I'm trying to repair Ububtu 15.10 crash/lockup boots up with no icons on screen, many repairs did not sove this problem, so created a dvd install for 15.10. But after all this, It comes back with "the root filesystem on /dev/sd1 requires a manual fsck." How does one do this ? I'm not a software dev/writer etc

I dual boot Ubuntu and Windows 7. I was browsing on FireFox in Ubuntu and all of a sudden I get some error message, so I rebooted.  Now when I try to boot into Ubuntu I get this message:  fsck from util-linux 2.26.2 /dev/sda6 contains a file system with errors, check forced. /dev/sda6: Inodes that were part of a corrupted orphan linked list found.  /dev/sda6: UNEXPECTED INCONSISTENCY; RUN fsck MANUALLY.         (i.e., without -a or -p options) fsck exited with status code 4 The root filesystem on /dev/sda6 requires a manual fsck  Busybox v1.22.1 (Ubuntu 1:1.22.0-15ubuntu1) built in shell (ash) Enter 'help' for a list of built-in commands.  (initramfs) _   How can I fix this?


Find all continuous functions that satisfy the Jensen inequality(I don't know why the problems states ''inequality'') $$f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2}$$  I've checked around stackexchange and google a bit, but none of the questions related to this problem gave me any hints on what I should do. The expression ''find all continuous functions'' confuses me. Am I supposed to determine some kind of a property that applies to all continuous functions that satisfy the property above or? Likewise there is a problem asking to find all continuous functions that satisfy$$f(x+y)=f(x)+f(y)$$ I'm sorry if this is a duplicate question, but even after reading all of those answers I've failed to find an adequate one. Also, another problem is that I'm not allowed to use derivations, and hence anything more complex than that.

Which functions $f:\mathbb{R} \to \mathbb{R}$ do satisfy $$f\left(\frac{x+y}{2}\right) = \frac{f(x)+f(y)}{2}$$ for all $x,y \in \mathbb{R}$  I think the only ones are of type $f(x) = c$ for some constant $c\in \mathbb{R}$ and the solutions of the Cauchy functional equation $f(x+y) = f(x)+f(y)$ and the sums and constant multiples of these functions. Are there other functions which are both midpoint convex and concave?


Can someone please tell me what purposes logarithms have in the everyday world? What non-theoretical applications are they in and when would one use them?

I am trying to gain a more intuitive feeling for the use of logarithms.   So, my questions: What do you use them for? Why were they invented? What are typical situations where one should think: "hey, let's take the $\log$!"?     Thanks for the great comments!      Here a short summary what we have so far:      History:      Logarithms were first published 1614   by John Napier   (mathematician/astronomer) . He needed   them for simplifying the   multiplication of large numbers.      Today’s uses:         In regression analysis: If you expect a predictor variable to follow   a power/exponential law, take the   corresponding logarithm to linearize   the relationship.   In finance to calculate compound interests.   Or more general: to calculate the time variable in growth/decay   functions. (Nuclear decay, biological   growth…)   In computer science to avoid underflow. (Cool trick! But seriously:   32-bit? Take a double ;-)   In the Prime Number Theorem   For handling very large/small numbers (pH, etc.)   Plotting (if your scale gets too large)


A great circle is a circle drawn on a sphere that is an "equator," i.e., its center is also the center of the sphere. There are $n$ great circles on a sphere, no three of which meet at any point. They divide the sphere into how many regions?      (The Art and Craft of Problem Solving, Page $37$, Problem $2.2.14$)   $2.2.12$ asks about the relation between vertices, edges and faces on a $3\text{-d}$ polyhedron, which is simply $V-E+F=2$.  $2.2.13$ asks about the number of regions an infinite plane can be split into using $n$ non-parallel lines, no three of which meet at any point. Here I checked a few cases, determined that $k=1$ and used $V-E+F=1$ to find that $f(n)=\frac 12 (n^2+n+2)$ where $f(n)$ is the number of regions.  For $2.2.14$, I am once again attempting to find $k$ such that I can use $V-E+F=k$. However, I am unsure how to define vertices or edges here. The few things I attempted all suggested different values of $k$ for different values of $n$.   I am unsure as to how I can determine $k$, as well as defining how vertices and edges are counted.  Additionally, it would be really helpful if there was a simple way to manually count the number of edges, vertices and faces, especially since making $4$ great circle on a sphere and reading the number of faces, vertices and edges using Geogebra $3\text{-d}$ was very difficult.

Find the recurrence relation satisfied by $R_n$, where $R_n$ is the number of regions into which the surface of a sphere is divided by n great circles (which are the intersections of the sphere and planes passing through the center of the sphere), if no three of the great circles go through the same point   From: Rosen Discrete Mathematics textbook  My attempt: I was unable to visualize these greater circles for values of $n \geq 4$. So, I launched GeoGebra and made the :     My initial planes were $x=y$, $x=-y$, and the $z=0$ plane. Now, I added a fourth yellow plane $y=z$. However, I still find it hard to understand how to calculate what number of new sections are formed. I am able to calculate the number of new sections in this specific case, but, I am unable to arrive at a general formula for the new number of sections, through recurrence.  I visited the following website -  - which happens to have a solution, where they mention the addition of $2(n-1)$ regions to the existing regions, after the addition of the $n$-th plane. However, I am unable to understand why exactly that is true.


Recently, I had to make a ruling that did not completely sit with me. The party's Evocation Wizard tried to cast a fireball on top of the party and claimed that due to their Sculpt Spells ability, nobody in the party took any damage. I looked up the definition from the rulebook which states this:  Beginning at 2nd Level, you can create pockets of relative safety within the effects of your Evocation Spells. When you cast an Evocation spell that affects other creatures that you can see, you can choose a number of them equal to 1 + the spell’s level. The chosen creatures automatically succeed on their Saving Throws against the spell, and they take no damage if they would normally take half damage on a successful save.  I interpreted this as simply stating, sculpt spells means creatures he chose, at MOST take half-damage (due to automatically succeeding saving throw) and IF they actually succeed on their saving throws, they will take NO damage. I felt like otherwise Evocation wizards will have absolutely no qualm in nuking their parties to take out enemies co-located with them with no penalty and with no limited resource. However the player who's wizard it is obviously counter-argued my approach. Is there some official guidance somewhere I missed on this issue?

According to an  class feature, they can create pockets of safety that allow the chosen creatures to:     ...automatically succeed on their saving throws   against the spell, and they take no damage if they would normally take   half damage on a successful save.   I'm reading this to say:   If there's a save, those in these 'pockets' automatically make it. If making a save would result in half damage, the 'pockets' take no damage.   So, if I'm reading this correctly, why not just say that those in the 'pockets' take no damage if there's a save? Why all the extra words?  When would someone in a Sculpt Spell's 'pocket of safety' take damage?


I would deeply appreciate it if you would answer this question, since I do not know or understand exactly the difference between inductive reasoning and abductive reasoning, which is a problem for me in my next philosophy evaluations.

Consider this statement:        Abductive reasoning typically begins with an incomplete set of   observations and proceeds to the likeliest possible explanation for   the set.       But couldn't the same be said about inductive reasoning? Someone finds a penny in a jar. Then they find a second and a third penny, so they conclude that all the coins in the jar are pennies.   Three pennies constitute an incomplete set, so how is that different from abduction?  What example of abduction would complement the following two deduction/induction sets?  DEDUCTION #1: All mammals have vertebrae; llamas are mammals. Therefore, llamas have vertebrae.  INDUCTION #1: The first three bones found in Cave X were vertebrae. Therefore, the other bones may represent mammals.   ABDUCTION #1: ???   DEDUCTION #2: All planets orbit stars. Earth is a planet. Therefore, Earth orbits a star.  INDUCTION #2: Astronomers have pronounced Object X a planet. The nearby Object Z is also a planet. Therefore, Object X and Object Z probably orbit the nearest star.   ABDUCTION #2: ???


I'm using ubuntu 20.04 now and I need to install cisco webex for important meetings but I'm unable to do it. So I would be super great and good if anyone in this community helps me out with this. I tried every method provided( only a few available in the internet), So please guys do help me with this. Thanks.

There is no one guide that I have tried that results in a fully working WebEx on Linux. Typically audio is the feature hardest to get working. How do I get WebEx working with audio on Ubuntu?


Is it possible to construct a matrix with non-zero off-diagonal entries whose eigenvalues are nonetheless equal to its diagonal entries?  EDIT: @ajotataxe pointed out that this holds for triangular matrices. My follow up is - is the converse true? If the Eigen values are the diagonals, does it have to be triangular?

I want to learn about matrices whose diagonal elements are the eigenvalues... but the matrix is neither diagonal nor triangular.  Is there a term for such matrices, and have they been researched?


I need to add multiple images with image descriptions form wp admin.  Admin Form:   Image <input type="file" name="image[]"/> Description <input type="text" name="imgdesc[]"/>  Image <input type="file" name="image[]"/> Description <input type="text" name="imgdesc[]"/>                  .                  .                  .  // number of image and description is dynamic  <?php wp_nonce_field('image', 'image_upload_nonce'); ?>   Here my PHP code during form submission.  <?php if (isset($_POST['image_upload_nonce']) && wp_verify_nonce($_POST['image_upload_nonce'], 'image')) {      require_once( ABSPATH . 'wp-admin/includes/image.php' );     require_once( ABSPATH . 'wp-admin/includes/file.php' );     require_once( ABSPATH . 'wp-admin/includes/media.php' );      //Here my doubt to handle multiple images     $attachment_id = media_handle_upload('image', 0);      if (is_wp_error($attachment_id)) {         echo $attachment_id->get_error_message();     } else {         // The image was uploaded successfully!     } } else {     echo "The security check failed, maybe show the user an error."; }   I don't know whether my approach is right. If not please correct me.

I have a WordPress form plugin and I use  to upload the files and get there ids directly and attached its ids to the post as a meta date, I used the following to did that:  The HTML of the form field is:  <input type="file" name="my_file_upload" id="my_file_upload">   And the php code was:  $attach_id = media_handle_upload( 'my_file_upload', $post_id ); if ( is_numeric( $attach_id ) ) {     update_post_meta( $post_id, '_my_file_upload', $attach_id ); }   And everything was work perfectly.  Now I am trying to upload multiple files my HTML code is:  <input type="file" name="my_file_upload[]" id="my_file_upload[]" multiple="multiple">   But I cant make the media_handle_upload function work with multiple files upload.  Any help will be appreciated.


So this is what I see now, but I cant get the bottom part (that's orange right now) to be viewed normally again, like the top part. I have no idea how this happened and I tried to google the problem but I am unsure what has even happened so I don't really know what to look for.  Can anyone explain what I can do to fix this?  Please keep in mind that I'm a beginner.

