The answer in the textbook says no. But I have a proof for it, so wanna know where the mistake is.  proof :  supposed M not compact.  Let { Ui } be a open sets covering of M, which doesn't have a finite subcovering.  Let {Uj} be a minimal subset of {Ui} such that {Uj} is still a covering of M. (in other word : when you remove any element from {Uj}, the remained {Uj} don't cover M any more.)  { xj : xj is an element of Uj , xj is different from xk when j is not k} You take a point xj from each Uj, which is different from any other points from other Ujs( in other word : which is not contained in any other Uj).  it's possible because {Uj} is minimal.  This set of xj has a accumulation point p in M.   Since {Uj} cover M, there exist a Uj which contains p.  because p is a accumulation point of xj and Uj contains p, Uj contains infinate many xj. This is a contradiction to the choice of xj. (since each xj is contained in only one Uj)  Hope to find my mistake. thank you very much.  --------------replies to comments-------------  (I can't post comment so I have to write it here)  @Max   My question is not that, is actually the reverse implication.

I've seen both counterexamples and proofs to "compact implies sequentially compact", and I'm not sure what's going on. Apparently there are compact spaces which are not sequentially compact; quick googling and wikipedia checks will turn up examples floating around; they tend to be variants of $[0,1]^{[0,1]}$ with the product topology.  Here's a demonstration(?):  $[0,1]^{[0,1]}$ is compact by Tychonoff's theorem.  So, we demonstrate failure of sequential compactness. Choose a unique binary representation for each $x\in [0,1]$. For each $n\in\mathbb{N}$, let $f_n : [0,1]\to[0,1]$ (an element of $[0,1]^{[0,1]}$) be the function which maps each $x$ to its $n$-th place digit in its binary expansion. Let $f_{n_k}$ be a subsequence of this sequence. Let $x'\in [0,1]$ be such that the $n_{2m}$-th digit is $0$ and the $n_{2m+1}$-th digit is $1$, for all $m\in\mathbb{N}$. Then $f_{n_k} (x')$ does not converge (it alternates between $0$ and $1$), and hence $f_{n_k}$ cannot converge. Thus we have found a sequence in $[0,1]^{[0,1]}$ without any convergent subsequence and so it is not sequentially compact.  (Aside: this is apparently based off of an example in Steen's Counterexamples in Topology, according to  ) Nevertheless, there's also some proofs(?) floating around that compactness of a space implies sequential compactness, along these lines (this proof(?) is of the contrapositive):  Suppose $X$ is not sequentially compact. By definition, this means there is some sequence $(x_n)$ over $X$ with no convergent subsequence. If any $x\in X$ had for each of its neighborhood $U$ infinitely many $n$ for which $x_n \in U$, then we could define a convergent subsequence of $(x_n)$, contradicting our assumption.  (Presumably this is done by choosing for each neighborhood a sufficiently-large-indexed term in that neighborhood.) Thus, for each $x \in X$ we can select an open set $U_x$ such that $x\in U_x$ but with $x_n \in U_x$ for only finitely many $n$. The collection $\mathcal{U}=\{U_x : x\in X\}$ is clearly an open cover of $X$. If $\mathcal{U}$ had a finite subcover $\{U_1, \dots, U_k\}$ then the union $U_1 \cup \cdots \cup U_k$ would contain all of $X$ but only contain $x_n$ for finitely many $n$, which is impossible. Thus $X$ is not compact, since we have found an open cover without a finite subcover.  (Aside: this proof is essentially the same as the proof appearing in Rudin's Principles of Mathematical Analysis for Thm 2.37 that infinite subsets of compact spaces have limit points.) So, what's going on here?  It can't be that what both the counterexample and the proof are telling us is correct.  Is there some subtle (or more embarassingly for me -- glaring) flaw in the proof?


I'm an undergraduate physics without much quantum mechanics at all under my belt. I'm studying functional analysis, and I want to know whether or not this will be useful for me in theoretical physics in the future. Some perceived benefits of studying functional analysis are:   It gives familiarity with spaces (Hilbert spaces especially) and linear operators in their most general form, which (so I hear) pop up all the time in quantum mechanics. I have noticed that the treatment of linear forms, bilinear forms, and duals, in pure functional analysis, complement what Penrose talks about in Road to Reality, where the dual of a vector is treated as a function which takes in a vector and spits out a real number. This is "weird" because I used to think of the dual to a vector as essentially another vector, but Functional analysis seems to spell this out and give all the needed isomorphisms to make sense of it all, in whatever form desired. It defines distributions in their most general form, which seems especially useful to make sense of, say, $\delta'$ and $\delta''$, where $\delta$ is the Dirac delta, should they arise in physics while solving a differential equation.   But of course, those three things could have been learned, possibly in a shorter amount of time, by reading from a physics book and taking a less "definition-theorem-proof" approach to the whole subject. On the other hand, the rigor, I think, might help me identify which assumptions are physical, which are definitions, and which are mathematical theorems.   But I'd like to ask: In what other ways is rigorous functional analysis useful for theoretical physics? And are there any other ways that it isn't useful?

The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into five specific questions.  Update February, 12, 2018: Since the question was put yesterday on hold as too board, I ask future to refer only to questions one and two listed below. I will ask a separate questions on item 3 and 4. Any information on question 5 can be added as a remark.         What are the most important and the oldest insights (notions, results) from physics that are still lacking rigorous mathematical   formulation/proofs.   The endeavor of rigorous mathematical explanations, formulations, and proofs for notions and results from physics is mainly taken by   mathematicians. What are examples that this endeavor was beneficial to   physics itself.       What are examples that insisting on rigour delayed progress in physics. What are examples that solid mathematical understanding of certain issues from physics came from further developments in physics itself. (In particular, I am interested in cases where mathematical rigorous understanding of issues from classical mechanics required quantum mechanics, and also in cases where progress in physics was crucial to rigorous mathematical solutions of questions in mathematics not originated in physics.) The role of rigor is intensely discussed in popular books and blogs. Please supply references (or better annotated references) to academic studies of the role of mathematical rigour in modern physics.   (Of course, I will be also thankful to answers which elaborate on a single item related to a single question out of these five questions. See update)  Related Math Overflow questions:     (related to question 1);  ;  .


I have upgraded to Disco Dingo, but right now I can't install MySQL 8 as it's not available from the official MySQL repository.  Is there any alternative repository or PPA from which I could install MySQL 8?

I have a Drupal site 8.6.10 on an Ubuntu server 18.04 with MySQL 5.7.25  I want to update MySQL to version 8.0  Here are the steps I followed :   I backed up my database. I uninstalled MySQL from my server with the commands :  $ sudo systemctl stop mysql $ sudo apt remove mysql-* $ sudo apt purge mysql-* $ sudo apt autoremove $ sudo dpkg -l | grep mysql | grep ii  I added the repository with the command :  $ wget https://repo.mysql.com//mysql-apt-config_0.8.12-1_all.deb  I installed the package with the command :  $ sudo dpkg -i mysql-apt-config_0.8.12-1_all.deb            My problem :   I install MySQL with the command :  $ sudo apt update $ sudo apt install mysql-server    When I do step 5, it installs MySQL 5.7 why does not it install version 8 ?


I want to add more memory to my pc. is there any tool that can scan my hardware tell me how much more memory i can fit, from which type (ddr2/3) in which slot?  Thanks

I am seeking advice on which memory to use with my motherboard and CPU. Below are my components and some relevant information extracted from their official websites.   NOTE: Although this is a very specific case, a general answer is equally good for me — and also alot more useful for everyone else!  CPU: AMD Phenom II X4 810   ASUS M4A785TD-V EVO listed as one of many  motherboards.   Motherboard: ASUS M4A785TD-V EVO   4 x DIMM, Max. 16 GB, DDR3 1800(O.C.)*/1600(O.C.)/1333/1066/800 ECC,Non-ECC,Un-buffered Memory Dual Channel memory architecture (Complete list of specs: ).   NOTE II: I wouldn't want to do any overclocking as I have no experience with that. So I think the 1333 MHz is the most appropriate. Since the higher frequencies are marked with "O.C."  Questions:   How can I be certain that a specific RAM will work well (or not work) together with my CPU and motherboard? (The Qualified Vendor List is a good starting point, but it's a bit limited and sometimes a bit outdated). Is it true that choice of memory is not independent of the processor? How?    I'm worried I'll be missing something essential when buying my next RAM chips :)


I'm looking to convert Park polygons from OSM into points.  The QGIS fTools  tool will convert a polygon to points at the vertices.  What is the equivalent function or work-flow in PostGIS?

I have PostGIS database, and want to extract lat, lon pairs sequence from Polygons (and MultiPolygons). As a very fresh PostGIS user, I'm able to just extract the Polygons:  SELECT st_astext("GEOMETRY"::geometry) FROM my_postgisdb;  which outputs Polygons and MultiPoligons.  How should I extract x, y pairs from these structures?


So, let's say I have a jar file called "a.jar" and another jar file called "b.jar".  In the b.jar we have a class called "c.class" and in the a.jar we have a class called "getmesomething.class" with a main function.  From the "getmesomething.class" I'd like to access the "c.class" methods and stuff.  But I do not know how to access "b.jar/c.class" from the main function in "a.jar/getmesomething.class".  I hope I spelled everything right and it isn't too confusing. :-)

I read the Java tutorials on Sun for JAR files, but I still can't find a solution for my problem. I need to use a class from a jar file called jtwitter.jar, I downloaded the file, and tried executing it (I found out yesterday that .jar files can be executed by double clicking on them) and Vista gave me an error saying "Failed to load Main-Class Manifest attribute from [path]/jtwitter.jar".  The guy who coded the .jar file wants me to import it, but where do I store the .jar file to import it in my code? I tried putting both the .jar file and my .java file in the same directory, didn't work.  The file I'm trying to work for is here:   I'm using JCreator LE.


What is the difference between     I am yet to see X   and     I have yet to see X   and in which situations would each be preferred?

He has  yet to receive an appointment.   He is yet to receive an appointment.      Is there any difference in meaning? Is one more correct than the other?


