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 |
|---|---|---|---|---|---|---|---|
CW2 0.787 0.703 0.702 0.909 0.848 0.635 0.657
------------------------------ -------- --------- ------- ---------- ------------ --------------- ------------
: Attack success rates and detector accuracy for adversarial examples on LeNet-VAE using a trip... | 2,101 | 644 | 1,276 | 1,789 | null | null | github_plus_top10pct_by_avg |
alysis on finite abelian groups which are used here and points out their immediate consequences for $G$-circulant matrices; some notation and conventions used in the remainder of the paper are established there. Section \[S:Gaussian\] investigates the spectra of some random $G$-circulant matrices whose entries are Gaus... | 2,102 | 667 | 2,436 | 2,117 | null | null | github_plus_top10pct_by_avg |
)$ of a directed set $\mathbb{D}$ (Def. A1.7), with $x$ and $y$ in the equations below being taken to belong to the required domains, define subsets $\mathcal{D}_{-}$ of $X$ and $\mathcal{R}_{-}$ of $Y$ as $$\mathcal{D}_{-}=\{ x\in X\!:((f_{\nu}(x))_{\nu\in\mathbb{D}}\textrm{ converges in }(Y,\mathcal{V}))\}\label{Eqn:... | 2,103 | 880 | 1,267 | 1,991 | null | null | github_plus_top10pct_by_avg |
4/3*s**2.
-(s - 2)*(4*s + 1)/3
Let m be -1 - (-4 + 0) - 2. Let g be m + 1 + -1 + -1. Factor -4/3*v**2 + 2/3*v**5 + 0*v**3 + 4/3*v**4 - 2/3*v + g.
2*v*(v - 1)*(v + 1)**3/3
Find y, given that 42*y**2 - 35*y**3 + 28*y - 60 + 83*y**2 - 108*y = 0.
-3/7, 2
Let z(g) = 9*g**2 + 24*g - 3. Let q(s) = -10*s**2 - 23*s + 4. Let j(l... | 2,104 | 646 | 2,028 | 1,830 | null | null | github_plus_top10pct_by_avg |
les.
By Thm. \[th:Coxgr\], $${T}_{i_0}{T}_{i_1}\cdots {T}_{i_{m-1}}(u_0)=
{T}_{i_1}{T}_{i_2}\cdots {T}_{i_m}(u_0)\quad
\text{for all $u_0\in {{\mathcal{U}}^0}$.}$$ Hence Lemma \[le:MLmap\] yields that $$\begin{aligned}
\Lambda '(u_0){\hat{T}}'(v_{\Lambda '})={\hat{T}}'(u_0v_{\Lambda '})
=&{T}_{i_0}{T}_{i_1... | 2,105 | 1,093 | 2,278 | 2,043 | null | null | github_plus_top10pct_by_avg |
z'_1}^{{\bf n}}\;
{{}^\exists}\omega_5\in\Omega_{z'_1\to z_3}^{{\bf n}}\cdots\\
\cdots{{}^\exists}\omega_{2j}\in\Omega_{z_j\to z'_{j-1}}^{{\bf n}}\,{{}^\exists}\omega_{
2j+1}\in\Omega_{z'_{j-1}\to x}^{{\bf n}}\;{{}^\exists}\omega_{2j+2},\omega_{2j+3}
\in\Omega_{x\to z'_j}^{{\bf n}}\\
\text{such that }~\omega_i\cap\o... | 2,106 | 717 | 1,510 | 2,176 | 3,650 | 0.770921 | github_plus_top10pct_by_avg |
}{h}\right)\left(\frac{h}{U_b} \right)^2 \frac{\left(\frac{\partial \overline{\theta}_n}{\partial z_n} \right)}{S_n^2}.$$
Using the definition of $Ri_b$ (see Sect. 2), we re-write $Ri_g$ as follows: $$Ri_g = Ri_b \frac{\left(\frac{\partial \overline{\theta}_n}{\partial z_n} \right)}{S_n^2}.$$ Similarly, $N^2$ can be w... | 2,107 | 2,996 | 3,218 | 2,276 | null | null | github_plus_top10pct_by_avg |
Faddeev-Popov method. Specifying to $SU(2)$, the Polyakov gauge is implemented by the gauge fixing conditions $$\label{eq:Pol1}
\partial_0 {\mathrm{tr}}\,\sigma_3 A_0=0\,, \qquad
{\mathrm{tr}}\,(\sigma_1\pm i\sigma_2) A_0 = 0\,,$$ where the $\sigma_i$ are the Pauli matrices. However, the gauge fixing is not comple... | 2,108 | 3,669 | 2,387 | 1,770 | 3,408 | 0.772623 | github_plus_top10pct_by_avg |
at 10:00:00 PM CT thru Sat 11/17/2001 at 11:00:00 PM CT
Sat 11/17/2001 at 8:00:00 PM PT thru Sat 11/17/2001 at 9:00:00 PM PT
Sun 11/18/2001 at 4:00:00 AM London thru Sun 11/18/2001 at 5:00:00 AM London
Outage: Swap names of NAHOU-SQEFM01P and NAHOU-SQLAC01P
Environments Impacted: EFM Accounting users
Purpo... | 2,109 | 3,767 | 510 | 1,454 | null | null | github_plus_top10pct_by_avg |
r_0}^2)<+\infty$ and this concludes the proof. $\Box$
We follow here the proof of Baccelli and Bordenave [@baccellibordenave Section 3.6], where the case of a fixed radius $R$ is considered. Recall that $\mathcal{T}$ and $\mathcal{T}_{-e_x}$ are the RST and DSF with direction $-e_x$, constructed on the same PPP $N$. W... | 2,110 | 1,190 | 301 | 2,316 | null | null | github_plus_top10pct_by_avg |
ntation of NHEK’s isometry group then requires $k-1-2h \neq 0$, otherwise there would be a lowest-weight state that would lead to a finite-dimensional (and hence non-unitary) representation. The same conclusion holds for either the vector or the tensor bases. The values of $h$ also depend on the regularity conditions w... | 2,111 | 1,982 | 2,197 | 2,105 | null | null | github_plus_top10pct_by_avg |
- w_0}_2^2}\\
\leq& \E{\lrp{\lrn{w_{k\delta} - w_0 - \delta \lrp{\nabla U(w_{k\delta}) - \nabla U(w_0)}}_2 + \delta \lrn{\nabla U(w_0)}_2}^2}\\
\leq& \lrp{1 + \frac{1}{n}}\E{\lrn{w_{k\delta} - w_0 - \delta \lrp{\nabla U(w_{k\delta}) - \nabla U(w_0)}}_2^2 }\\
&\quad + (1+n)\delta^2 \E{\lrn{\nabl... | 2,112 | 3,137 | 1,336 | 1,899 | null | null | github_plus_top10pct_by_avg |
l examine properties of those classes.
