Who has IE6 users viewing their site?

Question: I know the general advice is that its no longer necessary to support IE6, but I've also heard the best data is the analytics of actual users to your site. All of my sites are currently low traffic so I can't really use my data on this. Can anyone share their findings regarding IE6 and what types of sites (if any) are visited by IE6 and so should be supported?
Answer: Depends on your demographics.  Take these 2 sites I operate for example, both with HIGH traffic.
Site 1 - blog regarding coding, PDO & databases.  Demographic - tech forward, early adopters.
IE use TOTAL - 8.7%.
ie6 use - negligible.
Site 2 - retail site in a mature community with an average customer age of 46.
IE use TOTAL - 52%
ie6 use - 4.8%
Another option is to code for ie7+ and redirect all ie6 users to an "Update your ie version" page.
redirect ie6 users
redirect / block ie6 users
Answer: Here is the percentage of IE users for a website for a vacation city in the US. It gets approximately 50,000 visitors a month.
<code>Msie 9.0  2.6 %
Msie 8.0  42.6 %
Msie 7.0  13.9 %
Msie 6.0  2.6 %

Firefox   13.4 % (all versions)
Chrome    6.3 % (all versions)
Safari    16 % (all versions)
</code>
Answer: The most common users of IE6 are those where upgrades are a real headache - big corporate or public sector offices are the most common.
One of the reasons for this is that the intranet or some other internal web-based app only works in IE6. Consequently, everyone has to be upgraded simultaneously.
So if you're targeting big bluechip companies or public sector organisations, IE6 should be important to you.
Otherwise, get it working to a bare minimum, use cross-browser polyfills and provide a message in the FAQ about why your site doesn't look as amazing in IE6 as it does in Firefox.
Answer: This month my highest traffic site received 1.35% visitors from IE 6.
This has been going down. The same period last year had 3.5% and I suspect the rate will continue as computers get replaced and upgraded.
In September last year I officially discontinued support for IE 6 and 7 on one of my sites and that impacted about 7% of visitors at the time. This let me give neat features to most of the remaining 93%. Millions of visitors later, not a single complaint :)
Answer: This is what I've heard, it just worries me that W3Schools says there is about the same number of people on IE6 and Opera: http://www.w3schools.com/browsers/browsers_stats.asp
Answer: Stats from Google Analytics for my blog. Traffic is mostly tech and Wordpress related. Over the past month I had 13k visits, 23% were IE and broken down by version:
8.0
    2,128   72.01%
7.0
    421     14.25%
9.0 288     9.75%
6.0
    118     3.99%
That translates to about 0.9% IE6 usage.
Answer: Hobby related blog, 76,000 visits year to date.  IE6 makes up 2.26% of this.
Answer: Some really good specific answers here which is great. Very interesting to see the differences according to site demographics.
Just out of interest. StatCounter Global Stats are showing IE6 at 4.14% in April 2011 down from 10.13% in April 2010 so a significant downwards trend.
As Blowski stated, this is all very well unless you are supporting big blue chips or public sector where IE 6 is still in use. We are currently having to develop for the Ministry of justice and part of the contract is the system has to work on IE6.
Does anyone have any Paracetamol spare. I have a raging headache!
Answer: We only have 10% visitors using IE, most popular is Firefox with 45% followed by Chrome with 31%.
Of our IE users only 5% are on IE6, which means it represents 0.5% of the total.
Our site is probably considered more tech savvy than most sites though.  Which makes my life a lot easier as the developer for sure!
Answer: I write on HubPages about travel and my stats are:

IE (all flavors) - 34.60%

IE 8 - 74.13%
IE 7 - 18.16%
IE 6 - 5.22%
IE 9 - 2.47%
IE 5.5 - 0.01%
IE 999.1 - 0.01% (what's 999.1)

Firefox (all flavors) - 29.97%
Chrome - 19.42%
Safari - 12.39%
Opera - 1.59%
Opera Mini - 0.87%
Mozilla Compatible Agent - 0.54%
BlackBerry9700 - 0.08%
Mozilla - 0.07%
RockMelt - 0.07% (what's this?)
Answer: It really would depend on your audience. If you're targeting big corporations or schools, etc. the IT staff may not have had the resources needed to upgrade yet. I recently was testing out a site designed as an educational site targeted for elementary school kids, and was able to do on-site testing at a local school. Sure enough, the browser they were using was IE6, and there were a number of errors that popped up with the design that I had to go back and adjust for that old browser.
Answer: IE6 has too low of percentage to even count it.
Here are stats of browsers from a site that receives over 1 million unique hits a month.
<code>* -IE8 - 29.2%
* -FF 3.6 - 16.3%
* +Chrome 10/11 - 12.9%
* -IE7 - 11.4%
* +Safari5 - 7.7%
* +FF4 - 6.6%
* None - 5.5% Traffic requested from browsers with no header
* +IE9 - 3.8%
* Opera 11 - 0.4%
</code>
Comment: -1 What type of site? If it was "help-for-ie6-users.com" I am sure the proportion of IE6 would be significantly higher.

Who has IE6 users viewing their site?


Intro to automatic theorem proving / logical foundations?

Question: Is there any web-based course or materials about logic / automatic theorem proving? (I checked MIT's OpenCourseWare and I only found a vaguely related AI course)
Answer: There are basically two historical veins of automated theorem proving, either you accept a weakened logic in exchange for more automation eg ACL2, or you accept some fairly weak automation in exchange for a strong logic . Fortunately, there are some relatively modern tools such as Coq (and I suppose Isabelle/HOL) which support both veins of theorem proving.
If you want a short concrete taste of this, I'd suggest checking out this tutorial by adam chipala which exposits some techniques in Coq that are very clever which allow for easy reasoning in at least the context of programming language theory. That aside, all these websites have a number of good references for good tutorials both about proof assistants and how to use them.
Comment: it wasn't a book at first :) . Notice how it was first published as a book in 2013, 4-5 years after i linked it :)
Comment: just out of curiosity, how is http://adam.chlipala.net/cpdt/ a tutorial? It seems to be an entire book! How did you specifically had in mind to go through it?
Answer: I'll repeat the suggestion and highly recommend Frank Pfenning's course notes, which you can also find at the original course website (google "15-815 cmu").  Another book you can try is Jean Gallier's Logic for Computer Science: Foundations of Automatic Theorem Proving, recently recommended on a LambdaTheUltimate thread.
Answer: John Harrison "Handbook of Practical Logic and Automated Reasoning" - superbook
Answer: Materials for one course on Isabelle (previously mentioned) are available.
Answer: I haven't read any of these but they might be useful:
Some notes of Frank Pfenning.
A paper of Wirth.
Answer: Benjamin Pierce has a nice introduction to automatic theorem proving in his Software Foundations Courseware, using Coq.
Answer: Have you heard of the Coq proof assistant? It is quite popular here in France. The official webpage contains good documetation.


What are the major open problems in design theory nowaday?

Question: I gather that the question whether the Bruck-Chowla-Ryser condition was sufficient used to top the list, but now that that's settled - what is considered the most interesting open question?
Comment: I personally favor the Hadamard matrix (and related) conjectures as well as D-optimal designs of certain shapes.  Gerhard "Ask Me About Binary Matrices" Paseman, 2013.01.10
Comment: Shouldn't this question be made CW as there is no "right" answer?
Comment: @Felipe Voloch: Presumably the computational proof of Lam, Thiel, and Swiercz that there is no projective plane of order 10 (which is allowed by Bruck-Ryser).  I'm puzzled about this though - there are plenty of authors (Marshall Hall's in his book *Combinatorial Theory*, for example) who conjectured prior to the work of Lam et al. that there are only finitely many biplanes.  If true, this would imply that Bruck-Ryser-Chowla is not sufficient, since BRC allows infinitely many biplanes.
Comment: What of these designs http://en.wikipedia.org/wiki/Design_theory is meant :) ?
Comment: @AlexanderChervov: Basically, this one: http://en.wikipedia.org/wiki/Block_design. But I am open to other suggestions as well.
Comment: What's this result that you alluded to, giving a converse to Bruck-Chowla-Ryser?
Answer: Edit: Since this just became available on arXiv, Peter Keevash solved the existence conjecture of Steiner $t$-designs, which means that what I wrote below a year ago as one of the most important open problems in design theory is now settled.
Here's a brief summary of the history of progress on Gil Kalai's blog "Combinatorics and more":
http://gilkalai.wordpress.com/2014/01/16/amazing-peter-keevash-constructed-general-steiner-systems-and-designs/
Congratulations, Peter Keevash!

