How the mobile phones sending and receiving signals from the satellites? who is providing these services at free of cost?
I assume it doesn't connect to anything (other than the satelite I guess), is this right? Or it does and has some kind of charge?
Spaces in which "$A \cap K$ is closed for all compact $K$" implies "$A$ is closed." Let $X$ denote a topological space. For any $A \subseteq X$, consider two possible conditions on $A$.   $A$ is closed $A \cap K$ is closed, for all compact $K \subseteq X$.   If $X$ is Hausdorff, then clearly (1) implies (2). If $X$ is metrizable, then the converse holds; see .     Questions.         What are some Hausdorff topological spaces in which (2) does not   imply (1)?   For Hausdorff topological spaces: what weaker conditions than metrizability are known to imply that (2) implies (1)? Are there any interesting characterizations of those Hausdorff spaces in which (2) implies (1)? Frobenius Inequality Rank I was looking for an answer for this problem in terms of matrices, but I really don't know how to prove this result. The proposition says that:  Let $A\in M_{m\times k}(\mathbb{C})$, $B\in M_{k\times p}(\mathbb{C})$ and $C\in M_{p\times n}(\mathbb{C})$, then $\textrm{rank}(AB)+\textrm{rank}(BC)\leq \textrm{rank}(B)+\textrm{rank}(ABC)$ How to break the Y axis in an Excel sheet I want to break the Y-axis in an Excel sheet. How can I do that?  For example, suppose I have the data in a range from 0-7000 and then range from 22000-28000. I want a break in the Y axis from 8000-20000. How do you set, clear, and toggle a bit? I just notice it now as I am new to Illustrator.  When I am in RGB mode, blending transparency seems to be easier as mode such as Screen, Multiply or Overlay looks good naturally.  If I switch the document mode to CMYK then the image is getting messed up.  I'd like to know, if CMYK is not ideal for blending options? Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.   I’m not sure what to do. Would $f$ be differentiable simply if and only if both $u$ and $v$ were differentiable?   My thinking is that if the limit $$ \lim_{h \to 0}\frac{f(z+h)-f(z)}{h} $$  exists then it would be equal to  $$ \lim_{h \to 0}\frac{u(x+h)-u(x)}{h} + i\lim_{h \to 0}\frac{v(y+h)-v(y)}{h} $$  and therefore would exist if they existed. But that doesn’t seem quite right.  I also thought about using Cauchy-Riemann equations, but seeing that I’m trying to find ones that are differentiable rather than those that aren’t, I thought they wouldn’t be of much help. Simple way of finding the locus of $z$? I am tasked to sketch the locus of complex numbers $z$ that satisfies $$(z-2+i)^2 + (z^*-2-i)^2 + 2zz^* + 6 = 0$$ I was wondering if there’s a special trick to this question, or if this is only solvable by plugging in $z=x+iy$ ? I noticed that the second term is the conjugate of the first, and wanted to substitute $w = z-2+i$, however this gives me a complicated expression for $zz^*$ which makes it more confusing. Is there a trick I’m missing out? Thanks! Edit: I have already solved it through direct substitution (parabola intersecting real axis at $x=3$ and $x=-1$) but it took a good 5 minutes or so, expanding everything correctly, which seems rather long (I was attempting it under exam conditions). I was just wondering if it is possible to exploit the $w$ substitution I made in particular. Highlight elements in the matrix How to convert numbers between hexadecimal and decimal How do you convert between hexadecimal numbers and decimal numbers in C#? MySQL Access denied for user 'root'@'localhost' In my server, everytime I try to access MySQL I get the error:        Access denied for user 'root'@'localhost' (using password: NO)   when I try mysqladmin -u root -p password I get        Access denied for user 'root'@'localhost' (using password: YES)   How can I access MySQL in my Ubuntu server 12.04? What is cool about generics, why use them? I thought I'd offer this softball to whomever would like to hit it out of the park. What are generics, what are the advantages of generics, why, where, how should I use them? Please keep it fairly basic. Thanks. Diminishing returns / non-linear reputation from “great” answers Over time I realized a very annoying property of the Stack Overflow reputation system: Easy answers to popular question are rewarded with a lot more reputation points than actually great answers. In case anybody actually needs examples for this, here are two examples from :   gained me 420 rep, I invested 2 minutes writing it, and it only was a wild guess.   took me about an hour for the research and the math and gained me 40 rep.  