I know that IList is the interface and List is the concrete type but I still don't know when to use each one. Is there a better way to decide when to use the interface or the concrete type with some practical scenario.  I want to know why I use IList and why I use List in our project.
Can anyone explain to me why I would want to use IList over List in C#?  Related question:
Is there a word for describing people who know many things but superficially? Is there an appropriate word for the antonym of "full-stack", as in programming? Someone who knows a lot of things just as a full-stack programmer, but without mastering them. I shall assume that the sun is at rest, so before the half mass disappear, the orbit of earth is an ellipse. Apache SSL VirtualHosts on a single IP using UCC/SAN certificate I need to host several Apache virtual hosts with SSL from a single IP.  Now - I understand that because SSL wraps around the HTTP request, there's no way to know which host is being requested until a public key has been sent to the client first. This essentially breaks the possibility of SSL virtual hosts using a standard SSL certificate.  I have obtained a Unified Communications Certificate (UCC), otherwise known as a Subject Alternative Name (SAN) certificate. This allows me to serve the same certificate for multiple domains.  I would like this to be the certificate served by Apache for any SSL request - and then have Apache resolve the virtual host as usual, once the encryption has been established.  How should I configure Apache for this? I have tried to research how this can be done, but all I can find are quotes which say that it is possible, but no specifics:    wiki.apache.org/httpd/NameBasedSSLVHostsWithSNI     While Apache can renegotiate the SSL   connection later after seeing the   hostname in the request (and does),   that's too late to pick the right   server certificate to use to match the   request hostname during the initial   handshake, resulting in browser   warnings/errors about certificates   having the wrong hostname in them.   serverfault.com/questions/48334/apache-virtual-hosts-with-ssl     Incidentally, it is possible to have   multiple SSL-secured named virtual   hosts on a single IP address - I do it   on my website - but it produces all   sorts of warnings in the Apache logs,   and certificate warnings in the   browser. I certainly wouldn't   recommend it for a production site   that needs to look clean.   -David Jul 31 at 4:58   www.digicert.com/subject-alternative-name.htm     Virtual Host Multiple SSL sites on a single   IP address. Hosting multiple   SSL-enabled sites on a single server   typically requires a unique IP address   per site, but a certificate with   Subject Alternative Names can solve   this problem. Microsoft IIS 6 and   Apache are both able to Virtual Host   HTTPS sites using Unified   Communications SSL, also known as SAN   certificates.     Please help. Indentation of continued lines in algorithmicx Trying to get the indentation right within the algorithmic environment I run into trouble, and all the solutions posted so far have not been able to solve my problem as I'd like to see it solved.  I want continued lines to have an indentation w.r.t the initial line (new to this forum and yet unable to post images).  However, the best I get with what I've found on this forum is either a fixed indentation for all continued lines (i.e., no difference if the initial line was indented or not), or the same indentation as the initial line (see MWE below).  Anybody has an answer to this?  \documentclass[10pt, A4]{report} \usepackage{algorithm} \usepackage{algpseudocode}  \begin{document}  \begin{algorithmic}\raggedright  \State Define N\_crf as the number of points on the circumference of the hyperstreamline, which will define its cross-sectional area at each r  \For {n = 1 : number of tracts}  \State \parbox[t]{\dimexpr\linewidth-\algorithmicindent\relax}{define N\_crf points creating a unit circle around r(n,i), in the plane perpendicular to t(n,i).}\strut  \EndFor  \end{algorithmic}  \end{document} Setting: Let $\sum a_n z^n$ have radius of convergence $R$.  We have that  $$ R = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} $$  via Hadamard's formula for the radius of convergence.  Question: What are the radii of convergence for (i) $\sum a_n z^{2n}$ and (ii) $\sum a_n^2 z^n$?  Attempt for $\sum a_n^2 z^n$:   For ease of notation, let $R_1$ and $R_2$ denote the radii of convergence for power series $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ respectively. From Hadamard's formula, we then have  $$ R_2 = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n^2 \right|^{1/n}} = \left( \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} \right)^2 = R^2 $$   But what about $R_1$? Does time stretch all the way back for infinity or was there a point when time appears to start in the universe?  I remember reading long ago somewhere that according to one theory time began shortly before the creation of the universe.  Does time have a starting point of note? I'm not sure which of the following sentences is correct. Is the comma mandatory, optional or unnecessary? I've googled a bit about this topic, but I got confused.     Our mapping contains 2000 words, which map to more than one lemma.   or     Our mapping contains 2000 words which map to more than one lemma.   Context: In total, there are more than 2000 words.  