Hi I'm new in the world of android. So I tested a tutorial do fetch data from a XAMPP database and list it in my app with listview. Everything is like in the tutorial, so why my app doesnt't work? When I start the app i got an error message and the app crushes.  Thank you for your help!  public class MainActivity extends ActionBarActivity {  private TextView responseTextView;  @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_main);       this.responseTextView = (TextView) this.findViewById(R.id.responseTextView);       new GetAllCustomerTask().execute(new ApiConnector());   }  public void setTextToTextView(JSONArray jsonArray) {     String s  = "";     for(int i=0; i<jsonArray.length();i++){          JSONObject json = null;         try {             json = jsonArray.getJSONObject(i);             s = s +                     "ID : "+json.getInt("id")+"\n"+                     "Name : "+json.getString("name")+"\n\n";         } catch (JSONException e) {             e.printStackTrace();         }      }      this.responseTextView.setText(s);  }   private class GetAllCustomerTask extends AsyncTask<ApiConnector,Long,JSONArray> {     @Override     protected JSONArray doInBackground(ApiConnector... params) {          // it is executed on Background thread          return params[0].GetAllCustomers();     }      @Override     protected void onPostExecute(JSONArray jsonArray) {          setTextToTextView(jsonArray);       } }   }  public class ApiConnector {  public JSONArray GetAllCustomers() {     // URL for getting all customers       String url = "http://localhost/getAllCustomers.php";      // Get HttpResponse Object from url.     // Get HttpEntity from Http Response Object      HttpEntity httpEntity = null;      try     {          DefaultHttpClient httpClient = new DefaultHttpClient();  // Default HttpClient         HttpGet httpGet = new HttpGet(url);          HttpResponse httpResponse = httpClient.execute(httpGet);          httpEntity = httpResponse.getEntity();        } catch (ClientProtocolException e) {          // Signals error in http protocol         e.printStackTrace();          //Log Errors Here        } catch (IOException e) {         e.printStackTrace();     }       // Convert HttpEntity into JSON Array     JSONArray jsonArray = null;      if (httpEntity != null) {         try {             String entityResponse = EntityUtils.toString(httpEntity);              Log.e("Entity Response  : ", entityResponse);              jsonArray = new JSONArray(entityResponse);          } catch (JSONException e) {             e.printStackTrace();         } catch (IOException e) {             e.printStackTrace();         }     }      return jsonArray;   }   }  This is my logcat  04-06 22:17:21.550  23914-23914/diplomarbeit.at.dbfetchcontenttester E/AndroidRuntime﹕ FATAL EXCEPTION: main Process: diplomarbeit.at.dbfetchcontenttester, PID: 23914 java.lang.NullPointerException         at diplomarbeit.at.dbfetchcontenttester.MainActivity.setTextToTextView(MainActivity.java:34)         at diplomarbeit.at.dbfetchcontenttester.MainActivity$GetAllCustomerTask.onPostExecute(MainActivity.java:66)         at diplomarbeit.at.dbfetchcontenttester.MainActivity$GetAllCustomerTask.onPostExecute(MainActivity.java:53)         at android.os.AsyncTask.finish(AsyncTask.java:632)         at android.os.AsyncTask.access$600(AsyncTask.java:177)         at android.os.AsyncTask$InternalHandler.handleMessage(AsyncTask.java:645)         at android.os.Handler.dispatchMessage(Handler.java:102)         at android.os.Looper.loop(Looper.java:136)         at android.app.ActivityThread.main(ActivityThread.java:5105)         at java.lang.reflect.Method.invokeNative(Native Method)         at java.lang.reflect.Method.invoke(Method.java:515)         at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:792)         at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:608)         at dalvik.system.NativeStart.main(Native Method)

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I want to only return results in entityfieldquery that have a propertyCondition of 'field_entry_path' that is not empty.     $query = new EntityFieldQuery();   $query->entityCondition('entity_type', 'example')         ->propertyCondition('field_entry_path', '', 'NOT IN');   $result = $query->execute();   Thanks.

Is it possible to select all of the entities who's xyz field is empty?  I tried soemthing like this:  ->fieldCondition('field_name', 'value', NULL, 'IS NOT NULL');   However, this doesn't seem to work.  Any ideas?


I am in need of hints in proving this. I am unsure if this can be done using mathematical induction.

Wouldn't these two sets have the same cardinality?  If so, I am unsure of how to prove that two sets with the same cardinality have a bijective correspondence.


From googling around, installing guest additions on a VirtualBox Ubuntu guest seems quite complicated.  I've googled around and have found no "official" instructions on Ubuntu or VirtualBox.  Also, the searches I've found are quite old.  1 - Why are there no "official" instructions on Ubuntu or VirtualBox?  2 - is there a utility in the software centre that can do all this?  3 - If not, How to do it?  Thanks

I've recently installed Ubuntu on Oracle's Virtualbox.  Now I want to install the guest additions.  I started up my Ubuntu guest OS, clicked "Devices" and chose "Install Guest Additions". Nothing happened, and I don't see the CD icon on my desktop.  How can I make this work?


These   don't have a name in my profile page, but on their detail it clearly states that they are an orphaned tag wiki. Can we fix this inconsistency please?

If a user makes an edit to a tag wiki that subsequently becomes orphaned, the activity entries on their profile are left looking a bit broken. For example,  shows the following:    I believe that it used to say something like "orphaned wiki" in the marked sections, which would be preferable to nothingness.


I understand that temperature difference is the driving force for heat transfer but I have been wondering whether there would be any heat transfer, let's say if steam at 100 degree Celsius and water at 100 degree Celsius are passed through the two sides of a Heat Exchanger.

Suppose we have an experiment with two containers, one with ice at 0°C and the other with water also at 0°C (equal masses), and a thermally conductive barrier (also at 0°C) in contact with both the water and the ice, and in between them.  The whole experiment itself is insulated from the environment.  What is the final state of the system?  Does it remain unchanged, because with no temperature difference there is no heat flow?  Or does it random walk itself somehow to a final state with 50/50 water/ice slush on both sides?


I downloaded Landsat 8 imagery from Earth Explorer for a particular area.  I tried to get it with no cloud cover, but it did not show any results.  The least amount of cloud cover that I could get was 40%.  Is there a way that I can remove the cloud cover in ArcGIS for Desktop 10.5?  I have seen script on how to do it but I cannot figure out how to do it in ArcMap.  Does anyone know how you can remove cloud cover from Landsat imagery in ArcMap?

I have a land cover classification derived from Landsat TM imagery - I created this classification using ENVI. I would like to edit individual and groups of cells in some areas of the classification in order to improve the accuracy of the output by comparing it with aerial imagery.  Is there a way, using ArcGIS Desktop, to manually edit large groups of cells by selecting them and assigning them to a new or existing class?   I am aware of merging methods based on class statistics, but the area I'm classifying has a high amount of spectral confusion due to thin cloud cover - it seems like a manual edit is the only way to go.


<input type="text" id="target" />   How to do it with jQuery?

Is there a quick way to set an HTML text input (<input type=text />) to only allow numeric keystrokes (plus '.')?


I am using Ubuntu 14.04, and I want to decompress a 500 MB rar archive. I have installed the most recent version of rar and unrar from the terminal.  When I go to extract the contents from the archive the Archive Manager extracts them, but it takes a little while and at the end I get a message that says:      produced an error when extracting the file   and it gives me only the option of closing the Archive Manager. I'm desperate because I downloaded the same GTA San Andreas archive of different videos three times, and it always tells me the same thing which I do not understand.

I added a torrent for download about a month ago which is in .rar format.  Unfortunately, it doesn't seem to proceed any further than 91.01% due to unavailability of seeders.  Whenever I try to open or extract the torrent I get the following error:  An error occurred while loading the archive.   Command Line output:  ??? - the file header is corrupt.   I am using archive manager to extract the file.  Is there any possibility of extracting the file using any method?


My bluetooth does not detect any devices - phones, other laptops, bluetooth speaker, keyboards, etc.  It just keeps searching and searching.     I am very new to Linux, so I would really appreciate some help on this. Please tell me what additional information you guys need so that you can help me.  Output of: lspci -knn | grep Net -A2; lsusb  02:00.0 Network controller [0280]: Broadcom Corporation BCM43142 802.11b/g/n [14e4:4365] (rev 01)     Subsystem: Lite-On Communications Inc BCM43142 802.11b/g/n [11ad:66a5]     Kernel driver in use: wl Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 004: ID 04ca:2012 Lite-On Technology Corp.  Bus 001 Device 003: ID 0bda:57b3 Realtek Semiconductor Corp.  Bus 001 Device 002: ID 045e:07fd Microsoft Corp. Nano Transceiver 1.1 Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub   Thanks in advance!  Regards, Kristiyan

Bluetooth is on but can't find or be found by any other devices.  Output of sudo service bluetooth status:  ● bluetooth.service - Bluetooth service    Loaded: loaded (/lib/systemd/system/bluetooth.service; enabled; vendor preset: enabled)    Active: active (running) since ხუთ 2015-06-04 22:33:18 GET; 13min ago  Main PID: 26678 (bluetoothd)    CGroup: /system.slice/bluetooth.service            └─26678 /usr/sbin/bluetoothd -n  ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPAG ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPHS ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSource ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSink ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPAG ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/HFPHS ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSource ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Endpoint registered: sender=:1.63 path=/MediaEndpoint/BlueZ4/A2DPSink ივნ 04 22:39:14 Rangoo bluetoothd[26678]: Adapter /org/bluez/26678/hci0 has been enabled ივნ 04 22:39:14 Rangoo bluetoothd[26678]: bluetoothd[26678]: Adapter /org/bluez/26678/hci0 has been enabled   Output of lsusb:  Bus 003 Device 005: ID 0a5c:21d7 Broadcom Corp. BCM43142 Bluetooth 4.0   How can I fix it?


The de Broglie wavelength of any massive particle is $\lambda = \frac{h}{p}$. We know that if a large object (say, a baseball) is at rest, it will have $p=0$ and hence $\lambda$ will be infinite. This should allow us to observe quantum interference of the baseball. Online sources say something about the uncertainty principle: we can never be certain that $p=0$. There will always be some uncertainty in the value of $p$. If we want to decrease $\Delta p$, we have to increase $\Delta x$, the uncertainty in the position of the baseball. Why doesn't this allow us to observe quantum effects?

If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths.   What am I missing? Do we have to invoke earth's motion, motion of the galaxy etc. to resolve the issue?


Suppose that you can apply the Ratio Test to $\Sigma a_{n}$. Let $r$ be the limit of $|a_{n+1}|/|a_{n}|$. Show that $\lim\sup|a_{n}|^{1/n}=r$ as $n\rightarrow\infty$.  I know by definition of lim sup that $\forall\epsilon>0$,  $\exists N_{\epsilon}$  s.t. $x_{n}<r+\epsilon$  $\forall n>N_{\epsilon}$. Not sure how to apply that here though.

In Elias Stein and Rami Shakarchi's Complex Analysis textbook, we have the following exercise:     Show that if $\{a_n\}_{n=0}^\infty$ is a sequence of complex numbers such that $$\lim_{n\to\infty}\frac{|a_{n+1}|}{|a_n|}=L,$$ then $$\lim_{n\to\infty}|a_n|^{1/n}=L.$$    I've been trying to prove this with no luck. The only thing I've thought of doing is $$\lim_{n\to\infty}\left(\frac{|a_{n+1}|^n}{|a_n|^n}\right)^{1/n},$$but this hasn't lead me anywhere except dead ends. Will someone provide a hint for me about how to proceed? Thanks!  Minor update: I don't know if it's helpful yet, but I know we can write the limit as $$\lim_{n\to\infty}\left(\frac{|a_{n+1}a_n\cdots a_0|}{|a_n\cdots a_0|}\cdot\frac{1}{|a_n|}\right).$$This reminds me a lot of the geometric mean, which even has the exponents I'm trying to get...


