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 |
|---|---|---|---|---|---|---|---|
$\theta_0,\lambda>0$ be fixed. We assume that for every $%
\kappa \geq 0$ and $q\in {\mathbb{N}}$ there exist $\pi (q,\kappa )$, $%
\theta _{1}\geq 0$ and $C_{q,\kappa}>0$ such that for every multi-indexes $%
\alpha $ and $\beta $ with $\left\vert \alpha \right\vert +\left\vert \beta
\right\vert \leq q$, $(x,y)\in {\ma... | 3,801 | 2,415 | 1,826 | 3,722 | null | null | github_plus_top10pct_by_avg |
the actual flux and noise distribution in real images. These simulations are described in detail by @sanc04a. We applied the peak subtraction nucleus removal as well as [[galfit]{}]{} to a set of $\sim$2000 quasar images created in this way. Comparing input and output parameter values yielded mean magnitude offsets as... | 3,802 | 3,404 | 4,210 | 3,733 | null | null | github_plus_top10pct_by_avg |
onent $\pi m^2/q\hat E$ arising from a constant field of magnitude $\hat E=\hat Q/r_+^2$. For a large, cold black hole, the rate is exponentially small for $q\sim m$.
We conclude that a large field excursion $|\Delta\phi|\gg1$ requires a large source. Exponentially large sources are required to control curvature invar... | 3,803 | 2,425 | 2,069 | 3,824 | null | null | github_plus_top10pct_by_avg |
tially. Although the error bars in the far regions, i.e., $d > 0.36L$, tend to increase, the average electric fields stay within the error bars shown in Fig.\[res\_ele\].
Based on these discussions, we believe that the simulation results are reliable at least in the intermediate regime, i.e., $1\lambda_{{\rm D}}\lesss... | 3,804 | 2,407 | 3,578 | 3,798 | null | null | github_plus_top10pct_by_avg |
onance. In the first extreme, we assume a featureless density of states in the vicinity of the Fermi energy over an interval $[-2\w_0,2\w_0]$, i. e. $\rho_{\mu,\mu'\sigma}(\w)\to {\rm const.}$ in , and $\beta\w_0\gg 1$ so that the Bose function can be ignored. Then $\tau^{(2)}_{\sigma}(\w) $ will be dominated by the Fe... | 3,805 | 2,578 | 3,577 | 3,485 | 2,951 | 0.775864 | github_plus_top10pct_by_avg |
bar = \frac{h}{2\pi}.$$ Here $h$ is Planck’s constant, and the integral is thought of being over all paths with $\mathbf{x}(0)=0$ and $\mathbf{x}(t)=\mathbf{y}$.\
In the last fifty years there have been many approaches for giving a mathematically rigorous meaning to the Feynman integral by using e.g. analytic continua... | 3,806 | 2,667 | 3,315 | 3,338 | 3,414 | 0.772567 | github_plus_top10pct_by_avg |
L. upper limit on the Higgs mass in the SM is [@mh_smfits; @felcini] $$\label{mh_up}
{M_{\mathrm{H }}}< 220\,{\mbox{${\rm {GeV}}/c^2$} }\,,$$ if one makes due allowance for unknown higher loop uncertainties in the analysis. The corresponding central value is still rather imprecise: $${M_{\mathrm{H }}}= 71^{+75}_{-42}\p... | 3,807 | 2,532 | 4,330 | 3,631 | null | null | github_plus_top10pct_by_avg |
}{\text{\circle*{1.5}}}}}\oplus P_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}$, the map $\iota_s$ is just the difference map $a \oplus b \mapsto a - b$; on $P_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}\otimes_AP_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}$, $\iota_s$ is our fixed homotopy $\iota:P_{{\:\raisebox{1pt}{\tex... | 3,808 | 2,991 | 1,434 | 3,675 | 4,187 | 0.767458 | github_plus_top10pct_by_avg |
figure \[fig:maxdEdt\_vortexCells\]. This analysis is performed using the level sets $\Gamma_{s}(F)\subset\Omega$ defined as $$\label{eq:levelSets}
\Gamma_{s}(F) := \{{\mathbf{x}}\in\Omega : F({\mathbf{x}}) = s \},$$ for a suitable function $F:\Omega\to\mathbb{R}$. In figures \[fig:maxdEdt\_vortexCells\](a–c) we choos... | 3,809 | 1,610 | 3,244 | 3,695 | null | null | github_plus_top10pct_by_avg |
_1$) introduced in Proposition \[prop5\].
$\ell_1$-spectral clustering algorithm {#section5}
======================================
Now, we only consider graphs with an exact cluster structure whose edges have been perturbed by a coefficient $p \in [0,1]$.
