For sure it's a really silly question, but I can't find a solution: how can I change the font of just the formulas in a TeXLive document?  I want a style where the "f" (for "function") is elegant, slim, tall, a bit oblicuous and with serifs, similar to a little integral sign, and the "a" is nearly a circle, like this one:     Instead, I get a really awful style, with an "f" too litle and fat.    Does somebody know the name of the font and how can I change it?  All the best and thanks a lot!!
In a LaTeX article, the math characters are more "curvy" than the text characters:  \documentclass[12pt]{article} \begin{document}  $x^2 + y^2 = z^2$ \end{document}     In a beamer presentation, the math characters do not have the same curves:  \documentclass{beamer} \begin{document} \begin{frame}  $x^2 + y^2 = z^2$ \end{frame} \end{document}     Question  How can I get the beamer math to look just like the article math?  I would prefer if the solution was a single line (that I could place at the top of my LaTeX file) as opposed to something that needs to appear next to every piece of math.
Seasonal Loan Amortization Hi I can compute a Basic Loan Amortization Schedule, But now I'm trying to Calculate a Seasonal Loan Amortization Schedule . So for example A loan starts at January And Will go on for 3 years, with Monthly Payments. Interest is at 3% Annually and is compounded Annually. During the months of September, October, November, December It'll only accumulate Interest But no payments and principal. Principal is 100000. How Do I calculate Payments and interest. I would like to be able to write a Java class in one package which can access non-public methods of a class in another package without having to make it a subclass of the other class. Is this possible? Add a linebreak in an HTML text area How can i add a line break to the text area in a html page? i use VB.net for server side coding. I know that it is defined such that there is no more than one y-value output for any given x-value input, but I"m wondering WHY it is defined that way? Why can't we apply everything we know about functions to equations that have more than one y-value output for any given x-value input?   In short, what is the benefit or reason to define a function this way?  At the same time, a little historical context would also be appreciated (i.e., when the concept originated and why).  Thanks,  Moshe Covariance of Poisson and Conditional Binomial RV's Problem Statement  Let $X$ and $Y$ be random variables such that $X \sim \text{Poisson}(\lambda)$ and $Y|X \sim \text{Binomial}(x+1,p)$. Find $\text{Cov(X,Y)}$.  Attempt at a Solution  I would like to be able to write $Y$ as $X + Z$ where $Z$ is Poisson and independent of $X$, since then by  the variance is easy to compute. To this end, write $Y|X$ as a sum of independent binomials: $ Y|X = Z_1|X + Z_2|X, $ where  $Z_1|X \sim \text{Binomial}(1,p)=\text{Bernoulli}(p)$ and $Z_2 | X \sim \text{Binomial}(x,p).$ Then $Z_2 \sim \text{Poisson}(\lambda p)$, which we can obtain by directly computing the pdf: \begin{aligned} P(Z_2 = z) &amp;= \sum_x P(Z_2=z, X=x)\\ &amp;= \sum_x P(Z_2=z\mid X=x)P(X=x) \\ &amp;= \sum_{x=y}^\infty \frac{e^{-\lambda} \lambda^x}{x!}\frac{x!}{z!(x-z)!}p^z(1-p)^{x-z} \\ &amp;= \frac{(\lambda p)^z}{z!}e^{-\lambda p} \sum_{x=z}^\infty \frac{[\lambda(1-p)]^{x-z} e^{-\lambda(1-p)}}{(x-z)!} \\ &amp;= \frac{(\lambda p)^z}{z!}e^{-\lambda p}. \end{aligned} However, I cannot get the same approach to simplify for $Z_1|X$, which instead involves the CDF of $X$. I also tried this approach on $Y|X$ directly, hoping to obtain a sum in the form of the expectation of $X$, but I can't seem to reduce it. Even if I could, I'd still need to compute $E[XY]$ for the covariance. I suspect there may be a better approach than grinding through several more sums. Present Perfect vs. Present Perfect Continuous how are you?  Well, my biggest doubt at the moment is the difference between these two tenses. Actually, the more I study the more I have doubts with these tenses.      /         These similar threads helped me to clarify and reiterate my previous understanding.   I'm not posting in these threads because the site suggests avoiding asking for clarification (I don't know why because it would avoid new threads with the same content).  My main doubt is as follows:     I've lived in New York for two years.   In my understanding, the sentence above implies (1) that I lived in NY for two years and now I live in another place; or (2) I'm moving to another city after two years living in NY; or (3) I lived in NY for two years, then I moved to another place for some period and, finally, I'm returning. Is that correct?     I've been living in New York for two years.   Whereas the sentence above, in my understanding, implies that I lived in NY for two years and I still living there.  Anyway, many sources that I've already read say that these two sentences have the same meaning and are interchangeable. Therein lies my question. Is that correct? Because if these two sentences are interchangeable, it destroys all my understanding.  Thanks in advance. I read a novel where several enemy alien species were stranded together on an interdicted planet.  They had to recycle everything and keep hidden. By "keep hidden" I mean make sure there is no evidence of their presence visible from space. They recycled everything and lived in camouflaged dwellings.  The younger generation was building a mixed culture community until the older home species showed up.  One of the alien races had a body made of rings or donuts of gases that mixed to express itself. Members of this species could be taken over and controlled by rings transferred from another member of the species.  The book may be 20 years old or more. What does the term "86'd" relate to? What does it mean when someone or something is referred to as being "86'd"? Question about the proof of Ramsey's Theorem I was reading up on a proof of Ramsey's Theorem and I can't understand this part of the proof:      Pick a vertex $v$ from the graph, and partition the remaining vertices into two sets $M$ and $N$, such that for every vertex $w$, $w$ is in $M$ if $(v, w)$ is blue, and $w$ is in $N$ if $(v, w)$ is red. Because the graph has $R(r - 1, s) + R(r, s - 1) = |M| + |N| + 1$ vertices, it follows that either $|M| \geq R(r − 1, s)$ or $|N| \geq R(r, s − 1)$.   