text large_stringlengths 384 2.05k | rank_avg float64 1 4.19k ⌀ | rank_max float64 1 8.21k ⌀ | rank_min float64 1 5.03k ⌀ | rank_median float64 1 4.21k ⌀ | rank_by_avgsim float64 1 4.19k ⌀ | avgsim_to_github float32 0.77 0.85 ⌀ | dataset large_stringclasses 1
value |
|---|---|---|---|---|---|---|---|
star}=[0,1,2]^T$, then ${\a^\star}=[-2,0,1]^T$.
According to , if ${\a^\star}$ is optimal for $\h$, then $-{\a^\star}$ is also optimal for $\h$. To reduce redundancy, we restrict the optimal coefficient vector ${\a^\star}$ to be the one such that $\h^T{\a^\star}\geq0$ in the following.
\[lemma:aNonnegative\] If all t... | 3,101 | 2,139 | 2,676 | 2,875 | null | null | github_plus_top10pct_by_avg |
6)[$\theta_{i_3}$]{} (5431,-1786)[$\theta_{i_2}$]{} (3226,-1786)[$1$]{} (6578,-879)[$\theta_{i_4}$]{} (5829,-459)[$\theta_{i_5}$]{} (5063,-1344)[$\theta_{i_1}$]{} (2003,-1801)[$X$]{} (2483,-616)[$Y$]{} (1042,-879)[$Z$]{} (601,-1561)[( 1, 0)[3300]{}]{}
Then by the argument above, we see that $\Psi_p((\theta_1, \ldots, ... | 3,102 | 3,177 | 2,414 | 3,026 | 2,876 | 0.776386 | github_plus_top10pct_by_avg |
phi_{\Theta}(\Theta/ A\cap\ ^{w} B).$$ So the blocks $B_{H,L,x,y}$ and $B_{\Theta,\Theta,1,1}$ are equals up to permutation of the lines and the columns. In particular, these two matrices have the same determinant, up to a sign.
\[red2\] Let $\Theta$ be a finite group, and $\mu'$ the sub-algebra of $\mu_{R}(\Theta)$ g... | 3,103 | 1,801 | 1,108 | 2,909 | null | null | github_plus_top10pct_by_avg |
,r_p(\chi )({\alpha }_j,{\alpha }_i)=&q_{ij}q_{ji}=
r_p(\chi )({\alpha }_i,{\alpha }_i)^{c_{pi}}
\end{aligned}$$ for all $p,i,j\in I$. Hence $r_p(\chi )$ is again of Cartan type with the same Cartan matrix $C$. Thus $\chi '$ is $i$-finite for all $\chi '\in {\mathcal{G}}(\chi )$ and $i\in I$.
Let $C=(c_{ij})_{i,... | 3,104 | 2,550 | 1,543 | 3,038 | 3,841 | 0.769749 | github_plus_top10pct_by_avg |
}^{j}$. Since the contribution of the $j$-th receive beam to the throughput under the $\log$ function is given by $$\label{eq:alphapsinjR}
g_{\psi,n,j}={\mathbf{h}}_{\psi,V}^{j}\left({\mathbf{I}}_{N_t}+\frac{\rho}{N_t}\left({\widetilde{\mathbf{H}}_{\psi,V}}^{n}\right)^H{\widetilde{\mathbf{H}}_{\psi,V}}^{n,r}\right)^{... | 3,105 | 2,238 | 1,606 | 3,068 | 1,632 | 0.787378 | github_plus_top10pct_by_avg |
si\right>}$ on the carrier space of $D^{{\left(s\right)}}$.
In general, in order to break the Bell inequality it is necessary to consider a number of orbits. To this end one considers the orbits generated by $N$ pairs of vectors ${\left({\left|\varphi_n\right>},{\left|\psi_n\right>}\right)}$ and the corresponding oper... | 3,106 | 4,466 | 2,837 | 2,759 | null | null | github_plus_top10pct_by_avg |
\int_{\Gamma_-} g(y,\omega,E)^2 \tau_-(y,\omega)|\omega\cdot\nu(y)|d\sigma(y) d\omega dE \\
={}&{\left\Vert g\right\Vert}_{T^2_{\tau_-}(\Gamma_-)}^2,$$ where in the second step we applied the change of variables in integration explained in the proof of Theorem \[tth\] below (see Remark \[changevar\]), and noticed that ... | 3,107 | 2,757 | 2,169 | 2,754 | null | null | github_plus_top10pct_by_avg |
\frac{ \log n}{n} \log ^4 k\right)^{1/6} \quad \text{and} \quad
\tilde{\Delta}_{n,3} = \min \left\{ \Delta_{n,3}, \frac{U^2}{v} \overline{v} \frac{ k^{5/2}}{u_n^3 u^2} \frac{
\log n}{n} \log k \right\}.$$
A few remarks are in order.
The coverage probability is affected by three factors: the term $\Delta_{n,1}$, ... | 3,108 | 2,714 | 2,192 | 2,728 | null | null | github_plus_top10pct_by_avg |
mathbb{Z} \times \{0\})$.
Hence $T$ tiles $X_2$.
$S_1 \cup S_2 \cup S_3$ can be partitioned into sets of the form $S = \{x_1, x_2, x_3\}$, where $x_1 = (x,y) \in S_1$, $x_2 = (x+4,y+4) \in S_2$, $x_3 = (x+2,y+3) \in S_3$. Then $|S| = 3$, so we can construct the corresponding set $Y \subset \mathbb{Z}^3$ as in Lemma \... | 3,109 | 2,576 | 2,900 | 2,711 | 1,542 | 0.788479 | github_plus_top10pct_by_avg |
ex combination of observed features and membership distributions. We present an expectation-maximization based inference algorithm that learns latent variables and parameters iteratively, a scalable stochastic variation of the inference algorithm, and a method to learn the weights of HL-MRF structured priors. We evalua... | 3,110 | 2,621 | 783 | 3,081 | 2,894 | 0.776254 | github_plus_top10pct_by_avg |
1
20 30 1 6
25 6 0 1... | 3,111 | 6,875 | 1,263 | 1,271 | null | null | github_plus_top10pct_by_avg |
})
&h(\widetilde{{\mbox{\tiny\yng(1)}}})/h(\widehat{{\mbox{\tiny\yng(1)}}})
\end{pmatrix}\\
&=& (v_1\ v_2)
\begin{pmatrix}
\frac{Q}{Q-1} &\frac{Q}{Q-1}\\
\frac{Q(Q-2)}{Q-1} &\frac{Q(Q-2)}{Q-1}
\end{pmatrix}
\\
\rho(e_i)(v_3\ v_4) &=& (v_3\ v_4)
\begin{pmatrix}
h(\widetilde{{\mbox{\tiny\yng(2)}}})/h(\wid... | 3,112 | 582 | 2,371 | 3,201 | null | null | github_plus_top10pct_by_avg |
enient here, as we investigate linearity and reversibility. At the beginning, the three systems are in the state $|\Phi\rangle_A \otimes |\sigma\rangle_{BC}$. The probability of the outcome $q$ under consideration is given by $$\begin{aligned}
p_q(|\Phi\rangle_A) &=& \left\| \strut [(|\sigma_q\rangle_{AB}
\,_{AB}\l... | 3,113 | 5,646 | 345 | 2,522 | null | null | github_plus_top10pct_by_avg |
ensions. It turns out that a derivator is stable if and only if homotopy finite colimits and homotopy finite limits commute, and there are variants using suitable Kan extensions.
