text stringlengths 94 1.28M | meta dict |
|---|---|
\begin{document}
\title{
Effective bounds for the measure of rotations
}
\date{\today}
\author{Jordi-Llu\'{\i}s Figueras$^\clubsuit$}
\address[$\clubsuit$]{Department of Mathematics, Uppsala University,
Box 480, 751 06 Uppsala, Sweden}
\email{figueras@math.uu.se}
\author{Alex Haro$^\diamondsuit$}
\address[$\diamond... | {
"config": "arxiv",
"file": "1806.05517/circle.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: On the fundamental group of closed 3-manifolds
QUESTION [5 upvotes]: I know that every finitely presented group can be realized as the fundamental group of a compact, connected, smooth manifold of dimension 4 (or higher). In dimension 2 there are strong restriction on the fundamental group of closed manifolds.
I... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 5,
"question_id": 172406,
"subset_name": null
} |
\begin{document}
\thispagestyle{empty}
\begin{center}
\vspace*{1in}
\textsf{ \Large Recursive projections of symmetric tensors\\
and Marcus's proof of the Schur inequality}\\[.2in]
\textsf{S. Gill Williamson}\footnote{\url{http://cseweb.ucsd.edu/~gill}}
\end{center}
\thispagestyle{empty}
\hspace{1 pt}
\begin{c... | {
"config": "arxiv",
"file": "1406.5205/SchurIneqX.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
\begin{document}
\setlength{\baselineskip}{12pt}
\title{Sequentially Cohen-Macaulay Rees algebras}
\author{Naoki Taniguchi}
\address{Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki 214-8571, Japan}
\email{taniguti@math.meiji.ac.jp}
\urladdr{http://... | {
"config": "arxiv",
"file": "1406.3423/SCM_Rees__final_.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Generalized percolation problem
QUESTION [2 upvotes]: Consider a simple site percolation problem on, for example, a 2D square lattice. Each vertex is randomly either there or not with some probability. If two neighbouring vertices are present, then the edge between them is there too. If any connected component s... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 2,
"question_id": 1217714,
"subset_name": null
} |
TITLE: Pulsed transmission of electromagnetic waves through a plasma
QUESTION [5 upvotes]: A plasma has the following dispersion relation:
$$k^2 = \frac{\omega^2}{c^2}\left(1 - \frac{\omega_\mathrm{p}^2}{\omega^2}\right) $$
where $k$ is the magnitude of the wave-vector and $\omega$ is the angular frequency and $\omega_... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 5,
"question_id": 402426,
"subset_name": null
} |
TITLE: Rewriting $\cos^4 x \sin^2 x $ with exponent no higher than $1$
QUESTION [1 upvotes]: I'm having some trouble finishing this one off.
Rewrite with exponent no higher than $1$:
$$\cos^4 x \sin^2 x$$
The answer is:
$$\frac{2 + \cos(2x) - 2\cos(4x) - \cos(6x)}{32}$$
So I started like this:
$$\cos^4 x \sin^2 x =... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 4414175,
"subset_name": null
} |
\begin{document}
\maketitle
\begin{abstract}
In this paper we estimate the worst rate of exponential decay of degenerate gradient flows $\dot x = -S x$, issued from adaptive control theory \cite{anderson1986}. Under \emph{persistent excitation} assumptions on the positive semi-definite matrix $S$, we provide up... | {
"config": "arxiv",
"file": "2006.02935/final-SIAM.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Finding the limit $\lim_{n \to \infty}{\frac{\Sigma_{0}^{n}(1/n)}{\ln(n)}}$
QUESTION [1 upvotes]: Let
$$
\lim_{n \to \infty}{\frac{
\sum_{1}^{n}(\frac{1}{n})}{\ln(n)}}
$$
Please provide some hint or a solution.
Thanks!
REPLY [0 votes]: You can also notice that the numerator is the harmonic number which grows as... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 575701,
"subset_name": null
} |
TITLE: The equality of gradient between different calculations?
QUESTION [1 upvotes]: Suppose there is a problem
$$\min\limits_v\max\limits_x E(v,x).$$
$E$ is a concave function w.r.t. $x$. But w.r.t. $v$, $E$ is a convex function plus a concave function.
I can get $x^*=\arg\max\limits_x E(v,x)=\phi(v)$.
Since $E$ is ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 864045,
"subset_name": null
} |
TITLE: mysterious sum of two sequences
QUESTION [4 upvotes]: Let
$$S_1 = \sum_{n=1}^\infty \frac{1}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \cdots$$
$$S_2 = \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 4,
"question_id": 1616279,
"subset_name": null
} |
TITLE: Finding the voltage of an inductor in a RL series circuit
QUESTION [0 upvotes]: Here is the solution:
This assigned question is an odd one since it doesn't seem to have anything to do with phasors which is the chapter I am currently studying. I know that that the phase relationship in a RL circuit is that volta... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 106842,
"subset_name": null
} |
TITLE: Prove $m=3k+1 \quad m,k \in \mathbb Z \implies m^2=3l+1 \quad m,l \in \mathbb Z$
QUESTION [4 upvotes]: Suppose we call an integer "throdd" $\iff$ $m=3k+1$ for some integer
$k$. Prove that the square of any throdd integer is throdd.