I'm new to Blender and this site, so I apologize in advance if I'm not following any of the proper etiquette.  I'm no artist, but I'm trying to learn Blender so that I have some programmer art for me to work around in Unity.    I followed a tutorial for making a basic human model, I rigged it with rigify, and now I'm starting to export it following yet another tutorial.  The thing is, when I was trying to rig the model, I couldn't get the model to go transparent so that I could see the bones inside the model.  Eventually, I managed to get it into wireframe mode, but I can't get it back into solid mode.    It's probably just a display thing and not a property of the model itself, but I want to be sure.  I'm looking at the display options under the "Figure" pane in Blender, and none of the Display check boxes are checked, including the one that says "Wire".  I don't want to import a plain wireframe model into Unity, and even if that doesn't happen, this is functionality of Blender that I should really know anyway, so I'd appreciate any help that anyone has to offer.  If necessary, I can upload the .blend file, but I'm not sure what site people would prefer that I upload it to.


I a trying to grep for certain string after issuing the grpck -n ALL command so when trying grpck -n ALL | grep -i format, for example, I still see the whole output and not just the lines containing the format string.  I know I could direct the output to a file and use grep on that file but it has to be an easier way.  The grpck is just an example as I have noticed other commands that don't support grep.

The script I use is actually returning this output:  (source /Thetra/Commun/env_ora.sh >/dev/null; sh aclenv/arun)  geIlgif0t1 -DVORACLE geIlgif0t1 prg_25900: ACOMP=X geAhadlAd1 -DVORACLE geAhadlAd1 prg_25948: ACOMP=A syCcgge0t1 -DVORACLE syCcgge0t1 prg_26023: ACOMP=S2 syVcalq0t1 -DVORACLE syVcalq0t1 prg_26071: ACOMP=Y syVvali0t1 -DVORACLE syVvali0t1 prg_26119: ACOMP=Y syAedit0t1 -DVORACLE syAedit0t1 prg_26167: (1312) DBMS WARNING: Column not found in table. (-11238)   RETURN (-6)     END  END     END     IF cm_para_f2('VDEF','abQtip_0n1','unicite',syAedit0t1:$v_unicite)<>0      OR null_convert$(syAedit0t1:$v_unicite,'R') <> 'F' THEN SET syAedit0t1:$v_unicite TO 'R'     SET $v_tips_mrgl TO 'S'     SET $v_rfbt_iban, $v_rfbt_intitule, $v_orga_creancier, $v_orga_tip_adr1, $v_orga_tip_adr2,         $v_orga_tip_adr3, $v_code_docu, $v_tips_centre, $v_code_etab, $v_orga_tip_emetteur,  $v_orga_emetteur, $v_rfbt_compte, $v_orga_banque, $v_rfbt_emetteur TO     SELECT rfbt_iban, rfbt_intitule, orga_creancier, orga_tip_adr1, orga_tip_adr2, orga_tip_adr3 ACOMP=N syAvali0t1 -DVORACLE syAvali0t1 prg_26215: (2751) DBMS WARNING: Column not found in table. (-11238)  + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_imme_no)),1,4)),'&&&&')         + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_sepa_propriete_no)),1,5)),'&&&&&')     IF syAvali0t1:$v_unicite ='R' THEN  SET $v_sepa_rum3 TO $v_sepa_rum3 + substr$(to_string_using$(syAvali0t1:$v_ordr_direct,'&&&&&&&&&'),7,9)     ELSE ACOMP=N syAcalc0t1 -DVORACLE syAcalc0t1 prg_26263: ACOMP=N syAcalc0t2 -DVORACLE syAcalc0t2 prg_26311: ACOMP=N syAcalc0t3 -DVORACLE syAcalc0t3 prg_26359: ACOMP=N   To check for errors I use the following command:  (source env_ora.sh >/dev/null; sh aclenv/arun) | egrep '^ACOMP=$'   Output:  (1312) DBMS WARNING: Column not found in table. (-11238)   RETURN (-6)     END  END     END     IF cm_para_f2('VDEF','abQtip_0n1','unicite',syAedit0t1:$v_unicite)<>0      OR null_convert$(syAedit0t1:$v_unicite,'R') <> 'F' THEN SET syAedit0t1:$v_unicite TO 'R'     SET $v_tips_mrgl TO 'S'     SET $v_rfbt_iban, $v_rfbt_intitule, $v_orga_creancier, $v_orga_tip_adr1, $v_orga_tip_adr2,         $v_orga_tip_adr3, $v_code_docu, $v_tips_centre, $v_code_etab, $v_orga_tip_emetteur,  $v_orga_emetteur, $v_rfbt_compte, $v_orga_banque, $v_rfbt_emetteur TO     SELECT rfbt_iban, rfbt_intitule, orga_creancier, orga_tip_adr1, orga_tip_adr2, orga_tip_adr3 (2751) DBMS WARNING: Column not found in table. (-11238)  + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_imme_no)),1,4)),'&&&&')         + to_string_using$(str_to_val$(substr$(clip_str$(to_string$($f_sepa_propriete_no)),1,5)),'&&&&&')     IF syAvali0t1:$v_unicite ='R' THEN  SET $v_sepa_rum3 TO $v_sepa_rum3 + substr$(to_string_using$(syAvali0t1:$v_ordr_direct,'&&&&&&&&&'),7,9)     ELSE   We can see that grep is returning non matching lines.  When I redirect the stderr to stdout with this command:  (source /Thetra/Commun/env_ora.sh >/dev/null; sh /Thetra/Oracle/transfert/P2016.H.1/aclenv/arun) 2>&1 | egrep '^ACOMP=$'   As expected, the output is void.  Why grep is returning non matching lines when stderr is not redirected ?


I want to know how can I copy or shell copy multiple files within a bash script. What I mean is that cp /path/to/source/{file1,file2,file3} /path/to/dest  and scp /path/to/source/{file1,file2,file3} user@host:/path/to/dest  will work fine but as example #!/bin/sh scp /path/to/source/{file1,file2,file3} user@host:/path/to/dest  will throw an error like this: /path/to/source/{file1,file2,file3}: No such file or directory  If you will copy or shell copy a single file it works, so the problem are multiple files. Also it works if I would use * for all files but I do not want to copy all files. I should only copy selected files because in both folders are files with the same name but their content is different. Thereby to copy all files and then remove the not needed files would not work. For better understanding following would work: #!/bin/sh scp /path/to/source/file1 user@host:/path/to/dest  Also following: #!/bin/sh scp /path/to/source/* user@host:/path/to/dest  So it has something to do with the correct use of { ... } for multiple files which will work inside the terminal but not if I run the bash script in it. Thanks in advance. //Edit: I add the error if I try it with cp: cp: cannot stat '/path/to/source/{file1,file2,file3}': No such file or directory

Do I have to do any configuration to start brace expansion? When I run mkdir {1..10}, it just creates a dir naming {1..10}.


We know, according relativity theory, no information or matter  can travel with velocity bigger than light. However, consider the following situation: a completely empty water hose is hypothetically connected between the sun and the earth. After this, we turn on the water hose until it stay completely full,  next we turn off. When we turn on again here on the earth, the water will arrive instantly on the sun in order a person there, to receive instantly the information that the water hose was turned on here on the earth. This case, the information travel with velocity bigger than light, violating the relativity theory. How can this happen?

Is it possible for information (like 1 and 0s) to be transmitted faster than light?   For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end.   The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.  Would this actually work?


I have issues with a cell in google apps script where if a cell = "0:00" it needs to equal some text like "Unexcused Absence". when I run the code it gives me a blank cell.  function Boh() {    var sheet = SpreadsheetApp;    var ss = sheet.getActiveSpreadsheet().getActiveSheet();    var lastRow = ss.getLastRow();    var spreadsheet = SpreadsheetApp.getActive();    var b = 0;    var wCell = 'Work';    var x = new Date('3/16/2013 0:00:00');     for(var i=2;i<=lastRow;i++){    ss.getRange(i,10).activate();    if(x.setHours(0,0,0,0)  == ss.getRange(i, 17).getValue() && 'Work' == ss.getRange(i, 5).getValues()){       ss.getRange(i, 10).setValue('Unexcused Absence');    }    }

Can someone suggest a way to compare the values of two dates greater than, less than, and not in the past using JavaScript? The values will be coming from text boxes.


I'm using the template   %% bare_jrnl_compsoc.tex %% V1.3 %% 2007/01/11 %% by Michael Shell %% See: %% http://www.michaelshell.org/ %% for current contact information.   which can be downloaded from here:  for my paper. It works fine, except for one thing: I would like to use the descriptionenvironment, but the result is quite a mess:    The underlinings are not a problem; they will be erased later. However, it seems that the description environment has a problem if the word after \item[THIS WORD]is too long.  Is there any easy fix for this?  Thank you for your help!

I'd like to use a description environment together with the IEEEtran document class.  One of the labels is actually quite long (three words) so I need to use \IEEEsetlabelwidth to avoid having the text and the label overlap.  As apparently it determines the indentation of the whole text and not just the text on the first line, I get a skinny column that spans over a large number of lines.  \begin{description}[\IEEEsetlabelwidth{Very long label}\IEEEusemathlabelsep]   \item[Very long label] this text is spanning over multiple lines.  Since the label was very long and the label determined the indent of the text it really covers a large number of lines. \end{description}   The result is something like  Very long label   this text is spanning over                   multiple lines. Since the                    label was very long and                   the label determined the                   indent of the text it                   really covers a large                    number of lines.   While I would like something like  Very long label   this text is spanning over     multiple lines. Since the label was very     long and the label determined the indent     of the text it really covers a large      number of lines.   I don't have specific requirements for the body of the text, but it'd be nice if it was consistent across the several descriptions of the document (it is not the case at the moment).  I have tried to read the documentation of IEEEtran, but I'm quite confused.


South Africans are visa exempt for Ireland for 3 months.  However, if connecting in the UK on the way there, they have to clear UK immigration as Ireland is in the CTA.  The  states the following regarding South Africans going to Ireland via the UK:     You’ll usually need to apply for a UK standard visitor visa;   ;     You might be eligible for ‘transit without visa’ if [...] [you] have the right documents for your destination (for example a visa for that country)   and     You must also have an Irish biometric visa (marked ‘BC’ or ‘BC BIVS’ in the ‘Remarks’ section) and an onward flight ticket to the Republic of Ireland.   The second and third statements overlap but differ: the second statement implies you just need to have the right papers to enter Ireland (for a South African, a passport), while the third statement specifically says you need an Irish visa to connect the UK visa-free.  Judging by the first and third statements combined, it would appear that a South African, despite being visa exempt for Ireland, would need either a UK Standard visitor visa or an Irish visa if connecting in the UK.  Is this the case?

I am Lebanese Citizen and am planning a trip to Ireland this month. A valid Irish visa is already in hand and I am willing to reach there through the UK.   Will I need a transit visa in the UK for few hours for flight connections to Ireland?


Just noticed the Unicoins ad on the site and spent some time breaking rocks. Since it popped up 'today' (April 01) I am sure it isn't legit.  BTW, I bought 'no downvotes please' so please don't downvote ;)  Before it goes away! This is what it looked like.

Recently I saw a widget on the Stack Overflow website which says Stack Overflow now has its own currency called "unicoins". According to this widget, a user can earn reputation, customize Stack Overflow by changing its colors and the user can also remove the vote down button from their questions and answers by spending "unicoins".  This widget does not look real, because this is out of standard of the Stack Overflow website.  Also today is 1st April. Is Stack Overflow fooling us?