We begin by collecting the following characterizations which already appeared in the literature.
\[thm:stable-known\] The following are equ... | 3,114 | 2,974 | 2,854 | 2,625 | 2,120 | 0.782585 | github_plus_top10pct_by_avg |
ion of the functor $T_1$. The proof that $h^{-1}\cdot Y$ satisfies the first two conditions is similar to that of Lemma 3.7 of [@C2] and the rest is similar to the above case. Thus we skip them.
For (2), by using the argument explained from the last paragraph of page 479 to the first paragraph of page 480 in [@C2], it... | 3,115 | 2,313 | 1,803 | 2,910 | null | null | github_plus_top10pct_by_avg |
ly the axial symmetry as does a Dirac mass term, but also the above vector symmetry under phase transformations. Hence, a Majorana mass term leads to a violation of the fermion number, again a reason why such a possibility may be contemplated for neutrinos only within the Standard Model of the quarks and leptons and th... | 3,116 | 3,683 | 2,669 | 3,005 | null | null | github_plus_top10pct_by_avg |
$c(\sigma_{2},\sigma_{1})$ $\ldots$ $c(\sigma_{n-1},{\sigma_{1}\sigma_{2}\ldots\sigma_{n-2}})$ $c(\sigma_{n},{\sigma_{1}\sigma_{2}\ldots\sigma_{n-1}})$ $c(\sigma_{n+1},{\sigma_{1}\sigma_{2}\ldots\sigma_{n}})$ $c(\sigma_{n+2},\sigma_{2}\sigma_{3}\ldots\sigma_{n+1})$ $c(\sigma_{n+3},\sigma_{3}\sigma_{4}\ldots\sigma_{n+2}... | 3,117 | 3,562 | 2,946 | 2,871 | null | null | github_plus_top10pct_by_avg |
The baseline body weights and blood glucose levels of the gerbils are shown in Table [1](#T1){ref-type="table"}. No significant differences among the various groups were evident.
######
Baseline characteristics of tested gerbils^1^.
**All tested gerbils** **Gerbils in phase C** ... | 3,118 | 4,164 | 3,203 | 2,957 | null | null | github_plus_top10pct_by_avg |
leq &\left\vert \mu \right\vert ({\mathbb{R}}^{d})\times (2^{2hl(\delta
)}\theta (n_{\ast }))^{\rho _{h}(1+\delta )}=A(\delta )\theta (n_{\ast
})^{\rho _{h}(1+\delta )}.\end{aligned}$$If $l\geq l_{\ast }$ then $n(l)\geq n(l_{\ast })\geq n_{\ast }$ so that, from (\[reg11\]), $$d_{k}(\mu ,\mu _{n(l)})\leq \frac{C_{h,n_{\... | 3,119 | 1,293 | 776 | 3,208 | null | null | github_plus_top10pct_by_avg |
les.
First, we shall consider a vector bundle on a trivial gerbe. Consider a vector bundle $V \rightarrow \mathfrak{X} \equiv
X \times B {\mathbb Z}_k$, so $V = p_1^* E \otimes p_2^* \zeta$ for some bundle $E \rightarrow X$ and representation $\zeta \in {\mathbb Z}_k^{\vee}$.
The inertia stack $I_{\mathfrak{X}}$ is g... | 3,120 | 2,850 | 2,553 | 2,820 | null | null | github_plus_top10pct_by_avg |
{d-1} d\rho d\omega \nonumber \\
& \lesssim 1 + \lambda^{d-\gamma}. \label{ineq:KL1loc}\end{aligned}$$ Similarly, if $\gamma = d$, then for large $\lambda$, $$\int \lambda^d{\left\vert{\nabla}{\mathcal{K}}(\lambda y)\right\vert}\mathbf{1}_{B_1(0)}({\left\verty\right\vert}) dy \lesssim 1 + \log \lambda. \label{ineq:KL1... | 3,121 | 2,090 | 901 | 3,048 | null | null | github_plus_top10pct_by_avg |
the annular chamber.](method.eps){width="7cm"}
Experimental Results
====================
We investigated the velocity of the camphor boat on the solutions of various glycerol concentration $p$. The position of the camphor boat is described as a radial angle $\theta$ in the annular chamber, as shown in Fig. \[fig:vel... | 3,122 | 272 | 2,723 | 3,295 | 4,077 | 0.768241 | github_plus_top10pct_by_avg |
ing the CLUSTAL X program [@pone.0041904-Thompson1] and alignment is available from the authors upon request.
10.1371/journal.pone.0041904.t001
###### HIV-1 subtype C sequences.
{#pone-0041904-t001-1}
African region Country *N* Sampling date
---------------- -... | 3,123 | 5,403 | 2,209 | 2,209 | null | null | github_plus_top10pct_by_avg |
hi}}_{m,n}\right) = \prod_{i=0}^{N-1}\phi^{(i)}_{m,n}=1.\end{gathered}$$
We can then show that the Lax pair (\[eq:LP-ir-g-rat\]) is compatible if and only if the system (\[eq:dLP-gen-sys-1\]) holds.
