Assume that I have a table with N columns. And I need a subset for all combinations of columns. For example, If there are C1,C2,.....,Cn columns, I need   1D = {C1,C2,C3,C4,.....,Cn} 2D = {C1C2,C2C3,C1C3,.....,Cn-1Cn} // 2D is all combination set for 2 columns. 3D = {C1C2C3,C1C2C4,C1C2C5,......}   ...  I will use Vector&lt;Vector&lt;String&gt;&gt; setofNDSubset. (java)  I think it will be Vector(1D,2D,3D,......,ND). And I use jdbc.  Column number should be less than 10.  I need some advices for you. Thanks.
I want to write a function that takes an array of letters as an argument and a number of those letters to select.   Say you provide an array of 8 letters and want to select 3 letters from that. Then you should get:  8! / ((8 - 3)! * 3!) = 56   Arrays (or words) in return consisting of 3 letters each.
What are the technical differences between using a DSLR viewfinder and live view? The earlier question  asks for practical advantages of optical viewfinders. But what's the technical difference, and why does a camera behave differently in each mode?  For example, on my Nikon D5100:   Slower auto-focus — I saw this explained in the related issue, but just partially: "The other major drawback of live view is that because it requires the mirror to be locked up, it means that the auto focusing mechanism is unavailable."  option not available. No . The manual says that it's dangerous to shoot direct light, when it's on live-view. There's no range finder available.   Why are all these things different?  Live view also has some advantages, like:   automatic scene selection grid lines on the screen other smaller things, like possibly easier operation on a tripod where the viewfinder might be inconvenient to look through   Some of these things, like the tripod operation, are natural. But are there technical reasons the others can't be done with an optical finder? Are there other advantages enabled by live view for technical reasons? I am using LaTeX with the article document class. The Bibtex bibliography style that I am using is agsm, part of the Harvard family of bibliography styles.  I have two questions:  (1) If I cite an entry of type @book, then in the reference list I get publisher, address. I would like to re-arrange this order to address: publisher. Which part of agsm.bst should I modify?  (2) I would like to change single quotation marks ' ' to double quotation marks " " for setting off the title of entries of type @article. Which part of agsm.bst should I focus on? HTML Element Array, name="something[]" or name="something"? How do I get the  value of a character as an int in ? Illustrator Vector Graphics Appearing Pixellated I am trying to estimate summary statistics of points located inside a polygon. Each points in the point layer is associated with N attributes. My target is to summarize (say mean, min,..) the attributes of points located within a polygon and populate the attribute fields of the corresponding polygon.   I am looking for a solution using GeoPandas or other Python libraries.   import geopandas as gpd    gdf_points = gpd.read_file('/path_to_points.json') gdf_polygon = gpd.read_file('/path_to_polygons.json')  dfsjoin = gpd.sjoin(gdf_polygon ,gdf_points)   Now, how can I summarize the stats for each attribute in the point layer and add it to the polygon shapefile? Which function can I use?  I am looking for something that is functionally equivalent to ESRI ArcGIS  with How do I extend a List in Dart? Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$ Let $V$ be a real inner product space, and let $v_1,v_2, \dots ,v_k$ be an orthonormal set of vectors. How do you prove that  $$\sum_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot\|y\|?$$  When does the equality hold?  I've been trying to do this with the Bessel and Cauchy-Schwarz inequalities, but I can't make it work yet. Any help would be greatly appreciated. Square roots not on same height This part C\frac{1}{\sqrt{G}}\sqrt{\rho} doesn't seem to be on the same height as this part \sqrt{b}\sqrt{l} when compiled. What am I doing wrong?  \begin{flalign*} T=C\frac{1}{\sqrt{G}}\sqrt{\rho}\sqrt{b}\sqrt{l} &amp;&amp; \end{flalign*} What is the best Java email address validation method? What are the good email address validation libraries for Java?  Are there any alternatives to ? Database schema documentation for the public data dump and SEDE Stack Exchange releases "data dumps" of all its publicly available content roughly every three months , and also makes that information queryable over the Internet at the  (SEDE) (updated weekly, on Sunday). Over time, as new features and other bits of data are introduced to Stack Exchange sites, the "anatomy" of the data dump is likely to change. Prove that $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$   My proof is below. I am interested in other proofs.    My proof  Let   $$f (\mathrm X) := \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B)$$  Hence,  $$\begin{array}{rl} f (\mathrm X + h \mathrm V) &amp;= \mbox{tr} (\mathrm A (\mathrm X + h \mathrm V)^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A (\mathrm X ( \mathrm I + h \mathrm X^{-1} \mathrm V))^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I + h \mathrm X^{-1} \mathrm V)^{-1} \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I - h \mathrm X^{-1} \mathrm V + O (h^2)) \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) - h \, \mbox{tr} ( \mathrm A \mathrm X^{-1} \mathrm V \mathrm X^{-1} \mathrm B) + O (h^2)\\ &amp;= f (\mathrm X) - h \, \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) + O (h^2)\end{array}$$  Thus, the directional derivative of $f$ in the direction of $\mathrm V$ at $\mathrm X$ is  $$D_{\mathrm V} f (\mathrm X) = - \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) = - \mbox{tr} ( (\mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top})^\top \mathrm V ) = - \langle \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}, \mathrm V \rangle$$  and, lastly,  $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$ I'm currently working my way through Harvard's online abstract algebra lectures (if you're interested, you can find them ).  