Proving that $8\mid n(n^{2}-1)(3n+2)$
$24\mid n(n^{2}-1)(3n+2)$ for all $n$ natural problems in the statement.
If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$ Are token creatures considerd as a creature spell? Are token creatures considerd creature spells? For instince when I use  tap effect combined with  would it allow me to draw a card? Why can we treat quantum scattering problems as time-independent? From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:   Solve the time-independent Schrodinger equation to find the energy eigenstates.  There will be a continuous spectrum of energy eigenvalues. In the region to the left of the potential, identify a piece of  the wavefunction that looks like $Ae^{i(kx - \omega t)}$ as the incoming wave. Ensure that to the right of the potential, there is not piece of the wavefunction that looks like $Be^{-i(kx + \omega t)}$, because we only want to have a wave coming in from the left. Identify a piece of the wavefunction to the left of the potential that looks like $R e^{-i(kx + \omega t)}$ as a reflected wave. Identify a piece of the wavefunction to the right of the potential that looks like $T e^{i(kx - \omega t)}$ as a transmitted wave. Show that $|R|^2 + |T|^2 = |A|^2$.  Interpret $\frac{|R|^2}{|A|^2}$ as the probability for reflection and $\frac{|T|^2}{|A|^2}$ as the probability for transmission.   This entire process doesn't seem to have anything to do with a real scattering event - where a real particle is scattered by a scattering potential - we do all our analysis on a stationary waves.  Why should such a naive procedure produce reasonable results for something like Rutherford's foil experiment, in which alpha particles are in motion as they collide with nuclei, and in which the wavefunction of the alpha particle is typically localized in a (moving) volume much smaller than the scattering region? How do i know which wheels will fit my bike? my bike is:  and everything I have came with the bike, only now the axle of the rear wheel bent and the skewer has lost its grooves.  and I would like to replace the rear wheel with the 12 x 142mm version of:   I want to reuse the old casettes and disc break. I was told to buy new rotor bolts, will these do?   Will I be able to migrate all my previous parts onto this new wheel and will the wheel fit onto my bike?  update: A replacement axle would be prefered. What axle would work for my bike? Low Voltage AC Smoothing Capacitor Calculation I have a 9V AC source which will have a max load of 100mA.  I'm trying to figure the value of a smoothing capacitor with less than a 10% ripple.  I don't have a scope or else I'd just try a bunch out.  I'm just a hobbyist, but I'm trying to understand this.  Since I'm not sure if I'm doing this right, I'll just step through what I've done so far.  First I found this formula: $$V_{ripple}={V_p \over R_LC} \times \Delta T$$  I'm using 60Hz 9VAC that is full wave rectified and I want a 10% ripple so:  $$(9V \times .1)={9V \over R_LC} \times {1 \over 60Hz}$$  I'm calculating my resistive load with Ohm's law. $$R = {9V \over .1A} \quad R = 90 \Omega$$  So plugging that in I get: $$.9V={9V \over 90\Omega \; C} \times {1 \over 60Hz}$$  If I solve for C (admittedly using wolfram alpha), I get: $$C={1\over 540}F \quad C=1851 \mu f$$  1850µf seems pretty high to me...  And if I lower the ripple percent it get crazy high.  Is this the right way to find this?  Or did I screw up somewhere?  Also, my circuit has the capacitor between the full bridge rectifier's positive and negative outputs.  I've only seen this type of smoothing circuit, but maybe my circuit needs to change? C++ catching all exceptions Is there a c++ equivalent of Java's  try {     ... } catch (Throwable t) {     ... }   I am trying to debug Java/jni code that calls native windows functions and the virtual machine keeps crashing.  The native code appears fine in unit testing and only seems to crash when called through jni.  A generic exception catching mechanism would prove extremely useful. Proof that the set of all possible curves is of cardinality $\aleph_2$? I am reading George Gamow's book  and a certain assertion Gamow makes seems a little startling considering what I already know of the subject of infinite cardinality.     But the number of all geometrical points, though larger than the number of integer and fractional numbers, is not the largest one known to mathematicians. In fact it was found the variety of all possible curves, including those of the most unusual shapes, has a larger membership than the collection of all geometric points, and thus has to be described by the third number in the infinite sequence. [Gamow, 22]   He later does explicitly say the number of all possible curves is $\aleph_2$. But nowhere else can I find reference to this being true, nor does he provide any sort of reasoning to its validity.  