Differential-difference equations as symmetries {#continuous-defs}
===============================================
Her... | 3,124 | 2,284 | 3,211 | 3,064 | null | null | github_plus_top10pct_by_avg |
B$ has two disjoint edges, we can use a similar argument for $\cAp$, so suppose $\cBp$ is intersecting. Without loss of generality, suppose $\cBp= \{xy^\pr,y^\pr y\}$. Then $\cAp\sse \{xy, x^\pr y^\pr\}\cup \{A\in \binom{[n]}{2}:y^\pr\in A\}$, giving the bound $|n(\cAp)|\geq |\cAp|$. This completes the proof of the cla... | 3,125 | 2,020 | 1,909 | 2,813 | null | null | github_plus_top10pct_by_avg |
z_1,z_2,z_3)}(z_1,z_2,z_3)+\eta(z_1,z_2,z_3)(\overline{z_1},\overline{z_2},\overline{z_3})].$$
The projection $\Pi$ is $\PO(2,1)$-equivariant.
Let $A\in O(2,1)$ and $[z]\in \Bbb{H}_{\Bbb{C}}^2$. Then $$\begin{array}{ll}
\Pi [Az] &=[\overline{ \eta(Az)}Az+\eta(Az)\overline{Az}]\\
&=[\overline{\sqrt{-<A z, Az>... | 3,126 | 2,274 | 2,666 | 2,735 | 3,675 | 0.770779 | github_plus_top10pct_by_avg |
\left\lvert \frac{C}{b} \right\rvert^{\frac{1}{a}} \right) \\
&\quad - \frac{(k_{1} + k_{2})^{2} C^{2}}{4 \G(a)^{2}}
\g\left(a, \left\lvert \frac{C}{b} \right\rvert^{\frac{1}{a}} \right)^{2}
- \frac{(k_{1} + k_{2})^{2} b^{2}}{4 \G(a)^{2}}
\G\left(2a, \left\lvert \frac{C}{b} \right\rvert^{\frac{1}{a}} \right)^{2} \\
&... | 3,127 | 4,867 | 2,140 | 2,463 | null | null | github_plus_top10pct_by_avg |
1-\alpha)\mu t\right]}}{\leqslant}c||\rho||_\pi \,{\mathrm{e}}^{-\alpha^2\mu t/72 T}$ for $0{\leqslant}\alpha{\leqslant}1$.
Let $\Omega$ be the vertex set of the $R$-dimensional torus $\Gamma(n, R)$ and let $a$ and $b$ denote two arbitrary agents. By definition of the communication graph process, agents $a$ and $b$ ar... | 3,128 | 2,677 | 2,975 | 2,753 | 1,952 | 0.784182 | github_plus_top10pct_by_avg |
urrent. These terms were already considered in [@Ashok:2009xx] and it is straightforward to show that they do not modify . The second set contains the terms that multiply composites of (derivatives of) several currents (not including the regular terms). This includes for instance the current bilinears in equation . The... | 3,129 | 968 | 2,397 | 3,050 | 3,418 | 0.772538 | github_plus_top10pct_by_avg |
common empirical orders (EM1 for Chinese pupils and EM2 for LCSL). (a) Number of characters is set as the learning goal. (b) Accumulated usage frequency is set as the learning goal. $C_{min}$ is defined as the learning cost of $1775$ characters using the NOO method and it will be used in discussion of leaning efficienc... | 3,130 | 2,078 | 1,441 | 2,462 | null | null | github_plus_top10pct_by_avg |
ined by the Jacobi identity[@Hosseiny:2014dxa]. There are various kinds of extensions, which we list here in order.
- $T$-extension is always allowable: $$\left[L_n,L_m\right]= (n-m)L_{n+m}+\frac{c_T}{12}n(n^2-1)\delta_{n+m,0}.$$ This gives the Virasoro algebra.
- $B$-extension is only allowable for $\ell=1$: $$\... | 3,131 | 1,615 | 1,557 | 2,893 | null | null | github_plus_top10pct_by_avg |
rho_{\text{DM}}}{0.3 \, \frac{\text{GeV}}{\text{cm}^3}}}\right)$$ oscillating at a frequency equal to the ALP mass $m_a \sim$ kHz - GHz. The expected coherence time for this oscillation is set by the ALP coherence time $\tau_a \sim \frac{1}{m_a v^2} \sim 1 \text{ s} \, \left(\frac{\text{MHz}}{m_a}\right)$, leading to ... | 3,132 | 2,058 | 3,856 | 3,114 | null | null | github_plus_top10pct_by_avg |
any $j\in \mathcal{B}_2$. Here $k_j$ is the integer associated to $j$ defined in the paragraph before Equation (\[32’\]). We claim that $\widetilde{G}^{\ddag}_{\mathcal{B}_1, \mathcal{B}_2}$ is represented by a smooth closed subscheme of $ \mathrm{Ker~}\tilde{\varphi}/\tilde{M}^1$ and is isomorphic to $ \mathbb{A}^{l^{... | 3,133 | 2,309 | 1,441 | 2,915 | 2,513 | 0.779229 | github_plus_top10pct_by_avg |
indler trajectory of uniform linear acceleration of magnitude $g>0$, and $|\Psi\rangle$ is the Minkowski vacuum, the transition rate becomes [@schlicht] $${\dot {\cal F}}(\omega) = \frac{1}{2 \pi} \; \frac{(\omega /g)}{1+ \epsilon^2} \; \frac { e^{\frac{2\omega }{g} \tan^{-1}\left( g \epsilon \right)}}
{
e^{\frac{2 \... | 3,134 | 1,277 | 2,513 | 3,121 | 3,486 | 0.772019 | github_plus_top10pct_by_avg |
}s}\cdot{\frac{{d}}{{d}\tau}}\varphi(y+\tau\omega,\omega,E) {d}\tau \\
={}&\Big(e^{-\int_{t}^\tau\Sigma(y+s\omega,\omega,E){d}s}
\varphi(y+\tau\omega,\omega,E) \Big|_{\tau=t}^{\tau=b^i_{y,\omega}} \Big) \\
&+\int_t^{b^i_{y,\omega}} \Sigma(y+\tau\omega,\omega,E)e^{-\int_{t}^\tau\Sigma(y+s\omega,\omega,E){d}s}
\varphi(y+... | 3,135 | 2,000 | 2,098 | 2,771 | null | null | github_plus_top10pct_by_avg |
\xi_n \rbrace}({\mathit{s}}))$ is indeed a process per definition \[D:PROCESS\].