So here is what I have so far:
$$(3k+1)^2 = 3k+1$$
$$(3k+1)(3k+1) = 3k+1$$
Am ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 4,
"question_id": 541963,
"subset_name": null
} |
TITLE: Double Integral: Finding a suitable change of variables
QUESTION [0 upvotes]: Here is a question that I am trying to review:
Perform a suitable change of variables to rewrite the integral $\iint_R\ xy^2\,dA$
where $R$ is the region bounded by the lines $x-y=2$, $x-y=-1$, $2x+3y=1$, and $2x+3y=0$. Do not evaluat... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 1560422,
"subset_name": null
} |
TITLE: Prove that limited increasing or decreasing successions have a limit.
QUESTION [4 upvotes]: Be $u_n$ an increasing sequence of numbers ${(u_1,u_2,u_3, \ldots)}$ such that for all $\ n$, $u_{n-1}\le u_n$
Prove that if $u_n\le a, a \in \mathbb R$, for all n then $\lim_{n\rightarrow\infty}u_n =b $ for some number $... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 4,
"question_id": 3470123,
"subset_name": null
} |
TITLE: Area of curve in parametric equation
QUESTION [1 upvotes]: Given the curve defined by the parametric equations:
$$
x=7\cos{3t}\\
y=7\sin{3t}\\
0\le t\le2\pi
$$
What is the area of the region bounded by this curve?
Clearly,
$$
x^2+y^2=(7\cos{3t})^2+(7\sin{3t})^2=7^2
$$
which is a circle centered at the origin an... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 2304721,
"subset_name": null
} |
TITLE: quantifier restrictions in natural deduction
QUESTION [1 upvotes]: Universal elimination and existential introduction are easy. But when it comes to existential elimination and universal introduction, there are some restrictions which I don't fully understand.
Let me give an example:
Show that if ∀x(P(x) → Q(x)... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 1495874,
"subset_name": null
} |
TITLE: Can a scalar field transform nontrivially under a local special conformal transformation?
QUESTION [2 upvotes]: Is there any way to have a scalar field that transforms non-trivially under local special conformal transformations? Just by the index structure, I can see that the possibilities are
$$\begin{align}
\d... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 2,
"question_id": 230688,
"subset_name": null
} |
TITLE: finding value of $\sum^{10}_{i=0}\frac{1}{a_{i}}$
QUESTION [2 upvotes]: Let $a_{0},a_{1},a_{2},a_{3},\cdots \cdots a_{n}$ be a sequence of numbers satisying $(3-a_{n+1})(6+a_{n}) = 18$ and $a_{0} = 3.$ then find $\displaystyle \sum^{10}_{i=0}\frac{1}{a_{i}}$
from $18-6a_{n+1}+3a_{n}-a_{n}a_{n+1} = 18.$ So $6a_{n... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 2,
"question_id": 2127239,
"subset_name": null
} |
TITLE: number of combinations colouring 10 eggs with 4 colours if one or 2 colours can be used at the same time
QUESTION [0 upvotes]: I started to solve this question and realised, that if I just add up all the possibilities, it is going to take a lot of time:
Here is the complete question from the textbook:
Eggs that... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 2964913,
"subset_name": null
} |
TITLE: Do we distinguish two singular simplices if they have different vertex orders?
QUESTION [2 upvotes]: We define a $\textbf{singular $n$-simplex}$ in $X$ to be a continuous map $\sigma:\Delta^n\to X$ where $\Delta^n$ is the standard $n$-simplex. Now, as an example, Let $X$ be a singleton $\{p\}$. Then is the numbe... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 2,
"question_id": 4325168,
"subset_name": null
} |
TITLE: Electrostatics- Attraction between a negatively charged balloon and a plastic bottle
QUESTION [0 upvotes]: Let's say there is a negatively charged balloon. There is also a neutrally charged plastic bottle. You know that since the plastic bottle is an insulator, polarization occurs. Is it true that since the posi... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 477770,
"subset_name": null
} |
TITLE: Is the Avogadro's constant equal to one?
QUESTION [17 upvotes]: Question: Is the Avogadro's constant equal to one?
I was tasked with creating a presentation on Avogadro's work, and this is the first time I actually got introduced to the mole and to Avogadro's constant. And, to be honest, it doesn't make any math... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 17,
"question_id": 24034,
"subset_name": null
} |
\section{Hyperviscosity-based Stabilization}
\label{sec:robust_hyp}
As mentioned previously, the RBF-FD differentiation matrices corresponding to the discretized gradient operator (and occasionally even the Laplacian operator) can contain eigenvalues with positive real parts. Such eigenvalues can cause spurious growth... | {
"config": "arxiv",
"file": "1806.03798/Methods.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: There are 6 same apples and 8 same oranges. How many non-empty subset can be formed from those two kinds of fruits?
QUESTION [1 upvotes]: I thought it is $2^{14} - 1$ but I am not so sure. I think it is not a kind of multiplication principle, that is, $6 \cdot 8 = 48$, because in the context, the 6 apples are th... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 501167,
"subset_name": null
} |
\section{Proof of Main Theorem}
In this section, we give the proof of Theorem \ref{thm:algcycles}. The key idea is to give, for each unramified $[b]\in B(G,\upsilon)$, a factor $H_{[b]}(x)$ of the Hecke polynomial which kills the irreducible components of $p-\Isog\otimes\kappa$ which are $[b]$-dense.
