text: Simplifying (or reducing) fractions means to make the fraction as simple as possible. Simplifying the variable expression calculator, free printable worksheets for ordered pairs on a plot, integers multiply and divide games and questions, mcdougal littell algrebra 2 answers. Simplifying Complex Fractions: Algebra: Common Logs: Operations on Signed Numbers: Multiplying Fractions in General: Dividing Polynomials: Polynomials: Higher Degrees and Variable Exponents: … Expand the numerator, and leave the denominator as 50!. Apply the division rule of fractions by multiplying the numerator by the reciprocal or inverse of the denominator. A thorough review of fractions, equivalent fractions, and how to add, multiply and divide fractions is needed in order to understand the examples below. x not equal to –3" part.) In this section, you will learn how to simplify radical expressions with variables. $simplify\:\frac {x^2+14x+49} {49-x^2}$. 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# User talk:Bdamokos

## Welcome to Meta!

Hello Bdamokos, and welcome to the Wikimedia Meta-Wiki! This website is for coordinating and discussing all Wikimedia projects. You may find it useful to read our policy page. If you are interested in doing translations, visit Meta:Babylon. You can also leave a note on Meta:Babel (please read the instructions at the top of the page before posting there). If you would like, feel free to ask me questions on my talk page. Happy editing!

Bonjour Bdamokos, et bienvenue sur le Meta-Wiki de Wikimédia ! Ce site a pour but de coordonner et discuter de l’ensemble des projets Wikimédia. Il vous sera utile de consulter notre page sur les règles de Wikimédia. Si vous êtes intéressé par des projets de traduction, visitez Meta:Babylon. Vous pouvez aussi laisser un message sur Meta:Babel (mais veuillez d’abord lire les instructions en haut de cette page avant d’y poster votre message). Si vous le voulez, vous pouvez me poser vos questions sur ma page de discussion. À bientôt !

Olá Bdamokos! Seja bem-vindo ao Meta! Este site/sítio é dedicado à discussão e à coordenação de todos os demais projetos da Fundação Wikimedia. Talvez lhe seja útil ler a página contendo a nossa política (em inglês) antes de começar a editar. Se tiver dúvidas, sinta-se à vontade para me fazer perguntas em minha página de discussão, ou deixe uma mensagem para toda a comunidade na Babel, a versão do Meta da Esplanada. Boa sorte!

Hola Bdamokos! Bienvenido a la Meta-Wiki de la Fundación Wikimedia! Este sitio es para coordinar y discutir todos los proyectos de la Fundación Wikimedia. Tal vez le sea útil leer nuestra página de políticas (en inglés). Si le interesan las traducciones, visite Meta:Babylon. También puede dejar un mensaje en Meta:Babel (pero antes de hacerlo, por favor lea las instrucciones situadas en lo alto de la página). No dude en preguntar si tiene cualquiera duda, o pregunte en mi página de discusión. Buena suerte!

Ciao Bdamokos! Benvenuto sulla Meta-Wiki della Wikimedia Foundation! Questo sito serve a coordinare e discutere di tutti i progetti della Wikimedia Foundation. Potrebbe esserti utile leggere le nostre policy (in inglese). Se sei interessato a fare traduzioni, visita Meta:Babylon. Puoi anche lasciare un messaggio su Meta:Babel (ma per favore, leggi le istruzioni che si trovano all'inizio della pagina prima di scrivere). Se vuoi, puoi lasciarmi un messagio nella mia pagina di discussione. Buona fortuna!

Здравствуйте, Bdamokos, и добро пожаловать на Meta-Wiki Фонда Викимедиа! Этот сайт предназначен для координации и обсуждения вопросов, связанных со всеми проектами фонда. Для начала Вы можете ознакомиться с нашими правилами. Если Вы заинтересованы в работе над переводами, посетите Meta:Babylon. Вы также можете обсудить различные вопросы на странице Meta:Babel (пожалуйста, ознакомьтесь с инструкцией сверху, прежде чем писать). Если возникнут вопросы, не бойтесь задавать их мне на моей странице обсуждения. Удачи!

Hola {{PAGENAME}}! Benvingut a la Meta-Wiki de la Fundació Wikimedia! Aquest lloc està fet per a coordinar i discutir tots els projectes de la Fundació Wikimedia. Potser us serà útil llegir la nostra pàgina de polítiques (en anglès). Si us interessen les traduccions, visiteu Meta:Babylon. També podeu deixar un missatge a Meta:Babel (però abans de fer-ho, llegiu les instruccions situades al principi de la pàgina). No dubteu en preguntar si teniu qualsevol dubte. Si cal ho podeu fer en la meva pàgina de discussió. Bona sort!

Bdamokos, 你好！歡迎光臨維基媒體元維基！這個網站是為協調和討論所有維基媒體項目而設。我們的政策頁可能對您有用。如果您有興趣協助翻譯工作, 請參觀Meta:Babylon。你可在 Meta:Babel 留下口訊 (張貼之前請先讀該頁上指示)。若有問題, 請在我的討論頁問我 。祝

வணக்கம் Bdamokos, விக்கிமீடியா மேல்விக்கி! இற்கு நல்வரவு. இவ்விணையத்தளமானது கூட்டாகச் சேர்ந்து விடயங்களை விவாதிப்பதற்கென உருவாக்கப் பட்டது. விக்கித்திட்டங்கள். நீங்கள் எங்களின் பாலிசிகளையும் பாலிசி பக்கம் படித்தறியலாம். நீங்கள் மொழிபெயர்பில் ஆர்வமுடையவராகின், Meta:Babylon ஐப் பார்வையிடவும். நீங்கள் Meta:Babel இல் குறிப்பொன்றையும் விட்டுச் செல்லலாம். (பக்கத்தின் மேலேயிருக்கும் அறிவுறுத்தல்களை வாசித்தபின்னரே அங்கே செய்திகளை இடவும்). நீங்கள் விரும்பினால் எனது பக்கத்தில் செய்தியொன்றை விடவும் talk page. உங்கள் ஆக்கங்களை வரவேற்கின்றோம்!

--Aphaia 15:38, 17 December 2006 (UTC)

## File name

Hi Bdamokos, thank you for your translation. Would you let me make a silly question, if you are too much bothered with that; what means "add a" in Hungarian? I found it in the Hungarian title you have remaned, and now I'm curious about that because it sounds alike English, but those two lanuages have no similarity linguistically... --Aphaia 16:28, 17 December 2006 (UTC)

## Look and feel

Would you give a look to Wikimedia:Wikimedia:Fundraising translations/hu? (not published, just for check now) There is no Hungarian list of project as footer, as interim remedy, I put an English one instead. You are also invited to create a new one at Template:OurProjects2006. --Aphaia 18:05, 17 December 2006 (UTC)

## Foundation wiki

Bdamokos, would you join the editors' team there? Then give me/us your address and preferred account (same here?), if not, please forget. --Aphaia 21:23, 17 December 2006 (UTC)

## Visszavonás

Ezt a szerkesztésemet (pontosabban az ez előtti kettőt) direkt vontad vissza, vagy csak szerkesztési ütközés miatt véletlenül? Samat 00:46, 11 January 2009 (UTC)

## Thank you for translating

Hi Bence. I see that you are not only translating at translatewiki.net, but also here. I want to thank you for that. Cheers! Siebrand 12:42, 30 October 2009 (UTC)

Szia! Szerintem a javított mondat szebb lenne, ha úgy fogalmaznánk meg, ahogy tavaly volt, azaz „számíthatsz rá”, nem pedig „ott van”. Ehhez persze ragozni kell, de azt hiszem, ez a része működött az üzenetnek. Samat 23:13, 12 December 2009 (UTC)

## wmhu interwiki

Hi, Bence, the wmhu: interwiki prefix has just been activated on all Wikimedia projects. I hope you'll find it useful. --Nemo 14:50, 13 November 2010 (UTC)

Hi Nemo. Thanks for doing this, I don't think that many people link to our wiki, but anyway :). A minor note: just recently we have changed our domain from wiki.media.hu to wikimedia.hu (without a dot in the middle), the interwiki prefix still points to the old address. --Dami 20:54, 13 November 2010 (UTC)

## Translation Update

I want to thank you for your help translating throughout this year's fundraiser. The fundraiser has greatly benefited from all your contributions. Currently, the Kartika, Liliaroja, Abbas and Joan Gomà appeals need to be translated, as we are running appeals from editors. You can find all translation requests at the translation hub on meta and you can follow the progress of the fundraiser in real time by tracking the fundraiser statistics. It is important to check the Core Messages as many languages still need updating. Also if you haven't already, you can subscribe to the translators-l mailing list for all new requests and major changes. Many thanks for your help in truly making this a global fundraiser that you can edit.Klyman 19:33, 7 December 2010 (UTC)

## Wikimedia Conference

Hi Bence

I see the chapters meeting is no longer called Chapters meeting but Wikimedia Conference. I wonder if this means it is a bit more open to proposed chapters than in previous years. It happens that movement roles are planning a meeting just before the conference and we are interested in following it. Apart of that we are facing the same problems and opportunities as chapters and we feel we need to learn from others so we are also interested in attending the whole conference in general. So I would like If you could extend to us the invitation to attend. --Gomà 17:57, 31 January 2011 (UTC)

Hi Goma,

Sorry, I thought I had replied earlier, but apparently I forgot to hit the save button...

The Wikimedia Conference has been called this way for the past three years, mainly because it combines the Chapters', Developers' and Board meetings. Unfortunately, the Chapters meeting is still only open to chapters and those chapters in formation that were very well advanced in their recognition process at the time the final invitations were sent out.

As for the movement roles meeting, we sure welcome more active participation in the discussions and the work, but I am not in charge of invitations to that meeting. Please contact Austin or Jon Huggett to see how you can help out the process.

Best regards, --Dami 12:53, 4 February 2011 (UTC)

Hi Bence, wanted to give you a heads up that we have moved our bylaw official page on to the Wiki Canada web site. You are all welcome to register accounts on the Wiki and we look forward to your participation. Here is the interwiki link wmca:Bylaws Alan.ca 05:51, 4 February 2011 (UTC)

## Thank You

Bence :) On behalf of WMF I would like to thank you for your cooperation during the last fundraiser and we look forward for more fruitful and successful fundraisers over the next years. Thanks again :)--Melamrawy (WMF) 12:27, 9 February 2011 (UTC)

## Need help in discussion for an article nominated for Afd

Hello Bdamokos,

This is regarding a post of "Janos Boros" the Ex-Vice Mayor of Kolozsvar. You might not remember me, I am Kiran, an Indian by Szarmazas. My Magyar is a bit rusty, so I have to write in English. In 2009 there was nominated under Afd by some Romanian users. It was finally decided as "keep". It seems some RO Users have decided to nominate it again. I got the decision reviewed and the Admin was gracious enough to open it for discussion again. If you have the time, please do participate.