Definition \[D:PROCESS\] asserts that a process is a successively conjoint sequence of frames. To show contradiction, hypothesize that the frame sequence $\overline{\mho}_{\mathbf{F}}({\mathfrak{A}}^{\mathbb{N}}_{\lbrace \xi_n \rbrace}({... | 3,136 | 1,460 | 1,752 | 3,138 | null | null | github_plus_top10pct_by_avg |
n Fig.1. A simple calculation gives the following correction $\delta Q_W/Q_W=\delta_{cd}$ related to this renormalization $$\label{cd}
\delta_{cd}={{4\alpha Z}\over{3\pi Q_W}}
(1-4\sin^2\theta_W)\ln(\lambda_C/r_0)\approx -0.1\%.$$ Where $\theta_W\approx $ is the Weinberg angle, $\sin^2\theta_W\approx
0.2230$, see Ref. ... | 3,137 | 1,799 | 2,855 | 3,036 | null | null | github_plus_top10pct_by_avg |
gin{aligned}
{\boldsymbol{F}}^{(0)}(t)=
-\frac{g_p}{\pi^2a^2}\int d{\boldsymbol{z}} e^{-\frac{z^2}{2 a^2}} \int d{\boldsymbol{z}}' K_0(2|{\boldsymbol{z}}-{\boldsymbol{z}}'|)
\left[\left(\partial_t-{\boldsymbol{V}}_p\cdot\nabla_{{\boldsymbol{z}}'}-\frac{\gamma}{2}\nabla^2_{{\boldsymbol{z}}'}\right)\delta{\boldsymbol{w}}... | 3,138 | 2,684 | 3,080 | 2,931 | 2,013 | 0.78353 | github_plus_top10pct_by_avg |
g:=Range("$k$20:$k$1000"), strFormulaR1C1:="=and(R[]C7=""6. Negotiate"",R[]C11<25)", intColorIndex:=3
fctApply rng:=Range("$k$20:$k$1000"), strFormulaR1C1:="=and(R[]C7=""4. Develop"", R[]C11<15)", intColorIndex:=3
fctApply rng:=Range("$k$20:$k$1000"), strFormulaR1C1:="=and(R[]C7=""5. Prove"", R[]C11<20)", intCo... | 3,139 | 7,708 | 128 | 1,164 | 77 | 0.828315 | github_plus_top10pct_by_avg |
s.pdf "fig:"){width="\linewidth"}
A more detailed depiction of the previous reliability diagrams can be seen in Figure \[fig:nb:pos:scores:class\]. In this case, the posterior probabilities are not introduced in bins, but a boxplot summarises their full distribution. The first observation here is, for the *good* and *... | 3,140 | 2,240 | 2,518 | 2,010 | null | null | github_plus_top10pct_by_avg |
999.
E.Gross, A.L.Read and D.Lellouch, CERN-EP/98-094.
P.Janot in [*Proceedings of the Workshop on LEP-SPS Performance*]{}, Chamonix IX, Jan. 1999, 222.
---
author:
- Wensheng Cheng
- Yan Zhang
- Xu Lei
- Wen Yang
- Guisong Xia
bibliography:
- 'segmentation.bib'
- 'change\_detection.bib'
title: Semantic Change Patt... | 3,141 | 1,258 | 2,522 | 3,181 | null | null | github_plus_top10pct_by_avg |
$n^{0.6}$) 0.313 0.313 0.319 0.311 0.311 0.316 0.313
BLB($n^{0.8}$) 0.097 0.096 0.098 0.096 0.097 0.097 0.098
SDB($n^{0.6}$) 0.370 0.370 0.370 0.370 0.369 ... | 3,142 | 5,516 | 1,306 | 2,351 | null | null | github_plus_top10pct_by_avg |
="table"}** for the descriptive data of latency and error rate.
######
Working memory capacity and attentional control in Experiment 1 (means, with standard deviations in parentheses).
Indicators Low WMC High WMC
------------------------- ----------... | 3,143 | 2,163 | 4,022 | 3,186 | 1,260 | 0.791959 | github_plus_top10pct_by_avg |
$1$ $2.0$ $2.26$ $2.27$ $4.5$
$2$ $2.4$ $1.92$ $1.95$ $3.9$
$3$ $2.8$ $1.60$ $1.62$ $3.2$
$4$ $3.2$ $1.26$ $1.29$ $2.5$
$5$ $3.6$ $0.90$ ... | 3,144 | 3,457 | 3,606 | 3,164 | 1,955 | 0.784163 | github_plus_top10pct_by_avg |
erent transmit power to noise ratios are considered, i.e., $\rho=0$ dB and $\rho=10$ dB. The transmit powers of $30$ dBm and $40$ dBm are considered based on the existing studies on mmWave systems [@Khan5876482; @Pi11Aninmmvmbs; @akdeniz2014millimeter]. We note that the Gaussian approximations match the simulated PDFs.... | 3,145 | 900 | 2,353 | 3,041 | 2,927 | 0.776031 | github_plus_top10pct_by_avg |
:={}&\int_0^E{1\over{S_0(\tau)}}d\tau, \\[2mm]
\tilde f(x,\omega,\eta):={}& S_0(R^{-1}(\eta))f(x,\omega,R^{-1}(\eta)).$$ We find that there exists a constant $C_1>0$ such that \[inv\] \_[L\^2(GSI)]{}C\_1[f]{}\_[L\^2(GSI)]{}.
Let ${ f}\in L^2(G\times S\times I)$ and let $\{f_n\}\subset C_0^\infty(G\times S\times I^\cir... | 3,146 | 1,596 | 1,592 | 3,065 | null | null | github_plus_top10pct_by_avg |
bjects commute with left Kan extensions). And semi-additive derivators are precisely the left or right $\mathsf{FINDISC}$-stable ones, where $\mathsf{FINDISC}$ is the class of finite discrete categories. In general, this notion of “relative stability” yields a Galois connection between collections of derivators and cla... | 3,147 | 3,912 | 3,481 | 3,008 | null | null | github_plus_top10pct_by_avg |
nd spiral antennas. Furthermore, and exploiting the unique capabilities of CL excitation, we measured the emission from metals and semiconductors. For these materials, we can separate coherent and incoherent emission mechanisms, with further applications in nanoscale materials science.
