I'm using a grammar checking service. It tells me these kind of projects is wrong and should be changed to these kinds of projects. I'm not sure about the correctness of this suggestion, so I googled it on the Google Books website. You can take a look at the result  and .  Both searches returned many results, and these are from books, which I assumed to be correct. Could anyone help to explain? Thanks in advance.
A. These kinds of problem are to be avoided. B. These kind of problems are to be avoided.  Are both A and B grammatical? If not, why not? If so, after having noticed the parallelism between A and C, and between B and D, could we say that C and D are &quot;standard&quot; English, too?  C. These kinds of problem are ones to avoid. D. These kind of problems are ones to avoid.
What are good learning resources for a LaTeX beginner? Which book (free or otherwise) was the most useful to you when you started learning LaTeX?  I am frequently asked this question by friends who want to learn LaTeX, and I recommend the book which got me started, , but I feel that there might be better options around.  Also see . Why do light sources appear as stars sometimes? See for example this photo:    From my experience, the longer the exposure the stronger can this effect be observed. Is this correct? Are there any other factors that influence the creation of these stars (is there a better word for it, by the way?) And what exactly does technically happen? I have created an FME workspace which inputs a pipeline as well as other linear features which cross it (waterways, roads, railways, fences, other pipelines, etc).  The output is a point file which contains the crossing type.  What I would like to do is calculate the distance along the pipe from the start of the pipeline for each intersection.  So, as you travel along the pipeline, the distance attribute will increase.   I'm thinking that I'll need to use some of the linear referencing tools like MeasureGenerator, MeasureExtractor, or something like that, but I'm not sure how to do so.  Does anyone have an idea of how to do this? I have a 4GB DDR3 800Mhz recently I installed another 4GB. It turns out it's  DDR3 667MHz. Does it really matter I should own both rams 800MHz?    Slot1 shows recent RAM installation. ALSO I don't know if this is 1600MHz (it shows 800x2 and 667x2 for other) or just 800MHz ram. Can we get notification in the tab (change of title)? I'm usually running many different StackExchange sites in Firefox using tabs (using ReloadEvery to update every 5 minutes).  Right now to check for activity, I have to manually click on the tab to see if the envelope is lighted.  How about making the icon on the tab i.e. the title text change in some way, denoting that you have activity on the page?  We already add a message count for the chat tabs, so this shouldn't be very complicated.  Possible Example: After using gdalwarp to project and align-to-grid (via -tap) a number of rasters I noticed that the output rasters were significantly larger than the original rasters. A fairly thorough web search turned up :  Frank Warmerdam explained the reason: &quot;On careful review, the difference in the file in question is because gdal_translate uses the TIFFWriteScanline() interface to write the output file from within GTiffDataset::CreateCopy?(), and this only writes as much of the final 'strip' of the file as is required to complete image area. But gdalwarp goes through the blockio interface which writes the complete final strip, even the portion that falls off the end of the file.&quot;  This Trac issue is ~7 years old, however, and I know some changes to the GDAL utilities, including gdalwarp have been made since. I'd like to know if the above reasoning still holds and if the file size inflation I'm seeing is &quot;normal.&quot; The word &quot;normal&quot; here might be taken to mean unsurprising or expected but, more importantly: is there anything that can be done to mitigate the effects i.e. reduce the output raster file size? Below is a table of the file size inflation I'm experiencing. Input File Size (bytes)     Output File Size (bytes)    Inflation 1437380431                  1698334217                   18% 1428001178                  1698334433                   19%   41683165                   137036637                  228%  The input TIFF files were created in ArcGIS and thus have external Worldfiles, XML and DBF files but these do not make up the difference in file size. Here is a sample gdalwarp call as I've used it in all of these cases; the actual execution was handled by a Python subprocess (subprocess.Popen): $ gdalwarp -tap -tr 30 30 -t_srs &quot;+proj=aea +lat_1=20 +lat_2=60 +lat_0=40 +lon_0=-96 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs&quot; -co &quot;COMPRESS=LZW&quot; input_file.tif output_file.tif  I understand that in rare cases compression makes a larger file, but the effect is the same without the LZW compression. The ratios in the table are with LZW compression. How to show that the set of orthogonal n x n matrices forms a group under multiplication I am studying orthogonal matrices and I am not sure if to show if a set of orthogonal $n \times n$ matrices forms a group under multiplication. We must check each of the group axioms. I found that the axioms are:  Closure Associativity Existence of identity matrix Existence of the inverse matrix.  