The first class we consider involves the special case that the gauge bundle is a pullback from the base. This is equivalent to the statement that the subgroup $G$ of the gauge group that acts trivially on the base, also acts trivially on the fibers of the gauge bundle.
In this c... | 2,113 | 1,381 | 2,388 | 1,967 | null | null | github_plus_top10pct_by_avg |
per bounded by $\max_{i \in [d]}\big\{\ell_j\P[i \in I_j| i \in S_j]\big\} \leq {\ell_j}^2 e^{2b}/\kappa_j$. Therefore using triangle inequality, we have, $$\begin{aligned}
&&\Bigg\|\sum_{j =1}^n\E\big[(M^{(j)})^2\big]\Bigg\| \nonumber\\
& \leq & \max_{i \in [d]} \Bigg\{\sum_{j:i \in S_j} \frac{1}{(\kappa_j-1)^2} \Bi... | 2,114 | 1,047 | 1,600 | 2,066 | null | null | github_plus_top10pct_by_avg |
e maximization of KSE and the minimization of the mixing time**. Since KSE are easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time that could be interesting in computer sciences and statistical physics and gives a physical meaning to the KSE. We f... | 2,115 | 2,633 | 2,646 | 1,959 | null | null | github_plus_top10pct_by_avg |
andidate critical solution. We discuss its global causal structure and its symmetries in relation with those of the corresponding continously self-similar solution derived in the $\Lambda=0$ case. Linear perturbations on this background lead to approximate black hole solutions. The critical exponent is found to be $\ga... | 2,116 | 1,414 | 1,133 | 1,833 | null | null | github_plus_top10pct_by_avg |
N\] A *cone* ${\mathcal{C}}$ is a complete independent set of localized predecessor walks starting at ${\mathit{s}}_{\text{crux}}$.
[\[Stopping rule\]]{} We avoid the specificity of various stopping criteria (§\[S:CONE\_DESCRIPTION\]) by introducing the equivalent but arbitrary notion of localization.
\[S:CONE\_EDGE\... | 2,117 | 747 | 1,590 | 1,946 | 2,200 | 0.781865 | github_plus_top10pct_by_avg |
b{M}])
C^{\mathbb{M}}_{\mathbb{F}}[\sigma]C^*[\mathbb{F}]
x^*_{\overline{\mathbb{F}}}\\
&=& x_{\overline{\sigma_i\mathbb{M}}}
C[\sigma_i\mathbb{M}]
C^{\mathbb{M}}_{\mathbb{F}}[\sigma]C^*[\mathbb{F}]
x^*_{\overline{\mathbb{F}}}\\
&=&{\cal C}(\sigma_i\mathbb{M}, \sigma, \mathbb{F}).\end{aligned}$$
... | 2,118 | 424 | 1,308 | 2,350 | null | null | github_plus_top10pct_by_avg |
")) {
sendEmail(url.substring(7));
return true;
}
return false;
}
Q:
Move constructor for a map
I think I do understand "the basic IDEA" of move semantics, but now when I'm on the stage of implementing my own map I stopped and started to think about it when I was going to write a use case a... | 2,119 | 3,888 | 964 | 1,493 | 416 | 0.810371 | github_plus_top10pct_by_avg |
ified intercept model was 88.8%, using REML+standard, but 95.8% using REML+KR.
Using REML+Satterthwaite gave very similar results to REML+KR. Occasionally, there was some over‐coverage using REML+KR or REML+Satterthwaite, particularly when using a low number of trials (*K* = 5). For example, coverage was close to 99% ... | 2,120 | 262 | 3,159 | 2,005 | null | null | github_plus_top10pct_by_avg |
E1'$)-($E5'$) omitting the ones which involve $s_{n-1}$ and adding the following relations: $$\begin{gathered}
f_{*}s_{n-2}s_{n-3}\cdots s_3s_2s_1
s_2s_3\cdots s_{n-3}s_{n-2}f_{*} \nonumber\\
\quad =\, f_{*}s_{n-2}s_{n-3}\cdots s_3s_2f
s_2s_3\cdots s_{n-3}s_{n-2}\phantom{,} \tag{$R2^*$} \\
\quad =\, s_{n-2}... | 2,121 | 4,104 | 1,916 | 1,553 | 4,011 | 0.768648 | github_plus_top10pct_by_avg |
PAGE2._oF::z._ 6)'! ~~~L•~ • ; ' j I
... | 2,122 | 4,167 | 2,155 | 1,262 | null | null | github_plus_top10pct_by_avg |
{i,i;k}(\M_\muhat)\right)q^i,$$
On the other hand the mixed Hodge numbers $h^{i,j;k}(X)$ of any complex non-singular variety $X$ are zero if $(i,j,k)\notin
\{(i,j,k)|\hspace{.05cm} i\leq k,j\leq k,k\leq i+j\}$, see [@Del1]. Hence $h^{0,0;k}(\M_\muhat)=0$ if $k>0$.
We thus deduce that the constant term of $E(\M_\muhat... | 2,123 | 1,238 | 2,006 | 2,008 | 3,957 | 0.768981 | github_plus_top10pct_by_avg |
us harder than AES alone which does not have the decoding in noise problem. In particular, it is easily seen that if the Y-00 in the configuration of Fig. 2 can be broken, then each $AES_i$ itself can be broken.
\[htbp\]
[ {width="4.5in" height="2in"}]{}
The question arises as to what constitut... | 2,124 | 2,535 | 3,168 | 2,001 | null | null | github_plus_top10pct_by_avg |
e was a significant main effect of *family member* \[χ^2^(3) = 33.99, *p* \< 0.001\], as will be explained below (see section "Similarities and Differences Across Members Within One Family"). There was also a significant effect of the *ill child's age at diagnosis* \[χ^2^(1) = 5.07, *p* = 0.02\]: the older the ill chil... | 2,125 | 891 | 2,007 | 2,014 | null | null | github_plus_top10pct_by_avg |
ma_1}{\longrightarrow}
& U_i\\
\downarrow && \downarrow\\
S& =& S.