Warm regards Hangakiran 11:25, 23 March 2011 (UTC)

## Translator, We need you!

Dear Bdamokos,

You have helped us in previous years with translations and for that we are most grateful. Now we turn towards the 2011/12 fundraiser. It may seem forever away, but work has already begun getting everything ready to go. This year we want to have landing pages covering as many countries in as many languages as possible.

Right now, we want to figure out who is interested in translating for the fundraiser. This year we're hoping to have more of a solidified "core" group of translators that we can count on to have work done by a few key dates, but we'd also welcome help from people who are willing to just help out when they can.

If you would be interested please take a look at this little sign-up survey and fill it out http://survey.wikimedia.org/index.php?sid=13638&newtest=Y&lang=en. With that we can start building a list of people and filling any gaps in the languages we serve.

Many Thanks

Joseph Seddon (User:Jseddon (WMF))

Production Coordinator
Wikimedia Foundation
Jseddon (WMF) 01:00, 9 July 2011 (UTC)

Bence,

Thanks for this link. Dedalus 14:06, 29 August 2011 (UTC)

Your welcome, I put in a very short summary in English in our June report (http://meta.wikimedia.org/wiki/Wikimedia_chapters/Reports/Wikim%C3%A9dia_Magyarorsz%C3%A1g/June_2011); let me know if your have any questions in connection with the report. (I know that Google Translate is doing an awful job with Hungarian.) --Dami 14:10, 29 August 2011 (UTC)

## CentralNotice

Hi Bence, according to CentralNotice/Calendar the hu.wikipedia thank you notice was only intended for that project. Adding English as a language makes it show on en.wikipedia as well, which doesn't seem wise and would need more discussion. I removed en for now, we can discuss further there if you want. (Note that hu.wikipedia users with their UI language set to English will see the translation, that only depends adding the translation to the banner). Pcoombe (WMF) 12:57, 10 September 2011 (UTC)

Ok, that is fine with me. Thanks for catching that! --Dami 12:58, 10 September 2011 (UTC)

## Wikimedia Venezuela

Hello,

I am writing to ask you a question regarding the status of our still pending request of Wikimedia Venezuela to become a local Wikimedia Chapter. We have started gathering people and ideas since October 2010, organised a series of lectures for Wikipedia TEN. Our proposed bylaws have been reviewed by members of the ChapCom as early as May 2011. We were informed that in June-July 2011, our proposal was scheduled to be submitted to voting and, as of October 2, 2011, we are yet to receive a notification, either approval, rejection, suggestions...we have received only silence. What is going on? What has delayed the ChapCom to close the voting on our case? Working groups in other countries have submitted their proposals/requests to form a local WikimediaChapter more or less at the same time that we did, and they have been approved already. Why not Wikimedia Venezuela? What is wrong with us? If we were told what is wrong with us, we could work it out and fix whatever is needed...but with no input, we are left sitting in the waiting room for months..

Could you please tell us what is delaying our approval? What do we have to do?

Our people (37) is anxious and wondering what is going on. We were more people, but we feel dissapointed and discouraged, and this doesn't help us at all. Could you please give us an update?

Many, many thanks in advance from Venezuela.

--Jewbask 01:32, 3 October 2011 (UTC)

## Hungarian translation

I am working on this, Fundraising_2011/FAQ/hu and let me know the deadline / other-more importances. --Aranymalinko 13:00, 26 October 2011 (UTC)

## Wikimedia Kazakhstan

Hello Bdamokos, I am writing this message to get any update relating our application to be recognize as Wikimedia chapter. Is there any news? we have answered to all questions over month ago. Could you please give an update to us regarding this point? If we need any further action please contact me. Kind regards, --Ashina 05:44, 10 November 2011 (UTC)

Hi Ashina,

Thank you for the reminder, I will look into this and get back to you soon.

Sorry for the delay, --Dami 10:57, 10 November 2011 (UTC)

## email sent

Thank you for your prompt reply to my message! I sent an email to the chapcom email address.Thelmadatter 00:52, 10 January 2012 (UTC)

## Finance Meeting

Hey Bence, a more complete form is coming in the coming days :) Schiste 13:12, 22 January 2012 (UTC)

## A barnstar for you!

Hi! I just want to thank you and give you this barnstar for your help with the translation of the 2011 fundraiser! The fundraiser was the best we ever had, both in terms of the amount we collected and in terms of number of translations. We couldn't have done either one without the help we got from you and other translators. If you are interested, we made a report, which has some statistics about the translations.

And: I have one more request, and that is that you take this survey. You may have got an e-mail about it, and if you did, please ignore this. But if you didn't it would be great if you would take this survey too, so we can learn to improve the translation experience.

Again, thanks for your help with translations – you're awesome! Jon Harald Søby (WMF) 13:26, 24 January 2012 (UTC)

## Question for you

Hello, Bdamokos. You have new messages at Talk:Fundraising and Funds Dissemination/Recommendations.
You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

Hi. :) While I've not summarized the section in which you responded on the 27th quite yet, I have made a start at making sure I understand your position. That's always an important step in summarizing. :D If you have a chance, can you please stop by and let me know if I've got it right? Currently it's the last note in this section. --Maggie Dennis (WMF) 16:10, 30 January 2012 (UTC)

## Need help to finish translation of Template:Main Page/hu

Dear colleague! Please help us for transfer Magyar Main Page (Kezdőlap) to new unified design! Translation of Template:Main Page/hu was started by User:Tgr, but he does not have enough time to complete this work. Maybe you do finish this work? It would be perfect!

Just click to "edit-link" in every section and translate all values after "=". After complete translation need replace text in Kezdőlap to transcluding of {{Main Page/hu}} (as in Russian). Thanks in advance ;) --Kaganer (talk) 17:12, 3 April 2012 (UTC)

Maybe you now have time for this small task? --Kaganer (talk) 13:54, 2 September 2012 (UTC)
Hi Kaganer! Sorry, I know, I am terrible, but I don't think I have time for this :(. --Bence (talk) 11:20, 30 September 2012 (UTC)

## WMHU/TOU balance note

Hey Bence,

Just a note to let you know I adjusted the WMHU campaign (as well as the TOU campaign) to balance it out to the % that Philippe told me you guys had agreed upon (It was at 60% ToU and 40% WM-HU but is now reversed at 60% WM-HU and 40% ToU ). If you adjust your campaign or add/remove banners (before May 25th, it probably doesn't matter after that) could you drop me a line either on my talk page or by email? That'll let me know to go in and make sure the %s stay the same.

Thanks! Jalexander (talk) 03:28, 7 May 2012 (UTC)

Thank you, James. --Bence (talk) 08:54, 7 May 2012 (UTC)

## Liability for harm caused by incorrect medical information

Hi Bence

In this thread, veteran editor and former en.WP arbitrator en:User:Iridescent says:

If the WMF gets the balance wrong on coverage of Gibraltar, the worst that happens is complaints that Wikipedia is painting too rosy a picture of one side in a long-running territorial dispute; if the WMF gets the balance wrong on medicine, people die. (No, I don't think that's too apocalyptic. People believe Wikipedia more than they should; all it takes is one person to believe it when they read that watercress cures cancer—I can even provide a source for that one—and you're on very shaky legal ground, if someone manages to persuade a judge that the Medical Project is a de facto governing body and thus liable for the content of the medical articles.)

Could you possibly ask the foundation's legal team whether they can see Wikimedia Medicine heightening the foundation's liability for any harm caused by incorrect medical information on Wikimedia projects? If you have access to legal advice regarding Wikimedia Medicine's liability in that regard, it would be very welcome at this point, too. --Anthonyhcole (talk) 01:14, 30 September 2012 (UTC)

Hi Anthonyhcole,
These are interesting questions. I will see if the legal team at the WMF has anything to add, at least informally, but they cannot advise the community (and it is not entirely settled whether they can advise Affcom), so you will likely have to act on your own.
In general, chapters (and by extension WM Medicine) do not edit the content of the projects, nor do they influence editorial policy (at most, they might raise awareness over issues, and provide a venue for the community to have a debate) and they are legally independent from the WMF, to ensure that they are not liable for anything the WMF does or vica-versa. This fact is usually communicated quite often (see e.g. [1]), but it doesn't necessarily stop people from suing chapters (and while the cases are usually thrown out, it still costs money and time).
So even if the WMF cannot provide you with legal advice, this is an issue that has to be clear and discussed by you, to make sure you do not end up acting in a way that might be legally unwise.
(P.S. I am not a lawyer, so in all things legal, you should make sure to get proper advice.) --Bence (talk) 11:38, 30 September 2012 (UTC)
Bence has summed up the issue nicely. Doc James (talk · contribs · email) 17:03, 4 October 2012 (UTC)

## Imminent incorporation of Wikimedia Medicine

We are about to apply for incorporation. If you or any other AffCom members have any comments on the proposed bylaws, they would be very welcome at Talk:Wikimedia Medicine/Bylaws. --Anthonyhcole (talk) 05:48, 10 October 2012 (UTC)

Thanks Anthony for keeping me up to date, it is appreciated. As I said in my e-mail, the review will have to wait a bit, until there are a few more participants and some of the open questions on membership, structure, goals get fleshed out in a bit more detail. I don't expect that the bylaw review would require any big changes as a pre-condition for recognition, but given the time it takes to change the bylaws of an incorporated entity, pre-mature incorporation will certainly cause delays of possibly months in the time it takes to recognize WM Medicine. Best regards, --Bence (talk) 14:04, 14 October 2012 (UTC)

## re: Narrowing focus

I don't want to distract from the core of your comments by replying there, but in regards to "(it seems the editor experiments programme is currently costing more than the perhaps #1 visual editor..." That is very much untrue. With seven engineers, the VisualEditor, which includes work on the parser (aka Parsoid) under its umbrella, has the most resources of any single engineering project at the Foundation. Editor engagement experiments currently has only two engineers, and a total of seven people working on entire the team (and many non-technical staff currently split their time between it and other projects, like Dario, Maryana, etc.). Steven Walling (WMF) • talk 20:33, 15 October 2012 (UTC)

Ok, thanks for the clarification. (For the record, I simply compared the $.7k for VE I saw in the annual plan and the ~$1M requested in the FDC for the E3). --Bence (talk) 20:41, 15 October 2012 (UTC)
On a related note: [2] Steven Walling (WMF) • talk 22:30, 16 October 2012 (UTC)

## Wikivoyage

Hi Bence.