$f'(0)$ when $f(x)=x^2\sin(1/x)$, $f(0)=0$  This is presented as an MCQ and answer is given as "$f$ is differentiable at every $ x$ but $f'$ is discontinous at $0$ "  I calculated LHD and RHD at $0$ as $0$ and $f'(x)=2x\sin(1/x)-\cos(1/x)$ which is not defined at 0 thus the answer should be "$f$ is not differentiable at $0$"  Is this a misprint or am I missing something?

Assume this function has a value $0$ at $x=0$.  If the right hand derivative of a derivable function is equal to the right hand limit of the derivative function (same for the left), why aren't functions like the one above continuously differentiable?  For a function to be continuous, limits should be  finite and equal to value at that particular point.  For this function derivative using first principle yields $0$.  The RHD, LHD is $0$, I think. So why isn't the derivative continuous?  For finding the RHD and LHD, I have seen answers resorting to using known derivatives. My question is: why don't we use the first principle itself? Why do we get different answers then?


I am using the Android SE app. I want to know if my connection to Stack Exchange encrypted? Thanks.

I’d like to know the transmission of SE  Android app is encrypted or not with https. Please make me confirm.


After downloading and extracting them, how do I install the CMAKE binary files in Ubuntu 14.04 so that they're recognized with cmake --version?

Default cmake version of 14.04 is 2.8. How can I install cmake 3.2 and replace the default one? Or how can I upgrade 2.8 to 3.2?


If $\alpha$ is a real root of the equation $x^5-x^3+x-2=0$, find the value of $\lfloor\alpha^6\rfloor$, where $\lfloor x\rfloor$ is the least positive integer not exceeding $x$.  My approach is to bound the value of $\alpha^6=\alpha^4-\alpha^2+2\alpha$. First I proved the function $f(x)=x^5-x^3+x-2$ is monotone increasing by derivative. Then I argue that $1<\alpha<\frac32$ as $f(1)<0$ and $f(\frac32)>0$. Then I tried to create an upper and lower bound for $\alpha$, as such $$\alpha^6=\alpha^4-\alpha^2+2\alpha<\frac94\alpha^2-\alpha^2+2\alpha=\frac54\alpha^2+2\alpha<\frac{45}{16}+3=\frac{93}{16}$$ and $$\alpha^6=\alpha^4-\alpha^2+2\alpha>\alpha^3-\alpha^2+2\alpha=\alpha^2(\alpha-1)+2\alpha>2$$ Now we know that $\lfloor\alpha\rfloor\in\{2,3,4,5\}$. But I cannot proceed any further. Any idea, help, hint, or answer is appreciated. Thank you.

If $\alpha$ is a real root of the equation   $$x^5-x^3+x-2=0$$   find the value of $\lfloor {\alpha}^6 \rfloor$.      This one totally stumped me. We are asked to calculate $\lfloor {\alpha}^6 \rfloor$ without actually calculating the root or using wolfram alpha or any other calculator. I found that the above equation has only one real root by sketching its graph using calculus. I was also able to use the intermediate value theorem to conclude that $1<\alpha<2$ , but this is of little use while calculating $\lfloor {\alpha}^6 \rfloor$. Please help!


Can open-circuit voltage be treated as voltage to find power dissipated? I combined all the resistors (including Vlamp) to get one resistor of 40/6 Ohms (Correct me if I'm wrong). Using Ohm's law to find the current doesn't work since I don't know the voltage, Thus the title. I don't think so but I wasn't taught this in detail and Googling doesn't benefit since Wikipedia has a page  I already figured out that: Battery has open circuit voltage of 4V R1 = 5 Ohms R2 = 5 Ohms k = 0.2A/V When lamp on and Vlamp = 2V, Rbat = 10 Ohms   The lamp turns on if the voltage across the lamp is greater than 2V. When the lamp is on it has an internal resistance of 10 Ohms, and when it is off it acts like an open circuit.   This is what I calculated:    I'm getting Ilamp as 1/5, still trying to see how that will help... EDIT: My answer has been suggested as a duplicate. Is it the same question? NO. Is it the same answer? NO.    The only thing that is the same is the circuit, any objections?

This is my circuit. I need to find the power dissipated by Vlamp. So the lamp turns on if the Vlamp is more than 2V. When the lamp is on it has an internal resistance of 10 Ohms, and when it is off it acts like an open circuit.  How would I find the power dissipated? I know how to do it for Voltage sources and Resistors, but not elements like these.  One more thing, I already figured out that: Battery has open circuit voltage of 4V R1 = 5 Ohms R2 = 5 Ohms k = 0.2A/V When lamp on and Vlamp = 2V, Rbat = 10 Ohms   .


Is there tool or application that can set the brightness of the screen below the system minimum?

I have an Optimus Elite, and it has a minimum brightness setting. In certain apps, I can reduce the brightness below the safe minimum, but when I leave the app, the brightness is increased to the system-wide minimum.  Using , I can permanently set the brightness below the safe amount, and it will stay even after going to other apps. Or using , I can accomplish almost the same thing even without needing root (it displays a translucent 'filter' over the whole screen, reducing brightness/contrast but not actually changing the backlighting power amount).  What I want to know is where the minimum screen brightness is stored. I have a rooted phone with CyanogenMod 9, so I have permissions to edit anything and could change a config or sqlite entry, but I don't know where this value is stored. What I would like to do is use the status bar brightness slider to be able to slide to the actual minimum of the screen, rather than the OS-controlled minimum. Having an app is useful, but having the functionality without the app seems to be within reach, if only I knew where the OS is getting it's safe minimum setting.  Where is this "safe minimum brightness" setting stored? If I can change it, I can remove my apps and use native controls.


Here I am taking the definition of isomorphism to be an injective homomorphism.  Suppose we have two finite fields of the same characteristic, $\mathbb{F}_{p^n}$ and $\mathbb{F}_{p^m}$ with $m<n$. Is there always an isomorphism $\phi:\mathbb{F}_{p^m}\rightarrow \mathbb{F}_{p^n}$?  If $m|n$ then we could use the same construction $\mathbb{F}_{p^m}[X]/(P)$ where $P$ is an irreducible polynomial in $\mathbb{F}_{p^m}[X]$ such that $\deg(P)m=n$. Since this would produce a field of the same characteristic and cardinality, it would provide an isomorphism.  Does anyone have any references on this topic? Thanks in advance.

Blue was correct, I need to fix my understanding of this:     Finite fields have cardinality of a prime order because they have a prime subfield that has finite characteristic.    I do not completely understand why finite field of each characteristic is unique. Perhaps we look at a polynomial and express the finite field as a splitting field? And we use uniqueness of splitting fields?  Then, why is it that  $\mathbb F_{p^m} \subseteq \mathbb F_{p^n}$ if and only if $m$ divides $n$?


Need help with include vs. includes:     He's had hits with a massive number of artists that include so-and-so, so-and-so, and so-and-so.   Or should it be includes, agreeing with the word "number"?

This is from a recent article:     He was rushed to the hospital immediately and a battery of tests was   conducted.   Now shouldn't it be     He was rushed to the hospital immediately and a battery of tests were   conducted.   Which is correct and why is it correct? :)


Error mounting /dev/sda2 at /media/lubia/Media: Command-line   mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda2" "/media/lubia/Media"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0).   Metadata kept in Windows cache, refused to mount.  Failed to mount '/dev/sda2': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option.

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


I'm lost not sure what to do here.... I don't know how to configure my secure booting options. I don't which setting to change?

After installing the Windows 10 upgrade on my laptop, it ruined the grub boot manager, and I could only boot in windows 10. I fixed the boot manager using a live cd with the boot-repair tool, but it only recognized the Ubuntu partition, and not the Windows one.   So I edited the /etc/grub.d/40_custom file and added the following contents:  menuentry "Windows 10" {     set root='(hd0,3)'     chainloader +1 }   After running sudo update-grub2, I got an entry in the boot menu, but the partition does not load. It gives the following error:  Error: Invalid signature.     Does anybody know how one can overcome this error?   My most recent boot-repair dump is here: , and the partition I want to boot is this one:  sda4: __________________________________________________________________________      File system:       ntfs     Boot sector type:  Windows 8/2012: NTFS     Boot sector info:  No errors found in the Boot Parameter Block.     Operating System:       Boot files:        /bootmgr /Windows/System32/winload.exe


ok I know this is backwards but after spending half a day doing a clean install of Windows and updating drivers I'd prefer to not have to repeat the process.  I'd like to simply partition my SSD in half. Can I do this properly AFTER having already installed windows? is there a recommended(no malware) 3rd party app that can accomplish this?

I have just bought an HP laptop with Windows 7 (64 bit). It has a 500 GB HDD with three partitions: a small hidden system partition, a 12 GiB HP recovery partition, and a 450 GiB C: boot partition.  I would like to split this large C: partition into two partitions, leaving only 100 GiB for the system, and giving the rest to a new data partition.  Although the Windows built-in Disk Management utility has an option to shrink the bootable partition, it only allows me to shrink it roughly by half, even though only 20 GiB on the partition is used. As far as I understand, system unmovable files lie in the middle of the partition, preventing Disk Management utility to do what I want.    And since new HP laptops don't come with OS installation disks (they only allow you to create recovery disks yourself), I can't just repartition HDD and then reinstall OS.  So, is there a way to shrink the C: bootable partition and preserve Windows 7 working?  P.S.: I have tried to use the third-party  utility, and after shrinking the partition, Windows 7 stopped booting, with a . System recovery didn't work, and I had to do factory recover. Since this is a long process, I would like to avoid doing it again :) So, please, suggest only proven solutions.


I have the following:  list = ["player1", "player2", "player3"]   I want to find all possible combinations of two elements of that list, but with no duplicates. I have tried to work with the itertools.combinations() but without the desired result.  I'm looking for a result like this:  player1, player2 player1, player3 player2, player3   Can someone help me in the right direction?  Thanks in advance

I have a list with 15 numbers in, and I need to write some code that produces all 32,768 combinations of those numbers.   I've found  (by Googling) that apparently does what I'm looking for, but I found the code fairly opaque and am wary of using it. Plus I have a feeling there must be a more elegant solution.  The only thing that occurs to me would be to just loop through the decimal integers 1–32768 and convert those to binary, and use the binary representation as a filter to pick out the appropriate numbers.   Does anyone know of a better way? Using map(), maybe?