$\ell_1$-spectral clustering algorithm is developed in a Mat... | 3,810 | 1,538 | 1,509 | 3,783 | 837 | 0.799114 | github_plus_top10pct_by_avg |
conjugate of $p$, that is, $q=p/(p-1)$ for $1<p<\infty$, $q=\infty$ for $p=1$ or $q=1$ for $p=\infty.$
Recently, Kara\[1\] has defined the Fibonacci difference sequence spaces $\ell_{p}(\widehat{F})$ and $\ell_{\infty}(\widehat{F})$ by$$\ell_{p}(\widehat{F})=\left \{ x=(x_{n})\in \omega:{\displaystyle \sum \limits_{... | 3,811 | 2,399 | 3,182 | 3,296 | null | null | github_plus_top10pct_by_avg |
3
\end{pmatrix},\quad
\begin{pmatrix}
t & 0 & 0\\
-t & t^3 & 0\\
0 & 0 & 1
\end{pmatrix},\quad
\begin{pmatrix}
t & 0 & 0\\
0 & 1 & 0\\
t & -1 & t^3
\end{pmatrix},\quad
\begin{pmatrix}
1 & 0 & 0\\
0 & \rho t & 0\\
0 & t & t^2
\end{pmatrix},\quad
\begin{pmatrix}
1 & 0 & 0\\
0 & \rho^2 t & 0\\
0 & t & t^2
\end{pmatrix}$$ ... | 3,812 | 1,913 | 3,352 | 3,448 | 3,121 | 0.774727 | github_plus_top10pct_by_avg |
need to be the same. However, the results of the wave theory follow qualitatively those of Ref. [@qc-sb] while improving substantially the statistical convergence and increasing the length of the time interval spanned by a factor of $2-3$. Such results are particularly encorauging and suggest the possible application o... | 3,813 | 1,185 | 3,659 | 3,409 | null | null | github_plus_top10pct_by_avg |
{F_{p+1}, F_{p+2}, \ldots F_{v}\}
= \{T_{u+1}, T_{u+2}, \ldots, T_{u+(v-p)}\}$$ and $$\min F_{p+1} <\min F_{p+2} <\cdots <\min F_{v}.$$ Using these upper and lower sequences defined above, we can obtain a crank from expression in normal form called the [*standard expression*]{} of $w$.
Proof of Theorem 1.2
=======... | 3,814 | 3,058 | 3,208 | 3,386 | 1,172 | 0.793234 | github_plus_top10pct_by_avg |
Analysis
==================
The numerical values of the input parameters we used in our analysis are the following: $$\begin{aligned}
m_B=5.28\,GeV\,, m_{\pi}=0.14\,GeV\,, m_b=4.8\,GeV\,, m_c=1.4\,GeV\,,\nonumber\\
1/\alpha=129\,, G_F=1.6639\times10^{-5}\,GeV^2\,,
|V_{tb}V^*_{td}|=0.011\,.\nonumber\end{aligned}$$ The... | 3,815 | 2,049 | 2,667 | 3,455 | 2,812 | 0.776801 | github_plus_top10pct_by_avg |
rossianGlobalMin10], not every case is covered. For instance, if ${\mathcal{K}}\in L^1({\mathbb R}^d)$ and $2-2/d < m < 2$, stationary solutions are only known to exist for sufficiently large mass, and the behavior of smaller solutions is unknown. Moreover, convergence to these stationary solutions is only known in cer... | 3,816 | 2,136 | 1,572 | 3,759 | 1,217 | 0.792546 | github_plus_top10pct_by_avg |
ing non-unitary evolution in matter {#sec:analytical-numerical}
==============================================================================
In this section, we describe the numerical and analytical methods for calculating the neutrino oscillation probability by solving non-unitary evolution in matter.
Numerical ... | 3,817 | 1,161 | 2,360 | 3,879 | null | null | github_plus_top10pct_by_avg |
dual pairing of $S_d({\mathbb{R}})$ and $S'_d({\mathbb{R}})$ also by $\langle \cdot , \cdot \rangle$. Note that its restriction on $S_d({\mathbb{R}}) \times L_d^2({\mathbb{R}}, dx)$ is given by $(\cdot, \cdot )$. We also use the complexifications of these spaces denoted with the subindex ${\mathbb{C}}$ (as well as thei... | 3,818 | 1,555 | 2,946 | 3,452 | null | null | github_plus_top10pct_by_avg |
no free 2D vortices in the limit $u=0$. There are, actually, two options: i) looking for a composite vortex characterized by phase windings $q_1$ and $q_2$ in odd and even layers, respectively, forming a string of length $N_z$ perpendicular to the layers; ii) considering independent vortices $q_1=\pm 1$ only in odd la... | 3,819 | 2,072 | 4,014 | 3,698 | 1,682 | 0.786831 | github_plus_top10pct_by_avg |
ively. We use Cartesian coordinates and the Euclidean inner product[^1], so we shall not generally distinguish between ‘up’ and ‘down’ indices; summation from 1 to $n$ is implied whenever an index is repeated.
