text:
Talk:Psycholinguistics/What is a Word?

Peer Review: What is a Word?

Research: Can you find some more recent research? Some citations are older and may be out of date. On the other hand, there may not be any new information in that area. Just a suggestion to double check. The research you did include was well-explained and relevant to the topic.

Logic/Organization: The flow from idea to idea is good! I would suggest that if you start a new section and continue an idea from a previous section (ie: You talk about Sassure in two different sections), that you either link back to Sassure or give a brief overview on who he was to remind the reader. A reader may decide to skip to the second section where you wrote about Sassure and be a little confused.

Answers Questions/Makes Arguments: I thought you did well very at asking questions and answering them. You repeat questions throughout the text to help refocus the reader and to get them thinking.

Writing Style: Very good - few spelling or grammar mistakes and nice flow. Some sentences are a little long or should appear earlier in the paragraph, but for the most part your definitions are clearly stated and you gave examples to make it easier to understand.

Structure: Your structure flows well. For the most part, you state early on what you will be discussing in that section and you don’t ramble so your reader stays focused. There are a few paragraphs that may need to be expanded upon, or linked back to the previous text, but overall it was easy to follow.

I wanted to comment further on the citations. There’s a lot of good information in your text, but you are lacking some resources and there are many sections that have no citations at all. Unless the topic and definition was your original thought, you need to state where you took the information from. Overall, it is a great first draft! I really liked how to added new questions in various paragraphs. For example, in the section on “word relationships” you said “The correct meaning can be inferred from the context, but how does this occur?” It helps the readers refocus and perhaps come up with an answer themselves before moving on.

 * I’ve commented on individual sections in a word document. If you’d like that write up, feel free to email me through BLS.

Jenn Browning 20:31, 27 February 2011 (UTC)

title: Talk:Psycholinguistics/What is a Word?


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

title: File:Nm1.s11.team4.HW4.6.fig1.jpg


title: File:Nm1.s11.team4.HW4.6.fig2.jpg


title: File:Nm1.s11.team4.HW4.6.fig3.jpg


title: File:Nm1.s11.team4.HW4.6.fig4.jpg


title: File:Nm1.s11.team4.HW4.6.fig5.jpg


title: File:Nm1.s11.team4.HW4.6.fig6.jpg


text:
User:Egm6341.s11.team4.hylon/hw4

=Problem 4.6 Fix Runge phenomenon of Lagrangian Interpolation using nodes of Legendre Polynomial, Chebyshev Polynomial and equidistant nodes =

Given
Refer to lecture notes [[media:nm1.s11.mtg21.djvu|21-1]] for more details.

Objective
1. Use roots of Legendre Polynomial to the accuracy of $$10^{-6}$$. Plot $$f _n^L(x)$$ and $$f(x)$$.

2. Use roots of Chebyshev Polynomial, to the accuracy of $$10^{-6}$$ by Newton-cotes methods. Plot $$f _n^L(x)$$ and $$f(x)$$.

3. Comparison of Lagrangian Interpolation using three different types of nodes.

Using nodes of Legendre Polynomial

Using nodes of Chebyshev Polynomial

Since there the difference in above figure is not much clear, we plot above picture using $$n=6$$ again.

Comment
From above results, we see that:

Among three different types of interpolation nodes, using roots of Chebyshev Polynomial is much accurate and can best fix Runge phenomenon, although using roots of Legendre Polynomial can also settle it.

In this problem, Runge phenomenon happens only when we use odd number of nodes to do Lagrangian interpolation.

Problem is solved by Hailong Chen

Reference
1.	Lagrange_polynomial 2.	Legendre_polynomials 3.     Chebyshev_polynomials 4.     Gauss-Legendre_quadrature

title: User:Egm6341.s11.team4.hylon/hw4


text:
File:HW4 P6 A.png

= Summary=

title: File:HW4 P6 A.png


text:
File:HW4 P6 A error.png

= Summary=

title: File:HW4 P6 A error.png


text:
File:HW4 P6 B.png

= Summary=

title: File:HW4 P6 B.png


text:
File:HW4 P6 B error.png

= Summary=

title: File:HW4 P6 B error.png


text:
File:HW4 P6 C error.png

= Summary=

title: File:HW4 P6 C error.png


text:
Talk:Psycholinguistics/Parsing

Discussion #1

What you have here is a good start, but introduces a lot of information that can perhaps overwhelm the reader. I found that my understanding of parsing was largely helped by examples showing different kinds of sentences, and not only how they should be parsed, but how a mistake could be made (either in a garden path sentence, or if the reader is less familiar with the language). Parse trees can help provide a visual example of an abstract concept. When you describe thematic roles, give a sentence that demonstrates the various roles that the parts of the sentence can take on; show how this helps with parsing: a verb is unlikely to be an agent, a preposition unlikely to be a goal, and so on. Themes can work together with traditional parsing to try and determine meaning in a sentence.

In the section on Thematic roles, you speak about the “cost” of certain roles. Elaborate upon this. What is the cost? How is cost determined? What sorts of penalties would there be for choosing higher cost meanings, and are there any circumstances where it is actually beneficial to do so? When discussing semantic features, again, give an example of a sentence where the parsing is aided by the semantic features of a particular word. For example in the sentence “The fly's wings were buzzing rapidly,” knowing that a fly (itself possibly ambiguous, although linked with a noun and not a verb because of the possessive 's) has wings makes us more likely to classify wings as a noun, although it too can be a verb (consider “The fielder wings the ball back to the infield”). Also, why would a solid knowledge of grammar be both “critical for parsing to occur”, and “cause errors in parsing”. This seems contradictory. If it is true, expand on why this contradiction is possible.

The section on Serial and Parallel processing needs to be expanded. You give their definitions, but fail to describe whether one or the other is more prevalent (or more backed by research). Again, once the section has been expanded, examples of one sentence being processed both serially and in parallel would help the reader visualise the process.

The Garden Path section does a good job of describing the Garden Path Theory, but could use a little bit of history: where did it come from? What idea, if any, was used before? Why is it being questioned? Again, the section would benefit from examples that show how a bad parse can come out of nowhere after being led in a particular direction. But then, how is this parse corrected? Does the reader create a new parse, or simply overwrite the section that opens the “rabbit hole?” Also, what are the main shortcomings and benefits of Garden Path parsing? You begin to describe constraint satisfaction and briefly mention cross-linguistic studies without elaborating. Do they support or hurt the findings of Garden Path research?

Another potential area to investigate is that of computer parsing. Computers are actually (surprisingly?) able to parse sentences fairly adequately, although they do run into problems with garden path sentences and intentionally ambiguous sentences, moreso than humans. Computer parsing is largely dependent on how we understand human parsing, and tends to use a similar “most likely” system to parse, parsing sentences in the most likely manner. You may not have time to include a section on computer parsing, but you might want to glance briefly at the research if you have the time.

Largely, your article seems to be going in the right direction, albeit it requires a bit of expansion and explanation. Remember that although this page is being designed for a Psych class, it may get viewers who have considerably less experience with the subject. Examples help clarify key points, and can be re-used in new sections to highlight key differences between methods. Definitions of key terms are also useful if the expected audience is less familiar with the subject matter.

One final note on the structure of the article. At certain points, the article tends to either split a section that might be better together (such as talking about other models before talking about the problems with the Garden Path model), or including many ideas in one section that might be better served having separate sections (such as separate sections for thematic roles and semantic features). If it is simply a matter of working around the constraints of wikiversity, I suggest going to wikipedia (which has largely the same format, but more articles), and looking at the formatting of one of the “featured articles.” These articles are the “best of the best” at Wikipedia, and by clicking “edit” on them, you can see how some really neat formatting things get done. Furthermore, if you have any questions or would like clarification, just post on my user page, and I'll try and get back to you as soon as I can. Aericanwizard 22:22, 27 February 2011 (UTC)

Discussion #2

Overall, the author seems to understand the basics in the subject of parsing. The introduction is a simple but clear explanation about what the rest of the article will discuss in depth. It offers a clear definition what parsing is and touches upon the relevance of the article to the readers – it’s something they are doing even as they are reading the article!

The section about “What Causes Parsing?” is a little confusing. Bullet points are a great way to get the main point across, especially when someone is just skimming through the article. However, the information in the bullet points might need to be expanded upon, and some of the ideas are unclear. For example, under “thematic roles” a bullet point says, “- Focus on lexical information, such as frame analysis. They rely on interpreting words semantically in a sentence.” The ideas in this sentence are a quite vague, and need to be more developed.

The comparison between serial and parallel processing is important, but should also be expanded upon. The author asks good questions at the end of this section, but needs to research answers to these questions.

The theories of parsing are very interesting. The author explains garden path sentences well, elaborating on the metaphor behind the name and using it to illustrate how the Garden Path Model works. The article also explains the assumptions of the Garden Path Model and the principles it incorporates, such as late closure and minimal attachment. The effects of the Garden Path Model, such as the misconceptions that are difficult to change after the wrong interpretation of a sentence has already been made, are also clearly explained. The author cites research done by Christianson et al (2001) and explains the implications of the research. It might be helpful to explain more about the research so readers can understand how experiments are performed in parsing research. The author also briefly mentions the “Good Enough” theory and the Constraint Satisfaction Model under different headings. The Dependency Locality Theory and the Competition Model are outlined briefly under “Challenges to the Garden Path Model.” All these theories, though perhaps not as popular as the Garden Path Model, should be discussed in more detail and explained through research related to each theory.

The organization of the article is a little confusing. Under the heading of “Theories of Parsing,” the article lists the Garden Path Model, the Constraint Satisfaction Model, and Cross Linguistic studies. However, cross linguistic studies are not really discussed in this section. In addition, the Competition Model, the Dependency Locality Theory, and the “Good Enough” theory are not listed under the main title, but they are briefly discussed. The section about challenges to the Garden Path Model should not include the explanation of the Competition Model or the Dependency Locality theory. They should only be included in this section to discuss the contradictions between the models. The section for “Challenges to the Garden Path Model,” should be moved up to the section with the rest of the discussion about that model.

Overall, more articles should be included to back up the claims made in this article. General ideas need to be expanded upon through the article. The Garden Path Model, while important, should not be the only theory that is discussed in such detail. The layout and organization of the structure of the article should be more polished to help guide the reader through the article. However, the author has a strong outline of the important ideas that need to be discussed. The points that were explained were clear and concise. The author used language that readers will be able to understand, without making it sound too simple. This will be a strong article when additional research and more complete explanations of some of the topics are added.

title: Talk:Psycholinguistics/Parsing


text:
Talk:Psycholinguistics/Language and the Brain

Peer Edit of Chapter Draft - Language and the Brain

My first impression of this section was that it looked like a good layout, with essentially all of the major topics covered. I really liked the fact that you included a picture, and I thought the one you used was a good choice. It showed all of the major brain areas and their function, which was very helpful. Since the major areas that you focus on are speech and language, it might be nice to have a more complete picture of these particular areas with the structures that you talk about, but this image does give a good idea of relative size and location in the brain of these general areas.