CL Polarimetry
==============
!... | 3,148 | 2,073 | 3,939 | 3,290 | null | null | github_plus_top10pct_by_avg |
\ .$$ Thus likewise for the fermionic algebra, let us take $$b=\frac{\partial}{\partial\theta}\ \ \ ,\ \ \ b^\dagger=\theta\ ,$$ where it is understood that all derivatives with respect to Grassmann odd variables are taken from the left (left-derivatives). Consequently the supersymmetry generators are represented by $$... | 3,149 | 3,873 | 3,181 | 2,845 | null | null | github_plus_top10pct_by_avg |
\phi\rangle|^2) \,h_\alpha^{\dag}
h_\beta \;\;\label{eq:lagrangian}$$ where $\phi$ is the Standard Model Higgs doublet, and $i$ is summed over the down quark flavors ($i=d,s,b$). The vector quark has purely vectorial coupling to the photon and $Z$ boson, with respective charges $(Q_Q, -Q_Q \sin^... | 3,150 | 1,738 | 2,633 | 2,954 | null | null | github_plus_top10pct_by_avg |
)/(K_iL_i-1,K_\beta ^{{b^{}}(\beta )}-1\,|\,i\in I,
\beta \in R^\chi _+),$$ where ${b^{}}(\beta )$ is the order of $q^{(\beta ,\beta )}$ for all $\beta \in R_+$, is isomorphic to Lusztig’s small quantum group $u_q({\mathfrak{g}})$. This was observed *e.g.* in [@inp-AndrSchn02 Thm.4.3] by referring to results of Luszti... | 3,151 | 2,605 | 2,705 | 2,953 | 3,746 | 0.770391 | github_plus_top10pct_by_avg |
" 17
" Tampa " 9
Miami " 2
" Governor's Island " 14
" Bedloe's Island " 3
" Seavey's Island " 3
" For... | 3,152 | 5,716 | 1,353 | 2,063 | null | null | github_plus_top10pct_by_avg |
act, the first equation in is equivalent to $
\frac{2(\gamma-1)}{a}\eta(t)=\frac{\sigma'}{\sigma}+2\gamma{\kappa}.
$ Put this into the last two equations in , we have $$\left\{
\begin{array}{rl}
(\sigma\alpha)'=&\sigma'+2\gamma{\kappa}\sigma\\
(\sigma\varphi)'=&\frac{a\sigma}{4}\Big(\frac{\sigma'}{\sigma}+2\gamma{\ka... | 3,153 | 2,079 | 2,397 | 2,911 | null | null | github_plus_top10pct_by_avg |
\[fig:distrib\]a–c. The parameter sets of the model are given in Table \[tab:th\]; sets 1 and 2 correspond to small scattering length ($a=-4$ fm) and different weights of $s$-wave (largest and lowest possible), set 3 has $a=-25$ fm and largest possible weight of $s$-wave. It can be seen that the agreement with the dat... | 3,154 | 1,147 | 2,378 | 2,961 | null | null | github_plus_top10pct_by_avg |
must have $2 h=2v'-v\in
L$. The length of the nonzero vector $2h$ must then be at least $\mu(L)$. Since $|h|={\operatorname{area}}(L)/|v|$ this gives $2{\operatorname{area}}(L)/|v|\geq \mu(L)$, that is $$|v|\leq \frac{2{\operatorname{area}}(L)}{\mu(L)}$$ Hence $v'$ is uniquely determined if $|v|>2{\operatorname{area}}(... | 3,155 | 4,464 | 3,106 | 2,737 | null | null | github_plus_top10pct_by_avg |
suppression due to the large energy denominators is not fully effective. In this region outside validity of the theorem we show that second order correction terms in $W$, together with the leaking term $\mathcal{C}_{\alpha \beta}$, may not be totally negligible, and it could be detectable. If it were the case, it coul... | 3,156 | 1,310 | 3,027 | 3,191 | null | null | github_plus_top10pct_by_avg |
{1/2}\lambda_{DE}\right)^3 \int
d^3\mathbf{{u}}
&{}&
\Bigg\{
\frac{1}{2\alpha_\Lambda}
\Bigg\vert \mathbf{\nabla}
\left(\frac{\Lambda_{DE}}{8\pi\rho}\right)^{\alpha_\Lambda}
\Bigg\vert^2
-
\frac{\alpha_\Lambda}{\alpha_\Lambda-1}
\left(\frac{\Lambda_{DE}}{8\pi\rho}\right)^{\alpha_\Lambda-1}... | 3,157 | 4,075 | 2,683 | 2,778 | null | null | github_plus_top10pct_by_avg |
onumber\\
&(-a^2m^2+1/10e^4)r+a^2e^2m)\alpha r^5\cos(\theta)+(-2a^2\alpha^2m^2+2m^2)r^7-5e^2 mr^6+3e^4r^5\Big)(r\alpha \cos(\theta)-1)^5\bigg).\end{aligned}$$
In FIG. \[fig7\] we have shown the variation of the gravitational entropy density with the radial distance and the acceleration parameter using this new defini... | 3,158 | 1,934 | 2,683 | 3,075 | 3,310 | 0.773276 | github_plus_top10pct_by_avg |
nts of $D$ and $B$ decays. For a review of the $\Delta I=1/2$ rule see e.g. Ref. [@Buras:2014maa].
In kaon physics we consider $K \to\pi\pi$ decays. Employing an isospin parametrization we have [@Buras:2014maa] $$\begin{aligned}
{\mathcal{A}}(K^+\rightarrow \pi^+\pi^0) &= \frac{3}{2} A_2^K e^{i\delta_2^K}\,, \nonumber... | 3,159 | 3,220 | 3,303 | 2,918 | 1,563 | 0.788222 | github_plus_top10pct_by_avg |
Z^* {\mathcal H}_1^0$ for ${\mathcal H}_1^0 \simeq \eta^0_r$.
[^6]: If $\lambda_{s\eta 1}$ is small, ${\mathcal H}_2^0$ ($\simeq \eta_r^0$) decays into $Z^\ast {\mathcal A}^0$.
---
author:
- '**[Sarbari Guha and Samarjit Chakraborty]{}**'
title: '[**On the gravitational entropy of accelerating black holes** ]{}'
---... | 3,160 | 1,431 | 1,345 | 3,136 | null | null | github_plus_top10pct_by_avg |
tructions by using the MV code construction and then asking each server for the evaluations of $F$ at a point, as well as the values of a certain differential operator (similar to first order derivatives) at these points. For this to work we need two ingredients. The first is to replace the field $\F_q$ with a certain ... | 3,161 | 1,185 | 1,640 | 3,067 | 1,306 | 0.791343 | github_plus_top10pct_by_avg |
xtended Lagrange multipliers i.e. $V^{ext} = v_{a} H^{a} + v_{\mu }Z^{\mu}$ and $F^{ext}_{ab}= {\operatorname{Tr}}([ H_{a}, H_{b}]^{ext} V^{ext})$.