I've read  . If I understand the answers correctly, my "which map to more than one lemma" is a defining clause and no comma is required. But is it wrong to add one? Finding solution of non linear DE $x\ddot{x}-\dot{x}^2=1$ I am looking for help on how to find the solution of the following differential equation,  $$x\ddot{x}-\dot{x}^2=1,$$  which comes from solving the Euler-Lagrange equations for the lagrangian $L=x\sqrt{\dot{x}^2+1}$. It is from an exercise in my field theory course. My professor provided me with the solution $x(t)=c_1\cosh{\left(\frac{t-c_2}{c_1}\right)}$, which is a solution when plugged into the equation, but does not give any derivation.   Is there a way to solve this DE other than an educated guess? If so how? How do I show a function on 2-adic units is continuous (using the 2-adic metric)?   I'd be happy to learn the general rule or definition. But in particular I need to show that $f(x)=\dfrac{3x+1}{2^{v_2(3x+1)}}$ is continuous at all odd numbers.  Since the function is isometric in $\lvert\cdot\rvert_2$, i.e. since $\lvert f(x)\rvert_2=\lvert x\rvert_2$ every orbit of the function is duplicated, multiplied by any power of $2$.  This can therefore be formulated in various ways; as a function though the odd numbers, through the dyadic rationals, but the following seems good to work with.  If we let $n$ be a positive integer and $k$ be the power of $2$ we can define:  $f(2^k(2n+1))=(3(2n+1)+1)\cdot2^k\cdot\lvert3(2n+1)+1\rvert_2$  So $f(2^k(2n+1)=(3n+2)\times2^k\times\lvert3n+2\rvert_2$  Here is what I have so far:  I think to prove continuity in the 2-adic metric I need $\lvert x_n-x\rvert_2=0\implies\lvert f(x_n)-f(x)\rvert_2=0$  I think $k$ and $n$ are independent so I think I can examine them independently.  Taking $k$ to infinity brings both $x$ and $f(x)$ to zero so that seems to satisfies the continuity requirement.  Moving on to $n$; this seems to be an exercise in proving convergence within odd integers which are in a sense a subset of the 2-adic units.  I know all Cauchy sequences in these converge to 2-adic units but not much more than that.  However I do have a little insight into this particular function.  For example if we examine the inputs $x$ which map to any given output of $f(x)$, it can fairly easily be shown that these $x$'s take the form of a set $\left\{4^mp+\dfrac{4^m-1}{3}:m,n\in\mathbb{N}\right\}$ so, at least for any given output $f(x)$ the inputs always converge to $x=\frac{-1}{3}$ as the intervals between them become large powers of $2$.  In fact the orbit of the function $a(2^kx)=2^k(4x+1)$ on variation of $x$ and holding $k$ fixed is in a sense orthogonal to $f(x)$; which is a restatement of the above except not in closed form. I want to decrease the vertical space between the top of the page and the chapter heading. I have tried to follow the instructions for titlesec but I am not successful. I have tried the following two setups without any changes occuring.  First:  \documentclass[12pt]{report}   \usepackage[compact]{titlesec}   \begin{document}   \chapter{Characters}  The origin of the group determinant begins with Richard Dedekind in the late 1800's. He began to explore the idea after studying the discriminant in a normal field [A]. He made several observations about the group determinant, but was only able to prove some of them.   \end{document}   Second:  \documentclass[12pt]{report}   \usepackage{titlesec}   \titleformat{\chapter}[display]   {\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}   \titlespacing{\chapter}{0pt}{0pt}{0pt}   \begin{document}   \chapter{Characters}    The origin of the group determinant begins with Richard Dedekind in the late 1800's. He began to explore the idea after studying the discriminant in a normal field [A]. He made several observations about the group determinant, but was only able to prove some of them.   \end{document} Possible Duplicate:          Proof to the formula  $$1+x+x^2+x^3+\cdots+x^n = \frac{x^{n+1}-1}{x-1}.$$ CSS Pseudo-classes with inline styles Can we have the table name as "option" in MySQL? I am very, very new to MYSQL.I tried to create a table named "option". My SQL Query is :  create table option(   id int not null primary key auto_increment,  choice varchar(30)  )  While executing this query it shows the following error  Error Code : 1064 You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'option( id int not null primary key auto_increment, choice varchar(30) )' at line 1 (0 ms taken)  If I try with the table name as "choice" it is working.  can we have the table name as "option" in mysql?   thanks Find a recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s or two consecutive 1s. Note: Problem from "Kenneth Rosen's DM and it's applications" and solution from "Students solution guide for use with ... applications"  Let P(n) be the number of strings not containg two containing two consecutive zeros or two consecutive ones.  I got the answer  P(n)=P(n-1)+2P(n-2)+2P(n-3)+...+2P(0) +2  but then the book says the sequence also satisfies the recurrence relation  P(n)=2P(n-1)+P(n-2). I am not able to understand this part. Why shouldn't I mix tabs and spaces? What does this $\asymp$ symbol mean? (subject: analytic number theory) I'm reading a  by Andrew Granville on analytic number theory.  On page 22 of the paper, there appears a strange looking symbol, undefined.  I've circled it in red in the screenshot below.    Since it's not defined in the paper, I'm assuming it must be standard notation.   