I liked the descriptions of Broca’s and Wernicke’s areas. I don’t know a lot about the more specific names of brain structures, but as a reader, I was a little confused about what was meant by “area 44, 45 and 22”. Maybe you could elaborate on the importance of these, or else take this part out (I think the description would still be sufficient without it).

I thought the descriptions of the cerebral cortex and corpus callosum were good, and perhaps it might be helpful to expand a little on the idea of the two hemispheres of the brain (often language processing happens mostly in the left hemisphere so you could talk about this, and perhaps tie in some supporting research). In your descriptions of contralateral and ipsilateral processing, you might want to tie in the language aspect to justify including them in your chapter. You mention the motor aspect, but how do these affect language processing or production? It might be beneficial to include a short description of the auditory cortex, to tie in the aspect of hearing language as the first step in processing. In general, I think it would be even more effective to include this section (language localization) right after the section on the “major brain regions” (BEFORE the brain imaging section). I think this would help with the flow of the topics. A quick proof reading for sentence structure and flow will help smooth out this section as well.

Next, I would suggest putting the “Subcortical Structures” section. These descriptions are good, though structures such as the hippocampus and amygdala are pretty crucial and may warrant a sentence or two of their own to explain their importance. Again, it may help to tie the concept of language into this section. You could talk about how the emotion, tone, corresponding body language, or eye and facial expression all affect the way we process and understand language, as well as respond to it.

I would move the brain imaging section to the end, after the descriptions of the different structures. Now that we know what the important areas are, we can better understand their importance when you talk about the different ways of observing them. This section is good, and I think you’ve included all of the major techniques. A suggestion (and only a suggestion) would be that you might be able to make the section look a little more neat and tidy if you put the title at the start of the description instead of on separate lines since the descriptions are short anyway. So you would have: “CAT - Computed Axial Tomography, (CAT), is a method of brain imaging…” This might make it less choppy and broken up, but I think the way you have things could work as well.

I think it might be nice to have a little section at the end about the abnormal brain as it pertains to language. I know there is already a section on aphasias, but if someone were to read ONLY your chapter, it would definitely add to the completeness of the chapter since “language and the brain” is a pretty broad topic. You should include a brief overview of these things, and people can read the specific chapters to read about these in more detail. Aphasias, sign language, Braille, and dyslexia could be included in this section. Perhaps just to very briefly mention what these are, and what brain changes cause these abnormalities, as well as how the brain adapts to overcome them. It would be a nice ending to the chapter.

Overall, I would just suggest that you add in-text citations, so we can see which sources each bit of information came from. Also, when you are finalizing your chapter it is good to alphabetize your sources to make things easier to find. Finally, it might be good to add a sentence or two at the start of each section just to introduce what you will talk about before you start in with each of the sub-headings. I would also separate the concluding paragraph from your final section so it is easier to distinguish as being separate from the section itself.

Very interesting topic and chapter so far! I am looking forward to seeing the final version and what you will choose for your learning exercise. Keep up the great work!

--Cbrousseau 22:26, 27 February 2011 (UTC)


text:
Talk:Psycholinguistics/Morphology

Below is a critical review of the chapter morphology. I have not corrected for grammatical and spelling errors, however will notify the author privately with my suggestions. The review below is simply an overview of the chapter as a whole however, I will make mention to a few specific aspects of the chapter.

The author has covered the chapter of morphology in great detail, yet adhered to the predetermined word count. The introduction clearly identifies the area of focus and follows a logic sequence by beginning with the history of morphology and concluding with the present research. The author has presented a well thought-out chapter, which incorporates multiple sources including contrasting viewpoints. For example, as stated by the author, the past tense debate remains highly controversial among scholars of psycholinguistics. The author has provided substantial evidence to outline the arguments on both sides while remaining unbiased.

Given that the topic of morphology is very broad, I appreciate that the author has chosen to focus on certain aspects rather than attempting to incorporate too much detail within a limited word count. Inflectional and derivational morphology are covered in great detail providing more than adequate information on this area of morphology. With this being said, I do however have a few suggestions on areas that may deserve further insight.

Under the heading “What is a morpheme?” the author may want to address that affixes are not restricted to the English language. Being an introductory chapter this may not be common knowledge to the reader. The author could incorporate simple examples to expand on this thought. For example, in Piro, an Arawakan language, -kaka can be added to a verb to express “cause to”. Therefore, “salwa” which means, “to visit” can be transformed to “cause to visit” by adding –kaka, “salwakaka”.

In keeping with rules of word formation, the author may find tree diagrams useful as a way to incorporate visual aids. For example, the word “unsystematic” incorporates the prefix –un, the root system, and the suffix –atic, resulting in a three leveled tree. Tree diagrams are a great way to add clarity for visual learners.

While reading the chapter I did come across some areas that I found unclear. For example, the author mentions a NP (noun phrase) which includes a noun + person. I was under the assumption that a noun phrase can include a person, a determiner, or simply a standalone noun. I am not an expert in morphology and therefore did not make any changes to the text regarding this question. I am grateful that the author has chosen to bold key concept terms. This allows for easy scanning when defining a term (critical in traditional textbook chapters). The flow of the chapter is easy to follow and will structured with the incorporation of subheadings.

In regards to structural changes the author may want to remove the citations for Jay 2003. As recently mentioned by Dr. Newman this is unnecessary and may be reflected during evaluation. Overall I feel that this chapter is well written and contains ample evidence including a wide range of academic sources.

title: Talk:Psycholinguistics/Morphology


text:
Talk:Psycholinguistics/Components of Speech

Peer Review
I like that you listed what you will be discussing in the introduction, but it seems a bit incomplete. Maybe a bit more of a discussion on exactly what the components of speech are or their importance might be a nice addition to your intro?

Your page is very informative! A couple of suggestions that may help the reader to understand the information better and make it more interesting is if it were laid out differently, i.e. pictures, subheadings, tables ,etc. The paragraphs within the subheadings need a bit more distinction as the paragraph breaks are confusing without it. Bolding or even italicizing some key words may also help break the paragraphs up and signal to the reader some of the more important parts of the section. (For example, in the section on “Phonological rules”, you have a sentence stating, “The specific rules that outline the permissible combinations of phonemes are called phonotactic rules” You might want to consider highlighting or italicizing phonotactic rules.   I also corrected a bit of grammar issues but touched the original copy only minimally.

In reference to the suprasegmantal section: Overall, it is a very informative section and I especially liked the way it was wrapped up in the closing paragraph. I’m wondering if adding an audio clip of a computerized sentence free of human speech qualities might spruce it up. You can find out how to format this type of file to your page at: http://en.wikiversity.org/wiki/Help:Media. Another thing I found that could be taken as confusing is the first paragraph in which you speak of prosodic cues. It may be the wording that seems odd to me, but it also may need a *very brief* explanation on prosodic cues and what they are before jumping into them as suprasegmental properties.

The other sections are very good, but like I said before, they could use a little sprucing up. The section on ASL would be great with some pictures, especially to demonstrate hand configuration and its importance to the language or maybe even a picture of someone signing “mother” compared to someone signing “father” when you bring it up in the text. Also in the sign language section, the part in brackets in the following sentence seems redundant: “When signs in ASL differ only on one aspect the two can be considered to be a minimal pair (differing only in one contrastive aspect)”

As a whole, your page is full of important information and the main subheadings seem quite appropriate. However, it seems as though you are following the textbook too closely so some extra sources would be helpful to your chapter. The other major critique I have, as already stated, is the presentation and the lack of supplemental information to help with further understanding. It might be hard to find pictures to help out with your sections (with the exception of the section on ASL), but it might be worth looking into seeing if it is possible to add audio clips, which would make it much more interactive. Also remember to properly link your information to the sources that you have used in the reference section.

Aslwin 19:33, 27 February 2011 (UTC)


text:
Talk:Psycholinguistics/Language and Thought

The textbook chapter Language and Thought, written by Maged Aly, seemed to be an arduous read at first glance. However, the actual perusal of its contents revealed a pleasurable, informative and thought-provoking article. After several reads of the chapter in its entirety, I promptly consulted the rubric provided online, which directed any subsequent analysis to adhere generally to a few main aspects of the article, chiefly structure, organization, analysis, references and writing style. I have thereby attempted to use these key points as guidelines for my review of this chapter. Right off the bat, it is made readily apparent by the author’s introduction that the chapter does indeed strongly possess the characteristics of cohesiveness and coherency. The presence of logical flow is established via the author’s initial overview on the topic. The introduction is effective in bringing the reader up to speed on the current state of research conducted on language and thought in a concise manner, breaking down the subsequent sections and presenting them clearly. Moving onto the meat and potatoes of the chapter, the author guides the reader through the main concepts regarding language and thought in somewhat chronological order. The sections are divided clearly and logically; they are relatively easy to understand and are well-written, apart from a few spelling and grammar mistakes. References are cited for most points stated in the chapter, and the author has made an effort in being impartial and unbiased in the presentation of the theories. However, there were some aspects of the chapter such as the section on Memory and Language that could have been expanded further. There is an adequate amount of detail in the rest of the chapter, yet elaboration on certain points would most certainly have been welcome, the section on Aphasia and Thought being an example. Despite this shortcoming, the chapter was solid in its information overall. Another point of concern is the dependency of the chapter on one specific journal article, namely the information cited from” Leva, 2011”. Although there is undoubtedly a variation in both references and viewpoints, there was still an unshakeable feeling that a substantial portion of the chapter did indeed stem from the aforementioned journal article. However, this does not serve as a detriment to the quality of the chapter, and it is imperative to note that there is still a wealth of information to be gleaned overall. Ultimately, the author does a commendable job of integrating the many concepts and theories, presenting them in a way in which the relations between them are not difficult to comprehend. It was not a chore to read through the chapter, yet explanation or elaboration would have certainly softened the impact of the complexity of the information presented, especially for a reader like myself who is more or less ignorant about the topic. However, the chapter effectively did its job in conveying the ideas behind language and thought, and I am now considerably more knowledgeable about the topic than I was prior to reading it. The contents are written clearly using simple, understandable language, with a few exceptions mostly pertaining to the explanation of some of the more cryptic terminology used. As mentioned earlier, the author leads the reader on a logical train of thought, which results in a rather satisfying journey of knowledge by the time one gets to the end of the chapter. All in all, I find this chapter on Language and Thought to be informative, useful and an engaging read.

Ramz Aziz 23:28, 27 February 2011 (UTC)


text:
Talk:Psycholinguistics/Prosody

Very interesting topic! I posted some comments based off the rubric headings. It may seem like a lot, but they are just the small nit picky things that are a nuisance, I've been penalize many times so I try to remember them now. I've also taken a class with Dr. Newman before, and so I happen to know he can be picky. Hope it helps!