\end{array}$$ Applying this to $X\to S$ and $R\to S$, we obtain a commutative diagram $$\begin{array}{lcl}
{{\mathcal O}}_S^{m(X)}&
\stackrel{p_1^*(s)-p_2^*(s)}{\longrightarrow}
&{{\mathcal O}}_S^{m(R)}\\
\ \downarrow && \ \downarrow\\
{{\mathcal O}}_X&... | 2,126 | 2,429 | 2,616 | 1,872 | 3,302 | 0.773349 | github_plus_top10pct_by_avg |
ar
D^{(+)}$ is well-defined by the rule $x+[J,J]\mapsto x+\langle D,D\rangle$.
$$\begin{CD}
J @>\subseteq>> D \\
@VVV @VVV \\
\bar J @>\phi>> \bar D
\end{CD}$$
It is evident that $\phi$ is injective if and only if $\langle
D,D\rangle\cap J=[J,J]$.
Let $x\in\langle D,D\rangle\cap J$. Then $x{\mathbin\vdash}y=y{\math... | 2,127 | 1,154 | 1,763 | 1,822 | 2,442 | 0.77973 | github_plus_top10pct_by_avg |
{\dag}\,.$$ Here, the internal Hamiltonian $H$ of the closed system is represented by a Hermitian $N\times N$ matrix, whereas $V_k$ are $M$ vectors of length $N$ containing the information on the coupling of the levels to the continuum. The $V_k$ are assumed to be normalized to one, $V_k^{\dag}V_k=1$, and $\lambda_k$ i... | 2,128 | 733 | 2,234 | 2,038 | 2,518 | 0.779203 | github_plus_top10pct_by_avg |
, L_{j+1},$ $L_{j+2}, L_{j+3}$) are *of type II* if $j$ is even (resp. odd). Choose $j, j' \in \mathcal{B}$ with $j<j'$. By using the fact that $j'-j\geq 5$ if $j$ is even and $j'-j\geq 4$ if $j$ is odd, the proof of the surjectivity of the morphism $\psi=\prod_{j\in \mathcal{B}}\psi_j$ is similar to that of Theorem 4.... | 2,129 | 1,638 | 705 | 2,151 | 1,708 | 0.786578 | github_plus_top10pct_by_avg |
hey are first order formulations of GR. One has to first solve the connection in terms of the vielbein before calculating any scattering amplitudes of gravitons. The calculation in those theories is not simpler than a direct computation from the Hilbert-Einstein action.
Perturbative Expansion in $A$
------------------... | 2,130 | 642 | 2,317 | 2,018 | null | null | github_plus_top10pct_by_avg |
-1)/2}{N_t},$$ respectively, $$\label{}
{\mathbf{A}}_R=\frac{1}{\sqrt{N_r}}\left[ \mathbf{a}_R\left(\ddot{\theta}_{R,1}\right),\cdots,\mathbf{a}_R\left(\ddot{\theta}_{R,N_r}\right)\right]^T$$ and $$\label{}
{\mathbf{A}}_T=\frac{1}{\sqrt{N_t}}\left[ \mathbf{a}_T\left(\ddot{\theta}_{T,1}\right),\cdots,\mathbf{a}_T\le... | 2,131 | 1,673 | 1,988 | 2,002 | 3,370 | 0.772823 | github_plus_top10pct_by_avg |
mathcal{U}}^0,{{\mathbb{K}}^\times })}$ define ${t}_p^\chi (\Lambda )\in {{\mathrm{Hom}}({\mathcal{U}}^0,{{\mathbb{K}}^\times })}$ by $$\begin{aligned}
{t}_p^\chi (\Lambda )(K_{\alpha }L_\beta )=\Lambda (K_{{\sigma }_p^{r_p(\chi )}({\alpha })}
L_{{\sigma }_p^{r_p(\chi )}(\beta )})
\frac{r_p(\chi ) ({\alpha },{\al... | 2,132 | 2,133 | 2,146 | 2,009 | null | null | github_plus_top10pct_by_avg |
your doc object which, I assume, was created on the main thread. This might be the reason for the fault.
Generally, you should not access objects (especially UI elements) across differed threads, unless they are specifically designed to be thread-safe.
EDITED: You probably do not need a task here. Just do await savePic... | 2,133 | 2,039 | 702 | 1,507 | 2,301 | 0.781048 | github_plus_top10pct_by_avg |
nodes of $[\mu]$ mapped to $i$. Such a tableau is usually represented by drawing $[\la]$ with a box for each node $\fkn$, filled with the integer $T(\fkn)$. $T$ is *row-standard* if the entries in this diagram are weakly increasing along the rows, and is *semistandard* if the entries are weakly increasing along the ro... | 2,134 | 1,438 | 800 | 2,085 | 2,483 | 0.779393 | github_plus_top10pct_by_avg |
H^{\ast}$ using various magnetic measurements of $H_{irr}^{ab} (T)$: (a) Hg-1223, (b) Hg-1234, (c) Hg-1245, and (d) La-112. In (b) and (d) dashed lines indicate $H_{c2}^{ab} (T)$ from TDO measurements. In (d) we also illustrate $H_{c2}^{c}$ for comparison. We note reasonable consistency among different experimental tec... | 2,135 | 1,174 | 2,095 | 2,395 | null | null | github_plus_top10pct_by_avg |
mathbf{0}}$) the posterior has the same form as the prior with tractable updates; the same would be true for a non-baseline measurement (${\mathbf{x}}_t\neq{\mathbf{0}}$) if it were possible to set ${\bar{\nu}}^{-1}=0$ and to ignore the further information on ${\bar{\mathcal{A}}}$; such an approximation is described an... | 2,136 | 4,369 | 1,798 | 1,628 | null | null | github_plus_top10pct_by_avg |
/2001 at 6:00:00 PM CT thru Sun 11/18/2001 at 9:00:00 AM CT
Sat 11/17/2001 at 4:00:00 PM PT thru Sun 11/18/2001 at 7:00:00 AM PT
Sun 11/18/2001 at 12:00:00 AM London thru Sun 11/18/2001 at 3:00:00 PM London
Outage: General maintenance for ERMS CPR app server chewbacca.
Environments Impacted: ERMS CPR
Purpose:... | 2,137 | 1,648 | 810 | 1,606 | null | null | github_plus_top10pct_by_avg |
c(\mu)$ has weight $m+c(n(\mu) -
n(\mu^{t}))$, where $m=(n-1)/2$.