My question is how can you prove the set of all possible curves is of cardinality $\aleph_2$ and not $\aleph_1$ or $\aleph_0$? Can a multiclass sorcerer/cleric use the Metamagic class ability with non-sorcerer spells? For example, using Twinned Spell when casting cure wounds to heal two creatures instead of just one? Let $A_n$ denote an $n \times n$ tridiagonal matrix.  $$A_n=\begin{pmatrix}2 &amp; -1 &amp; &amp; &amp; 0 \\ -1 &amp; 2 &amp; -1 &amp; &amp; \\ &amp; \ddots &amp; \ddots &amp; \ddots &amp; \\ &amp; &amp; -1 &amp; 2 &amp; -1 \\ 0 &amp; &amp; &amp; -1 &amp; 2 \end{pmatrix} \quad\text{for }n \ge 2$$  Set $D_n = \det(A_n)$  Prove that $D_n = 2D_{n-1} - D_{n-2}$ for $n \ge 4$. I'm having trouble with the OpenLayers Plugin of Qgis and the map composer:  If I create an OSM-background layer and if I want to export this, the OSM-Layer looks perfectly all right in the normal qgis program window. But in the map composer and after export the layer has shifted relatively to my other shape layers (EPSG:32633 - WGS 84 / UTM zone 33N).  The second thing is that the output resolution of the exported osm-layer is very, very poor.   A really bad way of getting around this whole trouble would be to increase the screen resolution and make a screenshot of the map composition window of qgis. But I don't think this would be very professional. It also would cause a lot of pain :)   I'm using Qgis 1.8.0-Lisboa under Linux. The openlayers plugin is version 0.92. After some searching on stack / google I decided to ask this here, this is the second time I'm facing this issue this time with blender 2.8, previously with 2.7 and without a clue to how I got here.  Some of my objects appear hidden(10/12), and I can't seem to find a way to unhide them.  Solutions to the most common rookie mistakes seems to be   In local-view solved by pressing numpad / hidden by pressing H or Shift + H, unhiding with Alt + H   I'm not in local view, I can toggle visibility for 2/12 objects with Shift + H &amp; Alt + H, but the rest stays gray in the collection.  Last time I solved this by exporting the whole model as STL and importing it back again, I then had to re-group all the pieces but there must be a more simple solution.  Here's the .blend if someone wants to have a go at it: Save entire process for continuation after reboot I developed an algorithm for a fairly hard problem in mathematics which is likely to need several months to finish. As I have limited resources only, I started this on my Ubuntu 12.04 (x86) laptop. Now I want to install some updates and actually restart the laptop (the "please reboot" message is just annoying).  Is there a way to save an entire process including its allocated memory for continuation beyond a reboot?  Here is some information about the process you might need. Please feel free to ask for further information if needed.   I called the process in a terminal with the command "./binary &gt; ./somefile &amp;" or "time ./binary > ./somefile &amp;", I cannot really remember. It's printing some debug information to std::cerr (not very often). It's currently using roughly 600.0 kiB and even though this will increase, it's unlikely to increase rapidly. the process runs with normal priority the kernel is 3.2.0-26-generic-pae, the cpu is an AMD, the operating system is Ubuntu 12.04 x86. it runs since 9 days and 14 hours (so too long to cancel it ;-) ) Shapefile: "table1.shp"   Field name: "Name" Field name: "Result"   Flat file: "referenceTable"   Field name: "STREET" Field name: "AKA"   I need to compare the value "Name" in "table1.shp" to the value "STREET" in "referenceTable"  If the values are the same then put the "AKA" value into the "Result" in "table1.shp"     Here is my code.  I got stuck on accessing the elements from the array  import arcpy, os, sys, string from array import *   table1 = "G:\\xStreetNew\\table1.shp" table1_column = ['Name', 'Result'] referenceTable = "G:\\xStreetNew\\Test.gdb\\referenceTable" referenceTable_column = ['STREET', 'AKA']  referenceTable_List = [] with arcpy.da.SearchCursor(referenceTable, referenceTable_column) as rCur: for r_row in rCur:     reference_row = r_row[0].split(",")     referenceTable_List.insert(0,reference_row) ##print sorted(referenceTable_List)  Table1_Update_Cursor = arcpy.da.UpdateCursor(table1, "Name") for row in Table1_Update_Cursor:   if row[0] == None:   row[0] = row[0] else:   row[0] = row[0].replace(";",",")   Table1_Update_Cursor.updateRow(row)  table1_List = [] with arcpy.da.SearchCursor(table1, table1_column) as tCur: for t_row in tCur:     row = t_row[0].split(",")     table1_List.insert(0,row) ##print sorted(table1_List)  Table1_row = len(table1_List) Table1_column = len([table1_List]) ref_row = len(referenceTable_List) for i in range(0,Table1_row):  #Table Row   for ii in range(0,Table1_column):   #Table Column     print table1_List[i][ii]   Below was my old post.  Sorry for the confusion.  I have a shapefile named "table1.shp".     