I'm trying to create a tikz picture along the lines of    only with the blue colour fading out as it gets to the edge of the blue strip. Ideally, the blue bar should be fully blue in the middle (at the point (-1,0) to be precise), and white at the outer edges (the points (0,1) and (0,-1)).  The picture above was created as follows.  \documentclass{article} \usepackage{tikz,xcolor}  \begin{document} \begin{tikzpicture}     \draw[line width=0.25cm, blue]  (90:1)  arc [start angle=90, end angle=270, radius=1];     \draw[thick]                    (0,0)   circle [radius=1]; \end{tikzpicture} \end{document}

How can I shade a path witout filling? In particular, I wand to draw a curved arrow that starts colored blue and ends colored green, where in between it gradually changes its color. I can't find a way to shade a path without filling it.  The following code does not work, as it shades the filling area, although it compiles.  \documentclass{article} \usepackage{tikz} \usetikzlibrary{calc,automata,patterns,decorations,decorations.pathmorphing} \usetikzlibrary{fadings} \begin{document} \begin{tikzpicture}  \draw[path fading=south,very thick,top color=blue!80!white,       bottom color=green!80!white,->] (0,0) .. controls +(0,-1) and +(0,1) .. (1,-2);  \end{tikzpicture} \end{document}


Solve the equation $\cos^n(x) - \sin^n(x)=1,n \in \mathbb{N}-\{0\}$     If $n$ is even then $\cos^n(x) = \sin^n(x)+1$ is only possible if $\sin(x)=0$ therefore the solution is $x=k\pi, k \in \mathbb{Z}$.  I'm having problems with $n$ odd case.  UPDATE  For $n=1$ we have $\cos(x) - \sin(x)=1$ and by squaring we get $sin(x)cos(x)=0$ which leads to $x=k\pi$ or $x=\pm \frac \pi 2 + k\pi$. From these solutions, only $x=2k\pi$ and $x=- \frac \pi 2 + 2k\pi$ are valid.  Also $x=2k\pi$ and $x=- \frac \pi 2 + 2k\pi$ are solutions for all odd $n$

Solve $\cos^{n}x-\sin^{n}x=1$ with $n\in \mathbb{N}$  I have no idea how to deal with this crazy question. One idea came into my mine is factorization, but I can't go on... Can anyone help me please? Thank you.


Question:  Find  the integral $$I=\int\dfrac{1}{\sin^5{x}+\cos^5{x}}dx$$  my solution: since  \begin{align*}\sin^5{x}+\cos^5{x}&=(\sin^2{x}+\cos^2{x})(\sin^3{x}+\cos^3{x})-\sin^2{x}\cos^2{x}(\sin{x}+\cos{x})\\ &=(\sin{x}+\cos{x})(1-\sin{x}\cos{x})-(\sin{x}+\cos{x})(\sin^2{x}\cos^2{x})\\ &=(\sin{x}+\cos{x})[1-\sin{x}\cos{x}-\sin^2{x}\cos^2{x}) \end{align*}  then let $$\sin{x}+\cos{x}=t\Longrightarrow \sin{x}\cos{x}=\dfrac{1}{2}(t^2-2)$$  then $$\sin^5{x}+\cos^5{x}=t[1-\dfrac{1}{2}(t^2-2)-\dfrac{1}{4}(t^2-2)^2]=-\dfrac{1}{4}t(t^4-2t^2+4)$$ $$x+\dfrac{\pi}{4}=\arcsin{\dfrac{t}{\sqrt{2}}}\Longrightarrow dx=\dfrac{1}{\sqrt{2-t^2}}dt$$ so $$I=-4\int\dfrac{dt}{t\sqrt{2-t^2}(t^4-2t^2+4)}=-2\int\dfrac{1}{u\sqrt{2-u^2}(u^2-2u+4)}du$$ where $u=t^2$  Then I can't, because this wolf can't   Thank you for  you help

Solve the following indefinite integrals:      $$ \begin{align} &(1)\;\;\int\frac{1}{\sin^3 x+\cos^3 x}dx\\ &(2)\;\;\int\frac{1}{\sin^5 x+\cos^5 x}dx \end{align} $$   My Attempt for $(1)$:  $$ \begin{align} I &= \int\frac{1}{\sin^3 x+\cos ^3 x}\;dx\\ &= \int\frac{1}{\left(\sin x+\cos x\right)\left(\sin^2 x+\cos ^2 x-\sin x \cos x\right)}\;dx\\ &= \int\frac{1}{\left(\sin x+\cos x\right)\left(1-\sin x\cos x\right)}\;dx\\ &= \frac{1}{3}\int \left(\frac{2}{\left(\sin x+\cos x\right)}+\frac{\left(\sin x+\cos x \right)}{\left(1-\sin x\cos x\right)}\right)\;dx\\ &= \frac{2}{3}\int\frac{1}{\sin x+\cos x}\;dx + \frac{1}{3}\int\frac{\sin x+\cos x}{1-\sin x\cos x}\;dx \end{align} $$  Using the identities  $$ \sin x = \frac{2\tan \frac{x}{2}}{1+\tan ^2 \frac{x}{2}},\;\cos x = \frac{1-\tan ^2 \frac{x}{2}}{1+\tan^2 \frac{x}{2}} $$  we can transform the integral to  $$I = \frac{1}{3}\int\frac{\left(\tan \frac{x}{2}\right)^{'}}{1-\tan^2 \frac{x}{2}+2\tan \frac{x}{2}}\;dx+\frac{2}{3}\int\frac{\left(\sin x- \cos x\right)^{'}}{1+(\sin x-\cos x)^2}\;dx $$  The integral is easy to calculate from here.  My Attempt for $(2)$:  $$ \begin{align} J &= \int\frac{1}{\sin^5 x+\cos ^5 x}\;dx\\ &= \int\frac{1}{\left(\sin x+\cos x\right)\left(\sin^4 x -\sin^3 x\cos x+\sin^2 x\cos^2 x-\sin x\cos^3 x+\cos^4 x\right)}\;dx\\ &= \int\frac{1}{(\sin x+\cos x)(1-2\sin^2 x\cos^2 x-\sin x\cos x+\sin^2 x\cos^2 x)}\;dx\\ &= \int\frac{1}{\left(\sin x+\cos x\right)\left(1-\sin x\cos x-\left(\sin x\cos x\right)^2\right)}\;dx \end{align} $$  How can I solve $(2)$ from this point?


I'm making an adventure map in Minecraft.  I've been trying to make a key that opens a door and then deletes itself from your inventory. I got it to work flawlessly without NBT tags, using a trip-wire hook as a key.   After I assigned NBT tags to it thusly, tripwire_hook {display:{Name:"Key",Lore:["Opens one door"]}} the tripwire is now called a "Key" and describes exactly what it does and it even works to open the door. The command block that tests for the key in the players hand still works.  Unfortunately, the /clear @p command block will not recognize the item whether I add the NBT tag after "tripwire_hook" or not. Here is the command that I've used:  /clear @p tripwire_hook 1 {display:{Name:"Key",Lore:["Opens one door"]}}  Just to be safe, I tried the following:  /clear @p tripwire_hook 1 1 {display:{Name:"Key",Lore:["Opens one door"]}}  /clear @p tripwire_hook 0 1 {display:{Name:"Key",Lore:["Opens one door"]}}  And it will still not clear the item.  I'm using Minecraft 1.8.3. Can anyone please advise?

Recently I've been messing around with making a few minigames, and have used a few plugins to help make it easier to create and run them. However, a newer one I'm making requires me to use the /summon command in order to spawn zombies. However, no matter what I put in, I can't spawn hostile mobs. All other entities still spawn perfectly fine. Strangely, the /spawnmob command which comes with Essentials can summon hostile mobs fine. I would rather use /summon since it's more customizable though. Here's a list of plugins I have installed.   Essentials EssentialsChat HolographicDisplays PermissionsEx setspawn [A plugin I have made, just a simple timer] Vault VoxelSniper WorldEdit WorldGuard   Please let me know if you have any ideas on what I'm doing incorrectly or isn't functioning the way it should.


I installed Ubuntu 14.04 and I would like to know what the best way is to update my drivers? My machine is a XPS 8700 Graphics card AMD Radeon.  And why after install of Ubuntu on this machine I hear a sound on the PC like a ventilator like it's running very hard? By the way this ventilator works fine.

I am using a laptop and ubuntu 11.04. I would like the easiest way possible because I am new to linux.  here is my display information:  *-display              description: VGA compatible controller              product: Core Processor Integrated Graphics Controller              vendor: Intel Corporation              physical id: 2              bus info: pci@0000:00:02.0              version: 18              width: 64 bits              clock: 33MHz              capabilities: msi pm vga_controller bus_master cap_list rom              configuration: driver=i915 latency=0              resources: irq:41 memory:d0000000-d03fffff memory:c0000000-cfffffff ioport:e080(size=8)         *-communication UNCLAIMED              description: Communication controller


thanks in advance for your help. I mentioned most of what was on each adapter, I know some will not be of any help but didn't want to miss anything.  His computer model is: ASUS G47VW-BHI5N43 The original adapter (the one that was packed with his brand new computer) shows the following values:  Model ADP180 HB D Input 100-240V ~ 2.25A 50-60Hz Output 19V 9.5 A Roman numeral value "V" C.C.: B REV. 3 S/N H00W2AN04FL  The one that a seller has on ebay list for this same computer model shows the following values: (It is OEM ASUS adapter/charger and otherwise appears exactly like the original) Model ADB-150NB D  Input 100-240V ~ 2.0A 50-60Hz Output 19.5V - 7.7A Roman number value "V" C.C. A  REV. 3 S/N  W6W0944061108  The both show N193V85, not sure what that is.  It would be helpful to know whether or not this would work (and knowing why or why not would be even better)!  Thank you!

I have a Toshiba Satellite laptop. My charger has stopped working.  I have access to a Lenovo charger. Can I use this charger on my laptop?


Let $n \in \mathbb{N}$.   How to compute the splitting field of $x^n-2$ over $\mathbb{Q}$?  I did it like this:  $x^n-2=0  \Leftrightarrow x=\sqrt[n]{2}$  Then $x=\sqrt[n]{2}$ is the root of $x^n-2$.  So the splitting field is $\mathbb{Q}(\sqrt[n]{2})$.  I'm not sure if this is complete. Or can another root be found here?

Show that the splitting field of $X^n-a$ over a field $K$ is $K(\alpha, \zeta_n)$, where $\alpha$ is a $n$-th root of $a$ and $\zeta_n$ is a primitive $n$-root of unity.


If I told her I love her now, she'd probably not take it seriously.  If I told her I loved her now, she'd probably not take it seriously.  In the above sentences the speaker loves the person they're talking about as of the present, so i was wondering whether both the sentences would be applicable in this context, and whether both of them could be deemed grammatically correct.

Which is correct?        She was told that it was against the law to steal.      Or        She was told that it is against the law to steal.        Background information: The original context is that I was relating an incident via email, where my colleague told a customer that some of our actions were part of the organisation's policy. The policy is still valid, but the statement I used to relate the incident in my email went like this:    "Mr Jay was informed that it was our policy to do this."   And I received feedback that it should go like this instead:    "Mr Jay was informed that it is our policy to do this."


Here's what I know about dark matter: Astrophysicists realized the movements of galaxies and other astronomical bodies cannot be explained by the gravitational effects of matter known to be there, so either there is a lot of matter missing that doesn't react with light or general relativity needs to be fixed. For the purpose of this question, assume the former. I've read that this "dark matter" can't be composed of baryons (quarks and leptons). My question is how do we know that it can't be baryonic? After all, air is invisible. Maybe that's a bad analogy, but you get my point: Why can't there be matter that is invisible, yet composed of baryons?

There's more gravitational force in our galaxy (and others) than can be explained by counting stars made of ordinary matter. So why not lots of dark planetary systems (i.e., without stars) made of ordinary matter? Why must we assume some undiscovered and unexplained form of matter?