Sorry. I use your talk page because I dont have your email address with me. I am on the road. Just working with the WMF to migrate our Wikivoyage. Will be back home next week. Thanks for your comments and questions on our associations talk page. I am going to work through it. -- DerFussi 01:55, 24 October 2012 (UTC)

Thanks Stefan, have a safe trip! --Bence (talk) 12:44, 29 October 2012 (UTC)

## Re:Affiliations Committee is looking for members

Thanks! I have just sent you guys an e-mail :-) --Maor X (talk) 16:05, 12 December 2012 (UTC)

## Re: Affiliations Committee is looking for members

Hi Bence, thanks for the reminder. I believe Latinamerica is well represented in the AffCom (and actually, one of the members in the AffCom is from my local chapter). For that reason I'll pospone my application this time. Maybe in the future :-)

Cheers, Mahadeva (talk) 16:18, 13 December 2012 (UTC)

## Nudge

Hi Bence, I thought you might have useful perspective on this: Talk:Special Interest Groups -Pete F (talk) 20:26, 28 January 2013 (UTC)

## Membership criteria for WikiProject Med

Hi Bence. Any thoughts you or other committee members may have on the above would be very welcome at Talk:WikiProject Med#Membership fees (continued). --Anthonyhcole (talk) 07:03, 27 February 2013 (UTC)

Thanks, I've alerted AffCom and will take a look myself over the weekend. Thanks for the notice. –Bence (talk) 22:15, 28 February 2013 (UTC)
Cheers. Will you be attending the Milan conference? --Anthonyhcole (talk) 17:15, 1 March 2013 (UTC)
We are still debating internally who should go, but there will definitely be people from AffCom - there is a chance I will be one of them. Is anyone going from WikiPMEd? --Bence (talk) 17:24, 1 March 2013 (UTC)
Ocaasi and Daniel. I think the three of you meeting up, if you haven't yet, would be a really good thing, so I hope you do get to attend. :) --Anthonyhcole (talk) 14:39, 2 March 2013 (UTC)
Now it is confirmed, I will be going. I am really looking forward to meeting Ocassi and Daniel in person. Best, --Bence (talk) 21:22, 7 March 2013 (UTC)
Excellent. --Anthonyhcole (talk) 03:13, 8 March 2013 (UTC)

Ocaasi has had to withdraw because of schedule conflicts and has been replaced by Biosthmors, a very active medical editor/education outreach-er, who is also very active off-wiki in medical information dissemination. --Anthonyhcole (talk) 03:07, 14 March 2013 (UTC)

## Thank you

Thanks for your improvements / corrections to the Submit request template. Best, Winifred Olliff (Grants Administrator) talk 22:37, 21 March 2013 (UTC)

## Talk:Affiliations Committee/Resolutions/Budget request for 2013 annual meeting – April 2013

Just making sure that you notice the questions asked. odder (talk) 17:28, 6 May 2013 (UTC)

## Eyes, thoughts?

Hi Bence. We're close to finalising our membership criteria. Any thoughts you - or other AffCom members - may have would be appreciated. Talk:Wiki_Project_Med#Summing_up --Anthonyhcole (talk) 20:58, 10 May 2013 (UTC)

Thank you for the note – I've alerted AffCom to see if they have anything to add and will comment soon myself. Thanks again, –Bence (talk) 14:12, 11 May 2013 (UTC)
Thanks Bence. Don't feel obliged to comment, unless you want to. I'd just prefer that you noticed this, in case we start making some error you've seen before. --Anthonyhcole (talk) 11:24, 12 May 2013 (UTC)

Thanks for your insight there. The COI policy discussion is active now at Talk:Wiki Project Med Foundation/Conflicts of Interest. I've asked a question about whether the WMF expects us to seek funding outside the WMF. I vaguely remember having read that somewhere, do you know the answer? --Anthonyhcole (talk) 06:59, 23 May 2013 (UTC)

format: plain


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# check my work w/ this word problem

• Dec 16th 2009, 02:57 PM
extraordinarymachine
check my work w/ this word problem
ok so i'm not sure if my answers are right

An open box is to be formed by cutting four identical squares from the coners of a sheet of metal 20cm by 20cm, and folding up the metal to form sides. the capasity of the box must be $588cm^3$. what is the side length of the squares?

this is what i got

let x be the length of the missing sides

x(20-2x)(20-2x)=588
$4x^3-80x^2+400x-588=0$
$4(x^3-20x^2+100x-147)=0$

where is got a factor of (x-3)

and was left with $x^2-17x+49$

wich gave me x=15.44 or x=1.55

so the length can be 3cm, 15.44cm, or 1.55cm?
• Dec 16th 2009, 03:40 PM
skeeter
Quote:

Originally Posted by extraordinarymachine
ok so i'm not sure if my answers are right

An open box is to be formed by cutting four identical squares from the coners of a sheet of metal 20cm by 20cm, and folding up the metal to form sides. the capasity of the box must be $588cm^3$. what is the side length of the squares?

this is what i got

let x be the length of the missing sides

x(20-2x)(20-2x)=588
$4x^3-80x^2+400x-588=0$
$4(x^3-20x^2+100x-147)=0$

where is got a factor of (x-3)

and was left with $x^2-17x+49$

wich gave me x=15.44 or x=1.55

so the length can be 3cm, 15.44cm, or 1.55cm?

$x = 3$

$x^2-17x+49 = 0$

$x = \frac{17 \pm \sqrt{93}}{2}$

$x= 13.322$

$x = 3.678$

is it physically possible for $x = 13.322$ ???


text:
# If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then $x^{2000}+\frac{1}{x^{2000}}=$?

If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then

$$x^{2000}+\frac{1}{x^{2000}}=?$$

My try:

$$\left(x^{1000}\right)^2+\left(\frac{1}{x^{1000}}\right)^2=\left(x^{1000}+\frac{1}{x^{1000}}\right)^2-2$$

Continuation ?

• You have marked this algebra-precalculus. Your original equation $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ has no solutions in real numbers. So is there a tpyo or are you allowed complex numbers. – Anurag A Dec 1 '16 at 18:41
• $\frac{1+\sqrt{5}}{2} = 2\cos\frac{\pi}{5}$. – achille hui Dec 1 '16 at 22:11
• Why wouldnt we be allowed complex numbers? And the fact that x is complex doesn't effect solving the post. – fleablood Dec 1 '16 at 22:48

Note that $a = \frac{1+\sqrt{5}}{2}$ satisfies the equation $a^2 - a - 1 = 0$

Substituting $a=x+\frac{1}{x}$ gives:

$$0 = \left(x+\frac{1}{x}\right)^2 - \left(x+\frac{1}{x}\right) - 1 = x^2 - x + 1 - \frac{1}{x} + \frac{1}{x^2}$$

$$\iff \quad x^4 - x^3 + x^2 - x + 1 = 0$$

Multiplying by $x+1$ results in $x^5+1=0$, so $x$ is a complex $5^{th}$ root of $-1$ therefore $x^5 = -1$.

Then $x^{2000}+\frac{1}{x^{2000}} = \big(x^{5}\big)^{400} + \cfrac{1}{\big(x^{5}\big)^{400}} = (-1)^{400} + \cfrac{1}{(-1)^{400}} = 1 + 1 = 2$.

P.S. For a heavy-handed "solution" to the tune of "how to crack a nut with a sledgehammer", let Wolfram Alpha do all the work:

resultant[resultant[x^2 - a x + 1, a^2 - a - 1, a ], x^4000 - b x^2000 + 1, x] = (b-2)^4

• Niice. But, should be $x^5$ and not $x^{-5}$. – Physicist137 Dec 2 '16 at 17:29
• @Physicist137 Thanks for catching that. Edited and fixed. – dxiv Dec 2 '16 at 17:41

If $a_n=x^n+\frac{1}{x^n}$ then $a_n=a_1\cdot a_{n-1}+a_{n-2}=\phi\cdot a_{n-1}-a_{n-2}$ which is a second-order linear recurrence, where $\phi=\frac{1+\sqrt 5}{2}$. The initial conditions are $a_1=\phi$ and $a_2=a_1^2-2=\phi^2-2=\phi-1$, since $\phi^2=\phi+1$

• Helps to note that the $a_n$ are periodic ($a_6=-a_1$ and $a_{11}=a_1$). – lulu Dec 1 '16 at 18:51
• Yes, depending on how much an elementary solution OP wants, it would work just to use the recurrence and calculate $a_1, a_2, ...$ while using $\phi^2=\phi+1$ – Momo Dec 1 '16 at 18:57

Edit: Found another solution, removed old answer (it was incorrect anyway)

You have $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$. By simple algebraic manipulation you can get the $$x^4-x^3+x^2-x+1 = 0$$ Now notice that $x^4 = x^3-x^2+x-1$ and multiplying both sides by $x$ you get $x^5 = x^4-x^3+x^2-x=-1$.

Therefore $$x^{2000}+\frac{1}{x^{2000}} = ({x^{5}})^{400}+\frac{1}{(x^{5})^{400}} = (-1)^{400}++\frac{1}{(-1)^{400}} = 1+1 = 2$$

Here's another approach for the record.

1. The equation $x+ \frac{1}{x}=\alpha$ where $\alpha \in [-2,2]$ can be solved as follows. Identify $\alpha$ is $2\cos (\theta)$, and observe that letting $z=e^{i\theta}$,from the definition of $\cos (\theta)$, we have $$z+ \frac{1}{z}=2\cos(\theta)=\alpha.$$

2. Also, from the definition of $\cos$,

$$z^k + \frac{1}{z^k} = 2\cos (k \theta).$$

1. Now back to our question. Let $\alpha = \frac{1+\sqrt{5}}{2}$. Then $\cos(\theta) = \frac{1+\sqrt{5}}{4}$. This gives us $\theta = \pm \frac{\pi}{5} \mod 2\pi$. Therefore the answer to the problem is $2\cos (400\pi)=2$.
• That was a wonderful argument. – infinitylord Dec 2 '16 at 18:01

Let $\psi = \frac{1+\sqrt{5}}{2}$ $$x + \frac{1}{x} = \psi$$ $$x^2 + 1 = \psi x$$ $$x^2 - \psi x + 1 = 0$$ Use quadratic formula here to solve for $x$. Then plug that into the given expression.