I think this kind of question is inherently subjective, but I'll try my best to be as objective as possible by limiting myself to the classical kind of stuff that is expected to be covered in a well-rounded graduate level textbook if published in 2013. I also deliberately avoid repeating what is already said in The Princeton Companion to Mathematics. Also omitted are things that are clearly mentioned by Colbourn's "Opening the Door" and Anderson, Colbourn, Dinitz, Griggs' "Design Theory: Antiquity to 1950" in the Handbook of Combinatorial Designs.
One more caveat is that I personally don't see some branches of mathematics like coding theory and finite geometry any different than design theory. So my view must be biased toward interactions with those adjacent fileds, and I wouldn't be surprised if hardcore design theorists disagree with me at every turn in my post.
To clarify what I mean by the above caveat, for instance, take the Bruck-Chowla-Ryser theorem you brought up. If you see it from a finite geometric viewpoint, you can rule out the existence of finite projective planes of order $6$ and $14$. But as you mentioned, Lam proved the nonexistence of such planes of order $10$. So, to my eye, it's definitely one of the most interesting problems whether finite projective planes exist only for prime and prime power orders. Similarly, because many problems in coding theory are of design theory to me, a large chunk of my answer to "What's hot topics in error-correcting codes?" asked by Alex on MO counts as one of the more interesting problems in design theory. But I don't think every design theorist agrees with me here.
Anyway, one of the most important open problems about objects with the word "design" in their names is, in my opinion, the existence of Steiner $t$-designs. For total newbies, a Steiner $t$-design block size $k$ is an ordered pair $(V, \mathcal{B})$ of finite sets $V$ and $\mathcal{B}$, where $\mathcal{B}$ is a set of $k$-subsets of $V$ such that any $t$-subset of $V$ is contained in exactly one element of $\mathcal{B}$. The cardinality $\vert V \vert$ is the order of the design. A Steiner $t$-design of order $v$ and block size $k$ is written as $S(t,k,v)$. (Infinite Steiner designs have also been considered in design theory, but they haven't caught on, at least not yet.)
One of the main goals is to understand the spectrum of those parameters that admit the existence of an $S(t,k,v)$. The problem is said to originate Kirkman's study in the 19th century, and elementary combinatorics works relatively well for small $t$. The problem becomes extremely difficult for large $t$.
The most successful methods for finding $S(t,k,v)$s with larger $t$ is investigating interesting finite groups. For instance, as I said in the linked answer to Alex's question about coding theory, the known $S(5,8,24)$ has the the Mathieu group $M_{24}$ as its automorphism group. It is very interesting and often powerful to see interactions between $S(t,k,v)$s and, say, sporadic simple groups. But this line of work soon hits the wall because, for example, you would like to use a $t$-transitive group to find an $S(t,k,v)$ in its orbit and, alas, there are no $6$-transitive groups (other than the symmetric groups and the alternating groups). In fact, there are no known nontrivial $S(t,k,v)$ for $t \geq 6$ when apparently there isn't any plausible argument against their existence.
Wilson's existence theory (aka Wilson's Fundamental Construction published as a series of papers in J. Combin. Theory Ser. A) takes a different approach and proves, as its corollary, that the necessary conditions for the existence of an $S(2,k,v)$ (which can be obtained by a simple counting argument) are always sufficient for sufficiently large $v$. So, for $t=2$, the problem is solved in an asymptotic sense. This approach is very design theoretic (or the definition of "design theoretic" had changed a little by this), and there have been effort to generalize it to the case $t \geq 3$. Unfortunately, we've seen rather limited success, and while the case when $t=3$ has made some progress, only finitely many $S(t,k,v)$s are known for $t \geq 4$.
Steiner $t$-designs have numerous applications to other fields both inside and outside mathematics. This one-century-and-a-half old study gave a new, solid foundation to design theory by tidying up the mess of ad hoc techniques. So, I vote for "developing a general theory of existence of $S(t,k,v)$s" as one of the most interesting problems in design theory. (If you're familiar with design theory and are wondering why I put Wilson's existence theory only in the context of $S(t,k,v)s$ and not of $t$-designs of larger index $\lambda$, that's because such designs exist if $\lambda$ is sufficiently large, and also because the larger $\lambda$ case is mentioned in the intro section of the Handbook, which disqualifies the problem.)
But there are many other important and intriguing problems out there in design theory. For instance, the existence of difference sets is classical and has always been in the center of design theory because of its intrinsic importance (perceived by many) and connections to other fields. The recent revival of additive combinatorics/number theory may be a big push to the study of difference sets as well. It is closely related to the study of symmetric designs, which is already mentioned by Chris. Those classical problems like MOLS and others are often related and inter-winded. So, any of them is equally interesting, at least to my eye.
Also, as is the case with any other branch of math, design theory has also been driven by interactions with other fields. For instance, spherical $t$-designs are gaining more and more attention not only because of its combinatorial appeal but also because of its applications to numerical analysis, quantum information, and so on. So, the study of these types of designs may have a different flavor than traditional design theory like the one stemming from the Bruck-Chowla-Ryser theorem, but I think it's definitely among the most important subfields of combinatorial design theory.
Answer: Fix $\lambda>1$. Are there infinitely many symmetric $(v,k,\lambda)$ designs?
(The Hadamard conjectures would be at the top of my list though.)
Comment: I thought this somehow followed from Wilson's existence theorem. Now I see it doesn't.
Answer: These four below problems are interesting and still open conjecture in design theory and its related topics:
$1.$  There exist Ucycles for $k$-subsets of $[n]$, provided $k$ divides $Cr(n-1,k-1)$ and $n$ is sufficiently large.
$2.$ For $n≥6$ even, it is not possible to have a length $\frac{n^2}{2}$ cyclic covering word for the $(n−2)$-subsets of an $n$-set.
$3.$ For each $k≥3$, there exists a constant $c_k$ such that for all $v≥c_k$ and $λ≥1$, the $1$ block-intersection graph of any $BIBD(v,k,λ)$ is Hamiltonian.
$4.$ For each $k≥3$, there exists a constant $c_k$ such that for all $v≥c_k$ and $λ≥1$, the ${1,2}$-block-intersection graph of any $BIBD(v,k,λ)$ is Hamiltonian.
These four conjectures are respectively from:
$1.$ Chung, F., Diaconis, P., Graham, R.: Universal cycles for combinatorial structures. Discrete Math.110, 43–59 (1992)
$2.$ Stevens, B., Buskell, P., Ecimovic, P., Ivanescu, C., Malik, A., Savu, A., Vassilev, T., Verrall, H., Yang, B., Zhao, Z.: Solution of an outstanding conjecture: the non-existence of universal cycles withk=n−2. Discrete Math.258, 193–204 (2002)
$3.$ Jesso, Andrew T.(3-NF); Pike, David A.(3-NF); Shalaby, Nabil(3-NF) Hamilton cycles in
restricted block-intersection graphs. (English summary) Des. Codes Cryptogr.61(3), 345–353
$Also,$ I believe that Hadamard conjecture is a nice diamond in the conjectures land.
Answer: Personally, I am most interested in design theory with an "asymptotic flavor", and I think there are (edit: were, pre-Keevash) some very interesting open questions in this direction.
To cut to the chase, I think asymptotic design theory today is effectively searching for a constructive proof of Gustavsson's Theorem:  All "admissible" graphs $G$ which are sufficiently large and dense (i.e. $\delta(G) \gtrapprox (1-\epsilon(k)) v$) can be edge-decomposed into cliques of size $k$.
There are loads of spin-off questions, such as completion of sparse partial latin squares, construction of optimal packings and coverings, or imposing extra structure on the graph decompositions.
(edit: I do agree that the Hadamard conjecture is bigger, for sure.)


Can I import photos from iPad to iMac that aren't in camera roll?

Question: I lost all data on my iMac recently, including some 1500 photos.  These photos were synced to the iPad from iPhoto on my iMac.
How can I transfer them back to my iMac since they are not in the camera roll on my iPad?
Answer: iExplorer is an app that does the trick. I just tested it, and it works.
So it's quite simple and straightforward. Launch the app, and select you iPad from the sources, there will be a Photos section, and everything should be there.
The same thing happened to me once, but I used Time Machine to backup. It must be terrifying, anyway, hope it helps!
Comment: seems to work well


Does daycare help to speed up the development of motor skills?

Question: I have heard about studies that show second/third/etc children's motor skills develop quicker in an effort to keep up with their older sibling(s).  Is this also true for eldest children in a daycare setting with older children?  Are there studies to support this as well?
Comment: [NPR's Planet Money](http://www.npr.org/blogs/money/2011/08/12/139583385/preschool-the-best-job-training-program) describe studies on social skills by James Heckman, a Nobel-Prize-winning economist, suggesting that preschool is the best job-training program. The main issue is that preschool is the primary place where kids acquire social skills such as how to resolve conflicts, how to share, how to negotiate and how to talk things out, that are essential for been hired and keeping a job.
Comment: yeah, noticed my kids grip strength improved as they learnt to hold onto toys when other kids were trying to take them away :)
Answer: Children who are routinely challenged develop more quickly in the areas where they are challenged.
A day care may or may not challenge your child.  They vary incredibly in both programming and quality.
If you are concerned about your child's motor skills, get them used!  Throw a ball, play hopscotch, play an instrument, study martial arts, dance, whatever keeps him or her moving.
Answer: Kids know the difference between adults and others kids.  As much as they will try to emulate adults, they are more fascinated and interested in other kids.  Be it day care, Sunday school or neighborhood kids, kids will learn from older or more advanced kids, especially when they become at an age when they are actually interactive and want to play with other kids.
For my son's case, when he was in a multi-age home daycare (from 13-18 months), he learned to feed himself (combination of not having 1:1 adult attention and observing other kids) and "cook" as they had a large play kitchen (everything from handling pots & pans, opening up the oven and various shelves).  He wasn't really every playing with the others kids at this age, he'd just copy them and do his own thing.
If your day care separates kids out by age, you may find less of this modeling, since the kids will all be of the same developmental stage.
Answer: Rather than motor skills day care helps in improving independence, taking care of oneself and sharing, adjusting qualities. Since they have to share toys, they have to adjust to the other kids and they have to spend a large time of day without mom / grandparents who constantly fulfil their wishes, the qualities mentioned above improve. Also may improve their verbal skills since they get lot of children around to practice talking.


Distance education programs in physics

Question: I am a postgraduate in mathematics, shifting from mathematics to physics. I studied physics during my B.Sc.studies.I want to go for further studies in physics particularly in theoretical physics. I am in a job and cant afford regular classroom teaching. Could anyone tell me something about some distance education programs? or are there programs for mathematics graduates to work in theoretical physics areas like string theory?
Answer: A respectable online resource for learning physics outside the traditional classroom setting is Gerard 't Hooft's website "Theoretical Physics as a Challenge" (type into the search command "Gerard 't Hooft, Theoretical Physics as a Challenge").
Answer: There's a fantastic resource called by the National Programme on Technology Enhanced Learning. Check it out at http://nptel.iitm.ac.in/. They have a youtube channel as well http://www.youtube.com/nptelhrd where they post full courses online.
You will have to use these resources to study for the GATE and get into a good institute if you want to be paid for doing research. Considering you already have a BSc, I think you can do it if you devote your weekends to it. Leave a comment on this post if you need any more details.
Answer: aren't there 'distance universtiy courses' in your country ??
since you are a mathematician you have the 'math stuff' perhaps you should begin with the list given by Gerard T'Hooft at http://www.staff.science.uu.nl/~hooft101/theorist.html#bottom
there are good references of book and many of them can be 'downloaded' from the net :D