Now I know that you are bound to get more rep for answers that are useful to more people, and I'd say that's fine. But the current situation is quite extreme: 30% of my reputation is from 5 of my 330 answers, and they are definitely far from being my best ones.  A final example that is not from my profile, but more extreme: Do you really think  is worth 40000 reputation?  My proposition to improve that situation would be to make the reputation gain from a single answer non-linear, maybe even have it capped at a certain point. I'm not sure on how that non-linear function should look exactly, and would leave good proposals for that to users with more experience than me. What is the difference between a "link function" and a "canonical link function" for GLM What's the difference between terms 'link function' and 'canonical link function'? Also, are there any (theoretical) advantages of using one over the other?  For example, a binary response variable can be modeled using many link functions such as logit, probit, etc. But, logit here is considered the "canonical" link function. I want to use the get_option() function of wordpress in one of my theme's files, which is not related to WP, it is just located in the same directory of the other theme files. I need this file because of some extra IPN paypal related actions, but I need some values from the options table that exists in WP to be called in this page in order for it to work. I know I can't just use get_option() as this file is overlooked by wordpress. Is there any approach by including some parts of wordpress in my theme to make this functionality only work? Find a bijection from $\mathbb R$ to $\mathbb R-\mathbb N$ Find a bijection from $\mathbb R \to  \mathbb R-\mathbb N$. I want to set my function up such that all natural numbers get mapped to $n+.1$ and reals of the form $n+.1$ to $2n+.1$ is this correct? How to determine the cause of MacBook battery not charging? I see that the question &quot;why is my MacBook not charging?&quot; gets asked a lot. The problem is, there are multiple reasons. Possible points of failure are: charger, cable, magsafe connector, DC input board, logic board, battery. (Have I missed any?). What is the best sequence for a user to follow, to diagnose the problem? By way of example, here are the first steps that I usually try:  Make sure the charger is working. Either use your charger on a different Mac, or test a spare charger with your Mac.  Check the connection. There might be gunk in your port that's stopping the connector from lying flat.  Try resetting the SMC and PRAM.  If the computer boots, run Coconut Battery to determine battery status.   This is where I get a bit stuck. For example, I have a machine here that boots fine when plugged in, but not from battery. Disconnecting the MagSafe causes the machine to switch off. Sounds like it's a dead battery, except that Coconut reports the battery as detected, in good condition, but not charging. What steps should I take next? Specifically, I'm asking for a generic algorithm to help determine the source of the fault (preferably without swapping out lots of components one by one)? Combinations of selecting $n$ objects with $k$ different types Suppose that I am buying cakes for a party. There are $k$ different types and I intend to buy a total of $n$ cakes. How many different combinations of cakes could I possibly bring to the party? Fantasy Short Story that appeared in an anthology about 1968-1971 I read this short story around 1971.  The basic plot is for a steward to lead the king's son to another city state.  Along the way they have a number of interactions with people/subjects that demonstrate the immaturity of the son.  Last one involves the son beating up the suitor of a innkeeper's daughter.  When confronted by the steward, the son displays his contempt and chauvinistic regard of his future subjects and the steward kills him.  Turns out the trip was a test of his suitability to assume the crown and the steward explains to the king that he was not worthy.  Been looking in all the anthologies can seem unable to find it.  Thanks for your help How to Remove shortcut arrow from desktop icons? How do I turn off the arrow for desktop icons? The rulebook states that carrying capacity is the strength score times 15 (lbs). Find familiar allows me to get a hawk, which has a strength score of 5. This results in a carrying capacity of 75 lbs. This is well within the range of weights for small people such as gnomes or halflings. Does this mean my familiar can carry them and fly away (given they do not struggle)?