How is it that if $S\subseteq\mathbb{R}$ is a bounded infinite set, where $x=\sup(S)$, then every neighborhood of $x$ contains infinitely many points of $S$?

The question :     Let $D$ be a nonempty subset of the reals that is bounded above. Is the supremum of $D$ a limit point of $D$?   My Reasoning: I think this is false for these two cases. Case 1:If I look at $D = \{n \in \mathbb{Z} | n \le 0\}$ the supremum is $0$. And since I need a convergent sequence $\{x_n\} \subset D/\{0\}$ the converges to $0$ for it to be a limit point I can say in this case if I look at $\epsilon = \frac{1}{2}$ for the converges of the sequence it will fail to converge and so $0$ isn't a limit point.   Case 2: Also if I look at $D = {0}$ then the supremum is $0$. And $D$ is a subset of the reals. So if I look for a sequence $\{x_n\} \subset D/\{0\}$ I can't make one because $D/\{0\}$ is the empty set.   My question is this. Since the problem asked about an arbitrary subset of the reals $D$, can I define $D$ to give a counterexample like above or have I misunderstood the question?  --Thanks in advance.


I was trying to find the simplified form of ${100 \choose 0} + {100 \choose 1} + \ldots + {100 \choose 99} + {100 \choose 100}$. I was having a hard time finding a simple way to express the solution and I did not know how to do so without writing out the complete number. Does know what form I have to use?

Find the sum of the binomial coefficients $(^n_0)+(^n_1)+...+(^n_{n-1})+ (^n_n).$  I'm not good with the binomial theorem but I do know that $\sum_{k=0}^{n} (^n_k)x^{k} = (^n_0)+(^n_1)x+...+ (^n_n)x^n.$  Now comparing the binomial coefficients I can see some similarities, but the difference would be that $(^n_{n-1})$ and the $x^n$.  If I just have  $\sum_{k=0}^{n} (^n_k) = (^n_0)+(^n_1)+...+ (^n_n).$ then all I would be needing would be that $(^n_{n-1})$.  Any help?


For any $(x,y)∈ \Bbb N$ ,  x ~ y is an equivalence relation if and only if $xy$ is a perfect square. What are the equivalence classes? Here is my progress so far.  By the rules of multiplication we know that it is already symmetric and reflexive because for any $x∈\Bbb N$,$ x*x= {x^2}$  is by definition a perfect square and for any $x,y∈\Bbb N,xy=yx$ . But for transitivity and finding the equivalence classes I have hit a road block. My professor mentioned that prime factorization can be used but I just aren't seeing it.

Define a relation $\sim$ on $\Bbb{N}$ as follows. For any $a,b∈\Bbb N$, $a\sim b$ if and only if $ab$ is a perfect square. Show that $\sim$ is an equivalence relation. What are the equivalence classes?  So far I have $a\sim a$ so $\sim$ is reflexive, $ab\sim ba$ $\sim$ is symmetric, $ab=x^2$ and $bc=y^2$ prove $ac$ is a perfect square so $$ac =\frac{ab\cdot bc}{b\cdot b} = \frac{x^2\cdot y^2}{b^2} = \left(\frac{xy}{b}\right)^2$$ Therefore ac is square, ~ is transitive and an equivalence relation.  I think you use the equation $a=b^2a'$ to find the equivalence classes but I don't know how.


Such as a parent refusing to believe a child is ill? Hypochondriac is a person who constantly feels they themselves are ill. I am looking for a word to describe a person who refuses to acknowledge another person is ill.

Is there a word for the opposite condition of ? For example,  someone who denies being sick when they clearly are? I would just say that they are "in denial". Is there any other adequate word?  I thought about the obvious 'hyperchondria' but it doesn't seem to be used anywhere and doesn't look suitable as—from —just replacing 'hypo' by 'hyper' wouldn't fit well:     1555–65;  < Late Latin  < Greek,  neuter plural of hypochóndrios  pertaining to the upper abdomen (supposed seat of melancholy), equivalent to hypo- hypo- + chóndr ( os ) ensiform cartilage + -ios  adj. suffix


I have Samsung sf511 with Windows 7 Home preinstalled.  I installed Ubuntu 12.10 last night. First I downloaded ubuntu 12.10 DVD iso and burned a DVD. I rebooted and changed the boot option to DVD and let the Ubuntu DVD run. I selected "Install ubuntu alongside windows 7". In the next step I allocated the diskspace . Ubuntu installed perfectly and it ran OK.  I spent a good time exploring Ubuntu. When I restarted to start my work on Windows again and selected Windows 7 to boot, it showed blue screen after booting up (after logging in). I tried restarting several times but the same blue screen keep showing  at the same point of bootup. I also restored windows to an earlier time.  Left with no option I booted from Samsung provided windows recovery option. The recovery process ran fine but when it restarted to boot Windows for the first time all I see is a black screen. Nothing happens. It switches between dark command promt screen to a pitch black screen as if it's rebooting after every 10 seconds or so.  The laptop can be booted from the DVD Drive or USB drive but is not booting from Harddisk.  What should I do in order to use both Windows 7 and Ubuntu?

I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this?


Compute the limit as $n$ approaches infinity. $$  \frac{\sum_{0\le i\le n} \frac{n^i}{i!}}{e^n} $$  It is somehow between 0 and 1.

I'm supposed to calculate: $$\lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\frac{1}{2}$, which is a pretty interesting and nice result. I wonder in which ways we may approach it.


Let $f:X \to Y$ be a mapping. Its known that choice implies $f$ is surjective iff $f$ is right invertible. Are the following statements true?   Surjective iff right invertible is equivalent to choice. Bijective iff invertible does not require choice. Surjective iff right invertible does not require choice when $f$ is a linear map.

I read an Theorem that states:     Let $A$ and $B$ be non-empty sets, and let $f:A \to B$ be a function,   then the function $f$ has a right inverse if and only if $f$ is   surjective.   The Theorem proof uses Axiom of Choice. My question is, if Axiom of Choice is not true, then is this Theorem false? My question is because I tried to find a proof that not uses the axiom but I did not found it and this result is very important because it implies, with another statement, that a function $f$ has an inverse if and only if $f$ is bijective.


Im trying to figure out how to link two nodes in Python.  So far Ive found some pretty limited documentation , but it gives you no idea what arguments the operator takes or how to use it.  So for example lets suppose that I wish to create a diffuse node, a glossy node, and connect them to a mix node which is connected to the material output.  bpyops.material.new() bpy.ops.node.add_node(type="ShaderNodeBsdfGlossy", use_transform=True) bpy.ops.node.add_node(type="ShaderNodeBsdfDiffuse", use_transform=True) bpy.ops.node.add_node(type="ShaderNodeMixShader", use_transform=True)   How do you connect these nodes? And am I doing this right?

How can I connect nodes in a node group to the input or output sockets?  This connection here:    I can't figure out how to access the group node_tree, and the Group node as well as the Group input/output nodes seem to be different than normal nodes.  My script so far:  import bpy  for area in bpy.context.screen.areas:     if area.type == "NODE_EDITOR":         override = {'screen': bpy.context.screen, 'area': area} bpy.ops.node.select_all(override, action='DESELECT')  tree = bpy.context.object.active_material.node_tree nodes = tree.nodes links = tree.links   node = nodes.new(type='ShaderNodeMath') node.operation = "ADD" node.location = (100,0) node_add = node  node = nodes.new(type='ShaderNodeMath') node.operation = "GREATER_THAN" node.name = "greater" node.location = (-100,100) links.new(node.outputs["Value"], node_add.inputs[0])  node = nodes.new(type='ShaderNodeMath') node.operation = "LESS_THAN" node.name = "less" node.location = (-100,-100) links.new(node.outputs["Value"], node_add.inputs[1])  bpy.ops.node.group_make(override) bpy.ops.node.tree_socket_add(override, in_out='IN') bpy.ops.node.tree_socket_add(override, in_out='IN') bpy.ops.node.tree_socket_add(override, in_out='OUT')


This question from this site seems to be a SO question:    Unfortunately, it is all translated to my language so I couldn't search for the origin question. All the users are changed to Vietnamese names completely. I mean completely native Vietnamese names, not just the translated names.  I just want to report this.

of Stack Overflow, all content posted on Stack Exchange sites by their users (i.e. you wonderful people) has been provided to the whole universe under . For my fellow non-lawyers, that license basically means:   Anyone can use any Stack Exchange posts at any time without having to ask for permission Making money off of the copied content is permitted You don't even have to copy stuff from here verbatim; you can just use it as a starting point and make whatever edits you want There are just two rules you have to follow:   You have to provide . Simple links to the original post and author info are just fine. You have to  and allow other people to use your content, as long as they follow these very same rules. How meta!    (If you ever forget any of that, and want to refresh your memory, the license info is linked to in the footer of every page.)  There are, in fact, a lot of people who republish varying amounts of our content for assorted reasons. Unfortunately, there are some Stack Content Republishers Attributing Poorly and/or Excelling at Ranking (SCRAPERs, for short).  In this context, "attributing poorly" means any use that doesn't follow our attribution rules or make any other reasonable attempt at give credit. This can get pretty egregious; I've seen SCRAPERs that not only don't link back to SE originals, but also use fake author info and post dates to make it harder to find originals. By "excelling at ranking," I'm referring to copycat sites that end up higher in Google results than the original SE sites do for the same content. That's not necessarily wrong, but in some cases, it indicates inappropriate SEO hackery.  So, the question is: what can you do if you spot a SCRAPER?


Assume that I'm traveling at the speed of light in one direction. My brain is also traveling at the speed of light in that direction. Presumably there is at least one receptor site in my brain that is oriented in such a way that particles would need to travel faster than the speed of light to reach their destination receptor.  What would happen to those particles? Would my brain cease to function because these particles couldn't reach their destination?

Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling faster than the speed of light? (Relative to Earth that I just took off from.)


I have a series of coordinates. I know that I can cluster these using some of the basic methods like k-means or hierarchical clustering. I can also easily find out which is the closest neighbor to each coordinate.  However, how do I split the data into clusters, so that each cluster is exactly of size n, and that each coordinate only belongs to one cluster?   How could I do this in R, for example on this data and Euclidean distances:  data(iris) plot(iris$Sepal.Length, iris$Sepal.Width)

I have some points $X=\{x_1,...,x_n\}$ in $R^p$, and I want to cluster the points so that:   Each cluster contains an equal number of elements of $X$. (Assume that the number of clusters divides $n$.) Each cluster is "spatially cohesive" in some sense, like the clusters from $k$-means.   It's easy to think of a lot of clustering procedures that satisfy one or the other of these, but does anyone know of a way to get both at once?


Is there a way to sort Google Drive (either iOS or web version) by date that a file was added?  It drives me crazy that if I use Gmail to save an attachment to Drive, I can't locate that file immediately unless I know the name of the file (and then have to search it). Because 99% of time when I add a file to drive I want to access it immediately, and the easiest way to do that would be if I could sort drive by "date added".  Right now I only see a way to sort by "title" and "last modified" (same as recent). But most of the time when you add a file, it wasn't necessarily modified recently, so sorting by recent does not help at all.

Is there a way to sort files in a folder by the date of their creation?  I'm trying to figure out in which order my documents were created.