Writing Style
Conducting a thorough read over of your own work will assist in finding some small mistakes in language use, like tense errors, and mistakes in the use of plurals. Grammatical errors such as the use of commas can also be eliminated by a review. Incase your english classes were awhile ago, remember to separate clauses using a comma. Introductory terms like further, however, for instance, and therefore, should always be followed by a comma as well. Comma’s should also be used for long sentences, this makes the longer amount of information more understandable. In the use of the phrase, the idea that of the…, the word that can be eliminated to make the wording more concise, and also makes the writing more readable. In science, and published articles in particular, we use the most concise, but clear, wording; that is, the least amount of words required to accurately explain a concept. This is because we are generally explaining a more advanced topic, and so the least amount of words will assist our readers in a better understanding. Also, the chapter is about 500 words too short, so filling in around research articles and key points so that they are very clear will easily fill up this gap in word length.

Structure
The introduction of the paper should define terms that you will use throughout the text that may be ambiguous, or unknown to some readers. For information that they should know, but may not, refer them to another chapter of the psycholinguistics wikiversity page. A link to this chapter is helpful as well. When beginning a new section, the first paragraph acts like an introductory paragraph. Therefore, it should give a small intro for the first couple of sentences to bring readers up to speed, then outline the following subsections briefly so the reader knows what to expect. Also, in text citations should link down to the reference section. I recommend using the numbered citations, as that is a frequent format used in wikiversity; although making a linking APA-format in text citation could be possible.

Research
The inclusion of empirical evidence is crucial to validating your arguments in science writing, especially for an online information source. While direct quotes are typical evidence resources in literary writing, in science they are steered away from; and we were advised not to use them in class. Putting these quotations into your own words and explaining them is a much more universally accepted method. When introducing one of these papers as evidence to support your claim, briefly explaining the methods used to carry out their purpose before listing the results can assist readers see differences between studies. When listing more then one article with similar purpose and methods this would only to be done once. For using our classroom textbook as one of these resources, find the article that he discusses first, read it, and then cite that. For information in the textbook that he does not give a reference for, you do not need to cite it according to Dr. Newman as it is knowledge that you should be able to come up with on your own. Overall, in terms of research, I would like to see more of the relevant research articles mentioned, also incorporating opposite viewpoints to the ones that you have mentioned, the rubric for the chapter points this out as well. When using research more then 10 years old, it is always good to double check to see if there at least something that can be added on to the research you have included. That way the reader can be sure you did a thorough literature review. In terms of substance of the literature review I would have liked to see some move evidence to back up some of your claims. As well, I would have really liked to see a section on the neural basis of prosody, and knowing Dr. Newman, I’m pretty sure he would like to see it as well. A neat way that you might be able to include it, without having to make a full comprehensive discussion on it, could be through a mention of aprosodia and the lesioned areas associated with it, and how they result in deficits in prosody perception. Although I have not researched this topic myself, I’m sure you could find some more recent information on the subject. I do know of one article by Jonathan Rohrer et al. who published in the journal Cortex in 2010, title Receptive prosody in nonfluent primary progressive aphasias. Of course you wouldn’t have to discuss aphasias if it's not relevant, but it could lead you to other articles, and give you a feel for some of the neural aspects of prosody. Sometimes it is tricky though so ask Dr. Newman or Sarah for help if you can’t.

Reviewed by S. Walsh 23:48, 27 February 2011 (UTC)

title: Talk:Psycholinguistics/Prosody


text:
Talk:Psycholinguistics/Perception of Continuous Speech

I think you have done a very good job with this chapter. For the opening paragraph, you might want to use some simpler language to draw in possible readers that don’t have much experience with this topic. Also, I found a few places in the chapter where there was some missing punctuation and incorrect grammar. You did a very good job in simply explaining possibly complicated terminology such as assimilation, co-articulation, and epenthesis. The examples you laid out for those concepts, like using the words ‘come on’ and ‘warmth’ to explain how they would be applied in English goes a long way in helping to understand what they mean. I like the way you explained phoneme prototypes, as it made it pretty easy to understand and you wrote it in a clear and concise way. However, I think you could expand more on the voice onset time (VOT) section. I didn’t really understand it after reading it a few times over. I looked online and there is a lot of research available that you could cite. You also did a very good job in explaining phonemic restoration by using the study by Warren and Warren (1970). Their experiment helped illustrate very simple and useful examples of phonemic restoration and it went a long way in demonstrating your point. You described the gating task well, but I thought you could have gone deeper into how Grosjean (1980) actually put the task into action. It would further demonstrate to the reader how it works. The YouTube clip you posted showing how the McGurk effect works did an excellent job explaining what could be a complicated effect, but the clip makes it a lot simpler. You also might want to include some in-text citations in case a reader wants to see where you got the information from. You have the citations at the bottom of the page, so I suppose that may not be entirely necessary. --Charliekramer 00:16, 28 February 2011 (UTC)


text:
Talk:Psycholinguistics/Chronometry

Chapter Review: Chronometry
The chapter summary on Chronometry was structured and communicated well. It was nice to have such a well-defined outline at the beginning. The introduction was also precise and well written, but it might be nice to add some excitement to entice the reader to read on. Maybe some statements on what makes the models interesting and how they apply to real life. Overall very good introduction but as the reader I think it would be nice to have some interesting applications or facts to excite the reader about the presented topic.

Under the Naming Latencies section a lot of important knowledge was presented. I appreciated the clarity that the author used here. Especially in a textbook, format, for historical facts, it is so nice to read something that clearly states names and dates the way it is in this section. I also enjoyed the example with Steven Fraisse experiment, if gives a nice perspective and summary of the topic. Overall very good summary.

The Stroop Paradigm section clearly reiterated the classic study. I have no critiques on this section. It is well defined, and easy to understand and apply.

Picture/ Word Interference Tasks; I like how this section refered nicely to the definitions presented in the Stroop section. For a reader, it is really nice to have words emphasized ( like in this section in italics) to remind the reader that the presented definition is important. Also all of the studies presented nicely and precisely outlined the topic, its nice to read studies that 100% reiterate the presented knowledge rather than only kinda summarizes whats presented.

Implicit Priming; again very well structured and communicated. It might be nice for those who are new to cognitive psychology and linguistics to summarize priming generally. I found this section really interesting, the summary or Roelofs and Meyer’s experiment nicely flowed through and provided some interesting information. I really liked how at the end of this section you extrapolated and looked at the bigger picture. The last sentence about articulation is nice because it opens the reader’s mind and pushes them to really think about how to take what is presented and apply it to another topic. Very well done, there are some odd grammatical issues in this section.

The section on word frequency effects was again well written, very textbook-like. My only suggestion would be to add some “human “to it, meaning that with sections so heavy with research and findings its nice to add some sentences that in everyday terms confirm what the take home message is.

Interactive Models; for this section I would like to see a diagram or flow chart. I find with models it is much easier to understand when you can follow the sentences with a figure. I thought the last paragraph chronometric results not reconciling with interactive models was really interesting and well said. Its always nice as a reader to be given exceptions to the models presented.

The discrete Process Model section was good. Again I think it would be nice to see some accompanying diagrams or something because the two previous sections can be kinda word-heavy and hard to visualize.

Neuroimaging Research and the Time Course of Speech Production; this I found to be the most interesting section. It was nicely presented as well.

Overall, the chapter showed strong knowledge of the topic and was extremely well written. All the references were cited nicely and outlined important and interesting studies in the field. I think it would be nice to add a little more to the introduction on why this is important and what makes chronometry interesting. Also I would add a conclusion or key points of the chapter, those are always helpful. Very few spelling or grammatical mistakes. Overall very interesting and well written read, good job!

Em736458 00:34, 28 February 2011 (UTC)

title: Talk:Psycholinguistics/Chronometry


text: File:Hw4.1 1.png

title: File:Hw4.1 1.png


title: File:Fe1.s11.team2.HW4.4.fig1.jpg


text:
Talk:Psycholinguistics/Neural Basis of Speech Perception

For the most part, this chapter is thorough and covers the requisite bases, but, as is always the case, there is certainly some room for improvements.

The research was seemingly thorough, from a relatively wide variety of authors and time periods. However, I did note that the reference list was lacking any direct references to the original Wernicke papers, although his work is mentioned in the text. If the actual paper wasn’t used, it should be noted somewhere that it was Wernicke as cited in Source X, and not the original work. But other than small things like that, the papers cited contain information based on both lesion and imaging studies which provides a broad perspective.

The content is decently arranged, and follows a logical proceeding of knowledge for the general layout of the chapter. Within the individual topics the presentation of ideas were somewhat more muddled, and I felt could benefit from the implementation of more transitional language and some sort of coherent thread for the reader to follow along. For example, perhaps following the process of the perception of a word from start to finish, following the flow of a specific word through the various pathways and explain the functions of each part in relation to a specific word or phrase in order to give the reader that consistent context. This would help it feel less like reading a dense review paper and more like an educational tool and hopefully reduce the amount of rereading and head-scratching I found myself doing.

The content itself seems to be appropriate and hit the right notes, although perhaps weighted a little too heavily on the ventral stream. The chapter does mention that this imbalance is reflective of the literature, which may well be the case and therefore not much can be done, but as the uninitiated reader, it seems like there should be more to it (as it stands there are only 4 sentences or so), even if it is relatively speculative in comparison to the ventral stream research. I did very much enjoy the point about different interpretations of a study’s results, as most textbooks I’ve read often fall victim to that practice themselves, stating the author’s conclusions as fact without making any comment on the actual ambiguity involved.

As far as the writing style goes, I found it a little bit on the dense side, leaning more towards academic journal than educational tool, but it was generally well written. There were a few grammatical mistakes here and there, and some sentences that I felt might be missing a word or were phrased particularly confusingly. I've emailed my comments on this to the author and attached it ot the assignment submission.

My biggest criticism of the chapter as it stands right now is with its formatting. When discussing anatomy, particularly of the brain, I find it imperative that there are diagrams and visual aids of some sort, as the brain is without many obvious and familiar landmarks, especially to those not intimately acquainted with it, and the names of things are often somewhat abstract. Having visual aids will help not only to cement the information for more verbal learners, but will also provide a lifeline for the more visually inclined learners who will be totally lost in the long winded anatomical terminology. I also felt that the introduction was a little bit long, trimming and condensing it a bit would help give it more impact, and allow some of the information currently in it to be used to flesh out the body of the chapter instead. Lastly, a brief conclusion at the end to collect the reader’s thoughts and tie off the loose ends would be helpful to ensure that the reader has connected all the appropriate dots and provide an accepted conclusion that the reader can compare to the conclusions that they have drawn while reading the material. This could also work in reverse, having a definite conclusion clearly stated can serve as a “light at the end of the tunnel” to help readers understand the relevant parts of the material if they are finding it too challenging.