• Superior answer – Decaf-Math Dec 1 '16 at 18:34
• $x + \frac{1}{x} = \psi$ has no real solutions. – Anurag A Dec 1 '16 at 18:41
• @AnuragA Go for complex..? – Frank Dec 1 '16 at 18:53
• That might be very dificult to simplify. $(a+b\sqrt{c})^{2000} + \frac 1{(a+b\sqrt{c})^{2000}}$ might not be an acceptable answer. (Then again maybe it will work out nice.) – fleablood Dec 1 '16 at 23:00

Nice try of yours. You can further continue...: $$x^{2000} + \frac{1}{x^{2000}} = \left(x^{1000} + \frac{1}{x^{1000}}\right)^2 - 2 \\ x^{1000} + \frac{1}{x^{1000}} = \left(x^{500} + \frac{1}{x^{500}}\right)^2 - 2 \\ x^{500} + \frac{1}{x^{500}} = \left(x^{250} + \frac{1}{x^{250}}\right)^2 - 2 \\ \vdots \\ x^{n} + \frac{1}{x^n} = \left(x^{n/2} + \frac{1}{x^{n/2}}\right)^2 - 2 \\$$

In the case of $2000 = 2^4 \cdot 5^3$. That is, when you are done with all the $2$s, you will be left with $5$: $$x^{125} + \frac{1}{x^{125}} = \left[\left(x^{25}\right)^5 + \left(\frac{1}{x^{25}}\right)^5\right] =$$

We do basically the same you did: $$(a+b)^5 = {{5}\choose{0}}a^5 + {{5}\choose{1}}a^4 b + \cdots \\ (a+a^{-1})^5 = {{5}\choose{0}}a^5 + {{5}\choose{5}}b^{-5} + \cdots \\$$

Notice the intermediate terms: $${{5}\choose{1}}a^{4} a^{-1} + {{5}\choose{2}}a^{3} a^{-2} + {{5}\choose{3}}a^{2} a^{-3} + {{5}\choose{4}}a^{1} a^{-4} = {{5}\choose{1}}a^{3} + {{5}\choose{2}}a + {{5}\choose{3}}a^{-1} + {{5}\choose{4}}a^{-3}$$

That is: $$\left[x^{5} + \frac{1}{x^{5}}\right]^5 = \left[x^{5} + \frac{1}{x^{5}}\right] + 10\left[\left(x^{5}\right)^3 + \left(\frac{1}{x^{5}}\right)^3\right] + 5\left[\left(x^{5}\right)^5 + \left(\frac{1}{x^{5}}\right)^5\right]$$

You can keep doing so and simplifying to smaller and smaller terms. You can do this because: $${{n}\choose{k}} = {{n}\choose{n-k}} = \frac{n!}{k!(n-k)!}$$

That is, $(a + a^{-1})^n$ will have the terms $a^{-k} a^{n-k}$ and $a^k a^{-(n-k)}$ with the same coeficients. And this term forms: $$a^k a^{-n+k} = a^{k-n+k} = a^{2k-n} \\ a^{-k} a^{n-k} = a^{-k+n-k} = a^{-2k+n} = a^{-(2k-n)}$$

So, the coeficients opposite terms will be equal, then you will always be able to build terms like $x^k + 1/x^k$. Thus you can keep doing it until you are left only with the $x + 1/x$. It might take a while..... =D.

• @egreg Oh. Thanks. I'll fix. – Physicist137 Dec 2 '16 at 0:54

Just giving another way. $$x+\frac 1x=\frac{1+\sqrt2}{2}\\ x^2+\frac{1}{x^2}=\frac{-1+\sqrt5}{2}\\ x^4+\frac{1}{x^4}=-\frac{1+\sqrt5}{2}\\ x^8+\frac{1}{x^8}=\frac{-1+\sqrt5}{2}$$ Hence $$\left(x^8+\frac{1}{x^8}\right)\left(x^2+\frac{1}{x^2}\right)=\left(\frac{-1+\sqrt5}{2}\right)^2\\ x^{10}+\frac{1}{x^{10}}=\left(\frac{-1+\sqrt5}{2}\right)^2-\left(-\frac{1+\sqrt5}{2}\right)=2\iff(x^{10}-1)^2=0$$ Thus $x^{10}=1$ from which the result $2$.

• Top equation: Replace 2 with 5 – Improve Dec 2 '16 at 1:58


text:
# zbMATH — the first resource for mathematics

On the average number of real roots of a random algebraic equation. (English) Zbl 0609.60074
Let $$f(x)=a_ 0+a_ 1x+...+a_ nx^ n$$ be a random algebraic polynomial with independent random coefficients where $$a_ i\in N(0,1)$$, $$i=0,1,2,...,n$$. In this paper, the author estimates the average number of real roots of the equation $$f(x)=k$$, for the following cases:
(i) If $$k^ 2/n$$ tends to zero as n tends to infinity then EN(-1,1)$$\sim (1/\pi)\log (n/k^ 2)$$ and $$EN(-\infty,-1)=EN(1,\infty)\sim (2\pi)^{- 1}\log n.$$
(ii) If $$k^ 2/n$$ tends to a nonzero positive constant then EN(- $$\infty,\infty)\sim (1/\pi)\log n.$$
This problem can also be reformulated as follows: F(x)$$\equiv f(x)- k\equiv (a_ 0-k)+a_ 1x+a_ 2x^ 2+...+a_ nx^ n=0$$ where $$a_ 0-k,a_ 1,a_ 2,...,a_ n$$ are independent normal random variables with $$a_ 0-k\in N(-k,1)$$ and $$a_ i\in N(0,1)$$, $$i=1,2,...,n$$. Then the average number of real zeros of $$F(x)=0$$ is (i) and (ii).
On this line, the reviewer feels that one can study the following problem also: let g(x)$$\equiv a_ 0+a_ 1x+...+a_ nx^ n$$ where $$a_ i$$, $$i=0,1,...,n$$ are independent normal random variables and $$a_ i\in N(0,1)$$, $$i=0,1,2,...,j-1,j+1,...,n$$, $$a_ j\in N(-k,1)$$. Then what is the average number of real zeros of $$g(x)=0$$.
Reviewer: M.Sambandham

##### MSC:
 60H99 Stochastic analysis
Full Text:


text:
Spherical aberrationHTML5

QR code

Summary

You can modify the size (click and drag the flame) and the position of the object (click and drag the candle).

You can observe the spherical aberration that appears when the rays diverge from the optic axis.

Click and drag  the flame vertically to modify the size.

Click and drag  the candle horizontally to move it along the optic axis.

Learning goals

• To illustrate the spherical aberration phenomenon.


text:
# zbMATH — the first resource for mathematics

## Beale, J. Thomas

Compute Distance To:
 Author ID: beale.j-thomas Published as: Beale, J. T.; Beale, J. Thomas
 Documents Indexed: 65 Publications since 1973, including 1 Book
all top 5

#### Co-Authors

 30 single-authored 5 Hou, Thomas Yizhao 5 Lowengrub, John Samuel 5 Majda, Andrew J. 3 Layton, Anita T. 3 Ying, Wenjun 2 Greengard, Claude 2 Lifschitz, Alexander E. 2 Maida, Andrew 2 Nishida, Takaaki 2 Suters, W. Henry 2 Tlupova, Svetlana 1 Baker, Gregory R. 1 Bourgeois, Alfred J. 1 Chopp, David L. 1 Cottet, Georges-Henri 1 Eydeland, Alexander 1 Huberson, Serge G. 1 Kato, Tosio 1 Lai, Mingchih 1 LeVeque, Randall J. 1 Li, Zhilin 1 Rosencrans, Steven I. 1 Schaeffer, David G. 1 Shelley, Michael J. 1 Strain, John A. 1 Teramoto, Yoshiaki 1 Thomann, Enrique A. 1 Turkington, Bruce E. 1 Wilson, Jason R.
all top 5

#### Serials

 8 Journal of Computational Physics 7 Communications on Pure and Applied Mathematics 6 Mathematics of Computation 5 SIAM Journal on Numerical Analysis 3 Communications in Mathematical Physics 3 Communications in Computational Physics 2 Duke Mathematical Journal 2 Indiana University Mathematics Journal 2 Communications in Applied Mathematics and Computational Science 1 Archive for Rational Mechanics and Analysis 1 Journal of Differential Equations 1 Numerische Mathematik 1 Mathematical and Computer Modelling 1 Communications in Partial Differential Equations 1 SIAM Journal on Mathematical Analysis 1 SIAM Journal on Scientific Computing 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Journal of Turbulence 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the American Mathematical Society 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 RIMS Kôkyûroku Bessatsu
all top 5

#### Fields

 51 Fluid mechanics (76-XX) 34 Partial differential equations (35-XX) 27 Numerical analysis (65-XX) 4 Potential theory (31-XX) 4 Mechanics of deformable solids (74-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH Open