Distance education programs in physics


number of roots of an equation

Question: Plotting the equation $x^3-x^2 \sin(x)+\cos(x)$ I see that $x^3-x^2 \sin(x)+\cos(x)=0$ has only one real solution, is there a simpler way to see that it cannot have 3 real solutions?
Comment: One consideration is the sin and cos are less than $1$ in magnitude, so the function may be compared to $x^3-x^2+1$ which also is close to $x^3 - x^2 = x^2(x-1)$.
Answer: We have $f(x) = x^3-x^2\sin(x) +\cos(x)$, hence $f'(x)=(3-\cos(x))x^2-(2x-1)\sin(x)$, $f''(x)=(x^2-2)\sin(x) + 6x-(4x-1)\cos(x) $.
For $0\le x$ we have $\sin x\le x$, hence $f(x)\ge x^3-x^3+\cos(x)\ge \cos x$, hence any positive root of $f$ must be $\ge\frac\pi2$.
But already for $x\ge\frac 3 2$, we have $f(x)\ge x^3-x^2-1=(x-1)x^2-1\ge(\frac32-1)\frac94-1=\frac18>0$.
Therefore $f$ has no nonnegative root.
If $-\frac\pi2\le x\le 0$ then $\sin(x)\le \frac2\pi x$ and $\cos(x)\ge1+\frac2\pi x$, hence $f(x)\ge(1-\frac2\pi)x^3+1+\frac2\pi x$. The right hand side becomes $=0$ at $x=-1$ and has positive derivative. We conclude that $f(x)>0$ for $x> -1$.
Observe that $A\sin x+B \cos x=\sqrt{A^2+B^2}(\cos u\sin x+\sin u \cos x)=\sqrt{A^2+B^2}\sin(x+u)$ for some $u$, i.e.
$$\tag1 |A\sin x + B\cos x|\le \sqrt {A^2+B^2}.$$
Therefore we see that  $f(x)=x^3-x^2\sin x+\cos x$ can be estimated as
$$ f(x)\le x^3+\sqrt{x^2+1}<x^3+\sqrt{x^2+1+\frac1{4x^2}}=x^3+\left|x+\frac1{2x}\right|,$$
i.e. for negative $x$ by
$$ f(x)<x^3-x-\frac1{2x}=\frac{2x^2(x^2-1)-1}{2x} $$
The numerator is positive for $x^2>\frac{1+\sqrt 3}2$, i.e. for $x<-\sqrt{\frac{1+\sqrt 3}2}$, even more so for $x\le -\frac65$.
By the results so far, $f$ can have roots only in $(-\frac65,-1]$.
Between any two roots of $f$, there must be a root of $f'$.
If $f$ has moe than one root, it must have at least three roots (counting multiplicity) because $f(x)\to\pm\infty$ as $x\to\pm\infty$, hence $f'$ must have two roots in $(-\frac65,-1]$ (again, counting multipliciites) and finally $f''$ must have at least one root in $(-\frac65,-1]$.
Even a mild estimate for $\sin$ and $\cos $ in this interval should suffice to show $f''(x)<0$ here.
Answer: Let $f(x) = x^3$ and $g(x) = x^2 \sin(x) - \cos(x)$. Clearly
$$
|g(x)| \le x^2 + 1,
$$
and hence a necesary condition for $f(x) - g(x) = 0$ is that
$$
-\beta = \frac{1}{3}\big(-1 - \alpha_1^{-1/3} - \alpha_1^{1/3}\big) \le x \le \frac{1}{3}\big(1+\alpha_1^{1/3}+\alpha_2^{1/3}\big) = \beta
$$
where $\alpha_1 = \frac{29-3\sqrt{93}}{2}$ and $\alpha_2 = \frac{29+3\sqrt{93}}{2}$.
Now,
$$
g'(x) = x^2\cos(x) + (2 x + 1)\sin(x)
$$
implies $g'(x) > 0$ from $0 < x \le \frac{\pi}{2}$, meaning that $g(x)$ is strictly increasing in $0 < x \le \beta < \frac{\pi}{2}$, achieving its maximum at $x = \beta$ and minimum at $x = 0$.
Given that $g(0) < f(0)$, $\,f$ striclty increasing, and
$$
g(\beta) < \beta^2 \sin(\beta) < \beta^3 = f(\beta),
$$
there is no positive solution to $f(x) - g(x) = 0$ for $x \in [0,\infty)$.
The case $ x < 0$ is a bit more interesting. First, we see that
$$
g'(x) = 0 \quad \Longleftrightarrow \quad \frac{x^2}{2 x +1} = -\tan(x)
$$
meaning that $g(x)$ has a (unique) critical point $x_c$ in $\big(-\beta,0\big)$; moreover, $x_c \in [-\frac{1}{2},0)$ and it's a maximum (it's easy to see that $g'(-\pi/4) > 0$ and $g'(-\pi/12) < 0$).
In $x \in [-\frac{1}{2},0)$, $g(0) < f(0)$ and
$$
g(x) < -\cos(x) \le -\cos(-1/2) < -(1/2)^3 \le x^3 = f(x)
$$
implying that there is no solution for $f(x) - g(x) = 0$ for $x \in [-\frac{1}{2},\infty)$.
Finally, $g'(x) > 0 $ for $x \in [-\beta, -\frac{1}{2}]$, and then there is one (and only one) solution in that interval.
Hope I didn't made any mistakes.
Answer: It might be helpful to notice that it has an uneven number of solutions, since $x^3 \to \pm\infty$ for $x \to \pm\infty$. We can furthermore see that the function is not strictly even or odd (as it is composed of both an even function $\cos(x)$, and uneven functions $x^3, x^2\cdot\sin(x)$), this might hint at only one solution.
However, since the total function is made up of both polynomials of finite order and sinus/cosinus parts, it could have many more solutions - just compare it to the plot of
$$\frac{1}{100} x^3 - x^2\sin(x) + \cos(x).$$
So, to answer your question, there is no general way of deciding how many solutions such a function could have.

number of roots of an equation


Open cover of a particular set

Question: Find an open cover $\mathcal{G}$ of the set $E = \{ 1/n : n \in \mathbb{Z^{+}}\}$ such that any proper subset of $\mathcal{G}$ is not an open cover of $E$.
Comment: What topology? The one inherited from $\mathbb R$?
Comment: Yes we are working on the real number line.
Answer: Hint: for each positive integer $n$, find an open interval $O_n$ containing $1\over n$ that contains no other point of $E$. (I'm assuming you're working in $\Bbb R$ with the usual topology.)
Answer: The easiest way is to make sure that every member of $\mathcal{G}$ is needed in order to cover $E$. That means that for each $G\in\mathcal{G}$ you want a point $e_G\in E$ that is covered by $G$ and by no other member of $\mathcal{G}$. One easy way to do this is to arrange matters so that each member of $\mathcal{G}$ contains exactly one point of $E$, a different point for each $G\in\mathcal{G}$.
What if $E$ were the set of positive integers? Can you find open sets $G_n$ for $n\in\Bbb Z^+$ such that $G_n\cap\Bbb Z^+=\{n\}$? That shouldn't be too hard. And once you've seen the idea, it shouldn't be too hard to adapt it to your actual problem.
Answer: You can cover each point of $E$ with an interval so small that it contains no other points in $E$. Since this looks like it might be homework, I'll leave you to work out the cover explicitly.

Open cover of a particular set


Does the group of Diffeomorphisms act transitively on the space of Riemannian metrics?

Question: Let $M$ be a smooth manifold (maybe compact, if that helps). Denote by $\operatorname{Diff}(M)$ the group of diffeomorphisms $M\to M$ and by $R(M)$ the space of Riemannian metrics on $M$. We obtain a canonical group action
$$ R(M) \times \operatorname{Diff}(M) \to R(M), (g,F) \mapsto F^*g, $$
where $F^*g$ denotes the pullback of $g$ along $F$. Is this action transitive? In other words, is it possible for any two Riemannian metrics $g,h$ on $M$ to find a diffeomorphism $F$ such that $F^*g=h$? Do you know any references for this type of questions?
Comment: The quotient space $R(M)/\operatorname{Diff}{(M)}$ is sometimes called the space of Riemannian structures on $M$. See e.g. Berger's *[Panoramic view](http://books.google.com/books?id=d_SsagQckaQC&pg=PA501)*, p.501ff for some of its uses.
Answer: This map will not be transitive in general.  For example, if $g$ is a metric and $\phi \in Diff(M)$ then the curvature of $\phi^* g$ is going to be the pullback of the curvature of $g$.  So there's no way for a metric with zero curvature to be diffeomorphic to a manifold with non-zero curvature.  Or for example, if $g$ is einstein $(g = \lambda Ric)$ then so is $\phi^* g$.  So there are many diffeomorphism invariants of a metric.
Indeed, this should make sense because you can think of a diffeomorphism as passive, i.e. as just a change of coordinates.  Then all of the natural things about the Riemannian geometry of a manifold should be coordinate ($\Leftrightarrow$ diffeomorphism) invariant.
Comment: Good argument. :)
Answer: The group of C^1 diffeomorphism does not act transitively on the space of Riemannian metrics on a compact manifold. For example, two circles of different radius have different diameters and by pullback we can "copy" the metric of one of them on the other. Doing so we get two metrics on a circle with different diameters, hence they can not be C^1 related.
Thus, the point is that "the diameter" is a C^1-invariant hence an homotety of the metric change the diameter and the "new metric" have different diameter.
For non compact manifolds, by using a theorem of Nomizu, there exist both complete and non-complete riemannian metrics. See http://www.oberlin.edu/faculty/jcalcut/Nomizu_Ozeki_1961.pdf
Since "completeness" is a C^1 invariant we get that the group of C^1 diffeomorphism does not act transitively on the space of riemannian metrics.
h.
Answer: No. actually on closed surfaces, all metrics of curvature -1  module diffs+(S) is the teichmuller module space


Is a yeast starter required when brewing a lager?