Clebsch representation using the inverse map
--------------------------------------------
A canonical variat... | 3,820 | 922 | 3,465 | 3,501 | null | null | github_plus_top10pct_by_avg |
s the highest cold dust temperature, with a maximum of $\sim$40K while the median temperature of the N158-N159-N160 complex is 26.9$^{\pm2.3}$K (28.2 if we restrict the analysis to ISM elements with a 3-$\sigma$ detection in the SPIRE bands). Based on observations made with the TopHat telescope combined with DIRBE data... | 3,821 | 3,511 | 3,801 | 3,651 | 3,864 | 0.769656 | github_plus_top10pct_by_avg |
ix given by an orthogonal system $({\boldsymbol\eta}_k)_{k=1,\dots J}$ of non–zero functions from $L^2_d({\mathbb{R}})$, $J\in {\mathbb{N}}$, under the bilinear form $\left( \cdot ,\mathbf{N}^{-1} \cdot \right)$, i.e. $(M_{\mathbf{N}^{-1}})_{i,j} = \left( {\boldsymbol\eta}_i ,\mathbf{N}^{-1} {\boldsymbol\eta}_j \right... | 3,822 | 2,873 | 2,754 | 3,384 | null | null | github_plus_top10pct_by_avg |
given $H_3$ flux. More precisely, the components that are not connected by T-duality to a given $H_3$ flux are $f_{ab}^a$ and $Q_a^{ab}$ (with indices not summed). It is common procedure in the literature not to consider these fluxes, and we will also not consider them in this paper.
We then move to the representation... | 3,823 | 3,410 | 3,791 | 3,493 | null | null | github_plus_top10pct_by_avg |
BX}^\dagger)(\mathbf{BX}^\dagger)^T$$ and $\mathbf{c}_i\perp\mathbf{c}_j$ for $i\neq j$.
It is sufficient to prove that $\mathbf{m}_i\perp\mathbf{m}_j$ for $i\neq j$. From $\mathbf{A}=\mathbf{X}^T\mathbf{X}$ we have $$\mathbf{d}=\mathbf{Ae}=\mathbf{X}^T\mathbf{Xe},$$ $$2m=\mathbf{d}^T\mathbf{e}=\mathbf{e}^T\mathbf{X}^... | 3,824 | 2,615 | 3,174 | 3,483 | null | null | github_plus_top10pct_by_avg |
nt paths on ${{\mathbb S}}_0$. In addition, ${\mathfrak{S}}'$ is trivially a subset of ${\mathfrak{S}}'_0$ in [(\[eq:Ssupset\])]{}. Therefore, we have $|{\mathfrak{S}}_0|\leq|{\mathfrak{S}}'_0|$. This completes the proof of [(\[eq:piNbd\])]{} for $j=0$.
Here, we summarize the basic steps that we have followed to bound... | 3,825 | 2,162 | 2,875 | 3,535 | 3,507 | 0.771862 | github_plus_top10pct_by_avg |
inition, $\underline{N(k)} = eM$ where $M = \widetilde{S}_{c+k-1}\circ \cdots \circ \widetilde{S}_{c}(X)$, in the notation of . By Proposition \[shiftonO\] $M$ also has a finite filtration by standard modules and so [@GGOR Proposition 2.21] shows that $M$ is a finitely generated free module over ${\mathbb{C}}[{\mathfra... | 3,826 | 3,138 | 1,589 | 3,705 | null | null | github_plus_top10pct_by_avg |
gin{aligned}
\langle N_F^0 \rangle=L \int \frac{dk}{2\pi} \Big[ e^{\beta
\left(k^2/2m -\mu\right)}+1\Big]^{-1}.\end{aligned}$$ In the limit $T\to 0$ and using the fact that after resonance $\mu\simeq \epsilon_b/2$, the fraction of atoms that are unbound is exponentially small. Therefore, (\[N45\]) becomes $$\begin{alig... | 3,827 | 1,641 | 2,438 | 3,729 | null | null | github_plus_top10pct_by_avg |
^1]: Université de Lausanne, Faculté des lettres, Section de philosophie, 1015 Lausanne, Switzerland. E-mail: <Antonio.Vassallo@unil.ch>
[^2]: Ludwig-Maximilians-Universität München, Mathematisches Institut, Theresienstrasse 39, 80333 München, Germany. E-mail: <deckert@math.lmu.de>
[^3]: Université de Lausanne, Facul... | 3,828 | 2,451 | 4,108 | 3,820 | null | null | github_plus_top10pct_by_avg |
{\operatorname{Fun}}(\Gamma,k)$, the homology $H_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(\Gamma,E)$ of the category $\Gamma$ with coefficients in $E$ is by definition the derived functor of the direct limit functor $$\displaystyle\lim_{\overset{\to}{\Gamma}}:{\operatorname{Fun}}(\Gamma,k) \to k{\operatorname{\it\!-... | 3,829 | 3,307 | 2,654 | 3,410 | null | null | github_plus_top10pct_by_avg |
pear to want lag(). This is complicated, because your dates are not well-formed, but that is fixable:
select t1.entity, t1.submissionperiod,
lag(t1.submissionperiod) over (partition by t1.entity order by convert(date, '01-' + t1.submissionperiod)) as prev_submissionperiod,
t1.value,
lag(t1.value)... | 3,830 | 7,331 | 90 | 2,951 | 63 | 0.829519 | github_plus_top10pct_by_avg |
ial components of the S-matrixes and the phases for two systems are interdependent (also see [@Cooper.1995.PRPLC], p. 278–279): $$\begin{array}{cc}
S_{l}^{(1)}(k) = - S_{l}^{(2)}(k), &
\delta_{l}^{(1)}(k) = \delta_{l}^{(2)}(k) + \pi/2.