B-Parks 01:50, 28 February 2011 (UTC)


text:
Swahili I/Greetings

Hello
(To one person): Hujambo! (response: Sijambo!) (To More than one person): Hamjambo! (response: Hatujambo!) (Formal): Shikamoo. (response: Marahaba.) (Goodbye: Kwa heri. )

How are you?
How are you?: Habari yako? (Habari = News, Yako = Your -> Habari yako? = Your news?) How are you today?: Habari ya leo? (Ya = of, Leo = Today -> Habari ya leo? = News of today?) How are you this morning?: Habari ya asubuhi? (Asubuhi = Morning -> Habari ya asubuhi? = News of the morning?) How are you this afternoon?: Habari ya mchana? (Mchana = Afternoon -> Habari ya mchana? = News of the afternoon?) How are you this evening?: Habari ya jioni? (Jioni = Evening -> Habari ya jioni? = News of the evening?) Response: Nzuri, asante. (Nzuri = Good/Fine, Asante = Thank you -> Nzuri, asante = Fine, thanks.)

My name is ___________.
My name is ___________.: Jina langu ni ___________. (Jina = Name, -angu = My, ni = am/is/are -> Jina langu ni _____________. = My name is _____________.) What is your name?: Jina lako ni nani? (-ako = your, nani = who? -> Jina lako ni nani? = Your name is who?)

Excuse me.
Excuse me.: Samahani. (for attention)

I am from ___________.
I am from ___________.: Ninatoka nchi ya ___________. (Ninatoka = I-(PRES)-come from (IND.), Nchi = Nation, -a = Of -> I come from the nation of _____________.) Where are you from?: Unatoka wapi? (Unatoka = you-(PRES)-come from (IND.), Wapi? = Where? -> You come from where?)

Question Grammar
As you can probably see, Swahili questions are formed differently form English questions. Instead of "What is your name?" they say, "Your name is what?" Instead of "Where do you come from?" they say, "You come from where?" The interrogative pronoun comes last in the sentence, and the other words are arranged to make the sense make sense.

Exercises
Exercises

title: Swahili I/Greetings


text:
Talk:Psycholinguistics/DownsSyndromeLanguage

Peer Edit of: Language in Down's Syndrome

You have a good first version started but still some editing and grammatical corrections need to be done, with some sentences needing to be referenced. Also, inserting some pictures, tables or diagrams to break up the text would be a great addition to your chapter page. Some of your shorter heading sections need additional information but I realize this is a first draft, so I am sure you will do this. A concluding paragraph would be a nice finishing touch to wrap the chapter up.

Research- Try to keep reference formatting consistent throughout your chapter page. For example, (Thompson & Thompson, 2007) vs. Gardiner et al., (2010). You may want to look at additional research articles in order to add some more depth to some of your subject headings. Also, one thing for your references would be to alphabetize them. You may want to add more sources to your reference section, three (other than the textbook references) are probably not sufficient for your chapter depth. Also, one area to focus on is current research being conducted or future directions for your topic.

Organization - The initial overview/introduction you provide to the topic is great. One suggestion may be to divide it into subsections when you are talking about the different Down Syndrome sub types; ie Mosaic, trisomy etc. You could also consider this subsection outline for the Physical Attributes section. The overall layout of the page makes sense but a larger introduction and summary/conclusion section would add to your page.

The Language development and Language characteristics sections could be longer and more detailed as these should be the main focus of your chapter. I found myself asking the why and how of the underlying mechanisms that cause language development issues etc. The interventions section needs expansion as I am not quite sure what is supposed to go in this section so at this time I cannot really offer any concrete advice. I realize that this is your first draft and will be adding to it shortly. Some suggestions perhaps would be to put research areas of focus, new findings that relate to language development and more specific language issues for individuals with Down syndrome. Or is this section meant to explain methods to teach individuals who have these language delays? Will it include diagnostic tools for determining how delayed a person is in relation to language acquisition? There are lots of different options to include in this section.

Writing Structure/Style  - Some sentences are worded awkwardly in your chapter but I think it just needs some reviewing to fix this. Reading your chapter out loud helps with assessing any areas that need correction. There are some terms that you may want to explain or expand upon further so the reader has a better understanding (meiotic nondisjuncture, transverse palmar, plantar surface etc). This is a good solid foundation for your first draft and shows that you have researched your subject.

Overall your chapter is a good introduction to Language in Down’s Syndrome and as the term progresses I am sure you will add and edit it to make it even better. Adding some more historical aspects to the topic and further explanation of how language develops differently and the challenges that are faced, would ensure great improvement on an already great start! Another option is to add a history section, which could include focus areas such as major contributors to this area and progression of research and knowledge over time etc. Outside of doing a little more research and delving into some of the topics on a deeper level, I think you are on the right track to creating an interesting chapter to contribute to the overall Psycholinguistics page. Good work!

--Jchetwynd 22:22, 27 February 2011 (UTC)


text:
Talk:Psycholinguistics/Hemispheric Lateralization

I thoroughly enjoyed this chapter and felt like I learned a lot. I wasn’t expecting to realize how diverse lateralization can be and how many things there are that can affect it. I really liked the layout – I thought it was very organized and, for the most part, very easy to understand. However, there are a few things that I think could possibly cause a bit of confusion. These suggestions are minor but I think they could make your chapter even better!

In the introduction you state that “The hemispheric lateralization of language functions has been suggested to be associated […], and a variance amongst cultures.” By “a variance amongst cultures” I believe you mean that lateralization can be dependent on or influenced by one’s culture, but I found myself reading it over as I felt that that part of the sentence didn’t quite fit. For better flow, I would try re-wording it, or even including that fact in it’s own sentence.

With regards to Carl Wernicke, I was left wondering how the temporal lobe seems to disrupt language capabilities? It may be interesting to include if it is not too complicated. For example, predominantly, did it affect comprehension? Did it effect production? Or do we even know of a specific function affected by damage to the left temporal lobe? This information would be well suited in this section and might leave it even more complete.

Under “Split-Brain Patients” you explained a scenario of presenting a word to one hemisphere or the other. By “presented to the right hemisphere,” I just want to clarify that you mean that the word is shown on the patient’s left? It may be good to clear this up, as it might not be intuitive for all readers. However, it is a very interesting fact; I wonder if they even realize that they saw a word, and if it’s just a production issue where they say “nothing” because they cannot verbalize what they saw. From your explanation I gather that the latter is true.

I think there might have been a slight mix-up in a sentence in the “Wada test” section. I didn’t correct this because I want to be sure, but I think you may have mixed up left and right-handed people – 98% or right-handed have left dominant language, and 70% of left, correct? If so, that just needs to be switched in the last paragraph. Also in this section, I felt the sentence “It then serves to anaesthetize that side of the brain for approximately 10 minutes, after which it begins to wear off and the functions which were disrupted by the anaesthetic gradually return, often displaying aphasic errors” could be clearer. Do the aphasic errors occur when the patient is anesthetized? That would make sense to me intuitively but the sentence kind of tells me differently.

It may add to the organization to include subheadings under the umbrella heading “Electrical Stimulation, TMS and Imaging,” although this is just a thought and not absolutely necessary. I am not sure if it is necessary to have two “left” words in the sentence “Penfield found that stimulating the left frontal or temporal regions of the left hemisphere,” so thought I would bring it to your attention. Additionally, the following sentence seems to contradict the mentioned sentence; from what I gather, one sentence states that electrical stimulation accelerates speech and another inhibits or disrupts speech? Maybe I am reading it improperly, but I think it could probably be a little clearer.

In the TMS section, it may be worthwhile to give a quick explanation as to why the magnetic stimulation passing through multiple media would be an obvious drawback. For someone with no background in even a similar subject, they may not realize what this means. For example, you could add to the final sentence: “therefore is not always completely precise after traveling through so much media.” This is just a suggestion to make things that much more clear!

Finally for this section, it may be possible to improve upon the sentence under Imaging: “There has been some controversy regarding bilateral activation shown in fMRI studies […].” Would it make sense to break it up into more than one sentence, something like “However, there has been some controversy regarding bilateral activation shown in fMRI studies. It has been suggested that perhaps the right hemisphere is involved in aspects of speech that are not measured by such tests as the Wada procedure.” In my opinion, given that it still conveys your intended message, I believe this is a little easier to understand. The other sentence seemed a little long/run-on.

Lastly, I feel that a sentence under the “Culture and Lateralization” heading could be cleared up. The sentence “Asian languages show more bilateral activation during speech than European languages […] also show a good deal of bilateral activity” also seems a bit run-on and confusing by the end. I think it would provide more flow to end the sentence after explaining that Asian languages seem to depend more on the right-hemisphere. You could then say, “For example, Chinese characters are more pictorial and rely more on prosody, two aspects which emphasize use of the right hemisphere more than European languages.”

Ultimately, I learned more than expected from this chapter and honestly had a hard time finding things to improve upon. However, I believe my suggestions, though minor, would be beneficial to your chapter. I think you made great use of scholastic articles as well as textbook material and created a very thorough chapter on hemispheric lateralization that would allow anyone to learn something about the topic. If I were grading this, I would give it an A-range grade! Keep up the great work.

Grechukk 02:22, 28 February 2011 (UTC)


text:
User:Egm6341.s11.team4.KTH/HW4

=Problem 4.3=

Given
To prove Simple Simpson Error Theorem. Let, where,

Objectives
Show that

Solution
From given equation, the first derivative of e(t) is below.

Differentiate once more from eq(3.1) we get eq(3.2).

Substitute 0 into the eq(3.2), we get eq(3.3).

From the given equation about G(t). Calculate the first derivatives.

Calculate the first derivatives from eq(3.4).

Substitute 0 into the eq(3.5).

Given
From the equation of SSET.

Objectives
Find the relationship between $$ \zeta $$ and $$ \xi $$.

Solution
In the proof of SSET, we used transformation of variable.

Let

Substitute 1,-1 into the eq(2.2), we get eq(5.3) and eq(5.4).

From eq(5.3) and eq(5.4), we can get eq(5.5) and eq(5.6).

From addition of eq(5.5) and eq(5.6), we get eq(5.7)

From subtraction of eq(5.5) and eq(5.6), we get eq(5.8)

Substitute eq(5.7) and eq(5.8) into eq(5.2), we get eq(5.9).

title: User:Egm6341.s11.team4.KTH/HW4


title: File:Fe1.s11.team3.HW4.6.fig1.jpg


title: File:Fe1.s11.team3.HW4.1.fig1.jpg


title: File:Fe1.s11.team3.HW4.1.fig2.jpg


text:
User:Eml5526.s11.team4/HW4

= Problem 4.1 - Residue Projection for Modified Trigonometric Function Basis =

This problem refers to the previous Problem 2.9 and Problem 3.11

Problem Statement
Given the differential equation in strong form,

Consider the basis

Let, $$\displaystyle n=2,4$$ or $$\displaystyle 6$$ where $$\displaystyle ndof=n+1=3, 5$$ or $$\displaystyle 7$$ where ndof is the number of degrees of freedom and $$\displaystyle d=\left\{ {{d}_{j}};j=0,1,2.....n \right\}$$.