Question: Is using a yeast starter 100% essential when brewing a lager or can you use a few liquid vials?
Answer: You can make good beer by using yeast directly out of whatever packaging style your favorite yeast comes in.  You can always pitch more by buying more too.
However, IMO, better beer and great beer is made when using a starter.
Its a function of viability and vitality of yeast.  Pitching more packs increases the # of viable cells you pitch.  However, a starter increases the number of viable cells and increases the vitality of those cells.
A simple experiment on the power of yeast vitality is to brew up a beer with your favorite packaged yeast and toss it right in without a starter. Even use two packs! Plan your next brew session for when the primary ends.  Transfer your beer to secondary or bottling as you would have planned, then pitch a cup of the yeast slurry into your next beer.  Essentially what you have there is a great pitch of yeast with super vitality. (of course the cell # thing will contribute too.  But you can correct for that with the MrMalty calculator, although the results will be the same).  You'll get a faster ferment and if you taste the two finished beers side by side BLIND; the repitch will be better in most cases.
Here is further discussion on the same viability and vitality matter.
Comment: "Viability" and "vitality" in the same comment...  Sounds like you just read the post on the brew-dudes blog.  (Yeah, I subscribe to your blog and a host of others.  Keep postin' - there are readers out there!)
Comment: Awesome, just awesome. Thanks for visitin the site over there.  It certain was on my mind when writing up my answer.  Maybe I should drop a link in there, but I don't want to pimp you know???
Answer: The goal is to pitch an adequate number of viable yeast cells in order to get a good fermentation.  Whether you do that with a starter you built yourself or by buying more yeast does not matter.  A useful tool is Jamil "Mr Malty" Zainasheff's pitching rate calculator.
In the long run it's cheaper to buy yourself a 5 liter erlenmeyer flask and learn how to make a good starter. In a pinch though, buy more yeast.
Answer: I've brewed two 5 gallon batches of Lager, both times with dry lager yeast and both times without starters (the dry yeast package instructions said to sprinkle it into the wort, so that's what I did).
The first one turned out really well and the second one is currently bubbling merrily in my 40 degree basement.
I don't have any experience with liquid vials but in my experience it's not 100% essential to have a starter. However, I'm sure making a starter and pitching more yeast certainly couldn't hurt.
Comment: Really... Why is that?
Comment: Actually, pitching too much yeast (overpitching, in the vernacular) may produce acetaldehyde, a green apple flavor.  That being said, it takes a lot of yeast to overpitch.  On the order of fermenting a weak beer on a large yeast cake.
Comment: A starter is not recommended for dry yeast and can in fact be detrimental.
Answer: Always make a starter for all beers.
Use a growler if you have to.
Takes 15 minutes.
Since I have started making starters 2.5 years ago, I have not had one infection, I always know that my yeast is viable, I pitch near the correct amount of yeast, and my beer tastes better. No infections, and I brew once a week.
Answer: This way was suggested to me on a brewers guild mailing list I subscribe to:
you need to have a stir plate and a flask.  the flask really can be anything as long as it has a small mouth to it.
put a smack-pack or vial of liquid yeast with two cups of water and 1/3 cup of dry malt extract. allow it to sit and stir for 24 hours and you'll see up to a 5x increase in cell count.
like I said at the beginning,  this isn't my created way but one that was suggested to me. In my experience it works remarkably well.  I'd strongly suggest it.


How to restore plesk files correctly?

Question: Recently my server crashed. So I reinstalled Plesk and uploaded all databases to var/lib/mysql and site files to backup/vhosts.
How do I get it all back to normal?
Answer: you can directly restore your Plesk backup using the backup sections and all your files and databases will get restored automatically.
In case the automatic backup restoring fails, just create the site and databases manually, copy the files via FTP or File manager and import the databases via PhpMyadmin tool.
Answer: There are a few workarounds for manually accessing the file.
Plesk has an outline on a few advanced methods in an article from their Knowledge Base.
If you are on a Mac, the third-party "Stuffit" application is capable of reading these files. They offer a free version with basic functionality. There is a Windows version of Stuffit as well, however, it does not provide the same functionality.
Using Stuffit Expander to access your Plesk-generated backups manually
Download and install Stuffit Expander from their website.
Create your backup in Plesk and download to your Mac.
Right-click on the backup file and select Open With > Other.
Select Stuffit Expander from the application list.
You should now see your extracted directory. You will see a list of your domain directories.
Repeat the steps for each directory, such as httpdocs.
You should now be able to see all your files, and just restore the ones you need.
Answer: You should have applied your last server backup to restore everything. Now you need temporarily remove all files you uploaded previously, create databases and sites from Plesk panel (or from command line) and then upload files back.
Answer: I advise you just to upload your files via FTP and restore your database backup by means of Phpmyadmin.
If you previously created your Plesk backup, just use the toll to restore the backup via the Plesk backup section.

How to restore plesk files correctly?


Substitute Samsung Note 3 Cam for SLR for Product Shots for eCommerce?

Question: I'm wondering if instead of purchasing a SLR, if I can't just use my Samsung Galaxy Note 3 camera instead.  This is for eCommerce photos; women's clothing, tops and bottoms namely and some jewelry.  Amazon requires the file size to be 10MB, 72 pixels per inch, 200x200 to 2000 x 2000 dimensions and ratio 5:1 or 2:1 or 1:1.  The Note 3 cam has these options:  4:3 13M, 16:9 9.6M, 4:38M, 16:9 6M, 16:92.4M. Can I use one of these options on Note 3 to submit highest quality allowed on Amazon?  Thank you!
Answer: The "are you allowed" question is really up to Amazon; from the specs you've given, the answer seems to be "yes", and in fact from a pure megapixels view, by a long shot. 200×200 pixels is less than 1% of a megapixel, and you have 13 megapixels to work with.
But then you ask a perplexing question about "highest quality allowed". If by "quality" you simply mean "can this camera max out the file size allowed", the answer is again yes, because the 13mpix camera gives images of 4128×3096, which is obviously bigger than 2000×2000.
So why do I say "perplexing"? Well, it's because I'm concerned about the question you didn't ask about quality, which is whether your results will actually look good. This is kind of up to you (do you think they look good enough?), but also up your customers — do you want product photos that look like they were snapped with a phone camera, or do you want them to look really appealing?
You don't necessarily need a DSLR for this, but it'll give you a lot more options. In either case, what you'll need to really work with is the lighting.
Comment: Agreed - the resolution is there, but the actual quality of the output is going to be rubbish from a mobile device like the Note compared to even a cheap dslr.
Answer: The lack of raw support and limited dynamic range of the smartphone camera is going to make getting proper light box exposure of the products far more time consuming and difficult than using even a basic DSLR, let alone a good one.
Technically, with sufficient effort you could probably make a passable image with your Note's camera, but I personally wouldn't want to go through the aggravation and trouble it would be, particularly when the actual image quality likely still won't be near that of a decent DSLR.
Also, you will certainly need proper lighting and probably a soft box to get the lighting right.  Unless you want to use continuous power lights, having the ability to sync with multiple flashes would also be helpful, though continuous power lighting is also an option.
Answer: Product photography depends on creating a flatteringly accurate image of what you're selling. That goes far beyond filling the permissible pixels on your host site.
Accurate colour reproduction is very difficult to control with a camera that doesn't let you process raw files or set the correct white balance; an SLR or advanced compact camera can do that.
The wide-angle lenses of cell phone (and tablet) cameras will exaggerate the effects of distance: something close to the lens will look much larger than things that are father away. This is a problem for anything that isn't laid out flat and parallel to the camera, especially for three-dimensional products such as jewellery. Using a camera with a zoom lens, such as the kit lens that's included with most DSLRs, lets you control perspective and choose how you want your items presented.
So yes, you can use your Note to take the photos, but you'll still need to downsize them (and crop, as desired) before they can be uploaded. Using an SLR, however, will give you better results.


What could be causing water pressure to build up after changing my under sink filter?

Question: After I did a routine under sink water filter change, I am getting a powerful burst of water when I turn on the water dispenser that goes through the filter. It lasts only a second or so then the pressure drops to a slower flow. I removed the filter and looked for clogs or debris but didn't see any. It is the same filter that I previously had under the sink. I am concerned that the filter may not be working properly.
Comment: What type of filter? Carbon? Reverse osmosis?
Answer: You likely have air trapped somewhere it shouldn't.
Water doesn't compress so when you turn on the tap, the flow is the pressure from the city divided by the resistance of all the pipe between it and the tap.
If you have an air bubble, then when the tap is shut off the air will compress until the pressure matches that from the city.  When you turn the tap on, the flow will be the pressure from the air bubble divided by all the pipe between it and the tap.  Since there is much less pipe in this case, the flow is much higher.
The pressure in the air bubble quickly drops as the water is pushed out until you again match the original case.
This is especially noticeable if you have have a smaller pipe somewhere between the city and the air bubble than between the air bubble and the tap since obviously the flow is limited by the smallest (cross-sectional-area) pipe.
Depending on the size/shape of the filter, it could be air in the filter itself.  See if you can fully fill it with water before connecting it.
If you shut off the house water while making the change, then air could have gotten into any branch going to a higher location than your sink.  If you haven't tried running fresh water in every single location in your home, that may be all it takes to clear out the air.


What factors lead to rich crema on espresso?

Question: I love espresso, especially when it has a rich crema (the head that forms on top of a well made shot). I notice that some cafes produce this consistently while others never have more than a wisp on top. Which of the many factors that go in to pulling good espresso shots specifically contribute to the crema?
Answer: Crema is a food foam.  For crema to form and survive long enough for us to enjoy the espresso, something needs to hold the bubbles of the foam together.  In most food foams proteins help hold up the bubbles, but in crema it is a mixture of proteins and oils. This makes it hard to predict what makes good crema.  From practice, good crema comes from:

Enough pressure and well timed extraction
Fresh grind with a good grain size distribution
Darker roasts

There are also tradeoffs between stability of the crema and the amount of crema produced. The two don't seem to go together.  The crema also should have bubbles that pop and sprinkle the coffee aromatics into the air and our noses (like champagne).  The higher pressure extraction helps extract and emulsify the oils (about 0.1g ends up in one shot).  The darker roasts help with the Maillard reaction which creates the still unknown molecules that give crema its color and volume.
Answer: The crema is done by the fatty content of the coffee, the high pressure (a good expresso machine has about 15 bar of water pressure) help to extract much fat from the coffee.
Also the quality of the coffee can influence the fatty contents; a mix of arabica and robusta type coffee can give a better crema than 100% arabica.
Comment: I've found the beans to influence the crema greatly. I've had to experiment to find good beans.
Answer: McGee's On Food and Cooking also lists the mineral content of the water used as an important factor in crema.  He states that hard water will reduce the amount of crema produced but also that softened water causes over-extraction.
Grind size and the tamper pressure applied by the barista also make a difference to the amount of crema.  Though I don't have any results handy to back this up.  Around 30 pounds or pressure (13.5 kg) applied to tamp the grounds is considered optimal.  Test this on a scale to get a feel for it.  I've heard that some award-winning baristi will tamp with less pressure but grind the coffee finer to compensate.
As said before by SWrobel, beans should be freshly roasted 3 or 4 days prior.  Beans just roasted or within a day or two seem to produce much more crema but the crema produced is not as stable.  Possibly from too much CO2?
I am currently using a northern Italian style roast and it produces a nice think crema.  Would be interested if anyone has done any experiments on how roast profile affects crema.
Answer: If you source your beans from a local roaster and grind on demand you should have no problem producing crema.
The only issue is producing a crema made of fine bubbles. Too fresh and there is generally too much gas giving you a very bubbly crema.
The origin and processing of the bean can also play a huge factor. If you have ever tried Monsooned Malabar you'll see what I mean.
However at the end of the day you want a decent cup of coffee and taste is the only thing you can go by. There is no ideal age for beans. My favourite blend tastes best to me at around the 1.5-2 week mark and still produces a fine espresso.
Answer: Beans should be roasted within the last week. Ideal age is about 3-4 days past roasting, and of course they should be ground right before extraction.
Answer: Typically, Brazil coffee beans are used in espresso blends because of their ability to produce crema, which would remove the need for robusta type beans.
As for your answer, pygabriel has a more technical answer.