\subsection{Const... | {
"config": "arxiv",
"file": "2006.11745/maintheorem.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
\begin{document}
\bibliographystyle{plain}
\maketitle
\begin{abstract}
We give two results for computing doubly-twisted conjugacy relations
in free groups with respect to homomorphisms $\phi$ and $\psi$ such
that certain remnant words from $\phi$ are longer than the images of
generators under $\psi$.
Our first resu... | {
"config": "arxiv",
"file": "0806.4687.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Homeomorphism between $\mathbb{S}^1/(x\sim -x)$ and $\mathbb{S}^1$
QUESTION [1 upvotes]: I was reading this paper by Kim A. Frøyshov about the real projective plane and in part of the proof to show that it is homeomorphic to $\mathbb{S}^1$ they first showed it was homeomorphic to $\mathbb{S}^1/(x\sim-x)$. That p... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 4251622,
"subset_name": null
} |
TITLE: What is the intensity distribution behind the first beam splitter on an observation screen at the same distance like behind the second beam splitter?
QUESTION [0 upvotes]: Mach-Zehnder interferometer has been used, among other things, to measure phase shifts between the two beams caused by a sample or a change i... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 187655,
"subset_name": null
} |
TITLE: Why is kinetic energy defined as the measure of work an object can do due the virtue of its motion?
QUESTION [0 upvotes]: Saying that KE=1/2mv^2 holds even when magnitude or direction of force changes, so the expression is valid irrespective of how the body acquires the velocity shouldn't be correct as work done... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 358597,
"subset_name": null
} |
TITLE: Physical meaning of Legendre transformation
QUESTION [87 upvotes]: I would like to know the physical meaning of the Legendre transformation, if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates?
REPLY [24 votes]: There are already some nice answers r... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 87,
"question_id": 4384,
"subset_name": null
} |
TITLE: Convexity of the ratio of the standard normal PDF by its CDF
QUESTION [1 upvotes]: Is there some way to show that the following function $\psi$ is concave or convex? Here, $\phi$ and $\mathbf{\Phi}$ are the standard normal PDF and CDF, respectively.
$$\psi\left(u\right)=u+\frac{\phi\left(u\right)}{\Phi\left(u\ri... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 1323483,
"subset_name": null
} |
TITLE: What obstacles prevent three-valued logic from being used as a modal logic?
QUESTION [6 upvotes]: I am familiar with many of the surveys of many valued logic referenced in the SEP article on many valued logic, such as Ackermann, Rescher, Rosser and Turquette, Bolc and Borowic, and Malinowski. It is asserted in t... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 6,
"question_id": 695774,
"subset_name": null
} |
\section{Conclusions}
\label{sect:conclusion}
We presented a novel approach to extract a probabilistic dynamic description of hazardous thunderstorm regions from state-of-the-art nowcast data. We integrated the stochastic thunderstorm model in a stochastic, optimal trajectory planning tool, which maximizes the probab... | {
"config": "arxiv",
"file": "1806.02396/5_conclusion.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Elementary Number Theory: If $p$ and $a$ are natural numbers with prime $p$, and $p^4|a^3$, then $p^2|a$.
QUESTION [1 upvotes]: I'm reviewing the basic number theory from my undergrad program (so I can jump back into abstract algebra well enough), and I've come across this problem in the section regarding the Fu... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3594851,
"subset_name": null
} |
TITLE: $\iiint \frac{1}{x^2+y^2+(z-2)^2}dA$ where $A=\{x^2+y^2+z^2 \leq 1\}$ check my answer!
QUESTION [2 upvotes]: I would like someone to review my solution please, the original question is to calculate
$\iiint \frac{1}{x^2+y^2+(z-2)^2}dA$ where $A=\{x^2+y^2+z^2 \leq 1\}$
What I did:
First I changed variables to pol... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 2,
"question_id": 805932,
"subset_name": null
} |
TITLE: Galilean, SE(3), Poincare groups - Central Extension
QUESTION [11 upvotes]: After having learnt that the Galilean (with its central extension) with an unitary operator
$$ U = \sum_{i=1}^3\Big(\delta\theta_iL_i + \delta x_iP_i + \delta\lambda_iG_i +dtH\Big) + \delta\phi\mathbb{\hat1} = \sum_{i=1}^{10} \delta s_i... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 11,
"question_id": 104442,
"subset_name": null
} |
TITLE: Prove that $|\sum\limits_{k=1}^{n} a_{k}| \ge |a_{1}| - \sum\limits_{k=2}^{n} |a_{k}|$.
QUESTION [1 upvotes]: I am abjectly disappointed that I could not prove this statement on my own. I have tried it directly and by contradiction but hit a wall. Here is the statement (again) and my proof (thus far):
Prove th... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3969728,
"subset_name": null
} |
TITLE: show that the set is compact
QUESTION [0 upvotes]: Suppose $f$ is a reimann integrable function on [a,b]. Let V={$x\in[a,b]$ : $\int\limits_{x}^{b} f(t)dt$ is continuous}.Then show that V is compact
Clearly V is bounded.So we only have to prove that V is closed.For that I take a sequence $\{x_n\}$ in V which con... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 3847118,
"subset_name": null
} |
TITLE: how to interpret the solution of a linear system?