I have a Tensorflow.js model making predictions and I want to send a certain websocket message each time the predicted label changes. I have tried to store the latest label in a variable and compare that to the newest one. However, my "cat" websocket message is still activated each second even if the predicted label stays the same. Problem is probably some newbie mistake regarding the use of async function or storing the values - I would really appreciate any directions! Thank you so much. Code (cleaned to include only relevant bits):  let newLabel; let oldLabel;   async function app() {    const model = await tf.loadGraphModel(MODEL_URL);   console.log('Successfully loaded model');   const labels = ["cat", "dog", "human"];   console.log(labels);    const webcam = await tf.data.webcam(video);     var myPredict;     async function predictFunction () {     myPredict = setInterval (predictLoop, 1000);     }    async function predictLoop () {      ...      const result = await model.predict(t4d);      result.print();      result.as1D().argMax().print();      const labelIndex = result.as1D().argMax();      const predictionLabel = result.as1D().argMax().dataSync()[0];     newLabel = labels[predictionLabel];     const predict = await result.data();     const value = predict[predictionLabel];        document.getElementById("demo").innerHTML = `     I can see a: ${newLabel}\n     Confidence is: ${value}\n     `;      if (newLabel== "cat" && newLabel !==oldLabel){        var data = {         speed: 100       }       socket.emit("cat", data);       sendParam ("/sound", 1);   }      else {       socket.emit("other");        sendParam ("/sound", 2);     }        img.dispose();       result.dispose();       smalImg.dispose();       resized.dispose();       t4d.dispose();       tf.engine().endScope();       await tf.nextFrame();    }     oldLabel = newLabel;    predictFunction();   }   app();

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


I often see signals like this:  nickname > heroname is missing nickname > heroname is back   To make call heroname is missing I click on hero icon.  How to make call heroname is back? Are there more signals?

I know that there's a "Missing" command in the Chat Wheel that will report your lane missing, but that only does "Missing Top!" or "Missing Middle!" messages it seems. I've seen people call specific heroes missing before though:     How are they doing this? Is it some kind of hotkey I haven't found? Is it some complicated custom bind? Is it just something simple that I'm missing?


SETLOCAL EnableDelayedExpansion  FOR %%A IN (1 2 3) DO (   IF %%A EQU 1 (   SET CHOICE1=ABC   ECHO CHOICE1=%CHOICE1%   )   )     Output:  CHOICE1=   Why is CHOICE1 not getting set?

I have two examples of very simple batch files:  Assigning a value to a variable:  @echo off set FOO=1 echo FOO: %FOO% pause echo on   Which, as expected, results in:  FOO: 1  Press any key to continue . . .   However, if I place the same two lines inside an IF NOT DEFINED block:  @echo off IF NOT DEFINED BAR (     set FOO=1     echo FOO: %FOO% ) pause echo on   This unexpectedly results in:  FOO:  Press any key to continue . . .   This shouldn't have anything to do with the IF, clearly the block is being executed.  If I define BAR above the if, only the text from the PAUSE command is displayed, as expected.    What gives?    Follow up question: Is there any way to enable delayed expansion without setlocal?   If I were to call this simple example batch file from inside another, the example sets FOO, but only LOCALLY.   For example:   testcaller.bat   @call test.bat  @echo FOO: %FOO%  @pause    test.bat   @setlocal EnableDelayedExpansion  @IF NOT DEFINED BAR (      @set FOO=1      @echo FOO: !FOO!  )    This displays:   FOO: 1  FOO:  Press any key to continue . . .    In this case, it appears that I have to enable delayed expansion in the CALLER, which may be a hassle.


For a conference paper I have to use a custom package provided by the conference. This package contains the following line:  \renewcommand{\thesection}{\arabic{section}.}   which puts a dot after the number in a section title. Now, when I add a reference to a section, the dot is shown in the reference as well. MWE:  \documentclass{article} % real code: % \usepackage{myconference} % MWE code: \renewcommand{\thesection}{\arabic{section}.} \begin{document}  \section{First section} \label{sec:first} In Section~\ref{sec:first} the reference does not look good. \end{document}     The style guide of the conference does not specify the appearance of section references. Therefore, I would like to remove the dot in the reference (while keeping the dot in the title itself). I am not allowed to change the conference package, but I can modify the code of my own paper, including redefining \ref (or using a custom command for referencing) if necessary. Any ideas?

I wonder is there any way to change the format of section numbering from 1.1 to 1.1. ? I know this is trivial, but I really need to add one more dot after the section number. Does anybody know how to do that?  Thanks a lot


I am hitting a huge wall here. I got this code which checks on database result :  chosenSlotDAO.open();         Log.d("id", chosenSlotDAO.getId());         Log.d("isParked", chosenSlotDAO.getIsParked());         Log.d("parkedRow", chosenSlotDAO.getParkedRow());         Log.d("selectedSlot", chosenSlotDAO.getSelectedSlot());         String idStatus = chosenSlotDAO.getId();         String isParkedStatus = chosenSlotDAO.getIsParked();         String parkedRowStatus = chosenSlotDAO.getParkedRow();         String selectedSlotStatus = chosenSlotDAO.getSelectedSlot();         final String outputA = this.getOutput(this, slotA);          if(idStatus == id && isParkedStatus == isParked && parkedRowStatus != parkedA && selectedSlotStatus != slotA)         {             arriveTView.setText(alreadyParked + chosenSlotDAO.getParkedRow());         }         else if(idStatus == id && isParkedStatus == isNotParked && parkedRowStatus != parkedA && selectedSlotStatus != slotA)         {             Toast.makeText(getApplicationContext(),                  wrongParkingRow,                  Toast.LENGTH_LONG).show();             chosenSlotDAO.updateSlot(id, slotA, parkedA, isParked);         }         else if(idStatus == id && isParkedStatus == isParked && parkedRowStatus == parkedA && selectedSlotStatus == slotA)         {             chosenSlotDAO.updateSlot(id, slotA, setEmpty, isNotParked);              dbUpdateAdd.execute(slotA);             Intent myIntent = new Intent(ParkAArrive.this, ParkLeaving.class);             ParkAArrive.this.startActivity(myIntent);         }         else if(outputA.isEmpty())         {             arriveTView.setText(isFull);         }          else         {             Toast.makeText(getApplicationContext(),                      nowParked,                      Toast.LENGTH_LONG).show();             chosenSlotDAO.updateSlot(id, slotA, parkedA, isParked);             arriveTView.setText(chosenSlotDAO.getSelectedSlot());             dbUpdate.execute(slotA);         }   The class is started by tapping an NFC tag.  LogCat returns :  06-15 04:35:10.818: D/id(12294): 1 06-15 04:35:10.818: D/isParked(12294): 1 06-15 04:35:10.819: D/parkedRow(12294): ParkedA 06-15 04:35:10.819: D/selectedSlot(12294): SlotA 06-15 04:35:10.829: D/link(12294): http://parkit.byethost9.com/db_show_slot.php?slot_name=SlotA 06-15 04:35:11.681: D/line(12294): 14   It clearly shows that user is parked, parkedRow is ParkedA, and SlotA is SlotA. But the if does not work.  But when I start the activity again, nothing except  else if(outputA.isEmpty())         {             arriveTView.setText(isFull);         }          else         {             Toast.makeText(getApplicationContext(),                      nowParked,                      Toast.LENGTH_LONG).show();             chosenSlotDAO.updateSlot(id, slotA, parkedA, isParked);             arriveTView.setText(chosenSlotDAO.getSelectedSlot());             dbUpdate.execute(slotA);         }   works.  Where in the code am I doing wronggg?? Tell me if I left any required info untold..  UPDATE : It seems that I need to change my code so that it can compare String, and yes it's the problem I'm facing.

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?


In the instructions for Munchkin it says:  "You can discard a Race card at any time, even in combat" "You can discard a Class card at any time, even in combat"  but it doesn't state whether this applies to your hand, cards in play, or both. Does the rule apply to both?  Also, does this mean that a player may discard these cards during any phase, even when it's not there turn?

In Munchkin (or any of its various sets) the rules say that "You can discard a Class card at any time, even in combat: "I don't want to be a wizard anymore." When you discard a Class card, you become classless until you play another Class card." It also says the same thing for Races, Accents, etc. for the various game sets.  This wording suggests that the intent is that you can discard an "in play" Class at any time, but it isn't clear about such cards in the player's hand. I would prefer to discard the extra Elf card in my hand so that my opponent doesn't get it during the Charity phase. Can I discard the card rather than give it away?  Note: The rules I am using are the most current rules from the 1st Edition, 23rd printing of Munchkin published May 2012.


I am unable to install a new software or upgrade the existing ones. I have been getting insserv warning ()  Please help.

I am seeing  errors while trying to install Inkscapeor install any software for that matter.   When I try to use sudo apt-get install language-pack-en-base it shows the same  .   I also tried sudo dpkg-reconfigure locales and then tried to installInkscape - but it is not working.  abhilash@abhilash-Inspiron-3542:~$ sudo apt-get install inkscape [sudo] password for abhilash:  Reading package lists... Done Building dependency tree        Reading state information... Done The following additional packages will be installed:   gawk libgsl2 libgtkmm-2.4-1v5 libgtkspell0 libimage-magick-perl   libimage-magick-q16-perl libmagick++-6.q16-5v5 libwmf-bin python-numpy   transfig Suggested packages:   gawk-doc pstoedit dia | dia-gnome libsvg-perl libxml-xql-perl   python-uniconvertor ruby gsl-ref-psdoc | gsl-doc-pdf | gsl-doc-info   | gsl-ref-html imagemagick-doc gfortran python-dev python-nose   python-numpy-dbg python-numpy-doc xfig The following NEW packages will be installed:   gawk inkscape libgsl2 libgtkmm-2.4-1v5 libgtkspell0 libimage-magick-perl   libimage-magick-q16-perl libmagick++-6.q16-5v5 libwmf-bin python-numpy   transfig 0 upgraded, 11 newly installed, 0 to remove and 158 not upgraded. 8 not fully installed or removed. Need to get 0 B/16.9 MB of archives. After this operation, 107 MB of additional disk space will be used. Do you want to continue? [Y/n] y Setting up util-linux (2.27.1-6ubuntu3.3) ... insserv: warning: script 'K01runlcactivator' missing LSB tags and overrides insserv: warning: script 'runlcactivator' missing LSB tags and overrides insserv: There is a loop between service plymouth and procps if started insserv:  loop involving service procps at depth 2 insserv:  loop involving service udev at depth 1 insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true!     insserv:  loop involving service networking at depth 4 insserv: There is a loop between service plymouth and urandom if started insserv:  loop involving service urandom at depth 4 insserv:  loop involving service mountdevsubfs at depth 2 insserv: There is a loop at service runlcactivator if started insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: There is a loop between service runlcactivator and dns-clean if started insserv:  loop involving service dns-clean at depth 1 insserv: Starting runlcactivator depends on plymouth and therefore on system facility `$all' which can not be true! insserv: exiting now without changing boot order! update-rc.d: error: insserv rejected the script header dpkg: error processing package util-linux (--configure):  subprocess installed post-installation script returned error exit status 1 Errors were encountered while processing:  util-linux E: Sub-process /usr/bin/dpkg returned an error code (1) abhilash@abhilash-Inspiron-3542:~$    I have been told -      the problem is that you are stuck at the boot sequencing.    I see when I viewed the file [runlcactivator]  Now please suggest how do I "completely purge the program and scripts from /etc/init.d/ and /etc/rc? files." - as is suggested in the answer? What is the command line to do this?   I am not familiar with codes, so if instructions are specific I can just follow them as it is. Thanks for helping!