\end{array}
\label{eq.2.4.9}$$
Let’s consider a spherically symmetric quantum s... | 3,831 | 1,529 | 1,920 | 3,848 | null | null | github_plus_top10pct_by_avg |
ional regularization in place is determining how to trade off classification accuracy and gradient orthogonality. Our defense framework requires little computational overhead to filter operations such as blurs and sharpens, and is not particularly computationally intensive when there are VAEs to train. Training a numbe... | 3,832 | 3,509 | 1,188 | 2,950 | null | null | github_plus_top10pct_by_avg |
d we show below that this multifunction is infact the Dirac delta “function” $\delta_{\nu}(\mu)$, usually written as $\delta(\mu-\nu)$. This suggests that in $\textrm{Multi}(V(\mu),\mathbb{R})$*, every $\nu\in V(\mu)$ is in the point spectrum of $\mu$*, so that *discontinuous functions that are pointwise limits of func... | 3,833 | 3,577 | 3,959 | 3,350 | 3,173 | 0.774289 | github_plus_top10pct_by_avg |
astro-ph/0712.1202) Wang, W.-H., Cowie, L.L., Barger, A.J. 2004, [ApJ]{}, 613, 655 Wang, W.-H., Cowie, L.L., Barger, A.J. 2006, [ApJ]{}, 647, 74 Wang, W.-H., et al. 2007, [ApJ]{}, 670, L89 Webb, T. M. A., et al. 2006, [ApJ]{}, 636, L17 Wilson, G. W., et al. 2008a, [MNRAS]{}, in press (astro-ph/0801.2783) Wilson, G. W.,... | 3,834 | 1,554 | 3,264 | 3,545 | null | null | github_plus_top10pct_by_avg |
cal Higgs states in addition to the light CP-even (SM like) Higgs boson. The coupling of the Higgs bosons to the bottom quark depends on the MSSM parameters, particularly, $\tanb$. In addition, the couplings also depend on the bottom quark threshold corrections and the effect of these corrections have been the subject ... | 3,835 | 2,709 | 2,141 | 3,611 | null | null | github_plus_top10pct_by_avg |
{-\theta _{0}\xi _{1}(l)}\lambda _{n}^{-\theta _{0}\omega
_{1}(l)}\Phi _{n}(0))^{pm_{0}}\int_{{\mathbb{R}}^{d}}\frac{dx}{\psi _{p\eta
-l^{\prime }-p\chi }(x)}.\end{aligned}$$We conclude that $$\left\Vert \Psi _{\eta ,\kappa }\phi _{t}^{n,m_{0}}\right\Vert
_{2h+q,2h,p}\leq Ct^{-\theta _{0}\xi _{1}(q+2h)}\times \lambda _... | 3,836 | 1,439 | 1,755 | 3,895 | null | null | github_plus_top10pct_by_avg |
or a fixed set of parameters, statistical data are collected by running 30 independent simulations. In each run, a maximum displacement step of colloids ${d_{c}=0.01\sigma _{2}}$ and droplets ${d_{d}=d_{c}\sqrt{\sigma _{2}/\sigma _{\textrm{d}}}}$ ensures that Monte Carlo simulations are approximately equivalent to Brow... | 3,837 | 2,394 | 4,586 | 3,728 | 3,182 | 0.774219 | github_plus_top10pct_by_avg |
\[eq:SW:13\]). The remaining arbitrary quantities are arbitrary functions of the $x$’s and $u$’s, which have to be used to satisfy the conditions (\[eq:SW:18\]). However, in the particular case when the system (\[eq:SW:1\]) has two equations in two dependent variables, the two-dimensional matrix $L$ is defined by a sin... | 3,838 | 4,252 | 4,174 | 3,612 | 3,953 | 0.769023 | github_plus_top10pct_by_avg |
_2|\leq N$.
Let $V$ be the vase from the previous example. Then $V$ is not coarsely equivalent to $\mathbb R$.
According to the previous example $\sigma(V)=1$ and according to [@MMS Corollary 3.7] $\sigma(\mathbb R)=2$.