I'm just started using LaTeX, and I ran into a problem: The text starts way down in the page, so there is a lot of empty room. How do I move the text upwards?    Code:  \documentclass{report} \usepackage[utf8]{inputenc} \usepackage[norsk]{babel} \usepackage{titlesec} \usepackage{graphicx}      \title{THT310} \author{Eivind Hagen}    \titleformat{\chapter}[display]   {\Huge\bfseries}   {}   {0pt}   {\thechapter.\ }  \titleformat{name=\chapter,numberless}[display]   {\Huge\bfseries}   {}   {0pt}   {}      \begin{document} \begin{titlepage} \maketitle \end{titlepage}  \tableofcontents \newpage      \chapter{Introduksjon} \input{kapittel1} \chapter{del 2} \input{kapittel2}      \end{document}

I want to decrease the vertical space between the top of the page and the chapter heading. I have tried to follow the instructions for titlesec but I am not successful. I have tried the following two setups without any changes occuring.  First:  \documentclass[12pt]{report}   \usepackage[compact]{titlesec}   \begin{document}   \chapter{Characters}  The origin of the group determinant begins with Richard Dedekind in the late 1800's. He began to explore the idea after studying the discriminant in a normal field [A]. He made several observations about the group determinant, but was only able to prove some of them.   \end{document}   Second:  \documentclass[12pt]{report}   \usepackage{titlesec}   \titleformat{\chapter}[display]   {\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}   \titlespacing{\chapter}{0pt}{0pt}{0pt}   \begin{document}   \chapter{Characters}    The origin of the group determinant begins with Richard Dedekind in the late 1800's. He began to explore the idea after studying the discriminant in a normal field [A]. He made several observations about the group determinant, but was only able to prove some of them.   \end{document}


I am currently trying to install ubuntu 13.10 to dual-boot with windows 8.1 on my laptop. The laptop is a Lenovo Ideapad z400 touch. I am getting stuck at the Install Style screen because the installer is not recognizing windows being already there and I don't know how I should do the partitioning manually. The boot-repair pastebin is   I have about 70 GB of unallocated space on my hdd for ubuntu.  Here is the lbsk output:   ubuntu@ubuntu:~$ lsblk NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 931.5G  0 disk ├─sda1   8:1    0  1000M  0 part ├─sda2   8:2    0   260M  0 part ├─sda3   8:3    0  1000M  0 part ├─sda4   8:4    0   128M  0 part ├─sda5   8:5    0 839.7G  0 part ├─sda6   8:6    0   350M  0 part └─sda7   8:7    0    20G  0 part sdb      8:16   1  29.3G  0 disk └─sdb1   8:17   1  29.3G  0 part /cdrom sr0     11:0    1  1024M  0 rom       loop0    7:0    0 842.7M  1 loop /rofs    Here is the sudo blkid output:  ubuntu@ubuntu:~$ sudo blkid /dev/sda1: LABEL="WINRE_DRV" UUID="CC863F8F863F78D2" TYPE="ntfs" /dev/sda2: LABEL="SYSTEM_DRV" UUID="2241-C2D6" TYPE="vfat" /dev/sda3: LABEL="LRS_ESP" UUID="6C41-FE4B" TYPE="vfat" /dev/sda5: LABEL="Windows8_OS" UUID="284245254244F8D8" TYPE="ntfs" /dev/sda6: UUID="145447175446FACE" TYPE="ntfs" /dev/sda7: LABEL="PBR_DRV" UUID="8C0C487E0C4864F4" TYPE="ntfs" /dev/loop0: TYPE="squashfs" /dev/sdb1: LABEL="UUI" UUID="50B7-103F" TYPE="vfat"    Thanks.

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


At random times, the svchost process takes a lot of memory, and the PC becomes unusable. A screenshot is below.  Is it a known issue? How can I found out what causes it, and how can it be fixed?

I'm running Windows 7. It seems that svchost is eating up a lot of memory.   The user name for the particular svchost instance is "Network Service". The description is "Host Process for Windows Services".   Sometimes it eats up 50% of the CPU usage. Other times, it's just under 5%. I can't figure out when it's 50% and when it's not. But it fluctuates often -- even when I've just booted up and no programs were started.  How do I diagnose this?


Question:  Suppose $ \frac{1}{x^2}+x^2$ is an integer. Prove that $ \frac{1}{x^{2n}}+x^{2n}$ is an integer for all natural $n$.  Hint: Use Strong Induction   My attempt:  Base Case is trivial.  I.H: Assume the result is true for $n = 1,2, ...., k.$  Consider $n = k+1$.  $ \frac{1}{x^{2\left(k+1\right)}}+x^{2\left(k+1\right)}\ =\ \frac{1}{x^{\left(2k+2\right)}}+x^{2k+2}$.  I am not sure what to do from here and how to use the induction hypothesis.

I am to prove by induction that given that $a+1/a$ is an integer (i.e. belongs to Z  ) then $a^n+1/a^n$ is an integer too. I'm pretty much clueless here. Thanks in advance.


I'm testing parallel streams and I've found this strange (to me) result. In my test:  final int MIL = 1000000; IntStream s;  s = IntStream.rangeClosed(1, MIL);     long start = System.nanoTime(); s.filter(i -> i % 11 == 0)     .map(i -> i % 3)     .reduce(0, (subtotal, element) -> subtotal + element); long end = System.nanoTime();  System.out.println("NON PARALLEL reduce: " + (end - start));  s = IntStream.rangeClosed(1, MIL); long startP = System.nanoTime(); s.parallel().filter(i -> i % 11 == 0)     .map(i -> i % 3)     .reduce(0, (subtotal, i) -> subtotal + i); long endP = System.nanoTime();  System.out.println("    PARALLEL reduce: " + (endP - startP));     I get the following result:  NON PARALLEL reduce: 10156400     PARALLEL reduce: 31094100   that is the parallel stream is considerably slower. Why? If I susbstitute reduce() with sorted(), the result is opposite: parallel stream is significantly faster.

How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related:


I know he criticized Popper's critical rationalism as limited and dogmatic, but critical rationalism isn't like that, because critical rationalism does accept ideas which at first sound illogical and out of tune with accepted knowledge. If those ideas survive scrutiny, they are incorporated into or even change the existing body of scientific knowledge?  Did Feyerabend really understand Karl Popper?

I am reading Feyerabend's "Against Method", where he uses Copernicus's (and Galileo's confirmation) discovery of the fact that the Earth orbits around the Sun and other examples to show that irrational approaches can lead to legitimate scientific progress. He then claims that no unified epistemic principle or principles can be used to define science, and that science is best characterized by anarchy.   Is he confusing the way scientific truth is discovered with the way scientific truth is epistemically justified?   Even if it is true that Copernicus, Galileo and others used irrational methods to arrive at valid scientific discoveries, why does that affect science's special epistemic status compared to other fields of inquiry?


macOS is not permitting me to change the file permissions of any file! whenever I try to add the admin which is me, finder gives me this error:  you don't have necessary permission - operation not permitted  In spite of the fact that I am the sole user  I have tried chmod, again same error - operation not permitted  The permissions are as follows!    Screenshot of the operation not permitted error I getting

I have just learned about the "Rootless" feature in El Capitan, and I am hearing things like "There is no root user", "Nothing can modify /System" and "The world will end because we can't get root".  What is the "Rootless" feature of El Capitan at a technical level? What does it actually mean for the user experience and the developer experience? Will sudo -s still work, and, if so, how will the experience of using a shell as root change?


I have a simple code written in MySQL which returns the week number based on specific date:  Is there any equivalent in SQL Server? I was trying to use it by none function works  WEEK(ADDDATE(date,5-DAYOFWEEK(date)),3)

I am using sql server 2005. I just want to know is there something we can get the week number for the particular month. Example Date = '2008-10-16' Is there something we can have SELECT WEEK(Date). Or any better suggestion.


A random variable is defined by it distribution function. The density function is the derivative of the distribution function. Thus the density function exisst iff the distribution function is absolutely continuous. However, can we construct a distribution function without a density function, except for the finite discrete random variable(i.e. the distribution function is a step function)?  I think the hardness is that the distribution function is non-decreasing and upper-bounded by 1.

This is from Shreve's Stochastic Calculus for Finance II, Appendix A.3. Consider infinitely many independent coin tosses with outcomes $\omega_n$, $n = 1, 2, \dots$ such that $\omega_n$ can be either $H$ = heads or $T$ = tails. Define \begin{equation} Y_n\left(\omega\right) = \begin{cases}1 & \text{ if }\omega_n = H \\ 0& \text{ if } \omega_n = T\text{.} \end{cases} \end{equation}  Define $\displaystyle Y = \sum\limits_{n=1}^{\infty}\dfrac{2Y_n}{3^{n}}$. Shreve shows that $Y$ can only take values in the Cantor set, and since that particular set has measure zero, its Lebesgue measure is zero as well, thus it does not have a probability density function (since integrating such a density function would give a value of $0$). This part I understand, as well as my professor.  Now Shreve claims that $Y$ does not have a probability mass function.      If it did, then for some number $x \in C$ [the Cantor set] we would have $\mathbb{P}\left(Y=x\right) > 0$. But $x$ has a unique base-three expansion    \begin{equation} x = \sum\limits_{n=1}^{\infty}\dfrac{x_n}{3^{n}}\text{,} \end{equation}   where each $x_n$ is either 0, 1, or 2 unless $x$ is of the form $\dfrac{k}{3^{n}}$ for some positive integers $k$ and $n$. In the latter case, $x$ has two base-three expansions... In either case, there at most two choices of $w \in \Omega_{\infty}$ [that is, the infinite coin-toss space] for which $Y(\omega) = x$. In other words, the set $\{\omega \in \Omega; Y(\omega) = x\}$ has either one or two elements. The probability of a set with one element is zero, and the probability of a set with two elements is $0 + 0 = 0$. Hence $\mathbb{P}\left\{Y = x\right\} = 0$.   My professor and I were able to follow this until the statement "The probability of a set with one element is zero." Is this a true statement? How so?   I thought it would be perhaps the fact that the Lebesgue measure of $[a, a] = \{a\}$ is zero, but I don't see any reason why Shreve would only use the Lebesgue measure, since it is not a general probability measure.


Hello I write in es6 module to set in all elements (.product-category__item) the same height but I can't get any height :/  var measureElements = document.querySelectorAll('.product-category__item'); for(let item of measureElements) {     console.log(item.style.height)  // return nothing }

How do you get the rendered height of an element?  Let's say you have a <div> element with some content inside. This content inside is going to stretch the height of the <div>. How do you get the "rendered" height when you haven't explicitly set the height. Obviously, I tried:    var h = document.getElementById('someDiv').style.height;   Is there a trick for doing this? I am using jQuery if that helps.