Say there's a bin of balls numbered 1 through 39, how many ways are there to pick 4 increasing numbers in a row?   First I figured that it would be a permutation without repetition problem, so I got that the number of ways of picking 4 different balls without considering increase is $$\frac{39!}{4!(39-4)!} = 82,250.999966$$  Then I thought I need to divide by some factor that changes the problem from any order to only increasing order which I thought might be 4!, so I got: $$\frac{82,250.999966}{4!} =  3,427.124998$$ and rounded down to get $3,427$. I'm terrible at these counting problems so I probably did this wrong. Can someone help me out please?

I have to figure out a way to count how many sequences are there s.t:   My alphabet is $1$ up to $49$. Each number that is chosen, is chosen only once. The sequence is $6$ digits long. The sequence is in increasing order.  e.g that is a valid sequence: $(1, 2, 40, 42, 43, 49)$  and this is not: $(1, 2, 40, 25, 25, 12)$   I know that for the first 3 rules the answer is: $\binom{49}{6}\cdot 6!$  How do I deal with the fourth?


When looking at kernel version numbers installed in /boot using a work in progress command (find /boot/vm* -printf "%A@ %p\n") I see:  1469098968.0000000000 /boot/vmlinuz-3.13.0-92-generic 1477523408.0000000000 /boot/vmlinuz-3.2.0-113-generic 1476549941.0000000000 /boot/vmlinuz-4.4.0-43-generic 1477008540.0000000000 /boot/vmlinuz-4.4.0-45-generic 1470540722.0000000000 /boot/vmlinuz-4.6.3-040603-generic 1471805944.0000000000 /boot/vmlinuz-4.7.1-040701-generic 1472208664.0000000000 /boot/vmlinuz-4.7.2-040702-generic 1473382012.0000000000 /boot/vmlinuz-4.7.3-040703-generic 1474853146.0000000000 /boot/vmlinuz-4.7.5-040705-generic 1475960925.0000000000 /boot/vmlinuz-4.8.1-040801-generic 1477145804.0000000000 /boot/vmlinuz-4.8.4-040804-generic   What are the proper names for "w.xx.y-zzz" that follows the vmlinuz prefix?  The proposed duplicate link ()states the second segment is called the ABI Number. The answer below by muru states the fourth segment is the ABI Number however I believe both are wrong based on the links provided in my own answer below.  Keep in mind this question is about ALL four segments w.x.yy-zzz and not just the fourth segment zzz.

On Ubuntu, the string returned by uname -r is always of the form x.y.0-z-generic (i.e., 3.19.0-21-generic). Compiling Ubuntu's kernel ends up with a string that is of the form x.y.z (i.e., 3.19.8), the actual version of the kernel that is used. What does the z represent in the first case? Is that the EXTRAVERSION parameter or is it something else? How do I get the version string of my build of Ubuntu to match the official one?


I'm trying to change certain index values of this boolean array to false and it does change but when re-displayed in another method it doesn't print properly.   This is for an assignment at school. I've check memory locations and they are the same.  import java.util.Scanner; import java.util.Arrays; public class Lab11avst {     public static void main(String[] args)     {         Scanner input = new Scanner(System.in);         final int MAX = 100;         boolean primes[];         primes = new boolean[MAX];         computePrimes(primes);         displayPrimes(primes);     }      public static void computePrimes(boolean list[])     {         Arrays.fill(list, true);         for (int i = 1; i < list.length ; i++)         {             if (list[i] = true)             {                 for (int j = (i+1); j < 20; j+=(i+1))                 {                     list[j] = false;                     System.out.println( j+" "+list[j]);                 }             }         }     }     public static void displayPrimes( boolean x[])     {         for(int y = 1; y< (x.length); y+=1)         {             if(x[y] =true)             {                 System.out.print(y+ " ");             }         }     } }

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


I'm taking images of a light source in a scientific labratory, and I thought I had a good grasp on all these things, but now i'm second guessing myself after some results.  The most important thing is for me to get the most light intesity to my camera sensor from my source.  As we all know, the available light drops off as 1/r^2 from the source.  So, being closer in principle gives you a better chance of getting more light.    However, diferent lenses have different abilities to gather light, based on their aperture size (which is reported as an f-stop value).    So, a typical question for us is this:  If we have a given light source that we are imaging, and we have two different lenses with two different focal lengths but the SAME minimum f-stop (e.g. 1.4), which one will gather more light? Assuming we adjust the distance from the source so that each lens images the same size area.  so, maybe we have a 25mm f1.4 lens and a 50mm f1.4 lens.  If they're both positioned to image the same region (i.e., the 50mm lens is further from the source than the 25mm lens), which would gather more light?

I never understood what the f really stands for in the f-stop values, like f/1.8. Wikipedia explains it in various articles, but I still find it very confusing. What I understand, though, is that it has something to do with focal length.  Should I assume, therefore, that bigger focal lengths capture more light? For example, should 85 mm f/1.8 lens capture a lot more light than for example 24 mm f/1.8?  References to back up my confusion:  The article about  goes on to claim:     The amount of light captured by a lens is proportional to the area of   the aperture, equal to:            Where f is focal length and N is the f-number.   The "f-number" is mentioned here. But the article about  claims:     In optics, the f-number of an optical system expresses the diameter of the entrance pupil in terms of the focal length of the lens; in simpler terms, the f-number is the focal length divided by the "effective" aperture diameter.   This seems very recursive. Why does the aperture article refers to both the focal length and the f-number, when the latter article claims that f-number already carries the property of focal length?  What's going on here?


Is there any smart way of calculating the determinant of this kind matrix? \begin{pmatrix} 1 & 2 & 3 & \cdots &  n \\ 2 & 1 & 2 & \cdots & n-1 \\  3 & 2 & 1 & \cdots & n-2 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ n & n-1 & n-2 & \cdots & 1 \end{pmatrix} I encountered this in a problem for the case $n=4$. I need to find the inverse matrix. I doubt the idea of this problem is to calculate all the cofactors and then the inverse matrix in the usual way. I see the pattern here and some recursive relations... but I am not sure if this helps for calculating the determinant of the existing matrix.


Spin is the intrinsic angular momentum of a particle. The particle itself is elementary and is not spinning on its axis, and has this momentum even at rest. The absolute magnitude of this momentum cannot increase or decrease without changing the particle. The particle may have angular momentum in addition to its spin, increasing its total angular momentum linearly.   Rest mass is the intrinsic confined energy of a particle. The particle itself is elementary and does not physically contain internal energy (binding energy, elastic potential, vibrational, etc), and has this energy even at rest. The absolute magnitude of this energy cannot increase or decrease without changing the particle. The particle may have energy in addition to its rest mass, increasing its total energy linearly.   Would it therefore be correct to call spin "Rest angular momentum", in the same sense mass is "Rest energy". In what ways does this analogy break down?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does spin mean if not an actual spinning motion?


I read such an example： double * ptd; ptd = (double *) malloc(30 * sizeof(double));  It explains that  malloc() allocates memory but it doesn't assign a name to it. However, it does return the address of the first byte of that block.  Since malloc return the the address of the first byte of that block, I assume the correct way is assign the address to ptd directly without star(*). ptd = malloc(30 * sizeof(double));  The extra * would dereference the address. What's wrong with my assumption?

In , someone suggested in a  that I should not cast the result of malloc. i.e., I should do this: int *sieve = malloc(sizeof(int) * length);  rather than: int *sieve = (int *) malloc(sizeof(int) * length);  Why would this be the case?


Currently I am setting up a flow, with different send email actions. There is a requirement to send all those emails from a noreply address. I have entered and validated this address in the special purpose org wide addresses, and tried to add this to the flow 'sender address'. I have also set the type to 'orgwideemailaddress' but it does not seem to accept this. This seems to be different from a normal org wide address. The error I keep getting is about the 'Automated process user email' that this is incorrect. When I try to enter this however, I keep getting errors that the address is invalid (tried the label and email address both). The standard flow user set there is a different address and as the requirement is to use a noreply email address, the flow user cannot be changed into a different user to fit the noreply address, but it also cannot be a dummy, as it requires a license. Hope there is an answer to this! Thanks!

I am struggling to set the sender address when sending a simple email using the Flow's core email action.  No matter what I put in the sender address field, the running user's email (my email) appears as the sender.


if i hang mass loaded vinyl like curtains around the room,will it soundproof the room do other neighbours will not complain when im doing music in strange hours? what other options do i have for a rental apartment?  i know about this product  but i don't know if it will soundproof the room  thanks

I live in an old apartment building and the walls are thin. This is a problem because I love to listen to music -- sometimes at odd hours of the night. Yes, I can be an asshole in this way. But my neighbor bangs against the wall even when I'm being perfectly reasonable (his bedroom seems to share a wall with my living room). And it's not just the low frequencies that get to him. He knocks against the wall even when I turn the subwoofer off on my speakers, which are located on the opposite wall.   This is kinda unacceptable. This is my home! What can I do so that I can live in it the way I want?


I realized that the Mac OSX Sierra is taking more than 100GB+ on my machine. I don't think this is normal. I clicked on manage and I didn't see any very large system file.  I wonder how can I reduce the disk footprint of the system?  I have already optimized my document and personal storage, but I don't understand why the OS would take 100GB    Something is seriously wrong.... since the time I made this post. Now the OS has grown and taken up my entire disk.

Every few days I get notices on my MacBook that it's running or run out of hard drive space. Curiously, restarting the computer will enable me to recover gigabytes of space (this past time, it was able to recover about 2.2GB). However, I can't identify anything in my personal activity that consumed that space.  It's possible that it's a rogue iTunes podcast or a huge software update that my Mac is automatically downloading - would either of these reclaim the space upon a restart?  One possibility that I can think of is that FileVault has some sort of disk leak, allocating but not freeing files. Does this make sense? Is there a tool that I can run to determine where this space is going? Assuming it is FileVault, should I try to disable it? What's the best way to turn of FileVault on a nearly full computer?


I have always been puzzled by how do you arrive at Lagrangians?  That is, how do you know that the functional you need to get Newton's equations is  $$L  =  T-V(x)~?$$ Do you derive the Lagrangian first somehow or do you just guess the one which would satisfy the action to give equation's of motion? (because then you would need to know the equations of motion first.) Also, is the Lagrangian always equivalent to something resembling $T-V$, or there are other ways to determine it? More generally, is the action known before you know the equations of motion, or vice versa?  What I really wish to know is, was the Einstein Hilbert action discovered before field equations were? If so, how? My major doubt is how do you come across the Lagrangian if you don't know the equations of motion, and you can't guess $L$ then?

