StackExchange Site Showcase http://www.stackexchangesites.com gallery of sites built using StackExchange Sat, 20 Mar 2010 12:28:57 +0000 http://wordpress.org/?v=2.8.5 en hourly 1 Prove a set of vectors is lineary independent. http://mathoverflow.net/questions/18831/prove-a-set-of-vectors-is-lineary-independent http://mathoverflow.net/questions/18831/prove-a-set-of-vectors-is-lineary-independent#comments Sat, 20 Mar 2010 11:39:18 +0000 unknown (google) http://mathoverflow.net/questions/18831/prove-a-set-of-vectors-is-lineary-independent I am studying for a linear algebra test and just can't get a lead on this example... See more

]]> I am studying for a linear algebra test and just can't get a lead on this example question :

given an orthogonal base base in Rn {u1...un) and a set of vectors {y1...yn} where SUM( ∥ yi ∥2) < 1

prove that the set {u1+y1...un+yn} is linearly independent

I tried using the same technique used to prove that an orthogonal set is linearly independent,: showing that a linear combination of the set {u1+y1...un+yn} can only be 0 if all arguments are 0,

a1(u1+y1) + .. + an(un+yn) = 0

by taking the inner product of both sides :

SUM(< a1(u1+y1) + .. + an(un+yn),(uj+yj)> = <0,uj+yj>

but I was not able to draw any meaningful conclusion.

a lead anyone ?

]]> http://mathoverflow.net/questions/18831/prove-a-set-of-vectors-is-lineary-independent/feed/ 0 Is there a Stack Exchange Site to Answer Questions about Emigrating to Australia? http://meta.stackexchange.com/questions/5006/is-there-a-stack-exchange-site-to-answer-questions-about-emigrating-to-australia http://meta.stackexchange.com/questions/5006/is-there-a-stack-exchange-site-to-answer-questions-about-emigrating-to-australia#comments Sat, 20 Mar 2010 11:22:11 +0000 unknown (google) http://meta.stackexchange.com/questions/5006/is-there-a-stack-exchange-site-to-answer-questions-about-emigrating-to-australia Hi Folks The title says it all really.. Is there anything out there? Thanks Dave... See more

]]> Hi Folks

The title says it all really..

Is there anything out there?

Thanks

Dave

]]> http://meta.stackexchange.com/questions/5006/is-there-a-stack-exchange-site-to-answer-questions-about-emigrating-to-australia/feed/ 0 “2.” in markdown turns into “1.” http://meta.stackexchange.com/questions/5005/2-in-markdown-turns-into-1 http://meta.stackexchange.com/questions/5005/2-in-markdown-turns-into-1#comments Sat, 20 Mar 2010 10:34:45 +0000 Tomasz P. Szynalski http://meta.stackexchange.com/questions/5005/2-in-markdown-turns-into-1 When you type "1.", "2.", etc. in the editor, it creates a numbered list. But it... See more

]]> When you type "1.", "2.", etc. in the editor, it creates a numbered list. But it always creates a list that starts from 1, no matter what number you type.

So, when you type:

    > 1. Item number one.

    Commenting on item number one.

    > 2. Item number two.

    Commenting on item number two.

You get this:

  1. Item number one.

Commenting on item number one.

  1. Item number two.

Commenting on item number two.

Here is a real-life example of this bug. What the code should do instead is use the start attribute of the <ol> tag, e.g. for the second item it should generate <ol start="2">.

]]> http://meta.stackexchange.com/questions/5005/2-in-markdown-turns-into-1/feed/ 0 How do you store your script templates? http://ask.sqlservercentral.com/questions/5078/how-do-you-store-your-script-templates http://ask.sqlservercentral.com/questions/5078/how-do-you-store-your-script-templates#comments Sat, 20 Mar 2010 10:20:07 +0000 Ian Roke http://ask.sqlservercentral.com/questions/5078/how-do-you-store-your-script-templates I have, as I would imagine all you guys do, a large collection of template scripts... See more

]]> I have, as I would imagine all you guys do, a large collection of template scripts that make it easier for me to do certain tasks quickly.

I have several hundred but I imagine some people have thousands (poor you!) of scripts to store, maintain and require at a moment's notice.

I started to prefix the date to my scripts so I would have the datetime I created the script. This worked well until I was trying to remember when I wrote that particular script. Next I went to folders but now if I need a disk space script did I save it in the Maintenance, Tasks or Diligence folder?!!

How do you get round this?

]]> http://ask.sqlservercentral.com/questions/5078/how-do-you-store-your-script-templates/feed/ 0 Glycolosis, The Krebs Cycle and Electron transport http://merspi.com.au/questions/1460/glycolosis-the-krebs-cycle-and-electron-transport http://merspi.com.au/questions/1460/glycolosis-the-krebs-cycle-and-electron-transport#comments Sat, 20 Mar 2010 07:59:17 +0000 kangarow http://merspi.com.au/questions/1460/glycolosis-the-krebs-cycle-and-electron-transport How much are we required to know about: Glycolosis, The Krebs Cycle and Electron... See more

]]> How much are we required to know about: Glycolosis, The Krebs Cycle and Electron transport

These topics are so hard.