[(2)]{} The Poincaré series of $\Delta_c(\mu)$ as a graded ${{W}}$-module is $$\label{polystand} p(\Delta_c(\mu), v, {{W}}) =
v^{m+c(n(\mu)-n(\mu^t))} \frac{\sum_{\lambda}f_{\lambda}(v)
[\lambda\otimes \mu]}{\prod_{i=2}^n (1-v^i)}.$$
\(1) We need to co... | 2,138 | 1,426 | 2,212 | 1,971 | 3,204 | 0.774053 | github_plus_top10pct_by_avg |
label{eq:velocity_linear}\end{aligned}$$
Combining Eq. (\[eq:fp2\]) with the expressions for the density perturbations, we have that the total force can be split into the contribution from the density variations in the BEC by causes external to the particle (initial preparation, stirring forces in $V_{ext}$, ...), and... | 2,139 | 619 | 795 | 2,371 | 2,594 | 0.778606 | github_plus_top10pct_by_avg |
ace flattens and the worldsheet theory becomes free. More precisely we obtain a theory of $d$ free bosons, where $d$ is the dimension of the adjoint representation of the super Lie algebra. Among these bosons, some are commuting and some are anti-commuting, depending on whether they can be associated to bosonic or ferm... | 2,140 | 2,496 | 2,565 | 1,989 | 4,025 | 0.76858 | github_plus_top10pct_by_avg |
n explain a wide variety of seemingly unrelated phenomena observed in visual cortex and visual perception. These phenomena range from the details of responses of individual neurons, to complex visual illusions. Importantly, throughout, we used a base model trained on natural videos. Our work adds to a growing body of l... | 2,141 | 2,777 | 3,071 | 2,080 | null | null | github_plus_top10pct_by_avg |
}}\\
\leq& \int_0^1\int_0^s \E{\lrn{\nabla^2 f(x_T - y_T + s(y_T-v_T))}_2 \lrn{y_T - v_T}_2^2} ds dt\\
\leq& \frac{2}{\epsilon} \E{\lrn{y_T - v_T}_2^2}\\
\leq& \frac{72 d \delta \beta^2 \log^2 n}{\epsilon}
\end{aligned}$$ Where the second inequality is by $\lrn{\nabla^2 f... | 2,142 | 4,059 | 1,967 | 1,713 | null | null | github_plus_top10pct_by_avg |
] the cone $C\colon{\sD}^{[1]}\to{\sD}$ and the fiber $F\colon{\sD}^{[1]}\to{\sD}$ is defined in pointed derivators only, but the same formulas make perfectly well sense in arbitrary derivators. It turns out that a derivator is pointed if and only if $C$ is a left adjoint if and only if $F$ is a right adjoint. In that ... | 2,143 | 1,446 | 1,585 | 2,069 | 1,241 | 0.792162 | github_plus_top10pct_by_avg |
and $a \to \infty$ (the domain loses regularity), the two agree with an $\mathcal{O}(\varepsilon^{-2})$ bound.
Fractional Poisson problem {#inhomogenous}
==========================
We are now interested in using the walk-on-spheres process to find the solution to the inhomogeneous version of (\[aDirichlet\]), namely... | 2,144 | 999 | 1,729 | 2,062 | 2,941 | 0.775962 | github_plus_top10pct_by_avg |
**2 + 3502998*c**3*l + 478818*c**2*l**2 - 4*c*l**2 wrt c.
-12*l**2 + 21017988*l
Differentiate 2*g**2 + 2*g*j*t**2 + 7*g*t**2 + 40*g + 2*j*t**2 - j*t - 3*j - 104*t**2 + t with respect to g.
4*g + 2*j*t**2 + 7*t**2 + 40
Find the third derivative of -16*l**3*v - 727*l**3 - 11034*l**2*v + 4*l**2 wrt l.
-96*v - 4362
What is... | 2,145 | 2,686 | 2,679 | 2,166 | null | null | github_plus_top10pct_by_avg |
boratory of Software Development Environment (NLSDE)\
School of Computer Science and Engineering, Beihang Univerisity, Beijing, China
author:
- Yongwang Zhao
title: A survey on formal specification and verification of separation kernels
---
real-time operating systems ,separation kernel ,survey ,formal specificat... | 2,146 | 2,248 | 3,441 | 1,883 | null | null | github_plus_top10pct_by_avg |
.
Considering the boost behaviour of $s_x,s_y$, after the shift we may have $$c h_y+d\bar{h}_x=0. \label{hy}$$ We can define a set of charges, $$L_\epsilon=\int \{c\epsilon(x) h_x(x,y)+d\epsilon'(x)y\bar{h}_x(x)\}dx+\int\{c\epsilon(x)h_y(x) \}dy, \label{Qcharges}$$ where $\epsilon(x)$ is arbitrary smooth function on $... | 2,147 | 1,089 | 2,106 | 1,847 | 4,150 | 0.767738 | github_plus_top10pct_by_avg |
a^+(C_0)$,
2. for all $\beta\neq \xi$ in $\omega_1$, $\beta\notin \dot{U}(\xi,0)$,
3. for all $\xi,\alpha\in \omega_1$ $\dot{U}(\xi,\alpha)\subseteq \dot{U}(\xi,0)$ and has compact closure,
4. for each limit $\delta\in \omega_1$, the sequence $\{\dot{U}(\xi,\alpha):\alpha<\delta\}$ is a *regular filter*, i.e. eac... | 2,148 | 1,983 | 2,127 | 1,954 | null | null | github_plus_top10pct_by_avg |
ot Rz)d\sigma(z) \right|\\
& = \frac{1}{\omega_d}\left| \int_{{\mathbb{S}}^{d-1}} f(z)g(x\cdot z)d\sigma(z) - \int_{{\mathbb{S}}^{d-1}} f(Rz)g(x\cdot z)d\sigma(z) \right|\\
& \leq \frac{1}{\omega_d}\int_{{\mathbb{S}}^{d-1}} |f(z)-f(Rz)||g(x\cdot z)|d\sigma(z) \\
& \leq \|f\|_{\mathrm{Lip}}\frac{1}{\omega_d}\int_{{\math... | 2,149 | 1,278 | 1,842 | 1,960 | null | null | github_plus_top10pct_by_avg |
uhat(-z,w)$ should actually be a polynomial with non-negative integer coefficients of degree $d_\muhat$ in each variable.