55 Publications have been cited 1,736 times in 1,385 Documents Cited by Year
Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Zbl 0573.76029
Beale, J. T.; Kato, T.; Majda, A.
1984
Large-time regularity of viscous surface waves. Zbl 0545.76029
Beale, J. T.
1984
The initial value problem for the Navier-Stokes equations with a free surface. Zbl 0464.76028
Beale, J. Thomas
1981
Spectral properties of an acoustic boundary condition. Zbl 0325.35060
Beale, J. Thomas
1976
Acoustic boundary conditions. Zbl 0294.35045
Beale, J. Thomas; Rosencrans, Steven I.
1974
On the accuracy of finite difference methods for elliptic problems with interfaces. Zbl 1153.35319
Beale, J. Thomas; Layton, Anita T.
2006
High order accurate vortex methods with explicit velocity kernels. Zbl 0588.76037
Beale, J. T.; Majda, A.
1985
Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S.
1993
Exact solitary water waves with capillary ripples at infinity. Zbl 0727.76019
Beale, J. Thomas
1991
Validity of the quasigeostrophic model for large-scale flow in the atmosphere and ocean. Zbl 0811.35097
Bourgeois, Alfred J.; Beale, J. Thomas
1994
Vortex methods. II: Higher order accuracy in two and three dimensions. Zbl 0488.76025
Beale, J. Thomas; Maida, Andrew
1982
Vortex methods. I: Convergence in three dimensions. Zbl 0488.76024
Beale, J. Thomas; Maida, Andrew
1982
Rates of convergence for viscous splitting of the Navier-Stokes equations. Zbl 0518.76027
Beale, J. Thomas; Majda, Andrew
1981
Scattering frequencies of resonators. Zbl 0254.35094
Beale, J. Thomas
1973
A method for computing nearly singular integrals. Zbl 0988.65025
Beale, J. Thomas; Lai, Ming-Chih
2001
The existence of solitary water waves. Zbl 0379.35055
Beale, J. Thomas
1977
Acoustic scattering from locally reacting surfaces. Zbl 0332.35053
Beale, J. Thomas
1977
Convergence of a boundary integral method for water waves. Zbl 0858.76046
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John
1996
Large-time behavior of discrete velocity Boltzmann equations. Zbl 0637.76070
Beale, J. Thomas
1986
A convergent boundary integral method for three-dimensional water waves. Zbl 0980.76053
Beale, J. Thomas
2001
Large-time behavior of viscous surface waves. Zbl 0642.76048
Beale, J. Thomas; Nishida, Takaaki
1985
A convergent 3-D vortex method with grid-free stretching. Zbl 0602.76024
Beale, J. Thomas
1986
Large-time behavior of the Broadwell model of a discrete velocity gas. Zbl 0626.76080
Beale, J. Thomas
1985
A grid-based boundary integral method for elliptic problems in three dimensions. Zbl 1159.65368
Beale, J. Thomas
2004
On the accuracy of vortex methods at large times. Zbl 0671.76024
Beale, J. Thomas
1988
Eigenfunction expansions for objects floating in an open sea. Zbl 0336.76004
Beale, J. Thomas
1977
Nearly singular integrals in 3D Stokes flow. Zbl 1373.76153
Tlupova, Svetlana; Beale, J. Thomas
2013
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces. Zbl 1146.76044
Beale, J. Thomas; Strain, John
2008
The design and numerical analysis of vortex methods. Zbl 0491.76007
Majda, A. J.; Beale, J. T.
1982
A simple method for computing singular or nearly singular integrals on closed surfaces. Zbl 1388.65167
Beale, J. Thomas; Ying, Wenjun; Wilson, Jason R.
2016
Vortex blob methods applied to interfacial motion. Zbl 1115.76380
Baker, Gregory R.; Beale, J. Thomas
2004
A fast accurate boundary integral method for potentials on closely packed cells. Zbl 1388.65170
Ying, Wenjun; Beale, J. Thomas
2013
Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050
Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J.
1994
The existence of cnoidal water waves with surface tension. Zbl 0374.76018
Beale, J. Thomas
1979
Vortex methods for fluid flow in two or three dimensions. Zbl 0552.76026
Beale, J. Thomas; Majda, Andrew
1984
Smoothing properties of implicit finite difference methods for a diffusion equation in maximum norm. Zbl 1198.65161
Beale, J. Thomas
2009
A proof that a discrete delta function is second-order accurate. Zbl 1136.65017
Beale, J. Thomas
2008
Purely imaginary scattering frequencies for exterior domains. Zbl 0289.35067
Beale, J. Thomas
1974
Correction to the article “A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources” by Vaughan et al. Zbl 1175.65134
Beale, J. Thomas; Chopp, David L.; Leveque, Randall J.; Li, Zhilin
2008
Stability of boundary integral methods for water waves. Zbl 0885.35095
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John
1997
The onset of instability in exact vortex rings with swirl. Zbl 0883.76066
Lifschitz, Alexander; Suters, W. Henry; Beale, J. Thomas
1996
The approximation of weak solutions to the 2-D Euler equations by vortex elements. Zbl 0850.76491
Beale, J. Thomas
1991
Nonlinear behavior of model equations which are linearly ill-posed. Zbl 0679.35082
Beale, J. Thomas; Schaeffer, David G.
1988
Water waves generated by a pressure disturbance on a steady stream. Zbl 0437.76018
Beale, J. Thomas
1980
Partially implicit motion of a sharp interface in Navier-Stokes flow. Zbl 1277.76056
Beale, J. Thomas
2012
A partially implicit hybrid method for computing interface motion in Stokes flow. Zbl 1426.76547
Layton, Anita T.; Beale, J. Thomas
2012
A velocity decomposition approach for moving interfaces in viscous fluids. Zbl 1160.76327
Beale, J. Thomas; Layton, Anita T.
2008
Convergence of Euler-Stokes splitting of the Navier-Stokes equations. Zbl 0807.35108
Beale, J. Thomas; Greengard, Claude
1994
Solution of the Dirichlet problem by a finite difference analog of the boundary integral equation. Zbl 1411.31010
Beale, J. Thomas; Ying, Wenjun
2019
Uniform error estimates for Navier-Stokes flow with an exact moving boundary using the immersed interface method. Zbl 1326.76078
Beale, J. Thomas
2015
Methods for computing singular and nearly singular integrals. Zbl 1082.65516
Beale, J. Thomas
2002
Boundary integral methods for three-dimensional water waves. Zbl 0991.76049
Beale, J. Thomas
2000
Operator splitting for Navier-Stokes equations and Chorin-Marsden product formula. Zbl 0860.76063
Beale, J. Thomas; Greengard, Claude; Thomann, Enrique
1993
Vortex flows and related numerical methods. Proceedings of the NATO Advanced Research Workshop, Grenoble, France, June 15-19, 1992. Zbl 0818.00017
Beale, J. T. (ed.); Cottet, G.-H. (ed.); Huberson, S. (ed.)
1993
Large-time regularity of viscous surface waves. Zbl 0556.35109
Beale, J. Thomas
1983
Solution of the Dirichlet problem by a finite difference analog of the boundary integral equation. Zbl 1411.31010
Beale, J. Thomas; Ying, Wenjun
2019
A simple method for computing singular or nearly singular integrals on closed surfaces. Zbl 1388.65167
Beale, J. Thomas; Ying, Wenjun; Wilson, Jason R.
2016
Uniform error estimates for Navier-Stokes flow with an exact moving boundary using the immersed interface method. Zbl 1326.76078
Beale, J. Thomas
2015
Nearly singular integrals in 3D Stokes flow. Zbl 1373.76153
Tlupova, Svetlana; Beale, J. Thomas
2013
A fast accurate boundary integral method for potentials on closely packed cells. Zbl 1388.65170
Ying, Wenjun; Beale, J. Thomas
2013
Partially implicit motion of a sharp interface in Navier-Stokes flow. Zbl 1277.76056
Beale, J. Thomas
2012
A partially implicit hybrid method for computing interface motion in Stokes flow. Zbl 1426.76547
Layton, Anita T.; Beale, J. Thomas
2012
Smoothing properties of implicit finite difference methods for a diffusion equation in maximum norm. Zbl 1198.65161
Beale, J. Thomas
2009
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces. Zbl 1146.76044
Beale, J. Thomas; Strain, John
2008
A proof that a discrete delta function is second-order accurate. Zbl 1136.65017
Beale, J. Thomas
2008
Correction to the article “A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources” by Vaughan et al. Zbl 1175.65134
Beale, J. Thomas; Chopp, David L.; Leveque, Randall J.; Li, Zhilin
2008
A velocity decomposition approach for moving interfaces in viscous fluids. Zbl 1160.76327
Beale, J. Thomas; Layton, Anita T.
2008
On the accuracy of finite difference methods for elliptic problems with interfaces. Zbl 1153.35319
Beale, J. Thomas; Layton, Anita T.
2006
A grid-based boundary integral method for elliptic problems in three dimensions. Zbl 1159.65368
Beale, J. Thomas
2004
Vortex blob methods applied to interfacial motion. Zbl 1115.76380
Baker, Gregory R.; Beale, J. Thomas
2004
Methods for computing singular and nearly singular integrals. Zbl 1082.65516
Beale, J. Thomas
2002
A method for computing nearly singular integrals. Zbl 0988.65025
Beale, J. Thomas; Lai, Ming-Chih
2001
A convergent boundary integral method for three-dimensional water waves. Zbl 0980.76053
Beale, J. Thomas
2001
Boundary integral methods for three-dimensional water waves. Zbl 0991.76049
Beale, J. Thomas
2000
Stability of boundary integral methods for water waves. Zbl 0885.35095
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John
1997
Convergence of a boundary integral method for water waves. Zbl 0858.76046
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John
1996
The onset of instability in exact vortex rings with swirl. Zbl 0883.76066
Lifschitz, Alexander; Suters, W. Henry; Beale, J. Thomas
1996
Validity of the quasigeostrophic model for large-scale flow in the atmosphere and ocean. Zbl 0811.35097
Bourgeois, Alfred J.; Beale, J. Thomas
1994
Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050
Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J.
1994
Convergence of Euler-Stokes splitting of the Navier-Stokes equations. Zbl 0807.35108
Beale, J. Thomas; Greengard, Claude
1994
Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S.
1993
Operator splitting for Navier-Stokes equations and Chorin-Marsden product formula. Zbl 0860.76063
Beale, J. Thomas; Greengard, Claude; Thomann, Enrique
1993
Vortex flows and related numerical methods. Proceedings of the NATO Advanced Research Workshop, Grenoble, France, June 15-19, 1992. Zbl 0818.00017
Beale, J. T. (ed.); Cottet, G.-H. (ed.); Huberson, S. (ed.)
1993
Exact solitary water waves with capillary ripples at infinity. Zbl 0727.76019
Beale, J. Thomas
1991
The approximation of weak solutions to the 2-D Euler equations by vortex elements. Zbl 0850.76491
Beale, J. Thomas
1991
On the accuracy of vortex methods at large times. Zbl 0671.76024
Beale, J. Thomas
1988
Nonlinear behavior of model equations which are linearly ill-posed. Zbl 0679.35082
Beale, J. Thomas; Schaeffer, David G.
1988
Large-time behavior of discrete velocity Boltzmann equations. Zbl 0637.76070
Beale, J. Thomas
1986
A convergent 3-D vortex method with grid-free stretching. Zbl 0602.76024
Beale, J. Thomas
1986
High order accurate vortex methods with explicit velocity kernels. Zbl 0588.76037
Beale, J. T.; Majda, A.
1985
Large-time behavior of viscous surface waves. Zbl 0642.76048
Beale, J. Thomas; Nishida, Takaaki
1985
Large-time behavior of the Broadwell model of a discrete velocity gas. Zbl 0626.76080
Beale, J. Thomas
1985
Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Zbl 0573.76029
Beale, J. T.; Kato, T.; Majda, A.
1984
Large-time regularity of viscous surface waves. Zbl 0545.76029
Beale, J. T.
1984
Vortex methods for fluid flow in two or three dimensions. Zbl 0552.76026
Beale, J. Thomas; Majda, Andrew
1984
Large-time regularity of viscous surface waves. Zbl 0556.35109
Beale, J. Thomas
1983
Vortex methods. II: Higher order accuracy in two and three dimensions. Zbl 0488.76025
Beale, J. Thomas; Maida, Andrew
1982
Vortex methods. I: Convergence in three dimensions. Zbl 0488.76024
Beale, J. Thomas; Maida, Andrew
1982
The design and numerical analysis of vortex methods. Zbl 0491.76007
Majda, A. J.; Beale, J. T.
1982
The initial value problem for the Navier-Stokes equations with a free surface. Zbl 0464.76028
Beale, J. Thomas
1981
Rates of convergence for viscous splitting of the Navier-Stokes equations. Zbl 0518.76027
Beale, J. Thomas; Majda, Andrew
1981
Water waves generated by a pressure disturbance on a steady stream. Zbl 0437.76018
Beale, J. Thomas
1980
The existence of cnoidal water waves with surface tension. Zbl 0374.76018
Beale, J. Thomas
1979
The existence of solitary water waves. Zbl 0379.35055
Beale, J. Thomas
1977
Acoustic scattering from locally reacting surfaces. Zbl 0332.35053
Beale, J. Thomas
1977
Eigenfunction expansions for objects floating in an open sea. Zbl 0336.76004
Beale, J. Thomas
1977
Spectral properties of an acoustic boundary condition. Zbl 0325.35060
Beale, J. Thomas
1976
Acoustic boundary conditions. Zbl 0294.35045
Beale, J. Thomas; Rosencrans, Steven I.
1974
Purely imaginary scattering frequencies for exterior domains. Zbl 0289.35067
Beale, J. Thomas
1974
Scattering frequencies of resonators. Zbl 0254.35094
Beale, J. Thomas
1973
all top 5