 * 1. Find two equations that enforce boundary conditions for

 * 2. Find $$\displaystyle 1,3$$ or $$\displaystyle 5$$ more equation(s) to solve for $$\displaystyle \mathbf{d}={{({{d}_{j}})}_{n\times 1}}

(j=0,1,2....n)$$by projecting the residue $$\displaystyle P({{u}^{h}}$$)on the basis function$$\displaystyle {{b}_{k}}(x)$$with $$\displaystyle k=1,2,3\cdots \cdots

$$ such that the additional equation is linearly independent from the above equation in part2.

 * 3. Display $$\displaystyle 3/5/7$$ equations in matrix form $$\displaystyle \mathbf{KD=F}$$ Observe the symmetry properities of$$\displaystyle \mathbf{K}$$

 * 4. Solve for $$\displaystyle \mathbf{d}$$

 * 5. Construct $$\displaystyle {{u}^{h}}(x)$$and plot $$\displaystyle {{u}^{h}}(x)$$ versus $$\displaystyle {{u}_{exact}}(x)$$

Exact Solution
With the general solution

After applying boundary conditions

For the case n=2
since $$\displaystyle {{b}_{j}}=\left\{ 1,\sin x,\sin 2x \right\}$$ with $$\displaystyle {{d}_{j}}=\left\{ {{d}_{0}},{{d}_{1}},{{d}_{2}} \right\}$$,

Boundary Conditions:

Additional equation:

For the third condition, we project the residue on the basis function.

Where:

hence,

and

thus the projection is

Putting equation 4.1.6, 4.1.7 and 4.1.11 into matrix form, we can have

Result:

For the case n=4
The approximating solution

Enforcing the boundary conditions:

There still three additional equations which been derived from enforcing the projection of $$\displaystyle P(u)$$ on basis to be zero:

putting equations 4.1.15 to 4.1.20 in matrix form yields:

For the case n=6
The approximating solution

Enforcing the boundary conditions:

There still three additional equations which been derived from enforcing the projection of $$\displaystyle P(u)$$on basis to be zero:

putting equations 4.1.25 to 4.1.31 in matrix form yields:

Thus

Comparison of error
The maximum error for each case is listed below

It is seen that for the case n=4 the error is numerically zero, however the error has risen for n=6 making the solution suspect.

Problem Statement
Obtain the weak form for the equations of heat conduction with the boundary conditions $$T(0)=100$$ and $$\bar{q}=hT$$ .The condition on the right is a convection condition.

Solution

w= weighted function

integrating by part yields

The weak form is

Find $$T(x)\epsilon \upsilon $$ such that

=Problem 4.3: Heat conduction problem in a circular plate=

Problem Statement
Given the strong form:

where

 * $$R$$ || is the total radius of the plate
 * $$s$$ || is the heat source per unit length along the plate radius
 * $$T$$ || is the temperature
 * $$k$$ || is the conductivity
 * }
 * $$k$$ || is the conductivity
 * }
 * }

Assume that $$k, s,$$ and $$R$$ are given.

Part A: Construct the weak form
Multiplying the governing equation (1) by a weight function $$ w(r) $$ and integrating over the domains on which they hold: We rewrite Equ (4) in the equivalent form: Taking the derivative of a product for the first term, Since $$w(R)=0$$ and because of (2), the first term in the above vanishes. So the solution is obtained as follows according to Equ (5) and (6):

Part B: Consider quadratic trial solutions and weight functions
From the given information the equations for $$T(r)$$ and $$w(r)$$ are as follows: The weight function $$w(r)$$ must vanish at $$r=R$$. Also, the trial solution $$T(r)$$ must satisfy the essential boundary condition (3). Differentiating $$w(r)$$ and $$T(r)$$ to obtain the solution of the weak form,

Part C: Obtain a solution
Show that the temperature distribution along the radius is given by

Substituting Equ (10,12) into the weak form (7) to solove the differential equation with the boundary conditions, Evaluating the integrals and factoring out $$\beta_1$$ and $$\beta_2$$ gives As the above must hold for all $$\beta_1$$ and $$\beta_2$$, it follows that the terms in the parentheses must vanish. Rearranging it,

We can get $$\alpha_1$$ and $$\alpha_2$$ from the above 2 equations. Substituting (17) into (11) gives the weak solution.

Problem Statement:
Given the strong form for the circular bar in torsion shown above: $$ \begin{align} \frac{\mathrm{d}}{\mathrm{d}x}(JG\frac{\mathrm{d\phi}}{\mathrm{d}x})+m=0 \end{align} $$ $$ \begin{align} 0\leq x\leq 1 \end{align} $$ The natural boundary condition is given by: $$ \begin{align} M(x=l)=(JG\frac{\mathrm{d\phi}}{\mathrm{d}x})_l=\bar{M} \end{align} $$ The essential boundary condition is given by: $$ \begin{align} \phi(x=0)=\bar{\phi} \end{align} $$ Where m(x) is a distributed moment per unit length, M is the torsion moment, $$\phi$$ is the angle of rotation, G is the shear modulus, and J is the polar moment of inertia given by $$J=\frac{\pi C^{4}}{2}$$. In this equation, C is the radius of the circular shaft. 1.) Construct the weak form for the circular bar in torsion. 2.) Assume that m(x)=0 and integrate the differential equation given above. Find the integration constants using boundary conditions.

Solution:
1.) To construct the weak form, first, the strong form is multiplied by the weighting function $$w(x)$$ producing equation 4.4.1. Next, equation 4.4.1 is integrated over the domain $$\Omega$$ as shown in equation 4.4.2. This integral can be solved using integration by parts as derived in Fish and Belytschko Section 3.5.2 (shown below in general form). For the more specific case: $$ \Gamma_u=\left\{x=0\right\}$$ $$ \Gamma_t=\left\{x=L\right\}$$ $$ n\left\{x=0\right\}=-1$$ $$ n\left\{x=L\right\}=1$$ $$ f=JG\frac{\partial\phi}{\partial x} $$ Combining this with equations 4.4.2 and 4.4.3 produces: Given that $$w(x=0)=0$$ and by applying the natural boundary condition produces the weak form shown in equation 4.4.5. 2.) Assuming $$m(x)=0$$ produces the new strong form equation 4.4.6. Integrating with respect to $$x$$ results in equation 4.4.7. By applying the previously stated natural boundary condition, the coefficient of integration $$C_{1}$$ can be obtained as shown below.

References:
Solved by Dustan Simko

=Problem 4.5: Constraint Breaking for Weak Form Basis Functions=

Problem Statement:
Consider the following potential basis functions: Let $$\Omega=\left[\alpha,\beta\right]=\left[-2,4\right]$$. For $$\Gamma_{g}=\left\{\beta\right\}$$ and each of the above listed families of basis functions, find the corresponding family $$\tilde{F_{i}}=\left\{\mathbf{\bar{b}_{j}}\right\}$$ satisfying the constraint breaking solution (CBS) requirements. Recall that the CBS is a family of basis functions $$\left\{\bar{b}_j(x),j=0,1,...,n\right \}$$ such that $$\bar{b}_{0}(\beta)\neq 0$$ and $$ \bar{b}_{j}(\beta)=0$$ for $$j=1,...,n$$ 1.) Plot $$\mathbf{\left\{b_{j}\right\}}$$ and $$\left\{\mathbf{\bar{b}_{j}}\right\}$$ for $$j=1,2,3$$ 2.)Show $$\mathfrak{F}_{e}=\left\{e^{jx},j=0,1,2,3\right\}$$ is linearly independent on $$\Gamma$$
 * $$\mathbf{Polynomial}$$
 * $$\mathbf{Cosine}$$
 * $$\mathbf{Sine}$$
 * $$\mathbf{Fourier}$$
 * $$\mathbf{Exponential}$$

Polynomial
The polynomial basis function is given by $$\mathfrak{F}_{p}=\left\{x^{j},j=0,1,...,n\right\}$$. For $$\left\{j=0,1,2,3\right\}$$ the basis functions $$\left\{b_{j}\right\}$$ are as follows: The constraint breaking solution$$\left\{\bar{b}_j\right\}$$ for the polynomial basis function is shown below: In the specific case where $$\left\{\beta=4\right\}$$ the CBS becomes: The basis functions$$\left\{\bar{b}_j\right\}$$ satisfy the CBS requirements since$$\left\{\bar{b}_0(\beta)=constant\neq0\right\}$$ and $$\left\{\bar{b}_j(\beta)=0, for j=1,2,...,n\right\}$$. The following figure shows the original polynomial basis functions and the CBS basis functions for $$\left\{j=1,2,3\right\}$$:

Cosine
The cosine basis function is given by $$\mathfrak{F}_{c}=\left\{cos(jx),j=0,1,...,n\right\}$$. For $$\left\{j=0,1,2,3\right\}$$ the basis functions $$\left\{b_{j}\right\}$$ are as follows: The constraint breaking solution$$\left\{\bar{b}_j\right\}$$ for the cosine basis function is shown below: In the specific case where $$\left\{\beta=4\right\}$$ the CBS becomes: The basis functions$$\left\{\bar{b}_j\right\}$$ satisfy the CBS requirements since$$\left\{\bar{b}_0(\beta)=constant\neq0\right\}$$ and $$\left\{\bar{b}_j(\beta)=0, for j=1,2,...,n\right\}$$. The following figure shows the original cosine basis functions and the CBS basis functions for $$\left\{j=1,2,3\right\}$$:

Sine
The sine basis function is given by $$\mathfrak{F}_{c}=\left\{1,sin(jx),j=1,...,n\right\}$$. For $$\left\{j=0,1,2,3\right\}$$ the basis functions $$\left\{b_{j}\right\}$$ are as follows: The constraint breaking solution$$\left\{\bar{b}_j\right\}$$ for the sine basis function is shown below: In the specific case where $$\left\{\beta=4\right\}$$ the CBS becomes: The basis functions$$\left\{\bar{b}_j\right\}$$ satisfy the CBS requirements since$$\left\{\bar{b}_0(\beta)=constant\neq0\right\}$$ and $$\left\{\bar{b}_j(\beta)=0, for j=1,2,...,n\right\}$$. The following figure shows the original sine basis functions and the CBS basis functions for $$\left\{j=1,2,3\right\}$$:

Fourier
The Fourier basis function is given by So, the basis functions $$\left\{b_{j,k}\right\}$$ are as follows: The corresponding basis functions $$\left\{\bar{b}_{j,k}\right\}$$ satisfying CBS are shown below: The basis functions$$\left\{\bar{b}_{j,k}\right\}$$ satisfy the CBS requirements

 * $$\left\{\bar{b}_0(\beta)=1\neq0\right\}$$

 * $$\left\{\bar{b}_{j,k}(\beta)=0, for j,k=1,2,...\right\}$$.