[99]{}
B. Miller, J. Moore, and L. Stibich. *An invariant of metric spaces under bornologous equ... | 3,839 | 1,074 | 4,084 | 3,693 | null | null | github_plus_top10pct_by_avg |
mprises the inputs $(x_1,x_2)$, the outputs $(\delta_1,\delta_2,\delta_3,\delta_4)$ and a number of neurons in the hidden layers. If ${r}={{\left( {{{{x}}}_{1}}^{T},{{{{x}}}_{2}}^{T} \right)}^{T}}$ and $\delta=(\delta_1,\delta_2,\delta_3,\delta_4)^T$, then the output of the RBFN can be presented by $$\delta\left( r \ri... | 3,840 | 2,337 | 3,483 | 3,670 | null | null | github_plus_top10pct_by_avg |
iii). We see that $b$ is a 1-sided curve and $c$ separates a genus two subsurface containing $a, b$. Complete $\{a, b, c\}$ to a top dimensional pair of pants decomposition $P$ on $N$. We assumed that $\lambda([a])=[a]$. Since $a, b, c$ are pairwise disjoint, there exist $b', c'$ some representatives of $\lambda(b)$ an... | 3,841 | 1,671 | 2,469 | 3,520 | null | null | github_plus_top10pct_by_avg |
1\]. Assume the hypothesis in Theorem \[t1\], and form the polynomial $$P({\mathbf{x}})= h(x_1{\mathbf{u}}_1+\cdots+x_m{\mathbf{u}}_m)/h({\mathbf{e}}).$$ It follows that $P({\mathbf{x}})$ is hyperbolic with hyperbolicity cone containing the positive orthant. Since $\rk({\mathbf{u}}_i) \leq 1$ for all $1\leq i \leq m$ w... | 3,842 | 1,941 | 2,540 | 3,533 | 3,075 | 0.775009 | github_plus_top10pct_by_avg |
ic attractor to be that on which the dynamics is chaotic in the sense of Defs. 4.1. and 4.2. Hence
**Definition 4.3.** ***Chaotic Attractor.*** *Let $A$ be a positively invariant subset of $X$. The attractor* $\textrm{Atr}(A)$ *is chaotic on $A$ if there is sensitive dependence on initial conditions for* all *$x\in A$... | 3,843 | 2,781 | 4,010 | 3,454 | 2,307 | 0.780984 | github_plus_top10pct_by_avg |
this section we give the proof of Theorem \[J\].
**Step 1.** Let$$\omega _{t}(dt_{1},...,dt_{m})=\frac{m!}{t^{m}}1_{\{0<t_{1}<...<t_{m}<t%
\}}dt_{1}....dt_{m}$$and (with $t_{m+1}=t$) $$I_{m}(f)(x)={\mathbb{E}}\Big(1_{\{N(t)=m\}}\int_{{\mathbb{R}}^m_+}\Big(%
\prod_{i=0}^{m-1}P_{t_{m-i+1}-t_{m-i}}U_{Z_{m-i}}\Big)P_{t_1}... | 3,844 | 2,893 | 1,421 | 3,749 | null | null | github_plus_top10pct_by_avg |
athbf{u}}) & := \int_{\Omega} {\mathbf{u}}\cdot\nabla{\mathbf{u}}\cdot{\Delta}{\mathbf{u}}\, d{\mathbf{x}}, \label{eq:Rcub}\end{aligned}$$
so that $\R({\mathbf{u}}) = \R_{\nu}({\mathbf{u}}) + \R_{\textrm{cub}}({\mathbf{u}})$. The values of $\R_{\textrm{cub}}({\widetilde{\mathbf{u}}_{\E_0}})$ are also plotted in figur... | 3,845 | 2,176 | 3,346 | 3,521 | 2,046 | 0.783215 | github_plus_top10pct_by_avg |
ond to noiseless (top), constant noise 20 (middle), and constant noise 40 (bottom), respectively.[]{data-label="fig:boidsefficiency"}](witkowski-fig7-efficiency.jpeg){width=".7\columnwidth"}
We find however that from a certain noise level, the cost to signal is fully compensated by the benefits of signaling, as it hel... | 3,846 | 2,765 | 4,272 | 2,899 | null | null | github_plus_top10pct_by_avg |
ds=\int\limits_{0}^t{\mathbf{1}}_{[0,\tau)}(s)f(s)\,ds\, \\
\text{and }\,\left(A^*f\right)(\tau)=\int\limits_\tau^t f(s)\,ds=\int\limits_{0}^t{\mathbf{1}}_{[\tau,t)}(s)f(s)\,ds.\end{gathered}$$
If ${\mathbf{1}}_{[0,\tau)}$ and ${\mathbf{1}}_{[\tau,t)}$ are Hilbert-Schmidt-kernels, the above integral operators $A$ and ... | 3,847 | 2,618 | 1,158 | 3,815 | null | null | github_plus_top10pct_by_avg |
nal portfolios introduced in §4.1. Not surprisingly, the spectrum of ${\tilde{\sf \sigma}}_{ij}^{crv}$ is found to be highly degenerate. The eigenvector ${{\bf e}^{crv}}^{N}$ corresponding to the major eigenvalue is (exactly) equal to ${\hat{\beta}}_{i}$ \[cf. Eq. (\[438\])\], while the remaining $N-1$ minor eigenvecto... | 3,848 | 3,134 | 3,926 | 3,673 | null | null | github_plus_top10pct_by_avg |
ng the angular momentum of the final state up to $l=0$ and $l=1$, respectively. ](fig3)
The angular distribution of the emitted neutrons can be also calculated using the decay amplitude, Eq. (\[amplitude1\]). The amplitude for emitting the two neutrons with spin components of $s_1$ and $s_2$ and momenta ${\mbox{\boldm... | 3,849 | 2,883 | 3,939 | 3,564 | 2,860 | 0.776478 | github_plus_top10pct_by_avg |
that $c\in {\mathbb{C}}$ satisfies Hypothesis \[morrat-hyp\] and that $c\notin {\mathbb{Q}}_{\leq -1}$. Then the shift functor $\widetilde{S}_c$ restricts to an equivalence between $\mathcal{O}_{c}$ and $\mathcal{O}_{c+1}$ such that $\widetilde{S}_c(\Delta_{c}(\lambda)) \cong \Delta_{c+1}(\lambda)$ for all partitions ... | 3,850 | 2,890 | 2,186 | 3,507 | null | null | github_plus_top10pct_by_avg |
a certain subclass of finitely generated groups. We state the result and postpone the definition of the new notions to the corresponding section.