Is there a proof from the first principle that for the Lagrangian $L$,    $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$  in classical mechanics? Assume that Cartesian coordinates are used. Among the combinations, $L = T - nV$, only $n=1$ works. Is there a fundamental reason for it?  On the other hand, the variational principle used in deriving the equations of motion, Euler-Lagrange equation, is general enough (can be used to to find the optimum of any parametrized integral) and does not specify the form of Lagrangian. I appreciate for anyone who gives the  answer, and if possible, the primary source (who published the answer first in the literature).      Notes added on Sept 22: - Both answers are correct as far as I can find. Both answerers were not sure about what I meant by the term I used: 'first principle'. I like to elaborate what I was thinking, not meant to be condescending or anything near to that. Please have a little understanding if the words I use are not well-thought of. - We do science by collecting facts, forming empirical laws, building a theory which generalizes the laws, then we go back to the lab and find if the generalization part can stand up to the verification. Newton's laws are close to the end of empirical laws, meaning that they are easily verified in the lab. These laws are not limited to gravity, but are used mostly under the condition of gravity. When we generalize and express them in Lagrangian or Hamiltonian, they can be used where Newton's laws cannot, for example, on electromagnetism, or any other forces unknown to us. Lagrangian or Hamiltonian and the derived equations of motion are generalizations and more on the theory side, relatively speaking; at least those are a little more theoretical than Newton's laws. We still go to lab to verify these generalizations, but it's somewhat harder to do so, like we have to use Large Hadron Collider. - But here is a new problem, as @Jerry Schirmer pointed out in his comment and I agreed. Lagrangian is great tool if we know its expression. If we don't, then we are at lost. Lagrangian is almost as useless as Newton's laws for a new mysterious force. It's almost as useless but not quite, because we can try and error. We have much better luck to try and error on Lagrangian than on equations of motion. - Oh, variational principle is a 'first principle' in my mind and is used to derive Euler-Lagrange equation. But variational principle does not give a clue about the explicit expression of Lagrangian. This is the point I'm driving at. This is why I'm looking for help, say, in Physics SE. If someone knew the reason why n=1 in L=T-nV, then we could use this reasoning to find out about a mysterious force. It looks like that someone is in the future.


Let $n$ be a positive integer and $F$ a field. Let $W$ be the set of all vectors $(x_1, \dots , x_n)$ in $F^n$ such that $x_1+\dots +x_n =0$.      $1)$ Prove that $W^0$ (annihilator of $W$) consist of all linear functionals $f$ of the form $$f(x_1, \dots , x_n) = c \sum _{j=1}^n x_j.$$      $2)$ Show that the dual space $W^*$ of $W$ can be naturally identified with the linear functionals of the form $$f(x_1, \dots , x_n) =c_1x_1 +\dots +c_nx_n$$ on $F^n$ which  satisfy $c_1+\dots +c_n=0$.   Attempt: $(1) $Solving $x_1+\cdots+x_n=0$ and considering $x_n$ as the dependent variable, we get the basis vectors for $W$ as $\{\alpha_1,\alpha_2,\dots,\alpha_{n-1}\}$ where $\alpha_i=\big(\underbrace{\dots}_{0\text{'s}},\underbrace{1}_{i^{\text{th}}\text{coordinate}},\underbrace{\dots}_{0\text{'s}},-1\big)$  If $f\in W^0$ is expressed as $f(x_1,\dots ,x_n)=d_1x_1+\cdots d_nx_n$ then $W^0$ is the solution space to the system $AD=0$ where $A$ is the $n-1\times n$ matrix with $\alpha_i$ as it's $i^{\text{th}}$ row and $D=\big(d_1,\cdots,d_n\big)^T.$  Since $A$ is in row-reduced row echelon form, we set $d_n=c$ and hence we get  $$f(x_1, \dots , x_n) = c \sum _{j=1}^n x_j.$$  $(2)$ To find the basis $\{f_1,\dots,f_{n-1}\}$for the dual space $W^*$ we need $f_i$'s to satisfy $$f_i(\alpha_j)=\delta_{ij},1\le i,j\le n-1.$$ Looking at $\alpha_i$'s, it is natural to consider $f_i$ as $f_i(x_1,\cdots,x_n)=x_i,1\le i\le n-1$ so that $f_i(\alpha_j)=\delta_{ij},1\le i,j\le n-1.$  Thus $\{f_i\}_{i=1}^{n-1}$ is a basis for $W^*$ and if $f\in W^*$ then \begin{align} f=\sum_{i=1}^{n-1}f(\alpha_i)f_i\\ \implies f(\alpha)=\sum_{i=1}^{n-1}f(\alpha_i)x_i \end{align}     It looks like I am nowhere near in the second part of the problem. Help!    is a related post but the answers given uses tools which are not introduced in the book yet.

I don't understand the task from (b). Is it equivalent to : for every linear functional $f(x_{1}, ..., x_{n})=c_{1}x_{1}+...+c_{n}x_{n}$ on $F^{n}$ which satisfy $c_{1}+...+c_{n}=0$ there exists exactly one and unique functional that belongs to the dual space of $W$?  If it is so, could someone please give me a hint?


Recently, I have found this problem:  Given two natural numbers $m$ and $n$, find the number of tuples $(m,n)$ such that: $$m+n=\text{gcd}(m,n)+\text{lcm}(m,n)=9!$$  I hav completely no idea of how to do it because I am used to operate with the formula $\text{gcd}(m,n)\cdot\text{lcm}(m,n)$ and not with the sum $\text{gcd}(m,n)+\text{lcm}(m,n)$. In order to escape from this problem, I have tried to set $n=9!-m$ and then substitute for $n$, but here I am stuck agian because I have to work with: $$\text{gcd}(m,9!-m)+\text{lcm}(m,9!-m)$$ Any idea of how to proceed? Thanks.

We are given that $m$ and $n$ are positive integers such that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$.  We are looking to prove that one of numbers (either $m$ or $n$) must be divisible by the other.


I am trying to compare the string stored in a variable with three different strings and if none of them match then throw an error. I've tried to do this in a single if statement using the logical operator OR. But every time I am getting error even though the value stored in the variable is same as one of the possible value. Please find the snippets I tried.  if [[ "$TYPE" != "LOCAL" || "$TYPE" != "REMOTE" || "$TYPE" != "BOTH" ]]; then     echo -e "\n\tINCORRECT OR NULL ARGUMENTS PASSED. PLEASE VERIFY AND CORRECT THE USAGE MENTIONED AS BELOW: \n"     Usage     exit 1 fi   if [[ "$TYPE" != "LOCAL" ]] || [["$TYPE" != "REMOTE" ]] || [["$TYPE" != "BOTH" ]]; then     echo -e "\n\tINCORRECT OR NULL ARGUMENTS PASSED. PLEASE VERIFY AND CORRECT THE USAGE MENTIONED AS BELOW: \n"     Usage     exit 1 fi

I tried to check if the PHONE_TYPE variable contains one of three valid values.  if [ "$PHONE_TYPE" != "NORTEL" ] || [ "$PHONE_TYPE" != "NEC" ] ||    [ "$PHONE_TYPE" != "CISCO" ] then     echo "Phone type must be nortel,cisco or nec"     exit fi   The above code did not work for me, so I tried this instead:  if [ "$PHONE_TYPE" == "NORTEL" ] || [ "$PHONE_TYPE" == "NEC" ] ||    [ "$PHONE_TYPE" == "CISCO" ] then     :        # do nothing else     echo "Phone type must be nortel,cisco or nec"     exit fi   Are there cleaner ways for this type of task?


Evaluate integral $$\int \cos^2x\sin^4x\mathrm{d}x.$$   Attempt. Setting $\tan x=t$, gives: $$\int \cos^2x\sin^4x\mathrm{d}x =\int \frac{1}{1+t^2} \,\left(\frac{t^2}{1+t^2}\right)^2 \frac{\mathrm{d}t}{1+t^2}=\int \frac{t^4}{(1+t^2)^4} \mathrm{d}t,$$ which does not seem to be elementary.  Thank in advance for the help.

Suppose $\displaystyle P(x,y)$ a polynomial in the variables $x,y$.   For example, $\displaystyle x^4$ or $\displaystyle x^3y^2 + 3xy + 1$.  Is there a general method which allows us to evaluate the indefinite integral     $$ \int P(\sin x, \cos x) \text{d} x$$   What about the case when $\displaystyle P(x,y)$ is a rational function (i.e. a ratio of two polynomials)?   Example of a rational function: $\displaystyle \frac{x^2y + y^3}{x+y}$.    This is being asked in an effort to cut down on duplicates, see here:   and here:


I have a paper with 30 figures. I added all the figures before conclusion section. But after compiling the document, 10 figures are placed into the middle of the document and after the references. I applied \begin{figure}[!htbp] in the first of the figures definition.  How can I force the figure to stay in the place where I defined it in the paper, for example before  the references or conclusion sections?

Is there any package or a method to force LaTeX to keep floating environments like table and figure closer to where they are declared?


<?php $paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1; $args = array( 'posts_per_page' => 6, 'offset'=> 0, 'category' => 1, 'paged' => $paged );  $custom_query = new WP_Query( $args ); while($custom_query->have_posts()) :     $custom_query->the_post(); ?>   My Html code  <?php endwhile; ?> <?php     previous_posts_link('&laquo; Newer posts');     next_posts_link( 'Older posts &raquo;', $the_query->max_num_pages );     wp_reset_postdata(); ?>   What's wrong?

I have added a custom/secondary query to a template file/custom page template; how can I make WordPress use my custom query for pagination, instead of using the main query loop's pagination?  Addendum  I have modified the main loop query via . Why isn't pagination working, and how do I fix it?


I compiled the following code 3 times to get the table of contents. The problem is that section names links to wrong slides. A links to B1 and B links to B2. So, it's wrong by one slide. How can I fix it?   \documentclass{beamer}  \begin{document}  \frame{\tableofcontents}  \section{A} \frame{A}  \section{B} \frame{B1} \frame{B2}  \end{document}

When I include a table of contents in a Beamer slide show, each section entry in the TOC ends up linking to the second slide in that section. I would have expected it to link to the first slide. What am I doing wrong?:  \documentclass{beamer}  \begin{document} \begin{frame}{Test TOC}   \tableofcontents \end{frame}  \section{Section 1}  \begin{frame}   \frametitle{Test 1} \end{frame}  \begin{frame}   \frametitle{Test 2} \end{frame}  \end{document}   Just to clarify: when I click Section 1 in the TOC, it takes me to the slide Test 2.  UPDATE: I am actually not sure if it takes me to slide Test 2. When I click the link, the viewer (Evince and Okular) displays most of Test 2, but with a tiny strip of the slide Test 1 visible at the top of the window. I suspect that the viewer may treat the link as pointing to the very bottom of slide Test 1 and then aligns that with the top of the window. Could this be the explanation?


I was using Ubuntu 18.04 LTS before, but today when I erased and reinstalled the system. Now when I try to install or uninstall software, or change something, I get an error message:   "Incorrect permissions on /usr/lib/policykit-1/polkit-agent-helper-1 (needs to be setuid root)"    It does not allow me to enter the password as usual. I'm using Ubuntu 18.04 LTS

I'm getting this error message:  "Incorrect permission on /usr/lib/policykit-1/polkit-agent-helper-1(need to setuid root)"   Due to this problem I can't download any app.


First of all, is A ={φ} a set? If yes, then what are its subsets?  Note: • φ represents an empty set.  • A must have two distinct subsets,       (∵ n(A)=1, thus 2¹= 2)  My approach: According to me, if it has two subsets then they should be φ and φ. If it's so then they aren't distinct at all.

Is ∅ equivalent to {∅}? I think they are, but I am not sure? If anyone could clarify, that would be great. Thank you!


