Get CSS not-computed property-value with Javascript only
How do you read CSS rule values with JavaScript?
$V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $? Let $V$ be a vector space , $T:V \to V$ be a linear operator , then is it true that   $\ker (T) \cap R(T) \cong R(T)/R(T^2) $ ( where $R(T)$ denotes the range of $T$ ) ?    I know that the statement is true when $V$ is finite dimensional as I can show that if $V$ is finite   dimensional , then $\dim (\ker (T) \cap R(T))=rank (T) - rank (T^2)=\dim R(T)/R(T^2)$ ,   but I don't know what happens in general . Please help . Thanks in advance Word for someone that always has to be right Is there a word for someone that always has to be right? The person gets angry if they are not. Can anyone tell me how Google decides which image to use when it shows an image with the search results (as is the case with mobile search, sometimes)?  If you look at these mobile search results …    … and take the AliExpress.com result as an example, by inspecting  you can see that  used by Google seems to have no special declaration, etc. It is just the first JPG that appears in that page's HTML - so I was thinking maybe that's why it's the image that is used in the Google search results.  However, when you look at these mobile search results …    … and consider the Backpack Billboards result,  reveals that  being used is actually the seventh image declared in the HTML.  So can anyone shed any light on how Google determines which image to be displayed? I would like to know so I can then have control over which image is displayed for my site.  Update / Solution  Thanks to the answers, below, this is the code I have now added to my head HTML in order to get the thumbnail shown in Google when searching for backpack billboards:  &lt;script type="application/ld+json"&gt; {   "@context": "http://schema.org/",   "@type": "Product",   "name": "Regular Backpack Billboard",   "image": [     "https://backpackbillboards.com/wp-content/uploads/2017/12/backpack-billboards-1x1.jpg",     "https://backpackbillboards.com/wp-content/uploads/2017/12/backpack-billboards-4x3.jpg",     "https://backpackbillboards.com/wp-content/uploads/2017/12/backpack-billboards-16x9.jpg"    ],   "description": "Backpack Billboards feature a rechargeable battery which powers the internal LED lights providing a bright illuminated display for up to 8 hours.",   "sku": "BPBB8",   "brand": {     "@type": "Thing",     "name": "Backpack Billboards"   },   "offers": {     "@type": "Offer",     "priceCurrency": "USD",     "price": "299.00",     "priceValidUntil": "2020-11-11",     "itemCondition": "http://schema.org/NewCondition",     "availability": "http://schema.org/InStock",     "seller": {       "@type": "Organization",       "name": "Backpack Billboards"     }   } } &lt;/script&gt; Two logos in beamer after certain frame I am making a presentation which is devided in two parts. The first part is about experiments held in instute A and the second part is about experiments held in instute A and institute B.  Is it possible to add a second logo in a beamer presentation after a certain frame?  Let's say that this is a previous slide    This is a next slide I have a netbook that I want to install Ubuntu onto. I do have a good Mac computer that I can make a bootable USB drive from, but I'm confused on how to go about making it. How do I place a bootable ISO on a USB drive? Who's the random kid standing in the gathering at the end? Escape character in LaTeX I need to output the below text but since \ is a special character, I cannot:  [RegularExpression(@"\d+")]   Also sometimes I need use dollar sign $ as well but it seems to be a special char, too.  What is the way to escape those in LaTeX?  UPDATE:  I used \verb as suggested but I am unable to run commands inside it. Also, in the output the font and the opacity of the text is different than the default one:  \verb|[RegularExpression(\newline @"\d+")]| Use spray paint to make mask for pre-sensitised board? I'm about to etch my first simple board for a project. I have a pre-sensitised board that (as I understand the process) you expose to UV light, then develop the board in a sodium hydroxide solution, then etch. The UV light will negatively affect the protective lacquer and developing it after exposing washes away the lacquer, making the board ready to etch.  I got the lye and I got sodium persulfate for the etching but I did not have any transparent paper as I thought I did! And it's impossible for me to get a hold of it in time (= this weekend, I live far from the city and it's a small one and I haven't found any place that stocks it so I have to order online and that's sometime next week I'd get it at the fastest).   So I am looking for an alternative solution. What I am considering is printing the design to regular paper, cut out a mask carefully from this paper and place it over the board and paint a mask on. Spray paint most likely, then in theory I would have a UV mask.  Anyone see any flaws in this plan? Finding where source has branched from git I'm talking about at least two juvenile sci-fi novels, read between second and fourth  public grades (U.S.A.) which for me places them around 1956-9.  The protagonists are a brother and sister, presumably my (then) age. They are friends  with a single man, a scientist who has built a rocket ship. The scientist is little fey,  physically; a (relatively) large, round head, balding, short in stature and striking long,  thin hands and fingers.  