The question  has a work-around listed, but no information about the reason this function is suddenly not available for new images thought a quick check of an old post showed that previously generated medium size images are still medium size.  Is there any information if this has been discontinued, or is only temporarily broken?   I find this really useful, so I'd like to know if I should just wait a little longer, or if I should start manually resizing my images or using the workaround described in the answer there.  Question: Is the sudden loss continuing absence of Imgur resizing for new images still temporary, or permanent? ETA?  Thanks!

I noticed at the start of August 2018 that new images like https://i.stack.imgur.com/MJrvX.png no longer resize when an m is placed before .png.   Original image: https://i.stack.imgur.com/MJrvX.png Auto shrunk by page formated to about 609 pixels (desktop), but still full size.  l suffix: https://i.stack.imgur.com/MJrvXl.png . ~~ FAILS ~~  m suffix: https://i.stack.imgur.com/MJrvXm.png . ~~ FAILS ~~  t suffix: . ~~ FAILS ~~  s suffix: . But notice that image displayed is from the middle of the original image, where there is no detail -- ~~ FAILS ~~    Additional proof that this once worked on PNG images can be seen in:   Please restore this resizing functionality ASAP.


I'm trying to select data from one table and insert it into another table but I seem to have gotten myself tied up in knots, any advice would be appreciated  INSERT INTO replies (statId, reply, dates, userId) VALUES (:addComment, NOW(), :userId)                 SELECT s.statId FROM status AS s                 JOIN replies AS r ON s.statId = r.statId

I am trying to INSERT INTO a table using the input from another table. Although this is entirely feasible for many database engines, I always seem to struggle to remember the correct syntax for the SQL engine of the day (, , , , and ).  Is there a silver-bullet syntax coming from an SQL standard (for example, ) that would allow me to insert the values without worrying about the underlying database?


Is this possible to reduce the fontsize for display equations smaller than the normal text font size. I'm using the following tags:  \documentclass[10pt]{book} \usepackage{amsmath} \begin{document}  This is for test \beign{align} a+b=c \end{align}  \begin{gather} a+b=c \end{gather}  All amsmath environments follows... \end{document}   Giving each equations \small is a tedious way...

I am trying to mimic our institute's PPt-template for presentation foils using the beamer-class. The corporate quidelines prescribe the use of Helvetica as the main font. However, package helvet does not provide a good mathematical font. Therefore I want to replace it with the math font from the cmbright package:  \documentclass{beamer}  \usepackage{lmodern} \usepackage[T1]{fontenc}  %main font Helevtica \renewcommand{\familydefault}{\sfdefault} \usepackage{helvet}  %prevent beamer from meddling with math fonts \usefonttheme{professionalfonts}  %following lines borrowed from cmbright.sty \DeclareSymbolFont      {operators} {OT1}{cmbr}{m}{n} \DeclareSymbolFont        {letters} {OML}{cmbrm}{m}{it} \SetSymbolFont      {letters}{bold} {OML}{cmbrm}{b}{it} \DeclareSymbolFont        {symbols} {OMS}{cmbrs}{m}{n} \DeclareMathAlphabet{\mathit} {OT1}{cmbr}{m}{sl} \DeclareMathAlphabet{\mathbf} {OT1}{cmbr}{bx}{n} \DeclareMathAlphabet{\mathtt} {OT1}{cmtl}{m}{n} \DeclareMathAlphabet{\mathbold}{OML}{cmbrm}{b}{it} \DeclareMathSymbol{\alpha}{\mathalpha}{letters}{11} \DeclareMathSymbol{\beta}{\mathalpha}{letters}{12} \DeclareMathSymbol{\gamma}{\mathalpha}{letters}{13} \DeclareMathSymbol{\delta}{\mathalpha}{letters}{14} \DeclareMathSymbol{\epsilon}{\mathalpha}{letters}{15} \DeclareMathSymbol{\zeta}{\mathalpha}{letters}{16} \DeclareMathSymbol{\eta}{\mathalpha}{letters}{17} \DeclareMathSymbol{\theta}{\mathalpha}{letters}{18} \DeclareMathSymbol{\iota}{\mathalpha}{letters}{19} \DeclareMathSymbol{\kappa}{\mathalpha}{letters}{20} \DeclareMathSymbol{\lambda}{\mathalpha}{letters}{21} \DeclareMathSymbol{\mu}{\mathalpha}{letters}{22} \DeclareMathSymbol{\nu}{\mathalpha}{letters}{23} \DeclareMathSymbol{\xi}{\mathalpha}{letters}{24} \DeclareMathSymbol{\pi}{\mathalpha}{letters}{25} \DeclareMathSymbol{\rho}{\mathalpha}{letters}{26} \DeclareMathSymbol{\sigma}{\mathalpha}{letters}{27} \DeclareMathSymbol{\tau}{\mathalpha}{letters}{28} \DeclareMathSymbol{\upsilon}{\mathalpha}{letters}{29} \DeclareMathSymbol{\phi}{\mathalpha}{letters}{30} \DeclareMathSymbol{\chi}{\mathalpha}{letters}{31} \DeclareMathSymbol{\psi}{\mathalpha}{letters}{32} \DeclareMathSymbol{\omega}{\mathalpha}{letters}{33} \DeclareMathSymbol{\varepsilon}{\mathalpha}{letters}{34} \DeclareMathSymbol{\vartheta}{\mathalpha}{letters}{35} \DeclareMathSymbol{\varpi}{\mathalpha}{letters}{36} \DeclareMathSymbol{\varrho}{\mathalpha}{letters}{37} \DeclareMathSymbol{\varsigma}{\mathalpha}{letters}{38} \DeclareMathSymbol{\varphi}{\mathalpha}{letters}{39} \let\upDelta\Delta \let\upOmega\Omega \let\upGamma\Gamma \let\upTheta\Theta \let\upLambda\Lambda \let\upXi\Xi \let\upPi\Pi \let\upSigma\Sigma \let\upUpsilon\Upsilon \let\upPhi\Phi \let\upPsi\Psi  %doesn't seem to have an effect %\DeclareMathSizes{12}{12.5}{10}{10}  \begin{document} \begin{frame}  Some Math E$E$ \end{frame} \end{document}   This works quite well, except that the math letters are somewhat smaller than the normal Helvetica text. Is there a way to scale the fontsize, say by 1.1, if the typesetter is in math mode?


I'm checking for an empty jTable value, some of my jTable cells have no input but still not an empty string. How to check for empty strings in jTable?  I made 1 column and 4 rows. The first 2 rows have inputs. The last 2 rows have no input. The last two rows appears to have value, how can I check for an empty jTable value?  //Row 1 Value: James //Row 2 Value: Mark //Row 3 Value: <nothing> //Row 4 Value: <nothing>  int i = 0; while (i < jTable1.getRowCount()) {     if (jTable1.getValueAt(i, 0) != "") {         JOptionPane.showMessageDialog(null, "Is not empty");         i++;     } }  I was expecting to get only 2 message dialog. Thanks.

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


is there some algorithm in C# to encode url with symbols that can correct display in web-browser?  something like Base64.

I have an application which sends a POST request to the VB forum software and logs someone in (without setting cookies or anything).  Once the user is logged in I create a variable that creates a path on their local machine.  c:\tempfolder\date\username  The problem is that some usernames are throwing "Illegal chars" exception. For example if my username was mas|fenix it would throw an exception..  Path.Combine( _         Environment.GetFolderPath(System.Environment.SpecialFolder.CommonApplicationData), _   DateTime.Now.ToString("ddMMyyhhmm") + "-" + form1.username)   I don't want to remove it from the string, but a folder with their username is created through FTP on a server. And this leads to my second question. If I am creating a folder on the server can I leave the "illegal chars" in? I only ask this because the server is Linux based, and I am not sure if Linux accepts it or not.  EDIT: It seems that URL encode is NOT what I want.. Here's what I want to do:  old username = mas|fenix new username = mas%xxfenix   Where %xx is the ASCII value or any other value that would easily identify the character.


I need step by step procedure for imputing data using SVD in Matlab. Please provide resources if any !

I have read the great comments regarding how to deal with missing values before applying SVD, but I would like to know how it works with a simple example:          Movie1 Movie2 Movie3 User1     5             4 User2     2      5      5 User3            3      4 User4     1             5 User5     5      1      5   Given the matrix above, if I remove the NA values, I will end up having only User2 and User5. This means that my U will be 2 × k. But if I predict the missing values, U should be 5 × k, which I can multiply with singular values and V.  Would anyone of you fill in the missing values in the matrix above by first removing users with missing values and then applying SVD? Please provide a very simple explanation of the procedure you applied and make your answer practical (i.e. number multiplied with another number gives an answer) rather than using too much math symbols.  I've read the following links:


I added a new SharePoint app project into an existing web project solution. When I tried to deploy it am getting an error:  Error occurred in deployment step 'Install app for SharePoint':  Failed to install app for SharePoint.  There was a problem with activating the app web definition.   But when I removed the feature1.feature file, it is geeting deployed successfully.   What is the reason?  Is there any better solution?  What is this feature1.feature file for?

I created a test MVC sharepoint app succesfully in a solution. Now I need to integrate this into a main solution project.   But when I added a SharePoint MVC App into the solution and hit F5, I am getting following error:  Error occurred in deployment step 'Install app for SharePoint':  Failed to install app for SharePoint. Please see the output window for details.   Detailed stack trace:  CorrelationId: 50583239-71cb-4b07-8bcb-4bbc51a22631      ErrorDetail: There was a problem with activating the app web definition.      ErrorType: App      ErrorTypeName: App Related      ExceptionMessage: Microsoft.SharePoint.SPException: Exception from HRESULT: 0x81070964 ---> System.Runtime.InteropServices.COMException: Exception from HRESULT: 0x81070964 at Microsoft.SharePoint.Library.SPRequestInternalClass.EnableModuleFromXml(String bstrSetupDirectory, String bstrFeatureDirectory, String bstrUrl, String bstrXML, Boolean fForceUnghost, ISPEnableModuleCallback pModuleContext) at Microsoft.SharePoint.Library.SPRequest.EnableModuleFromXml(String bstrSetupDirectory, String bstrFeatureDirectory, String bstrUrl, String bstrXML, Boolean fForceUnghost, ISPEnableModuleCallback pModuleContext) --- End of inner exception stack trace --- at Microsoft.SharePoint.Administration.SPElementDefinitionCollection.ProvisionModules(SPFeaturePropertyCollection props, SPSite site, SPWeb web, SPFeatureActivateFlags activateFlags, Boolean fForce) at Microsoft.SharePoint.Administration.SPElementDefinitionCollection.ProvisionElements(SPFeaturePropertyCollection props, SPWebApplication webapp, SPSite site, SPWeb web, SPFeatureActivateFlags activateFlags, Boolean fForce) at Microsoft.SharePoint.SPFeature.Activate(SPSite siteParent, SPWeb webParent, SPFeaturePropertyCollection props, SPFeatureActivateFlags activateFlags, Boolean fForce) at Microsoft.SharePoint.SPFeatureCollection.AddInternal(SPFeatureDefinition featdef, Version version, SPFeaturePropertyCollection properties, SPFeatureActivateFlags activateFlags, Boolean force, Boolean fMarkOnly) at Microsoft.SharePoint.SPFeatureCollection.AddInternalWithName(Guid featureId, Int32 compatibilityLevel, String featureName, Version version, SPFeaturePropertyCollection properties, SPFeatureActivateFlags activateFlags, Boolean force, Boolean fMarkOnly, SPFeatureDefinitionScope featdefScope) at Microsoft.SharePoint.SPFeatureCollection.AddInternal(Guid featureId, Version version, SPFeaturePropertyCollection properties, Boolean force, Boolean fMarkOnly, SPFeatureDefinitionScope featdefScope) at Microsoft.SharePoint.SPFeatureCollection.Add(Guid featureId, Boolean force, SPFeatureDefinitionScope featdefScope) at Microsoft.SharePoint.SPUserSolutionCollection.EnsureWebFeaturesActivated(SPUserSolution solution) at Microsoft.SharePoint.Packaging.SPUserCodeSolutionDeploymentGroup.ActivateSolution(SPWeb web, SPUserSolution solution) at Microsoft.SharePoint.Packaging.SPUserCodeSolutionDeploymentGroup.Deploy() at Microsoft.SharePoint.Administration.SPAppTask.DeployOperation() at Microsoft.SharePoint.Lifecycle.MonitoredTaskExecution.DoTask()      Source: AppWeb      SourceName: App Web Deployment   Can somebody shed a light on this issue? :)


