Is it possible (and also meaningful) to do two PhDs?
Is doing two PhDs a good path?
When I open the terminal on my Mac, this is what it shows:  australia:~ rod$   I don't live in Australia, don't have anything to do with Australia, nor have ever setup terminal as Australia.   Where does that name come from, why is it there, what does it mean and how do I change it (or should I even change it at all)? What does \x mean in C/C++? How do I connect to a WPA wifi network using the command line? So basically, I'd like to use iwconfig to connect to my wifi network when I'm not inside X. But I just don't see a way to do it in the man page. Any idea? What is the difference between    a parameter passed by reference a parameter passed by value?   Could you give me some examples, please? What's different about photographing at sunrise vs. sunset? I usually get better light at sunrise (compared to sunset). I do though hate to wake up early in the morning to use that light ;)  What are the biggest differences between sunrise and sunset? I have encountered a statement in Lang's Algebra (Revised Third Edition, page 53) concerning morphisms of objects that seems strange to me: "In practice, in this book we shall see that most of our morphisms are actually mappings, or closely related to mappings."  I have always been under the impression that the terms 'mapping' and 'morphism' are synonymous in the context of categories. Perhaps it is just the case that Lang defines the two in a way that they disagree, but I can't find such an instance. Are they in fact different? If so, what is an example of a morphism that is not a mapping? Jensen's Inequality implies convexity? Suppose $\phi$ is a real function on $\mathbb{R}$ such that $$\phi \Bigl(\int_0^1f(x)\,dx\Bigr)\leq \int_0^1 \phi(f)\,dx$$ for every real bounded measurable function $f$. Prove that $\phi$ is then convex.    This one is in Rudin's Real and Complex Analysis, page 74, and, to be quite honest, I am unsure what my first step to solve this problem should even be. To help think of a general methodology, I attempted this similar question, from page 71 of the same book:      Assume $\phi$ is a continuous real valued function on $(a,b)$ such that $$\phi\Bigl(\frac{x+y}{2}\Bigr)\leq\frac{\phi(x)+\phi(y)}{2}$$ for all $x, y\in (a,b).$ Prove that $\phi$ is then convex (the conclusion does not follow if continuity is omitted from the hypothesis).   I take it that the latter question is just a special case of the former (assuming $\phi$ is bounded on $(a,b)$), so I attempted to solve the latter problem first. My attempt was to note that \begin{align*} \phi\big(\lambda x + (1-\lambda)y\big) &amp;\leq \phi\Bigl(\frac{2\lambda x + 2(1-\lambda)y}{2}\Bigr) \\ &amp;\leq \frac{1}{2}\Bigl(\phi\bigl(2\lambda x\bigr)+\phi \bigl(2(1-\lambda)y\bigr)\Bigr) \\ &amp; \leq \phi\bigl(\lambda x\bigr)+\phi\bigl((1-\lambda)y\bigr) \end{align*} with the latter inequality justified simply by applying the hypothesis again twice to the previous expression.   From here, however, I am stuck; I cannot justify "popping out" the $\lambda$ and the $(1-\lambda)$ in the last inequality via some bound afforded by the hypothesis and/or the continuity of $\phi$. The reasoning my book uses is as follows:   Since $(3+i)(3-i) = 10$, $10 + \langle 3+i\rangle = 0 + \langle 3+i\rangle $. Also, $i + \langle 3+i\rangle = -3 + \langle 3+i\rangle = 7 + \langle 3+i\rangle$. So, $\mathbb{Z}[i]/\langle 3+i\rangle = \{k + \langle 3+i\rangle \mid k = 0,1,\ldots ,9\}$, since $1 + \langle3+i\rangle$ has additive order $10$.   I do not understand why the additive order of $1 + \langle 3+i\rangle$ is $10$, or why the fact that $(3+i)(3-i) = 10$, shows the additive order or $1 + \langle 3+i\rangle$  is $10$. If someone could please explain this I would greatly appreciate it.   Note: I apologize for not using MathJax to write this post. I intend to learn it over the coming weekend. I have the following reference:  @MISC{EX2012,   author = {{S}ingle {A}uthor {O}rganization},   year = {2012},   title = {Example} }   A citation for this is breaking after "Author", but extending beyond the margin, as shown in the following example layout in the PDF:  Demo text demo text demo to margin Demo text which cites it (Single Author Organization, 2012) and flows over the margin.   How can I solve this? I am using natbib and citing with \citep{EX2012}. Blender 2.8 contains a number of HDRi's in it by default for the LookDev. I'd like to know how to use them in final renders (EEVEE or Cycles), because quite frankly they appear fantastic. Can you grammatically end a sentence with "with"? Do you want to come with? Can I come with?  I seem to hear this construction more often in recent years, but it still grates on my ear. I know it's often said that one shouldn't , but I class that rule along with  (i.e. — pedantic tosh). Is it always informal/casual speech to end a sentence with &quot;with&quot;? Was it ever thus? Operation not permitted turning off airplay mirroring What are the most commonly used and basic Apache htaccess redirects? This question is here so we can offer users who are looking for information on how to make one or more common or basic redirects in Apache using the htaccess file. All future questions pertaining to finding information that is that is covered by the question should be closed as a duplication of this question. .  