\[thm:intro2\] Let $G$ be a shortlex combable group with its word metric $d$. Then ${\mathcal{F}}(G,d)$ has the Schauder basis [*(see Theorem \[thm:shortlex\])*]{}.
We men... | 3,851 | 2,841 | 1,454 | 3,586 | null | null | github_plus_top10pct_by_avg |
athbf{P}_{B},\mathbf{R}_{B}\right)$, and $\left(\mathbf{Q}_{C},\mathbf{R}_{C}\right)$, and in the CbD approach the joint distribution imposed on them allows, say, $\mathbf{P}_{A}$ and $\mathbf{P}_{B}$ to be unequal with some probability.
Here we compare the NP and CdB approaches applied to the simplest contextual case... | 3,852 | 4,399 | 4,271 | 3,629 | 2,879 | 0.776374 | github_plus_top10pct_by_avg |
iven by M=-. \[magnetization\] The pressure becomes anisotropic [@Karmakar:2019tdp; @PerezMartinez:2007kw] due to the magnetization acquired by the system in presence of strong magnetic field which results in two different pressure along parallel and perpendicular to the magnetic field direction. The longitudinal press... | 3,853 | 1,329 | 2,467 | 3,592 | null | null | github_plus_top10pct_by_avg |
± 0.0 19 ± 1.0 19.6 ± 2.0 19.6 ± 0.5 20.6 ± 2.0 21 ± 1.0 22.6 ± 3.0 22.3 ± 1.5
Rifampicin 25.6 ± 1.5 28.6 ± 0.5 27.6 ± 1.1 31.6 ± 2.5 28.3 ± 2.8 33.3 ± 1.1 30.3 ± 2.0 34.3 ± 2.0
25 ... | 3,854 | 6,080 | 2,704 | 2,420 | null | null | github_plus_top10pct_by_avg |
sum_{i=l}^n x_i <
\sum_{i=l}^n
y_i\}.$$ Denote by $t_1$ the number of components in $x$ which are equal to $x_n$ while $t_2$ the number of components in $y$ which are equal to $y_n$. If $t_1=t_2=t$ , $x_nx_d\leq x_{n-t}^2$, and $y_ny_d\leq y_{n-t}^2$, then we can also deduce that $x\not\in
M(y)$.
Using the lemmas abov... | 3,855 | 3,039 | 3,024 | 3,514 | 3,972 | 0.768891 | github_plus_top10pct_by_avg |
begin{array}{ll}
S &\xRightarrow{r_1}ABCD\xRightarrow{(r_2r_3r_4r_6r_8r_9)^n}a^nABb^nc^nCD
\xRightarrow{r_2r_3}a^{n+1}EFb^{n+1}c^{n+1}AD \\
& \xRightarrow{r_5r_7}a^{n+1}FCb^{n+1}c^{n+1}ED\xRightarrow{r_{10}r_{11}r_{12}}a^nb^nc^n
\end{array}$$ (in the last phase, the sequences $r_{10}r_{12}r_{11}$ and $r_{12}r_{10}r_{11... | 3,856 | 2,484 | 3,252 | 3,487 | 2,302 | 0.781047 | github_plus_top10pct_by_avg |
{\rm [lat]}}$ for the positive- and negative-parity nucleons via three-point functions with the so-called sequential-source method [@Sasaki:2003jh]. In practice, we evaluate $g_{V,A}^{\pm{\rm [lat]}}(t)$ defined as $$g_{V,A}^{\pm{\rm [lat]}}(t)
=
\frac
{
{\rm Tr}\ \Gamma_{V,A}
\langle B(t_{\rm snk})
J_\mu^{V,A}(t)
\ove... | 3,857 | 3,706 | 293 | 3,770 | null | null | github_plus_top10pct_by_avg |
/P}, & \text{if} & i=d\,\\
0, & \mbox{if} & i\neq d, \end{array} \right.$$ it follows that $\Ext_R^{n-i}(M,\omega_R)\iso \Ext_R^{n-i}(U,\omega_R)$ for all $i\neq d,d+1$. Thus for such $i$ we have $\Ext_R^{n-i}(M,\omega_R)$ is Cohen-Macaulay of dimension $i$ if not the zero module.