How To Avoid Using Cliches In Storylines?

Question: How is it possible to avoid cliches in storylines that you are writing? Obviously, there are external sources of influences as you read more and more. It would be possible that we are subconsciously and unaware that we are crafting a story that bears similar resemblance to a story that we particularly like.
Comment: @justkt: Because at the end of the day, nobody wants to sound like every other Tom, Dick, and Harry. We all want to be one in a million. Imitation may be the sincerest form of flattery, but flattery will get you nowhere. Of course, you should take my comment with a grain of salt. (oh, wait, that's cliches in *writing.* I imagine JFW just doesn't want to be a hack. :) )
Comment: "Clichés are the spanners and the screwdrivers in the toolbox of language."
Comment: What's your purpose for avoiding cliches in your plot?
Comment: @Lauren - I asked because I think the best answers will come when we know what JFW wants to avoid and even more importantly what (s)he wants to achieve.
Comment: If you take into account the often-repeated phrase "there are only seven stories" and the number of works written over the years, it seems unlikely that you're going to find something that is entirely novel throughout. Just sayin...
Comment: [Tropes are not bad](http://tvtropes.org/pmwiki/pmwiki.php/Main/TropesAreNotBad).
Answer: Layered, nuanced characters and depth of story will help you avoid cliches.
Look, we're all writing a lot of the same stuff.  Good guys, bad guys, boy meets girl, she gets kidnapped, blah blah blah.
Cliche's arise when:
1) the characters behave in a certain way without the proper background.
2) They only behave this certain way
Hank, the grizzled veteran cop who is a drunk and is just waiting to get his twenty years so he can retire... that is right out of the cliche book.  But, if your story outlines why Hank is the way he is, and also gives him more dimension, then Hank is no longer a cliche.  Hank  becomes a real character.  Making Hank a drunk cop is great, but maybe he's into racquetball or model trains or something.  Nobody in life is just one way.  Your characters shouldn't be either.  If you can make Hank's recreational racquetball somehow figure into the story so that Hank can overcome his obstacles and save the day, well, good times!
On the flip side, you can't go giving every character extensive background intros and laundry lists of interests.  This is the art, finding the middle ground between shallow characters and boring your reader to death.  The best do it so well that you don't even notice.  The worst, well, I'm sure you can think of some examples.
Answer: Cliche characters lack depth.  Come up with strong motivations, fears, desires, etc... and think about the implications to the character's behavior due to these factors.  Don't write the perfect "good guy" or the purely evil "bad guy."  Make them interesting.  Give the character an unusual trait/history, and make it important to the story.
Cliche themes shift with the zeitgeist.  Vampire movies/stories have become cliche, thanks to Twilight.  Zombies are cliche as well.  If you're going to write for one of these genres and want to avoid being cliche, approach the story from a fresh angle.  Sean of the Dead (zombie/rom-com) and Zombieland (zombie/coming-of-age) are examples.
Keep in mind that cliche stories can be successful.  See Avatar.  It's Dances with Wolves set in space, with fairly shallow characters and a predictable ending.
There's a good podcast by the Writing Excuses guys on avoiding cliches.
Answer: Don't try to avoid clichés just for the sake of avoiding them - no matter how original you think your idea is, some reader somewhere will see it coming from a mile away. Instead, try to make people give a darn.
My favourite example of this is in video game design: you can have a character X asking players deliver an item Y to location Z. The player may initially go "yawn, it's a bloody FedEx quest." There's two major schools of design here: Make the video game full of boring delivery quests where nothing of interest happens (you get points while having boring old time! Whee!) or make a few delivery quests where interesting things take place, and the player can see that you didn't just rev up the automatic quest generation wizard built in the game editor. It's still a FedEx quest, but people actually had fun playing it, so they won't really complain. Mission accomplished.
So, if your fascinating plotline is mercilessly picked apart by nitpickers in TVTropes, that's not a bad thing - it happens to everyone and every story. The bad thing is when all of the readers yawn in unison and join the aforementioned TVTropes nitpickery because they know all about your story without even reading it.
Answer: Find a good editor, and when you hand over the manuscript, let the editor know that this is a particular issue for you, and ask the editor to keep an eye out for it. If you know that you read a lot of one writer, mention that writer to the editor and say "I like this person, but I want to make sure I'm not unduly influenced."
There's a reason you can't really "proofread yourself." It's very hard to see your own biases.
Answer: TV Tropes is a good resource for looking up clichés in literature as well as other media.
Comment: BE WARNED. TVTropes is KNOWN to suck people into black holes of lost weekends. I have never gotten out of TVTropes in under three hours. It is a fabulous site, but pack for a long stay. Bring food and drink. :)
Answer: As has been said, depth and variety can turn a cliché into something engaging.
What's interesting is the way some writers use clichés to their advantage.  It happens more in television than other forms -- and it happens in ensemble cast shows more than other television.  If there will be depth added in later episodes, the audience needs to get through the first hour (the pilot) without a huge amount of background.  Clichés become a sort of shorthand for introducing characters and even plot elements.
The spoiled rich girl may have deeper layers to her, but in the early part of the story she's only needed as a comic annoyance when paired against the hero.  She may come off as a cliché at first, to be given depth when her part of the story comes along.
Hank, the drunk burn-out cop mentioned by gmoore, may not become a "real character" until the reader has accepted him as a cliché and moved on.
The most skillful writer will introduce a quirk or two for every character so that even secondary characters never seem like clichés.
Answer: A renowned songwriter and artist from my country, Juan Luis Guerra, states he listens continuously to all the music on the media; he says it helps him avoid doing the same thing everyone else is doing.
The extrapolated advice seems to be: Read a lot, aware of what you're doing. When you write, you'll know what to avoid. If you don't read the clichés and get to know them, you won't know to avoid them.


App to hand write notes

Question: I am looking for an app that would be good for taking hand written notes on a 10 inch screen tablet
The closest app that i found is "note everything"  What makes it short of my requirements is
1(most important) Drawn notes that i can write on are each 1 tablet screen size.  I want something that can be scrolled down forever as i need more space.  Something the way a normal document works.  At worst it should let me instantly page another full canvas forward, not have to create a new note for every page
2. text notes and hand written notes are separated into separate files.  I would like the whole note to be hand written, but be able to add typed ares
3. There are no lines in the paint section.  Makes it hard to write
Can anyone suggest anything better?
Answer: Quick notes is alright.
Comment: This app only allows one page per note.

App to hand write notes


How to synchronize local files with those on the remote server whenever they change?

Question: I need to synchronize the project folder on my local machine with the same folder on the server so that when I change the local or the remote file they are immediately synchronized. How can I do this?
Comment: Which OS is installed on the server and local machine? Also what kind of latency would be acceptable. How much data and how many files changes are you expecting?
Answer: Source version control software (CVS, SVN, git, etc) is typically exactly what you want in this type of situation.
They do not provide immediate synchronization, but I suspect that you want to re-think why you need that. There will likely be trouble if your production server is updated every time you change a file on your desktop. What if you hit save half-way through some changes?
If you don't want to mess with keeping a history of changes, use a utility like rsync to keep the two systems synchronized periodically.
If you're positive that you must have immediate synchronization, then there is likely no need to have a copy on both systems. Just mount the directory from the server on your desktop (via sshfs, mapped network drive, etc) and make the changes directly to the files.
Answer: Personally, I'd go with what i_grok suggested by using SVN, P4 or Git. Reason being, is that what happens when you make a bad change to your code and now you've sent your site down the tubes. However you can do as i_grok also suggested with a mapped network drive or sshfs or you can write a custom python script within your working directory to auto-upload.
You can use the watchdog python library. and actually someone appears to have done some of the work for you, so you could just go here and plug it in.


Putting a spoon in boiling tea brings the froth down. Why?

Question: Two questions really:
1. Why does putting a spoon in boiling tea bring the froth down?
2. Also, the tip of spoon (outside tea) never heats up. I cannot imagine that normal air can have so much of a cooling effect. The heat conduction from spoon inside tea should be far more than cooling effect of air. Isnt it?
Answer: Taking the more Physics related question: if your teaspoon is made from stainless steel it has a considerably lower thermal conductivity than mild steel or (if you're at a swish tea party) silver. Depending on how much of the teaspoon is out of the tea it's entirely reasonable for the tip of the spoon to stay reasonably cool.
Your first question is more Physical Chemistry than Physics. I don't know the answer, but if inserting a spoon breaks the foam it's either because the metal surface acts as a nucleation point for the bubble walls to collapse, or possibly whatever surface active species is stabilising the foam adsorbs onto the metal rather than at the air water interface and this collapses the bubble walls. I don't think there are any strongly surface active species in tea, so the foam is probably easy to collapse.
Answer: Tannic acid reacts with the chromium in stainless steel to generate chromium tannate, which is a surfactant.
Comment: Wouldn't that make the tea foam more when the spoon is added?
Answer: The tip of a spoon very much heats up if the spoon is made of silver rather than steel. Just try a silver spoon and you'll find it is completely unusable for hot tea.


How to calculate optimal standard deviation bands for trading?

Question: I am trading with standard deviation bands (6 bands) on de-trended data. How can I find the most profitable  signals with neural network or GA with standard deviation bands? Should I first find the slope  degree of n bars of trend line (for example, 50 bars linear trend line slope is 30 degree) then calculate bands distance to price the finally find the probability distribution of the signals? Is this the correct method? Any comments welcome from people with a good grasp of signal processing and knowledge of probability.
Answer: You need to define the parameters over which you are searching (i.e. # of bands, slope of trendline, some function relating slopes to trendline, etc.). Then you can use your favorite optimizer to identify which parameters satisfy your P&L objective.
Of course, your approach is a surefire way to lose money since this curve-fitted model will not generalize out-of-time. There is no theoretical reasoning on why the parameters and functional form that your optimizer identifies need explain future returns. It's also not clear what your strategy is -- trend-following or mean-reversion on breaks -- which suggests there is not much of a theoretical underpinning here.
A better approach along your lines of going long/short and certain bands would be the attached paper by Marco Avellaneda @ NYU. Better still is taking a step back and making empirical observations about the market and then fitting a theory (what statisticians call the "data generating process") to explain your observations. Then try to build a model that reflects your theory.
Answer: Calculating standard deviation is a little bit complex. Standard deviation is used for prediction from past data. For calculating it firstly calculate mean of group of data, than subtract mean from each data, take square of each result and create sum, than divide this by the total number of data minus one. The sum of all the squared differences is then divided this by number less than total data. The square root of this number is called standard deviation.
Comment: This question isn't about how to calculate standard deviation.
Comment: Yeah, this answer has nothing to see with the question...