#### Cited by 1,553 Authors

 31 Chae, Dongho 25 Hou, Thomas Yizhao 16 Beale, J. Thomas 15 Constantin, Peter 15 Xin, Zhouping 14 Park, Jong Yeoul 14 Wu, Jiahong 14 Zhang, Zhifei 13 Tice, Ian 12 Cordoba, Diego 12 Li, Zhilin 10 Fefferman, Charles Louis 10 Gancedo, Francisco 10 Gibbon, John D. 10 Huang, Xiangdi 10 Wang, Yongfu 9 Frota, Cicero Lopes 9 Li, Jing 9 Liu, Jianguo 9 Lowengrub, John Samuel 9 Nazarov, Sergeĭ Aleksandrovich 9 Shkoller, Steve 9 Wang, Yanjin 9 Wang, Yuzhu 9 Zhao, Jihong 8 Elgindi, Tarek Mohamed 8 Liu, Qiao 8 Ohkitani, Koji 8 Shibata, Yoshihiro 8 Tornberg, Anna-Karin 8 Yamazaki, Kazuo 7 Cortez, Ricardo 7 Fan, Jishan 7 Hmidi, Taoufik 7 Koumoutsakos, Petros D. 7 Kukavica, Igor 7 Lai, Mingchih 7 Majda, Andrew J. 7 Masmoudi, Nader 7 Rousset, Frédéric 7 Vasseur, Alexis F. 7 Yao, Zhengan 7 Ye, Zhuan 7 Ying, Wenjun 7 Zhang, Zujin 6 Castro, Ángel 6 Chen, Qionglei 6 Constantin, Adrian 6 Coutand, Daniel 6 Deng, Shengfu 6 Dong, Boqing 6 Greengard, Leslie F. 6 Guo, Boling 6 Holm, Darryl D. 6 Kang, Yong Han 6 Kerr, Robert M. 6 Knio, Omar M. 6 Lasiecka, Irena 6 Li, Dong 6 Liu, Wenjun 6 Pizzocchero, Livio 6 Solonnikov, Vsevolod Alekseevich 6 Sun, Shuming 6 Taniuchi, Yasushi 6 Walther, Jens Honoré 6 Wang, Changyou 6 Wang, Shu 6 Xiang, Zhaoyin 6 Zabusky, Norman J. 5 Ambrose, David M. 5 Amick, Charles J. 5 Benameur, Jamel 5 Caflisch, Russel E. 5 Campos Pinto, Martin 5 Gadyl’shin, Rustem R. 5 Ghoniem, Ahmed F. 5 Gómez-Serrano, Javier 5 Ha, Tae Gab 5 Jimbo, Shuichi 5 Jiu, Quansen 5 Kawashima, Shuichi 5 Miao, Changxing 5 Spirito, Stefano 5 Titi, Edriss Saleh 5 Veerapaneni, Shravan Kumar 5 Vicente, André 5 Vicol, Vlad C. 5 Wang, Yinxia 5 Wei, Guowei 5 Wen, Huanyao 5 Wolf, Jörg 5 Wright, J. Douglas 5 Yuan, Baoquan 5 Zhou, Yong 5 Zhu, Shengguo 4 Bae, Hantaek 4 Barnett, Alex H. 4 Benabderrahmane, Benyattou 4 Boukhatem, Yamna 4 Boyd, John Philip ...and 1,453 more Authors
all top 5

#### Cited in 228 Serials

 124 Journal of Computational Physics 71 Archive for Rational Mechanics and Analysis 67 Journal of Differential Equations 49 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 48 Communications in Mathematical Physics 43 Journal of Mathematical Analysis and Applications 41 Journal of Fluid Mechanics 37 Physica D 33 Communications in Partial Differential Equations 31 Physics of Fluids 30 Mathematical Methods in the Applied Sciences 29 Journal of Mathematical Fluid Mechanics 24 Journal of Mathematical Physics 20 SIAM Journal on Mathematical Analysis 19 Mathematics of Computation 16 Computers and Fluids 16 Applied Mathematics Letters 15 Communications on Pure and Applied Mathematics 15 Applied Mathematics and Computation 15 Journal de Mathématiques Pures et Appliquées. Neuvième Série 15 Journal of Nonlinear Science 14 Computers & Mathematics with Applications 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Discrete and Continuous Dynamical Systems 13 ZAMP. Zeitschrift für angewandte Mathematik und Physik 13 Journal of Functional Analysis 13 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 13 Nonlinear Analysis. Real World Applications 12 Computer Methods in Applied Mechanics and Engineering 12 Advances in Mathematics 11 Boundary Value Problems 10 Applicable Analysis 9 Journal of Computational and Applied Mathematics 9 Journal of Scientific Computing 9 Acta Mathematica Sinica. English Series 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 SIAM Journal on Control and Optimization 8 Applied Numerical Mathematics 7 Journal of Statistical Physics 7 Numerische Mathematik 7 Journal of Evolution Equations 6 Annali di Matematica Pura ed Applicata. Serie Quarta 6 Proceedings of the Japan Academy. Series A 6 Quarterly of Applied Mathematics 6 Chinese Annals of Mathematics. Series B 6 Journal of the American Mathematical Society 6 Bulletin of the American Mathematical Society. New Series 6 European Journal of Mechanics. B. Fluids 6 Journal of Hyperbolic Differential Equations 6 Nonlinear Analysis. Theory, Methods & Applications 5 Physics of Fluids, A 5 Applied Mathematics and Optimization 5 Inventiones Mathematicae 5 Mathematische Annalen 5 Transactions of the American Mathematical Society 5 Acta Mathematicae Applicatae Sinica. English Series 5 SIAM Journal on Scientific Computing 5 Journal of Mathematical Sciences (New York) 5 NoDEA. Nonlinear Differential Equations and Applications 5 Discrete and Continuous Dynamical Systems. Series B 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Communications on Pure and Applied Analysis 5 Annals of PDE 4 Journal of Engineering Mathematics 4 Nonlinearity 4 Theoretical and Computational Fluid Dynamics 4 Journal of the Mathematical Society of Japan 4 Journal of Soviet Mathematics 4 Numerical Functional Analysis and Optimization 4 Proceedings of the American Mathematical Society 4 SIAM Journal on Numerical Analysis 4 Siberian Mathematical Journal 4 Zeitschrift für Analysis und ihre Anwendungen 4 Acta Applicandae Mathematicae 4 RAIRO. Modélisation Mathématique et Analyse Numérique 4 Revista Matemática Iberoamericana 4 Applied Mathematical Modelling 4 Proceedings of the National Academy of Sciences of the United States of America 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Annals of Mathematics. Second Series 4 Journal of Turbulence 4 Science China. Mathematics 3 Transport Theory and Statistical Physics 3 Wave Motion 3 BIT 3 Studies in Applied Mathematics 3 Mathematical and Computer Modelling 3 Japan Journal of Industrial and Applied Mathematics 3 Applications of Mathematics 3 Computational Mathematics and Mathematical Physics 3 Calculus of Variations and Partial Differential Equations 3 Computational and Applied Mathematics 3 Advances in Computational Mathematics 3 Abstract and Applied Analysis 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Living Reviews in Relativity 3 Discrete and Continuous Dynamical Systems. Series S 3 Evolution Equations and Control Theory 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Annales de l’Institut Fourier ...and 128 more Serials
all top 5

#### Cited in 36 Fields

 1,017 Partial differential equations (35-XX) 992 Fluid mechanics (76-XX) 195 Numerical analysis (65-XX) 65 Mechanics of deformable solids (74-XX) 60 Geophysics (86-XX) 44 Statistical mechanics, structure of matter (82-XX) 35 Dynamical systems and ergodic theory (37-XX) 26 Systems theory; control (93-XX) 24 Probability theory and stochastic processes (60-XX) 20 Optics, electromagnetic theory (78-XX) 20 Biology and other natural sciences (92-XX) 18 Functional analysis (46-XX) 17 Real functions (26-XX) 17 Classical thermodynamics, heat transfer (80-XX) 16 Ordinary differential equations (34-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 15 Global analysis, analysis on manifolds (58-XX) 14 Operator theory (47-XX) 11 Integral equations (45-XX) 10 Approximations and expansions (41-XX) 9 Differential geometry (53-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Mechanics of particles and systems (70-XX) 6 Astronomy and astrophysics (85-XX) 5 Relativity and gravitational theory (83-XX) 4 Quantum theory (81-XX) 3 Functions of a complex variable (30-XX) 2 Topological groups, Lie groups (22-XX) 2 Potential theory (31-XX) 2 Sequences, series, summability (40-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Computer science (68-XX)


text:
By Topic

• Abstract

SECTION I

## INTRODUCTION

### D. Analysis

The analysis phase has a twofold objective: (1) verify that the digital evidence produced by the automation on the TS is coherent with the alibi timeline; (2) discover any unwanted evidence left by the automation. In order to accomplish these tasks a digital forensic analysis has been arranged according to the methodology presented in [65]. With respect to a real case, the DFA has full knowledge about methods, procedures and technologies adopted to construct the digital alibi. As a consequence, the analysis may be better targeted. The TS has been implemented as a Virtual Machine (VM) in order to speed-up and simplify the overall analysis procedure. Moreover, the use of a VM allows to create different snapshots of the system in order to analyze differences between the state before and the state after the execution of the automation procedure. The analysis mainly focused on the following aspects.