From the context, I'm assuming it means something like "as compared to", or "with reference to", but that's just a guess.  Can anyone identify the symbol, even better explain what it means and/or provide a reference?  Is there a name to speak the symbol?  Thanks in advance. Integrating $\int \sin^n{x} \ dx$ I am working on trying to solve this problem:     Prove: $\int \sin^n{x} \ dx = -\frac{1}{n} \cos{x} \cdot \sin^{n - 1}{x} + \frac{n - 1}{n} \int \sin^{n - 2}{x} \ dx$   Here are the steps that I follow in the example that I am reading:     $u = \sin^{n - 1}{x}$      $du = (n - 1) \cdot \sin^{n - 2}{x} \cdot \cos{x} \ dx$      $v = -\cos{x}$      $dv = \sin{x} \ dx$            $\int \sin^n{x} \ dx =  \sin^{n - 1}{x} \cdot \sin{x} \ dx$      $\int \sin^n{x} \ dx = \underbrace{\sin^{n - 1}{x}}_{u} \cdot \underbrace{-\cos{x}}_{v} - \int \underbrace{-\cos{x}}_{v} \cdot \underbrace{(n - 1) \cdot \sin^{n - 2}{x} \cdot \cos{x} \ dx}_{du}$      $\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \cdot \cos^{2}{x} \ dx$      $\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \cdot \left(1 - \sin^{2}{x}\right) \ dx$   Here is where I get lost. How did we go from $\int \sin^{n - 2}{x} \cdot \left(1 - \sin^{2}{x}\right) \ dx$ to $\int \sin^{n - 2}{x} \ dx - (n - 1) \int \sin^{n}{x} \ dx$? Even more specifically, where did $\sin^{n}{x}$ come from?     $\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \ dx - (n - 1) \int \sin^{n}{x} \ dx$   I get this part.     $n\int \sin^n{x} \ dx = -\cos{x} \cdot \sin^{n - 1}{x} + (n - 1)\int \sin^{n - 2}{x} \ dx$      $\int \sin^n{x} \ dx = -\frac{1}{n} \cos{x} \cdot x \ \sin^{n - 1}{x} + \frac{n - 1}{n} \int \sin^{n - 2}{x} \ dx$   Could someone please explain what I am missing?  Thank you for your time. Is there a way to install fonts on wine?   I'm looking to install fonts so i can use them to render text differently on various apps. Specifically myriad. Why are American-style options worth more than European-style options? Why are American-style options worth more than European-style options?   I realize I can exercise American-style options anytime before the  expire, but I can only exercise European-style options during their  "exercise period" (usually right when they expire, but no earlier).   So it makes sense that an American option is worth at least as much as  a European option.   But why is it worth more? If I exercise my American option early, I  may make more money than waiting until expiration, but I also may make  less. Mathematically, there's no advantage, since I'm equally likely  to make as much money by waiting for expiration.   Mathematically speaking, is there ever a good reason to exercise an  American option early?   I realize people don't always behave logically, but even the formulas  that valuate options show that American options are worth more.   EDIT (answering comments):    Many of the comments people made would apply to lookback options  (), but not to American  options.  American options can do everything European options can and more. I  understand that, and that means American options can't be worth any  LESS than European options, but I'm still not clear on how you would  mathematically calculate this extra value.  @Aaronaught: "The difference between an American and European  option is the difference between getting N chances to get it right (N  being the number of days 'til expiration) and getting just one  chance. It should be easy to see why you're more likely to profit  with the former, even if you can't accurately predict price  movement."    REPLY: I don't think you really get N chances. Once you exercise the  option, that's it, no more chances. And, if you decide not to exercise  the option today, and the underlying's price falls, you can't go back  in time and exercise it yesterday.    @jdsweet: Think of it this way, if you traveled back through time  one month - with perfect knowledge of AAPL's stock price over that  period - which happens to peak viciously then return to its old price  at the end of the period - wouldn't you pay more for an American  option?    REPLY: Well, no. I'd simply buy a cheaper European option that expires  right at the spike. Or, I'd buy a European option that expires later,  and sell it when the spike occurs. American options don't give you  precognition, so you're still guessing as to when to sell/exercise.    @jdsweet: "one of the more common reasons people exercise (as  opposed to sell) an American option before expiration is if an  unexpected dividend (larger than remaining time value of the option)  was just announced that's going to be paid before the option contract  expires"    REPLY: This makes sense. I'm actually trading FOREX options, so there  is no dividend. In that scenario, are European and American options  worth the same? Creation timestamp and last update timestamp with Hibernate and MySQL For a certain Hibernate entity we have a requirement to store its creation time and the last time it was updated.  How would you design this?   What data types would you use in the database (assuming MySQL, possibly in a different timezone that the JVM)?  Will the data types be timezone-aware? What data types would you use in Java (Date, Calendar, long, ...)? Whom would you make responsible for setting the timestamps&mdash;the database, the ORM framework (Hibernate), or the application programmer? What annotations would you use for the mapping (e.g. @Temporal)?   I'm not only looking for a working solution, but for a safe and well-designed solution.