I edited my question, since I was able to find more information about this topic. This group is called $O(n)$. To check the four axioms I did: Let $A \text{ and } B \in O(n)$, denoted as orthogonal matrices and assume that $C=AB$, then, Closure :  To prove that $C \in  O(n)$ we must prove that $C$ is a real $n \times n$ orthogonal matrix with uni-modular determinant. Since A and B are real $n \times n$ matrices, $C$ is also a real $n \times n$ matrix so, $C^TC=(AB)^T AB=B^T A^T AB = B^TB=I$  Associativity :  Matrix multiplication is associative, so the law holds for $O(n)$ group elements.  I am not sure if this is enough to prove associativity. Identity element :  The $n \times n$ identity matrix $I_{n \times n}$ represents the identity element.  In this case I am not sure if this is enough to prove the identity element. Inverse element :  Let $A^{-1}$ be the inverse of $A$, then we need to prove that  $A^{-1} \in  O(n)$ since $(A^{-1})^T=(A^T)^{-1}$. We have that: $(A^{-1})^T A^{-1}=(A^T)^{-1} A ^{-1}=(AA^T)^{-1}=I^{-1}=I$  Can anyone check if what I did is correct? I also would like to know if I can prove the associativity and the identity element in a better way. thanks Permalink rewrite with custom post type and custom taxonomy I think thats a quick one:  I've got:   Custom post type: Food  Custom taxonomy (Registered to Food): Fruits Terms in Fruits: Apple, Orange, Cherry   If I type in example.com/food?fruits=Apple,Cherry, I get all posts in Fruits with the terms Apple and Cherry, thats great!  But I would like to type in example.com/food/fruits/Apple,Cherry or example.com/food/Apple,Cherry to get the same result.  I´ve tried different permalink and rewrite plugins related to custom posts but nothing helped.  Thank you,  David No updates since a long time Using Ubuntu, I have a habit of running: sudo apt update sudo apt upgrade   on every startup. But for a month, I guess, there have been no updates whatsoever. The message shows: All packages are up to date  Now I am starting to worry. Can there be a fault in my update manager? As far as I know, I've made no changes to the package manager settings. But no updates for almost a month seems kind of weird. Any feedback would be helpful. Thanks. How to use induction to prove the product rule for higher derivatives? How do I show through mathematical induction that   \begin{equation} \frac{d^n}{dx^n}[f(x)\cdot g(x)] = \sum_{k = 0}^{n} \binom{n}{k} \frac{d^k}{dx^k} [f(x)] \cdot \frac{d^{n-k}}{dx^{n-k}} [g(x)] \end{equation}  which is the product rule for higher derivatives? The text for  says:     {1}{G}, {T} : Target creature you control fights another target creature. (Each deals damage equal to its power to the other.)   Does this have anything to do with combat? Or is it just direct damage between two creatures? For example, can one of the creatures have defender? Or what if one of them is tapped?   I've been assuming it is more like the damage dealt by a .  Also: are the two creatures then “tapped” until their next untap step? ie: could you use Ulenvald Tracker to make two creatures fight in your pre-combat step, then enter the combat phase with a creature who just “fought” untapped? Could you make two creatures fight who are both tapped? Does one wing of fly contain harmful microbes and the other contain only antibodies? There was  study but the conclusion and it's source's relability seemed a bit off. How come a house flies one wing contain all microbe and the other don't. What is a reasonable sample size for correlation analysis for both overall and sub-group analyses? I am running Pearson's correlation on an overall sample of 400 respondents.   When I isolate male and female responses, my sample becomes 220 male responses and 180 female responses.   If I further isolate male and female responses by (say) age groups, some sample sizes become as low as 35 responses (for example, for females over the age of 65).  My question: How good are these sample sizes for correlation analysis? (I am looking at the relationship between income levels and overseas travel.)   (I think this has something to do with margin of error but how does this apply to inferential analysis which is based on probability. I can understand its role in descriptive statistics such as results of a political poll). The add comment link and comment box overlaps bounty box The following you could have seen in  (sorry, I've commented there, so you won't see it anymore) in Chrome 35.0.1916.153 m (current version). Notice how the add comment link overlaps the bounty box:    The same you can observe with a comment box on other sites, e.g. at this time in :    Could you shift it a bit down ?  