The following figure shows the original fourier basis functions and the CBS basis functions for $$\left\{j=1,2,3;k=1,2\right\}$$:

Exponential
The exponential basis function is given by So, the basis functions $$\left\{b_j\right\}$$ are as follows: The corresponding basis functions $$\left\{\bar{b}_j\right\}$$ satisfying CBS are shown below: The basis functions$$\left\{\bar{b}_j\right\}$$ satisfy the CBS requirements

 * $$\left\{\bar{b}_0(\beta)=1\neq0\right\}$$

 * $$\left\{\bar{b}_{j}(\beta)=0, for j=1,2,...\right\}$$.

The following figure shows the original exponential basis functions and the CBS basis functions for $$\left\{j=1,2,3\right\}$$:

References:
Solved by Dustan Simko and Woo Rhee

= Problem 4.6 - Strong and weak form of elastic bar problem with variable distributed spring =

Problem Statement
Consider an elastic bar with a variable distributed spring p(x) along its length .The distributed spring imposes an axial force on the bar in proportion to the displacement. Consider a bar of length l,cross-sectional area A(x),young's modulus E(x)with body force b(x) and boundary conditions as follows

a. Construct the strong form

b. Construct the weak form

Solution
First consider an element of this elastic bar.

From the force equilibrium i.e D'Alembert's principle,

taking the limit as $$\Delta x\rightarrow 0$$

for the governing ODE

Boundary conditions are

So the strong form is

The weak form derivation:

integrating by parts for the first term yields

which can be expanded as follows

Let w (0)=0 be the essential boundary condition.

The the weak form is as follows

Find u(x) smooth enough and satisfy u(0)=0,such that

=Problem 4.7: CGX Project and Tutorial=

From the lecture slide Mtg23

Problem Statement

 * 1) install cgx.
 * 2) Read manual; sign up with user group to ask questions if any, also access archive.
 * 3) Reproduce the basic examples:disk, cylinder, sphere, sphere-volume, airfoil.
 * 4) Write a report for "dummies": explain how to install and run cgx.

Final Report
Installation and run:
 * 1) Download the windows-version of Calculix from its website, and then install it on computer.
 * 2) Run the CalculiX Command: [Start] [Programs] [bConverged][CalculiX] [CalculiX Command]
 * 3) Reproduce the basic examples

A. The “disc” problem
1. First switch to the directory of working ‘E:\Documents\ccx’.

2. Then input the command ‘cgx –b disc.fbd’, there will appear another command “CalculiX Graphix”.

3. Input the command” pnt [  ]” and then plot all the points with the command ‘plot p all b’. For example, ”PNT py  0.0  1.0 0.0” is used to define a point which is located at (0,1,0).

PNT py     -0.00000        1.00000        0.00000

The figure is showed below.

4. Input the command” line    ” and the “gsur '+|-'BLEND| ' '+|-'  '+|-' -> .. (3-5 times)and then plot all the lines and surfaces with command ‘plus’. For example, “LINE L001 P00I P001 p0 4 ” is used to define a arc line which pass through points P00I and P001 and its center point is p0 and radius is 4.

LINE L001 P00I P001 p0 4

GSUR A001 + BLEND - L003 - L002 - L001 - L004

The figure is showed below.

5. You can use mouse on the Graphix command to rotate and zoom in or out the figure.

6. Input the command ‘ELTY all QU4’ to assign the element type and then ‘mesh all’ to mesh the geometry, and then left-click on the marginal area on the Graphix, then on ’Viewing’ and continue to ‘show all elements with light’ and ‘Toggle Element edges’, as showed in following figures

B. The “cylinder” problem
1. First switch to the directory of working ‘E:\Documents\ccx’.

2. Then input the command ‘cgx –b cylinder.fbd’, there will appear another command “CalculiX Graphix”.

3. Input the command” pnt [  ]” and then plot all the points. Input the command” line    ” and the “gsur '+|-'BLEND| ' '+|-'  '+|-' -> .. (3-5 times)and then plot all the lines and surfaces. The figure is showed below

4. Use the command “seta |'n'|'e'|'p'|'l'|'c'|'s'|'b'|'S'|'L'|'se' <name ..> ['n'|'e' <name” to define some sets to be used in further loading operations. For example, “SETA p1 p p1” is to define a set of points which contains point p1.

5. You can use mouse on the Graphix command to rotate and zoom in or out the figure.

6. Input the command ‘ELTY all QU4’ and ‘mesh all’, and then left-click on the marginal area on the Graphix, then on ’Viewing’ and continue to ‘show all elements with light’ and ‘Toggle Element edges’, as showed in following figure.

C. The “sphere” problem
1. First switch to the directory of working ‘E:\Documents\ccx’

2. Then input the command ‘cgx –b sphere.fbd’, there will appear another command “CalculiX Graphix”.

3. Input the command” pnt [<x> <y> <z>]” and then plot all the points with the command ‘plot p all b’. For example, ”PNT py  0.0  1.0 0.0” is used to define a point which is located at (0,1,0). The figure is showed below.

4. Input the command” line <p1> <p2> <cp|seq> ” and the “gsur '+|-'BLEND| ' '+|-' <line|lcmb> '+|-' -><line|lcmb> .. (3-5 times)and then plot all the lines and surfaces with command ‘plus’. For example, “LINE L001 P00I P001 p0 104 ” is used to define a arc line which pass through points P00I and P001 and its center point is p0 and radius is 104. The figure is showed below.

5. Input the command ‘ELTY all QU4’ and ‘mesh all’, and then left-click on the marginal area on the Graphix, then on ’Viewing’ and continue to ‘show all elements with light’ and ‘Toggle Element edges’, as showed in following figure.

D. The “sphere-volume” problem
1. First switch to the directory of working ‘E:\Documents\ccx’

2. Then input the command ‘cgx –b sphere-volu.fbd’, there will appear another command “CalculiX Graphix”.

3. Input the command” pnt [<x> <y> <z>]” and then plot all the points. Input the command” line <p1> <p2> <cp|seq> ” and the “gsur '+|-'BLEND| ' '+|-' <line|lcmb> '+|-' -><line|lcmb> .. (3-5 times)and then plot all the lines and surfaces. The figure is showed below

4. Input the command” gbod 'NORM' '+|-' '+|-' ->( 5-7 surfaces )” to define a volume. For example, “GBOD B001 NORM + A006 - A003 - A004 + A002 + A001” is to define a volume which consists of these above areas. GBOD B001 NORM + A006 - A003 - A004 + A002 + A001

5. Input the command ‘ELTY all he20’ and ‘mesh all’, and then left-click on the marginal area on the Graphix, then on ’Viewing’ and continue to ‘show all elements with light’ and ‘Toggle Element edges’, as showed in following figure.

E. The “airfoil” problem
1. First switch to the directory of working ‘E:\Documents\ccx’

2. Then input the command ‘cgx –b airfoil.fbd’, there will appear another command “CalculiX Graphix”.

3. Input the command” pnt [<x> <y> <z>]” and then plot all the points with the command ‘plot p all b’. For example, ” PNT P05D     0.00118       -5.37045        0.00000” is used to define a point which is located at (0.00118,-5.37045,0.00000). The figure is showed below.

4. Input the command ”seqa ['pnt' .. <=>]|['afte'|'befo' .. <=>]|['end' .. <=>]” to define a sequential set. For example, “SEQA S005 pnt  P010 P00C P00A P01C” is used to define a sequential point set which pass through points P010 P00C P00A P01C sequentially.

SEQA S006    pnt  P01A P00A P00C P00E P00G P00I P00J P00K P00L P019

5. Input the command ”lcmb ['+|-' '+|-' '+|-' ->  ..(up to 14 lines)]| ['ADD' '+|-' '+|-' -> '+|-' ..(up to 14 lines)]” to combine lines. For example, “ LCMB C001 + L015 + L01X + L01Y + L016” is used to combine the lines of C001, L015 + L01X + L01Y, L016.

LCMB C001 + L001 + L002 + L00A + L00L + L009

6. Input the command” line <p1> <p2> <cp|seq>” and the “gsur '+|-'BLEND| ' '+|-' <line|lcmb> '+|-' -><line|lcmb> .. (3-5 times)and then plot all the lines and surfaces with command ‘plus’. For example, “LINE L001 P00I P001 p0 104 ” is used to define a arc line which pass through points P00I and P001 and its center point is p0 and radius is 104. The figure is showed below.

7. Input the command ‘ELTY all QU4’ and ‘mesh all’, and then left-click on the marginal area on the Graphix, then on ’Viewing’ and continue to ‘show all elements with light’ and ‘Toggle Element edges’, as showed in following figure.

References:
=Problem 4.8 Finding the mass and stiffness matrix for a dynamic system =

The following problem was assigned in Lecture 23 and is a modification to Fish and Belytschko's problem 3.4 on page 72.

Given data
The following given partial differential equation (PDE) is provided in strong form with boundary and initial conditions. The PDE is a second-order constant coefficient wave equation with a first order term.

The basis and weighting functions are provided respectively as

With

Problem statement
Find $$\textbf{F}(t)$$ and the mass matrix, $$\displaystyle{ \tilde{ \mathbf{ M}}}$$

Developing the Weak Form
Starting with the strong form we derive the weak form by multiplying an arbitrary weight function and then integrate by parts.

Evaluating with the basis and weighting functions
Evaluating term by term.

Here we note that $$u^h$$ is a function of time as well as space. For this to be true, the coefficients $$a_0,a_1,a_2, a_3$$ must be functions of time. Note that in a final Finite Element formulation, such as a Galerkin Formulation, $$u^h$$ is assumed to be separable into spatially dependent and time dependent terms. This would allow us to explicitly integrate in time (the exception being for nonlinear equations).

Further, note

This reduces the unknowns to three, and provides three governing equations. Evaluating the temporal term gives the last components.

Solving the system of equations
By the generality in $$\beta_i$$ we now have a system of equations, namely

We now have three equations and three unknowns $$(\alpha_1(t), \alpha_2(t), \alpha_3(t))$$. We note that $$\alpha_0''=-4\sin(2t)$$

Linearizing the system of equations
We now linearize the system by introducing three new equations

We now have six equations and six unknowns. The task now remains to solve six simultaneous ODE's.

So that we now have the linear system of ODE's, which may be solved as follows

Calculate an integrating factor

Now multiplying by the integrating factor and recognize the left hand side is the total derivative

In theory the solution can be calculated with a symbolic toolbox. However, the solve times were excessively large are intractable. This suggests another approach or a complicated temporal behavior. We note that numerical integration would overcome this challenge.

