} $$     (4.8)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Now substitute in the the I terms into the appropriate places. The equation below groups terms that need to be substituted.

 * {| style="width:100%" border="0"

$$  \displaystyle V'=L(C\frac{\mathrm{d^3}v_{c}}{\mathrm{d} t^3})+R(C\frac{\mathrm{d^2} v_{c}}{\mathrm{d} t^2})+\frac{({C}\frac{\mathrm{d} v_{c}}{\mathrm{d} t})}{C} $$     (4.9)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

The final product after substitution is the alternate circuit equation:

$$  \displaystyle LI''+RI'+\frac{1}{C}I=V' $$     (4.2)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

We are also asked to derive the second alternate circuit equation
 * {| style="width:100%" border="0"

$$  \displaystyle LQ''+RQ'+\frac{1}{C}Q=V $$     (4.3) from the original circuit equation.
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Once again use the capacitance equation which also states:

 * {| style="width:100%" border="0"

$$  \displaystyle Q=Cv_{c} $$     (4.12)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Take the first and second derivative:

First Derivative:
 * {| style="width:100%" border="0"

$$  \displaystyle Q'=C\frac{\mathrm{d} v_{c}}{\mathrm{d} t} $$ (4.13) Second Derivative:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle Q''=C\frac{\mathrm{d^2} v_{c}}{\mathrm{d} t^2} $$     (4.14)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

The C term is constant and does not change when the derivative is taken.

Group the original circuit equation like in the previous problem so that parentheses mark terms that should be substituted for Q terms:
 * {| style="width:100%" border="0"

$$  \displaystyle V=L(C\frac{\mathrm{d^2}v_{c}}{\mathrm{d} t^2})+R(C\frac{\mathrm{d} v_{c}}{\mathrm{d} t})+\frac{(Cv_{c})}{C} $$     (4.15)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

After substituting, the final product is the second alternate circuit equation: :{| style="width:100%" border="1" $$  \displaystyle LQ''+RQ'+\frac{1}{C}Q=V $$     (4.3)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Author
Solved and typed by - Chris Stewart

Reviewed By -

Statement
Derive the equation of motion of the spring-mass-dashpot in Fig. 53, in Kreyszig 2011 p.85, with an applied force $$r(t)$$ on the ball.

Solution
Kinematics:
 * {| style="width:100%" border="0"

$$  \displaystyle y=y_k=y_c $$     (2.0)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Kinetics:

 * {| style="width:100%" border="0"

$$  \displaystyle r(t)=my''+{{f}_{k}}+{{f}_{c}} $$     (2.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle {{f}_{k}}=k{{y}_{k}} $$     (2.2)
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$$  \displaystyle {{f}_{c}}=c{{y}_{c}}' $$     (2.3)
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Rearranging equations:

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$$  \displaystyle r(t)=my''+k{{y}_{k}}+c{{y}_{c}}' $$     (2.4)
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$$  \displaystyle y=y_k=y_c $$     (2.5)
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Equation of motion:

$$  \displaystyle r(t)=my''+ky+cy' $$     (2.6)
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Author
Solved and typed by - --Egm4313.s12.team1.essenwein 23:06, 25 January 2012 (UTC)

Reviewed By -

Statement
For the spring-dashpot system on p.1-4 [[media:iea.s12.sec1.djvu|(of sec.1 notes)]], draw the Free Body Diagram's and derive the equation of motion (2) p.1-4.

Solution
Free Body Diagrams:

By definition:

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$$  \displaystyle a=y'' $$     (3.0)
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Because only two forces are acting on the dashpot and they are in opposite directions, they are equal in magnitude.

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$$  \displaystyle ky = cv = f_{I} $$     (3.1) The resulting acceleration of the mass, m, must be the difference of the applied force $$f(t)\!$$ and the internal force $$f_{I}\!$$.
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$$  \displaystyle y'' \propto f(t)-f_{I} $$     (3.2)
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Using Newton's second law:
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$$  \displaystyle my'' = f(t) - f_{I} $$     (3.3)
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Rearranging, this yields: :{| style="width:100%" border="1" $$  \displaystyle my'' + f_{I} = f(t) $$     (3.4)
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Author
Solved and Typed By: Egm4313.s12.team1.armanious 20:09, 25 January 2012 (UTC)

Reviewed By:

Statement
Derive the equation of motion of a spring-dashpot system in parallel (see Figure 1 below), with a mass and applied force $$f(t).$$ Figure 1

Solution
Kinematics, Kinetics, and Relations equations as interpreted from picture