The rocket ship's final preparation is to slop a viscous, clear gloop over EVERYTHING, inside and out from a pail with a paintbrush. In flight, there is an encounter with the moon, and a very small planet with (non-threatening) inhabitants not physically unlike the fey rocket scientist. The planet orbits either the moon or the earth, not the sun, and strangely, some kind of mushroom(!) theme runs through the books. Really.  That's it. That's all I got (I was nine at the most, fer chrissake). My recollection tells me there was concealment from parents, a particular name for the planet and people  and flight through a spatial fog. I mention these things separately because I am less sure  of them than the previous two paragraphs. The author was blissfully unrepentant of the laws  of physics:  Earth gravity on a micro-planet, fog in space and super-gloop to ready the  ricketiest rocket. Worked for me.  I'm guessing even Richard, my previous mentor/savior might not be familiar with these.  Anybody? Author, titles? Or do you just recognize one of these? Is there a technical reason to use > (<) instead of != when incrementing by 1 in a 'for' loop? Abstract class with all concrete methods I tried to install Tor on my new version of Ubuntu, but it seems that Tor is not available in the repositories.  How else can I install and use Tor? Are mixed geometry types allowed in shapefiles? Does the shapefile support mixed geometry types (ie. point and polygon all in the same file)? What race (species?) is Star Lord's dad? At the end of the new Guardians of the Galaxy Vol. 2 Trailer we meet Star Lord's father:                                  Dad appears to be human. But Peter Quill's mother said in the first film that his father was a      "being made of pure light".    What race (species?) is Star Lord's father in the MCU? I tried to use this for the last part of my table, but I can't get a vertical line at the end. Does anyone know?   \begin{tabular}{|CC|C|C|C|C|C|C|C|C|C|C|}\hline \Tab{Method Based on \\\hline       Radiography\\Magnetic Particle (A.C.)\\ \\Eddy Current\\Dye Penetrants\\ Ultrasonics} &amp; \Tab{ \\\hline \\ Wet \\ Dry \\ \\ \\ \\} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Minute Surface Cracks }~}  \\\hline       N\\ G\\F\\F\\F\\P}  &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Deeper Surface Cracks      }~}  \\\hline            F\\G\\G\\G\\G\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Internal Cracks      }~}  \\\hline            F\\N\\N\\N\\N\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Fatigue Cracks      }~}  \\\hline            P\\G\\G\\N\\G\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Internal Voids      }~}  \\\hline            G\\N\\N\\N\\N\\G}           &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Porosity and Slag in Welds      }~}  \\\hline            G\\N\\N\\P\\N\\F}           &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Thickness      }~}  \\\hline            F\\N\\N\\P\\N\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Stress Corrosion      }~}  \\\hline            F\\G\\F\\N\\G\\F} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Blistering      }~}  \\\hline            P\\N\\N\\N\\N\\F} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Corrosion Pits      }~}  \\\hline            G\\N\\P\\N\\F\\P} \\\hline &amp; \multicolumn{11}{l}{G=Good;F=Fair;P=Poor;N=Not suitable.} \\ \hline \end{tabular} \label{tab:NDETechniques} \end{table}   It comes out like this: Should I always disconnect event handlers in the Dispose method? Why doesn't the definition of a category require an explicit notion of morphisms equality? I am learning basics of the category theory (CT).  I do understand that CT is a modern powerful framework to describe various branches of mathematics in a unified way.  I do admit that category's definition tells a lot about the whole thing and focuses on the most important properties, shadowing unnecessary details. However, the more I go forward, the more it feels like it should explicitly require a notion of morphisms equality (like it does with morphism composition). It feels so because equality or inequality of morphisms arises everywhere, since the very beginning: any commutative diagram eventually reduces to an equality of two different paths and many other things involve equality as well. Even composition is defined grounding upon an (implicit) equality!  I'll try to give an example of my concern. Consider $\mathbb{SET}$. Its objects are sets and morphisms are functions. Now, let's recall that functions are sets as well - to be more precise, a function $f : A \mapsto B$ is a subset of a $A \times B$ obeying certain properties, which I omit. Thus, one could argue that $f$ is both a morphism between objects $A, B \in Obj(\mathbb{SET})$ and an object defined as a set of pairs $\{ (a_1 \in A, b_1 \in B), ..., (a_n \in A, b_n \in B) \}$ and those are equal because both are essentially exactly the same thing.  I hope my concern is clear and I need some kind of "conceptual insight" from knowledgeable people to move forward. Please give me the right perspective. How do I reference photographs with a separate numbering system to figures in latex? I am writing a book, and would like to be able to have the photographs labelled with an independent numbering system to my figures.  In the text I would refer to, for example, figure X and separately to photograph X, so I want them to have different numbering systems, just as equations and figures do.  Is it possible to have a different \begin{figure} environment so that the numbering can be separated?