Combining Layers using ArcMap?

Question: How do I combine two shapefiles into one shapefile?
My GPS unit tells me this:

(arcpad 8 juno) the map projection for *.shp does not match the
  current map projection

If you could provide more insight into the error message that would be useful.
Answer: The Append or Merge geoprocessing tools are suitable for combining two datasets. You can execute them from ArcToolbox which you will find in ArcMap (or ArcCatalog for that matter).
The ArcPad error message is a different problem (and probably should have been posted as a separate question). Shapefiles have a spatial reference associated with them (usualy in a .prj file), so does the map. The error message states that the two are different and the data cannot be reprojected. ArcPad 8 can actually deal with different projections, but this support is rather limited and is not as comprehensive as in ArcGIS Desktop, which can reproject data on-the-fly for just about any projection. See FAQ:  What projections, datums, and related parameters does ArcPad 8.x support? for details.
You can change the map projection to match that of the shapefile, if it's supported. You can also do the opposite - reproject the shapefile to the coordinate system used by the map. Reprojection of feature data can be done via the Project geoprocessing tool.
Answer: Most commonly the default projection for GPS units is not a projection at all, but Lat lon.
You may be able to change that to the projection of your data, which would remove the message you are getting.
The other way would be to re-project your data.
After combining your shape files (if that is still what you want to do) you can simply set the projection of the document to the same projection as your default in the gps.
Then right click on the layer and select data> export.
Be sure to check the "same as data frame" check box, and select a location.
Walla! your new shape file is in the projection that the data frame is in.

Combining Layers using ArcMap?


How to extract Solve results as variables

Question:
Possible Duplicate:
Assign the results from a Solve to variable(s)

In the following example:
Clear[g1, z1, a, g2, z2]
sa = Solve[ g1 == 1 + l z1/(z1^2 + a), a]
sb = Solve[ g2 == 1 - l z2/(z2^2 + b), b] /. z2 -> z1 + l

This gives me solutions for a and b that are in the form
{{ a -> astuff }}
{{ b -> bstuff }}

I want to use this result in a secondary computation, and did so by cut and pasting from the Solve[] results like so
 Solve[ astuff == bstuff, z1 ]

How can I just extract those results without cut and pasting?  I don't like the cut and paste dependency since I'd have to redo it all if I make any sort of correction to the first couple identities.
Comment: You can use `Part` to extract the relevant bits.
Answer: You could use ReplaceAll (/.):
Clear[g1, z1, a, g2, z2]
sa = Solve[g1 == 1 + l z1/(z1^2 + a), a]
sb = Solve[g2 == 1 - l z2/(z2^2 + b), b] /. z2 -> z1 + l

Solve[(a /. sa[[1]]) == (b /. sb[[1]]), z1]

Here the /. command is used to manipulate the expressions a and b according to the rules given by sa and sb.


Sharepoint 2007 to 2010 conversion and authentication

Question: I'm consulting on a project that needs help passing authenticated user to other .Net applications on the same domain from Sharepoint to standard .Net & classic asp sites.  Currently in SP 2007, the .ASPXAUTH cookie gets written and can be accessed through the membership provider in an ASP.Net website via:
<code>Membership.GetUser.ProviderUserKey.ToString()
</code>
In 2010, it's using claims based (federated) and writing a FEDAUTH cookie.  I need to upgrade these other subdomain deployments to be able to access the cookie credentials the same way that the one above is and this method is not working for the new cookie.  Any ideas?  I'm not a SP developer... I'm mainly standard .Net, so more info about SP is beyond me.
EDITS:
I've done some more research and it seems that one suggestion is to use a security token service (STS) and then use the FedUtil to redo my apps to authenticate to it.  Is there already an STS being published with the Sharepoint application for me to use?  I'm going to assume that connecting to this will be difficult from the 1 classic asp site that is still out there, but good for the .Net deployments.
More research, there seems to be a Claims aware .Net web application project in WIF download.  Is this just a prebuilt version of what I need to add to my web.config to make it claims aware?  Also, does SP2010 automatically include the WIF and ADFS 2?  The more I read, the more this sounds like a lot of server infrastructure upgrades and that's not something I'm going to have control over.  I really need to know if SP2010 is already using all the tools I need/found and how to go about doing it.
Answer: There's a good article here: Configuring SharePoint 2010 and ADFS v2 End to End
.
SP 2010 includes an STS but there is no GUI as there is for ADFS, It's all PowerShell.
When you create a claims-aware SP web application, it automatically does the FedUtil stuff for you. In SP, it's all under the hood. SP 2010 does NOT include ADFS. You need Windows Server 2008 R2 (preferably) and ADFS v2.0 is a separate download.
SP only does authorisation based on claims. You still need ADFS to authenticate.
The claims-aware web app. in WIF gives you the plumbing and displays the claims but you still need to do the FedUtil part to "bind" to ADFS. Refer How to: Build an ASP.NET Relying Party Application


Unhide dock when key pressed

Question: I am currently hiding my dock. I would like to unhide it whenever a the fn key is pressed. Is this possible?
Answer: You can assign that fn to show/hide dock in Keyboard shortcuts, but you will override the original fn key.
Or you can create a Service in Automator that act upon a keystroke
use this action pack to act upon key and do what you want building up your workflow.
Comment: That's not going to work with the `fn` key.
Comment: nop, but you can assign other that does everything
Comment: That action pack allows you to type a keystroke, not use a keystroke to activate an automator action
Answer: The fn key is a modifier key that lets you use a software function key F1-F19 when held down, instead of the built-in hardware F key functions (brightness, volume, etc.)
So it's not possible to use that particular key on its own as a keyboard shortcut, just as it's not possible to use the shift key on its own.
The best you can do is set the shortcut to F13 using System Preferences > Keyboard > Keyboard shortcuts, which on my particular keyboard is just above the fn key…

Unhide dock when key pressed


solve equation of form $x = a - (b - x)^c$

Question: Is there a general solution (for $x$) to an equation of the form $x = a - (b - x)^c$ ?  If there is no general solution, please suggest a strategy for getting a numerical answer.  In the case I care about immediately, two different computer algebra systems got as far as $x = 50\,000 - (100 - x)^{500\,000}$ and then got stuck when asked for a numeric answer.
Comment: If you let $b-x=y$, you get a nicer equation $$b - a = y - {y^c}$$
Answer: Assuming $a,b,x$ are reals and $c$ is an integer, your equation becomes
$$ a-(b-x)^c-x = 0$$
which can be converted to
$$a-x-\sum_{i=0}^c \begin{pmatrix} c \\ i \end{pmatrix} b^ix^{c-i} = 0$$
using the binomial theorem.
For $c > 4$, there is no general solution for this polynomial by the Abel-Ruffini theorem. However, it may be possible that for certain specific conditions on $a, b \in \Bbb R$ that allow it to be solved.
Answer: With Mathematica
<code>FindRoot[50000 - (100 - x)^500000 == x, {x, 99}, AccuracyGoal -> 20,
WorkingPrecision -> 50]
</code>
I get x = 98.999978364173304772436016428458876920765894232268
You can get more accurate values by increasing the WorkingPrecision.
You can use Newton's Method with something like this.
Answer: If such an x exists it will be between 98 and 99, and by between them I mean it's going to be very close to 99.
Using maple I could maybe get close just by messing around with it.  If such an x exists it is between x = 98.9999783650000000000000000000000000000000000000000000001 and x = 98.9999783650000000000000000000000000000000000000000000000
The fact that maple chokes on it tells me that an x likely does not exist.  I used this expression to look for it:
limit(ln(50000-x)/ln(100-x), x = 98.9999783650000000000000000000000000000000000000000000000, left)
This gives the answer: 4.999035752*10^5
and limit(ln(50000-x)/ln(100-x), x = 98.9999783650000000000000000000000000000000000000000000001, left)
which provides an answer of: 5.001346887*10^5
Edit: I've now tried it in maple and wolfram alpha, and managed to exceed computation time on wolfram alpha for non pro members, and I managed to hang my laptop with maple, as it appears that 4GB of memory wasn't enough.
Comment: These CAS libraries likely do not stock the requisite solvers to compute the solution to that extreme precision, I would imagine.


Difficulty playing piano due to my small hands and short fingers, anyway around it?

Question: I have really small hands, and short fingers. On a piano I can reach an octave and a little more, but my octave is generally very sloppy. A lot of songs require some crazy octaves like Liszt's Liebestraum. The part where the melody is played by octaves and leads up to the cadenza (I think that's what it's called). Also, like Revolutionary, the main melody is octave. I generally just lower my hand a little bit and point my hand upward then play with the edge of my fingers. It's doable but inconvenient. I can generally play chords that span an octave, but can't play the octave well...so I doubt there's anyway around it unless I get surgery on my hands or something.
Comment: Are you asking for special techniques for playing octaves with small hands? Are you asking for something not answered here: http://music.stackexchange.com/questions/8013/do-the-hands-sizes-affect-piano-learning-performance ?
Answer: It sounds like my fingers are a similar length to yours. I found that the important part of reaching the octaves confidently was flexibility rather than length. Your thumb and pinky finger (or even your ring finger) can bend back further than you might think. Never force it though. As with most aspects of playing, I'm afraid it just takes time and practice to stretch comfortably.
Try playing octave scales regularly to get your hands used to it. Also try playing scales using 7th and 9th intervals (instead of octaves). It doesn't sound very tuneful, but it can help build up your strength and accuracy. From there, try running up and down scales playing full octave chords (i.e. play the major chord for whatever your root note is... e.g. C major, D major, E major, and so on). If you're feeling adventurous, try playing 1st or 2nd inversions instead so you get used to your hand being at slightly different angles.
Always warm up a little with scales etc. before you do the stretching though, and go slowly at first. You need accuracy before building up speed. Also, try to keep your hand relaxed at all times so you can stretch safely. Given enough time, you might be surprised by how far your fingers will reach.
Answer: There are advantages to small hands as far as quickness in passages requiring tight, compact scale work.  Some people with big fingers stumble over their length in these situations, others have fingers too large to slide between the black notes which is another disadvantage.
I'd say longish fingers that aren't too fat giving you a reach of a tenth is ball parking "ideal" and short fat fingers without reaching an octave or being able to slide between black notes is the least ideal.
Nevertheless, diligent people create workarounds and make great music regardless of their natural build.  Milan kundera said the concept of idyll is the worst thing to ever befall the human race because we feel forever inept compared to the perceived possibility of perfection we can't reach.  I tend to agree, best just presume you can become strong following known practices, a bit of your own gut instincts and working hard to make it happen.
Oh and least important of all is to have fun.  Joking
Answer: Of course, with problems of matching instrument and player anatomy there is always the last resort of changing the instrument to something comparable but better-suited.
With the piano, the standard concert instrument is the grand piano, and the grand piano very much has a standardized key width.  So unless you are playing at a level where you are expected to bring your own instrument, the piano is really not accommodating different player anatomies.
While upright pianos are not really used in concert, the situation may be different for cembali and some other keyboard instruments like celesta.
Smaller key sizes but a significantly different playing style and repertoire differing from the percussive character of the piano, are offered by organs, harmoniums, accordions, particularly chromatic button accordions where even small hands can easily span two octaves.  While few people are expected to bring their own organ to a concert, the other instruments can reasonably be bought and/or at least transported personally.
At any rate, it might be worthwhile seeing whether acquiring skills on a more hand-friendly instrument variant can offer new perspectives.  Whether to make a full switch at some point of time may be a different question.
Answer: I can confirm the stretching aspect.  The distance between tip of pinky and tip of thumb on my left hand is noticeably longer than on my right hand.  This is due to 8-10 years of typical left hand positions of playing large intervals.  Now I find myself attempting to play a major 10th that involves white and black keys (example: E major, 5 on E, 2 on B, 1 on G#) <- difficult....
Note: I am 6'2 and have bigger than average hands.
Answer: Stretching could be very effective, because the tissues between the fingers are stretchable. There is a good device to carry out that.
www.increasehandspan.com/test


