All Questions
155,583
questions
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Dirac operator and Levi-Civita connection in curved space-time
The Dirac operator in curved space-time is defined as $D = \gamma^{\mu}D_{\mu}$ where $D_{\mu} = \partial_{\mu} + \omega_{\mu a b} \sigma^{ab}$. Here The connection
\begin{equation}
D_{\mu} : \Gamma (...
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Does there exist a 5-connected planar graph that is perfect?
I asked this question on math stack, but didn't get any response, so I ask it here.
In a previous post, I proved that no 5-connected maximal planar graph is perfect. (A perfect graph is a graph $G$ ...
- 1,781
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Defining polynomial of compositum of splitting fields
Let $L_1,...,L_n/K$ be finite separable field extensions. Then the compositum extension $L:=L_1\cdot ...\cdot L_n/K$ is also finite and separable. Thus by the primitive element theorem, there are $\...
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Ratio of Gaussian measure over Euclidean balls
Let $\nu\in\mathcal P(\mathbf R^d)$ be the standard Gaussian distribution $\mathcal N(0,I_d)$.
Denote by $\mathscr B$ the class of Euclidean balls $B_r(x)$ (centered in $x\in\mathbf R^d$ with radius $...
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Properties of Poisson Integral and Traces of functions in Sobolev space $W^{1,2} (\mathbb D)$
Let $W^{1,2}(\mathbb D)$ be the complex valued Sobolev space on $\mathbb D$ where $\mathbb D $ is the open unit disk of the complex plane. By definition, $W^{1,2} (\mathbb D)$ is the set of all ...
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Ec primes are quite surely not random, but keep it quite! [closed]
Ec primes or probable primes are not random. I am convinced.
Ec primes are primes of the form $(2^n-1)\cdot 10^d+2^{n-1}-1$, where d is the number of decimal digits of $2^{n-1}$.
$215$, $69660$, $...
3
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109
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Institutional approach to linear algebra
In Diaconescu's book Institution Independent Model Theory, it is mentioned on p. 37 that linear algebra can be viewed as an institution. Specifically, we have the following
Definition. An institution ...
- 9,107
3
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1
answer
296
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Is $\mathbb Z$ prime in the class of abelian groups?
Let $B$, $C$, and $D$ be abelian groups such that $\mathbb Z\times B$ is isomorphic to $C\times D$.
Is there a group $E$ such that $C$ or $D$ is isomorphic to $\mathbb Z\times E$?
Reference: page 263 ...
- 1,502
2
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39
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Lexicographically largest incidence matrix
I have simple algorithmic question, but I can't find any source where this algorithm is explained in details.
Let's assume that we have incidence (with 0 and 1 values) matrix of size $m\times n$. Let ...
- 491
3
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Decomposition of forms in $\operatorname{SU}(4)$-manifold
$\DeclareMathOperator\Spin{Spin}\DeclareMathOperator\SU{SU}$Let $(X,\Omega,\omega,J)$ be a manifold with an $\SU(4)$ structure. Since $\SU(4)\subset\Spin(7)$, $X$ also has a $\Spin(7)$-structure. I ...
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In the construction of $K^c$ for sequences of measures, why do we only add measures of cofinality $\omega_1$?
$\require{cancel}$
I have a question about the definition of $K^c$ for sequences of measures in Mitchell's "The Covering Lemma" chapter in the Handbook. I will give the definition he gives ...
- 185
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41
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Comparing semiring of formulas and Lindenbaum algebra
This is motivationally related to an earlier question of mine.
Given a first-order theory $T$, let $\widehat{D}(T)$ be the semiring defined as follows:
Elements of $\widehat{D}(T)$ are equivalence ...
- 20.7k
2
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1
answer
174
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Rate of convergence of the Riemann zeta function and the Euler product formula
We consider the Euler product formula $$\sum_{n=1}^\infty \frac{1}{n^s}=\prod_p \frac{1}{1-p^{-s}}$$
I have two questions about this equality:
1)Does the rate of convergence of each side ...
- 452
4
votes
1
answer
165
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Detailed exposition of construction of Steenrod squares from Haynes Miller's book
$\DeclareMathOperator\Sq{Sq}$Chapter 75 of Haynes Miller's book on algebraic topology contains a beautiful construction of the Steenrod squares $\Sq^i$.
Roughly speaking, it goes as follows. All ...
- 41
1
vote
1
answer
150
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Huygens' trigonometric inequality
Prove that $$1-(4/3(\sin^3 \theta/2))/(\theta-\sin\theta)<(1-\cos\theta/2)(3/5-(3/1400)\pi^2/n^2)$$ holds for $0\le\theta\le\pi/2.$
This an unproved inequality due to Christian Huygens. I am ...
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