I just got serial downvoted, and I suspect it's .  When do the scripts run, and would this instance be detected?  It also looks like someone serial un-upvoted said nemesis, which is also poor behavior, as much as I dislike the guy. Is that detected as well?

I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back?


Hi I was going through closure concept in JavaScript. I am finding it difficult to understand it. Can someone please help me?  function a(name) {  return function () {   console.log( "Hello "+ name);  } } var b = a("MyName"); b();   According to closure, inner function will have access to its outer function's variables even after the execution of outer function is compeled and it's no more present in stack. Can some one please explain how inner function is able to access its variable even after execution for outer function is completed. I have tried above code and it's working as expected but I am confused?

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


I'm thinking of running a Pathfinder campaign for Skype (text only) and I don't have a group of players. How can I go about recruiting people for play-by-chat games instead of in-person? Are there any online sites in which you can look for people that are looking to play in an online play-by-chat RPG Campaign?

I'd really like to learn how to play pen-and-paper RPGs.  I know that it takes a few players to actually sit down and play, but I'm not at all sure where to find more gamers.  How do I find existing groups to join? Or, are there any resources online that may help me find existing RPG groups or players?


Please change the tag search to be case insensitive. Also, optionally set that text entry field to be lower case since tags are predominantly lower case.   The screen shot show what happens if you start typing i, o, s...

Selecting the tags for this question is kind of annoying in the iOS app because the tag search is case-sensitive and my iPhone keeps "correcting" ios when I type on the dash.  The site tag search seems to be case insensitive, so I'd expect the app to behave the same.   the text entry field should be programmed to not be sentence case even if caps are entered intentionally, the internal search should be case insensitive.      This fix is also needed on the tags search on the main site feed browsing pane.


I attached an image with a limit, how can I solve that limit? If I use mean value theorem for integral it will be indeterminate form infinity * zero.

$$f(x)=\lim_{n\to\infty}\biggl(n\int_0^{\pi/4}(\tan x)^n\,dx\biggr)$$ I try to this way, $\tan x\ge x$, when $x\in(0,\frac\pi4)$, but this turns out to be $\tan x\ge0$, which is obvious even without calculation. I think it can be solved by using the squeeze rule but I can't find a proper scaler to meet $A=g(x)\le f(x)\le h(x)=A$ when $n\to\infty$   $\color{red}{Edit}$: According to@Khallil's advice, I can solve that $f(n)+f(n+2)=\frac1{n+1}$, and it's trivial that $\frac1{n+1}=f(n)+f(n+2)\le 2f(n)\le f(n-2)+f(n)=\frac1{n-1}$. So $f(x)=\frac12$.  This is easy and quick. Btw, is there any other idea?  $\color{red}{Edit[2]}$: I find that @Byron Schmuland 's method is especially useful in a specific kind of problem. $$f(x)=\lim_{n\to\infty}\int_0^1\frac{x^n}{1+x}dx$$,for example, Let $X_,...,X_n$ be i.i.d. random variables with density$f(x)=1$ on $(0,1)$, CDF(cumulative density function) of $X$ is $F(x)=x$. Now let $M=\max(X_1,\dots,X_n)$, its density function is: $f_M(x)=nx^{n-1}$ for $x\in(0,1)$ Also, it's also not hard to see that $M\to1$ in distribution as $n\to\infty$. So,$$f(x)=\lim_{n\to\infty}\int_0^1\frac{x^n}{1+x}dx=\lim_{n\to\infty}\frac1n\int_0^1{f_M(x)\frac{x}{x+1}dx}=\lim_{n\to\infty}\frac1nE(\frac{M}{M+1})=0$$ Although this simple example can be solved by other ways more easily, but this gives us another perspective.


I am new in php, I have 3 arguments in a function  function cal($x,$y,$op){ $z=$x.$op.$y; return $z; } echo cal(3,4,'/');   And I also try this:  $z=$x$op$y;   and I am getting 3/4 as answer but I want 0.75

I have 3 variables like this: $first = 2; $second = 5; $operation = '*';  how can I programaticly assign the solution to this math problem to the $answer variable? I have tried eval(), but that does not work.


Prove that if M and N are closed linear spaces and $M \perp N$, then $M \oplus N$ is a closed linear space.  I'm having trouble starting this one. Do I need to consider cauchy sequences in each M and N?

I'm working on the following problem set.  Let $\mathcal{H}$ be a Hilbert space and $A$ and $B$ orthogonal subspaces of $\mathcal{H}$.  Prove or disprove:  1) $A \oplus B$ is closed, then $A$ and $B$ are closed.  2) $A$ and $B$ are closed, then $A \oplus B$ is closed.  I could prove 1) and if my proof is correct, it even holds if $\mathcal{H}$ is just an inner product space.  Unfortunately, I can't manage to prove 2). Since $\mathcal{H}$ is by assumption a Hilbert space and I didn't use that fact to prove 1), I should probably use it here.  It means that $A$ and $B$ are also complete. Given some convergent sequence in $A \oplus B$, I want to show that the limit is also in  $A \oplus B$. Here I'm stuck. I want to use the completeness of $A$ and $B$, but I don't see how to obtain suitable Cauchy sequences.  Can anyone drop me a hint? Or is my approach all wrong?


All cells containing a nucleus present MHC-I, while some specialized cells present MHC-II in addition to that. Since erythrocytes lack any MHC why do natural killer cells not attack them?    It is my understanding that any cell which starts presenting foreign peptides on MHC-I will undergo apoptosis after Th finds them, or if they stop presenting anything at all, they will be eliminated by the NKs.  So what mechanism prevents erythrocytes from being destroyed by the immune system?

Do red blood cells have no MHC? (I have often heard that they do not.)  If so why are they not destroyed by immune cells?


In Heisenberg's book "The Physical Principles of the Quantum Theory", he presents the following derivation of the Schrödinger Equation from his own, Matrix-based, Quantum Mechanics.  A matrix $x$ has components $x(a'a'')$ (the indices indicate that in this coordinate system the matrix $a$ is diagonal, that is, the basis vectors are eigenvectors of $a$). He starts by proposing the existence of matrices of continuous indices, such that  matrix multiplication $$xy(a'a'')=\sum_{a'''}x(a'a''')y(a'''a'')$$ is replaced by $$xy(a'a'')=\int_{-\infty}^{\infty}x(a'a''')y(a'''a'')da'''$$ He then proposes that the continuous correspondent of the Identity Matrix $I$ is the Dirac-Delta function, such that $$I(a'a'')=\delta(a'-a'')$$ His derivation of the Schrödinger Equation is as follows. To transform  the Hamiltonian  Matrix $H$ from a coordinate system in which the coordinate matrix $q$ is diagonal into a system in which the Hamiltonian is diagonal, in which the Hamiltonian will be denoted $W$, the components of which are the system's allowed energy levels. The equations for this transformation are: $$S^{-1}HS=W$$ or $$HS=SW$$ such that $$\int H(q'q'')S(q''W')dq''=S(q'W')W'$$ with $W'$ being $W$'s diagonal components He then proposes (in one dimension) the following forms for the $q$ and $p$ matrices in the position basis" $$q(q'q'')=q'\delta (q'-q'')$$ $$p(q'q'')=\frac{\hbar}{i}\delta'(q'-q'')$$ He then shows they obey the Commutation Relation $pq-qp=\frac{\hbar}{i}$ but his proof of the commutation relation uses integration by parts incorrectly, having the integral of the Dirac Delta's derivative be $$\int f(\xi)\delta(a-\xi)d\xi=f'(a)$$ instead of $$\int f(\xi)\delta(a-\xi)d\xi=-f'(a)$$ Usingintegration by parts incorrectly once again, he argues that $$qS(q'W')=\int q'\delta(q'-q'')S(q''W')dq''=q'S(q'W')$$ and $$pS(q'W')=\frac{\hbar}{i}\int \delta'(q'-q'')S(q''W')=\frac{\hbar}{i}\dfrac{d}{dq'}S(q'W')$$  So we replace in $H(q,p)S=SW$ $$H\left(q',\frac{\hbar}{i}\dfrac{d}{dq'}\right)S=W'S$$ Which is evidently the Time-Independent Schrödinger Equation, which can be solved for the energy Eigenvalues $W'$  But this is derived with a wrong value for $p$ because the derivation uses a wrong process of integration by parts. The immediately obvious choice would be to have $p(q'q'')=-\frac{\hbar}{i}\delta'(q'-q'')$, so that integrated with the transformation matrix it becomes$\frac{\hbar}{i}\dfrac{d}{dq'}$, but I just can't seem to make it fit the Commutation Relation.  Can anyone help solve this?

I am reading and following along the appendices of , and trying to learn how he derives Schrödinger's Equation from his Matrix Mechanics, but I have run into a bit of trouble. It seems like for his derivation to work, it must be necessary for the integral of a function times the Dirac Delta Function's derivative be: $$\int^{\infty}_{-\infty}f(\xi)\delta'(a-\xi)d\xi=f'(a). \tag{36}$$ But the actual identity is $$\int^{\infty}_{-\infty}f(\xi)\delta'(\xi-a)d\xi=-f'(a).$$ Does anybody care to explain why it is like this in Heisenberg's book, or provide a derivation along the same vein, but with the correct identity for the delta function?


As a standard for my file/dir naming I use something like putting date and tags string into the file name separated by underscore, eg:  2015_03_10_usa_nyc_vacations_album_pictures   For a long time I have used software's like Recoll, but usually it gives much more records than I need. Since my naming is pretty consistent I think there should be a way to scriptsize it using find command.  Although I know how to perform find searches for single conditions I am not sure how to  find multiple criteria/conditions. That is, how do I find all the files whose names satisfy certain conditions. Let consider the following examples that contain    {2015} AND {  {album} OR {picture}  }  {album} AND {vacations} AND NOT {2015}

I would like to search for files that would not match 2 -name conditions. I can do it like so :   find /media/d/ -type f -size +50M ! -name "*deb" ! -name "*vmdk"   and this will yield proper result but can I join these 2 condition with OR somehow ?


I have two raster layers. They come with the same cell size (100x100m), the same extent and are projected in the same CRS (+proj=utm +zone=33 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs). My problem is, that they are not exactly congruent, they are off by ca. 50m.   How can I make them congruent using ArcGIS 10.3 on Windows 10?