Are there some good books about scriptwriting to study?

Question: After a little googling I found this:
The Complete Book of Scriptwriting
What are other good examples?
Comment: Community wiki?
Comment: @neilfein Of course, I flagged it to moderators since first seconds.
Answer: I think Story by Robert McKee is good. It may not go into some of the technical details you may want, but is a great book on how to tell a story.
Answer: I think 'Screenplay - the Foundations of Screenwriting' by Syd Field is considered to be "The Bible" in this area. Great book.
Answer: There is great support for script writers and film makers available from the BBC, including free advice and film showcasing.
They also have a published guide to writing, including sample screenplays by both professional and amateur writers, with in-depth reviews on each.

Filmmaking - guides, how-tos, case studies and behind-the-scenes
Showcasing - submissions page (note as of 9th February 2013 process is suspended indefinitely)
Writer's Guide - screenplay, novel, memoirs, radio play
Answer: The first book you should buy is The Screenwriter's Bible by David Trottier. This is the complete guide to formatting in hard copy. While you may rely on software to format, knowing your formatting is equally as important.
Syd Fields' - The Foundation of Screenwriting is also a great place to start. This offers the basic steps in regard to screenwriting.
But truthfully, if you want to learn how to write in a screenplay format, with all the elements of the three act structure, inciting incident and big event, the mid-point turn and the third act turn, character arc, subtext, foreshadowing, and everything else that comes with a great script, then you need to write and read.
I spent a year at Trigger Street reading and reviewing screenplays for others. While it was a year of frustration - you tell someone their script is weak and they tend to tell you to go fish - but the reward was coming away with a great deal of knowledge about what doesn't work.
Films are visual media, not dialog-driven media, unless you are Tarantino. Knowing how to direct the camera with the written word without ever giving a camera direction is a skill that can be learned.
The first important thing about screenwriting is this:
The field is very tough to break into. If you don't live in L.A. the chances of your work being found and produced are so infinitesimal that it can be discouraging. Get an L.A. post office box and a cell with an L.A. phone number and be prepared to go there at the drop of a hat.
But don't do that until you learn to write.
Second, you need to write about a dozen scripts before you get this down. With editing and polishing you may invest several years to learn the craft.
Finally, there are a great number of businesses that will take your money to "teach" you how to get in to the business. There are websites that profess they have producers come to them for new and exciting scripts. There are quite a lot of people who claim to be experts. Since the advent of the internet there is a whole cottage industry created to get you to fork over money.
Don't. Spend your time writing, and reading other's scripts at places like Trigger Street or wherever (I am not shilling for Triggerstreet, btw).
Plus, IMDB is your friend. When someone tells you they have the path, then look them up on IMDB. If they truly have produced films, you'll know. If they are full of beans, you very well could find that out too.
Most likely, you will not get any action there at Trigger Street or Zoetrope, but you will get a wealth of knowledge you cannot get by forking over 700 bucks for a three-day weekend with some guy who makes his living cashing your check and not actually working in the industry.
But the best advice is to move to L.A., get a job at a studio or with a prodco and meet people.
That, more than books, tutorials, lectures, and workshops that are all trying to sell you something wrapped up in the disguise that they have the secret to getting famous in Hollywood, is the best way to get into the business.
Good luck.
Keep in mind a fool and his money are soon parted. In this realm, that goes double.
Answer: William Goldman, author of The Princess Bride and the script for Butch Cassidy and the Sundance Kid, wrote Adventures in the Screen Trade and Which Lie Did I Tell, both of which are essentially memoirs that have insights into how he became a successful screenwriter. (They're also a lot of fun to read.)
Answer: Screenwriting:
The Complete Idiot's Guide to Screenwriting
Playwriting:
Writing for the Stage: A Practical Playwriting Guide


Conditional Probability

Question: Andy, Bob and Charley have all been serving time for grand theft auto.  The warden plans to release two of them next week at random.  However Andy is friends with one of the guards who offers to tell Andy the name of one of the prisoners being released other than himself at random.  Andy declines as he believes that if he had that information then his chances would decrease to $\frac{1}{2}$ instead of $\frac{2}{3}$.  Is Andy's concern justified?
This Problem seems obvious that his concern isn't justified, i'm just having trouble proving that's the case.  What I thought is that I would try and show that $$P(A \mid B \cup C)=\frac{2}{3}$$
Where $A$ is the event that Andy gets released $B$ is the event that Bob gets released, and $C$ is the event that Charley gets released.
Comment: How does the guard choose which name to tell in the case that he has multiple valid options?  If he always picks the lowest in alphabetical order from those available to choose from disregarding A, then the guard telling him that Charley is being released will imply that Bob is not being released changing Andy's probability to 100%... Similarly being told that Bob is being released changes things as well.  To make the problem unambiguous, you need to specify that the guard will choose one of the available names to tell uniformly at random.
Comment: True, thanks I've edited
Answer: This is a variation on the standard Monty Hall problem in that the jailer has full knowledge and chooses accordingly. We'll add the assumption that in the event $B,C$ are both being released the jailer chooses which to name uniformly at random.
At the start the state space has three elements $AB,AC,BC$ each with probability $\frac 13$.  Let $X$ be the event "the jailer says $B$".  If the jailer says $B$ then Andy knows that $AC$ is impossible.  But the probability that the true state is $AB$ must be calculated via Bayes Theorem.  We see that $$P(AB\,|\,X)=\frac {P(X\,|\,AB)\times P(AB)}{P(X\,|\,AB)\times P(AB)+P(X\,|\,BC)\times P(BC)}=\frac {1}{1+\frac 12}=\frac 23$$
Thus Andy learns nothing about himself from whatever the jailer says.
Intuitively:  This is not surprising.  In all states of the world the jailer will be able to name someone so the fact that he can name someone conveys no information.
Note:  to make the problem more like the Monty Hall problem, suppose, after saying $B$ to Andy the jailer offers Andy the chance to swap cells with $C$.  The above shows that Andy should decline!  Poor $C$ is down to a $\frac 13$ chance.  Indeed, Andy did get information regarding $C$.  The fact that the jailer named $B$ and not $C$ is evidence for the statement that $C$ is not being released. Thus Andy should stay in his own cell.

Conditional Probability


What kind of ear protection offers the best compromise between protection and sound fidelity?

Question: Useful when your drummer is loud. (that china still banging in your head after a session)
Comment: I think your description should be revised to: Useful when you play with a drummer at all--unless you play with the jazz flavor or stand 50 feet away.
Answer: The issue with a lot of ear protection is that it doesn't attenuate frequency evenly across the board. In particular, it will tend to reduce treble and mids more than bass, leaving you with a rather muffled sound. There are a number of ear plugs that seek to address this and provide even volume attenuation across the spectrum.
For $10-12 Etymotics sell some that I've heard good things about. For a much more expensive solution, you can get ear plugs custom fitted for your ear canal. These work much better, but are generally over $200. I have friends with these and they say they work very, very well in clubs and at concerts.
Answer: I have custom fitted plugs and recommend them highly. Your ears are valuable, delicate, and not as fixable/correctable as your eyes.
Cost was ~$125, if I'm recalling correctly. They should last you several years, but not forever, as your ears keep growing/stretching your entire life. (i.e., 'grandpa ears') The main cost of the plugs is the 'filter' that fits into them. Make sure you ask for a filter appropriate for a musician.
Most audiologists will guarantee the fit for a year or so. My audiologist was also happy to generate (for free) a second set of molds for me so I could get my canal phones set up as custom-fit in-ear monitors. (search the net for places that will take your molds + canal phones and send you back the customized product)
Answer: I've used the Etymotics and I recommend them for attending concerts or playing gigs. They're not too bad, and reasonably comfortable - but - do they provide enough protection when being exposed to very loud instruments quite regularly?
I don't think they do. I've stopped wearing them at our regular band practices and now wear normal ear plugs rated at SNR 36 DB.
Ok, most people probably do not want to do this. It seems a bit uncool and potentially extreme. Probably someone would say "your band is playing too loud then!"
Well, yes, they are! The other guys in my band think it's rock n roll to play very loud and ear plugs are not "cool" to them. They don't care about hearing loss - I can't change them unfortunately and I can never get them to turn down. A lot of young people who play in bands that I know are like this.
But luckly I'm not bothered by what others think, so I wear ear plugs now when practicing with the full band. I already have some hearing loss from music - I know this because I get my hearing tested at work. (I work in an office - my hearing loss is not work related). Further losing my hearing or getting tinnitus is not worth it. To hell with looking cool.
Once you get used to ear plugs it's not such a big deal. I don't really find the sound frequency issues a problem with normal earplugs once you're used to them - not for practicing anyway. But during gigs I do prefer to wear the Etymotics so I can hear the full sound better.
If I have spare money one day, I think I will invest in the custom fitted plugs that yassarian mentions.
Answer: A sort of separate answer - what we do in my band wherever possible is have all the speakers at the front of the stage so all we get on stage are monitors. This means it is quiet enough to talk normally to each other, while keeping the volume out front sufficiently high.
Admittedly this doesn't work so well in small venues, but on bigger stages and at festivals it really helps with avoiding ear pain!