QUESTION [1 upvotes]: i have the following reduced echelon form matrix
[(1,0,1,)(0,1,0)(0,0,0)] and the solutions are (2,1,0)
EDIT This should be the system of linear equations
$$
\left\{
\begin{matrix}
x&+&&&z&=&2\\
&&y&&&=&1\\
\end{matrix}
\right.
$$
now I am ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 302072,
"subset_name": null
} |
TITLE: Showing that $S^2 \vee S^4$ is not homotopy equivalent to any closed 4-manifolds.
QUESTION [6 upvotes]: I am working on a problem that asks to show that $S^2 \vee S^4$ is not homotopy equivalent to any closed $4$-manifold. My only understanding of manifolds is from Hatcher's chapter on Cohomology (chapter 3) so ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 6,
"question_id": 2758152,
"subset_name": null
} |
TITLE: Why is it that $ V_{+}(I) \cup V(J) $ = $ V_{+}(I \cap J), $ where $ I $ and $ J $ are homogeneous ideals of a graded ring $ S$?
QUESTION [0 upvotes]: Define $ V_{+}(I) = \lbrace \mathfrak{p} \in \text{Proj}(S) \;|\; \mathfrak{p} \supset I \rbrace. $
I can see that $ V_{+}(I) \cup V_{+}(J) \subset V_{+}(I \cap ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 3117848,
"subset_name": null
} |
TITLE: How the quotients of central series forms a Lie algebra
QUESTION [1 upvotes]: Let $G$ be a group. Then the subgroups of the central series are $\gamma_1(G)=G$, $\gamma_2(G)=[\gamma_1(G),G],..., \gamma_n(G)=[\gamma_{n-1}(G),G]$. Then in the reference paper given below it is given that the direct sum $\bigoplus_{n... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3343840,
"subset_name": null
} |
TITLE: Categorical Kähler differentials and the Leibniz rule
QUESTION [4 upvotes]: From nlab, the module of Kähler differentials over some category $\mathcal{C}$ is the free functor:
$$\Omega: \mathcal{C} \to \mathsf{Mod_{\mathcal{C}}}$$
left-adjoint to the (forgetful) embedding:
$$u: \mathsf{Mod}_{\mathcal{C}} \cong \... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 4,
"question_id": 361187,
"subset_name": null
} |
TITLE: Conditional Statements: "only if"
QUESTION [23 upvotes]: For some reason, be it some bad habit or something else, I can not understand why the statement "p only if q" would translate into p implies q. For instance, I have the statement "Samir will attend the party only if Kanti will be there." The way I interpre... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 23,
"question_id": 617562,
"subset_name": null
} |
TITLE: Surface integral of a sphere inside a cylinder
QUESTION [1 upvotes]: Find the surface area of the portion of the origin-centred sphere of radius $R=4$ that lies inside the cylinder $x^2 +y^2=12$ and above the $xy$ plane.
Does this question make sense? How can surface area lie inside the cylinder given that the ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 2626642,
"subset_name": null
} |
TITLE: Isotropy of Apollonian disk-packing
QUESTION [6 upvotes]: Is there any sense in which the "epsilon-tail" of an Apollonian disk-packing (by which I mean the union of the disks of radius less than epsilon) exhibits more and more statistical isotropy as epsilon goes to zero?
Here's one example of the kind of thing ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 6,
"question_id": 184536,
"subset_name": null
} |
TITLE: Applications of idempotent ultrafilters
QUESTION [12 upvotes]: Recently Justin Moore has posted a solution to the amenability of Thompson's group F. A key(?) step exploits the existence of idempotent ultrafilters on $\mathbb N$ to construct an idempotent measure on the free non-associative semigroup on one-gener... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 12,
"question_id": 107391,
"subset_name": null
} |
TITLE: Exactly how does an oscillating electric field produce an oscillating magnetic field?
QUESTION [1 upvotes]: Let's say we have a capacitor which is connected to a sinusoidal voltage source, that means that the electric field within the capacitor is a sinusoidal function(assuming that the capacitor is a parallel ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 287061,
"subset_name": null
} |
\begin{document}
\maketitle
\stepcounter{footnote}\footnotetext{School of Mathematics and Computer Sciences and the Maxwell Institute for Mathematical Sciences,
Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK. E-mail: S.Foss@hw.ac.uk and awr2@hw.ac.uk}
\begin{quotation}\small
The asymptotic tail beha... | {
"config": "arxiv",
"file": "0806.0490.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
\vspace*{-8pt}
\section{Motivating observation: nonstationary noise in neural network training}\label{sec:motivation}
\vspace*{-6pt}
\begin{figure}[t]
\begin{subfigure}{.32\textwidth}
\centering
\includegraphics[width=0.9\linewidth]{sections/cifar.png}
\caption{\small ResNet18 on Cifar10}
\label{fig-main_correl... | {
"config": "arxiv",
"file": "2006.04429/sections/motivation.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: What restrictions are on th sum of two fourth powers?