Kinematics:
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$$ \displaystyle y=y_{k}= y_{c} $$     (1.0)
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Kinetics:
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$$  \displaystyle f(t)=my'' + f_{k}+f_{c} $$     (1.1)
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Relations: -Force of spring relation:
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$$  \displaystyle f_{k}=ky_{k} $$     (1.2) -Force of dash-pot relation:
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$$  \displaystyle f_{c}=Cy'_{c} $$     (1.3)
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Putting kinematics, kinetics, and relations together:
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$$  \displaystyle y=y_{k}=y''_{c} $$     (1.4) Using kinetic relationship
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$$  \displaystyle f(t)=my''_{c}+f_{k}+f_{c} $$     (1.5)
 Using the kinematics and relations equations:
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$$  \displaystyle f_{k}=ky_{k}=ky_{c} $$     (1.6)
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$$  \displaystyle f(t)=my''_{c}+ky_{c}+f_{c} $$     (1.7) Using dash-pot relation:
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$$  \displaystyle f_{c}=Cy'_{c} $$     (1.8)
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 * }
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$$  \displaystyle f(t)=my''_{c}+ky_{c}+Cy'_{c} $$     (1.9)
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Final Equation
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$$  \displaystyle f(t)=my''_{c}+Cy'_{c}+ky_{c} $$     (1.10)
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Author
Solved and typed by Egm4313.s12.team1.silvestri 20:44, 25 January 2012 (UTC)

Reviewed By -

title: User:Egm4313.s12.team1.wyattling


text:
Big bang/A critique of The self-reproducing inflationary universe

(Review Paper) Cited in

Points Made
With space continually expanding as well as the six points made on why the big bang scientifically could not happen there is just cause for being against the theory.

Methods
From the article researched it outlined six main points on why the big bang could not have happened. First being was there anything before the big bang? How could everything in our known universe appear from nothing? The common scientific question to many scientists researching this subject is what came first the universe or laws that determine its evolution? All a hard thing to grasp or even have a way to figure it out. Second problem with the big bang theory is they say space is flat. It is not flat in fact space can be curved. The forth problem has to do with the timing of the "big bang". The theory suggests all part of the universe started expanding at the same time. How did all the different parts synchronize the expansion. Did some one give a command? The fifth problem with the big bang theory existing is how the universe became so homogeneous. How can something be so large and at the same time some mechanism that can create galaxies at a whole? Scientists can not even grasp a way on how this can be tested or even found out. The final point made in the article was by Albert Einstein he questioned if God had any part in the creation in the universe basically because the above points support why the big bang could not have happened

Results
Over time space is expanding therefore the big bang theory of a fireball exploding in a second is false.The big bang theory asserts that the universe was created in one giant cosmic fire ball and from there the universe continued to evolve. The inflation theory contradicts the big bang theory in that there are numerous cosmic fireballs constantly expanding verses one evolving.


text:
Big bang/a critique of Big-Bang Nucleosynthesis Revisited.

(Review Paper) Cited in

Dueterium found in the universe matches that which was predicted to exist due to the big bang
First, Deuterium abundance does not have a current known cosmological explanation and is therefore associated with the big bang as this is the only force capable of creating an abundance. The same is true for other rare elements. Second, the discovery of blue dwarf galaxies that have an abundance of light elements such as helium and a scarcity of heavy elements such as oxygen and neon show that these are young systems, which is significant due to their positioning .

Methods
The author theorized that the amount of deuterium found in the universe in present day could only be explained by the occurrence of a large cosmological event, namely the big bang. The author then measured the amount of deuterium in the universe

Results
The amount of deuterium found in the universe was found to be too large to be explained by any known cosmological events combined. It is then deduced that even the most simple big bang models could account for this abundance.


text:
Panspermia/A critique of The dark side of the universe: from Zwicky to accelerated expansion

(Review Paper) Cited in

Points Made
The universe is not only still expanding, the expansion is accelerating! This supports the big bang, because if it's expanding, a long time ago it must have been smaller, which is the principle of big bang .

Methods
First they measured the number of galaxies, and then they used this information to measure global geometry which is basically the shape of the universe.

Results
They found out that the method was inaccurate and some of the inaccuracies could be corrected through infrared technology.


text:
Big bang/A Critique of Introduction to Plasma Astrophysics and Cosmology

(Review Paper) Cited in

The Universe is made up of Plasma
In order to prove the theory of Plasma Astrophysics and Cosmology, Kristian Birkeland observed that plasma is present on Earth and filled with electrons and flying electric ions of all kinds.

Rationale
Additionally, he observed an identical pattern in space which concludes that material matter is found in 'empty space'. Essentially, this theory supports the universal concept that matter was not created through a universal force, but rather was always present. The Big Bang Theory is counter-intuitive to Birkeland's positive observations.

Results
The Northern Lights are an example that supports Birkeland's observations. The Northern Lights are made up entirely of plasma (electrons and electric ions) and behave in the same fashion as plasma in space.


text:
Big bang/a critique of Cosmic Background Radiation

(Review Paper) Cited in

Method
They measured the cosmic microwave background (CMB) radiation temperature using formulas and then compared it to the required CMB.


text:
Big bang/Slow and steady wins the race.