The lectures come complete with notes and homework problems.  Of course, since I don't actually go to Harvard, I can't hand in the homework assignments to find out if I'm doing them correctly.  So I've decided to try to crowd source the grading of my solutions.  I'll post individual questions as I finish them and wait for comments.  I would like to get critiques of not just my reasoning but the style of my write ups as well.  Also, any alternative approaches to the problem would be welcome.  I've looked for forums dedicated to these kinds of OCW courses but have not been able to find any.  This surprises me.  It seems like, with the advent of these free online educational resources, an online meeting place for those who take advantage of them would be a natural offshoot.  So this might be a bit of an experiment.  Unless I'm the 873rd person to post something like this here.  If that's the case, sorry for being so long winded.  Anyway, on with the question.  This one is assigned in the 4th lecture.     Let $V$ denote the Klein 4-group.  Show that $\operatorname{Aut}(V)$ is isomorphic to $S_3$.   (I've moved my solution below to keep this question from showing up in the unanswered list.)  Thanks... get the value from force:RecordData on Init handler Is there a way we can get the value from force:RecordData on init ? I am getting the onclick event of a button.  &lt;aura:handler name="init" value="{!this}" action="{!c.doInit}"/&gt;     &lt;aura:attribute name="recordId" type="String"/&gt;      &lt;aura:attribute name="showButton" type="Boolean" default="false"/&gt;     &lt;aura:attribute name="Opportunity" type="Object"/&gt;        &lt;aura:attribute name="parentOpp" type="Object"/&gt;     &lt;aura:attribute name="oppLoadError" type="String"/&gt;     &lt;force:recordData aura:id="oppRecordLoader"                       recordId="{!v.recordId}"                       fields="Id,                               Name,                               AccountId,                               Cohort_Sem__r.End_date__c,                               LeadSource,                               Staff_Referral_Detail__c,                               lead_source_detail__c"                       targetRecord="{!v.Opportunity}"                       targetFields="{!v.parentOpp}"                       targetError="{!v.oppLoadError}"                       /&gt;   JS:  doInit: function(component, event, helper) {                     var opp = component.get("v.parentOpp");                   console.log('Name Value: '+ opp.Name);     }   Error:     Action failed: c:createIWSRecord$controller$doInit [Cannot read   property 'Name' of null] quickActionHandlerHelper.js failed to create   component - forceChatter:lightningComponent How does one parse XML files? Is the “sum of all natural numbers” unique? A while ago, there was a great hype about the “identity” $$\sum_{n=1}^{\infty} n = -\frac{1}{12}.$$  Apart from some series manipulations where the validity seems to be at least questionable, the derivation of this always goes through the zeta function:  Where the series converges, the zeta function is defined by $$\zeta(s) = \sum_{n=1}^{\infty}\frac{1}{n^s}$$ and outside that range by analytic continuation. And it turns out that inserting $s=-1$ formally results in $$\zeta(-1) = -\frac{1}{12} = \sum_{n=1}^\infty n$$  However looking at the series in isolation, there is no indication that the zeta function should be chosen.  An obvious way to get an analytic function that at one point gives the sum of all natural numbers is $$f(x) = \sum_{n=1}^{\infty} nx^n$$ at $x=1$, however (not surprisingly) that function diverges at $1$.  Therefore my question:     Is it possible to get another finite value for the series by analytic continuation of another series?   Concretely, do there exist continuous functions $f_1, f_2, f_3, \ldots$ such that   On some non-empty open subset $S$ of $\mathbb C$, $f(x)=\sum_{n=1}^\infty f_n(x)$ converges to an analytic function. At some point $x_0$, $f_n(x_0) = n$ for all positive integers $n$. The analytic continuation of $f$ is well defined and finite at $x_0$. $f(x_0) \ne -1/12$   What if we demand the functions $f_n$ to be analytic rather than just continuous? Where do I suggest new Stack Exchange sites? Is there an appropriate place to suggest new Stack Exchange based sites, perhaps a place for them to be voted upon?  I wish there was a Stack Exchange site for Aviation (both real-life and simulated). Will my software work on the next version of Windows "Dark L" is "L" at the end of the word or after a vowel sound. Example: ball, pull.  "Light L" is "L" at the beginning or before a vowel sound. Example: light, love.  There are 4 explanations of how to pronounce "dark L":   1st explanation: the tongue tip must contact the ridge right behind the upper teeth. 2nd explanation: before the tongue tip must contact the ridge right behind the upper teeth, you must curl the tongue and make sound like /r/ before make the /l/ as in the 1st explanation. 3rd explanation: just put the tongue between upper and lower teeth is enough to make the dark L 4th explanation: the tongue tip must contact the ridge right behind the upper teeth &amp; the back of the tongue raises up (a British teacher teaches that).   see this vid:  and  for more info  So what is the correct way to make the "dark L"? I don't know how to integrate $\displaystyle \int\frac{1}{x^{4}+1}\mathrm dx$. Do I have to use trigonometric substitution?