QUESTION [2 upvotes]: I've got an equation of the form
$$ a^4+1=2b. \qquad(\star) $$
By well-known results regarding the sum of two squares, $b$ must be the sum of two squares. But does $(\star)$ force any other restrictions on $b$ as a result of the l... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 2,
"question_id": 529040,
"subset_name": null
} |
TITLE: What makes quantum decoherence different from dissipation?
QUESTION [6 upvotes]: From my understanding quantum decoherence and dissipation are completely different ways of modelling information loss to the environment. Dissipation can be modeled using the Caldeira-Leggett model which uses an effective Hamiltonia... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 6,
"question_id": 169915,
"subset_name": null
} |
\chapter{Puiseux algebras} \label{algebras}
\section{Monoid Algebras}
\label{sec:molecules of PA}
Let $M$ be a monoid and let $R$ be a commutative ring with identity. Then $R[X;M]$ denotes the ring of all functions $f \colon M \to R$ having finite \emph{support}, which means that $\supp(f) := \{s \in M : f(s) \neq 0... | {
"config": "arxiv",
"file": "2006.09173/tex/ch6.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
\section{Interpreting the Machine Learning Models}
\label{subsec:interpretation}
In this section, we analyze how the structure of different learned controllers~$i,j \in \C$ differ across the network as reflected by parameters~$\beta^{(i)},\beta^{(j)}$ in (17) of the main manuscript. What does this tell us about the net... | {
"config": "arxiv",
"file": "1806.06790/interpretMLmodels.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: holomorphic complex function such that $f(\frac{1}{n})=n\space$ but $f$ is not identically $1/z$
QUESTION [4 upvotes]: Question: Find a function $f(z)$ holomorphic on $\{0<|z|<1\}$ such that $f(\frac{1}{n})=n\space$ for each integer $n >1 $, but so that $f$ is not identically $1/z$.
I attempted to solve this an... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 4,
"question_id": 1187005,
"subset_name": null
} |
TITLE: Solving for a square as the sum of 2 evens
QUESTION [0 upvotes]: Let $m$ and $r$ be an even, and $n$ be odd
Let the following be a square defined as the sum of two even numbers
$$m^2 = 10 n + r $$
Examples that would satisfy this equation:
$$ \begin{array} {c|rrrr} \\ \hline m & 4 & 6 & 14 & 16 & 24 & 26 & 34... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 1964896,
"subset_name": null
} |
TITLE: $x=r\cos \theta$ and $y=r\sin \theta$ determine partial derivative
QUESTION [0 upvotes]: My question is the same as this one: $x =r\cos \theta$ and $y = r\sin\theta$, determine $\frac{\partial r}{\partial x}$ and $\frac{\partial \theta}{\partial x}$
except that I do not know how to prove that $$ \frac{\partial \... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 4466787,
"subset_name": null
} |
TITLE: Probability of getting a higher value from a normal distribution
QUESTION [1 upvotes]: You have two independent random variables $X$ and $Y$ each of a zero mean, unit variance distribution. What is the $P(X>5Y)$?
REPLY [2 votes]: Perhaps surprisingly, the answer is $1/2$. Aside from callculus's approach, there... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3320903,
"subset_name": null
} |
TITLE: Product of "reversed" numbers
QUESTION [1 upvotes]: Consider any 2 binary numbers, e.g.: 10101011 ; 11111101 and their product, say P.
"Reverse" (mirror image) all the digits of the 2 numbers, e.g.: 11010101 ; 10111111
and consider their product, say M.
Question
Is there any simple math relation between P and M ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 760981,
"subset_name": null
} |
TITLE: What is the fifth digit from the left of $12345678987654321\times625$
QUESTION [1 upvotes]: We have been calculated $$12345678987654321\times625$$
Then what is the fifth digit from the left of this number?
I can rewrite it as $$12345678987654321\times625={\underbrace{111111111}_{9\text{times}}}^2\times25^2=(11... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3986362,
"subset_name": null
} |
\begin{document}
\bibliographystyle{plain}
\newfont{\teneufm}{eufm10}
\newfont{\seveneufm}{eufm7}
\newfont{\fiveeufm}{eufm5}
\newfam\eufmfam
\textfont\eufmfam=\teneufm \scriptfont\eufmfam=\seveneufm
\scriptscriptfont\eufmfam=\fiveeufm
\def\frak#1{{\fam\eufmfam\relax#1}}
\def\bbbr{{... | {
"config": "arxiv",
"file": "0806.0640.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Munkres' Unit Circle Example - Topology on Domain
QUESTION [1 upvotes]: Consider the $S^1 = \{ x \times y | x^2 + y^2=1 \}$ as a subspace of $\mathbb{R}^2$. Let $F:[0,1) \rightarrow S^1$ be defined by $t \mapsto (\cos(2\pi t),\sin(2\pi t))$. Will the inverse image of an open set containing $(1,0)\in \mathbb{R}^2... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 2916298,
"subset_name": null
} |
\begin{document}
\title{Arc-Search Infeasible Interior-Point Algorithm for Linear Programming}
\author{Yaguang Yang\footnote{\normalsize NRC, Office of Research, 21 Church Street,
Rockville, 20850. Email: yaguang.yang@verizon.net.} \\
}
\date{\today}
\maketitle
\begin{abstract}
Mehrotra's algorithm has been the ... | {
"config": "arxiv",
"file": "1406.4539/infeasibleNoProof.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Checking an "equivalence of products" in the notes on deformation quantization by Allen C. Hirshfeld and Peter Henselder
QUESTION [1 upvotes]: These notes are a great introduction to deformation quantization but I failed to check the validity of the statement p.9, right before (5.18).