I know that java doesn't support static Top-Level classes, and only nestled classes can be static.   But, wherever I read about these nestled static classes, it says you have to initialize these classes with the "new" keyword.   Is this not instancing? if yes, how are we instancing "static" classes?   Does this mean we can have multiple instances of this class running simultaneously? Can we store these on variables just like non-static classes?  If this is true, then is the "static" modifier just a modifier used to access the nestled class without instantiating the container class?  Any Light shed on these questions are very welcome. Thanks!  EDIT: This question is different than the questions it has been marked duplicate against as I am NOT asking what the static modifier does to an object, nor am I asking if static classes exist. I know what static nestled classes are, and how static objects behave, but the static nestled class'es peculiar behaviour of being instantiatable by using the"new" keyword (which is used to create an instance of an object). Static classes can usually not be created instances of in OOP, and I was asking is this different in java. can you create instances of static classes in java.

To be specific, I was trying this code:  package hello;  public class Hello {      Clock clock = new Clock();      public static void main(String args[]) {         clock.sayTime();     } }   But it gave the error      Cannot access non-static field in static method main   So I changed the declaration of clock to this:  static Clock clock = new Clock();   And it worked. What does it mean to put that keyword before the declaration? What exactly will it do and/or restrict in terms of what can be done to that object?


Is it possible to read and write Word (2003 and 2007) files in Python without using a COM object? I know that I can:  f = open('c:\file.doc', "w") f.write(text) f.close()   but Word will read it as an HTML file not a native .doc file.

for working with MS word files in python, there is python win32 extensions, which can be used in windows. How do I do the same in linux? Is there any library?


The original question before it was marked as duplicated question:  I was wondering if one construct a non-continuous function $f:X\to Y$ between two topological spaces $X$ and $Y$, such that $f$ sends every convergent net into convergent net... I want to see an example...  Thanks in advance.  Edition:  Can Someone construct a non-continuous function $f:X\to Y$ between two topological spaces $X$ and $Y$, such that $f$ sends every convergent net into convergent net... I want to see an example...  Thanks in advance.  My own Answer:  Consider a two point set $X:=\{x,y\}$ with a topology $\mathcal{T}=\{\emptyset,\{x\},\{x,y\}\}$.  Define $f:X\to X$ by $x\mapsto y$ and $y\mapsto x$.  Then, since $f^{-1}(\{x\})=\{y\}$ where $\{x\}\in\mathcal{T}$, $f$ is not continuous.  On the other hand, pick any convergent net $\{x_\lambda\}_{\lambda\in\Lambda}$ in $X$.  We claim that $f(x_\lambda)$ converges to $y$.  Note that there is only one neighborhood of $y$, $\{x,y\}$, since $\{y\}$ is not open. Then, it follows that $\forall\mu\in\Lambda$, $\mu\prec\lambda\Rightarrow f(x_\lambda)\in\{x,y\}=X$. where $\prec$ is the preorder on the given directed set $\Lambda$.

Let $f:(X,\mathcal T)\to (Y,\mathcal S)$ be a function between topological spaces. Let for any convergent net $(x_\alpha)$ in $X$, $(f(x_\alpha ))$ be convergent in $Y$. Is $f$ continuous?  (It seems to be true in completely regular spaces).


I am not connected with the internet .  So I need to download mpeg4 plugin and h264 plugin for playing videos . Please comment a line for downloading? I am new to ubuntu

I have a friend who has got a computer that is not connected to the Internet. Is there any way to install software offline easily?


For a number theory problem, I have to figure out all couples $(m,n)$ of positive integers which verify the equation      $$m^{n^2}=n^m$$   I just don't know what to do. Thanks !

I saw this in quora.  What are all the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$?  Solutions I have found so far:  $a = 2^4 = 16, b = 2, a^{b^2}  = 2^{4\cdot 4} =2^{16}, b^a = 2^{16} $.  $a = 3^3, b = 3, a^{b^2} = 3^{3\cdot 9} =3^{27}, b^a = 3^{3^3} =3^{27} $.  In the general case, $a$ and $b$ have the same set of prime divisors, so let $a =\prod_P p_i^{a_i}$, $b =\prod_P p_i^{b_i} $ with each $a_i \ge 1, b_i \ge 1$.  $b^a =b^{\prod p_i^{a_i}} =(\prod p_j^{b_j})^{\prod p_i^{a_i}} =\prod p_j^{b_j\prod p_i^{a_i}} $  $a^{b^2} =a^{\prod p_i^{2b_i}} =(\prod p_j^{a_j})^{\prod p_i^{2b_i}} =\prod p_j^{a_j\prod p_i^{2b_i}} $  Therefore, for each $p_j$, $b_j\prod p_i^{a_i} =a_j\prod p_i^{2b_i} $.  I haven't gotten any further than this.  I conjecture that there are no other solutions.


For questions like  where code works perfectly fine and there does not seem to be an issue, is is ok to answer the question with a different form of the question just because:     The question is ambiguous... Waiting for more details from the OP, and then I will can update my answer.     ?

Sometimes we get questions where the problem can't be reproduced given the information OP mentioned. Sometimes we get questions where OP posts code and asks why the code doesn't work where in fact the code does work.   Here is  I just ran into in the edit queue. However, we've all seen them.  In the example  the question basically saying "When using your code in an isolated environment it works. This is not the first or tenth time I've seen these sort of answer.   Should users post these sort of answers? Are they useful for the site? Why?  Note: This is not about whether or not to close such questions. I think that's clear.


I have 2 million samples and using a 60/20/20 split for train, validation and test. Validation and train accuracy are very close to each other at 80% and 85% respectively but test accuracy much lower at 55%. I know that we aren't supposed to monitor the test losses for each epoch but I checked and the test loss was increasing after 10 epochs but train and validation losses were both decreasing. What am I doing wrong?

I'm training a neural network and the training loss decreases, but the validation loss doesn't, or it decreases much less than what I would expect, based on references or experiments with very similar architectures and data. How can I fix this?    As for question        to which this question is inspired, the question is intentionally left general so that other questions about how to reduce the generalization error of a neural network down to a level which has been proved to be attainable, can be closed as duplicates of this one.  See also dedicated thread on Meta:


My sister is selling her old dirt bike through Gumtree. She got an email this morning saying the following:  Cheers for the prompt responses! please consider it sold and cancel every other appointment regarding it, I am buying it for dad moving to a new house and I am ready to pay your full asking price, I have read through the advert and I'm totally satisfied with it and I will be glad if you can get back to me with some pics if available, sadly I won't be able to come for the pick up due to my disabilities, I loss my hearing and being on a wheelchair but I have a courier agent that will help me to pick it up at your preferred location. Regarding the payment I can only pay via PayPal or direct deposit ETF at the moment and I will be responsible for all the PayPal fee/charges on this transaction kindly get back to cme with your PayPal email and the pick up location so that I can  the courier agent about it now?  This is a classic scammy email:  Prompt responses? What prompt responses? We don't know you. Disabilities that prevent you being here in person? Hmm, ok. Get back with some pics? We had lots of pics on the listing. You'll be responsible for the PayPal fees? Sounds like you want to do "friends and family" instead of "goods and services", for whatever reason.  Is this a common/normal scam? How does it work?

I am selling a mower on Craigslist and I received this in a text:     FRM: Harry Luong      SUBJ: Re: Hey, is still for sale?      MSG: Great I saw the detail on the Ad and I'm okay with the price & condition and i want you to consider it sold. I will be securing the payment by sending you (Bank check) Via USPS next day delivery and i will handle the Shipping my self with my private Mover that will come down there for the pick up after the check cleared. I'II need your full name and Address or po box for the check to be issued out to you Thanks   Is this a scam?


Here is my code public with sharing class estimatevsPipeline {     @AuraEnabled     public static List<Opportunity> getestimatevsPipeline() {         return [             SELECT SUM(amount_ge_og__c) sumAmount             FROM Opportunity             WHERE                 ((IsClosed != TRUE                 AND ForecastCategoryName IN ('Commit', 'Commit at Risk'))                 OR StageName = 'Closed Won')                 AND RecordType.DeveloperName != 'Targets'                 AND Type IN ('Internal to GE Parent', 'Internal to BHGE', 'External')                 AND forecast_pipeline_exception_ge_og__c != TRUE                 AND CloseDate = THIS_QUARTER                 AND Id IN (                     SELECT OpportunityId                     FROM OpportunityTeamMember                     WHERE                         (UserId IN ('0051H000009S5D2QAK', '00512000007jB49AAE', '0051H00000Aw9VbQAJ')                         OR UserId = '0051H00000AwEezQAF')                         AND TeamMemberRole != 'Following'                 )         ];     } }

Here is my code `  global with sharing class ReportsListController {     public String dcarr { get; set; }    public static ReportsColumnMap__c repcols { get; set; }    public ReportsListController() { } // empty constructor    @RemoteAction   global static List<ReportsColumnMap__c> getRepCols(String dcarr) {             List<ReportsColumnMap__c> repcols =          [SELECT ColumnName__c,SObject__c ,COUNT(ID) FROM ReportsColumnMap__c WHERE ColumnName__c IN ('OWNER','FIRST_NAME','LAST_NAME','TITLE','COMPANY','LEAD_SOURCE','RATING','STREET','EMAIL') AND SObject__c !='null' GROUP BY SObject__c ,ColumnName__c];     return repcols;   } }   `


I'm writing a book in LaTeX. This is my output:   Is it possible to change the text "Capitolo" ("Chapter" in italian) with something else, for example "Experience"?  Thanks in advance  \documentclass[oneside]{book} \usepackage[italian]{babel} \usepackage[utf8]{inputenc} \usepackage{amsmath,amssymb,amsfonts} % Typical maths resource packages \usepackage{chemfig} \usepackage[version=3]{mhchem} \usepackage{graphics}                 % Packages to allow inclusion of graphics \usepackage{color}                    % For creating coloured text and background  \usepackage[colorlinks,citecolor=blue,linkcolor=blue]{hyperref}                 % For creating hyperlinks in cross references. It should be after the color package. The option colorlinks produces colored entries without boxes. The option citecolor=blue changes the default green citations to blue. \usepackage[   a4paper,   margin=12mm, ]{geometry} \usepackage{times}  \usepackage[T1]{fontenc}  \DeclareGraphicsExtensions{.pdf} \parindent 1cm \parskip 0.2cm \topmargin 0.2cm \oddsidemargin 1cm \evensidemargin 0.5cm \textwidth 15cm \textheight 21cm  \def\R{\mathbb{ R}} \def\S{\mathbb{ S}} \def\I{\mathbb{ I}} \makeindex   \title{Laboratorio di Chimica Organica II}  \author{\htmladdnormallink           % Puts a hyperlink on to the author's name {Marco Atzori}{} {\copyright 2018 }}   \date{ }  \begin{document} \maketitle  \addcontentsline{toc}{chapter}{Indice} \pagenumbering{roman} \tableofcontents \chapter{Identificazione di una sostanza organica incognita}\normalsize   %\addcontentsline{toc}{chapter}{Preface} \pagestyle{plain} La sostanza da identificare è la numero 24. Nell'identificazione di una sostanza organica incognita la prima analisi da eseguire è la ricerca di un eventuale carattere acido o basico. A tale scopo, se ne verifica la solubilità in tre soluzioni acquose: HCl al 10\%, NaOH al 10\%, e $\ce{NaHCO_{3}}$ al 10\%. La sostanza non risulta avere un carattere acido perché non è solubile in acido cloridrico, mentre lo è in idrossido di sodio. A questo punto, bisogna ricavare una stima della forza dell'acido che si vuole identificare: la sostanza non è solubile in bicarbonato di sodio. Il saggio per l'identificazione dei fenoli con $\ce{FeCl_{3}}$ ha dato esito negativo, quindi un primo indizio è che si tratti di un acido carbossilico debole, presumibilmente aromatico. \pagestyle{headings} \pagenumbering{arabic}  \include{ch1} \include{ch2}  \include{index}  \addcontentsline{toc}{chapter}{Index} \end{document}

I am using fancyhdr. With that, using the command  \renewcommand{\chaptername}{Lecture}   has no effect. How can I change the name "Chapter" into something else?