Moreover we have the exact sequence $... | 3,858 | 3,173 | 2,692 | 3,320 | 3,011 | 0.775458 | github_plus_top10pct_by_avg |
egin{array}{ccc}
z^4+\zeta ^2-r^2 \eta ^2 & -2 r z^2 \eta
& 2 r \zeta \eta \\
2 r z^2 \eta & z^4-\zeta ^2-r^2 \eta
^2 & - 2 z^2 \zeta \\
2 r \zeta \eta & 2 z^2 \zeta & z^4-\zeta ^2+r^2 \eta ^2 \\
\end{array}
\right) \ ,$$ with the corresponding spinor representation $$\Omega = \frac{1}{\sqrt{f} } \left( z^2 \mathbb{I} ... | 3,859 | 3,005 | 1,126 | 3,744 | null | null | github_plus_top10pct_by_avg |
ment4}
\frac{d}{dt}\mathcal{W}_K(t)\le&
-\sigma_K\beta_K\int_M 2 (\gamma-1)\left[\left| \nabla_i\nabla_jv+\frac{\eta_K}{n(\gamma-1)}g_{ij}\right|^2+({\rm Ric}+Kg)(\nabla v,\nabla v )\right]vu\,dV\notag\\
&-\sigma_K\beta_K\int_M2\left[(\gamma-1)\Delta v+\eta_K\right]^2vu\,dV.\end{aligned}$$
Thus, when ${\rm Ric}\ge-Kg$... | 3,860 | 2,928 | 3,014 | 3,371 | null | null | github_plus_top10pct_by_avg |
g the following result.
\[thm:old\] Let $s\in{\mathbb{N}}$ and $K\ge1$. Let $G$ be an $s$-step nilpotent group $s$, and suppose that $A\subset G$ is a finite $K$-approximate group. Then there exist a subgroup $H$ of $G$ normalised by $A$ and a nilprogression $P_{\text{\textup{nil}}}(x;L)$ of rank at most $K^{O_s(1)}$ ... | 3,861 | 3,023 | 2,246 | 3,609 | 2,519 | 0.779197 | github_plus_top10pct_by_avg |
mall category, and let $A\colon {\mathcal C}\to {\mathsf{Sets}}$ be a functor. We describe a construction to be found in [@MM] of a pair of adjoint functors $f^*\colon {\mathcal{B}}({\mathcal C})\to {\mathsf{Sets}}$ and $f_*\colon {\mathsf{Sets}}\to {\mathcal{B}}({\mathcal C})$. The functor $f_*$ is easier to define an... | 3,862 | 3,979 | 3,949 | 3,573 | null | null | github_plus_top10pct_by_avg |
nitary group $U(n)$: let $\langle \cdot,\cdot\rangle'$ be an arbitrary inner product on $\mathbb{C}^n$. Define a new inner product $\langle \cdot,\cdot\rangle$ by setting $$\langle \xi,\eta\rangle:=\int_{g\in G} \langle g\xi,g\eta\rangle'd\mu(g),$$ where $\mu$ is an invariant probability Haar measure on $G$. It is stan... | 3,863 | 2,706 | 2,106 | 3,437 | null | null | github_plus_top10pct_by_avg |
chi_h\in V_h} \3bar v-\chi_h \3bar \le C_A \left(\sum_{K\in \mathcal{T}_h} h_K^{2s} \|v\|_{s+1,K}^2\right)^{1/2}.$$
The abstract theory of the interior penalty discontinuous Galerkin method can be entirely based on Assumptions [**[I1]{}**]{}-[**[I3]{}**]{}.
\[lem:wellposedness\] Assume [**[I1]{}**]{}-[**[I2]{}**]{} h... | 3,864 | 2,227 | 2,502 | 3,436 | null | null | github_plus_top10pct_by_avg |
mented in an efficient way in $O(L)$ flops. Thus, the complexity of quantizing all the $K$ real-valued approximations is $O(KL)$. Selecting a coefficient vector from the quantized vector set in step \[item:outline:Select\] has a cost of $O(KL)$. Step \[item:outline:Recover\] takes $O(L)$ flops. In summary, the complexi... | 3,865 | 1,760 | 3,100 | 3,496 | 3,492 | 0.77197 | github_plus_top10pct_by_avg |
$\rm 2$ to $\rm 18\,GHz$ with a resolution of $\rm 0.1\,MHz$. We measured the reflection $S$-matrix element $S_{aa}$ first for the unperturbed system, which corresponds to the situation, where no additional antenna is inserted at position $c$. Then we perturbed the system by inserting another antenna at position $c$ w... | 3,866 | 1,423 | 2,179 | 3,970 | null | null | github_plus_top10pct_by_avg |
After using the Poisson identity for each integer and performing the integrations over $\phi_i$ and $A$, the resulting expression becomes Z=\_[{J\_[1,ij]{}},{J\_[2,ij]{}}, {J\_[z,i]{}}]{} [e]{}\^[-H\_J]{}, \[Z2\] H\_J= \_[ij ; a,b]{} (K\^[-1]{})\_[ab]{} J\_[a,ij]{} J\_[b,ij]{} + \_i J\_i\^2, \[H\_J\] where $a,b=1,2$ ... | 3,867 | 2,863 | 4,116 | 3,601 | 3,108 | 0.774826 | github_plus_top10pct_by_avg |
his also means that the Dirac Lagrangian is already in Hamiltonian form.[@GovBook; @FJ]
[^22]: Again, this conclusion is in perfect analogy with what happens for a real and a complex scalar field.[@GovCOPRO2]
[^23]: Note that up to a total time derivative term this function is indeed real under complex conjugation, b... | 3,868 | 2,924 | 1,577 | 3,567 | null | null | github_plus_top10pct_by_avg |
ed D\]) and (\[1st quantized alg\]), and denoted $\tilde{p}(v_{12})=\tilde{p}_{12}$. Comparing with (\[gauge tf r\]), we find that the second line has the form of the gauge transformation with the parameter $$\begin{aligned}
D_\eta\Lambda_{{\mathcal{S}}_1{\mathcal{S}}_2}\
=&\
- D_\eta\Big(D_{{\mathcal{S}}_1}F\Xi A_{{\... | 3,869 | 1,334 | 3,061 | 3,816 | null | null | github_plus_top10pct_by_avg |
t is interesting that for $b=2$ and 4, the smallest value of $\phi$ is obtained for $u=u_\theta$, which is not the case for $b=3$ fractal.