Context: let $(\mathcal{A},... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3882457,
"subset_name": null
} |
\begin{document}
\begin{abstract}
Let $Z$ be a germ of a reduced analytic space of pure dimension.
We provide an analytic proof of the
uniform Brian\c con-Skoda theorem for the local ring $\Ok_Z$;
a result which was previously proved by Huneke by
algebraic methods.
For ideals with few generators we also get much
... | {
"config": "arxiv",
"file": "0806.3700.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
\begin{document}
\begin{abstract}
P-E. Caprace and N. Monod isolate the class $\ms{X}$ of locally compact groups for which relatively amenable closed subgroups are amenable. It is unknown if $\X$ is closed under group extension. In this note, we exhibit a large, group extension stable subclass of $\X$, which suggests... | {
"config": "arxiv",
"file": "1406.2974/Wesolek_a_note_on_relative_amenability_2.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: According to the epsilon delta definition, Is a function differentiable at its end points $[a,b]$?
QUESTION [1 upvotes]: $$∀x\in A, ∀ϵ>0, ∃δ>0, \text{ s.t. } |x−c| <δ ⟹ \left|\frac{f(x) − f(c)}{x-c} −L\right| < ϵ $$
My doubt is that given the epsilon delta definition of differentiability, if a function is r... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3422072,
"subset_name": null
} |
TITLE: Solving Using Integrating Factors Found By Inspection
QUESTION [0 upvotes]: Can the Differential Equation below be solve using Integrating Factors Found By Inspection? If yes, how?
$$2x^5y'=y(3x^4+y^2)$$
REPLY [0 votes]: OK OK another way!
substitute : $y=(zx)^{2}$
$y'=2xz^{2}+2zz'x^{2}$
$2x^{5}(2xz^{2}+2zz'x^{... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 4561990,
"subset_name": null
} |
TITLE: Show there is a continuous isomorphism $l_{\infty}\rightarrow \left(l_1\right)^* $
QUESTION [3 upvotes]: Let $\left(l_1\right)^*$ be the dual space to $l_1$. Each $f \in \left(l_1\right)^*$ is a continuous linear functional over $l_1$. There is constant $C \in \Bbb R$ such that $|f(x)|\le C|x|_1, \forall x\in l_... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 3,
"question_id": 1729002,
"subset_name": null
} |
TITLE: How do I prove that a statistic is a pivot?
QUESTION [1 upvotes]: In this example I have a sample out of a distribution with density $P_{\theta}(x) = 2x^{\theta} e^{−\theta x^2} I_{x \ge 0}$.
I know that for all $i \ge 1$ we have $X_i^2 \sim Exp(\theta)$.
If $\theta = 1$, then $T_1 = 2\sum_{1 \le i \le n}X_i^2 \... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3970068,
"subset_name": null
} |
TITLE: Example of a topology on R except usual topology, with exactly one limit point for each converging sequence
QUESTION [0 upvotes]: A convergent sequence in R has exactly one limit point, if R is under usual topology. Give an example of another topology on R with this property.
REPLY [1 votes]: Given a topologica... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 2501762,
"subset_name": null
} |
\begin{document}
\tikzstyle{arrow}=[thick, <-->, >=stealth]
\tikzstyle{vertex}=[circle, draw, inner sep=1pt, minimum size=6pt]
\maketitle
\abstract{The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least $r$ edges, the super lin... | {
"config": "arxiv",
"file": "2006.03567.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
\begin{document}
\begin{abstract}
We report on the construction of a database of nonhyperelliptic genus 3 curves over $\Q$ of small discriminant.
\end{abstract}
\maketitle
\section{Introduction}
Cremona's tables of elliptic curves over $\Q$ have long been a useful resource for number theorists, and for mathematicia... | {
"config": "arxiv",
"file": "1806.06289/g3database.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Calculate area of a figure based on vertices
QUESTION [3 upvotes]: Possible Duplicate:
How quickly we forget - basic trig. Calculate the area of a polygon
How to calculate the area of a polygon?
If I know all the vertices of a particular polygon/figure, is there a generalized method/formula to calculate the ar... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 3,
"question_id": 102891,
"subset_name": null
} |
TITLE: What are the differences of two electron current?
QUESTION [1 upvotes]: I often see two definition of current in the book and literature, and I am a little bit confused.
The current density
$$\textbf{J}_1(\textbf{r})=\frac{-ie\hbar}{2m_e}\sum\limits_{n\textbf{k}}\{\psi^*_{n\textbf{k}}(\textbf{r})\nabla\psi_{n\t... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 456371,
"subset_name": null
} |
\section{Introduction}
Graph neural networks (GNNs)~\cite{gori2005new,scarselli2009graph} are an emerging deep learning model for analyzing graph structured-data.