Whats the point in this question? The idea while not perfect is catch the most commonly asked questions regarding redirects using the  htaccess on the Apache platform either on  some type of lamp or a live server. The type of answers should be generally those that you could imagine are used by 100,000’s of sites world-wide and are constantly asked here at Pro Webmasters repeatedly over and over in various forms.  A few examples of the type of answers we are looking for:   How can I redirect non-www to www? How can I redirect a sub domain to the main domain? How can I redirect a sub folder from domain to a root or a subdomain?  How can I redirect an old URL to a new URL?   A few examples of the types of answers that we are not looking for:   Answers that do not involve a redirect. Any answers relating to NGinx, IIS or any other non-Apache platform. Answers that involve custom and complex string or query removals.   Resources for Advanced to Complex Mod_Rewrite Rules:      Please note: that this question is still in construction and may need some refining either by myself or a real moderator of Pro Webmasters, if you have any concerns or questions . A simple inequality for floor function Question:  Is exception handling in Java actually slow?  Conventional wisdom, as well as a lot of Google results, says that exceptional logic shouldn't be used for normal program flow in Java.  Two reasons are usually given,   it is really slow - even an order of magnitude slower than regular code (the reasons given vary),     and    it is messy because people expect only errors to be handled in exceptional code.     This question is about #1.  As an example,  describes Java exception handling as "very slow" and relates the slowness to the creation of the exception message string - "this string is then used in creating the exception object that is thrown. This is not fast."  The article  says that "the reason for this is due to the object creation aspect of exception handling, which thereby makes throwing exceptions inherently slow".  Another reason out there is that the stack trace generation is what slows it down.  My testing (using Java 1.6.0_07, Java HotSpot 10.0, on 32 bit Linux), indicates that exception handling is no slower than regular code.  I tried running a method in a loop that executes some code.  At the end of the method, I use a boolean to indicate whether to return or throw.  This way the actual processing is the same. I tried running the methods in different orders and averaging my test times, thinking it may have been the JVM warming up.  In all my tests, the throw was at least as fast as the return, if not faster (up to 3.1% faster).  I am completely open to the possibility that my tests were wrong, but I haven't seen anything out there in the way of the code sample, test comparisons, or results in the last year or two that show exception handling in Java to actually be slow.  What leads me down this path was an API I needed to use that threw exceptions as part of normal control logic.  I wanted to correct them in their usage, but now I may not be able to.  Will I instead have to praise them on their forward thinking?  In the paper , the authors suggest that the presence of exception handlers alone, even if no exceptions are thrown, is enough to prevent the JIT compiler from optimizing the code properly, thus slowing it down.  I haven't tested this theory yet. Tangent bundle : is a manifold I have studied what a differentiable manifold is, and what a tangent space at a given point is, and read the proof that its dimension is equal to the dimension of the manifold. Here a tangent vector is a derivation on the germs of differentiable functions at a point.  Now I am trying to see that the tangent bundle is indeed a differentiable manifold. I get that for an open set $U$ in Eucliden space, it takes the form $U \times \mathbb R^n$ with the vector $\sum a_i x_i$ giving the tangent vector $\sum a_i \partial /\partial x_i$. Now the book says that it is "obvious" that these glue up and give a differentiable manifold.  I may be stupid; but I will be grateful if somebody can hold my hand through this "obvious" statement. "Who wants ice-cream?" — Should I say "(not) I" or "(not) me"? Where does Google Chrome automatically save pages? Does the Planck scale imply that spacetime is discrete? On a quantum scale the smallest unit is the , which is a discrete measure.  There several question that come to mind:   Does that mean that particles can only live in a discrete grid-like structure,  i.e. have to "magically" jump from one pocket to the next? But where are they in between? Does that even give rise to the old paradox that movement as such is impossible (e.g. )? Does the same hold true  for time (i.e. that it is discrete) - with all the ensuing paradoxes? Mathematically does it mean that you have to use difference equations instead of differential equations? (And sums instead of integrals?) From the point of view of the space metric do you have to use a discrete metric (e.g. the ) instead of good old Pythagoras?   Thank you for giving me some answers and/or references where I can turn to.  Update: I just saw this call for papers - it seems to be quite a topic after all: Is Reality Digital or Analog? FQXi Essay Contest, 2011. , , . One can find some pretty amazing papers over there. Studying the equation $\ln(x)- 1+ x^2=0$