Applications {#sec:examples}
============
Let us now turn to specific examples for which we construct the dual RR fluxes corresponding to various centrally-extended non-a... | 3,162 | 1,997 | 963 | 3,214 | 3,509 | 0.771859 | github_plus_top10pct_by_avg |
trix} id&0\\ 0&(w)_1 \end{pmatrix}$. Note that $\mathrm{O}(A(2\delta, 2b, 1)/\pi A(2\delta, 2b, 1), \bar{q_i})(\kappa)$ is not contained in $\mathrm{SO}(L_i/\pi L_i, \bar{q_i})(\kappa)$. Thus it suffices to show that the restriction of $\varphi_i(\kappa)$ to the above subgroup of $H_i(\kappa)$, which is given by lettin... | 3,163 | 2,234 | 2,552 | 2,742 | null | null | github_plus_top10pct_by_avg |
Assume that $Y$ has the Chevalley-Kleiman property and let $P\subset X$ be a finite subset. Since $\pi(P)\subset Y$ is finite, there is an open affine subset $Y_P\subset Y$ containing $\pi(P)$. Then $g^{-1}(Y_P)\subset X$ is an open affine subset containing $P$.
Conversely, assume that $X$ has the Chevalley-Kleiman pr... | 3,164 | 2,372 | 2,730 | 2,862 | 3,664 | 0.770836 | github_plus_top10pct_by_avg |
does not divide $i_G(x) $ for every element of prime power order $x\in A\cup B$ if and only if $G$ has a central Sylow $p$-subgroup, i.e. $G=O_p(G) \times O_{p'}(G)$ with $O_p(G)$ abelian.
Our results provide an improvement of [@BCL Theorem 1.1] in the case of only two factors, since in that paper products of $n$ pair... | 3,165 | 1,875 | 1,488 | 3,059 | null | null | github_plus_top10pct_by_avg |
e construction of $G'$. There is a ‘universal’, ‘maximal’ extension $\tilde{G}_{\rm max}$, which extends $G$ by the group of all automorphisms of the total space of ${\cal E}$ that cover the action of the elements of $G$ on $X$. It fits into a short exact sequence $$1 \: \longrightarrow \: {\rm Aut}({\cal E}) \: \longr... | 3,166 | 2,911 | 2,783 | 2,630 | null | null | github_plus_top10pct_by_avg |
\(5\) C (O) 0.41\*\*\* 0.60\*\*\* 0.50\*\*\* 0.68\*\*\* --
\(6\) R (O) 0.32\*\* 0.35\*\*\* 0.67\*\*\* 0.52\*\*\* 0.63\*\*\* --
\(7\) PSC 0.24\*\* 0.50\*\*\* 0.33\*\*\* 0.50\*\*\* 0.62\*\*\* 0.46\*\*\* --
\(8\) ... | 3,167 | 666 | 2,739 | 3,065 | null | null | github_plus_top10pct_by_avg |
t the situation is with getting that Tenaska agreement signed? it is on a list to be assigned to HPL in the sale and I don't think it has ever been executed--I know you left me a message a week or so ago about this--is there any information that i owe you ?
can you take care of these---I have no idea what this or th... | 3,168 | 1,713 | 1,967 | 3,479 | null | null | github_plus_top10pct_by_avg |
ian comparison theorem yields the additional error term $C \mathrm{E}_{2,n} +
\frac{1}{n}$ given in , for some universal positive constant $C$. Similarly, can be established along the lines of the proof of , starting from the bound . In this case we pick up an additional error term $C \tilde{\mathrm{E}}_{2,n} + \frac{... | 3,169 | 3,749 | 2,614 | 2,706 | 3,488 | 0.772012 | github_plus_top10pct_by_avg |
. The virial radius is 264 $h^{-1}$ comoving kpc and is indicated by the white circles.
In Fig. \[fig:haloradz2\] we show the same quantities as in Fig. \[fig:halo\] as a function of radius for the haloes with $10^{11.5}$ M$_\odot<M_\mathrm{h... | 3,170 | 1,246 | 3,187 | 3,128 | null | null | github_plus_top10pct_by_avg |
DE which is separable in $r$ and $\bar{r}$. It is therefore equivalent to the system
\[eq:4.15\] (a)2-3=,(b)2 -3=,
where $\Omega$ is a real separation constant. Equation (\[eq:4.15\].b) can be solved in a way similar way to (\[eq:4.15\].a). Defining
\[eq:4.16\] g(r)=h\^[(1)]{}(r),
equation (\[eq:4.15\].a) can be wr... | 3,171 | 5,636 | 3,452 | 2,644 | 4,056 | 0.768417 | github_plus_top10pct_by_avg |
{1pt}{\text{\circle*{1.5}}}}}(A),\\
HP_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(\overline{A_\#}) &\to HP_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}({\widehat}{A_\#}),
\end{aligned}$$ and the cone of the first map is isomorphic to $HP_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(j_!M^\Delta_\#)$. Since $j_!$ is exact, w... | 3,172 | 2,801 | 2,484 | 2,867 | 2,924 | 0.776055 | github_plus_top10pct_by_avg |
to $\cS$ to create a larger star. If $|D|\ge 2$ then for any $d\in D$ we have that $\cI\cup\{S\setminus\{d\}\mid S\in\cS\}$ is a larger intersecting subfamily of $\cH$ than $\cI$, a contradiction. Therefore $|D|=1$ and, without loss of generality, $D=\{1\}$.\
Let $\cF$ be the largest sunflower in $\cS$ with core $\{1\}... | 3,173 | 2,159 | 2,306 | 2,859 | null | null | github_plus_top10pct_by_avg |
non-saturated sets from the preimage topology. It is therefore possible to rewrite Eq. (\[Eqn: IT\]) as
$$U\in\textrm{IT}\{ e;\mathcal{V}\}\Longleftrightarrow e(U)=V\textrm{ if }V\in\mathcal{V}_{\textrm{comp}},\label{Eqn: IT'}$$
and to compare it with the following criterion for an *injective, open-continuous* *map*... | 3,174 | 3,028 | 3,314 | 3,040 | 1,757 | 0.785923 | github_plus_top10pct_by_avg |
_1|e_3)&(z_1|e_4)\\
(z_2|e_1)&(z_2|e_2)&(z_2|e_3)&(z_2|e_4) \end{pmatrix}
\begin{pmatrix} p\\q\\r\\s\end{pmatrix} &=
\begin{pmatrix} (e_5|b_3)\\
(e_6|b_3)\\
(z_1|b_3)\\
(z_2|b_3)
\end{pmatrix}.\nonumber\end{aligned}$$
Writing the projectors as matrix equations given above entails solving systems of linear equations. T... | 3,175 | 1,012 | 2,982 | 3,086 | 3,574 | 0.771468 | github_plus_top10pct_by_avg |
, \ t\in(0,1],\end{aligned}$$ where $B$ is a standard Brownian motion in a filtered probability space $(\Omega,\mathcal{F}, \mathbb{F}, P)$.