In [@hausel-letellier-villegas] we prove that (\[mainconj\]) is true under the specialization $(q,t)\mapsto (q,-1)$, namely, $$E(\M_\muhat;q):=H_c(\M_\muhat;q,-1)=
q^{\frac{1}{2}d_\muhat}\H_\muhat... | 2,150 | 1,292 | 1,273 | 2,000 | 2,234 | 0.781577 | github_plus_top10pct_by_avg |
} + \hat{V}_{\rm l} \right)
\left|\psi_{1}\right>
&=& E_{1}\left|\psi_{1}\right> \; , \\
\left(\hat{H}_0 + \hat{V}_{\rm r} + \hat{V}_{\rm l} \right)
\left|\psi_{2}\right>
&=& E_{2}\left|\psi_{2}\right> \; . \end{aligned}$$ By symmetry, good approximations to these two defect states are given by the eve... | 2,151 | 5,159 | 220 | 1,680 | null | null | github_plus_top10pct_by_avg |
nergies taken from Ref. [@aud95]. We define the deformation parameter $\beta_{2}$ and average pairing gap $\langle\Delta\rangle$ [@sau81; @ben00; @dug01; @yam01] as $$\begin{aligned}
\beta_{2}^{\tau}&=\dfrac{4\pi}{5}\dfrac{\int d\bold{r} \varrho^{\tau}(\bold{r})r^{2}Y_{20}(\hat{r})}
{\int d\bold{r} \varrho^{\tau}(\bold... | 2,152 | 2,716 | 2,859 | 2,244 | null | null | github_plus_top10pct_by_avg |
_V\|K\|_2h_{1,n}^{1/2}$ and the characteristics $A=R$ and $v=22$, and the lemma will follow by application of Talagrand’s inequality. We just need to estimate $Eg^2(t,X)$. We have, making several natural changes of variables, $$\begin{aligned}
Eg^2(t,X_1)&=&
E\Big\{\int f^{1/2}(x)K\Big(\frac{x-X_1}{h_{1,n}}\Big)L\Big(... | 2,153 | 535 | 1,907 | 2,124 | null | null | github_plus_top10pct_by_avg |
.
@wever2018ensembles ([-@wever2018ensembles]) utilise genetic algorithms to build nested dichotomies. In their method, a population of random nested dichotomies is sampled and runs through a genetic algorithm for several generations. The final nested dichotomy is chosen as the best performing model on a held-out vali... | 2,154 | 170 | 3,098 | 2,325 | null | null | github_plus_top10pct_by_avg |
gned}$$ then the [*rank-breaking*]{} estimator in achieves $$\begin{aligned}
\label{eq:bottoml_3}
\frac{1}{\sqrt{\ld}}\big\|\widehat{\ltheta} - \ltheta^*\big\|_2 \; \leq \; \frac{32\sqrt{2}(1+ e^{4b})^2}{\chi_{\beta_1}}\frac{d^{3/2}}{{\ld}^{3/2}}\sqrt{\frac{d\log d}{n\ell} }\;,
\end{aligned}$$ with probabilit... | 2,155 | 1,670 | 1,650 | 2,035 | null | null | github_plus_top10pct_by_avg |
B_{ij}eH_{c+j} =eJ^{i-j}\delta^{i-j}$. Multiplying this identity on the right by $e$ and applying Lemma \[grade-elements\] and Corollary \[morrat-cor\](1) gives $$eJ^{i-j}\delta^{i-j} e = \operatorname{{\textsf}{ogr}}(B _{ij}eH_{c+j})e
=\operatorname{{\textsf}{ogr}}(B_{ij} eH_{c+j}e) =\operatorname{{\textsf}{o... | 2,156 | 1,433 | 1,101 | 2,212 | null | null | github_plus_top10pct_by_avg |
nfinite chain of adjoint morphisms.\[item:sf5\]
Combining \[thm:stable-lim-III,thm:stab-op\], we see that \[item:sf1\] implies \[item:sf4\], which clearly implies \[item:sf3\], while \[item:sf3\] implies \[item:sf2\] since the cone is a composite of a right extension by zero with a pushout. And \[item:sf2\] implies \[... | 2,157 | 1,984 | 1,634 | 1,886 | 3,334 | 0.773045 | github_plus_top10pct_by_avg |
{\overset{}{\longleftrightarrow}}}u_{2l}\}$}}}
\bigg)\bigg(\prod_{\substack{l,l'\ge1\\ l\ne l'}}{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{{{\cal C}}_{{\bf k}}(u_{2l})\,\cap\,{{\cal C}}_{{\bf k}}(u_{2l'})={\varnothing}\}$}}}\bigg){\nonumber}\\
\times\underbrace{\sum_{{\partial}{{\bf k}}'=y{\vartriangle}z}\frac{w_{{... | 2,158 | 860 | 1,978 | 2,153 | null | null | github_plus_top10pct_by_avg |
thrm{th}}$ coordinate is $$\label{eq:new.gamma}
\gamma_{{\widehat{S}}}(j) = \mathbb{E}_{X,Y, \xi_j}\Biggl[ \left|Y- t_{\tau}\left(
\hat\beta_{{\widehat{S}}(j)}^\top X_{{\widehat{S}}(j)} \right) \right|-
\left| Y-t_{\tau}\left( \hat\beta_{{\widehat{S}}}^\top X_{{\widehat{S}}} \right) \right| +
\epsilon ... | 2,159 | 2,119 | 2,520 | 1,969 | null | null | github_plus_top10pct_by_avg |
that the required data for a homotopy $\mathcal Comm$-inner product consists of,
- a derivation $d\in \mathrm{Der}(F _{\mathcal Lie}\,C[1])$ of degree $1$, with $d^2=0$,
- a derivation $g\in \mathrm{Der}_d (F_{\mathcal Lie,\,C[1]}C[1])$ over $d$ of degree $1$, with $g^2=0$, which imduces a derivation $h\in \mathr... | 2,160 | 2,420 | 2,228 | 2,006 | 2,044 | 0.783237 | github_plus_top10pct_by_avg |
4pt 3pt](0.1,0)(0.1,0.4)
\end{pspicture}},{
\begin{pspicture}(0,0.1)(0.2,0.4)
\psline[linewidth=1pt, linestyle=dashed,dash=4pt 3pt](0.1,0)(0.1,0.4)
\end{pspicture}},{
\begin{pspicture}(0,0.1)(0.2,0.4)
\psline[linewidth=1pt](0.1,0)(0.1,0.4)
\end{pspicture}},{
\begin{pspicture}(0,0.1)(0.2,0.4)
\psline[linewidth... | 2,161 | 1,403 | 2,028 | 2,041 | 1,645 | 0.787273 | github_plus_top10pct_by_avg |
Here, $\chi = \alpha^{-m}$.
