What's a good symbol for an alternative group addition? Kind of like \oplus but not \oplus because this already has a common meaning in group theory. :P
i like oplus. people familiar with the direct sum are unlikely to be confused by it. i like $\star$ for an arbitrary operation but if you want some way of notationally signaling a commutative operation it may not be ideal for that purpose.
amsmath has \boxplus which is exactly what it sounds like.
i've seen people overset or underset symbols on plus. like dots or lines.
as in convo with real live people around?.............I forgot that this is a thing.....and it will remain only a thing as we are going to be remaining in a stay at home state up here..... :(
@copper.hat I wish my English was good..I signed up for a some math site to earn some money. I got full points in mathematics (high school math but except probability). I failed because my English was bad. Those who are good at English are very lucky.
i was really impressed with one of mine, and then i heard him speak spanish. the grammar was fine (as far as i could tell) but his accent was worse than mine ever was.
this is reminding me vaguely of those problems in calculus books where you're given a family of curves and asked to find an ODE having that family as solutions. but i don't want to guess.
To set the stage, let me recall the definition of the box-counting dimension of a set $F \subset \mathbb R^n$.
The lower and upper box-counting dimensions of a subset $F$ of $â„ť^n$ are given by
$$\underline{\dim}_B F = \underline{\lim}_{\delta\to 0} \frac{\log N_\delta(F)}{-\log \delta}$$
$$\over...
@Thorgott Hm, I'm not currently reading through a book, so I figured I could use the definition which says that $F/K$ is purely inseparable if the separable degree of $F/K$ is $1$. Now, the separable degree I take as the degree of $S/K$ where $S$ is the separable closure of $K$ in $F$ (so it consists of all elements in $F$ which are separable over $K$).
@ShaVuklia Say the characteristic is $p$. Pick $\alpha\in L$ and let $P$ be its minimal polynomial. Write $P=Q(X^{p^n})$ with $n$ as large as possible. Then $Q$ is irreducible and separable (why?), so it is the minimal polynomial of $\alpha^{p^n}$ and $K(\alpha^{p^n})/K$ is a separable subextension of $L/K$, which forces $\alpha^{p^n}\in K$ by the inseperability hypothesis.
@epsilon-emperor I was going to suggest that you answer your own question. Your question is well-posed and so should pass the PSQ test, the answer would be a benefit to the site.
I see that you've deleted it, but you can undelete it.
@epsilon-emperor PSQ = "Problem Statement Question" or "Poorly Stated Question" depending on whom you ask. There are site standards on what is a well-posed question.
(Please skip to the end for a word on notation)
For $F \subset\mathbb R^n$, where $F\ne \varnothing$, we have $$0 \le \underline\dim_B F \le \overline\dim_B F \le n$$
and hence $$\dim_B F \le n$$
where $\dim_B F$ denotes the box-counting dimension of $F$. $\underline\dim_B F$ and $\overline\dim_...
the issue, i think, is that it's pretty easy to spot questions that don't meet standards even if you don't know or have any interest in how to solve a well-posed problem.
On several occasions, I've asked questions with excruciating detail of what I've tried and all typed in beautiful MathJax but it just gets ignored. My last few questions are a good example of this. How do I improve my posts so as to get answers, etc?
as a practical matter, the upvote standard seems to be more a vote of 'i am interested in this' rather than 'this is a well posed problem,' so fewer people are likely to click that button. that isn't the actual standard you see spelled out if you hover over the upvote button, which is "this question shows research effort, it is useful and clear."
i expect some people who are hair triggers on downvoting obvious junk, but don't understand the mathematical substance of question, would say that they don't know whether it shows research effort or is useful or clear if they can't understand the question
yeah, but if i read a post on higher category i wouldn't be able to tell if it was beautifully written word salad or an actual question, so i probably wouldn't upvote even if the mathjax was clear. although i tend not to downvote unless something is borderline abuse of the site. i'm a fan of commenting.
i like if the main point of the question is made clear in a paragraph or two. i don't see supplemental information like definitions and such to contribute to 'length'
Too long is likely to be ignored. But it's important to define non-obvious notation and to indicate what you've tried and where you’re stuck. I thought your question was reasonable.
I have a quick question about the site. Does upvoting old answers or commenting bump a question in some sense? Idk if this is an issue but people seem to yell at each other a lot for "necrobumping" stuff on the internet at large.
@leslietownes Got it! I just edited one of my questions and started it with "Main Theme of the Question" summarized in a few lines. Left the actual details for later paragraphs.
@Quin i think people are making trivial edits to 5-yr old questions. Very annoying. Upvotes don’t bring it to the forefront. Not sure about comments.
im a big fan of really simple stuff so im probably the target audience for a lot of the dumb posts. maybe it feels dumb because it is so simple, but a lot of people (in particular, myself) are no so clear in their thinking so the simple stuff is a great help
well now you can use google to pretty quickly locate duplicates. before google indexed that stuff you had, maybe the internal search function? which wasn't as good
so you'd have many more people answering versions of the same question. it was harder to validate that gut feeling of "this has to be a duplicate."
i do think the site is better at closing duplicates than it used to be.
hi i have a doubt regarding crammer's rule (Determinants).If D=0 then either there is infinite number if soln or no soln. But what if D=0 and one of the other determinants(D1,D2,D3) is zero
The first matrix can be used to do a "squeeze mapping"which is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a rotation or shear mapping
The second matrix can be used for the same purpose? Which one is more preferable?
the second family is just the subset of the first family with positive coefficients, parametrized slightly differently. so if you care about mapping the first quadrant to itself, i guess you would want to limit to that
that's the only difference i notice. absent context i have no view on what is preferable
Also I read that, $\bigg\{\begin{pmatrix} e^{s} & 0 \\ 0 & e^{-s} \end{pmatrix},s\in\Bbb R\bigg\}$ is the one parameter matrix flow of the geodesic flow
Does that mean $\bigg\{\begin{pmatrix} s & 0 \\ 0 & 1/s \end{pmatrix},s\in\Bbb R\bigg\}$
is also the one parameter matrix flow of the geodesic flow?
without getting into what 'the geodesic flow' is, note that you can't have s equal to zero in that second parametrization, and that the first parametrization gives you a group homomorphism from the additive group of reals to a group of invertible matrices, and the second does not
this may be an obstacle to your second map having nice properties, such as arising from a 'flow'
but this would be buried in the definitions of what that flow is
it can't be answered at the current level of detail
well, i can't think of a good answer. i assume 'multivariable calculus' tops out at approximately dimension 3 (i.e. while it may introduce more abstract tools it does not expressly bill them as such). that's mostly where i'm getting stuck.
if you flow a simple closed curve in the plane by its curvature, it eventually becomes convex, if it wasn't before, and it converges to a point in the appropriate sense, and if you scale the flowed curves so that they have constant area, the resulting family of curves converges to a circle. i think that is a cool and intuitive low dimensional result.
and a lot of it can be motivated via multivariable calculus, but as far as i know, eventually you need to appeal to PDE (which you can mostly use as a black box) and some pretty gross formulas.
In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surfaces evolves under mean curvature flow if the normal component of the velocity of which a point on the surface moves is given by the mean curvature of the surface. For example, a round sphere evolves under mean curvature flow by shrinking inward uniformly (since the mean curvature vector of a sphere points inward). Except in special cases, the mean curvature...
what you'd expect. differentiate the family of curves appropriately and you get the curvature
or mean curvature i guess in the general case
that you can do this might be where PDE comes in, at least in general