This community has some absolute rock stars and as a community, we should have a badge to help these individuals stand out for their thoughtful and planned out answers.  badge request   badge name: "The most generic responce"     This badge can be achieved if a user can reach an impressive 300 downvotes on one of their posts

Regarding subjective questions, if you post an answer and get a lot of downvotes, your reputation take a hit, right?  Well, what if you want to stand by your answer?  It's not offensive because it isn't flagged as such, but for whatever reason it just rubs some people the wrong way, and they downvote it.  If you've got the cojones to stand behind your answer regardless of how it effects your rep, how about a badge for that?  Maybe something like, being downvoted 5 times but leaving your answer up for a certain period of time after the 5th downvote.


Number which can be expressed as sum of two squares in two different ways -  e.g - a). $85 = {2^2} + {9^2} = {6^2} + {7^2}$ b). $125 = {2^2} + {11^2} = {5^2} + {10^2}$  I do not need more example. I just need way/formulas. So, Can anyone tell me the way/formulas through which I can find infinitely many such numbers?

I'm looking for some help disproving an answer provided on a  I posted about computing the number of double square combinations for a given integer.    The original question is from the Facebook Hacker Cup       Source: Facebook Hacker Cup   Qualification Round 2011      A double-square number is an integer $X$   which can be expressed as the sum of   two perfect squares. For example, 10   is a double-square because $10 = 3^2 + 1^2$.   Given $X$, how can we determine the   number of ways in which it can be   written as the sum of two squares? For   example, $10$ can only be written as $3^2 + 1^2$   (we don't count $1^2 + 3^2$ as being different). On the other hand,   $25$ can be written as $5^2 + 0^2$ or as   $4^2 + 3^2$.      You need to solve this problem for $0 \leq X \leq 2,147,483,647$.      Examples:      $10 \Rightarrow 1$      $25 \Rightarrow 2$      $3 \Rightarrow 0$      $0 \Rightarrow 1$      $1 \Rightarrow 1$   In response to my original question about optimizing this for F#, I got the following response which I'm unable to confirm solves the given problem correctly.       Source:       Again, the number of integer solutions   of $x^2 + y^2 = k$ is four times the   number of prime divisors of $k$ which   are equal to $1 \bmod 4$.      Knowing this, writing a program which   gives the number of solutions is easy:   compute prime numbers up to $46341$ once   and for all.      Given $k$, compute the prime divisors of   $k$ by using the above list (test up to   $\sqrt{k}$). Count the ones which are   equal to $1 \bmod 4$, and sum. Multiply   answer by $4$.   When I go through this algorithm for $25$, I get $8$ which is not correct.          For each prime factor (pf) of $25$ ($5$, $5$ are prime factors of $25$)         if pf % $4$ = $1$ (true for both $5$'s), add $1$ to count      return $4$ * count (count would be $2$ here).          So for $25$, this would be $8$


I'm relatively new to latex, and I'm trying to get a test bibliography working. I'm just going through the sharelatex section on biblatex () and am just running their example code. However, instead of showing a few lines of text with citations within and then a list of references, I only get the text with citations. The list of references is not shown at all.  I'm using TexStudio, if that means anything.  The code in question is as follows:  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[english]{babel}  \usepackage{biblatex} \addbibresource{sample.bib}  \begin{document}     Let's cite! The Einstein's journal paper \cite{einstein} and the Dirac's      book \cite{dirac} are physics related items.       \printbibliography  \end{document}   and sample.bib contains:  @article{einstein, author =       "Albert Einstein", title =        "{Zur Elektrodynamik bewegter K{\"o}rper}. ({German}) [{On} the electrodynamics of moving bodies]", journal =      "Annalen der Physik", volume =       "322", number =       "10", pages =        "891--921", year =         "1905", DOI =          "http://dx.doi.org/10.1002/andp.19053221004", keywords =     "physics" }  @book{dirac, title={The Principles of Quantum Mechanics}, author={Paul Adrien Maurice Dirac}, isbn={9780198520115}, series={International series of monographs on physics}, year={1981}, publisher={Clarendon Press}, keywords = {physics} }  @online{knuthwebsite, author    = "Donald Knuth", title     = "Knuth: Computers and Typesetting", url       = "http://www-cs-faculty.stanford.edu/~uno/abcde.html", keywords  = "latex,knuth" }  @inbook{knuth-fa, author = "Donald E. Knuth", title = "Fundamental Algorithms", publisher = "Addison-Wesley", year = "1973", chapter = "1.2", keywords  = "knuth,programming" }   EDIT: Just to clarify, Actual Output  Expected Output   EDIT 2:  Adding biber as the default bibliography still gives the same output, but also gives the following messages:      Process started: biber.exe "test"  Use of uninitialized value $llabel in concatenation (.) or string at C:\Users\~\AppData\Local\Temp\par-5072696d617263682d4956\cache-6bef6bfac2f8155f13b160f6720d3dbe6a10b684\inc\lib/Biber.pm line 675.  Use of uninitialized value in string eq at C:\Users\~\AppData\Local\Temp\par-5072696d617263682d4956\cache-6bef6bfac2f8155f13b160f6720d3dbe6a10b684\inc\lib/Biber/SortLists.pm line 77.  INFO - This is Biber 1.8 INFO - Logfile is 'test.blg' INFO - Reading 'test.bcf' WARN - Warning: Found biblatex control file version 2.7, expected version 2.5 INFO - Found 2 citekeys in bib section 0 INFO - Processing section 0 INFO - Looking for bibtex format file 'sample.bib' for section 0 INFO - Decoding LaTeX character macros into UTF-8 INFO - Found BibTeX data source 'sample.bib'  Process exited with error(s)   With bibtex it gives the following:      Process started: bibtex.exe "test"  This is BibTeX, Version 0.99d (MiKTeX 2.9) The top-level auxiliary file: test.aux I found no \citation commands---while reading file test.aux I found no \bibdata command---while reading file test.aux I found no \bibstyle command---while reading file test.aux (There were 3 error messages)

I'm trying to use biblatex and when I compile my document I get an error like the following:  Windows  data source C:\Users\<username>\AppData\Local\Temp\par-5061756c\ cache-890efc00b3ca6b775c7d44a325c1349fb2a3a3bd\inc\lib/Biber/LaTeX/recode_data.xml not found in .   Mac  data source /var/folders/v2/rld0ls7d2935gkvqv5hfr1x00000gn/T/par-616c616e/ cache-cdd483146f82a9655ce063f848d5139480fbf872/inc/lib/Biber/LaTeX/recode_data.xml not found in .   Linux  data source /tmp/par-6963617269756d/cache-f37ab610b7d79b2720a8ee3732849c6821705520 /inc/lib/Biber/LaTeX/recode_data.xml not found in .


I want to know what the benefits/advantages are of protecting a question? Because only preventing to answer by <10 reputation seems not so effective/efficient (as 10 reputation can easily be achieved for user with 1 rep. ex: if only 5 suggested edits approved!)  So, there should be suitable advantages and importance for protected questions. Maybe future request to update or apply new effective similar to protection so that standard and canonical questions (essential part of information/knowledge based Questions) can be secured!

Questions can be protected (i.e. marked "highly active").   What does it mean for a question to be protected? Why are some questions protected? Who can protect and unprotect questions? Who can answer a protected question? How are protected questions displayed? When should I protect or unprotect a question? When does the Community user protect a question?


I have file1.txt    this is the original text   line2   line3   line4   happy hacking !     and file2.txt    this is the original text   line2   line4   happy hacking !   GNU is not UNIX     if I do: diff file1.txt file2.txt I get:    3d2   < line3   5a5   > GNU is not UNIX     How is the output generally interpreted? I think that < means removed but what do 3d2 or 5a5 mean?  If I do:    $ diff -u file1.txt file2.txt   --- file1.txt        2013-07-06 17:44:59.180000000 +0200   +++ file2.txt        2013-07-06 17:39:53.433000000 +0200   @@ -1,5 +1,5 @@    this is the original text    line2   -line3    line4    happy hacking !   +GNU is not UNIX     The results are clearer but what does @@ -1,5 +1,5 @@ mean?


I am looking for remove my profile picture and keep default Google account profile picture.

How do you actually view and delete profile pictures from a Google account? For example, in Google Drive, if I click on the picture of me in the top right corner > click change > under your photos, click the one photo > it shows the current one and all of the old ones, but I’d like the option to view them in full size and delete them. How can this be done? I tried looking in Google Photos and nothing is there.  Note: I sometimes get confused as to which Google product I'm using. I see this picture in Google Drive, but it's also used across all Google products I log in to.


I have looked at different web tools for calculating confidence intervals for effect size like Cohen's d for within-subject design. My experience from this survey tells me that there are different ways to estimate within SD because results I got differs on both effect size and confidence intervals. They usually use correlations between variable to estimate pooled variance. Can anyone point me to adequate way of calculating these things?  In addition I mainly use effect size confidence intervals to determine when intervals are non-overlapping the zero effect as hypothesis testing. Does this produce the same results as using a standard confidence interval for the difference directly?  Thanks!

