Incorporating Built-In Function Options/Parameters into Shorthand
Is it possible to insert arguments into functions when they're used like Function@ or //Function?
How can friction do no work in case of pure rolling? K-Means clustering for mixed numeric and categorical data My data set contains a number of numeric attributes and one categorical. Say, NumericAttr1, NumericAttr2, ..., NumericAttrN, CategoricalAttr, where CategoricalAttr takes one of three possible values: CategoricalAttrValue1, CategoricalAttrValue2 or CategoricalAttrValue3. I'm using default . It works with numeric data only. So my question: is it correct to split the categorical attribute CategoricalAttr into three numeric (binary) variables, like IsCategoricalAttrValue1, IsCategoricalAttrValue2, IsCategoricalAttrValue3 ? Why is it usually "friend of his", but no possessive apostrophe with "friend of Peter"? As  shows, we nearly always use the possessive form of personal pronouns for friend of mine/his/ours/etc.  But when it comes to actual names, we prefer  without the possessive apostrophe. That preference is even more marked with, say, . Not that I think the usage itself is particularly American - it's much the same with .  Personally, I find friend of him grates. In general I've no strong feelings either way as to whether it's friend of Peter or friend of Peter's (though I deplore the possessive in ), but in line with many others, I really don't like the possessive in relation to things like countries.  Why is this?   Edit: Noting an apparent "progression" (pronoun -> person -> nation) marked by reduction in use of the possessive, I checked at a finer "granularity". NGram shows that although it does occur,  virtually "flatlines" against friend of mine. But the bias reduces through of you, of us, and by the time I get to  it's much less extreme. There seems to be something "egocentric" about the double possessive.  Presumably when babies learn to speak, they soon notice that possessive pronouns, possessive apostrophes, and the word "of", all do the same job. Parents would correct a child who says "of mine's", but probably wouldn't even notice the same "redundancy" in "of Peter's". Younger speakers are unlikely to even be talking about something "of America's". Perhaps as we mature we tend to discard the "double possessive" for the more "distant" things that only adults are likely talk about, but we keep it for "closer" people because that's how we spoke when we were younger.  EDIT2 I note that I'm a great fan of him is vanishingly rare compared to ...fan of his, but with ...fan (of John) the double possessive occurs far less often than ...friend (of John's). Usage seems to be affected by the noun before "of" as well as the one after it. This is getting complicated... $e^{mx}$ in solving second order differential equations In a book I am reading on differential equations, the author writes about the solution to a homogenous, linear, second order differential equation with constant coefficients. The author says something like, "Let us suppose that the solution is of the form $y=e^{mx}$ " . After this the author introduces the characteristic equation of a differential equation of the form mentioned above, and proceeds to describe how to solve it w/ undetermined coefficients, variation of parameters, etc.   How did mathematicians first come up with this "assumption" that the solution was of the form $y=e^{mx}$? And, are there any other forms of solutions for these types of equations? When should N-Gons be used, and when shouldn't they? Support for N-Gons (polygons consisting of more than 4 vertices) has been in Blender for a while now, but many of us still may not know when to use them, and how to do so effectively.  In what situations do N-Gons really come in handy? When should they be just plain left out? Do they have any place in finished models? Noetherian property for exact sequence Let $0 \to M' \xrightarrow{\alpha} M \xrightarrow{\beta} M'' \to 0$ be an exact sequence of $A$-modules. Then $M$ is Noetherian is equivalent to $M'$ and $M''$ are Noetherian.  For the ''$\Leftarrow$'' case:  I guess if we let $(L_n)_{n\geq 1}$ be an ascending chain of submodules of $M$, then $(\alpha ^{-1}(L_n))_{n\geq 1}$ is a chain in $M'$, and $(\beta(L_n))_{n\geq 1}$ is a chain in  $M''$. For large $n$ both these chains are stationary. Then why we know the chain $(L_n)$ is stationary?   Thanks! Best way to center a  on a page vertically and horizontally? Best way to center a &lt;div&gt; element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too? Book about a boy who travels to a parallel universe to get a book I can't remember the gender of the main character.  I remember bits and pieces from different books, but I think they're all part of the same series. The pieces may not be in order or from multiple books.   