I would like to get all values from fielname "Name" from this table and put them into a list. Able to output each element from the list     So far, I'm able to create a list but not too sure how to get to value "AVENUE 33" or "CHAPMAN ST"  This is my code:  import arcpy, os, sys, string from array import *   table1 = "G:\\xStreetNew\\table1.shp" referenceTable = "G:\\xStreetNew\\Test.gdb\\referenceTable" cursor = arcpy.da.UpdateCursor(table1, "Name") for row in cursor: if row[0] == None:     row[0] = row[0] else:     row[0] = row[0].replace(";",",") cursor.updateRow(row) table1_column = ['Name'] table1_curObj = arcpy.da.SearchCursor(table1, table1_column) table1_List = [] for row in table1_curObj:    table1_row = row[0].split(",")    table1_List.insert(0,table1_row)    print table1_List[0] $K/F$ is a field extension of finite degree $n$. How can I prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$, so the ring of $n\times n$ matrix over $F$ contains an isomorphic copy of every extension of $F$ of degree $\leq n$? Learning ArcPy? Where can I start to learn ArcPy? I am currently trying to develop my modeling skills, and following a tutorial found on YouTube. The tutorial teaches how to create an anvil. At 19:10 or so into the video, a subdivision surface modifier is used to create a smooth, soft look.  However, when I do the same, mine looks very sharp and generally bad.  Any ideas why? I will include the blend file below, I appreciate your time and suggestions.    This is his when he subdivides, which is very different from mine when I do the same at the same settings. (I cannot post more pictures because I am new, but if you check the blend file I attached, you should be able to see the difference.   This is what it looks like when I subsurf without the base face. Statistical inference when the sample "is" the population Imagine you have to do reporting on the numbers of candidates who yearly take a given test. It seems rather difficult to infer the observed % of success, for instance, on a wider population due to the specifity of the target population. So you may consider that these data represent the whole population.   Are results of tests indicating that the proportions of males and females are different really correct? Does a test comparing observed and theoretical proportions appear to be a correct one, since you consider a whole population (and not a sample)? Condition on a,b and c satisfying an equation(TIFR GS 2017) Let $a,b,c$ be positive real numbers satisfying $$(1+a+b+c)\left(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=16,$$ then $a+b+c=3$.  I thought about the application of the AM-GM-HM inequality, but in vain. I also thought about splitting 16 into factors and comparing but went nowhere. Any ideas. Thanks beforehand. Why do researchers need universities? This is a follow-up question to  and probably an even more naive question. If I'm understanding the answer correct, professors need funding to do research, but once they get it, the university takes some of the grant as overheads (to pay for office space, electricity, etc), and the cut the university takes is substantial.  Given that then, why do professors need universities? One could just apply for the grant as per normal, and once one gets it, buy a slightly bigger house and convert one of the rooms into a lab. One loses nothing to overheads, gets to work from home, has zero teaching duties, can choose to settle anywhere (no two-body problem!), and can even monitor an experiment 24/7. This gets even easier if one works in a field that doesn't need a physical lab. Further, presumably the grant covers postdoc salaries, so one would still be able to pay for postdocs (although probably not PhD students since a professor without a university will not be able to award a degree).   The obvious answer is that one cannot apply for a grant without a university, but Google indicates that's not the case, e.g.  only looks at one's previous accomplishments &amp; potential applications of the research result, both of which are independent of the university. I suppose one could lose journal access, but there's always stuff like arXiv / ResearchGate, emailing the authors of the desired paper, or even Scihub (oops). It's conceivable that not working for a university loses one some prestige, since one can no longer claim to be a professor. However even then I'd expect at least some academics to choose this path, valuing the convenience &amp; extra research funding over prestige.  If the answer to this varies from field to field, I'm most interested in the sciences. Check out the below program.   try {     for (String data : Files.readAllLines(Paths.get("D:/sample.txt"))){         String[] de = data.split(";");         System.out.println("Length = " + de.length);     } } catch (IOException e) {     e.printStackTrace(); }   Sample.txt:   1;2;3;4 A;B;; a;b;c;   Output:   Length = 4 Length = 2 Length = 3   Why second and third output is giving 2 and 3 instead of 4. In sample.txt file, condition  for 2nd and 3rd line is should give newline(\n or enter) immediately after giving delimiter for the third field. Can anyone help me how to get length as 4 for 2nd and 3rd line without changing the condition of the sample.txt file and how to print the values of de[2] (throws  ArrayIndexOutOfBoundsException)?