Denote as $\Sigma_G$ the collection of all smooth functions $\sigma: [0,1]\times\mathbb{R}\rightarrow [\underline{\sigma},\overline{\sigma}]$ with $$\sup\limits_{(t,x)\in[0,1]\ti... | 3,176 | 1,889 | 430 | 3,261 | null | null | github_plus_top10pct_by_avg |
, filtered by order of differential operators, such that*
1. there is an equivalence of categories $U_c {\text{-}{\textsf}{mod}}\simeq B{\text{-}{\textsf}{qgr}}$;
2. there is an equivalence of categories $\operatorname{gr}B{\text{-}{\textsf}{qgr}}\simeq \operatorname{{\textsf}{Coh} }(\operatorname{Hilb(n)})$.
{#i... | 3,177 | 2,062 | 1,818 | 3,078 | 2,392 | 0.780244 | github_plus_top10pct_by_avg |
ion to its variance. Practical applications of principal portfolios have already been considered by several authors, for example, Poddig and Unger (2012) and Kind (2013).
In this paper we present a perturbative calculation of the principal portfolios of the single-index CAPM in the large $N$ limit. The results of this... | 3,178 | 2,376 | 3,140 | 2,663 | null | null | github_plus_top10pct_by_avg |
differential equations, it is interesting to note that the property of order 4 perfect squares is preserved here : these two terms are such that their higher order terms cancel perfectly, what makes their associated equations of motion second order. For example the term : $$\begin{aligned}
\begin{split}
\sqrt{-g} \; ... | 3,179 | 4,659 | 2,436 | 2,535 | null | null | github_plus_top10pct_by_avg |
t the range $R(I+ P_0)$ is dense that is, \[evo17-a\] =L\^2(GSI).
As in the proof of Lemma \[csdale0\] (note that here the assumptions are somewhat weaker), we have for all $\phi\in D(P_0)$, (we write $L^2=L^2(G\times S\times I)$) \[ineq\] & P\_0,\_[L\^2]{} =-[E]{},\_[L\^2]{} +\_x,\_[L\^2]{}+ CS\_0,\_[L\^2]{}\
=& (-+C... | 3,180 | 1,300 | 2,523 | 3,146 | null | null | github_plus_top10pct_by_avg |
c{16}{64}=0,25$.\
Note that the optimal strategy saturating this limit always exists. To see this let $\alpha={\left(\underline{a}_1,\ldots,\underline{a}_8,\underline{b}_1,\ldots,\underline{b}_8\right)}$ be one of configurations for which $c(\alpha)$ attains its maximal value. Then the Bell inequality is saturated for ... | 3,181 | 3,864 | 3,671 | 3,034 | null | null | github_plus_top10pct_by_avg |
e $\xi_{\rm neq} g'(x)$ is a multiplicative contribution due to nonlinear coupling to {$q_k$}-subsystem. It is thus important to note that the presence of multiplicative noise and a fluctuating barrier are associated with nonlinearity in $g(x)$.
Second, the Langevin equation (12) is non-Markovian. The origin of this n... | 3,182 | 4,010 | 3,097 | 2,999 | 2,648 | 0.778166 | github_plus_top10pct_by_avg |
as discussed in the previous section, would have real entries such that $\alpha =
1$ and $\beta = 2$, and thus the limiting spectral distribution $$\label{E:GOE-limit}
(1-p) {\mathcal{N}}(0,1) + p {\mathcal{N}}(0,2).$$ The slightly simpler nature of this limiting distribution (note that the parameter $p$ plays only one... | 3,183 | 1,992 | 3,022 | 2,741 | null | null | github_plus_top10pct_by_avg |
\beta_{k-1}$ and the nonzero eigenvalues of $\mathbf{A}=\mathbf{X}^T\mathbf{X}$ are $\alpha_1>\alpha_2>\cdots>\alpha_{k}$. Further suppose that for $1\le i\le k-1$ we have $\beta_i\ne\alpha_i$ and $\beta_i\ne\alpha_{i+1}$. Then the eigenvector $\mathbf{b}_i$ of $\mathbf{B}$ can be written by $$\mathbf{b}_i=\sum_{j=1}^k... | 3,184 | 2,869 | 3,348 | 2,864 | null | null | github_plus_top10pct_by_avg |
it, and all the higher components $M_\#([n])$, $n \geq
2$, together with the transition maps $\iota_f$, can be recovered from $M_\#([1])$ and this extra structure.