It seems that it happens on more than just Stack Overflow (maybe all sites ?). How to assign dynamic Ids for ui:inputDate element inside aura:iteration? As title says, How do I assign dynamic Ids for ui:inputDate elements inside aura:iteration?  Here is the reproducible version of the problem I am facing:  HelloWorldApp.app  &lt;aura:application &gt;     &lt;c:inputDateExample /&gt; &lt;/aura:application&gt;   inputDateExample.cmp  &lt;aura:component &gt;     &lt;aura:handler name="init" value="{!this}" action="{!c.doInit}"/&gt;     &lt;aura:attribute name="datesList" type="List" /&gt;     &lt;table&gt;         &lt;aura:iteration items="{!v.datesList}" var="dateItem"&gt;             &lt;tr&gt;                 &lt;ui:inputDate aura:id="date-id"                                value="{!dateItem}"                                displayDatePicker="true"                               blur="{!c.fldChanged}"/&gt;             &lt;/tr&gt;         &lt;/aura:iteration&gt;     &lt;/table&gt; &lt;/aura:component&gt;   inputDateExampleController.js  ({     fldChanged : function(component, event, helper) {         console.log('Value changed');         //How do I find from which date element, event is fired??         //The below method finds both date elements because the Id is not unique         var dateComponent = component.find('date-id');         console.log(dateComponent);         console.log(dateComponent[0].get("v.value"));     },     doInit : function(component,event,helper){         var datesArray = [];         datesArray.push("2017-01-01");         datesArray.push("2017-01-31");         component.set("v.datesList",datesArray);     } })   This produces the below output and I need to find which element user is clicking on??    Notes:   I can assign unique Id for tr element but not sure how to use that inside component.find() method. I can assign dynamic id for plain input tags but there is too much markup involved for making these similar to lightning date element. I tried giving html5 data attributes for ui:inputDate but it doesn' accept.   Any workarounds or anything I am missing here? Expressing the area of the cross section of a cylinder I was able to solve similar questions where a triangle was involved, but this one has had me looping and pondering on it for the past week.  The Condition: Let $r$ be a positive constant. Consider the cylinder $x^2+y^2\leq r^2$ and let C be  part of the cylinder that satisfies $0\leq z\leq y$.  The questions:  (1) Consider the cross section of $C$ by the plane $x=t(-r\leq t\leq r)$ and express its area in terms of $r,t$  (2) Calculate the volume of $C$, and express it in terms of $r$.  (3) Let $a$ be the length of the arc along the base of the circle $C$ from the point $(r,0,0)$ to the point $(r cos\theta,r sin\theta,0)(0\leq\theta\leq\pi)$. Let $b$ be the length of the line segment from the point $(r cos\theta, r sin\theta, 0)$ to the point $(r cos\theta, r sin\theta, r sin\theta)$. Express $a$ and $b$ interms of $r,\theta$  (4)Calculate the are of the side of $C$ with $x^2+y^2=r^2$, and express it in terms of $r$.  Here are the expected answers(which I keep failing to get to):  (1) $\frac{1}{2}(r^2-t^2)$  (2) $\frac{2}{3}r^3$  (3) $r\theta$ and $r sin\theta$  (4) $2r^2$ Can I force WordPress to use  instead of ? How does C compute sin() and other math functions? Determining functions from specifications... my high school teacher asked this question today, and I am struggling to find an answer that will work. The question is outlined below:  Give an example of a cubic polynomial, defined on the open interval (-3,3), which reaches both its maximum and minimum values. Which cyan colored line is produced in the Thomson e/m apparatus? Related:   After reading Lisa Lee’s OP on an electron deflection tube, although she had some misunderstandings on its operation, I still believe that her question is still relevant. If one looks at the Thomson e/m tube filled with helium gas (made by ), the tracer light is created by de-excited electrons, not by an electron beam interacting with a phosphor as in Lisa Lee's OP. That is, the accelerated electrons scatters off of a low pressure helium gas and emit a tracer line to follow the electrons path, as shown below.     Now if you look at the bright line spectrum of helium,     One can clearly see that there are two “cyan” color lines around 500 nm. Following in Lisa Lee’s footsteps, there is a series of question one can ask: (1) which line is emitted by the Helium gas atoms? Or are both lines emitted? (2) How can a variable accelerating voltage for the electrons always produce the same tracer line color? In theory, I assume that if I decreased the energy of the electron beam, I could produce red (around 670 nm) or yellow (around 590 nm) tracer lines, but that doesn’t happen. Somehow, it appears to me that the e/m tube is “tuned” just right so that the emitted light is always this “cyan” color. Why?