I'm designing a circuit that allows one to switch between two different 5V sources, which is then fed into a 3.3V regulator IC. I'm targeting low cost and low board size, and I'll take a solution around $1-$2 in cost. Power supply is an integrated 5V rail on a system and the 5V USB rail for debugging.    The answers there aren't satisfactory for me. The voltage drop on the diode brings the 5V input too low with fluctuations on the 5V rail (ie a lower voltage 5V rail may exceed the bottom limit of my LDO). I'm mainly just wanting a solution that prevents back-feeding of any power source. I also want power to only come from USB if it's plugged in.

I am making a circuit which is powered by a lipo battery of 11.1V(3.7V*3). I need to check for the lipo's under-voltage so that the circuit automatically switches to a second lipo when the first one drops below the cutoff voltage. I am open to using arduino and relays but no diodes(as they lead to large power loss).


Bill arrives between 5:00 and 5:30 and waits 10 minutes. Will arrives between 5:10 and 5:40 and waits 5 minutes. What is the probability that they meet each other?

Problem:     Two people are to arrive at the same location some time between 3pm   and 4pm. They both arrive at random times within the hour and only   stay for ten minutes. Since they only go one time, what is the   probability that they will meet during that hour?   I have found the correct answer to this problem here (the second formula P2):      $$ P2 = 1 - \frac{(1-w_1)^2 - (1-w_2)^2}{2} = w_1 + w_2 - \frac{w_1^2}{2} - \frac{w_2^2}{2} $$  Plugging in ($1/6$) for both $w_1$ and $w_2$ is $11/36$ which is the correct answer.  But I don't understand how they came to that conclusion and what formula they derived it from. Any help in explaining this would be much appreciated!


Basically, I've computed a few values by hand, and those followed the pattern in the question. Wolframalpha also claims that this function equals the Kronecker delta function which follows $$\delta_{ij} = \begin{cases}0 &\text{if } i \neq j \\1 &\text{if }x=1\end{cases}$$ Why is this the case?

Let $n$ be a positive integer. Prove that   \begin{align} \sum_{k=0}^n \left(-1\right)^k \binom{n}{k} = 0 . \end{align}   I tried to solve it using induction, but that got me nowhere. I think the easiest way to prove it is to think of a finite set of $n$ elements, but I can't find the solution.


is it possible to write a text above and below the \rightsquigarrow? I am trying \xrightsquigarrow[\text{b}]{\text{a}}, but it is not working.

Please refer the attached image. I want to write \omega \in \mathbb{R} below sup as shown in the equation in the image. How should I do it?


Let $X$ be a Banach space for which there exists a constant $\beta<\infty$ such that for every finite-dimensional subspace $B$ of $X$ , $d(B,\ell_2^n)\le\beta$ (where $\dim B=n$). Then $X$ is isomorphic to a Hilbert space.  $d(B,\ell_2^n):$ Banach-Mazur distance  $\ell_2^n=(\mathbb{R}^n,||\cdot||_2)$   Any hints would be appreciated.

If $X$ is a separable infinite-dimensional Banach space and $C\in\mathbb{R}^+$ is an upper bound for the Banach-Mazur distance $d(E,\ell_2^n)$ for all $n\in\mathbb{N}$ and all $n$-dimensional $E\leq X$, why must $X$ be isomorphic to $\ell_2$?  I've been thinking along the following lines: let $\{x_n:n\in\mathbb{N}\}$ be a countable, dense, linearly independent set in $X$ and let $E_n=\langle x_1,\dots,x_n\rangle$ for all $n$. Now for each $n$ there's a linear isomorphism $T_n:E_n\rightarrow\ell_2^n$ such that $\|T_n\|\|T_n^{-1}\|\leq C$. If we can somehow put together these $T_n$ to form a linear isomorphism $T:\cup_nE_n\rightarrow\cup_n\ell_2^n$ = {finite-length sequences in $\ell^2$}, then this extends by continuity to a linear isomorphism $\bar{T}:X\rightarrow\ell_2$.  But how do we get $T$ from the $T_n$? Each $T_n$ is only defined on finitely many of the $x_i$. Maybe some sort of infinite series? Or can we choose each $T_n$ so as to agree with $T_{n-1}$, and still keep the $\|T_n\|\|T_n^{-1}\|\leq C$ property?  Many thanks for any help with this!


I want to buy a open jaw flight to South America. Bucharest - Buenos Aires at the beginning of January Bogota/Barranquilla/Cartagena(Colombia) - Bucharest, somewhere between 10 and 16 April.  When is the best time to buy them? Is it cheaper to buy them both on the same time or separately?

There is a common story that airline ticket prices rise significantly if you buy them less than two weeks before departure.  And that any time before that will yield standard prices.  Is that advice valid for flying during holiday seasons?  As an example: if I want to fly coast to coast USA on December 7th, must I buy my ticket ASAP, or would I get a similar price buying on November 21st?


I trying to create a circuit with only one 555 to send HIGH on output(3) for very short time, like 200ms, then set LOW for something like 20~30 seconds.  Then I'm just need turn on circuit, then:  a) fast HIGH (~200ms) b) long LOW (~20-30s)  I already able to make a "default" 555 circuit with stable HIGH/LOW in same timing (1000ms/1000ms), but I'm getting trouble to make this with different HIGH and LOW timmings.  Thanks.

I'm attempting to make a simplistic solenoid driver circuit using a standard astable 555 timer configuration with a TIP122 NPN transistor. The problem with the current circuit is that the output is typically high and goes low only for short durations. I'd like to invert this but I'm not sure how.    Ideally I would like a high output every 1 second that lasts only for 100ms.  Do I just need to change RC values or utilize the 555 differently?  (The schematic shows a 556, which is what I am currently using. The lamp-looking squiggle is the solenoid and I have added a 1N4001 diode across it in reverse bias.)


I have a queueable class that makes callouts (@future(callout=true)) in the execute method. When I manually test this, everything works correctly. But when I set up my test class, it gives me the "You have uncommitted work pending. Please commit or rollback before calling out" error. I don't have any DML statements apart from in my testSetup class. And I have Test.startTest() and Test.stopTest() surrounding the enqueueJob.  I can test the callouts (and they test successfully) if I call this method directly, but I can't test the execute method (which calls the callout method).  i.e. this works:  QueueClass.makeCallouts(list);   But this doesn't (gives the commit error):  System.enqueueJob(new QueueClass(list));   For reference, here is the portion of my execute class that runs prior to the error:  settings = tokens.getInstance(id); Boolean updated; if (settings.Access_Expiration__c < Datetime.now()){     //stuff that doesn't run } else {     updated = True; } if (updated){     makeCallouts(list); }   Can we not test callouts from queueable apex, can I not test the execute method, or am I missing something?

I have an after insert trigger that invokes queueable Apex which makes a callout.  The trigger and callout work fine in the UI and I don't get any errors in normal operation.  However, my unit test keeps failing with the "uncommitted work pending" error despite all my attempts to separate the callout.  I've used a testVisible variable to disable the callout from the trigger so that I can invoke the queueable job explicitly in a startTest/stopTest block after the DML that fires the trigger.  I've pored over the callout class to make sure it's not doing any DML beforehand.  Anyway, if it was doing DML, I should get the uncommitted work pending errors in the UI, right?  I've tried API version 37 and version 41 but the unit test still fails.   I've had a case open with Salesforce premier support for 6 weeks now but haven't made any progress.  Any suggestions?  The unit test:  @isTest static void testCallout() {     // Disable the callout while setting up data.     CCx_EHR_CMCT_Services.isQueueSendEnabled = false;      // Set up the data and execute the DML.     / ...     insert act;      // Set up the http mock     // ...      // Now enable and execute the callout     Test.startTest();     CCx_EHR_CMCT_Services.isQueueSendEnabled = true;     Test.setMock(HttpCalloutMock.class, mock);     System.enqueueJob(new QueueSendToRedox(new List<ActivityHL__c>{act}, desk)));     Test.stopTest();  }   Trigger:  trigger HL_ActivityHL_c on ActivityHL__c (before insert, before update, after insert) {     if (Trigger.isAfter) {         if (Trigger.isInsert) {             CCx_ClientDataDomain.sendEHRClinicalComm(Trigger.new);         }     } }   Trigger handler class:  public without sharing class CCx_ClientDataDomain {     public static void sendEHRClinicalComm(List<ActivityHL__c> triggerNew) {     // do some processing here.     // ...     // then queue the callout job.     System.enqueueJob(new CCx_EHR_CMCT_Services.QueueSendToRedox(             deskActivities.get((Id) desk.getDeskId()), desk));     } }   Queueable job class with callout method:  public with sharing class CCx_EHR_CMCT_Services {     // isQueueSendEnabled is an attempted workaround for unit tests     @testVisible     private static Boolean isQueueSendEnabled = true;      public class QueueSendToRedox implements Queueable, Database.AllowsCallouts {         private List<ActivityHL__c> activities;         private CCx_DeskHierarchySelector.Desk desk;         private Boolean isEnabled;          public QueueSendToRedox(List<ActivityHL__c> activities, CCx_DeskHierarchySelector.Desk desk) {             this.activities = activities;             this.desk = desk;             this.isEnabled = isQueueSendEnabled;         }          public void execute (QueueableContext context) {             if(this.isEnabled) sendClinicalCommToRedox(activities, desk);         }     }      public static void sendClinicalCommToRedox(List<ActivityHL__c> activities, CCx_DeskHierarchySelector.Desk desk) {         // Set up data for the callout.  No DML actions are executed before the callout.         HttpRequest req = buildRequest();         // ...          // Callout         Http http = new Http();         HttpResponse resp = http.send(req);     } }


I have a server that returns a String of this format: {"success":true,  "visible":false,  "data":      {"ref":"asfdasfsadfaeweatsagsdfsad",       "userRef":"asdfsadfsa","accountType":"REAL",balance":43}, "code":"2200", "msg":null, "msgRef":null, "successAndNotNull":true, "failedOrNull":false, "failed":false, "failedAndNull":false}`  Then I extract the data by doing this: val jsonObj : Any! = JSONObject(serverResponse.toString()).get("data").toString()  and I end up with this String: "{"ref":"safdasfdwaer",  "userRef":"fdgsgdsgdsfg",  "accountType":"REAL",  "balance":43}"  Is there an efficient way to extract the the values into a HashMap with key what is on the left of ":" and value what is on the right of ":"? I have already seen the answer here () but I am not allowed to to use regex

What is the best way to convert a JSON code as this:  {      "data" :      {          "field1" : "value1",          "field2" : "value2"     } }   in a Java Map in which one the keys are (field1, field2) and the values for those fields are (value1, value2).  Any ideas? Should I use Json-lib for that? Or better if I write my own parser?