The mass and stiffness matrices
As requested we list the mass and stiffness matrices from equation (8.12)

title: User:Eml5526.s11.team4/HW4


text:
Swahili I/Numbers and Time

1-10
1 = Moja (adj. -moja) 2 = Mbili (adj. -wili) 3 = Tatu (adj. -tatu) 4 = Nne (adj. -nne) 5 = Tano (adj. -tano) 6 = Sita 7 = Saba 8 = Nane 9 = Tisa/Kenda Kenda is used in a different dialect mostly from Burundi, Rwanda and D.R.C but Tisa is used by Tanzania and Kenya more often.

10 = Kumi

10-20
11 = Kumi na moja (Na = And -> Kumi na moja = Ten and One) 12 = Kumi na mbili 13 = Kumi na tatu ... 20 = Ishirini (21 = Ishirini na moja... )

Tens
30 = Thelathini 40 = Arobaini 50 = Hamsini 60 = Sitini 70 = Sabini 80 = Themanini 90 = Tisini

100+
100 = Mia moja (101 = Mia moja na moja... ) 200 = Mia mbili ... 1,000 = Elfu

Time
Swahili time is expressed very differently from standard time in other parts of the world. Instead of midnight and noon, Swahili time is based on sunset and sunrise. As most Swahili-speaking countries are located near the equator, sunset and sunrise are mostly constant year-round, and defined to be 6:00 P.M. and 6:00 A.M., respectively in standard time. Hence, 6:00 A.M. is the zero hour (0:00 or 12:00) in Swahili time, 7:00 A.M. is the first hour of the day (1:00 in the Morning) and so on. An easy translation to Swahili time is to subtract six hours from the standard clock time, which is how many natives adjust. For example, 11:30 A.M. in standard time is 5:30 in the morning in Swahili time. Instead of A.M. and P.M., Swahili time expresses the hour followed by the portion of the day.
 * Alfajiri = early morning, before the sun has fully risen
 * Asubuhi = morning, roughly between sunrise and noon
 * Mchana = daytime, between sunrise 6:A.M. and sunset 6:00 P.M.
 * Jioni = evening, between sunset 6:P.M. and sunrise 6:00 A.M.
 * Usiku = night time, from sunset until early morning again

As with standard time, the hour (saa) is expressed first, followed by the minutes (dakika). There are also abbreviations for half past (nusu, half) and others (kasorobo, less a quarter). Here are some examples of time-telling to help you understand how it is done.

Advice
You should make flashcards for these with the actual digits on one side and the Swahili word on the other and quiz yourself, looking at both sides and saying, aloud, what is on the other.

Exercises
/Exercises/

title: Swahili I/Numbers and Time


text:
User:Eml5526.s11.team3.hylon/Homework 4

=Problem4.1 Solve for trial solution of the PDE using sine basis=

Problem Statement
Given $${{b}_{i}}(x)=[1,\sin (x),\sin (2x),\cdots ]$$.

$$1).$$ Find two equations that enforce boundary conditions for $${{u}^{h}}(x)=\sum\limits_{j=0}^{n}{{{d}_{j}}{{b}_{j}}(x)}$$.

Natural boundary condition: $$-\frac{d{{u}^{h}}(x=0)}{dx}=4$$;

essential boundary condition: $${{u}^{h}}(x=1)=0$$.

$$2).$$ Find one more equation to solve for $$\underline{d}=\left\{ {{d}_{j}} \right\} (j=0,1,2)$$by project the residue $$P({{u}^{h}})$$ on a basis function $${{b}_{k}}(x)$$ with $$k=0,1,2 $$, such that the additional equation is linear independent from the above two equations in $$(1)$$. $$3).$$ Display three equations in matrix form $$\underline{K}\underline{d}=\underline{F}$$, observe symmetric property of $$\underline{K}$$. $$4).$$ Solve for $$\underline{d}$$. $$5).$$ Construct $$u_{2}^{h}(x)$$ and plot $$u_{2}^{h}(x)$$ vs. $$u_{2}^ – (x)$$. $$6).$$Compute $$u_{2}^{h}(x=0.5)$$ and Error $${{e}_{2}}(x=0.5)=u(x=0.5)-{{u}^{h}}(x=0.5)$$. $$7).$$ Repeat $$1)-6)$$ for $$n=4,n=6$$. $$8).$$ Plot $${{e}_{2}}(x=0.5)$$ vs. $$n$$ Refer to lecture slide [[media:fe1.s11.mtg18.djvu|18-2]] for more information.

Solution
When n =2

1.

Equation enforcing natural boundary condition:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

{{d}_{1}}+2{{d}_{2}}=-4

$$
 * }

Equation enforcing essential boundary condition:
 * {| style="width:100%" border="0"

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

{{d}_{0}}+0.8415{{d}_{1}}+0.9093{{d}_{2}}=0

$$
 * }

2.

Equation from projection:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.9194{{d}_{1}}+5.6646{{d}_{2}}=3

$$
 * }

3.

Display three equations in matrix form:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\left( \begin{matrix}  0 & 1 & 2  \\   1 & 0.8415 & 0.9093  \\   0 & 0.9194 & 5.6646  \\ \end{matrix} \right)\left( \begin{matrix}   {{d}_{0}}  \\   {{d}_{1}}  \\   {{d}_{2}}  \\ \end{matrix} \right)=\left( \begin{matrix}   -4  \\   0  \\   3  \\ \end{matrix} \right)

$$
 * }

$$K$$ is non-symmetric.

4.

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\left( \begin{matrix}  {{d}_{0}}  \\   {{d}_{1}}  \\   {{d}_{2}}  \\ \end{matrix} \right)={{\left( \begin{matrix}   0 & 1 & 2  \\   1 & 0.8415 & 0.9093  \\   0 & 0.9194 & 5.6646  \\ \end{matrix} \right)}^{-1}}\left( \begin{matrix}   -4  \\   0  \\   3  \\ \end{matrix} \right)=\left( \begin{matrix}   4.7162  \\   -7.4908  \\   1.7454  \\ \end{matrix} \right)

$$
 * }

5.

The approximate solution:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\text{u}_{2}^{h}\text{(x)=4}\text{.7162-7}\text{.4908sin(x)+1}\text{.7454sin(2x)}

$$
 * }

6.

Error between exact solution and approximate solution at point x=0.5.

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

error(x=0.5)=-0.0311

$$
 * }

When n =4

1.

Equation enforcing natural boundary condition:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

{{d}_{1}}+2{{d}_{2}}+3{{d}_{3}}+4{{d}_{4}}=-4

$$
 * }

Equation enforcing essential boundary condition:
 * {| style="width:100%" border="0"

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

{{d}_{0}}+0.8415{{d}_{1}}+0.9093{{d}_{2}}+0.1411{{d}_{3}}-0.7568{{d}_{4}}=0

$$
 * }

2.

Equations from projection:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.9194{{d}_{1}}+\text{5}.\text{6646}{{d}_{2}}+\text{11}.\text{9400}{{d}_{3}}+\text{13}.\text{2291}{{d}_{4}}=3

$$
 * }

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.\text{5454}{{d}_{1}}+\text{3}.\text{1777}{{d}_{2}}+\text{5}.\text{7946}{{d}_{3}}+\text{3}.\text{8212}{{d}_{4}}=\text{1}.\text{379}0\text{9}

$$
 * }

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.\text{7944}{{d}_{1}}+\text{4}.\text{7568}{{d}_{2}}+\text{9}.\text{2993}{{d}_{3}}+\text{8}.0\text{195}{{d}_{4}}=\text{2}.\text{1242}

$$
 * }

3.

Display five equations in matrix form:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\left( \begin{matrix}  0 & 1 & 2 & 3 & 4  \\   1 & 0.\text{8415} & 0.\text{9}0\text{93} & 0.\text{1411} & -0.\text{7568}0  \\   0 & 0.\text{9194} & \text{5}.\text{6646} & \text{11}.\text{9400} & \text{13}.\text{2291}  \\   0 & 0.\text{5454} & \text{3}.\text{1777} & \text{5}.\text{7946} & \text{3}.\text{8212}  \\   0 & 0.\text{7944} & \text{4}.\text{7568} & \text{9}.\text{2993} & \text{8}.0\text{195}  \\ \end{matrix} \right)\left( \begin{matrix}   {{d}_{0}}  \\   {{d}_{1}}  \\   {{d}_{2}}  \\   {{d}_{3}}  \\   {{d}_{4}}  \\ \end{matrix} \right)=\left( \begin{matrix}   -4  \\   0  \\   3  \\   \text{1}.\text{379}1  \\   \text{2}.\text{1242}  \\ \end{matrix} \right)

$$
 * }

$$K$$ is non-symmetric.

4.

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\left( \begin{matrix}  {{d}_{0}}  \\   {{d}_{1}}  \\   {{d}_{2}}  \\   {{d}_{3}}  \\   {{d}_{4}}  \\ \end{matrix} \right)={{\left( \begin{matrix}   0 & 1 & 2 & 3 & 4  \\   1 & 0.\text{8415} & 0.\text{9}0\text{93} & 0.\text{1411} & -0.\text{7568}  \\   0 & 0.\text{9194} & \text{5}.\text{6646} & \text{11}.\text{9400} & \text{13}.\text{2291}  \\   0 & 0.\text{5454} & \text{3}.\text{1777} & \text{5}.\text{7946} & \text{3}.\text{8212}  \\   0 & 0.\text{7944} & \text{4}.\text{7568} & \text{9}.\text{2993} & \text{8}.0\text{1949}  \\ \end{matrix} \right)}^{-1}}\left( \begin{matrix}   -4  \\   0  \\   3  \\   \text{1}.\text{379}1  \\   \text{2}.\text{1242}  \\ \end{matrix} \right)=\left( \begin{matrix}   \text{4}.\text{7491}  \\   -\text{13}.\text{1144}  \\   \text{8}.\text{2}0\text{87}  \\   -\text{3}.\text{6116}  \\   0.\text{8830}  \\ \end{matrix} \right)

$$
 * }

5.

The approximate solution:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\text{u}_{4}^{h}\text{(x)=4}.\text{7491}-\text{ 13}.\text{1144sin}\left( \text{x} \right)\text{ }+\text{8}.\text{2}0\text{87sin}\left( \text{2x} \right)\text{ }-\text{ 3}.\text{6116sin}\left( \text{3x} \right)\text{ }+\text{ }0.\text{8830sin}\left( \text{4x} \right)

$$
 * }

6.

Error between exact solution and approximate solution at point x=0.5.

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\text{ error(x=0}\text{.5)=0}\text{.0069}

$$
 * }

When n =6

1.