More generally, over all components, we write $$c_1^{\rm rep}({\cal O}_{\mathfrak{X}}(m)) \: = \: \left( \frac{m}{k} J, \cdots,
\frac{m}{k} \alpha^{-m} J, \cdots \right).$$ Multiplication of components of ch$^{\rm rep}$ multiplies not only the cohomology classes, but also the coefficients.... | 2,162 | 2,060 | 1,983 | 2,049 | null | null | github_plus_top10pct_by_avg |
with two $d$s in different rows. If $T$ is $d$-bad, then we can express ${\psi_{d,1}}\circ{\hat\Theta_{T}}$ as a linear combination of semistandard homomorphisms using Lemma \[lemma5\] together with Lemma \[newsemilem\]. For example, if $$\begin{aligned}
T&=\young(11111122248{10},369{11}{12},57)
\\
\intertext{then ${\p... | 2,163 | 1,809 | 1,977 | 1,964 | 1,150 | 0.793463 | github_plus_top10pct_by_avg |
_2}\cdot{\vec{p}})$,
$({\vec{\sigma}_1}\cdot{\vec{p}})({\vec{\sigma}_2}\cdot{\vec{q}})$, $({\vec{\sigma}_1}-{\vec{\sigma}_2})\cdot({\vec{q}}\times{\vec{p}})$
: All possible PC and PV NLO operational structures connecting the initial and final spin and angular mom... | 2,164 | 2,473 | 2,839 | 2,028 | 3,551 | 0.771588 | github_plus_top10pct_by_avg |
$ and $\mathcal{T}_{-e_x}$ respectively denote the RST and DSF of direction $-e_x$ constructed on the same PPP $N$. Then, for $0<\alpha<1/3$: $$\lim_{r\rightarrow +\infty} {{\mathbb P}}\big(\mathcal{T}\cap B((r,0),r^\alpha)=\mathcal{T}_{-e_x}\cap B((r,0),r^\alpha)\big)=1.$$ The approximation also holds if we replace $r... | 2,165 | 419 | 1,327 | 2,140 | 2,026 | 0.783379 | github_plus_top10pct_by_avg |
^\*\_0(\^\*,v)=[**F**]{}\_0\^\*(v),v.
Suppose that the assumptions (\[scateh\]), (\[colleh\]), (\[sda2a\]), and (\[sda2b\]) are valid. Using integration by parts and Green’s formula we have the following.
For all $\psi,\psi^*\in \tilde {{{\mathcal{}}}H}$ one has \[adjoint7\] \_0\^\*(\^\*,)=\_0(,\^\*), where $\tilde{\... | 2,166 | 252 | 2,241 | 2,329 | null | null | github_plus_top10pct_by_avg |
erical coordinate system centered at the middle of the torus $( \rm r \ sin
\theta_s
cos\phi,r \ \rm sin \theta_s
sin\phi,r \ \rm cos \theta_s)$ $${\rm r \ sin\theta_s} = R + a \ \rm cos\theta$$ $${\rm r \ cos \theta_s} = a \rm \ sin\theta$$ $${\rm r } = \sqrt{R^2 + a^2 + 2 a R \ \rm cos\theta}$$ and defining $$\... | 2,167 | 3,206 | 2,044 | 2,087 | null | null | github_plus_top10pct_by_avg |
serious concern.
The original sample consisted of 306 Angolan respondents. For this analysis, parents who have children both in the country of origin and in the Netherlands are omitted because this would not allow exploring the different mediation paths of interest and test opposite hypotheses. Missing data and the a... | 2,168 | 368 | 2,753 | 2,337 | null | null | github_plus_top10pct_by_avg |
if you use fork/wait, you could get the exit code from the status code in the wait* functions:
int status;
if (wait(&status) != -1) { // similar for waitpid, wait4, etc.
if (WIFEXITED(status)) {
exit_code = WEXITSTATUS(status);
} else {
// handle other conditions, e.g. signals.
}
} else {
... | 2,169 | 6,176 | 51 | 1,762 | 920 | 0.797696 | github_plus_top10pct_by_avg |
-\al_i/2},$$ where $\al_1,\ldots,\al_r$ and $\be$ are nonnegative constants. The class $\pi_{SH}(\Th)$ includes both harmonic priors $\pi_{EM}(\Th)$ and $\pi_{JS}(\Th)$, which are given in (\[eqn:pr\_em\]) and (\[eqn:pr\_js\]), respectively. Indeed, $\pi_{SH}(\Th)$ is the same as $\pi_{EM}(\Th)$ if $\al_1=\cdots=\al_r=... | 2,170 | 1,156 | 2,064 | 2,159 | null | null | github_plus_top10pct_by_avg |
2}$ by $f^\alpha$ (and $f^{3/2}$ by $f^{\alpha +1}$) in the definition of $\hat f_n(t;h)$ the only $\alpha$ for which $\int_{-B}^Bw^2g''(0)dw=0$ for all $f$ twice differentiable with $f(t)\ne0$ is $\alpha=1/2$.\]. Thus, we have $$\int_{-B}^Bw^2g^{(i)}_{t,w}(0)dw=0\ \ {\rm for}\ \ i=1,2,3,$$ and we conclude, from this, ... | 2,171 | 1,013 | 1,647 | 2,134 | null | null | github_plus_top10pct_by_avg |
Pancreas
In-field tumor responses
------------------------
Twenty six lesions were targeted in nineteen patients (Table [3](#T3){ref-type="table"}). They included 15 pancreatic masses, 4 regional metastatic lymph nodes and 7 distant metastatic lesions. Of the 15 pancreati... | 2,172 | 332 | 2,345 | 2,583 | null | null | github_plus_top10pct_by_avg |
l) {
collateral.setPrice(new BigDecimal(map.get("Price")));
}
if (map.get("Par") != null) {
collateral.setPar(new BigDecimal(map.get("Par")));
}
if (map.get("mkt_val") != null) {
collateral.setMarketValue(new BigDecimal(map.... | 2,173 | 1,040 | 175 | 2,221 | 752 | 0.80079 | github_plus_top10pct_by_avg |
0.000 0.000 0.000 0.000 0.000
SDB($n^{0.8}$) 0.000 0.000 0.000 0.000 0.000 0.000 0.000
TB 0.062 0.070 0.074 0.070 0.060 0.074 0.064
6 ... | 2,174 | 5,321 | 590 | 1,729 | null | null | github_plus_top10pct_by_avg |
{j}$ if $L_{j}$ is *of type* $\textit{I}^o$ (resp. *of type* $\textit{I}^e$).
- $v_i$ and $y_i$ are blocks of $m_{i, i}$ as explained in the description of an element of $\tilde{M}(R)$ above, and $\bar{\gamma}_i$ is as explained in Remark \[r33\].(2).