(Review Paper) Cited in

Slow and Steady Wins the Race
In order to properly understand Bondi’s theory of the steady state which rivals the Big Bang theory, we must first examine the 3 basic laws of physics. These laws hold true under any circumstance and can even be related to our universe. According to Bondi matter must be created at a continuous slow and steady rate as opposed to an initial explosion of matter as proposed by the Big Bang Theory. His theory can be proven using the tried and true laws of physics which are tangible and can proven again and again in any circumstance. The big bang theory abandons these laws and requires assumptions to be made that do not follow these principles.

Methods
Bondi theorized the Steady-State theory by examining the laws of physics that can tangibly be proven in a lab and coming to a logical conclusion about the creation of the universe.

Results
According to the first law of physics, moving objects will remain in motion which applies to the steady state theory that suggests constant expansion of matter as opposed to an initial "Big Bang".

title: Big bang/Slow and steady wins the race.


text:
Big bang/a critique of Scientists Gather Proof Against Big Bang in Older Stars

(Review Paper) Cited in


text:
Big bang/a The Big Bang —A Hot Issue in Science Communication

(Review Paper) Cited in

Astronomers support the big bang theory
The big bang theory is a comprehensive explanation of how the universe came to existence.

Scientists are lacking creditability
Individuals who refute the big bang theory fail to mention the scientists and their credentials that support them. Further research has shown that many of these scientists are from Creationists Research Institute. .

Support of Many Sciences
There are many scientific fields that support the big bang theory. Including cosmology, astronomy, quantum physics and chemistry.

Always Being Tested
The big bang theory is always being tested, therefore, more knowledge is gained to support the theory.

Public Representations
Highly influential public figures misunderstand the big bang theory and therefore misrepresent the theory to the public.


text:
Big bang/A Critique of Two world systems revisited: a comparison of plasma cosmology and the Big Bang

(Review Paper) Cited in

Contradicted by observations
There is no proof that the three entities (inflation field, dark matter, and dark energy) needed for the big bang to have happened.

Methods
Pointed out flaws in the liberal way they used variables in the mathematical formulas to fit what was required of the theory.

Results
BIG BANG NUCLEOSYNTHESIS

It used the baryon density that would fit whatever model they needed it to. Therefore, Baryon was a free variable in their equation and could occupy whatever numerical values that would correlate with their requirements.

LARGE-SCALE STRUCTURE AND VOIDS

Since the theory of the big bang states it began about 14 Gy ago, these large scale structures and void could not have formed in this amount of time.

They would need to generate final velocities of 600 km per hour to account for the voids and observed velocities have ranged from 200-250 km per hour. Therefore contradicting the current model of the big bang theory.


text:
Big bang/aThe Big Bang---A Hot Issue in Science Communication

(Review Paper) Cited in


text:
Big bang/a critique of The Universe Has No Beginning? Doubts About The Big Bang Theory

(Review Paper) Cited in

The Universe Has No Beginning? Doubts about the Big Bang Theory
There is considerable possibility that time reversal exists in the universe. This possibility increases upon the greater discoveries of black matter. Even if black matter were to be removed from the theory, the Big Bang Theory would be hypothetically removed as well since the Big Bang Theory could not exist without it. Since black matter has not yet been proven to exist, it is too early to treat the Big Bang as anything more than just a theory.

Rationale
The factual validity of the big bang theory is called into question through two thought experiments. In thought experiment one, consider that a light ray can arrive at an observer after a far less distant source, if it is delayed by being bent around the horizon of a black hole, for example. It’s later arrival would appear to effectively reverse time. This thought experiment is based on the presumption that black matter exists, and that it has a gravitational effect on light.

The second thought experiment questions the validity of “c” or the speed of light, being constant. The current measurement of 186,282 miles per second was calculated based on an unobstructed light signal over a short distance. How, then, can one explain how a light source can arrive at two places of equal distance at different times?


text:
Big bang/a critique of The foundation of the theory of the universe dark energy and its nature

(Review Paper) Cited in

Expansion is accelerating and a model to explain dark energy
A mathematical model demonstrates why stars appear to be accelerating in their speed away from us. The universe is expanding due to the mechanical momentum of time since the big bang. Since the boundaries are moving, it will cause a negative pressure which will equal to the energy. This will cause the universe to expand at an accelerated rate.

Method
The mathematical model predicts the energy of a graviton that counters dark energy. It takes the three spacial dimensions as well as time into consideration.

Result
The results were that the dark energy predicted in the model causes accelerated growth of the universe which we could detect as greater redshift in further stars which supports the big bang theory being correct.