Operating System and Applications: All the system structures containing information about executed applications (e.g., Registry, Prefetch and Superfetch files, Pagefile, and so on) have been analyzed in order to verify whether the automation produced artifacts. Any evidence being part of the alibi (accesses to websites, creation of documents, etc.) has been also collected in order to reconstruct the alibi timeline.

Timeline: This analysis focused on the identification of all the files accessed or modified during the construction of the alibi in order to detect any relationship with the automation that generated them.

File Content: All the files modified during the alibi timeline have been analyzed in order to find any suspicious trace that may be linked to the execution of the automation.

Low-level search: A set of signatures of the automation has been used to perform a deep low-level scan of the entire hard disk (including allocated and unallocated space) in order to find any possible clue of the automation.

The above activities have been carried out by using the following digital forensic tools. RegRipper2 [66] has been used to analyze the Windows Registry. IECookiesView [67], IEHistoryView [68] and IECacheView [69] have been used to analyze the browser activities. AccessData Forensic Toolkit [70] has been used for the storage media analysis, and in particular the DT Search engine has been adopted to perform the low-level signature search. The Superfetch files have been analyzed by means of SuperFetch Dumper [61]. All the traces revealed by the analysis confirmed the alibi, while no clue about the automation was found.

SECTION VII

## CONCLUSION

This paper presents a methodology to generate a set of digital evidence that could be exploited by a party in a trial in order to claim an alibi. With respect to common anti-forensic techniques, which are typically based on information tampering, our methodology relies on the construction of an automation. The automation is a program able to simulate a series of human activities on a computer at a given time. They include local operations such as document writing and music playing, as well as remote operations such as Web surfing and email sending. Using this approach, it is possible to construct a digital alibi involving trusted-third-parties such as ISPs and companies providing services via Internet. The problem of avoiding or deleting unwanted traces left by the automation is also addressed. Finally, a case study on a target system running Windows 7 is presented in order to show a real application and implementation of the proposed methodology. A computer forensic analysis of the target system has confirmed the alibi and has revealed no unwanted evidence about the presence and execution of the automation. Apart some differences, the same methodology can be extended to any digital device equipped with a modern operating system, such as Android smartphones [71], [72].

This work highlights the need of an evolution in approaching legal cases that involve digital evidence. Digital evidence are circumstantial evidence and should be always considered as part of a larger behavioural pattern, which requires to be reconstructed by means of traditional investigation techniques. To sum up, the plausibility of a digital alibi should be always verified cum grano salis.

### ACKNOWLEDGMENT

The authors would like to thank friends from IISFA (International Information System Forensics Association) for their support, their valuable suggestions and useful discussions during the research phase. In particular to Gerardo Costabile (President of IISFA Italian Chapter), Francesco Cajani (Deputy Public Prosecutor High Tech Crime Unit Court of Law in Milano, Italy), Mattia Epifani and Litiano Piccin of IISFA Italian Chapter.

We would like to thank V.Q.A. Elvira D'Amato (Head of the Centre Against Child Pornography on the Internet, Postal and Communications Police, Italian Ministry of the Interior), Lieutenant Colonel Antonio Colella (cybercriminologist and Italian Army Officier) and Moti Yung (Google Inc. and Columbia University) for their worthy advices and support.

A special thank goes to Mario Ianulardo, Computer Crime Lawyer (Naples, Italy) for the endless and interesting discussions on the probative value of a false digital alibi.

## Footnotes

A. Castiglione, G. Cattaneo, G. De Maio and A. De Santis are with the Department of Computer Science, University of Salerno, Via Ponte don Melillo, Fisciano I-84084, Italy

Corresponding author: A. Castiglione (castiglione@ieee.org)

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

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text:
/ akbir khan / blog

# golang's rand and concurrency

April 27, 2020

This is a bug I encountered when writing a ray-tracer in Golang and thought it was worth a quick share.

### The Idea

When rendering an image using a ray-tracer, each pixel value can theoretically be calculated independently, making parallelisation an attractive prospect. When rendering the image, we iterate through each position and call the sample method to calculate RGB value for that pixel:

Go makes running threads (go routines) really simple and so the idea was to split the for loop into separate threads. Where the k-th thread would calculate the [k, 2k, ... , nk]-th position pixels within the row.

Now lets check the runtimes:

# Single Thread
Elapsed: 1m54.230536119s
Elapsed: 4m13.680876913s

Unfortunately this didn’t speed things up, even worse, it increased the runtime!

### The Bug

If threading was making my program slower, then each thread was clearly unable to act independently. So lets check out sample method:

After some debugging (shout out pprof), I noticed that an incredible amount of time was being used by math/rand and the associated synchronisation overhead. Taking a quick look at the source code, I notice that the package is globally locked:

For random number generators (RNGs) this makes perfect sense, as RNGs generally calculate the next random number based on the previous, and we’d like RNG to be consistently random across processes. This is good behaviour — however not ideal in our situation.

### The Fix

To circumvent this issue and gain all the speed benefits of threading, we’d need to provide each thread its own RNG. Thankfully this is fairly simple within go, as the rand package has methods to create unique RNGs, which can be created for each thread independently.

and subsequently update all the existing math/rand calls must be switched to call our RNG instead:

### The Results

After some tuning of the number of threads to use (as suggested by a friend 2*NumCores), my final speed up was:

# Multiple Threads
Elapsed: 23.765684225s

which was a nice 4x speed up!


text:
# Atmospheric focusing

This effect operates similarly to the patterns made by sunlight on the bottom of a pool, the difference is that the light is bent at the contact point with the water while the shock wave is distorted by density variations (e.g. due to temperature variations) in the atmosphere. Variations of wind can cause a similar effect. This will disperse the shock wave at some places and focus it at others. For powerful shock waves this can cause damage farther than expected; the shock wave energy density will decrease beyond expected values based on uniform geometry (${\displaystyle 1/r^{2}}$ falloff for weak shock or acoustic waves, as expected at large distances).


text:
# Solution - A Particle of Mass M And Charge (−q) Enters the Region Between the Two Charged Plates Initially Moving Along X-axis with Speed Vx - Coulomb’s Law

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#### Question

A particle of mass and charge (−q) enters the region between the two charged plates initially moving along x-axis with speed vx (like particle 1 in Fig. 1.33). The length of plate is and an uniform electric field is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL2/ (2mv_s^2).

#### Solution

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Solution for question: A Particle of Mass M And Charge (−q) Enters the Region Between the Two Charged Plates Initially Moving Along X-axis with Speed Vx concept: Coulomb’s Law. For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)
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# Re: Help get math turned back on in Chrome

From: Dave Barton <dbarton@mathscribe.com>
Date: Fri, 8 Feb 2013 12:06:03 -0800

Message-Id: <EE106B53-3755-4C2D-A99C-C182B12B6D57@mathscribe.com>
I agree with all this. Here's how I see it: HTML has had text, images, and links since basically the beginning, so they're supported everywhere. If you want to add them to a web page, e-mail message, blog post, help page, wiki article, etc., they pretty much just work. The same now goes for tables, form elements, basic css, javascript, etc. Browser vendors now have a lot of developers working on things like CSS 3 modules, WebRTC, integration with mobile hardware, etc. There are also slightly older features like <canvas>. These newer things that aren't supported everywhere yet are often imitated to varying extents by javascript libraries, also known as "polyfills", "shims", or "shivs". (There are so many synonyms because it's such an important and common tool.) An early common example was excanvas, for imitating <canvas> on old IE.

Meanwhile, some kind of [itex] element has been around since the beginning, but has never really been fully supported. The excellent MathJax library does a lot of things. Like other polyfills, it's fine in itself for some purposes, and it's way better than nothing for all purposes, but it's definitely not the same as native browser support. We're hearing a lot about it because it's the only organized and actively funded [itex] support today.

Without getting sidetracked with MathJax details, the question is whether browsers should support a [itex] tag natively, sooner rather than later. For instance, no one is suggesting that all browser vendors support music notation in their core engines. But mathematics is fundamental and extremely important, the basis of half of education and all of science and technology. Without it we wouldn't have modern life, and if (when) we make it easier to use it and grow it (through new research), the benefits to humanity will be enormous. This is why, as Paul points out, standards bodies such as HTML5 and EPUB3 have definitively answered this question. Math support, through MathML, is required. It's worth it; it's been approved; let's just do it.

But what is the cost? The answer is that a fraction of a developer on each of the major browser engines - webkit, mozilla, trident/IE, and maybe Opera - would do it, far less than is being spent on other HTML5 technologies. This is the price to have formulas and equations (and ultimately many mathematical tools using them) "just work" on everything - digital textbooks, help sites like stack overflow, social sites like google+ or facebook, online tutoring, online journals, etc., etc. This is what I think we should pitch to everyone. If you think this is worth making happen now, instead of waiting another 15 years (seriously), please discuss and support this effort.

For google+ users, I urge you to share either or both of these, or create your own post:
https://plus.google.com/u/0/104139857168801904129/posts - the Feb 7 (yesterday) post

If someone would write something on facebook, we could like or share that as well. Finally, please go to http://code.google.com/p/chromium/issues/detail?id=152430 and star it (in the upper left corner) if you haven't already.