It seems that for calculation of Cohen's $d$ (an estimate of effect size), you should use the difference in means (or in one-sample case, from baseline), divided by $SD$, if that information is available: $$ \frac{\bar X_1 - \bar X_2}{SD} $$ However, when you only have the $t$-statistic and the degrees of freedom ($\rm df$) available, what is the formula for Cohen's $d$? In the one-sample / paired-sample case, it's intuitive how to derive $d$ from $t$, since $t$ is calculated as the difference in means over standard error: $$ t = \frac{\bar X_1 - \bar X_2}{SE} = \frac{\bar X_1 - \bar X_2}{\frac{SD}{\sqrt{N}}} $$ so $d$ equals: $$ d = \frac{\bar X_1 - \bar X_2}{SD} = \frac{t}{\sqrt{N}} $$ And that's what you find in online articles such as . But for independent samples, the equation is listed instead as: $$ d = \frac{2t}{\sqrt{\rm df}}  $$ as seen , or even:  $$ d = t \sqrt{\frac 2 N} $$ So where does the "$2$" come from? Is it related to the formula for pooled SD?


As everybody knows, we can get the flair of a particular account by clicking on the "got flair?" link given below the gravatar and reputation on the account's profile.   But is there any way to get all the associated accounts' flair as the only flair (i.e., a single flair showing the combined reputation of all accounts, such as Stack Overflow, Meta Stack Overflow, Area 51, Super User, etc.)?   That way, instead of copying all the flairs' coding (i.e. JavaScript), I can make one copy and paste at my site.  How can I get a flair, which shows the reputation of all my associated accounts?

Is it possible to get a combined flair like the ones on Area 51?  See follower list on the right side of an  for examples.


I've been using  but then I realized that there is   They sound like they are pretty much the same.  I always hear wilcoxons referred to as wilcoxon rank sums.  In SciPy how are they different and how can I know which one to use?  My data is rarely normally distributed which why I use these non-parametric tests instead of t-tests.

I was wondering what the theoretical difference is between the Wilcoxon Rank-Sum Test and the Wilcoxon Signed-Rank Test using paired observations. I know that the Wilcoxon Rank-Sum Test allows for a different amount of observations in two different samples, whereas the Signed-Rank test for paired samples does not allow that, however, they both seem to test the same in my opinion. Can someone give me some more background / theoretical information on when one should use the Wilcoxon Rank-Sum Test and when one should use the Wilcoxon Signed-Rank Test using paired observations?


Having done bachelors in electronics and instrumentation and a research experience in the field of image processing and computer vision and some publications in the same, what are the possible MS options where I can study computer vision and image processing? Can I opt for MS in robotics, computer science, signal processing?  My confusion is regarding the fact that I was a bachelors student in a different field. Would it be difficult for me to change to a masters program in this other field?

Can I be admitted to graduate school in a different field from my degree?  Specific cases include:   If I've taken plenty of advanced courses in field X in the process of completing a degree in another field, can I apply to graduate school in X? What if I haven't taken many courses in X, but I have acquired a good grasp of X through self-study or working in a related field? What if I've never studied X, but I have done very well in an unrelated field?  Could I be admitted to graduate school in X on the basis of general intellectual promise, and then make up the missing background after enrollment?   Note that this question is an attempt to provide a comprehensive answer, to avoid the need for a profusion of field-specific questions on this topic (see the associated ). Please feel free to edit the question or answer to improve them.


Let $[x]$ be the greatest integer function. How to find  $\displaystyle\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^{n}\left(\left[\frac{2n}{k}\right]-2\left[\frac{n}{k}\right]\right)$?

Problem: Evaluate $$ L=\displaystyle \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^{n} \left(  \left\lfloor \frac{2n}{k} \right\rfloor -2\left\lfloor \frac{n}{k}\right \rfloor \right).$$  Please help me with this one.  I tried using the sandwich theorem by first constructing the following  $$ 2 \geq \left\lfloor \frac{2n}{k} \right\rfloor -2\left\lfloor \frac{n}{k} \right\rfloor \geq -1 $$ and then summing over. But the limit of the two bounds are different so sandwich theorem doesn't help!. Is it possible to construct sharper bounds?  Also I observed that if we ignore question of continuity, etc. then we can write,  $L= \displaystyle \int ^{1}_{0}\left\lfloor \frac{2}{x} \right\rfloor -2\left\lfloor \frac{1}{x} \right\rfloor dx$  Now I am able to compute the above integral. But is the above process correct? If then how can make it rigorous? Or if any other approach is possible, please tell.


Below was actual task:-     Now ,  I have 2 SQLite files with few common tables. File A which I have stored in APK / IPA which I am restoring on App Launch into Actual SQLite DB called File C, and for, File B which I am downloading after user Authentication,  I am trying to Append File B Byte[] to File C,and it successfully appends the bytes but,  However I check file size by browsing the file location after appending the file its size gets increased but,  if I perform select statement on tables which are from file B I am not getting records from the table of it.  I am using FileMode.Append for APPENDING File B byte[] into File C   using (BinaryWriter bw = new BinaryWriter(new FileStream(FilePath, FileMode.Append)))                         {                             byte[] buffer = new byte[2048];                             int len = 0;                             while ((len = br.Read(buffer, 0, buffer.Length)) > 0)                             {                                 bw.Write(buffer, 0, len);                             }                         }

If I have a large number of SQLite databases, all with the same schema, what is the best way to merge them together in order to perform a query on all databases?   I know it is possible to use  to do this but it has  of 32 and 64 databases depending on the memory system on the machine.


How to find limit of   $$\lim_{n\rightarrow \infty} n(x^{1/n}-1)$$  Via L'Hopital's rule   $$\lim_{n\rightarrow \infty} n(x^{1/n}-1) =  \lim_{n\rightarrow \infty} \frac{1}{n} x^{\frac{1}{n}-1} / \frac{-1}{n^2} =\lim_{n\rightarrow \infty} x^{\frac{1}{n}-1} / \frac{-1}{n}$$  but that doesn't help.

How to find the limit of: $$ \lim_{x\to \infty }x\left(\sqrt[x]{a}-1\right)$$ Without using L'hôspital rule.  I've tried to bound the term and use the squeeze theorem but I couldn't find the right upper bound. I've also tried to convert $a^\frac{1}{x}$ to $e^{\frac{1}{x}\ln{a}}$ but it didn't help me.  Whats the right way to evaluate that limit?


I have a new laptop Asus GL552v (ITerabyte, 128GB SSD and core i7600hq with WIN 10 home) I would like to install ubuntu as what I do work mostly with Linux. I have read several blogs and comments on how to get this done but nothing seems to be working. I have disabled fast startup, enabled CLI in Bios, I have tried to install using both liveCd and liveUsb but nothing works. Really, I often get to the page where i'm asked whether to try ubuntu or install, whenever i choose install, it brings out ubuntu window with some dots showing the progress, then it hangs at the last dot and stays lke that for several minutes to hours without showing any other option neither does it get past that. I have followed all the instructions and methods i could read online. is this problem peculiar to asus GL552V or is it because i only have win 10 home basic? or is there any other thing that i should do that I haven't done? I would appreciate any help in getting this done. Thanks

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


I'm still new to how to make a package. How do you create the package in .sty format? Is the origin of .tex then changed to .sty?

Sorry to start a subjective question, but want to understand "own.sty" file.  Other than all \usepackage{} what sort of other commands can be added to the makeyourown.sty file.  Can you include \let command, and \newcommands in it.   What sort of precaution / structure newbies should follow.


I know it's recommended to edit a post if there's improvement. But as a personal preference, I'm often proud of having an upvoted question or answer without a revision history, and I'll admire if someone has one. So at last is it a commended practice to be so?

Bronze/Silver/Gold badges awarded for having 10/50/200 questions which have not had any edits.  Includes questions at least a week old that are still open.  Encourages people to review their questions before submitting (some people like to submit, then review, but by the time they've submitted the edited version it's halfway down the main page and gets a bump, even within the 5 minute edit window).


I would like to start shooting RAW instead of jpeg. I am wondering if i need to still worry about setting ISO, aperture and shutter speed. If so, why?

With such good post production in editors like Adobe is there any real benefit in shooting with manual settings when you can change just about everything in any shot you take?


I learned that if we measure the spin angular momentum of an electron in one direction $J_z$, we get $\pm \frac{1}{2} \hbar$.  But if we measure the magnitude of the angular momentum $\mathbf{J}^2$, we should get $\frac{3}{4} \hbar^2$.  What experiment gives the latter result? As @user1585635 notes, measuring $J_x$, $J_y$, and $J_z$ separately and summing their squares gives $\frac{3}{4} \hbar^2$.  This is not what I'm looking for.  First, if I measure $J_z$, measure angular momenta in three directions separately, and measure $J_z$ again, the two measurements of $J_z$ aren't guaranteed to be the same, since $J_z$, $J_x$, and $J_y$ don't commute.  But $\mathbf{J}^2$ commutes with $J_z$. Second, when the spin is not $\frac{1}{2}$, say it's $j$, summing the squares of components of $\mathbf{J}$ gives 3ℏ²𝑗², where 𝐉² should be ℏ²𝑗(𝑗+1) doesn't always give $\hbar^2 j(j+1)$.  (Thanks to @MichaelSeifert for pointing that out) This question is not a duplicate of . That question is about how $\mathbf{J}^2$ is derived mathematically. Mine is about how it is confirmed experimentally.

I simply have no idea how this result is found $$I=\hbar  \sqrt{\ell(\ell+1)}.$$ The result seems to just be dumped in textbooks rather than explained. I can get the result that $I_z=\hbar m_j$. Please explain as clearly as possible how this is derived.  Also, any pointers towards any books/videos that may help me learn quantum mechanics would be appreciated.


Show that $S=\mathbb R^2\setminus\{(a,b):a,b\in\mathbb Q\}$ is path connected.   By definition of path connected, there should exist continuous mapping $f:[0,1]\rightarrow \mathbb R^2$ s.t. $f(0)=a,f(1)=b$ for all $a,b\in\mathbb R^2$. I have utterly no idea how to find such map. Please help.

Possible Duplicate:          As the topic,if $A\subset\mathbb{R^2}$ is countable, does $\mathbb{R^2}\setminus A$ path connected??? I know the answer is it is path connected but not sure how to prove it.


I need to extract more than 2k files from 1000 folders..the problem is, each folder has a zipped folder inside and inside this folder, there is another folder called "fileholder" which contains some temp.processed filetype that I need to get. Is there any way to search for all these files and copy them to another location? or do I have to extract all of the zip files?   I have ran:   find -type f -iname \*.PROCESSED   but that does not search inside the zipped files. Can someone point me to the right direction?

I'm trying to find out what modules  in cpan. So I've used  to mirror it. My problem is that I need to iterate through the archives that are downloaded, and grep the files that are in the archives. Can anyone tell me how I might do this? preferably in a way that tells me which file in the archive and what line it's on.  (note: they aren't all tarballs some are zip files)


Where can I post 'helpful ideas' that are not being asked directly, but are being asked indirectly?  I see some of the vigilant members being very vigilant with innocuous comments or requests for more information or generally helpful but not specific enough comments which get pinged for being 'off topic'.  As a classroom teacher of some 25 years I do notice when someone needs help but may not be articulate enough or skilled enough to know exactly what to ask or how to ask it. I find these sites unnecessarily exacting and frustrating and I'm sure others do, too.