Equation enforcing natural boundary condition:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

1{{d}_{1}}+2{{d}_{2}}+3{{d}_{3}}+4{{d}_{4}}+5{{d}_{5}}+6{{d}_{6}}=-4

$$
 * }

Equation enforcing essential boundary condition:
 * {| style="width:100%" border="0"

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

{{d}_{0}}+0.8415{{d}_{1}}+0.9093{{d}_{2}}+0.1411{{d}_{3}}-0.7568{{d}_{4}}-0.9589{{d}_{5}}-0.2794{{d}_{6}}=0

$$
 * }

2.

Equations from projection:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.9194{{d}_{1}}+5.6646{{d}_{2}}+11.9400{{d}_{3}}+13.2291{{d}_{4}}+7.1634{{d}_{5}}+0.4780{{d}_{6}}=3

$$
 * }

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.5454{{d}_{1}}+3.1777{{d}_{2}}+5.7946{{d}_{3}}+3.8212{{d}_{4}}-3.5658{{d}_{5}}-10.2830{{d}_{6}}=1.3791

$$
 * }

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.7944{{d}_{1}}+4.7568{{d}_{2}}+9.2993{{d}_{3}}+8.0195{{d}_{4}}-1.1704{{d}_{5}}-11.2633{{d}_{6}}=2.1242

$$
 * }

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

$$\displaystyle 0.6438{{d}_{1}}+4.1330{{d}_{2}}+9.4191{{d}_{3}}+11.9619{{d}_{4}}+8.2745{{d}_{5}}+0.0450{{d}_{6}}=1.9900
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

$$
 * }

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

0.2388{{d}_{1}}+2.0049{{d}_{2}}+6.7285{{d}_{3}}+14.0213{{d}_{4}}+19.8920{{d}_{5}}+18.3258{{d}_{6}}=1.2402

$$
 * }

3.

Display seven equations in matrix form:

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

$$\displaystyle \left( \begin{matrix}  0 & 1 & 2 & 3 & 4 & 5 & 6  \\   1 & 0.8415 & 0.9093 & 0.1411 & -0.7568 & -0.9589 & -0.2794  \\   0 & 0.9194 & 5.6646 & 11.9400 & 13.2291 & 7.1634 & 0.4780  \\   0 & 0.5454 & 3.1777 & 5.7946 & 3.8212 & -3.5658 & -10.2830  \\   0 & 0.7944 & 4.7568 & 9.2993 & 8.0195 & -1.1704 & -11.2633  \\   0 & 0.6438 & 4.1330 & 9.4191 & 11.9619 & 8.2745 & 0.0450  \\   0 & 0.2388 & 2.0049 & 6.7285 & 14.0213 & 19.8920 & 18.3258  \\ \end{matrix} \right)\left( \begin{matrix}   {{d}_{0}}  \\   {{d}_{1}}  \\   {{d}_{2}}  \\   {{d}_{3}}  \\   {{d}_{4}}  \\   {{d}_{5}}  \\   {{d}_{6}}  \\ \end{matrix} \right)=\left( \begin{matrix}   -4  \\   0  \\   3  \\   1.3791  \\   2.1242  \\   1.9900  \\   1.2402  \\ \end{matrix} \right)
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

$$
 * }

$$K$$ is non-symmetric.

4.

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\left( \begin{matrix}  {{d}_{0}}  \\   {{d}_{1}}  \\   {{d}_{2}}  \\   {{d}_{3}}  \\   {{d}_{4}}  \\   {{d}_{5}}  \\   {{d}_{6}}  \\ \end{matrix} \right)={{\left( \begin{matrix}   0 & 1 & 2 & 3 & 4 & 5 & 6  \\   1 & 0.8415 & 0.9093 & 0.1411 & -0.7568 & -0.9589 & -0.2794  \\   0 & 0.9194 & 5.6646 & 11.9400 & 13.2291 & 7.1634 & 0.4780  \\   0 & 0.5454 & 3.1777 & 5.7946 & 3.8212 & -3.5658 & -10.2830  \\   0 & 0.7944 & 4.7568 & 9.2993 & 8.0195 & -1.1704 & -11.2633  \\   0 & 0.6438 & 4.1330 & 9.4191 & 11.9619 & 8.2745 & 0.0450  \\   0 & 0.2388 & 2.0049 & 6.7285 & 14.0213 & 19.8920 & 18.3258  \\ \end{matrix} \right)}^{-1}}\left( \begin{matrix}   -4  \\   0  \\   3  \\   1.3791  \\   2.1242  \\   1.9900  \\   1.2402  \\ \end{matrix} \right)=\left( \begin{matrix}   4.7500  \\   -257.2133  \\   341.5391  \\   -261.6497  \\   128.7012  \\   -38.5828  \\   5.5312  \\ \end{matrix} \right)

$$
 * }

5.

The approximate solution:

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

u_{6}^{h}(x)=4.75-257.2133\sin (x)+341.5391\sin (2x)-261.6497\sin (3x)+128.7012\sin (4x)-38.5828\sin (5x)+5.5312\sin (6x)

$$
 * }

6.

Error between exact solution and approximate solution at point x=0.5.

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

$$\displaystyle
 * style="width:92%; padding:10px; border:2px solid #ff0000" |
 * style="width:92%; padding:10px; border:2px solid #ff0000" |

\text{ error(x=0}\text{.5)=0}\text{.0086}

$$
 * }

Plot of Error(x=0.5) Vs. n

title: User:Eml5526.s11.team3.hylon/Homework 4


text:
Swahili I/Dates

Swahili dates are constructed in the following manner: Tarehe (Date) + (Number of Day in Month) + (Month) + (Day of Week)

Day Numbers
1st = Moja/Kwanza 2nd = Pili/mbili 3rd = Tatu 4th = Nne 5th = Tano 6th = Sita 7th = Saba 8th = Nane 9th = Tisa 10th = Kumi 11th = Kumi na moja 12th = Kumi na mbili 13th = Kumi na tatu 14th = Kumi na nne 15th = Kumi na tano 16th = Kumi na sita 17th = Kumi na saba 18th = Kumi na nane 19th = Kumi na tisa 20th = Ishirini 21st = Ishirini na moja 22nd = Ishirini na mbili 23rd = Ishirini na tatu 24th = Ishirini na nne 25th = Ishirini na tano 26th = Ishirini na sita 27th = Ishirini na saba 28th = Ishirini na nane 29th = Ishirini na tisa 30th = Thelathini 31st = Thelathini na moja

Months
January = Januari February = Februari March = Machi April = Aprili May = Mei June = Juni July = Julai August = Agosti September = Septemba October = Oktoba November = Novemba December = Desemba

Days of the Week
Monday = Jumatatu Tuesday = Jumanne Wednesday = Jumatano Thursday = Alhamisi Friday = Ijumaa Saturday = Jumamosi Sunday = Jumapili

Additional Vocab
Mwaka = Year (cl. 3/4) Mwezi = Month (cl. 3/4)

title: Swahili I/Dates


text:
Talk:Psycholinguistics/Development of Speech Production

Peer Review
Overall, the chapter is in very good condition, presenting relevant purpose of the topic with critically analyzed information. However, there are certain aspects that must be considered. I will be writing my thoughts on this discussion page starting from the first section of the chapter and will make my way through each section by giving feedback on certain parts that can be better developed.

The introduction states its purpose strongly by posing related questions about the topic and by explaining how these questions will be answered later on in the chapter. By doing so, it is grabbing the reader’s attention and giving a clear hypothesis. There are several grammar mistakes however that should be fixed and there are also problems with some of the sentence structures. When asking a question, for example, instead of saying "What affects a child's first words such that 'doggie' usually comes before 'hand'", the author can say "What influences the words a child will use first such as 'doggie' which is usually learned before 'hand'?". In prelinguistic speech production section, the word ‘vocalization’ in the first sentence is used twice, causing repetition. Choice of another word can make the sentence sound much better. It is important to remember that once a sentence starts with a past tense it should continue in that same tense, so it will flow better and be consistent. For example in "many researchers have documented this development and suggest growth...", ‘suggest’ should be rewritten as ‘suggested’ so that the sentence will not interfere with the reading flow.

In the 1st, 2nd, 3rd, 4th and 5th stages, certain sentences are confusing and the order of these sentences can be changed so they make more sense. For example, ‘Stage 2’ is lacking punctuation marks such as commas. The sentence as follows, "Furthermore, infants reduce their crying and laughing or giggling occurs" can be changed to "At this stage, infants reduce their crying, laughing, and giggling occurs". In this case, the reader is having trouble interpret the content of the essay, hoping that this is what the author is trying to say, which means then there is a problem with the organization of that sentence. Another example, in section "Stage 3", the sentence starting with "they show a desire to explore and develop new sounds, and many of their vocalizations are vowel-like", can be reversed and say instead "Many of their vocalizations are vowel-like, and they show a desire to explore and develop new sounds". Since next sentence start with "These sounds..”, it now flows much better. In section "Stage 4" there is a lot of new terms introduced however, they are all missing the essential quotation marks that come with them. The "reduplicated babbles" and the "veriegated babbles" for example both need quotation marks. Lastly, in the "5th stage" section, a researcher called "Papaelion" is mentioned but is not cited, so it is compulsory to include references to each new researchers and studies.

In Phonological Development’ section, one of the sentences mention "theories about patterns and rules children and infants use, while developing their language" however; the paragraph does not continue to define these theories. By doing so, it leaves a question mark on the reader as they are expecting to learn and get more feedback about these theories. In ‘Patterns of Speech’ section, the author is using relevant authoritative sources and giving great examples which make it easier for the reader to understand the section. There are again, however, certain structural problems causing confusion in some sentences. In the first sentence for example, "Infants will develop their speech production slightly differently, depending on their personalities and personal development" does not sound proper and therefore, should be changed to "...slightly different from one another, depending on their personality and their personal development".

The ‘Factors affecting Development of Phonology’, the body part of the chapter, is well backed up with powerful evidence. The research here for example shows how social feedback facilitates an infant’s rapid phonological learning. The ‘Words and Referents’ section of the chapter also have very strong sources reflecting contrasting viewpoints of different research done on the same subtopic, showing a critical analysis of all the given information. The body part of the chapter contains the major expected elements and describes them in detail.

There are mainly grammar errors on the ‘First Words’, ‘Vocabulary Spurt’, ‘over/ underextension’, and ‘Learning and Making New Words’ section that the author should pay attention to again. The author in these sections used a variety of different sources making the point for each section. In the ‘over/underextension’ section however, the sources need to be stated more clearly so that the reader knows exactly which study is related to which researcher. The ideas are original and the author is without a doubt delivering the thesis statement. The logical flow, meaning the effective use of transition statements and linking them, can be better developed. The transitions between sentences and paragraphs have to be clear, but the overall discussion of the researcher’s findings is well supported, which keeps the reader’s interest on the chapter. (76.11.66.75 03:25, 28 February 2011 (UTC))