They have achieved state-of-the-art performances in node prediction tasks on a graph in various fields such as biochemistry~\cite{NIPS2015_5954}, computer v... | {
"config": "arxiv",
"file": "2006.08550/source/main/introduction.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: How to show that $A,I,I_A$ all lie on same line?
QUESTION [0 upvotes]: In triangle ABC suppose we join AI (I is incentre ) and $II_A$ ($I_A$ is excentre) , how can we say that <$AII_A$ is 180 ° ( that is they lie on a straight line . Or in other way how to show that $AI$ line extension and $AI_A$ cuts $BC$ at sa... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 4404246,
"subset_name": null
} |
TITLE: Why Newton's method work ? i.e. why $\lim_{k\to \infty }f\left(x_k-\frac{f(x_k)}{f'(x_k)}\right)=0$?
QUESTION [0 upvotes]: We want to find the zero of a function, and Newton method allow us to do it : Newton Method on Wikipedia. But I don't understand how it work. The explanation goes as following : Let $x_0$ (w... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 2127625,
"subset_name": null
} |
TITLE: Taylor series of $\sqrt{1+x}$ using sigma notation
QUESTION [7 upvotes]: I want help in writing Taylor series of $\sqrt{1+x}$ using sigma notation
I got till
$1+\frac{x}{2}-\frac{x^2}{8}+\frac{x^3}{16}-\frac{5x^4}{128}+\ldots$ and so on.
But I don't know what will come in sigma notation.
REPLY [1 votes]: allow... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 7,
"question_id": 732540,
"subset_name": null
} |
TITLE: L1 norm of difference between two probability distributions over a finite set
QUESTION [1 upvotes]: Let $P$ and $Q$ be two probability distributions over a finite set $\mathcal{A} = \lbrace 1,2,\dots, a\rbrace$,
show that
$\|Q-P\|_1 = 2 \max_{A \in \mathcal{A}} (Q(A) - P(A))$,
where $\|Q-P\|_1 = \sum_{k=1}^{a} |... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3835146,
"subset_name": null
} |
TITLE: Show $b_n=\frac{\int_{0}^\epsilon \cos^n(x) dx}{\int_{\epsilon}^{1/2} \cos^n(x) dx}\to\infty.$
QUESTION [1 upvotes]: I want to show the sequence $$b_n = \frac{\int_{0}^\epsilon \cos^n(x) dx}{\int_{\epsilon}^{1/2} \cos^n(x) dx} $$
tends to $\infty$ for every $ \epsilon : \frac{1}{2} > \epsilon > 0$
Solution:
\beg... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 3483253,
"subset_name": null
} |
TITLE: About cycling in simplex method
QUESTION [0 upvotes]: First of all I apologize if you find my question silly as I am not a student from math background.
So far I know when the same basic variables reappear in a later iteration, we say that cycling occurs. My question is: Suppose in one iteration, $x_{1}, x_{2}, ... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 4069100,
"subset_name": null
} |
\newcommand{\orb}{\mathop{\mathrm{Orb}}\nolimits}
\newcommand{\wchain}[1]{\widetilde{P}_{#1}}
\section{Preliminaries}
\subsection{A primer on the Chinese Restaurant Process}
\label{sec:CRPprimer}
The Chinese Restaurant Process,
introduced by Dubins and Pitman, is a particular example of a two parameter family of sto... | {
"config": "arxiv",
"file": "1406.7043/TPFF.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
\begin{document}
\title{Light bending in a two black hole metric}
\author{M. Alrais Alawadi}
\email{100044354@ku.ac.ae}
\affiliation{
Department of Mathematics,\\ Khalifa University of Science and Technology,\\ Main Campus, Abu Dhabi,\\ United Arab Emirates}
\author{D. Batic}
\email{davide.batic@ku.ac.ae}
\affilia... | {
"config": "arxiv",
"file": "2006.03376/main.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: identity of $(I-z^nT^n)^{-1} =\frac{1}{n}[(I-zT)^{-1}+(I-wzT)^{-1}+...+(I-w^{n-1}zT)^{-1}]$
QUESTION [3 upvotes]: I am trying to understand the identity
$$(I-z^nT^n)^{-1} =\frac{1}{n}[(I-zT)^{-1}+(I-wzT)^{-1}+...+(I-w^{n-1}zT)^{-1}] \quad (*),$$
where $T \in \mathbb{C}^{n\times n},z\in \mathbb{C}$ and the spect... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 3,
"question_id": 1092526,
"subset_name": null
} |
TITLE: Does a measurable function to the reals have to map every set to a Borel set?
QUESTION [1 upvotes]: If we have a measure space $(X,S,\mu)$ and an $S$-measurable function $f:X\to \mathbb R$, then by the definition of measurability $f^{-1}(B)\in S$ for every Borel set $B$. Does this work the other way around? Is $... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 4111055,
"subset_name": null
} |
TITLE: How to find this formula in this dihedral group of transformations of the plane?