I showed up here to write a perfectly normal rant about misaligned pixels, and there's a big fat checkbox cluttering up the "Ask" page:    WHAT THE EEEEK IS THIS NEW ABOMINATION?


Suppose I have a Person entity with a status associated with it status can be ACTIVE/INACTIVE/BLOCKED Which table design would be better ? Just one table Person(id, name, status) Or Two tables with a foreign key reference from Person to Status table. Person(id, name, status_id) Status(id, name) It is much easier to manage the implementation with just one Person table. But do anyone see any future problems associated with this approach?

I find this comes up a lot, and I'm not sure the best way to approach it.   The question I have is how to make the decision between using foreign keys to lookup tables, or using lookup table values directly in the tables requesting it, avoiding the lookup table relationship completely.  Points to keep in mind:   With the second method you would need to do mass updates to all records referencing the data if it is changed in the lookup table. This is focused more towards tables that have a lot of the column's referencing many lookup tables.Therefore lots of foreign keys means a lot of joins every time you query the table. This data would be coming from drop down lists which would be pulled from the lookup tables. In order to match up data when reloading, the values need to be in the existing list (related to the first point).   Is there a best practice here, or any key points to consider?


I do not get why  $$\cos a\cdot \cos b+\sin a\cdot \sin b = \cos (b-a)$$  Thank you for your help

The "" formulas often come in handy, but it's not immediately obvious that they would be true.  \begin{align} \sin(\alpha \pm \beta) &= \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \\ \cos(\alpha \pm \beta) &= \cos \alpha \cos \beta \mp \sin \alpha \sin \beta \end{align}  So what I want to know is,    How can I prove that these formulas are correct? More importantly, how can I understand these formulas intuitively?   Ideally, I'm looking for answers that make no reference to Calculus, or to , although such answers are still encouraged, for completeness.


When I run an ls -la /, some files/folders it gives output like: -rw-r-----.   1 root root         0 Jan 18  2020 1 drwxrwx---.   3 root root      4096 May 24  2016 ade lrwxrwxrwx.   1 root root         7 Feb 27  2018 bin -> usr/bin So, what is the meaning the point (.) at the end in the permisions? -rw-r-----. drwxrwx---. lrwxrwxrwx. I thank in advance who can help me.

What does the last dot in the file permission attribute mean?  me@ubuntu:~$ ls -l total 8 drwxr-xr-x   4 me me      4096 Dec 21 13:14 snap drwxr-xr-x. 14 me docker  4096 Dec 21 15:50 work           ^           |--------- what does this dot means?   This is shown by Ubuntu 18.04 LTS on a 9p mounted partition.  Linux ubuntu 4.15.0-43-generic #46-Ubuntu SMP Thu Dec 6 14:45:28 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux   Mount:  /home/me/work on /home/me/work type 9p (rw,relatime,sync,dirsync,access=client,trans=virtio)   I never saw this dot before and don't see any documentation explaining it.


Shrinking drive space, need help! Ok I don't know how to word this nor have any searches produced results I need, i checked for the hyperfil.sys (no go btw) as i cleared that out, and i think this is a virus (unplugged my network cable), and what leads me to think virus is that my drive space (free) is literally shrinking in front of my eyes as im watching it...and I know i have a masive drive so i should have a few hundred gigs still left free...so what do you all think is going on here? virus or something else? i don't want to try and download any thing or install anything till i sort this out.

How can I visualize which folders and files are taking up all of the space on my hard drive?  I'm getting some conflicting reports on the size of hard drive contents. Namely what is and isn't there and what folders are actually using the space.   I need to know which of the files or folders the culprits behind all this hidden bloat. Also there should be a print option to get it on paper.


My 8 year old daughter takes 3 melatonin just to be able to sleep, goes to bed at 830, reads till ten,wakes at 6. what to do? she seems well rested, but is getting two hours less than regulation, at 8 instead of 10.

We put him to bed at 9pm and he stays up til 1am or later. When I go to check on him he is always playing with his hands and sometimes talking. I ask him why he is awake and not trying to sleep and he says it's because he just wants to play. He never comes to tell us that he is having a hard time sleeping or that there is anything wrong. The weird thing is that he used to be the first one to fall asleep out of 3 boys and the staying up started a few months ago. He does this every night and on top of keeping us awake, he is now waking up his brothers.   About a month or so ago, we decided to punish him by grounding him from video games. He doesn't want to be grounded, but he still keeps doing it. Nothing we do seems to be helping and it seems to be getting worse. I have talked to him about why it is so important to get enough sleep and why it's even more important for kids. He also gets plenty of exercise and time to play during the day.   I'm really starting to wonder if he is doing it just to be defiant. If anyone has any suggestions I would greatly appreciate it.  The problem is that he is being disruptive to everyone in the house and it has been EVERY night for the last 3 months.   He is tired and emotional during the day, and it is causing his brothers to be tired during the day while they are at school.   Because he is tired during the day he doesn't really want to be as active as he used to be. However, I do still encourage him to be active. We have always had a bedtime routine. We have asked him many different times if he is just having trouble sleeping, if he is uncomfortable, and if there is something wrong. He always tells us that he just wants to play.   At the beginning of all this he told me that he wants to be the one to decide when he goes to sleep and when he wakes up. Which is why I would even ask if it was out of defiance.   We really didn't want to get to the point of punishing him, but nothing else seemed to help and it was only after he started keeping his brothers awake.   It's not like we haven't asked him what he thinks would help or what would help him sleep better. He ALWAYS says that he just WANTS to stay up and play because it is fun. We know it is important for him to get enough sleep, and I'm worried because I don't think he is (and he's preventing the rest of us from getting enough, too).


I have just started learning about multivariate distributions using Mathematical Statistics with Applications by Wackerly, Mendenhall and Scheaffer but I find their explanation a bit confusing, could someone please recommend a good text for learning about multivariate distributions?

I'm interested in getting some books about multivariate analysis, and need your recommendations. Free books are always welcome, but if you know about some great non-free MVA book, please, state it.


*I've changed this question as below.  Let me have a function such as $ f(k) = \exp(j 2 \pi k ) $,  where $k$ is real value.  Using Euler's formula, we can write $f(k)$ as below,  $$ f(k) = \exp(j  2 \pi  k ) = \cos(2\pi k)+j \sin(2\pi k).$$  If $k$ is integer, this always goes to 1.  Up to here, nothing is weird and makes sense.  However, if the equation goes to  $$f(k) = \exp(j2\pi k)=e^{j2\pi k}=(e^{j2\pi})^k = (\cos(2\pi)+j\sin(2\pi))^k=1^k=1$$  What I want to know is this above equation makes sense or not.  Thank you in advance.

I am confused about something: \begin{eqnarray}     (e^{2 i \pi})^{0.5} = (e^{2 i \pi \cdot 0.5})= e^{i \pi}=-1 \end{eqnarray} but \begin{eqnarray}      e^{2 i \pi}=1~ and~ 1^{0.5}=1  \end{eqnarray} where is my mistake??  thanks


First I create Dagger Component and Module. @Singleton @Component(modules = {UploadModule.class}) public interface UploadComponent {     void inject(UploadS3ToMap requestHandler); }  Module: private Map<String, String> uploadMap = new HashMap<String, String>();  @Singleton @Provides Map<String, String> getUploadMap() {     return uploadMap; }  And than trying to use it in my Class: @Inject Map<String,String> getUploadMap;  getUploadMap.put("test", "testIssue"); return getUploadMap.toString();  And I have an Exception: nulljava.lang.NullPointerException What is wrong with it?

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Why do my Tweets not appear on my followers' timelines - I just wrote a plain sentence (without any @ mentions or hashtags) and tweeted it. Should it not appear on my followers timelines?  I need to know if I tweet a simple sentence if it should appear on my followers' timelines because my tweets have not. I am not using some protected tweets or anything like that.  Is there anyone who I can contact for one on one help/support regarding this issue?

My replies are not showing up in other people's mentions. I tried tweeting several friends, my other accounts but my tweets just won't appear in their mentions? They do appear on my own Twitter page. It's been almost 24 hours now and it's pretty frustrating.


If I have an 8G USB and I create an installer iso, which  occupies only a fraction of the available space, something like:  $ lsblk -o model,NAME,SIZE,TYPE,fstype,state /dev/sdb MODEL            NAME    SIZE TYPE FSTYPE  STATE USB DISK 2.0     sdb     7.5G disk iso9660 running                  ├─sdb1  325M part iso9660                   └─sdb2  416K part vfat     and  $ sudo fdisk -l /dev/sdb Disk /dev/sdb: 7.5 GiB, 8011120640 bytes, 15646720 sectors                         ^^^^^^^^^^ available Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x64c1c041  Device     Boot Start    End Sectors  Size Id Type /dev/sdb1  *        0 665599  665600  325M  0 Empty /dev/sdb2        3984   4815     832  416K ef EFI (FAT-12/16/32)   (note: I'm aware these partitions aren't aligned).   ISO image occupies 600k sectors out of 16 million available. I've tried to add a partition onto the free space, so I could use it for general file storage, but my partition editor (cfdisk) threw an error. Is it possible to add a partition and filesystem onto the free space? if so how?

I have a USB device and i'm trying to create it in a way that it has 2 partitions: one for a live linux disc and the other for document storage.  I created the partitions using gparted and and set a boot flag to the one I want to use as the live disc. Now, I have a usb like this:  Disk /dev/sdc: 14.6 GiB, 15623782400 bytes, 30515200 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0xc3072e18  Device     Boot   Start      End  Sectors  Size Id Type /dev/sdc1       8439808 30515199 22075392 10.5G 83 Linux /dev/sdc2  *      51200  8439807  8388608    4G  b W95 FAT32   I then used dd to flash an Ubuntu iso to /dev/sdc2  sudo dd if=/dev/shm/ubuntu-17.04-desktop-amd64.iso of=/dev/sdc2 bs=4M   When the disc is flashed onto the usb drive, I try to boot from my laptop and it shows "Operating system not found". When i try to use qemu/kvm, it shows a kernel panic like this:    How would I be able to do this properly?