Can anyone simply for this - Really, Really well, so that I can finally understand each step of the process.

I've already read on the internet, seen other people asking for simpler animations and gone through animations and with my teacher, and yet, I still do not understand.

thank you.

]]> http://merspi.com.au/questions/1460/glycolosis-the-krebs-cycle-and-electron-transport/feed/ 0 Using GETDATE() in SQL Function…. http://ask.sqlservercentral.com/questions/5075/using-getdate-in-sql-function http://ask.sqlservercentral.com/questions/5075/using-getdate-in-sql-function#comments Sat, 20 Mar 2010 05:04:30 +0000 avaneesh_1@ http://ask.sqlservercentral.com/questions/5075/using-getdate-in-sql-function Hi all, I want to fetch the current date or today's date to fetch some data from my... See more

]]> Hi all, I want to fetch the current date or today's date to fetch some data from my database. Now the problem is I want to do this using sql function and since sql function does not allow usage of GETDATE() how can i do it...

Please advice. Thanks Avaneesh Bajoria.

]]> http://ask.sqlservercentral.com/questions/5075/using-getdate-in-sql-function/feed/ 0 Need best query to select Rows 6 to 8 from a table containing 10 rows http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-rows-6-to-8-from-a-table-containing-10-rows http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-rows-6-to-8-from-a-table-containing-10-rows#comments Sat, 20 Mar 2010 04:47:25 +0000 venkat reddy Ravu http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-rows-6-to-8-from-a-table-containing-10-rows can anybody provide me cost effective query for my title question,also im not... See more

]]> can anybody provide me cost effective query for my title question,also im not expecting cursors in this context. thanks in advance.

]]> http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-rows-6-to-8-from-a-table-containing-10-rows/feed/ 0 Need best query to select 6to8 rows from a table containing 10 rows http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-6to8-rows-from-a-table-containing-10-rows http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-6to8-rows-from-a-table-containing-10-rows#comments Sat, 20 Mar 2010 04:47:25 +0000 venkat reddy Ravu http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-6to8-rows-from-a-table-containing-10-rows can anybody provide me cost effective query for my title question,also im not... See more

]]> can anybody provide me cost effective query for my title question,also im not expecting cursors in this context.thanks in advance.

]]> http://ask.sqlservercentral.com/questions/5074/need-best-query-to-select-6to8-rows-from-a-table-containing-10-rows/feed/ 0 How do you motivate a precise definition to a student without much proof experience? http://mathoverflow.net/questions/18820/how-do-you-motivate-a-precise-definition-to-a-student-without-much-proof-experien http://mathoverflow.net/questions/18820/how-do-you-motivate-a-precise-definition-to-a-student-without-much-proof-experien#comments Sat, 20 Mar 2010 02:51:35 +0000 YL http://mathoverflow.net/questions/18820/how-do-you-motivate-a-precise-definition-to-a-student-without-much-proof-experien When introducing students to highly technical definitions for seemingly intuitive... See more

]]> When introducing students to highly technical definitions for seemingly intuitive concepts (e.g., homotopy, continuity), how do you motivate the necessity of the definition? On the one hand, you would hope that the students are mathematically mature enough to appreciate a rigorous definition such as the epsilon-delta formulation of continuity. But if they are not (for example, epsilon-delta arises in their first truly proof-based class), are there standard cautionary tales that are especially convincing in conveying the worth of the technical definition?

(Context: I am teaching a course for students many of whom have not taken classes beyond linear algebra. The course serves as an introduction to proofs, and one part of the curriculum is continuity; for some of the students, this is the only place they will ever encounter epsilon-delta.)

]]> http://mathoverflow.net/questions/18820/how-do-you-motivate-a-precise-definition-to-a-student-without-much-proof-experien/feed/ 0 Does 2^m = 3^n + r have finitely many solutions for every r? http://mathoverflow.net/questions/18817/does-2m-3n-r-have-finitely-many-solutions-for-every-r http://mathoverflow.net/questions/18817/does-2m-3n-r-have-finitely-many-solutions-for-every-r#comments Sat, 20 Mar 2010 02:00:19 +0000 Dave R http://mathoverflow.net/questions/18817/does-2m-3n-r-have-finitely-many-solutions-for-every-r Is it true that for every integer $r$, the equation $2^m = 3^n + r$ has at most a... See more

]]> Is it true that for every integer $r$, the equation $2^m = 3^n + r$ has at most a finite number of integer solutions? I understand that this is a special case of Pillai's conjecture, which is unsolved.

If the statement is true, then can we verify the finiteness of the solution set using modular arithmetic? To be precise, is the following proposition true?

$$\forall r,\ \exists M,\ \exists N,\ \forall m,n \ge N,\ \ 2^m \not\equiv 3^n + r \pmod{M}$$

I have verified the proposition for $0 \le r \le 12$, and found the least possible modulus $M(r)$ for each $r$ in this interval. Note that $M(r) = 2$ if $r$ is even.

$M(1) = 8$, $M(3) = 3$, $M(5) = 1088$, $M(7) = 1632$, $M(9) = 3$, $M(11) = 8$.

]]> http://mathoverflow.net/questions/18817/does-2m-3n-r-have-finitely-many-solutions-for-every-r/feed/ 0