Trouble finding if a string exists in an ArrayList
How do I compare strings in Java?
Real valued analytic function defined on a connected set is constant Let $G$ be a connected set and $f : G \rightarrow \mathbb{C}$ a real valued analytic function. Prove that $f$ is constant.    My idea to prove the result is to prove a subset $A \neq \varnothing$ of the connected set $G$ is both open and closed. So $G=A$ Take $f(w) = a$ $$A = \{z\colon z \in G, f(z) = a\}$$ Now I want to show that $A$ is infinite. How to do it? After that it is easy to prove $A=G$. I know that Windows XP 32-bit can be configured, through , to support more than 3.5&nbsp;GB of RAM.  Is there a good tutorial to do this with Windows 7 32-bit?  As to why I don't simply use 64-bit Windows 7: The software for my Internet connection (cell phone-as-modem) will only work in 32-bit environments. Firstly, I apologise if my thinking is completely incorrect - I am by no means a physicist (yet!), I have included layman illustrations to hopefully assist in explaining my thinking.  I am imagining the big bang to be, for lack of a better word, an explosion, thus the universe to be progressively expanding:    Therefore, to me it seems logical to suggest that there is an edge.  If this is the case, then is it reasonable to suggest that explosion + edge = 'bright edge'? Where light projects in all directions at the edge, not just outwards into the 'nothingness'.     So, this brings me to my question: why, when someone looks deeply enough 'at the edge' do they see an absence of light?   Again, apologies if I'm jumping to irrational conclusions &amp; am way off. Mistakenly filed as Exempt from income tax witholdings for entire year 2019 I am a basic 30 year old filing Single, W2, healthy working individual. No dependents, no additional schedules, capital gains or losses other than Student Loan interest expense.   I started a new job in January 2019 and somehow during my new hire enrollment, "I or someone" marked in my file as Exempt... I am pretty familiar with filing my own 1040 (as its pretty basic)and I know for a fact that I would never for under any reason think that I am Exempt from absolutely anything tax related. Nobody in my new job's HR department reached out to confirm whether this Exemption was correct or not with me personally. My CPA said that anytime they receive an Exempt W-4 form, that they automatically return the form to the employer to confirm.   I unknowingly went 11 full months in 2019 without any taxes being withheld. Of course my paycheck was more than before, but I also got a better/higher salary job, so I never thought about the difference being from not paying taxes. And, no I do not print out my paystubs. It’s all through Paycom and it clearly shows you your gross pay &amp; a "$XXX" amount in deductions/withholdings - kicker is, you have to click the drop down menu to actually see the entire breakdown. At which point, I never saw the big $0 in taxes being withheld... I know the taxes have to be paid one way or another, but I don't feel like I should be entirely responsible for a $5k-$6k tax liability for a HR clerical error. Even if I did actually input it incorrectly the first time.   Is there a way to check with the IRS to see if they indeed receive my file as Exempt and if they did actually return it to my Employer? I’m just wondering if either HR forgot to follow up with me or even IF the IRS does actually cull these exempt requests in the first place? I don't have the liquidity to simply pay the IRS all at once.   What would be my best option going forward? Browse for Servers does not display local instance I just installed SQL Server and SQL Server Management Studio but it doesn't show anything in servers list and I don't know how to connect to it.  This shows that I have installed SQL Server:        But in this image you can see that my Browse for Servers dialog is empty:        Network servers is empty too. Math.cos() gives wrong result Prove directly from the definition of the Ito's integral I am trying to solve the exercises from the book Stochastic differential equations -An Introduction with applications by Bernt Oksendal and I am stuck on 1 question.  Prove directly from the definition of Ito's integral that   $$\int_0^t B_s^2 dB_s=\frac{1}{3}B_t^3-\int_0^t B_s ds$$  I have tried for a couple of hours but I simply cannot prove it . I would be grateful if somebody could help me out , even a hint would be very helpful What tips and advice do you have for photographing the Aurora Borealis? I find that at the end of a long day, I sometimes have a large number of programs running. All which I will need to use tomorrow. Normally, this isn't an issue, I can simply lock the machine and come back tomorrow. My problem arrises when windows update launches in the middle of the night and force restarts my computer. That in turns closes all my open software. I of course save everything regularly so I don't loose anything, but I waste time reopening all of those resources whenever there is a restart.   [EDIT]  I should clarify that I still want to be able to restart my computer when an update comes down. Preventing the restart only delays the problem until later. I should have been more specific in that I want to be able to recover my working environment after a restart for any reason. Things like scheduled maintence, power loss, updates, and software installs.  [EDIT]  I can't simply have them setup to launch at startup becasuse those files change from week to week. So I need something that monitors what I have open, and gives me the option to "recover" those software sessions when I log back in.  Anyone have any suggestions on what I can do? I'd even be willing to purchase software to do this for me if that is the only option.  Thanks What setting causes OS X to let you resize windows behind the dock? I've set up my fair share of Macs over the years, but I've never been able to pinpoint what setting tells OS X that you're ok with being able to drag-resize a window vertically so that it goes behind the dock (assuming the dock is in its default position at the bottom of the screen), as opposed to only being able to resize it vertically so that it is touching the top of the dock's "space".  My work computer is a 21" iMac Core 2 Duo and it drives me crazy because I'll quickly drag-resize a window larger by pulling down and to the right but instead of staying locked vertically above the dock it'll slide behind it which I don't like so then I've gotta jiggle the window around to get it all back into visible space... my home computer (6 core tower) doesn't have this problem even though I've, from what I can tell, set it up nearly identically.  Both machines running the latest version of snow leopard.  Here's a video captured from my machine at home showing the window resize behaviour I prefer. If it helps at all I can do another one from my work machine tomorrow showing the windows resizing behind the dock. Traveling to the US with new passport, visa on the old one I have a valid B1/B2 US visa expiring about a year from now. The passport it's in expired a few years ago, and I recently got a new one.   The passport number does not match, but the national ID number, mentioned in both, does (it used to be the same as your national ID, but not anymore)  Can I travel to the US carrying both passports? Or is it asking for trouble? (I read a few years ago that it was possible, but that might have changed)  Should I just get a new visa to avoid potential complications? Is there a formal proof for $(-1) \times (-1) = 1$? It's a fundamental formula not only in arithmetic but also in the whole of math. Is there a proof for it or is it just assumed? Which is more idiomatic in a bash script: `|| true` or `|| :`? I don't do terribly much shell scripting, so I was a little surprised when I was reading  and I saw the syntax they used in this documentation:     A non-zero return from the command in any submodule causes the processing to terminate. This can be overridden by adding || : to the end of the command.   I had to look up that || : was a shorthand for forcing a command to exit successfully.  Anytime I've had to make a command exit successfully, I used || true.  Is || : considered to be more idiomatic? How to partially hide content in beamer latex? As a Graduate Mathematics student, my interest lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications of Number theory to physics. I have heard Applications of linear algebra and analysis to many branches of physics, but not number theory.  Waiting forward in receiving interesting answers! What are Virtual Methods? Why would you declare a method as "virtual".   What is the benefit in using virtual? In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermions to take vevs? Why does the Replace() string method not modify my string variable? Combining php arrays I have the following arrays in PHP (okay they are a bit bigger but the idea is what counts).  $array1 = array(1 =&gt; 'a', 2 =&gt; 'b'); $array2 = array(3 =&gt; 'c', 4 =&gt; 'd');   Essentially I want to combine the two arrays as if it were something like this  $array3 = array(1 =&gt; 'a', 2 =&gt; 'b', 3 =&gt; 'c', 4 =&gt; 'd');   Thanks Why do quantum effects dominates when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance? We say that when the thermal de Broglie wavelength is much smaller than the interparticle distance, the gas can be considered to be a classical or Maxwell–Boltzmann gas. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles.  $(V/N)^{1/3} &lt; \lambda_{th} $. My question is why do quantum effects dominate?