I am new to Linux and I'm trying Ubuntu 20.04.1 on a USB key to see what it's like. I wanted to watch a movie on Prime Video using Firefox, but I couldn't : it asked me to allow DRM, which I did. But still, I wasn't able to watch my movie (says an error occured) and I tried on Netflix (error F7355): issue is the same. I have been looking on the internet for a solution but I couldn't find any. I have :  Updated Firefox using sudo apt install --only-upgrade firefox Changed media.libavcodec.allow-obsolete;false to true in Firefox about:config Checked that I have OpenH264 and Widevine plugins activated Tried commands I found online... Such as sudo apt-get install libavcodec-extra, sudo apt-get update && apt-cache search libavcodec-extra, sudo apt-cache search libav | grep extra- or sudo apt-cache search libav | grep extra-...  Most of the posts I found were pretty old. It seems like i'm missing this "libavcodec" but I don't really know what it is nor how I should get it. I can play YouTube videos, however Twitch videos do not work (Error 4000) Could anyone help me ? I was happy with my Linux experience so far, but I'm a bit disapointed that it's so hard to do something as simple as watching a stream ! Thanks a lot and sorry for my english, I'm not a native speaker.

Netflix quit and displayed error codes F7355-1204 and F7363-1260. It will go to the point where the movie is downloading but stops and displays the error codes. My os is Ubuntu 12.04 on a 32 bit machine. Netflix was working fine on the pipelight approach. Reinstalled firefox 52.0.2. Fixed libavcodec. Have yet to reinstall pipelight.  What are these error codes, and how do I fix them.


My internal HDD has bad sectors and I can't access to 1 part of 3. It's really slow and it usually don't let me to copy data. I'm searching for softwares to fix this and save my files. What do you suggest? I don't wanna lose my files. edit: I can't open disk softwares ( like hddtune ) while hdd is inserted.

A friend of mine recently gave me a laptop that wasn't booting past the Windows screen. I replaced the hard drive with a new one and put the old hard drive in my comp. to try and recover the data.  Windows 7 didn't recognise the main OS partition indicating some filesystem corruption (disk manager showed it as a RAW drive instead of NTFS). Incidentally, the hard drive has two other partitions: the small 100 MB one was fine in Windows and the 10 GB Recovery partition was fine after Windows ran a disk check).  Then I booted up with a Linux live CD (Slax) and the filesystem was recognised fine. However, when trying to copy files, many files would cause errors each one holding up the copy process by about a minute. I'm copying about 120 GB of data with thousands of bad files so this means it takes forever to copy.  There are big files (videos and photos) and small files (documents).  What I need is a way to copy files from a dying HD so:   if a file is bad, it fails silently (not interactively) it fails quickly (< 1 seconds ideally) it optionally deletes the bad file from the destination (not necessary)   so that the process can be done overnight.  Do you know a live CD where copy behaves like that or parameters to cp I can use or the settings for ddrescue I need to use or some other method to do this (I'm a linux noob)?  Alternatively, do you know a way to mount a broken filesystem in Windows (it looks like there are errors in important locations so Windows doesn't recognise it as NTFS). Then I can try xcopy.


As I know, in a XML comment for a C# type/method, it is possible to reference a generic type in a  tag like so:   ///<see cref="name.space.typename&lt;T&rt;(paramtype)">   But I think, there was another syntax, which is less clumsy? Something, to get rid of those html entities '<'? I cannot find it right now. Can somebody help?

When writing xml documentation you can use <see cref="something">something</see>, which works of course. But how do you reference a class or a method with generic types?   public class FancyClass<T> {   public string FancyMethod<K>(T value) { return "something fancy"; } }   If I was going to write xml documentation somewhere, how would I reference the fancy class? how can I reference a FancyClass<string>? What about the method?  For example in a different class I wanted to let the user know that I will return an instance of FancyClass<int>. How could I make a see cref thing for that?


My opponent controls , a 7/6 hexproof creature. I control two s, which give opponents' creatures -1/-0. Would Dampening Pulse affect the hexproof creature? I think it would because it's not directly targeting the hexproof creature.

Note: this is intended to be a canonical question about whether or not a spell or ability targets so there are multiple sub-questions.   Can Hexproof or Shroud save my creature from ? What about a  that was cast for it's Overload cost? Does shroud prevent me from using the Monstrosity ability of a creature, or from giving it more counters with Proliferate? Can I cast an Aura Enchantment on one of my creatures with Shroud, or an opponent's creature with Hexproof? Or can I use the Equip ability to attach an equipment to one of my creatures with Shroud? Will 's ability trigger when my opponent plays ? And will I have to sacrifice my  if my opponent casts ? Will Shroud or Hexproof prevent an opponent from choosing me with 's ability? Will Hexproof keep one of my creatures from being affected by ? If an Aura or Equipment is attached to a creature with Hexproof, does the Hexproof protect the attached permanent?


I'm trying to make a bool specialization for this code in Microsoft Visual Studio 2017.  BinaryParser.h:  #pragma once  #include <stdint.h> #include <array> #include <vector> #include <string>  #include "Deserializable.h" #include "ParserError.h"   class Deserializable; class BinaryParser { public:     BinaryParser(const uint8_t* in, size_t in_len);      size_t GetRemaining();      template <class T>     T Get(bool check=true)     {         static_assert(std::is_base_of<Deserializable, T>::value, "Type does not implement Deserializable.");          T obj = T();         obj.Deserialize(this, check);         return obj;     }      template <>     bool Get(bool check);  private:     const uint8_t* data;     size_t size;     size_t index = 0; };   BinaryParser.cpp:  #include "stdafx.h" #include "BinaryParser.h"   BinaryParser::BinaryParser(const uint8_t* in, size_t in_len) {     data = in;     size = in_len; }   size_t BinaryParser::GetRemaining() {     return size - index; }   template <> bool BinaryParser::Get(bool check) {     if (check && GetRemaining() < sizeof(bool)) throw ParserError();      uint8_t r = data[index];     index += sizeof(bool);     return r; }   Unfortunately, whenever I do:  BinaryParser p(...); bool a = p.Get<bool>();   I get this error:  LNK2019 unresolved external symbol "public: bool __thiscall BinaryParser::Get<bool>(bool)" (??$Get@_N@BinaryParser@@QAE_N_N@Z) referenced in function _wWinMain@16   I've been banging my head against the wall for the past 2 hours trying to figure this out. I had a template specialization for uint8_t and it compiled, but bool, uint16_t and uint32_t gave me this error (unsigned int __thiscall BinaryParser::Get<unsigned int>(bool) in the case of uint32_t for example).  I also don't get any errors if I comment out bool a = p.Get<bool>(); but leave the declaration and definition.

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I have a list of names and I want to print each element of the list in a different line without a for loop. So, after some research I found this example: print(*names, sep='\n'), witch results in exactly what I want. But what does this * character before the list name means?

Does * have a special meaning in Python as it does in C? I saw a function like this in the Python Cookbook:  def get(self, *a, **kw)   Would you please explain it to me or point out where I can find an answer (Google interprets the * as wild card character and thus I cannot find a satisfactory answer).


I am running a python program from a terminal in my Ubuntu machine as,   $ python test.py   But my whole program will be stopped if I close the terminal, Is there any way of running this python program in the background so that if I close my terminal then it still keeps on running?  And also after running this program in the background, how do I find out my actual program whether it is still running or not if I am logging back again to that terminal?

How do I run a program in the background of a shell, with the ability to close the shell while leaving the program running? Lets say my UI is having problems or for some reason, I need to boot up a program from the terminal window, say, nm-applet:  nm-applet   When it's started, it occupies the foreground of the terminal window.  Is there any simple way to run the program in the background without needing to leave the terminal open or have it occupy the whole terminal?  On that note, I did find a way to run programs from the terminal and have it allow for other inputs, by appending an ampersand (&) to the command as such:  nm-applet &   But this isn't much use as any processes started in the terminal are killed once the terminal is closed.


I have a VF page within a Lightning component.  When a user saves the form I need to generate a PDF of the new data.  I created another VF page to render the data as a PDF and a Controller.  What is the best method to invoke the PDF VF page and make sure it is after the new record is saved since I would like to attach the PDF to the record.  P

Is  post still valid as a solution to download a pdf from third-party site, then displaying it in a Visualforce page?   This is what I'm doing in my code:  Visualforce page  <apex:page controller="pdfDownloadController" sidebar="false" showHeader="false" contentType="application/pdf">     <script>         window.location.href = "data:application/pdf;base64,{!pdf}";     </script> </apex:page>   Apex Class  public class pdfDownloadController {      public String getPdf() {         HttpRequest req = new HttpRequest();         req.setEndpoint('https://www.irs.gov/pub/irs-pdf/fw4.pdf');         req.setMethod('GET');                                    // Make call         Http client = new Http();         HttpResponse rsp = client.send(req);          return rsp.getBody();      }  }   This is what loads when I go to this Visualforce page in lightning:    It doesn't appear to work when I go to classic either.  UPDATE:  As suggested by sfdcfox suggested, I used his method to display the pdf. That didn't work, but I did see these errors in the web console (Firefox):    I tried Chrome got a different browser response:    This what I get in the debug log from the response body. It looks like a pdf:


The wizards learn magic at Hogwarts, but what about "normal" education. Muggles learn English, Math etc. Is this not noticed when they make contact with muggles that they can't do basic math that you learn from age 11 and up. Do Hogwarts teach the kids things that are in the normal curriculum for those ages, or is it something that they do on their spare time? Or is this something that is considered irrelevant for wizards?

I always wondered if children who graduate from Hogwarts have an education that is actually worth while in the real world.  Do the children learn math and English?  I can see History of Magic as practical. I know of Arithmancy, but that's the study of the magical properties of numbers, not math.   Since Hogsmead is one of the very last all-magical towns, it's a fair assumption that a majority of the students at Hogwarts will be living in non-magical towns or cities. If practical classes (like math or English) aren't taught, then how do these students function in the non-magical cities?


Problem: I am not sure how to go about deleting all "duplicate" records so that only distinct records are left.  So from this:  ╔══════╦════════════╦════════╦════╗ ║ date ║ dupe_count ║ field1 ║ id ║ ╠══════╬════════════╬════════╬════╣ ║ x    ║         48 ║ y      ║ a  ║ ║ x    ║         48 ║ y      ║ b  ║ ║ x    ║         48 ║ y      ║ c  ║ ║ x    ║         48 ║ y      ║ d  ║ ║ x    ║         48 ║ y      ║ e  ║ ║ x    ║         48 ║ y      ║ f  ║ ║ x    ║         48 ║ y      ║ g  ║ ║ x    ║         48 ║ y      ║ h  ║ ║ x    ║         48 ║ y      ║ i  ║ ╚══════╩════════════╩════════╩════╝   To this:  ╔══════╦════════════╦════════╦════╗ ║ date ║ dupe_count ║ field1 ║ id ║ ╠══════╬════════════╬════════╬════╣ ║ x    ║          1 ║ y      ║ a  ║ ╚══════╩════════════╩════════╩════╝   Any ideas?