- $\tilde{e_i}=\begin{pmatrix} \mathrm{id}\\0 \end{pma... | 2,175 | 814 | 1,892 | 2,113 | 2,811 | 0.776802 | github_plus_top10pct_by_avg |
le {\displaystyle (\psi,\phi_{j-})_{\mu}^{(+)}=-\sum_{i=0}^{N}b_{i}^{-}(\phi_{i+},\phi_{j-})_{\mu}^{(-)}}}\\
b_{j}={\displaystyle \left((\psi,\phi_{j+})_{\mu}^{(+)}+\sum_{i=0}^{N}b_{i}^{-}(\phi_{i+},\phi_{j+})_{\mu}^{(-)}\right)}\end{array}\label{Eqn: FRBC1}$$
where $(\phi_{j\pm})_{j=1}^{N}$ represents $(\phi_{\vareps... | 2,176 | 986 | 2,694 | 2,070 | 2,682 | 0.777902 | github_plus_top10pct_by_avg |
, \\
&=& \Bigg\langle -(\nabla\MM{l})^T\cdot\MM{\pi}
-\phi\diamond a,\operatorname{ad}_{\MM{u}}\MM{w}
\Bigg\rangle
+ \Bigg\langle {\frac{\delta \ell}{\delta a}}\diamond a,\MM{w}\Bigg\rangle , \\
& = & \Bigg\langle {\frac{\delta \ell}{\delta \MM{u}}},\operatorname{ad}_{\MM{u}}\MM{w}\Bigg\rangle
+ \Bigg\langl... | 2,177 | 1,915 | 2,036 | 2,097 | null | null | github_plus_top10pct_by_avg |
------------------------------ --
Finally, we discuss the dipole state in $^{30}$Ne. Compared to the response functions in $^{26}$Ne and $^{28}$Ne, that for $^{30}$Ne is quite different, because this nucleus is well deformed as shown in Table \[GS\]. The giant resonance is split into $K^{\pi}=0^{-}$ and $1^{-}$ mode, ... | 2,178 | 1,792 | 2,672 | 2,128 | null | null | github_plus_top10pct_by_avg |
p. 306] the left-hand side of is also zero and hence $\beta_{\cD,P}^{(k')}=0$ for all $0\leq k'< \deg \cD$.
Finally, combining properties \[prop:4\], \[prop:5\], and \[prop:6\] in Lemma \[lemma:global-realization\] together with Step \[step1\] above, it immediately follows that $\beta_{\cC,P}^{(k)}=\beta_{\cD,P}^{(k'... | 2,179 | 1,401 | 786 | 1,992 | null | null | github_plus_top10pct_by_avg |
ght)^{1/6}
\right],\end{aligned}$$ where in the second inequality we have used the fact that $\mathbb{P}(\mathcal{E}^c_n) \leq \frac{1}{n}$ by and have absorbed this lower order term into higher order terms by increasing the value of $C$. By a symmetric argument, we have $$\mathbb{P}( \sqrt{n}||\hat\theta - \theta|... | 2,180 | 1,369 | 1,572 | 1,943 | null | null | github_plus_top10pct_by_avg |
mod8$.
\[ab0\] Suppose $n\equiv3\ppmod8$, and $a$ is even, with $6\ls a\ls n-7$. Let $b=n-a-3$. Then $S^{(a,3,1^b)}$ has an irreducible summand of the form $S^{(u,v,2)}$.
Using Theorem \[main\], we need to show that there is a pair $u,v$ with $u+v+2=n$ such that $S^{(u,v,2)}$ is irreducible and $\mbinom{u-v}{u-a}$ is... | 2,181 | 3,147 | 1,775 | 1,986 | 1,818 | 0.785452 | github_plus_top10pct_by_avg |
}\,\langle X\rangle$ be a free associative dialgebra [@Loday:01]. Products in ${\mathrm{Alg}}\,\langle X\rangle$ and ${\mathrm{As}}\,\langle X\rangle$, also in ${\mathrm{Di}}{\mathrm{Alg}}\,\langle X\rangle$ and ${\mathrm{Di}}{\mathrm{As}}\,\langle X\rangle$ are denoted identically. There is no confusion because by the... | 2,182 | 803 | 2,086 | 2,029 | null | null | github_plus_top10pct_by_avg |
urthermore its peak high is increasingly reduced due to the destruction of the Kondo effect in a strong effective magnetic field. Therefore, the spectral properties shown in Fig. \[NRG\_fig-ph-asymmetry\] are consistent with those of an effective Anderson model in the attractive $U$ regime.
### Inelastic contributions... | 2,183 | 219 | 2,380 | 2,341 | 1,796 | 0.785653 | github_plus_top10pct_by_avg |
24% 228 23% 167 14%
CDG Definition ... | 2,184 | 6,863 | 1,283 | 447 | null | null | github_plus_top10pct_by_avg |
$u$]{} (4891,-113)[$1$]{} (3226,-1823)[$1$]{} (2498,-1809)[$P$]{} (3481,-1823)[$1/P$]{}
The shape of the faces $(23)$ is also a hyperbolic pentagon, the faces $(12)$ and $(45)$ are hyperbolic quadrilaterals with three right angles, and the faces $(61)$ and $(56)$ are hyperbolic right triangles. Note that when $P=1, Q<... | 2,185 | 3,794 | 2,213 | 2,042 | null | null | github_plus_top10pct_by_avg |
$\pi$ as a factor be zero so that this equation is considered in $R$. Note that $\bar{h}_i$ and $\bar{h}_j$ are invertible as matrices with entries in $R$ by Remark \[r33\]. Thus $m_{i,j}'=\bar{h}_i^{-1}\cdot {}^tm_{j,i}'\cdot \bar{h}_j$. This induces that each entry of $m_{i,j}'$ is expressed as a linear combination ... | 2,186 | 399 | 1,156 | 2,373 | 3,550 | 0.771596 | github_plus_top10pct_by_avg |
ed by $$\begin{gathered}
\left\{
\begin{aligned}
{\varepsilon }(K_i)=&\,1,\quad {\varepsilon }(E_i)=0, &
{\varepsilon }(L_i)=&\,1,\quad {\varepsilon }(F_i)=0, \\
{\varDelta }(K_i)=&\,K_i\otimes K_i,&
{\varDelta }(L_i)=&\,L_i\otimes L_i,\\
{\varDelta }(K_i^{-1})=&\,K_i^{-1}\otimes K_i^{-1},&
... | 2,187 | 1,531 | 1,977 | 1,889 | null | null | github_plus_top10pct_by_avg |
ng to associated graded objects that maps $U_c{\text{-}{\textsf}{mod}}$ precisely to $\operatorname{{\textsf}{Coh} }(\operatorname{Hilb(n)})$.
