Let $U$ denote the set of all $n\times n$ matrices $A$ with complex entries such that $A$ is unitary. Then $U$, as a topological subspace of $\mathbb{C}^{n^2}$ is,   Compact, but not connected. Connected, but not compact. Connected and compact. Neither connected nor compact.   I know what the terms are but I am really not getting the idea how to solve this. Please help.
Is the set of all unitary matrices in $M_2(\mathbb{C})$ is compact? I can show that as determinant map is continuous so unitary matrices are closed but how to show they are bounded?   Please help.
The  page says that Box-Jenkins is a method of fitting an ARIMA model to a time series. Now, if I want to fit an ARIMA model to a time series, I will open up SAS, call proc ARIMA, supply the parameters $p,d,q$ and SAS will give me AR and MA coefficients. Now, I can try different combinations of $p,d,q$ and SAS will give me a set of coefficients in each case. I select the set with the lowest Akaike information criterion.  My question is: where in the above procedure did I use Box-Jenkins? Am I supposed to use Box-Jenkins to come up with initial estimates of $p,d,q$? Or did SAS use it internally somehow? Rule of thumb for number of bootstrap samples In Salesforce Marketing Cloud (SFMC), I want to unsubscribe a contact from a single publication list by using a form on a landing page.  I also want to create an Unsub event in SFMC when they submit the form.  There is some sample code from SFMC Help documents  that seems to do that for external sites. Will it work in a SFMC hosted landing page? Do I need to edit the code much? SQL Server: Extract Table Meta-Data (description, fields and their data types) Understanding the definition of the order of an entire function in Ahlfors's Complex Analysis Let $f: \mathbb C \to \mathbb C$ be an entire function. The order of $f$ is defined by $$\lambda=\limsup_{r \to \infty} \frac{\log \log M(r)}{\log r}, $$ where $$M(r)=\max_{|z|=r} |f(z)| .$$  Ahlfors in his Complex Analysis claims that     "According to this definition $\lambda$ is the smallest number such that       $$M(r)\leq e^{r^{\lambda+\varepsilon}} $$ for any given $\varepsilon &gt; 0$ as soon as $r$ is sufficiently large."   Why is this true?  My attempt:  We know that $$\lambda=\lim_{\rho \to \infty} \sup_{r \geq \rho} \frac{\log \log M(r)}{\log r}. $$  From the definition of the limit we have that for any $\varepsilon&gt;0$, there exists some $\rho_0&gt;0$, such that $$\left\lvert \sup_{r \geq \rho} \frac{\log \log M(r)}{\log r}-\lambda \right\rvert \leq \varepsilon ,$$ for every $\rho \geq \rho_0$. In other words $$\frac{\log \log M(r)}{\log r} \leq \lambda+\varepsilon $$ for every $r \geq \rho_0$. From here it is easy to see that $$M(r)\leq e^{r^{\lambda+\varepsilon}}, $$ for all $r \geq \rho_0$. I cannot see why $\lambda$ is the smallest number with this property.  Thanks in advance. Can black holes form in a finite amount of time? How can I generate isometric sprite sheets from 3D animations? Can anyone tell me if I should use inspire or inspires in this phrase?     An extraordinary leader whose vision, values, integrity and boundless curiosity inspires all who follow in his footsteps. CSS Pseudo-classes with inline styles I thought I remembered hearing the food agency  say that you should never reheat chicken meat after the initial cooking. However, I cannot find the statement of it anymore. Now I'm starting to suspect my memory.  Could this statement be true?  Is it unsafe to reheat chicken? Prove $[0, 1]$ and $(0, 1]$ are equinumerous by use of bijection What my thought was that the bijection was a piecewise function:  $f(x) = 1/n+1$ if $x = 1/n$ for some $n \in \Bbb N$ and $x=1/n$ if $x \neq1/n$ for some $n \in \Bbb N$.  However, the textbook says this is incorrect. I don't actually see why. Was it a matter of brackets or the open variable $(0,1]$, which is what I tend to think. Why can't I import "pygtk" with Python 3.2 from PyDev? Solidify conundrum? I stumbled across a solidify issue, I cannot wrap my head around. I have a simple mesh, consisting of three faces.  When adding a solidify modifier, I expect to get an object with three walls, where every angle is square. However, whatever I try, tweaking the various solidify parameters, what I get is something like the following, with a skewed rim.  Did I hit a bug, or is it a limitation of the solidify modifier? Is there a workaround? What is attached to this spigot and how to remove Deleting array elements in JavaScript - delete vs splice How to avoid WSP deployment globally using Visual Studio 2010? How can we avoid the Globally Deployment of a WSP using Visual Studio 2010? Cannot create an array of LinkedLists in Java...? How do I copy Team Fortress 2 to other computers? Is there a way to get the (to-be-generated) SQL from a Hibernate Criteria?  Ideally, I would have something like:  Criteria criteria = session.createCriteria(Operator.class);  ... build up the criteria ... ... and then do something like ...  String sql = criteria.toSql()  (But this of course does not exist)   The idea would then be to use the SQL as part of a huge 'MINUS' query (I need to find the differences between 2 identical schemas - identical in structure, not in data - and the MINUS is not supported by Hibernate)  (BTW I know I can check the SQL from the log files) how to remove object from NSDictionary