What is the best way to remove duplicate rows from a fairly large SQL Server table (i.e. 300,000+ rows)?  The rows, of course, will not be perfect duplicates because of the existence of the RowID identity field.  MyTable  RowID int not null identity(1,1) primary key, Col1 varchar(20) not null, Col2 varchar(2048) not null, Col3 tinyint not null


I have installed MacTex 2016 (equivalent to TexLive 2016) on my computer. That distribution contains the package pgfplots, but as I found out with the \pgfplotsversion-command, it's version 1.13.  However, the most recent version is 1.14 and as the documentation uses that version, I encounter some problems because some commands are new to the current version.  Unfortunately I was not able to update the package, by downloading it and moving it to my texmf-folder. Has anybody an idea on how to update from 1.13 to 1.14?  Many thanks in advance!

I'm trying to compile a document that only works with an up-to-date distribution, so I'd like to know: how do I update my distribution? Please provide screenshots where appropriate.  List of answers           To keep an eye on what’s going on at CTAN you may subscribe to the  or the RSS feed feed://www.mail-archive.com/ctan-ann@dante.de/maillist.xml


I have been strugling a lot to solve this question, but couldn't figure out where to start.  $$ \lim_{x \to \infty } \sqrt{n} . \underbrace {\sin(\sin(\sin ... (\sin (1))...))}_{n...times..} $$  I think maybe I should assume the part inside brackets as $y$.  But what next??  Any hints/suggestions?

I was asked today by a friend to calculate a limit and I am having trouble with the question.  Denote $\sin_{1}:=\sin$ and for $n>1$ define $\sin_{n}=\sin(\sin_{n-1})$. Calculate $\lim_{n\to\infty}\sqrt{n}\sin_{n}(x)$ for $x\in\mathbb{R}$ (the answer should be a function of $x$ ).  My thoughts:   It is sufficient to find the limit for $x\in[0,2\pi]$ , and it is easy to find the limit at $0,2\pi$ so we need to find the limit for $x\in(0,2\pi)$.  If $[a,b]\subset(0,\pi)$ or $[a,b]\subset(\pi,2\pi)$ we have it that then $$\max_{x\in[a,b]}|\sin'(x)|=\max_{x\in[a,b]}|\cos(x)|<\lambda\leq1$$ hence the map $\sin(x)$ is a contracting map.  We know there is a unique fixed-point but since $0$ is such a point I deduce that for any $x\in(0,2\pi)$ s.t $x\neq\pi$ we have it that $$\lim_{n\to\infty}\sin_{n}(x)=0$$  So I have a limit of the form "$0\cdot\infty$" and I can't figure out any way on how to tackle it.  Can someone please suggest a way to find that limit ?  Note: I am unsure about the tags, please change them if you see fit.


I'm using PDO after migrating away from the mysql library. What do I use in place of the old real_escape_string function?  I need to escape single quotes so they will go into my database and I think there may be a better way to handle this without add(ing) slashes to all my strings. What should I be using?

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


Is there an easy way to set up E-Mail notification when a Windows 2008 server's hard disk is getting full?

I was wondering if there is an easy way to trigger an e-mail alert on Windows Server 2008 when any logical disk partitions become low on space.  I have 2 SQL servers that have come close to running out of disk space because of the DB log files.  Thanks, Ryan


If  $\lim_{n \rightarrow \infty}f{\left(n\right)}=k$  and $f{\left(x\right)}$ is periodic and continuous, is that enough to imply that $f{\left(x\right)}$ is a constant function?

I stumbled upon this question in my course, and I am out of ideas. Let $f$ be a periodic function $$f(x)=f(x+l), \qquad l>0$$  Prove that if it is not constant, then $\lim_{x\to 0}f\left(\frac1x\right)$ does not exist.  I don't understand why it's true, let alone how to prove it.


There is a user account that has a suspension message on Mi Yodeya that says they are suspended network-wide until 2025. However, they have several other accounts, and none of them appear to be suspended. The user voted to close a question on Mathematics today, so they are clearly not suspended. Is this suspension message specific to the site? Did the moderators for the site erroneously choose this message, or does it not mean what I think it means? The other possibility is that it is a bug and that they are supposed to be suspended network-wide, but are not. This may not be a duplicate of , since the user is suspended "network-wide" on just one site, not all sites but a few. In that case, the user in question had been manually unsuspended on just one site by a moderator there. While it might be possible that local moderators unsuspended the user on all of their other sites but one, this may not be the case here.

A user has been active on one of the sites recently, even though they're concurrent suspended network-wide on the rest of the network. How is this possible, and is it possible to evade a network suspension on only one site?


I need to know when the hdd is a bottleneck, to improve my batch code on Windows 10 I am looking for a command line for cmd/batch similar to this one, but that helps me to know the disk load percentage. (This is not about the disk space).  wmic cpu get loadpercentage  thank you

On Windows, there's a GUI "Task Manager", and there's also a great little command-line "tasklist.exe" which lets me see most of the same data but in text that's really easy to parse from a script.  Is there an analogous command-line tool for "Resource Monitor"?  I'm looking for something that will list global CPU/disk/network/memory usage, and/or per-process usage.


I have been having this problem:   My most recent trouble-shooting step is what Ulrike Fischer suggested in  . Now it seems cm-super is not correctly installed on my PC (I see a .pk rather than a .pfb in the log) even though I do have it in MikTeX Package Manager   I have refreshed FNDB and updated formats in MikTeX Options (Admin) after installing cm-super.  Googling leads me to  , but I don't know how to follow the advice. Could someone please tell me how to execute M.A. solution "updating pdftex.map by running initexmf --mkmaps" in Windows MikTeX 2.9?   And what else do you think I may have missed?  Thanks a lot.

According to this question: , to get rid of the error, a scalable font must be loaded.   Package lmodern no longer seems available in MikTeX; all the "lm-something" package my repository offers are shown below:   Given that I install cm-super font family and add \usepackage[T1]{fontenc} to my document. But the error is still there.   MWE (excerpt from ):   \documentclass[12pt,letterpaper]{moderncv}        % possible options include font size ('10pt', '11pt' and '12pt'), paper size ('a4paper', 'letterpaper', 'a5paper', 'legalpaper', 'executivepaper' and 'landscape') and font family ('sans' and 'roman')  \usepackage[T1]{fontenc} %\usepackage{lmodern}  % modern themes \moderncvstyle{banking}                            % style options are 'casual' (default), 'classic', 'oldstyle' and 'banking' \moderncvcolor{blue}                                % color options 'blue' (default), 'orange', 'green', 'red', 'purple', 'grey' and 'black' %\renewcommand{\familydefault}{\sfdefault}         % to set the default font; use '\sfdefault' for the default sans serif font, '\rmdefault' for the default roman one, or any tex font name %\nopagenumbers{}                                  % uncomment to suppress automatic page numbering for CVs longer than one page  % adjust the page margins \usepackage{geometry}  \usepackage{import}  % personal data \name{My}{Name} \title{Curriculum Vitae}                               % optional, remove / comment the line if not wanted \address{my address, line 1, line 2, line 3, postcode}{}{}% optional, remove / comment the line if not wanted; the "postcode city" and and "country" arguments can be omitted or provided empty    %---------------------------------------------------------------------------------- %            content %---------------------------------------------------------------------------------- \begin{document} %\makecvtitle  Undergraduate electrical and electronic engineer completing the final year of a master's degree.   \end{document}   What do I do to make the error go away? Thanks. Your help is appreciated.   Update: I followed the step Ulrike Fischer suggested in  . Now it seems cm-super is not correctly installed (I see a .pk rather than a .pfb in the log) even though I do have it in MikTek Package Manager   I have refreshed FNDB and updated formats in MikTek Options (Admin) after installing cm-super.  Googling leads me to  , but I don't know how to follow the advice. Could someone please tell me how to execute M.A. solution "updating pdftex.map by running initexmf --mkmaps" in Windows MikTek 2.9? And what else have I missed?


So this is the thing I've got to prove: $ (A \cap C = B \cap C ) \land ( A \cup C = B \cup C ) \Leftrightarrow A = B $  I can understand this intuitively but the formal proof is taking me some time. So far, I've got this:   $ (A \cap C \subset B \cap C ) \land (B \cap C \subset A \cap C ) \land ( A \cup C \subset B \cup C ) \land ( B \cup C \subset A \cup C ) \Leftrightarrow (A \subset B) \land (B \subset A) $  $ (\forall x) (x \in A \land x \in C \Leftrightarrow x \in B \land x \in C ) \land (\forall x) (x \in A \lor x \in C \Leftrightarrow x \in B \lor x \in C ) \Leftrightarrow (\forall x)(x \in A \Leftrightarrow x \in B) $  But I feel like going nowhere. I assume this has something to do with the transitive property, but I'm not sure how to apply it here.

Prove or give a counterexample:  $$(A ∪ B = A ∪ C) \land (A ∩ B = A ∩ C) \implies B = C.$$  I think this is true, but I am not sure how to show it. I don't know if there are any manipulations with unions and intersections that allows me to move things around. Thanks in advance for any hints.


I would love to comment on & participate in discussion on the various Stack Exchange sites, but I don't have enough reputation. The one I have the most reputation on () has 46 rep points. Not enough to do anything productive. As a software engineer, I often Google to find out how to do something, and find the question has already been asked or answered on Stack Overflow, but just reading other people's questions and answers doesn't give me any reputation.  So what do I need to do to increase my reputation enough to prove I'm not a troll?

I understand that reputation can be gained by answering questions. However, it seems that more often than not the questions do not contain all the required information to give an answer. Since new users can not comment questions and ask for more details, this creates a sort of catch-22.  Any good advice on how to get initial reputation, given the new user restrictions?


For one calculation I need to round to 2 decimals during the calculation.   Relevant code:  count = 500; price = 0.00077 pounds = 150,000 double value = ((350 - count) * price) * (pounds / 100);   To get the result I need, (350 - count) * price must round to 2 decimal places before doing the pounds / 100 so how might i round to 2 decimal places during a calculation?

What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -> 0.91239 0.912300 -> 0.9123   What is the best way to achieve this in Java?