Special relativity, spacetime, velocity and units

Question: We all know that space and time are the fundamental units, means no mathematical expression can express their relation to other variable fundamentally. But as we know that moving rod has a contracted length and dilated time which depend on the velocity of that rod w.r.t. an inertial frame in which the motion is happening. So it's a natural question that space and time measurements are not alone to be measured in any inertial frame but one has to specify velocity also. It sounds like 3d space and 1d time have another dimension (velocity) to be included in their totality. So velocity is also a form of space and time. So what is wrong here?
Answer: The units of space are meters (and square meters and cubic meters)
The units of time are seconds
The units of velocity are meters per second
So the units of velocity are not independent of the units of space and time.

In classical mechanics, we can measure the position of an object using only three dimensions, for example distances x, y and z in some cartesian frame of reference. We can measure the speed of an object by measuring how those distances change after some interval of time. We have only needed four dimensions x,y,z and t but two separate measurements. We can measure the length of an object using only one dimension - though we make separate measurements (along that one dimension) of each end.
In special relativity, all the above is also true and is exactly the same.
What special relativity tells us is that two observers will disagree about the measured length of an object if one is moving relative to the object and one is stationary relative to the object. The Lorentz equation describes how those two observers' measurements disagree. Each observer still only needs one spatial dimension to measure the length of the object in their own frame of reference.
Comment: it was in classical mecanics too so why did it not arise there?
Comment: @AbhinavAnand: I'm not sure which concept you mean by "it" in your comment. I have expanded my answer. Maybe that helps?
Comment: i have something to say to you in good length,but u don`t mention email id,please if u could.
Comment: How about [The h bar](http://chat.stackexchange.com/rooms/71/the-h-bar) chat room?
Comment: Well I have to wait then,need more reputation points.
Answer: As I have said space should include velocity in itself as extra dimension and same is true for time.Now as our saying if velocity is a form of space and also of time then the space and time both can be expressed in terms of velocity also. so what comes now that we will have two equations one expressing space-velocity relationship and other time-velocity relationship and inquiring these two spacial relativity expressions one can eliminate velocity from them and the only reality lefts behind and that is space time amalgamation which is a characteristic of relativity both special and general.
so i think in this way we reach our satisfaction.


To generate Flickr Gallery in my wordpress site which plugin to use

Question: recently I've checked some of the plugins that generate album from flickr photos but most of them don't work. Here is my purpose:
I want to display images that are hosted in my flickr account. Suppose, I went to a tour. Now I want to show my readers those photos as a gallery. Not all the photos from the photostream will be included, only those which are seperated by tags or somehow. I hope you've understood my problem.
Now, which plugin to use (it has to be free btw)? I'm almost get tired checking most of the available plugins and finding not working on the latest wordpress. So, I need your help.
If there's no possible way to fetch photos from flickr now, is there any other way to host my photos on different location and then creating gallery in my wordpress site?
Please make sure that it goes fine with the current version of wordpress software.
Comment: Plugin Recommendations are offtopic.
Answer: This plugin helps you for you to fulfill your requirements.
http://wordpress.org/plugins/awesome-flickr-gallery-plugin/
Comment: This doesn't work.


Derivation of formula for electric field between parallel plates

Question: So the electric field between two parallel plates is given by $E = V/d.$ How do you derive this?
Answer: Recall that the potential difference between two points $a$ and $b$ is given by
$$\Delta V=-\int_{a}^{b} \vec{E}\cdot d\vec{\ell}.$$
Consider evaluating this integral for two paralell plates, i.e. the point $a$ is in one plate and the point $b$ is in the other plate. Then, we know that the electric field between paralell plates (assuming they are very close together) is of the form
$$\vec{E}=E\hat{x},$$
where $\hat{x}$ is a unit vector perpendicular to any of the plates. Now, because the path integral that I quoted for the potential difference is path independent, I can take $d\vec{\ell}=d\vec{x}=dx\hat{x}$. Then:
$$\Delta V=-\int_{a}^{b} E\hat{x}\cdot dx\hat{x}.=-\int_{a}^{b}Edx=E(a-b).$$
In your notation, $\Delta V=V$ and $(a-b)=d$ (the sign is just a matter of the use), so, translating the above result we have
$$V=Ed \Longrightarrow E=\frac{V}{d}.$$
Answer: The second more complex possibility (but without integrals) is using the expression for capacitor
$$Q = V C$$
Since the total charge is
$$Q = \sigma A$$
and electrical field of one charged plate is
$$E' = \frac{\sigma}{2 \epsilon_0}$$
noting that there are two plates with opposite fields you get
$$E = \frac{\sigma}{\epsilon_0}$$
Combining those with expression for parallel plate capacitance
$$C = \frac{\epsilon_0 A}{l}$$
you get your expression.
But the usual derivation goes in the opposite direction ;-)


Does my electric panel need replacing?

Question: How can I tell if my electric panel needs replacing? Got up today and suddenly I lost power to a tandem breaker the breakers weren't tripped. Then realized I also lost my water pump. The water pressure switch needs to be replaced. Also have little to no power on another breaker on the same side of the box. The other breakers on that side seem to be working ok. The tandem breaker was changed, still no power. Seems like the connector to the breaker has no power even though the back of the panel has power. Any information would be helpful.
Answer: You need to check out a few additional things. From the information you've provided, your panel and breakers could be fine, but the wiring between panel and fixtures could be damaged. You can use a non-contact electrical tester to check the wiring at a few points. Start with the cables exiting your panel, and see if you can follow along to the fixtures that aren't working. If the tester indicates no power immediately outside the panel, then the problem is inside your panel. Otherwise, a little detective work can help you identify where the wiring problems may be.

Does my electric panel need replacing?


Exponential Distribution Probability question

Question: The lifetimes of three different types of computer components follow exponential distributions with parameters 1,2, and 3 (in particular, that means that the average lifetimes for the three types are 1,2, and 3 years) i.e. $$f_1(x_1) = e^{-x_1}, f_2(x_2) = \frac{1}{2}e^{-\frac{x_2}{2}}, f_3(x_3) = \frac{1}{3}e^{-\frac{x_3}{3}} $$ with support sets x_i = 0, i = 1,2,3. One component from each type is randomly sampled and the corresponding lifetimes recorded. Find $$P(X_1 > 5X_2>10X_3)$$
Comment: You need to enclose subscripts and superscripts that don't consist of a single token in braces to form a group.
Comment: thanks joriki. I think Fab got to it before me haha so wherever you are thank you Fab.
Answer: I get $1/374$ when I evaluate
$$
P\left(X_1 > 5 X_2 > 10 X_3\right) = \int_0^\infty dx_3 \  f_3\left(x_3\right) \int_{2 x_3}^\infty dx_2 \ f_2\left(x_2\right) \int_{5 x_2}^\infty dx_1 \ f_1\left(x_1\right).
$$
Answer: The basic solution technique would be something as follows...
If the failure of the first element happens at time $x$, then the failure of the second element will have to happen before a time $5x$ or greater, and event that happens with probability
$$\int_0^{5x} \frac{1}{2}e^{-\frac{t}{2}}dt = \left.-e^{-\frac{t}{2}}\right|_0^{5x} = 1-e^{-\frac{5x}{2}}$$
If you integrate the above function for all possible values of $x$ weighted by their relative probability (the first probability density function) you get
$$\int_0^\infty e^{-x} (1-e^{-\frac{5x}{2}}) dx = \int_0^\infty (e^{-x}-e^{-\frac{7x}{2}}) dx = 1 - \frac{2}{7} = \frac{5}{7}$$
So $P(X_1 > 5X_2) = \frac{5}{7}$.
Your problem is slightly more complicated, but should be solvable using the same principle.


What is "latency" in a digital recording studio?

Question: What is "Latency" in a digital recording studio?
Do I need to be worried about it? What is an "acceptable" level of latency?
What's the best way of reducing latency?
Answer: Latency is the amount of time it takes sound to travel from the source to your ears. It occurs in digital and analog setups. For example: the further you stand from your speakers the longer the latency, due to the speed of sound (~1 ms/foot or ~3 ms/meter).
In a digital studio setup your signal is traveling into your sound card where it's converted from analog to digital, mixed with other digital signals, placed on an output buss, converted back to analog, amplified and then transmitted to speakers or headphones for you to hear. That entire process takes some finite amount of time and that's usually what people are referring to when they talk about latency in a digital studio setup.
The best way to combat latency is to use hardware that supports hardware monitoring. This is where the input signals from your live sources and your playback sources (the tracks being played back on your computer) are mixed in the hardware and not in the DAW software on your computer, before being converted back to analog and sent to your monitoring setup. Hardware monitoring provides the lowest level of latency possible — less than 1 ms. Low enough that you can't really perceive the difference between the sound from say, your voice hitting your ears and the sound picked up by your microphone and sent through your hardware setup and back to your headphones hitting your ears. It feels nearly instant and that's important when you're trying to perform. If latency gets to be too large you start to hear an echo of your performance in your monitors as it takes a perceptibly longer amount of time for the signal to travel through the system and reach your ears through the monitors than it does coming straight from the source (like your mouth in the case of singing).
Software monitoring via the DAW can cause latency to spike as your signal will have to travel in to the DAW software running on your machine, get mixed, and then get sent back to your interface for D/A conversion. Modern computers, while fast, are still general computing devices and in a busy DAW project or with too many plugin effects on a live monitored signal, software-based monitoring can get terribly laggy. If you can't avoid software monitoring make sure you're not putting a lot of effects (ideally no effects at all) on the signal you're monitoring and keep the number of effects on the playback tracks to a minimum to keep the CPU use light while monitoring.
Up-to-date drivers are also a good idea. If you're on Windows ASIO drivers are a huge improvement over DirectSound drivers. On a Mac the CoreAudio library is quite awesome and supported natively by anything worth using to record.
Comment: Hardware monitoring latency should be less than 1 ms.
Answer: "Latency" is the amount of time it takes a digital sample of audio to travel from point A to point B.
For example... The amount of time it takes for audio to travel from the input of a digital mixer to the output.
It is important to keep the Latency as low as possible when mixing for a live concert or when monitoring for a recording.
Answer: Latency shouldn't be much higher than a handful of milliseconds (12–20, maybe), if possible. The lower the better, of course. You can improve your latency a number of ways—upgrading your sound card drivers, different hardware, etc. I'd recommend looking into setting up ASIO for your computer if you're having severe latency issues.