Boy somehow ends up in a mirror universe that's darker and seems to have no people. He has to travel to a certain office(?) building and steal a book. I think this is towards the end of the book (I can't remember the events leading up to it). I think he finds the portal in a forest or something behind his school. He goes into the ocean with mermaids or something and has to save the ocean from pollution. Aliens exist and are observing Earth, because they think it's undeveloped and are waiting for them to be advanced enough. His mother ends up in hospital and he does something to save her. He goes to Ireland(?) and enters a mountain or something to find a race of people. I can't remember who showed him how, but I'm pretty sure she used magic. He goes to Mars and saves a race from war with themselves(?). This place was hidden inside an illusion. He's also grouped with a linguist that learned their language. He travels to another world where there's a prince. I can't remember, but I think it might've been part of a tournament. His sister goes to a robot planet through a portal. I think the actual planet was a robot/AI and had lots of little robots on it. Can't remember what happens here, but he goes there and saves her from something.   It was set a few years ago, when computers weren't common (his family got one early in the first book, I think).  Thanks in advance if someone finds it. Integer solutions to the equation $a^3+b^3+c^3=30$ Let $T$ be a linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T$ for some $\lambda\in\mathbb{R}.$ Then which of the following is/are true?  $1.\|T(x)\|=|\lambda|\|x\|$ for all $x\in\mathbb{R}^n.$  $2.$ If $\|T(x)\|=\|x\|$ for some non-zero $x\in\mathbb{R}^{n}$, then $\lambda=\pm 1.$  $3.T=\lambda I$ where $I$ is the identity transformation on $\mathbb{R}^{n}.$  $4.$ If $\|T(x)\|&gt;\|x\|$ for a nonzero vector $x\in\mathbb{R}^{n},$ then $T$ is singular.  According to me since $T^{2}=\lambda T$ we have $T$ satisfies the polynomial $x^{2}-\lambda x.$ So choices for its minimal polynomial are $x,x-\lambda,x(x-\lambda).$ So $3$rd option is clearly incorrect and $4$th option is not satisfied if $T=I$ and hence correct one. I am confused in first two options . Please help me. Thanks in advance. The category Set has the property that any morphism f can be decomposed into an epimorphism $e$ and a monomorphism $m$ with $f$ = $m\circ e$. (The intermediary set object is the image of $f$.)  Is there a name for this construction?  Is there a name for this property of categories?  In Set, the intermediary object is unique up to isomorphism. Is this the case for all categories with the property? The main effect will be non-significant if the interaction is significant? How to exit from an application which doesn’t exit on press back button? Find the set of $n\in\Bbb Z^+$ with $M=\{n,n+1,n+2,n+3,n+4,n+5\}$ partitionable into two sets Find the set of all positive integers $n$ with the property that the set $M=\{n, n + 1,n + 2,n + 3,n + 4,n + 5\}$ can be partitioned into two sets such that the product of the numbers in one set equals the product of the numbers in the other set.   If $n=1$ them $M=\{1,2,3,4,5,6\}$ and there is no such partition, so $n \ge 2$.  If the prime $p|n$ then either $p|2$ or $p|3$ or $p|5$ which means either $p=2$ or $p=3$ or $p=5$.  Suppose $n=2k$. Then $M=\{2k, 2k + 1,2k + 2,2k + 3,2k + 4,2k + 5\}$. I have no idea how to proceed. Altering layer's CRS to correct Layer Misalignment in QGIS I've got a vector layer in my project which isn't aligned with the rest of the project (see attached JPEG).  These are work files so I'm not sure when they were created or how they might have been messed with since they were created.  We moved from ArcGIS to QGIS a couple of years ago.  The infilled blue vector layer is the one I need to move, slightly north and east, so that it correlates to the blue line (also a vector).  All layers (and the project) are currently in EPSG:27700 - OSGB 1936.   If I need to create a new CRS based on OSGB 1936 and give it some new parameters, then how would I go about this?  Further information:  This is on Exmoor in SW England, and the data is uniformly almost exactly 8m out to the SW point to point - i.e I need to shift it 8m NE. I am looking for a word that describes both of these activities, however the word coding does not seem to be suitable.   Likewise with encryption and decryption, cryption does not work well. What does the "static" modifier after "import" mean? Can we have the table name as "option" in MySQL? I am very, very new to MYSQL.I tried to create a table named "option". My SQL Query is :  create table option(   id int not null primary key auto_increment,  choice varchar(30)  )  While executing this query it shows the following error  Error Code : 1064 You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'option( id int not null primary key auto_increment, choice varchar(30) )' at line 1 (0 ms taken)  If I try with the table name as "choice" it is working.  can we have the table name as "option" in mysql?   thanks A clock near the surface of the earth will run slower than one on the top of the mountain.  If the equivalence principal tells us that being at rest in a gravitational field is equivalent to being in an accelerated frame of reference in free space, shouldn't the clock near the earth run increasingly slower than the other clock over time?  If those two clocks are considered to be in two different frames of acceleration, the one near the earth will have a greater acceleration than the one on the mountain, and thus over time, their relative velocity will increase over time which will increase the time dilation.  Or is this not a proper use of the equivalence principle? Integrate $\int \frac{25 - x^2}{x^4} \operatorname d\!x$