As we know, triangular numbers are a sequence defined by $\frac{n(n+1)}{2}$. And it's first few terms are $1,3,6,10,15...$. Now I want to calculate the sum of the sum of triangular numbers. Let's define $$a_n=\frac{n(n+1)}{2}$$ $$b_n=\sum_{x=1}^na_x$$ $$c_n=\sum_{x=1}^nb_x$$ And I want an explicit formula for $c_n$. After some research, I found the explicit formula for $b_n=\frac{n(n+1)(n+2)}{6}$. Seeing the patterns from $a_n$ and $b_n$, I figured the explicit formula for $c_n$ would be $\frac{n(n+1)(n+2)(n+3)}{24}$ or $\frac{n(n+1)(n+2)(n+3)}{12}$. Then I tried to plug in those two potential equations, If $n=1$, $c_n=1$, $\frac{n(n+1)(n+2)(n+3)}{24}=1$, $\frac{n(n+1)(n+2)(n+3)}{12}=2$. Thus we can know for sure that the second equation is wrong. If $n=2$, $c_n=1+4=5$, $\frac{n(n+1)(n+2)(n+3)}{24}=5$. Seems correct so far. If $n=3$, $c_n=1+4+10=15$, $\frac{n(n+1)(n+2)(n+3)}{24}=\frac{360}{24}=15$. Overall, from the terms that I tried, the formula above seems to have worked. However, I cannot prove, or explain, why that is. Can someone prove (or disprove) my result above?

Let $t(n)$ denote the n$^{th}$ triangular number.  Let $T(n)$ denote the sum of the first $n$ triangular numbers.  Is there a formula for $T(n)$?


I think there should be a markdown counting of suggestion limit, like how many I applied and how many I've left. Or is it already there and I didn't get it yet?

We need a hard rate limit on suggested edits, to limit the damage someone can do with blasting the review queue with minor edit suggestions.  Case in point:  peppered the site with a whopping 133 tag-only edit suggestions in 2 hours and 15 minutes. That's one edit every minute on average, but towards the end he was entering a new suggestion every 20 seconds. He only stopped because a  drew enough rejections to have him banned from entering more.  If there was a limit to the number of suggested edits you can enter in a time period we could have stopped this guy earlier. No <2k user needs to edit hundreds of tags across that many questions in 2 hours time.  Considerations   There are cases where a retag drive or tag burninate justifies editing a larger number of posts, but I'd be fine if such tasks were limited to people with 2k+ reputation. A retag or burninate job requires a minimal engagement with the community to know when they are justified anyway. The suggested edit review process, by itself, was clearly not enough to stop this barrage. It cannot be seen as a rate limiting measure, at least not as a sufficiently efficient one.  The vast majority of the edits made in the above example were too minor, leaving spelling, grammar and formatting mistakes in the post untouched. The user was going too fast to pay attention to such details anyway. Yet this user has 98 approved edit suggestions, but all but 6 or 7 I'd have rejected as too minor, so the review process itself is broken.   What should be limited   The number of review votes reviewers have is already limited; I burned through 20 reviews in short order just reviewing the suggestions from just this one user. Certainly the number of unreviewed suggestions should be limited to let reviewers catch up with a user like this. I'd say having 20 outstanding suggested edits pending review is plenty. Suggested edits should be made with some consideration; we don't want minor edits, so if you are suggesting more than 20 in an hour (that's 1 every 3 minutes) you are not improving posts anymore, you are gaming the system to gain reputation.


I'm trying to get user time zone with a script from JS. The result of this JS is passing successfully to the backend, but as I know, when the JS result have passed to the backend the shortcode is already loaded. So, I'm looking for a solution how can I get the user time zone and get this result in a shortcode. Thanks to this thread (), I have this:  add_action( 'wp_ajax_my_action', 'my_action_callback' ); add_action( 'wp_ajax_nopriv_my_action', 'my_action_callback' ); add_action( 'wp_enqueue_scripts', 'theme_name_scripts' ); add_shortcode('tagtest', 'timezone');  function theme_name_scripts() {     wp_enqueue_script( 'script-name', plugins_url( '/assets/js/timezone.js', __FILE__ ), array('jquery'), '1.0.0', true );     wp_localize_script( 'script-name', 'MyAjax', array(         'ajaxurl' => admin_url( 'admin-ajax.php' ),         'security' => wp_create_nonce( 'my-special-string' ),     )); }  function my_action_callback() {     $whatever = strval( $_POST['whatever'] );     echo wpse_301294_whatever($whatever);     wp_die(); }  function wpse_301294_whatever($whatever) {     return $whatever; }  function timezone(){     $tz = wpse_301294_whatever(); // here I'd need the $whatever parameter but how can I get if the shortcode has already rendered?     $timestamp = time();     $dt = new DateTime("now", new DateTimeZone($tz));     $dt->setTimestamp($timestamp);     $hour = $dt->format('G');     // echo '
' . $tz . '
';     return '
' . $hour . '
';; }   If you could guide me with some code would be very nice, but I'd like also understand the workflow that I should follow because I don't understand if how could this be possible if when the JS pass to the backend, the shortcode is already rendered.  Thanks in advance.

I'm really newbie in Wordpress development (around 24 hours ago). I'm trying to build a custom plugin that detects the hour of the user depending on their time zone (not time zone of the Wordpress site) to achieve that, I'm making a shortcode that executes a short Javascript code (in this JS I get the local time of the client side) the result of this JS script I need to get it in the function that executes the shortcode. I have this:  PHP  function range_hour($atts, $content = null){      wp_register_script( 'custom-script', plugins_url( 'assets/js/timezone.js', __FILE__ ), array( 'jquery' ) );     wp_enqueue_script( 'custom-script' );     $tz = 'America/Bogota';     $timestamp = time();     $dt = new DateTime("now", new DateTimeZone($tz));     $dt->setTimestamp($timestamp);     $hour = $dt->format('G'); }   Javascript  Intl.DateTimeFormat().resolvedOptions().timeZone   As you can see in the JS code I'm getting the timezone of the client, until here all fine, but in the PHP code I need to get this result, to replace "America/Bogota" for the JS result. Any ideas how can I achieve this? I'm thinking to make an endpoint, pass the data from JS to that endpoint, but again... How can I get this result in the shortcode function?  Thanks in advanced.


Let$(X,d)$ be a metric space, $A$ nonempty, compact subset of $X$. Let $$\mathrm{dist}(A,B)=\inf_{\substack{a\in A\\b\in B}}d(a,b).$$ I want to show that for every compact subset $B$ of $X$ disjoint from $A$ $\mathrm{dist}(A,B)>0$. I tried to show it using the extreme value theorem. Since $A,B$ are compact, then so is $A\times B$, $D:A\times B\to (0,\infty)$ defines a metric on $A\times B$, so if $f:A\times B\to (0,\infty)$, $\inf f = \mathrm{dist}(A,B)$ showing that $f$ attains it's minimum, that is $\inf f = \min f$ would complete the proof, but I'm not sure how to show $f$ is continuous. Any hints? Edit: I'm familiar with that linked proof, but I was trying to use a different method, using extreme value theorem, but I'm not quite sure how to prove continuity of $f$ for $D((a,b),(c,d))=d_1(a,c)+d_1(b,d)$.

Claim: Let $X$ be a metric space. If $A,B\in X$ are disjoint, if A is compact, and if B is closed, then $\exists \delta>0: |\alpha-\beta|\geq\delta\;\;\;\forall\alpha\in A,\beta\in B$.  Proof. Assume the contrary. Let $\alpha_n\in A,\beta_n\in B$ be chosen such that $|\alpha_n-\beta_n|\rightarrow0$ as $n\rightarrow \infty$.  Since A is compact, there exists a convergent subsequence of $\alpha_n\;(n\in\mathbb{N})$, $\alpha_{n_m}\;(m\in\mathbb{N})$, which converges to $\alpha\in A$.  We have   $$|\alpha-\beta_{n_m}|\leq|\alpha-\alpha_{n_m}|+|\alpha_{n_m}-\beta_{n_m}|\rightarrow0 \;\;\;as\;\;m\rightarrow\infty.$$ Hence $\alpha$ is a limit point of B and since B is closed $\alpha\in B$, contradiction.  Is my proof correct? I feel as though I am missing something simple which would trivialize the proof.


I have downloaded Oracle VM virtual Box and while creating virtual machine, it was showing only ubuntu 32 bit.It was not showing 64 bit,please help me to solve my problem.

I've installed VM VirtualBox v. 4.3.8 on my Ubuntu 12.04 LTS (Lenovo G500S with Intel 1005M processor) and I can't configure any 64-bit guest (nor Windows, neither other OS). Inslalation of Win 8.1 64-bit under 32-bit profile obviously fails... My processor supports VT-x technology, but in my BIOS there is no enable/disable option for VT-x. Is there any way to force VirtualBox to support 64-bit guest ?


I've found both of these amazing answers on Superuser: one to convert a series of images to a video with cross-dissolves between them, and another to convert a video to a high-quality gif. My follow-up question to both of those is, how can I do this in one command, for multiple images (could be 3 images, or could be 20).  @LordNeckbeard and other ffmpeg superusers, can you help me out?  Here's the answers that have helped so far:  Images to Video with cross-dissolve:   Video to Gif:

With 5 images I have to create a video of 60 seconds in ffmpeg, each image has to display for 15 seconds. after  15 seconds, first image has to fade out and 2nd image has to fade in, after that 2nd image has to fade out, 3rd image has to fade in..etc. Please guide me how can I achieve this using ffmpeg commands.


Is there any formula to compute $\sum_{k=1}^n\frac {1}{k^k}$? Where the value of $k$ ranges from $1$ to $n$.

Earlier today, I was talking with my friend about some "cool" infinite series and the value they converge to like the Basel problem, Madhava-Leibniz formula for $\pi/4, \log 2$ and similar alternating series etc.  One series that popped into our discussion was $\sum\limits_{n=1}^{\infty} \frac{1}{n^n}$.  Proving the convergence of this series is trivial but finding the value to which converges has defied me so far. Mathematica says this series converges to $\approx 1.29129$.  I tried Googling about this series and found very little information about this series (which is actually surprising since the series looks cool enough to arise in some context).  We were joking that it should have something to do with $\pi,e,\phi,\gamma$ or at the least it must be a transcendental number :-).  My questions are:   What does this series converge to? Does this series arise in any context and are there interesting trivia to be known about this series?   I am actually slightly puzzled that I have not been able to find much about this series on the Internet. (At least my Google search did not yield any interesting results).


I'm trying to grep for a instance "test" in /etc/oratab. But wanted to display only the line that doesn't begin with a comment. Below are the lines from /etc/oratab file:  #test:/u01/appl/oracle/test/db/tech_st/12.1.0.2:N test:/b001/app/oracle/testrac/db/tech_st/12.1.0.2:N         # line added by Agent   This is how I'm trying to get the details I'm interested in (placed the below in a shell script:  DB_NAME=test env_var=`cat /etc/oratab |grep $DB_NAME |grep -v '#' |cut -d":" -f 2` echo $env_var   The problem here is, as the 2nd line also has a comment at its end, it is also being ignored.   Please help.  Regards, RA

I try to search for lines that start with "1" using   ls -1 | grep ^1*   but it returns lines that do not start with 1. What I am missing here?


I want to make a list of lists in python. I am initializing this list like:  n = 3 adj = [[]]*n   So now when I print adj, I get:  [[], [], []]   ...which is fine.  Now, I want to append values to a particular list (one particular index). I have done this:  adj[0].append(1)   Hence, my expected output is:  [[1], [], []]   However the output is:  [[1], [1], [1]]   I can't seem to understand why this is so. Probably I am not understanding something about how Python's lists work, or am making an utterly silly mistake. Any help would be greatly appreciated.  Additionally, I would really appreciate a suggestion as to how I can get my desired output.

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?