Why does this creates aliased arrays ?!! is this a expected behavior ? In [57]: p=[[]] * 3  In [58]: p[0].append(2)  In [59]: p Out[59]: [[2], [2], [2]]

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?


namespace DelegatePractise1 {  public delegate int AddDelegate(int x, int y);  class Calculator {     MathOps opsObj = new MathOps();     static void Main(string[] args)     {          AddDelegate addDelInstance = new AddDelegate(opsObj.Add);//getting error here          int sum = addDelInstance(2, 3);         Console.WriteLine("{0} sum", sum);         Console.Read();      } }  public class MathOps {      public int Add(int x, int y)     {         return x + y;     } }   }  when i initialize the object 'opsObj' inside the main then the error doesn't come anymore. Can you explain why do i need to include the object initialization inside the main for this case. I am new to oop concept. Thanks in advance

Consider:  namespace WindowsApplication1 {     public partial class Form1 : Form     {         public Form1()         {             InitializeComponent();         }          private void button1_Click(object sender, EventArgs e)         {             //int[] val = { 0, 0};             int val;             if (textBox1.Text == "")             {                 MessageBox.Show("Input any no");             }             else             {                 val = Convert.ToInt32(textBox1.Text);                 Thread ot1 = new Thread(new ParameterizedThreadStart(SumData));                 ot1.Start(val);             }         }          private static void ReadData(object state)         {             System.Windows.Forms.Application.Run();         }          void setTextboxText(int result)         {             if (this.InvokeRequired)             {                 this.Invoke(new IntDelegate(SetTextboxTextSafe), new object[] { result });             }             else             {                 SetTextboxTextSafe(result);             }         }          void SetTextboxTextSafe(int result)         {             label1.Text = result.ToString();         }          private static void SumData(object state)         {             int result;             //int[] icount = (int[])state;             int icount = (int)state;              for (int i = icount; i > 0; i--)             {                 result += i;                 System.Threading.Thread.Sleep(1000);             }             setTextboxText(result);         }          delegate void IntDelegate(int result);          private void button2_Click(object sender, EventArgs e)         {             Application.Exit();         }     } }   Why is this error occurring?     An object reference is required for the nonstatic field, method, or property 'WindowsApplication1.Form1.setTextboxText(int)


I think that the question is contained in the title. Suppose we begin from something that is false for example $1=0$. Is it possible using only $\Rightarrow$ (and of course $\lnot ,\wedge,\lor$)  to prove any possible statement? It has been ages since i studied logic at the university so i would prefer a simple explanation (if possible)

Possible Duplicates:             I heard a professor of mathematics explaining that the following conslusions are true.   $\textrm{False}\Rightarrow \textrm{True}$ $\textrm{False}\Rightarrow \textrm{False}$   Could someone please explain to me why both conclusions are true? I am especially interested in the first case. I'd like to hear two explanations if possible: One for mathematicians and one for non-mathematicians. :-)


I used the Software Updater and at the end it said     Failed to download repository information   Check your Internet connection     I saw an article said use sudo apt-get update  I tried and it said  Ign:1 cdrom://Ubuntu 18.04.1 LTS _Bionic Beaver_ - Release amd64 (20180725) bionic InRelease Err:2 cdrom://Ubuntu 18.04.1 LTS _Bionic Beaver_ - Release amd64 (20180725) bionic Release   Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs Hit:3 http://mirror.ehost.vn/ubuntu bionic InRelease Hit:4 http://mirror.ehost.vn/ubuntu bionic-updates InRelease Hit:5 http://mirror.ehost.vn/ubuntu bionic-backports InRelease Hit:6 http://mirror.ehost.vn/ubuntu bionic-security InRelease Hit:7 http://archive.canonical.com/ubuntu bionic InRelease          Reading package lists... Done                           E: The repository 'cdrom://Ubuntu 18.04.1 LTS _Bionic Beaver_ - Release amd64 (20180725) bionic Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   I also saw a post saying that I should go to Settings and select Select best server in Download from in the Ubuntu Software tab.   However, when I closed that window this appeared:    I pressed Reload and it ran a cache update, but when it finished it again said      Failed to download repository information   Check your Internet connection      Details   E:The repository 'cdrom://Ubuntu 18.04.1 LTS _Bionic Beaver_ - Release amd64 (20180725) bionic Release' does not have a Release file.   My network is totally fine.

When updating I got this error message:  W:Failed to fetch cdrom://Ubuntu 11.10 _Oneiric Ocelot_ - Release amd64 (20111012)/dists/oneiric/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs W:Failed to fetch http://ppa.launchpad.net/synce/ubuntu/dists/your_ubuntu_version/main/source/Sources  404  Not Found   What to do?


As the title suggests, I want to calculate a standard congruence that can either be done with successive squaring or using indices. To calculate $11^{25} \; (mod \; 29)$ I'm not sure how to use indices. Do we take the index of 25 with base 11? We know 11 is a primitive root mod 29, how can that help us here?

I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two:   $13^{100} \bmod 7$ $7^{100} \bmod 13$   I've also heard of this formula:  $$a \equiv b\pmod n \Rightarrow a^k \equiv b^k \pmod n $$  But I don't see how exactly to use that here, because from $13^1 \bmod 7$ I get 6, and $13^2 \bmod 7$ is 1. I'm unclear as to which one to raise to the kth power here (I'm assuming k = 100?)  Any hints or pointers in the right direction would be great.


How do I check if a variable is equal to any element of an array?  var myButton = document.getElementById("myButton"); var myVar; //myVar value is set to "One", "Two" or "Three" sometime later  myArray = ["One","Two","Three"];  myButton.onclick = function () {     if (myVar === myArray) {         alert ("it's a match!");     } else {                 alert ("it's not a match!");         } };

What is the most concise and efficient way to find out if a JavaScript array contains a value? This is the only way I know to do it: function contains(a, obj) {     for (var i = 0; i < a.length; i++) {         if (a[i] === obj) {             return true;         }     }     return false; }  Is there a better and more concise way to accomplish this?


I am just curious: Are there any 64 bit Linux systems, which support a 32 bit version of Apache? As far as I know, a 64 bit Linux system supports only an Apache 64 bit and a 32 bit Linux system supports only an Apache 32 bit.  Edit  My motivation was just to know, if and which Linux distribution also provide 32 bit packages for applications and / or libraries.

I have a 64-bit (amd64 a.k.a. x86_64) Debian or Ubuntu installation. I need to run 32-bit (i386/i686) programs occasionally, or to compile programs for a 32-bit system. How can I do this with a minimum of fuss?  Bonus: what if I want to run or test with an older or newer release of the distribution?


Tools: React v 0.14   Jquery 1.11.2  I've hit a wall and I'm not sure if it's because I'm not sure if it's because of a big Reactjs jQuery no-no that I could be unaware of.  Now I know that React can handle click events for me,   but I just wanted to test out some css-transitions on my page and I've already built event handlers in jQuery that work on a standard html version of basically the same application(non-Reactjs).  Now that I'm trying it on my reactjs version though onClick events from my jQuery file are not firing.  To give you a quick idea of the probelm here's a snippet:  $(document).ready(function(){     var $window = $(window);     console.log("This is will output! yah!!");     $('.burger').on('click', function() {       console.log("Oh crap,not outputting when I click! boo!!"); ...   Is there any major reactjs reason(virtual-dom, jQuery compatibility issues) no-no I'm not aware of that could be causing this failure? Or is it kosher to do what I'm(at least for fast testing reasons) and it should work so long as I coded up the jQuery right?

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


One of my players (of a rogue) said that he heard of DM's allowing the familiar to be carried on the players body. He use his familiar to help him in combat and get advantage on the attack roll. I said it's okay for me and allowed it. But later in fight I played a goblin and obviously attacked his familiar in his pocket, to take his advantage away. He said that it shouldn't be possibly because his familiar hides in a pocket and can't be targeted. I didn't allow that because it would obviously break the game. He said that many DM's bend the rule like this and allow this. I would like to hear whether anyone has ever allowed this change of the rules, and whether it did or will break the game.

We're a new group playing DnD 5e. Three of us have no prior experience (and I'm one of them, never played the earlier editions) whilst two of us have some to good experience with other editions.  I'm DMing Rise of Tiamat and I'm really struggling with giving the players any kind of challenge. We've got a Paladin with Sentinel and a Halberd, almost stopping everything in its tracks when they attack, a Wizard with Fireball (he might have found a spellbook), Minor Illusion and the Tiny Hut spell (which really messes up any kind of surprises I have in store for the night), a Druid which doesn't do much and a Rogue which died last session because of PVP (he got the option to sacrifice one player by an evil fountain spewing blood, he took it - and it didn't pay off in the end).  Just a bit of context.  My question is this: our Wizard is because of his familiar (a rat which he has on the inside of his robe) constantly throwing advantage on all of his D20 rolls. I said I won't allow this in the future sessions because the familiar needs and initiative, and also needs to somehow confuse or do whatever with the mobs to allow advantage.  He does, however, claim that the familiar gives him an advantage on all skill checks as well, in and out of combat. Is this according to the rules?


Firstly before I explain, here is the code in C:  #include <stdio.h>  void printSize(char* str);  int main() {     char a[100] = "StackOverflow";     printSize(a);     return 0; }  void printSize(char* str) {     int n = sizeof(str) / sizeof(char);     printf("%d" ,n); }   As you can already see, I am trying to get my function to print the value "100" as 100 is the size that I have allocated to my char array a. However I am getting 8 as my answer. Now I know why I am getting 8 here because it's printing the size of the pointer. So my question is, if I can't use this method to print out the value of "100" then how can I find out the memory allocated to a from inside the function?  Thanks

First off, here is some code:  int main()  {     int days[] = {1,2,3,4,5};     int *ptr = days;     printf("%u\n", sizeof(days));     printf("%u\n", sizeof(ptr));      return 0; }   Is there a way to find out the size of the array that ptr is pointing to (instead of just giving its size, which is four bytes on a 32-bit system)?


I am struggling with the positioning of a node above a tikz path. The path is curved and connects two nodes with "to". Here is a MVE:  \documentclass[a4paper,twoside,11pt]{book} \usepackage{tikz} \begin{document}  \begin{tikzpicture}[scale=1,transform shape] \draw[->,thick,out=0,in=180] (1,0) to (5,1) node[above,pos=0.5,sloped] {text}; \draw[->,thick] (1,3) -- (5,4) node[above,pos=0.5,sloped] {text}; \end{tikzpicture} \end{document}   The node is above the line in the case with "--" but not with the "to". What I am missing here?  I am pretty sure I had something similar working in the past...

I have found a strange behavior in TikZ. When using the \draw ... to ... syntax and trying to place nodes along the line with the node[...]{...} syntax, the nodes do not turn up at the expected location.  \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture}   \draw(0,0) to[out=60,in=120] (1,0) node[midway]{x}; \end{tikzpicture} \end{document}     How is this done properly?


In the prologue of A Game of Thrones it is described how Gared runs for his life, when he and other two rangers encounter with White Walkers. But this happens north of the Wall.  In the first chapter, we find Lord Eddard executing him outside the walls of Winterfell. Hundreds of miles south of the Wall.  How did Gared get through the Wall? Is this a plot inconsistency? He can't have deserted the Watch after reporting the incident. If he did Night's watch would have known about the White Walkers.

In the first series of the TV show several things apparently bypass  to reach Winterfell:   The Night's Watch member  captured near Winterfell and executed by Ned. The Direwolf & her pups found immediately after the execution  and the other Wildlings travelling with her   If The Wall is approximately the same along its length it would presumably be impassible. Is the only option for them to go around the western end (since it stops at the Shadow Tower)? Is this clarified in the book? Are other methods mentioned in subsequent books?


I've tried so many different websites trying to find cheap lightroom film emulations.  I'd like to achieve looks like these:

Could you recommend a good source of presets for Lightroom?