Imagine I have this blogging / ecommerce website with 1000 posts / products. And I've built a sitemap for it, which is dynamically generated. Basically it's a list with a bunch of &lt;url&gt; and &lt;lastmod&gt; tags.  I'm pretty sure that the crawlers expect me to update the &lt;lastmod&gt; dates for whatever product or blogpost that I edit and change the text content (or change the images). Add something new, update information, etc. Basically, anything that users will SEE differently when they enter my page. This makes sense.  But my question is:  I have a dynamic single page website. So I don't keep static pages. I generate and render them (server-side) at run time. So what if I decide that all of my blogposts now should render inside a &lt;main&gt; or &lt;article&gt; tag instead of a div? Or what if I add some structured meta data to add price and review properties for my products, or to add structured data for breadcrumbs.  You see what I mean? The content that the user sees hasn't changed. But I've updated some tags that the CRAWLER will interpret differently. The text/image content is the same, but the HTML content has changed. And this could even have impact on my ranking, since I'm throwing in new tags that might get me better SEO.  But now what should I do? The changes I made now will render the 1000 posts / products in a different way with the new tags (in the perspective of the crawler). Should I update the &lt;lastmod&gt; tag to ALL of my 1000 urls in my sitemap?  The user will still see the same text/image content and will not notice any difference.  If I do update all the 1000 &lt;lastmod&gt; tags, won't the crawler think that it's "weird" that now all of my urls have been updated on the same day? Since they'll all have the same &lt;lastmod&gt; tags. Does it make sense?  Please, any help is appreciated. Thanks
I'm currently building a sitemap for my web app.  Note: my app is a single page app built with React and Firebase.  Basically I wan to index blogPost and product pages. So I intend to generate my sitemap dynamically (on server). It's a small website (around 500 pages).  I want to build something like this:  &lt;urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"&gt;   &lt;url&gt;     &lt;loc&gt;       https://www.myproject.org/blog/some-blog-post-slug     &lt;/loc&gt;     &lt;lastmod&gt;2019-11-14T20:22:43.502+00:00&lt;/lastmod&gt;     &lt;changefreq&gt;weekly&lt;/changefreq&gt;     &lt;priority&gt;0.8&lt;/priority&gt;   &lt;/url&gt;   &lt;url&gt;     &lt;loc&gt;       https://www.myproject.org/dp/some-product-slug     &lt;/loc&gt;     &lt;lastmod&gt;2019-11-15T13:08:52.127+00:00&lt;/lastmod&gt;     &lt;changefreq&gt;weekly&lt;/changefreq&gt;     &lt;priority&gt;0.8&lt;/priority&gt;   &lt;/url&gt; &lt;/urlset&gt;   And I keep the following properties in my database, both for blogPosts and products:  createdAt: &lt;Timestamp&gt; lastModifiedAt: &lt;Timestamp&gt;  // UPDATED EVERYTIME I UPDATE THE RECORD   And I'm thinking about using my lastModifiedAt value as the &lt;lastmod&gt; tag for the sitemap.  So far, so good! Everytime I update my blogPost or product objects in my database. The next time the sitemap is requested, the new modifiedDate will show on those that have been changed.  QUESTION  But what if I make a change not in the database itself, but in the way I render all the product pages, for example.  Imagine that I've added some structured data tags to display rich results on google, with price, reviews etc. So my product info is the same, but from that point on, all of my product pages will render those extra tags that I need to be re-indexed.  Example (add a structured data tag with the product price):   &lt;div property="schema:price" content="119.99"&gt;&lt;/div&gt;   In that situation, will I have to update all &lt;lastmod&gt; for all the products? How Google will know that it needs to re-crawl those pages and be able to see the structured data tags?  What if I change only the styles for the productPages? Do I have to update the &lt;lastmod&gt; for every product in this case?