SIncerely, Dave Barton

On Feb 8, 2013, at 9:26 AM, Paul Topping wrote:
> I agree with all of this but it prompts me to make some additional points:
>
> While we might feel that we are “at the beginning of mathematics use on the web”, such words are not so great when making a campaign for MathML support as they imply that the revolution has yet to happen. It is the kind of thing that people say when they hope something will happen. As I argued earlier in this thread, it has already happened. MathML is in use in many places and is the de facto standard for representing mathematics.
>
> One way this kind of thinking can be used is to remind people that HTML5 is a standard that every browser maker has embraced and it is at the heart of EPUB3 ebook standards. Both of these standards are committed to by various communities and represent decisions that no one is going to go back on. Both standards include MathML. So any browser that doesn’t implement it eventually is not going to be fully HTML5-compliant. I mean this in a practical sense, not in the sense that a standards lawyer might mean it. If a browser says that it does HTML5, then that sets up expectations. As evidence, we see that many people thought that when browsers came out with HTML5 support that that automatically included MathML support since the standard implies that. They are a bit surprised to learn that browsers’ HTML5 implementations are not yet complete. We should use this in our arguments. Why don’t browser makers put effort into adding MathML support since they are committed to doing so and will have to do it eventually?
>
> MathML is an internal technology. Someday the only people that will know the term are programmers. People who work with mathematics on computers will only know see functionality that does the job, not its underlying standards. Right now we have to use the term “MathML” explicitly because it is all we have. But when talking to the communities that stand to benefit from this technology, such as education and accessibility, we should bear in mind that they are not interested in implementing standards but in benefitting from the technologies they enable. Choose your words carefully or risk sounding like a geek trying to push his/her favorite technology.

Received on Friday, 8 February 2013 20:06:34 UTC

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# EXTENDED ANALYSIS OF THE $\Pi$ BENDING VIBRATION-ROTATION SPECTRUM OF ArHCl BY INTRACAVITY FAR INFRARED LASER/MICROWAVE DOUBLE RESONANCE SPECTROSCOPY

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/17290

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1987-RE-07.jpg 164.8Kb JPEG image

 Title: EXTENDED ANALYSIS OF THE $\Pi$ BENDING VIBRATION-ROTATION SPECTRUM OF ArHCl BY INTRACAVITY FAR INFRARED LASER/MICROWAVE DOUBLE RESONANCE SPECTROSCOPY Creators: Robinson, R. L.; Ray, D.; Gwo, D.- H.; Saykally, R. J. Issue Date: 1987 Publisher: Ohio State University Abstract: The lowest $\Pi$ bending state in ArHCl has been more fully characterized using far infrared laser/microwave double resonance spectroscopy. This analysis includes a reassignment of the far infrared spectrum of $ArH^{35}Cl$ previously reported by Ray et al. and Marshall et al., as well as an analysis of the $ArH^{37}Cl$ spectrum. The following new molecular constants have been determined for the $\Pi$ state in $ArH^{35}Cl: \nu = 1018.6861(3) GHz, B = 1740.9(1) MHz, q_{1} = -49.1(3) MHz, \nu = .2603(2) D, eq Q_{aa} = 5.6(2.7) MHz$, and $eqQ_{bb}-eqQ_{cc} = -73.2(2.7) MHz$; and for $ArH^{37}Cl: \nu = 1018.4700(3) MHz, B = 1691.4(2) MHz, q_{1} = -47.0(3) MHz, \nu = .2606(1) D, eq Q_{aa} = 4.0(1.8) MHz, and eqQ_{bb} - eqQ_{cc} = -57.3(1.8) MHz$. The new value of the rotational constant gives much better agreement with the value calculated by Hutson1 from the M5 double minimum potential surface than the previous value. Thus with the recently reported spectrum of the I bending vibration of $ArHCl^{2}$ this analysis provides further strong support for a double minimum character in the van der Waals surface. In addition, the powerful combination of the double resonance technique, to assign complicated spectra, with the sensitive intracavity spectroscopic technique has been demonstrated Description: $^{1}$. J.M. Hutson, J. Chem. Soc. Faraday Trans. 2, 82, 1163 (1986). 2. R. L. Robinson, D. -H. Gwo, D. Ray, and R.J. Sayakally, J. Chem. Phys. 86, in press (1987) Author Institution: Department of Chemistry, University of California; Joint Institute for Laboratory Astrophysics and Department of Chemistry, University of Colorado URI: http://hdl.handle.net/1811/17290 Other Identifiers: 1987-RE-7


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Next: THOMSEN PARAMETER Up: Berryman et al.: Analysis Previous: KNOWN INEQUALITIES AND THOMSEN

THOMSEN PARAMETER

An important anisotropy parameter for qP-waves is Thomsen's parameter , defined by

= a-c2c.   Formula (avea) for a may be rewritten as

a = <(+2)^2 - ^2+2> + <+2>^2 <1+2>^-1,   which can be rearranged into the convenient and illuminating form

a = <+2> - [<^2+2> <1+2> -<+2>^2] <1+2>^-1.   This formula is very instructive because the term in square brackets is again in Cauchy-Schwartz form, so this factor is nonnegative. Furthermore, the magnitude of this term depends principally on the fluctuations in the Lamé constant, largely independent of . Clearly, if ,then this factor vanishes identically, regardless of the behavior of . Large fluctuations in will tend to make this term large. If in addition we now consider the combination

2= [<+2><1+2> - 1] -[<^2+2><1+2> -<+2>^2],   we find that the first bracket on the right hand side is again in Cauchy-Schwartz form, which makes it always positive unless , in which case it vanishes. Similarly, the second term always makes a negative contribution unless , in which case it vanishes.

The properties of the isotropic layers making up the anisotropic rocks depend on mineralogy, porosity, and fluid content. We can gain some insight into how the relative sizes of and are related to mineralogy by considering the measured values of these stiffnesses for quartz and calcite. Simmons and Brace (1965) report measured values of about 28 to 31 GPa for the shear modulus of fused quartz, and measured values of about .027 to .032 GPa-1 for the compressibility, corresponding to values of about 13 to 16 GPa for . (These measurements were made for confining pressures of 0.1 MPa to 10 GPa.) Wilkens et al. (1984) gave ultrasonic velocity values measured in single crystals of quartz and calcite that yield values of about 44 GPa for the shear modulus of quartz, 8.4 GPa for for quartz, 31 GPa for the shear modulus of calcite, and 55 GPa for for calcite. (These measurements were made without accounting for the anisotropy in quartz and calcite crystals. See Aleksandrov and Ryzhova (1961) for measured values of all the elastic stiffnesses, for single calcite crystals and quartz crystals.) Both the static and the dynamic measurements show that values in quartz and calcite are similar, whereas the values differ considerably for the two minerals, with being larger than for calcite and smaller than for quartz. We also know that vp/vs ratios in sandstones are close to 1.5, and vp/vs ratios are about 1.8 to 2.0 for sedimentary rocks containing calcite, dolomite, or feldspar (e.g., Wilkens et al., 1984; Castagna et al., 1985). If is approximately equal to , the vp/vs ratio is 1.7. Rocks having larger than have vp/vs ratios larger than 1.7, and rocks having smaller than have vp/vs ratios smaller than 1.7.

Although the stiffnesses of clay minerals can be found in the literature (e.g., Katahara, 1996), it is more useful to consider instead the velocities of rocks containing clays (e.g., Tosaya and Nur, 1982; Han et al., 1986) because the clays themselves typically contain micropores and the location of the clays in the microstructure (e.g., lining pores, or between grains) is more important than mineralogy, for elastic properties (Caruso et al., 1985; Wilkens et al., 1986). Porosity does not directly affect and values of the grains, but since it affects the velocities, it affects the vp/vs ratio. Clay content and the presence of pores both tend to increase vp/vs ratios (Castagna et al., 1985). If randomly-oriented flat cracks are present, they will also tend to increase the vp/vs ratio, since vs is more sensitive than vp to flat cracks (Wilkens et al., 1984).

Fluctuations in in the earth have important implications for oil and gas exploration. Gassmann's well-known results (Gassmann, 1951) show that, when isotropic porous elastic media are saturated with any fluid, the fluid has no mechanical effect on the shear modulus , but can have a significant effect on the bulk modulus , and therefore on . Thus, observed variations in have no direct information about fluid content, while observed variations in , especially if they are large variations, may contain imporant clues about variations in fluid content. So the observed structure of in (Pwavep) strongly suggests that small positive and all negative values of may be important indicators of significant fluctuations in fluid content.

If the finely layered medium is composed of only two distinct types of isotropic elastic materials and they appear in the layering sequence with equal spatial frequency, then we find that

2= (_2-_1)(_2-_1) + (_2-_1) (_1+2_1)(_2+2_2).   This result agrees with Postma (1955) except for an obvious typographical error in the denominator of his published formula. This formula shows clearly that if then Thomsen parameter is identically equal to zero as expected. Also, if but , then (Postma) implies , as we inferred from (Pwavep).

Now, we can use this formula to deduce the smallest possible value of the right hand side of (Postma). The shear moduli must not be equal, so without loss of generality we suppose that .Then, the numerator is seen to become negative by taking towards negative values and . The smallest value can take is determined by the bulk modulus bound . So we may set in both the numerator and denominator. This choice also makes the factor as small as possible in the denominator, thus helping to magnify the effect of the negative numerator as much as possible. The result so far is that

2= 34(_2-_1_2) (-_1+_2/3-_1_1+2_1).   The parameter may vary from to plus infinity. At , the second expression in parentheses is positive; but, this expression is also a monotonically decreasing function of and approaches -1 as .Thus, the smallest value of Thomsen's parameter is given by

= - 38_2-_1_2 -38.   This result differs by a factor of 2 from the corresponding result of Postma (1955), which was obtained improperly by allowing three of the four elastic constants to vanish and also using a physically motivated but unnecessary restriction that both and must be nonnegative. If we had used the nonnegativity constraint on the 's, the present result would have changed to

= 1 - _2-_12_2 -14,   which is the same inequality as that found by Postma, but his equality differed from that in (restricted) and was in fact improperly obtained.

As a final point about the formula (arearranged), we note that it implies in general that

a <+2>,   so we have an upper bound on in finely layered media stating that

2 (<+2><1+2>-1) = (<v_p^2><v_p^-2> - 1),   where the final form is true for layered media having constant density.

Before concluding this section, we want to note one further identity for .The general formula can be rearranged to give

= 2[<(+)+2> <1+2> -<++2> <+2>].   This formula is not in Cauchy-Schwartz form, but is nevertheless probably the simplest form of the result for this anisotropy parameter. In particular, it is easy to see from this form that if either or , then the right hand side vanishes identically. The first result is well-known and the second has been known since Postma's (1955) work to be true for two-constituent periodic layered media [also see (Postma)]. The present result generalizes Postma's observation in this case.

Next: THOMSEN PARAMETER Up: Berryman et al.: Analysis Previous: KNOWN INEQUALITIES AND THOMSEN
Stanford Exploration Project
11/11/1997