Why is that $|M| \geq R(r − 1, s)$ or $|N| \geq R(r, s − 1)$? I know from the proof of $R(3,3) = 6$ that given a vertex, at least $3$ are guaranteed to be either red or blue, so what is the pigeonhole argument for the general case? How can I automatically save screen shots by the press on the Prt Scr button? I want a screen shot to be saved automatically to a location I specify, as soon as I press the Prt Scr button on my keyboard, or the Alt+Prt Scr combo. I also want the date and time to be used as file name for each new screen shot. And I want the files to be saved as PNG images.  Is there a Windows program that would allow me to do just this? I don't want any other fancy features like editing and making notes, etc. just a plain simple program that will either automatically save the screen shots to a pre-set location or prompt me where I want to save it. I don't want to go through MS Paint to save the shots.  I guess what I'm after is a little bit of Linux behavior of Print Screen, but only for Windows. And I additionally want the files to be named by the date and time they were taken.  Update:  Meanwhile, I have found one called Greenshot. But I don't know how to get the file name pattern right.  This is the default pattern.  ${capturetime:d"yyyy-MM-dd HH_mm_ss"}-${title}   Can someone explain this? Why do they have the title capturetime and the quotation marks? It produces file names like this.  2013-01-26 15_24_28-Greenshot.png   And this is what it says about the file patterns in the program description.  ${YYYY} year, 4 digits ${MM} month, 2 digits ${DD} day, 2 digits ${hh} hour, 2 digits ${mm} minute, 2 digits ${ss} second, 2 digits ${NUM} incremental number, 6 digits ${title} Window title ${user} Windows user ${domain} Windows domain ${hostname} PC name   How do I get files that include year, month and day, separated by a dash, followed by hour, minute and second? I want to include a time for uniqueness of the file name. TSA broke a lock for which they have a master key. How can I claim compensation? Python: [Errno 2] No such file or directory: 'lines.txt' Set a default parameter value for a JavaScript function How much money did Harry Potter have? So, we know Harry . By descriptions from the books, it looks like he had enough money to spend during his school years with plenty to spare for later life.  Is there an estimate on how much money he had? How much would that be in muggle money? Was he extremely rich?  I'm thinking here that he could have received more than just an inheritance. For example, anonymous supporters could have given him money through the bank while he was a baby, or when he was about to go to Hogwarts, and he wouldn't have known (not even Dumbledore would have known). If the matrix $A^3 = 0$, is $A$ singular? How can I reuse existing materials, objects, etc from an existing .blend? Tools to measure the nonrandomness of database I was working on historical data looking for anomalous patterns that we would not expect to occur at random. I'd like to create a scheme to analyze data and markets to test for statistical significance and consistency over time.  Question : Are there some tools we could use to evaluate the nonrandomness of a database? What do we use usually to say that something is random or not (statistically)? Figure we work with change in some value over time. How to apply for a UK standard visitor visa as a family? Modules over commutative rings I'm trying to get my head around modules, and there's a problem that's bothering me regarding scalar multiplication from the left vs from the right.  In many books/articles I've read, the author may refer to a left $R$-module $M$, and then continue to talk of terms such as $xr$, where $x\in M$, $r\in R$. What is right scalar multiplication in a left module? Does it even make sense to talk about it?  I've been trying to show that over a commutative ring, right scalar multiplication and left scalar multiplication are the same thing, but I've not managed it so far. I've googled it to no avail, and I can't see why the distinction between left and right modules disappears when the base ring is commutative.  Thanks for any replies! Do electrons move around a circuit? We could imagine a simple electronic circuit composed by a power source and a resistor.   It is usual find descriptions as "The moving charged particles in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom, and can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors." (wikipedia ). That made me imagine electrons going from power -, running by the wires, crossing the resistor and returning to power +, where they suffer a new kick to power -. All that at near the speed of light.  In this model, it is easy to define "electrical current intensity" as proportional to the number of electrons per second that cross one specific point of the circuit.  However, looking for the physics of resistivity, I can read the phrase "The actual drift velocity of electrons is very small, in the order of magnitude of a meter per hour." (wikipedia ). This is a complete different point of view, where electrons are more or less fixed around a fixed position (or moving very slowly), an electricity is a wave of "collisions" or "jumps" of electrons, like in a Newton's cradle (or "do the wave" as public in a football match). Obviously, we do not need severals hours from the switch on to the light on.  So, the question is, do electrons move around a circuit ? References to band theory are welcome.  A related question is: if electrons doesn't moves along the circuit, what is "electrical current intensity"?  Note: I known there are similar questions already posted, but answers of the ones I've read are not very detailed (could be I've not found the best ones). Please, be a few patient before "close vote".