QUESTION [1 upvotes]: In the group of all the bijections of the Euclidean plane onto itself, let $f(x,y) \colon = (-x,y)$ and $g(x,y) \colon = (-y,x)$ for all points $(x,y)$ in the plane. Let $$G:= \{f^i g^j | i=0,1; \ g=0,1,2,3 \}... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 497227,
"subset_name": null
} |
TITLE: A slicker proof that an object must be initial
QUESTION [8 upvotes]: If $\mathcal{C}$ is a category and $\lambda:\Delta_D \to id_{\mathcal{C}}$ is a cone for the identity functor, and $F:J \to \mathcal{C}$ is a functor such that $F\lambda:\Delta_D \to F$ is a limiting cone, then it follows that $D$ is an initial... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 8,
"question_id": 97562,
"subset_name": null
} |
TITLE: Convolution of indicator functions with values in a finite field
QUESTION [1 upvotes]: This is something I haven't seen online yet, indicator functions with values in a finite field. Probably for a good reason, but I would like to know why, and if there are still things that can be said. For instance what can we... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 1572917,
"subset_name": null
} |
TITLE: Omega Notation and Average Running Time Problem
QUESTION [0 upvotes]: if we have an algorithm that average running time of randomized algorithm A for input of size n is equal to $\theta(n^2)$.
why there would be an input data such that A solve it in $\Omega(n^{3n})$?
REPLY [0 votes]: Because $\Theta\left(n^2\r... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 912265,
"subset_name": null
} |
TITLE: Properties of the matrix rank
QUESTION [0 upvotes]: Let $I$ be the identity matrix $n\times n$, B a matrix $n{\times} n$ and $c$ a constant. Are these properties correct?$\DeclareMathOperator{rank}{rank}$
$$\rank(cB)=c\rank(B),$$
$$\rank(I-B)=n-\rank(B).$$
REPLY [1 votes]: Both are wrong:
The first would imply,... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 3850236,
"subset_name": null
} |
TITLE: How to prove $A^{n\times n}=I_n\Rightarrow A^n=A^{f(n\times n)}$?
QUESTION [1 upvotes]: Let $A\in M_2(\mathbb{Z})$ s.t. there is a positive integer $n$ satisfying $A^n=I_2$.
Show that $A^{12}=I_2$.
I have no idea where to start. Suggestions?
REPLY [0 votes]: Let $\alpha,\beta$ be the eigenvalues of $A$. Then $\... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 1277826,
"subset_name": null
} |
TITLE: Expected number of vertices a distance $k$ away in a random graph?
QUESTION [4 upvotes]: Given a random (undirected and unweighted) graph $G$ on $n$ vertices where each of the edges has equal and independent probability $p$ of existing (see Erdős–Rényi model). Fix some vertex $u\in G$. I want to know what is the... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 4,
"question_id": 627670,
"subset_name": null
} |
TITLE: find minimal polynomial in ${GF(3^2)}$
QUESTION [0 upvotes]: is this solution right ... when ${\alpha =g }$ and ${ \alpha = g^2 }$
REPLY [1 votes]: Here is a computer check, using sage:
sage: R.<x> = PolynomialRing( GF(3) )
sage: R
Univariate Polynomial Ring in x over Finite Field of size 3
sage: F.<g> = GF(... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 3491992,
"subset_name": null
} |
TITLE: On energy levels and emission of photons
QUESTION [1 upvotes]: This is a very basic question but I cannot seem to find the answer anywhere.
Say we have an atom in ground state. Its first energy level is 2 eV. An incoming photon of energy 2.5 eV hits an electron in the atom (with the lowest energy level) which i... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 187196,
"subset_name": null
} |
TITLE: Prove that $\gamma$ is a measure
QUESTION [0 upvotes]: Let $Q = \{A \subset \mathbb{R}: A \text{ countable or } A^c \text{ countable} \}$ and $\gamma: Q \to \{0,1\}$, where $\gamma(A) = 0$ if $A$ is countable, $\gamma(A) = 1$ otherwise.
I struggle with showing one of the properties that this is a measure,
$$
\ga... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 0,
"question_id": 1995070,
"subset_name": null
} |
\begin{document}
\begin{frontmatter}
\title{On a generalization of the global attractivity for a periodically
forced Pielou's equation}
\author[waseda]{Keigo Ishihara}
\ead{keigo.i.123@gmail.com}
\author[waseda]{Yukihiko Nakata\corauthref{cor1}}
\ead{yunayuna.na@gmail.com}
\corauth[cor1]{Corresponding author}
\address... | {
"config": "arxiv",
"file": "1006.3379.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
TITLE: Do we draw a distincton between a number as an element of the reals, and an element of the naturals?
QUESTION [1 upvotes]: I see in some explanations of attempts to formalize numbers such as Von Neumann's ordinals like in this rather philosophical question that we can draw a distinction between a real number '1'... | {
"config": null,
"file": null,
"set_name": "stack_exchange",
"score": 1,
"question_id": 4519784,
"subset_name": null
} |
\begin{document}
\title[Sugery and Excision for $\lambda_{FO}$]{Surgery and Excision for Furuta-Ohta invariants on Homology $S^1 \times S^3$ }
\author{Langte Ma}
\address{MS 050 Department of Mathematics, Brandeis University, 415 South St., Waltham MA 02453}
\email{ltmafixer@brandeis.edu}
\maketitle
\begin{abstract... | {
"config": "arxiv",
"file": "2006.04197/Surgery_and_Excision_for_the_Furuta-Ohta_Invariant.tex",
"set_name": null,
"score": null,
"question_id": null,
"subset_name": null
} |
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