I have a raster file that is projected not detailed enough. Every pixel in the raster should be replaced, just a bit.  With ArcGIS I calculated the offset per pixel. I couldn't find a way to do this offsetting in ArcGIS, so I switched to python. I found out that I can get the current envelope with ogr with :   env = geom.GetEnvelope() print "minX: %d, minY: %d, maxX: %d, maxY: %d" %(env[0],env[2],env[1],env[3])   And now I have to change these to the (already calculated) new origin.   Here is some sample code:      ## From gdal info page      wkt = "LINESTRING (1181866.263593049 615654.4222507705, 1205917.1207499576 623979.7189589312, 1227192.8790041457 643405.4112779726, 1224880.2965852122 665143.6860159477)" geom = ogr.CreateGeometryFromWkt(wkt) env = geom.GetEnvelope()   I have to say that I don't entirely understand the envelope function. Is this a function that returns the minX etc from the projection? Or does it just calculates this all from the geometry?   Does anybody now how to change this or knows another workaround?


So I'm doing some random practice for an upcoming exam, and I don't know if it's the fact that I've been reviewing for hours and my brain isn't functioning, or something in this code is wrong.  I'm attempting to make a very simple java program that asks the user for the amount of numbers they wish to enter (totalNum), create an array that long, and then ask the user for each individual value.  After it asks the user for each value in the array, it prints the array.  Here is my code:  import java.util.Scanner; public class Practice1 {   public static void main(String[] args) {     Scanner s = new Scanner(System.in);     System.out.println("How many numbers would you like to store?");     int totalNum = s.nextInt();      int[] numbers= new int[totalNum];       for (int i = 0; i>totalNum; i++) {         System.out.println("Number" + i + " :");         numbers[i] = s.nextInt();         i++;     }     numbers.toString();     System.out.println(numbers);   } }   When I run it it asks the user for the numbers I want to store, then prints [I@33909752 and stops.  I've done dozens of programs like this and for the life of me I can't figure out where I went wrong.    Any help would be appreciated, thanks!

In Java, arrays don't override toString(), so if you try to print one directly, you get the className + '@' + the hex of the  of the array, as defined by Object.toString():  int[] intArray = new int[] {1, 2, 3, 4, 5}; System.out.println(intArray);     // prints something like '[I@3343c8b3'   But usually, we'd actually want something more like [1, 2, 3, 4, 5]. What's the simplest way of doing that? Here are some example inputs and outputs:  // Array of primitives: int[] intArray = new int[] {1, 2, 3, 4, 5}; //output: [1, 2, 3, 4, 5]  // Array of object references: String[] strArray = new String[] {"John", "Mary", "Bob"}; //output: [John, Mary, Bob]


I am new to Spring Boot and JPA in general. I've seen examples of adding JPA annotations on field declarations such as this:  @Entity public class Fizz {     @Id     @GeneratedValue(strategy = GenerationType.IDENTITY)     private Long id;      // other fields      public Fizz(Long id) {         super();          setId(id);     }      // setter defined here      public Long getId() {         return this.id;     } }   ...as well as examples putting the same annotations on the getters like this:  @Entity public class Fizz {     private Long id;      // other fields      public Fizz(Long id) {         super();          setId(id);     }      // setter defined here      @Id     @GeneratedValue(strategy = GenerationType.IDENTITY)     public Long getId() {         return this.id;     } }   I'm wondering if they are semantically equivalent or if there are different use cases where you'd choose one over the other. I ask because I'm actually writing my Spring Boot/JPA app in Groovy where you typically don't define getters:  @Canonical @Entity class Fizz {     @Id     @GeneratedValue(strategy = GenerationType.IDENTITY)     Long id }

This question is somewhat related to .  But I want to know which is better? Access via properties or access via fields? What are the advantages and disadvantages of each?


The following packages have unmet dependencies: vlc : Depends: vlc-nox (= 2.2.1-3) but 3.0.0~~git20151218+r62827+34~ubuntu15.10.1 is to be installed    Recommends: vlc-plugin-notify (= 2.2.1-3) but it is not going to be installed    Recommends: vlc-plugin-samba (= 2.2.1-3) but it is not going to be installed   What do I do?

I've added many PPAs using the add-apt-repository command. Is there a simple way to remove these PPAs? I've checked in /etc/apt/sources.list for the appropriate deb lines but they aren't there.   This is on a server system so a command line solution would be great!


I am trying to prove that $A-(B-C)=(A-B) \cup (A\cap C)$ For the first statement, I do: Let $x \in A-(B-C)$ means that $x \in A$ and $x \notin (B-C)$ $x \notin (B-C)$ means that $x \notin B$ or $x \in C$ $(*)$ Therefore $x \in A-(B-C)$ means that $x \in A$ AND ($x \notin B$ or $x \in C$) For the second statement, I do: Let $x \in (A-B)$ means that $x \in A$ and $x \notin B$ $x \in (A \cap C)$ means that $x \in A$ and $x \in C$ Therefore, $x \in (A-B) \cup (A\cap C)$ means that $x \in A$ AND ($x \notin B$ or $x \in C$) $(*)$ Those two are the same so these sets are equal. I'm not sure if I did the $(*)$ parts correctly. Can someone give me some guidance?

Show that  $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$  This is an exercise I was trying to do ( not homework ) and I got stuck as follows:  Working from $A \setminus ( B \setminus C )$:  $x \in A \wedge x \notin ( B \setminus C )$ $x \in A \wedge ((x \in B \wedge x \in C) \vee (x \notin B \wedge x \in C) \vee (x \notin B \wedge x \notin C) )$  At this point I'm not sure how to proceed.  Working from the other side $ ( A \setminus B) \cup ( A \cap C ) $:  $ x \in ( A \setminus B) \cup ( A \cap C ) $  $ x \in ( A \setminus B) \vee x \in ( A \cap C ) $  $ ( x \in A \wedge x \notin B ) \vee ( x \in A \wedge x \notin C ) $  $ x \in A \wedge (x \notin B \vee x \notin C ) $  $ x \in A \wedge x \notin ( B \cap C ) $  $ A \setminus ( B \cap C ) $  I could also use some formating tips like how display logical not and how to get the lines to display properly without blank lines inbetween. :-)


I am trying to make a program where I enter the name of a shape and it tells me how many sides it has. I cannot seem to get it to work. Can anyone explain how to do this?  import java.util.Scanner;  public class Shapes {    public static void main(String[] args) {     Scanner reader = new Scanner(System.in);     String shape;      System.out.print("Enter shape: ");     shape = reader.next();      if (shape == "hexagon") {         System.out.println("A hexagon has 6 sides.");     }      if (shape == "decagon"); {         System.out.println("A decagon has 10 sides.");     }     }  }

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?


I have 13 inch mid 2010 macbook pro. Just installed new 1T hard drive but now am hesitating on what to do next. I have my old hard drive converted to external drive and a back up drive as well.

I will be installing a new 500GB hard drive in my macbook.  It is a late 2008, aluminum, 13-inch screen.  Once I install it, how do I get an operating system that's 10.7 or newer (downloaded from the App Store) on to the bare/unformatted drive?


I have an input of type file. 'Choose File' will be displayed on the button and beside it, 'No file chosen' will be displayed. But i want to change the button color and text of the button.    <form action="demo_form.asp">   Select a file: <input type="file" name="img" class='customBtn'>   <input type="submit"/> </form>   I tried adding some css  .customBtn input[type='file'] {   color:#f00 }   Can some one help me on this?

How do you style an input type="file" button?


In category theory, we always use many composition notation. And in computer science, we often use category theory to describe problems.  Usually, we use g ∘ f to stand the composition of "g after f"  Also, we use f ; g to stand the composition of "f before g"  But the ; is a common used syntax of line end in computer program, is there any substitutable notation of ; ?

We have $ (f \circ g) = x \mapsto f(g(x)) $ however since I read left to write it always seems backwards to me.  Is there a symbol like $ ( g \ggg f) = x \mapsto f(g(x)) $.  It is especially grating in situations like.  $$  \require{AMScd} \begin{CD} X @>{f \circ g}>> Y \\  @VVgV @AAfA \\ g(X) @>{id}>> g(X)\end{CD} $$


Which one is better in case of a phonon calculation and does DFPT also have small negative frequencies near Gamma due to the numerical noise? What are their advantages and disadvantages?

When proposing or predicting new materials, whether in the bulk or in two dimensions, it is important to discuss the stability of the system. This is usually done through thermodynamics and(or) lattice dynamics. A feasible way to determine the dynamical stability of a material is by modeling its phonon band structure.   I see that two popular methods of modeling the phonon band structure are:  (a) the frozen phonon / finite displacement method (as implemented in phonopy)  (b) Linear Response Theory / Density Functional Perturbation Theory (as implemented in Quantum ESPRESSO (ph.x)  Are the two methods equivalent or is one more reliable/accurate than the other, and if so, why?


A duplicate question probably exists, but I couldn't find one. Please let me know if one is found and I'll delete this.    We know that:  $$\sum_{r=0}^n r=\frac12n(n+1)$$ and that: $$\sum_{r=0}^n r^3 =\frac14 n^2(n+1)^2$$ and these are easily proven by induction: $$\frac{n(n+1)}{2}+(n+1)=\frac{n^2+n+2n+2}{2}=\frac{n^2+3n+2}{2}=\frac12(n+1)(n+2)$$ and: $$\frac{n^2(n+1)^2}{4}+(n+1)^3=\frac{n^2(n+1)^2+4(n+1)^3}{4}$$ $$= \frac{(n+1)^2(n^2+4n+4)}{4}=\frac 14(n+1)^2(n+2)^2$$  We can see that, from the results obtained, $$\sum_{r=0}^n r^3 =\bigg(\sum_{r=0}^n r\bigg)^2$$  What I am curious to know is, is there a reason why this is the case, other than the numbers just showing this?  Thanks in advance.

Using induction it is straight forward to show $$\left(\sum_{k=1}^n k\right)^2=\sum_{k=1}^n k^3.$$ But is there also a geometrical interpretation that "proves" this fact? By just looking at those formulas I don't see why they should be equal.


I want OneDrive to have the exact files and folder structure of a folder on my local computer. Syncing OneDrive causes the files in the cloud to download and only uploads files that I add to the local folder while the OneDrive app is running. How can I make the local folder unchangeable and the Cloud folder mirror from the local folder by uploading local files that aren't in the cloud and replacing or duplicating the files into the cloud from local files that have the same name and location in both local and cloud drives and different hash values?   Please note: The folder is almost 160 gigs and I currently only have access to a very slow connection so I have to keep the files that are already uploaded and can't just recopy the entire folder into the cloud like when I had fiber optic.  The folder contains 18,873 Files so manually comparing files is also not possible.     To future readers with the same problem: Using the command net use described in the duplicate problem will not allow replacing the cloud version with the local version because it maps the drive as if using the onedrive app(where OneDrive automatically downloads synced folders:      Whereas the way described below maps the drive as I needed:

I'm a web developer and I have Windows 10 installed on a very small SSD (128GB).  The problem is, when I want to save my file to a cloud service, I need to store the files on my computer, so that the OneDrive or the Google Drive client can synchronize them.  My free space is very low, so I can't afford that.  Is it possible to save files to the cloud (directly), without them needing to first download them to my computer?


Yesterday I did an update on IOS that was available in my iPad 2 (I think it was 9.3.2). After that it's asking me to configure and take some steps to reopen but after trying a while it says that the activation server is not available and won't open. Not even the home page.   I have done an update before without problems. What can I do?