Return now to the abelian situation: we are given an associative unital algebra $A$ over a field $k$, and our monoidal category is ${{\mathcal C}}= A{\ope... | 3,185 | 2,179 | 2,675 | 2,888 | 2,187 | 0.781936 | github_plus_top10pct_by_avg |
)\phi)(x,\omega)=\int_S\ol\sigma(x,\omega',\omega,E)\phi(x,\omega')d\omega',\quad \phi\in L^2(G\times S),$$ and where $\Gamma'_{-}=\{(y,\omega)\in \partial G\times S\ |\ \omega\cdot\nu(y)<0\}$, while $\gamma'_-:\tilde{W}^2(G\times S)\to \Gamma'_{-}$; $\gamma'_-(\psi)=\psi|_{\Gamma'_{-}}$ is the trace mapping (see sect... | 3,186 | 1,579 | 1,566 | 3,188 | null | null | github_plus_top10pct_by_avg |
f{FINDISC}$ be the class of finite discrete categories. Since $\emptyset\in\mathsf{FINDISC}$, any left or right $\Phi$-stable derivator is pointed. It is easy to see that ${\mathsf{Stab}_L}(\mathsf{FINDISC}) = {\mathsf{Stab}_L}(\{\emptyset,2\})$, where $2$ denotes the discrete category with two objects, and similarly f... | 3,187 | 2,920 | 3,184 | 2,945 | null | null | github_plus_top10pct_by_avg |
e first claim of the lemma by letting $\beta =\beta '={\alpha }$ and $E'=E$, $F'=F$. The second claim follows from $$\begin{aligned}
{\varDelta }(E)-K_{\alpha }{\otimes }E-E{\otimes }1\in &\mathop{\oplus }
_{\beta ,\gamma \in {\mathbb{N}}_0^I, \beta +\gamma ={\alpha },\,\beta ,\gamma \not=0}
U ^+(\chi )_\be... | 3,188 | 2,127 | 2,807 | 2,847 | null | null | github_plus_top10pct_by_avg |
-1/2} \right)^2 spacetime vector,
\otimes \left( \psi^{1-2}_{-1/2}, \overline{\psi}^{1-2}_{-1/2}
\right)$
... | 3,189 | 5,383 | 1,009 | 2,530 | null | null | github_plus_top10pct_by_avg |
en the dimensionality of the spaces $G$, $S$ or $I$ in fact), with the exception that typically only charged particle fields (are assumed to) obey CSDA version of the transport equation (cf. ), while non-charged particles obey the standard linear BTE (cf. ). Thus with very minor modifications, and in particular if one ... | 3,190 | 1,425 | 2,523 | 2,960 | null | null | github_plus_top10pct_by_avg |
g(y+a^i_{y,\omega}\omega,\omega,E)\Big( e^{-\int_{a^i_{y,\omega}}^\tau\Sigma(y+s\omega,\omega,E)ds}\varphi(y+\tau\omega,\omega,E) \Big|_{\tau=a^i_{y,\omega}}^{\tau=b^i_{y,\omega}} \Big){d}y{d}\omega{d}E \\
&+\int_{S\times I}\int_{G_{\omega}}\sum_i \int_{J^i_{y,\omega}} \Sigma(y+\tau\omega,\omega,E)e^{-\int_{a^i_{y,\om... | 3,191 | 2,472 | 2,504 | 2,818 | null | null | github_plus_top10pct_by_avg |
on $C=C_1\otimes\cdots \otimes C_r$, say with $\operatorname{{\textsf}{ogr}}C_j=D_j$ and $\operatorname{{\textsf}{ogr}}C=D$. Moreover, by Theorem \[main\], respectively Proposition \[pre-cohh\] combined with Lemma \[thetainjA\], respectively Proposition \[app-c-prop\] combined with Lemma \[thetainjC\], there is an equa... | 3,192 | 2,324 | 1,423 | 3,234 | 2,662 | 0.778042 | github_plus_top10pct_by_avg |
n by cytokines (IL-6) and activation of thyroid-stimulating hormone receptor (TSH-r). In addition, OF have been shown to display the immunoregulatory molecules major histocompatibility complex MHC class II (HLA-DR) and intercellular adhesion molecule-1 (ICAM-1), and also are capable of secreting chemokines and cytokine... | 3,193 | 5,371 | 1,739 | 2,434 | null | null | github_plus_top10pct_by_avg |
(\Omega \otimes \Omega) E = -
(\Omega \otimes \Omega) [I_{k^2} \;\;\;\;\; 0_{k^2 \times k}] =
\Big[ - (\Omega \otimes \Omega) \;\;\;\;\; 0_{k^2 \times k} \Big].$$ The top derivative in is more involved. By the product rule, $$\frac{d \left( \alpha^\top \otimes I_k
\right) (\Omega \otimes \Omega) }{d \psi} ... | 3,194 | 5,417 | 318 | 2,666 | null | null | github_plus_top10pct_by_avg |
frac{1}{\Psi _{\eta ,\kappa
}(x,y)}$$Now, by a standard calculus, ${\Psi _{\eta ,\kappa }(x,y)}\geq C_{\kappa }%
\frac{\psi _{\kappa }(x-y)}{\psi _{\eta +\kappa }(x)}$ (use that $\psi
_{\kappa }(x-y)\leq C_{\kappa }\psi _{\kappa }(x)\psi _{\kappa
}(-y)=C_{\kappa }\psi _{\kappa }(x)\psi _{\kappa }(y)$), so (\[TR6d\]... | 3,195 | 1,590 | 2,104 | 3,102 | null | null | github_plus_top10pct_by_avg |
1(v) &{\stackrel{x}{\longrightarrow_{}}} & E_2(v) \label{nruleE1}\\\vdots&&\vdots \nonumber\\
D_k(v) &{\stackrel{x}{\longrightarrow_{}}} & v \label{nruleDk}\\E_k(v) &{\stackrel{x}{\longrightarrow_{}}} & v \label{nruleEk}\\E_k(v) &{\stackrel{z}{\longrightarrow_{}}} & v \label{nruleEkz}\\L_1 &{\stackrel{\ell_1}{\longrig... | 3,196 | 1,338 | 2,578 | 3,097 | 1,496 | 0.788827 | github_plus_top10pct_by_avg |
t case, the emission probability for charges $\pm q$ is proportional to a Boltzmann factor of the form $$\begin{aligned}
e^{-\frac{1}{T}\left(m\pm\frac{qQ}{r_+}\right)}= e^{-\frac{m}{T}\left(1\pm\frac{q}{\sqrt{2}m}(1-e^{2\Delta\phi})\right)}.\end{aligned}$$ If $|\Delta\phi|\gg 1$, the discharge rate is fast if the WGC ... | 3,197 | 4,699 | 3,156 | 2,928 | null | null | github_plus_top10pct_by_avg |
nction for the network is set as the (weighted) sum of the error activations across each layer. We utilize the $L_{all}$ formulation presented in the original paper, which places a non-zero loss on the error unit activity in every level in the network. Except where stated otherwise, results presented here use a model t... | 3,198 | 2,588 | 2,535 | 2,255 | null | null | github_plus_top10pct_by_avg |
$X:={{\rm{Spec}}}(S_\triangle)$ and $Y:={{\rm{Spec}}}((S_\triangle)^W)$, then both $X$ and $Y$ are normal, irreducible, affine algebraic varieties. Since the action of $W$ on $X$ is free, the dominant morphism $\phi : X \to Y$ is unramified in codimension $1$. So we can use Theorem \[cor1\] to get $$\la{DiffIden}
\D(S... | 3,199 | 2,306 | 1,354 | 3,160 | null | null | github_plus_top10pct_by_avg |
eaker result, which is significantly stronger than the result of [@Mikl] for subfamilies of $\binom{[n]}{\leq 3}$.
\[bigchvatal\] Let $\cH\sse \binom{[n]}{\leq 3}$ be a downset, and let $\cI\sse \cH$ be a maximum intersecting family. If $|\cI|\geq 31$, then $\cI$ is a star. Hence $\cH$ is EKR when $\i(\cH)\ge 31$.
Of... | 3,200 | 1,979 | 1,117 | 3,045 | 1,706 | 0.786603 | github_plus_top10pct_by_avg |
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