Shrink exFAT partition Is there any way to shrink an exFAT partition?   The windows disk manager has the "Shrink" option greyed out. Let's say I have some XML like this  &lt;channel&gt;   &lt;item&gt;     &lt;title&gt;This is title 1&lt;/title&gt;   &lt;/item&gt; &lt;/channel&gt;   The code below does what I want in that it outputs the title as a string  $xml = simplexml_load_string($xmlstring); echo $xml-&gt;channel-&gt;item-&gt;title;   Here's my problem.  The code below doesn't treat the title as a string in that context so I end up with a SimpleXML object in the array instead of a string.  $foo = array( $xml-&gt;channel-&gt;item-&gt;title );   I've been working around it like this  $foo = array( sprintf("%s",$xml-&gt;channel-&gt;item-&gt;title) );   but that seems ugly.  What's the best way to force a SimpleXML object to a string, regardless of context? 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Example:  \newcommand\examplemacro{%     \somecommand%     \othercommand% }   Being a software engineer first and a LaTeX user a distant second, I would expect:  \newcommand{\examplemacro}{     \somecommand{}     \othercommand{} }   Is there a reason for doing it the former way, or is it merely a matter of habit? Verification that $\lim_{x \to a}\frac{f(x)-f(a)}{x-a}$ and $\lim_{h\to 0}\frac{f(a+h) -f(a)}{h}$ are equivalent definitions of the derivative. I wanted to verify that for definition of the derivative it is true that:  $$ \lim_{x \to a}\frac{f(x)-f(a)}{x-a}= \lim_{h\to 0}\frac{f(a+h) -f(a)}{h}$$  If I denote $h=x-a$,  we can  let $x\to a$, this means that $h \to 0$. Also notice that $f(x)=f(a+h)$ $$ \lim_{x \to a}\frac{f(x)-f(a)}{x-a}=\lim_{h \to 0}\frac{f(a+h)-f(a)}{h}$$ As desired. Is the main idea here really just to use a variable substitution? I suppose there is some formal theorem I also use here that when $f(x) \to y$  we can let $g(f(x)) \to g(y)$ if the function $g$ is continuous. Cancellation of Direct Products How do I specify a pointer to an overloaded function? Virtual member call in a constructor With biblatex, alphabetic style, I have     &lt;author&gt;. &lt;title&gt;   But I want to have a colon ":" instead of the period "." after the author:     &lt;author&gt;: &lt;title&gt;   What do I have to change? How to make a disk image and restore from it later? I'm a new Linux user. I've reinstalled my Wubi from scratch at least ten times the last few weeks because while getting the system up and running (drivers, , etc.) I've broken something (X, grub, unknowns) and I can't get it back to work. Especially for a newbie like me, it's easier (and much faster) to just reinstall the whole shebang than try to troubleshoot several layers of failed &quot;fixing&quot; attempts. Coming from Windows, I expect that there is some &quot;disk image&quot; utility that I can run to make a snapshot of my Linux install (and of the boot partition!!) before I meddle with stuff. Then, after I've foobar'ed my machine, I would somehow restore my machine back to that working snapshot. What's the Linux equivalent of Windows disk imagers like  or ?  Note: I found a similar question: I am using an USB port as a power supply. Is there a way I can take the weak 5V of a regular laptop USB and transform if to 100V+ while begin in the smallest package possible. I've heard of boost converters but they are usualy too big. I want something that has the size of like a normal USB key.   What I want to do is to charge up around 5 capacitors at 100+V and then discharge them later. Power efficiency not a concern for me.  It would be helpful to include a schematic of the circuit. How can I remove the white pixels around the edges when exporting a transparent GIF? How to use a custom time in browser to test for client vs server time difference I need an adjustment layer which will invert in the same way as when you select some text in a text layer All the info about TLP on the surface looks more like advertisement and marketing to me, I can't see any detailed comparison to default configurations. What are the precise differences compared to default (K/L)Ubuntu installs under the hood, are they really effective?  Update: And if they really are, why aren't they a part of a default config? Prove by contradiction (not using a calculator) that $\sqrt6 + \sqrt2 < \sqrt{15}$? Cannot see pictures on Stack Overflow Let $a_1,a_2,a_3,\ldots$ be reals. Prove that if $\sum_{n=1}^{\infty} a_n^{2}$ converges, then so does $\sum_{n=1}^{\infty} \frac {a_n}{n}$.   For this I have shown the case for when $ a_n^{2} \le\frac {|a_n|}{n}$ $\Rightarrow$ $ |a_n|\le\frac {1}{n}$ $\Rightarrow$ $\frac {|a_n|}{n} \le \frac{1}{n^{2}}$ and we know that $\sum_{n=1}^{\infty} \frac {1}{n^{2}}$ converges and hence $\sum_{n=1}^{\infty}\frac {a_n}{n}$ converges by the comparison test. Now considering $ a_n^{2} \ge\frac {|a_n|}{n}$ $\Rightarrow$ $\frac {|a_n|}{n} \le a_n^{2}$ $\rightarrow$ combining the two cases for any n we have: $\frac {|a_n|}{n}\le\frac{1}{n^{2}}+a_n^{2}$ Hence using the comparion test again we know that $\sum_{n=1}^{\infty} a_n^{2}$ converges and $\sum_{n=1}^{\infty} \frac {1}{n^{2}}$ converges hence the sum converges so we can conclude that $\sum_{n=1}^{\infty} \frac {a_n}{n}$ is absoluetly convergent $\Rightarrow$ convergent.  Not to sure if this is correct, any help would be much appreciated, many thanks. I have read the thread regarding , but it does not answer my question.  I am confused about the notation for change in Physics. In Mathematics, $\delta$ and $\Delta$ essentially refer to the same thing, i.e., change. This means that $\Delta x = x_1 - x_2 = \delta x$. The difference between $\delta$ and $d$ is also clear and distinct in differential calculus. We know that $\frac{dy}{dx}$ is always an operator and not a fraction, whereas $\frac{\delta y}{\delta x}$ is an infinitesimal change.   In Physics, however, the distinction is not as clear. Can anyone offer a clearer picture?