{#intro-1.3}
We take our cue from the theory of semisimple Lie algebras. When $n=2$, $U_c$ is isomorphic to a factor of $U(\mathfrak{sl}_2)$ [@EG Section 8] and, for all $n$,... | 2,188 | 1,843 | 819 | 2,224 | 2,664 | 0.778026 | github_plus_top10pct_by_avg |
ge with Conditional Format code
I'm very new to VBA (and any sort of programming in general), so I'm not sure how to proceed here. I'm guessing my error has something to do with overlapping ranges for my conditional formats as I also got errors when the code was set up a different way that were resolved once the rang... | 2,189 | 6,186 | 99 | 1,505 | 27 | 0.836377 | github_plus_top10pct_by_avg |
2m+1}$$ $$\mathrm{and}~ M_k=L_{2m+k} \mathrm{~if~} k\geq 2.$$ Here, $M_i$ is $\pi^i$-modular. We caution that the hermitian form we use on $L^{2m}$ is not $h$, but its rescaled version $\xi^{-m}h$. Thus $M_i$ is $\pi^i$-modular, not $\pi^{2m+i}$-modular.
\[d49\] We define $C(L)$ to be the sublattice of $L$ such that $... | 2,190 | 1,870 | 2,231 | 1,891 | 1,742 | 0.78619 | github_plus_top10pct_by_avg |
frac{\partial (S_0\phi)}{\partial E}}}+\omega\cdot\nabla_x\phi+CS_0\phi.$$
A. In the first instance, we assume that $g=0$. Let $\tilde P_{C,0}$ be the smallest closed extension defined above. Using the these notations, the problem (\[p-s1-b\])-(\[p-s3-b\]) is equivalent to $$\begin{aligned}
\label{eq:problem_x}
(\tild... | 2,191 | 625 | 1,510 | 2,201 | 3,815 | 0.769939 | github_plus_top10pct_by_avg |
{l-1})
T_{l-2}(\lambda_{l-1}-\lambda_{l-2})...T_{m}(\lambda_{m+1}-\lambda_{m})T_{m-1}(\lambda_{m}-s),$$ and for $\lambda_{l-1}\leq a\leq b<\lambda_{l}$ by $$\label{promenade2}U_\Lambda (t,s):= T_{l-1}(t-s).$$ By [@LASA14 Theorem 3.2] we know that $({{U}}_\Lambda)_{\Lambda}$ converges weakly in $MR(V,V')$ as $|\Lamb... | 2,192 | 1,422 | 617 | 2,334 | 3,785 | 0.770097 | github_plus_top10pct_by_avg |
expression for the transition probability is given as $${\cal F}(\omega) = \int_{-\infty}^{\infty} du \, \chi(u) \int_{-\infty}^{\infty} ds \, \chi(u -s) e^{- i \omega s} \, W_{\Theta_0, \epsilon}(u,u-s)
\label{transitionprobability}$$ where $\chi(\tau)$ is the smooth switching function which vanishes for $\tau < \tau... | 2,193 | 3,085 | 3,436 | 2,188 | null | null | github_plus_top10pct_by_avg |
above do not necessarily agree. For example, in the starburst galaxy He 2–10, \[\]/and \[\]/ indicate $>39,000$ K [@he2-10opt], whereas mid–infrared line ratios indicate $<37,000$ K [@roche]. The [ $2.06$ ]{}/ observed by @vr would indicate $=39,000$ K using the conversion of @dpj. At poor signal–to–noise, @vr measur... | 2,194 | 2,284 | 3,250 | 2,409 | null | null | github_plus_top10pct_by_avg |
ubset \D_4$. The manifold $L^{n-4k}_{int}$ is divided into the disjoint union of the two manifolds (with boundaries) denoted by $(L^{n-4k}_{int,x
\downarrow}, \Lambda_{x \downarrow})$, $(L^{n-4k}_{int,y},
\Lambda_{y})$.
1\. The structure group of the framing $(\Psi_{int,x \downarrow},
\Psi_{\Lambda_{x \downarrow}})$ f... | 2,195 | 698 | 1,404 | 2,229 | null | null | github_plus_top10pct_by_avg |
R node
4 neural unit Terminal node
In the AOG, each OR node encodes a list of alternative appearance (or deformation) candidates as children. Each AND node uses its children to represent its constituent regions.
More specifically, the top node is an OR node, which represents a certain semantic part, *e.... | 2,196 | 3,449 | 1,282 | 1,970 | null | null | github_plus_top10pct_by_avg |
nent, nor on the presence of further derivative operators.
To proceed we use the expression of the currents in terms of the bosonic fields $X^a$. First let us focus on the leading term in the expansion . We consider the OPE: \[dXdXOneTerm\] X\^a(z) X\^b(w) = ... + [\^[ab]{}]{} \_[a\_p a\_[p-1]{}...a\_[2]{} a\_1]{}(z-w... | 2,197 | 2,518 | 2,670 | 2,177 | null | null | github_plus_top10pct_by_avg |
ft(u^2+1\right)^3} & 0 & 0 & 0 & 0 & 0 & 0 \\
\mathcal{D}_{\Phi \Phi} & -\frac{2 \left(u^2-1\right)^2}{\left(u^2+1\right)^3} & \frac{4 \left(u^2-1\right)^2}{\left(u^2+1\right)^3} & -\frac{2 \left(u^2-1\right)^2}{\left(u^2+1\right)^3} & \frac{2 \left(u^2-1\right)^2}{\left(u^2+1\right)^3} & 0 & 0 & 0 & 0 & 0 & 0 \\
\ma... | 2,198 | 2,782 | 1,658 | 2,036 | null | null | github_plus_top10pct_by_avg |
/n)T_{K_C}(t/n)\Big]^n\right\Vert}
\leq e^{t(CM+{\left\Vert \Sigma-CS_0I\right\Vert}+{\left\Vert K_C\right\Vert})}.$$
Therefore, by Trotter’s product formula ([@engelnagel Corollary 5.8, p. 227]) we have for ${\bf f}\geq 0$, and for all $t\geq 0$ that G(t)[**f**]{}=\_[n]{}\^n[**f**]{}0, and thus $\phi\geq 0$ by . This... | 2,199 | 545 | 1,570 | 2,097 | null | null | github_plus_top10pct_by_avg |
es. One set consists of the seven periods of $f_1-f_7$ observed in 2007, while we complemented this list with the period of $\mathrm{F}_2$ detected in 1975 to create another set. We selected $\mathrm{F}_2$ because it was the second largest amplitude peak in 1975, which makes it a good candidate for an additional normal... | 2,200 | 3,751 | 2,121 | 2,306 | null | null | github_plus_top10pct_by_avg |
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