After just accepting the iOS 7.0 upgrade dialog on my iPad, the gears spin for a moment and it looks like the download will start, but then the install fails.    Is this something I can fix?


I just arrived in Amsterdam (by train) and realized I left my passport home in Switzerland. I am a US citizen residing in Switzerland, and I have my Swiss resident permit with me. I have a flight back to Zurich in a few days, and I'm wondering if I'll have any trouble with passport checks when flying. In theory because both countries are part of Schengen and I have a residence permit in a Schengen country, it should be fine, but I'm wondering if anyone has firsthand experience about this situation. Is there any real risk?

I am currently located in the Netherlands and have lived here for 4 years. I have a working visa for the Netherlands and would like to go on vacation to another country in Europe. I however do currently not have my passport as i sent it to an embassy for a visa application. Will I still be able to travel inside of Europe without a passport if I have my residency ID?  I have a resident permit, not a true Dutch ID. And I own a passport that is currently in transit.  I have called with the KLM and the service employee's conclusion was that I do need to carry my passport with me when i am going to fly, so it seems all I can do is wait and hope my passport is returned to me in the next few days as the amsterdam US consulate (who currently holds my passport) is incredibly difficult to contact for urgent matters.


To prove that two processes $(X_t)$ and $(Y_t)$ has the same distribution, I proved that $X_t\sim Y_t$, but my teacher said that it's not enough, I have to prove that they I the same finite dimensional distribution, i.e. that $(X_{t_1},...,X_{t_n})$ and $(Y_{t_1},...,Y_{t_n})$ has same distribution for all $t_0<...<t_n$. So could you give me an example of processes s.t. $X_t\sim Y_t$ for all $t$, but $(X_t)$ and $(Y_t)$ has not the same finite dimensional distribution ? I can't find any.

Would someone be able to offer a layman's explanation of what is means when two stochastic processes are a Modification of each other and when they are Indistinguishable?  My Stochastic Analysis notes define the following:  a) $\textit{The stochastic processes X and Y are called a modification of each other if}$ \begin{align} P(X(t) = Y(t)) = 1 \quad \textit{for all t $\in$ I} \end{align}  b) $\textit{The stochastic processes X and Y are called indistinguishable}$ \begin{align} P(X(t) = Y(t) \,\,\,\textit{for all $t \in I$}) = 1 \end{align}  I interpret this to mean that:  (a) for each $t$ in $I$ the probability that the processes are equal is equal to 1.  (b) the probability that the entire path of the processes X is equal to the entire path of the process Y, is equal to 1.  I don't understand the difference between the two statements. The first seems to examine the processes at each point. The second examines the paths of the processes (which are made up of the points!).  Is anyone able to provide a motivational explanation as to why (a) does not mean that the paths are the same? I find it counter intuitive since if the processes are equal at each point then surely their paths are the same?  The classic example I've been given which (apparently) shows the two processes to be a modification and not indistinguishable is:  $\textbf{Example:}$ Let $\Omega = [0,\infty), \mathcal{A} = \mathcal{B}([0,\infty))$ and $P$ be a probability measure on $\mathcal{A}$ which has a density. Define two stochastic processes $(X(t): t \ge 0)$ and $(Y(t): t \ge 0)$ by \begin{align} X(t)(\omega) =  \begin{cases}  1, \text{ if $t = \omega$},\\ 0, \text{ otherwise} \end{cases} \quad Y(t)(\omega) = 0 \quad \text{for all $t \ge 0$ and all $\omega \in \Omega$.} \end{align} Then $X$ and $Y$ are modifications of each other but $X$ and $Y$ are not indistinguishable.   $\textbf{Question:}$ With regard to the example above if $t = 0$ and $\omega = 0$ then $X(0)(0)= 1$ but $Y(0)(0) = 0$, then how can their probability be equal to 1 at this point? Hence how can they be a modification of each other?  Many thanks,  John


I have a rank-ordered logit model in which the various independent variables are pertinent for some cases but not others. For example, cases 1, 2, 3, & 4 might have variables A & B that are relevant whereas cases 5 & 6 might have variables B, C, & D that are relevant. My question is, prior to running the regression, do I need to code the data in any special way to indicate that only certain variables are applicable to certain cases, or will the regression extract the correct coefficients to use on the applicable cases. I appreciate any specific or conceptual guidance you may have on this.  Thank you!

Consider a statistical problem where you have a response variable that you want to describe conditional on an explanatory variable and a nested variable, where the nested variable only arises as a meaningful variable for particular values of the explanatory variable.  In cases where the explanatory variable does not admit a meaningful nested variable, the latter is usually coded either as NA in the data set, or if it is coded with a value, that value is merely a placeholder that does not have any meaningful interpretation.  This situation tends to arise whenever you have an explanatory variable indicating the existence of a thing, and one or more nested variables describing the characteristics of that thing.  Some examples of this kind of situation in statistical problems are the following:   The explanatory variable is an indicator of whether a survey participant is married, and the nested variable is some characteristic of the spouse (e.g., education, age, etc.); The explanatory variable is an indicator of the presence of an item in a space, and the nested variable is a measure of some characteristic of the item (e.g., size, distance, etc.); The explanatory variable is an indicator of the occurrence of an event and the nested variable is a description of some characteristic of the event (e.g., duration, magnitude, etc.).   In these kinds of situations, we often want to build a regression-type model (in the broad sense that includes GLMs, GLMMs, etc.) describing the relationship between the response variable and the other variables.  It is not obvious how to deal with the nested variable in this type of model.  Question: How do we deal with the nested variable in this type of model?    Note: This question is designed to give a generalised answer to a recurring question on  regarding nested variables in regression (see e.g., , ,  and ).  This question is designed to give a generalised context-independent example of this problem.


I am new to Java. I was reading someone's solution to a question and I encountered this:          int[] ps = new int[N];         for (int i = 0; i < N; i++)             ps[i] = input.nextInt();          int[] counts = new int[1005];         for (int p : ps)             counts[p]++;   What do the last two lines do?

Consider:  List<String> someList = new ArrayList<String>(); // add "monkey", "donkey", "skeleton key" to someList     for (String item : someList) {     System.out.println(item); }   What would the equivalent for loop look like without using the for each syntax?


I need a script which will list out all the users with the database owner permission for a specific database.

I've searched around all over and haven't found a conclusive answer to this question.  I need a script that can give ALL permissions for an associated role.   Any thoughts, or is it even possible?  This gets me CLOSE - but I can't seem to flip it around and give the summary for roles, rather than users.     WITH    perms_cte as (         select USER_NAME(p.grantee_principal_id) AS principal_name,                 dp.principal_id,                 dp.type_desc AS principal_type_desc,                 p.class_desc,                 OBJECT_NAME(p.major_id) AS object_name,                 p.permission_name,                 p.state_desc AS permission_state_desc         from    sys.database_permissions p         inner   JOIN sys.database_principals dp         on     p.grantee_principal_id = dp.principal_id ) --role members SELECT rm.member_principal_name, rm.principal_type_desc, p.class_desc,      p.object_name, p.permission_name, p.permission_state_desc,rm.role_name FROM    perms_cte p right outer JOIN (     select role_principal_id, dp.type_desc as principal_type_desc,     member_principal_id,user_name(member_principal_id) as member_principal_name,    user_name(role_principal_id) as role_name--,*     from    sys.database_role_members rm     INNER   JOIN sys.database_principals dp     ON     rm.member_principal_id = dp.principal_id ) rm ON     rm.role_principal_id = p.principal_id order by 1


Knowing that $9a^2+8ab+7b^2 \le 6$, prove that $7a+5b+12ab \le 9$. I have found the same question , but the answer looks wrong. You can't just add two inequalities like him. It's like you would multiply the second one with $-1$, which changes its sign, and then add them.  Here is my try: $$9a^2 + 9b^2 + 18ab - 2b^2 - 10ab - 6 \le 0 \Longleftrightarrow\\ (3a+3b)^2 - 2(b^2+5ab+3) \le 0 \Longleftrightarrow\\ b^2+5ab+3 \ge 0 \Longleftrightarrow\\ 25a^2 - 12 \le 0 \Longleftrightarrow\\ a \in \left[-\frac{2\sqrt{3}}{5}, \frac{2\sqrt{3}}{5} \right]$$

If we assume that $a,b$ are real numbers such that $9a^2+8ab+7b^2\le 6$, how to prove that :  $$7a+5b+12ab\le9$$


From the technical details it seems that HTC one (m7) has 2Gb of RAM, but if I check the RAM usage the smartphone shows that I am using around 900 Mb of 1.5Gb. There is something that I do not understand?

I bought a new tablet, but Android (2.3.1) shows that it has only 150MB free of 256MB, and it should have 512MB.  I checked the file /proc/meminfo, MemTotal information. It only shows 256MB. Is there a possibility that the Android "hid" 256MB of RAM from the user?


I have been exploring this website for my queries and many times I find stuff mentioned as  update-grub2   and   update-grub   Surprisingly, many of the things to be updated for grub2, I update in grub and it works. Then what is the difference between them (in Ubuntu 18.04)?

I'm making some changes on my grub file under /etc/default/grub. In some tutorials I have seen sudo update-grub and others sudo update-grub2. What is the difference?


Someone recently downvoted something on stackoverflow, and then the user was deleted. Because of the deletion, I'm not sure what was downvoted or why, as there is no link provided like there are for every other action in my timeline. is there a way to figure out what was downvoted? this seems like a pretty easy way to troll someone.

Message appearing when a user was removed.     It seems I lost 1765 reputation points on Stack Overflow yesterday. The reason given in my history is "removed", with the description of "User was removed ()". I don't understand what that means. What caused this?


I want to prove Schröder–Bernstein theorem for 2 finite sets $A, B$ of the same cardinal. I do it with induction on the cardinal number of $A, B$. In the inducative step, I write:   Let $A, B$ sets such that $|A|=|B|=n+1$ for some $n\in\omega$. Here, I want to use the the inducative assumption for the sets $A-\{a\}, B-\{b\}$ for some $a\in A, b\in B$. For choosing the above $a,b$, do I need to use the axiom of choice?

I recently read a proof that had the following in it: "since $A$ is non-empty, we can find an element $x$ in $A$." This proof did not mention the axiom of choice, but it seems to me that it would be required to make the proof formal. Would I not require a choice function to allow me to find/pick some element $x$ from $A$ after noting that A is non-empty? Thanks


Is there a word for an acronym whose first word is identical to the acronym?  There are real-world examples.  However, none come to mind so I will fabricate one here.     Face   Acuity   Characteristics   Expressions        F.A.C.E.   If there is already  word for it I think it should be called an 'initialistic initialism'.   Or an 'initialised initialism'.  Edit: I am aware I have used' acronym' and 'initialism' interchangeably, my question applies to both.  EDIT: Although "GNU: GNU Not Linux" is a case of this and is known as a recursive acronym. The example I use as well as "IRIS: Iris Recognition Immigration System" are not recursive as the word Iris actually means something. Said another way "GNU: GNU Not Linux" could just as easily be "PNU: PNU Not Linux", the same is not true of IRIS.

The example I am thinking of is GNU, which stands for "".  It may be that there are no other examples. And maybe that's the whole joke. I was just wondering.