Finally, one should note that in the case $b=3$, for the globular state of a solitary 3D chain ($u>u_\theta$), the coordinates of the corresponding fixed point are $A_G=0$ and $B_G... | 3,870 | 885 | 2,853 | 3,835 | 2,092 | 0.782834 | github_plus_top10pct_by_avg |
[@C2]). Moreover, since $M_0^{\prime\prime}$ is *free of type II* and nonzero, we have a morphism from $G_j$ to the even orthogonal group associated to $M_0^{\prime\prime}$ as explained in Section \[red\]. Thus, the Dickson invariant of this orthogonal group induces the morphism $$\psi_j : \tilde{G} \longrightarrow \m... | 3,871 | 2,717 | 2,737 | 3,574 | 4,085 | 0.768185 | github_plus_top10pct_by_avg |
2}^j{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{z_i{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf m}}+{{\bf k}}$}}
{\overset{}{\longleftrightarrow}}}z'_i\}$}}}\bigg)\bigg(\prod_{\substack{i,i'\ge
2\\ i\ne i'}}{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{{{\cal C}}_{{{\bf m}}+{{\bf k}}}(z_i)\,\cap\,{{\cal C}}_... | 3,872 | 2,544 | 3,055 | 3,549 | null | null | github_plus_top10pct_by_avg |
s A$, and the other is a right module ($A$ just happens to have both structures at the same time). It is better to separate them and introduce the functor $${\operatorname{\sf tr}}:A{\operatorname{\!-\sf bimod}}\to k{\operatorname{\it\!-Vect}}$$ by ${\operatorname{\sf tr}}(M) = M \otimes_{A^{opp} \otimes A} A$ – or, eq... | 3,873 | 2,722 | 1,900 | 3,551 | 4,103 | 0.768088 | github_plus_top10pct_by_avg |
imes\tau_b{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{m'_b,n'_b\text{ even}\}$}}}\sum_{\substack{
{\partial}{{\bf m}}''={\varnothing}\\ {\partial}{{\bf n}}''={\overline{b}}{\vartriangle}x}}\frac{w_{{{\cal A}}{^{\rm c}}\cap{{\cal B}}{^{\rm c}}}
({{\bf m}}'')}{Z_{{{\cal A}}{^{\rm c}}\cap{{\cal B}}{^{\rm c}}}}\,\frac{w... | 3,874 | 2,531 | 2,141 | 3,553 | null | null | github_plus_top10pct_by_avg |
fined as the number of examples of class $j$ that were classified as class $i$ by the binary classifier. In other words, a class is assigned to $\mathcal{C}_{i1}$ if it is less frequently confused with $c_1$ than with $c_2$, and to $\mathcal{C}_{i2}$ otherwise. Finally, the binary classifier is re-trained on the new me... | 3,875 | 4,720 | 3,862 | 3,608 | 564 | 0.805549 | github_plus_top10pct_by_avg |
CP asymmetry is different depending on the value of $r$. For $r a\ll 1$ increasing $a$ results in enhancement of the CP asymmetry, while for $r a \gg 1$ it is suppressed. These two cases correspond to the charm and kaon cases, respectively. It follows that the $\Delta I=1/2$ rule in kaons reduces CP violating effects, ... | 3,876 | 1,081 | 2,700 | 3,738 | null | null | github_plus_top10pct_by_avg |
x}}-{\mathbf{x}}_0) = 0
\}$ for $\mathbf{n} = [1,0,0]$ and ${\mathbf{x}}_0 = [1/2,1/2,1/2]$ is shown in figures \[fig:RvsE0\_FixE\_small\](f)-(h), where the transition from cellular structures to a localized vortex structure as enstrophy increases is evident.
The results corresponding to large values of $\E_0$ are sho... | 3,877 | 2,361 | 3,707 | 3,794 | 3,249 | 0.773763 | github_plus_top10pct_by_avg |
\text{-}Grmod}}$ consisting of ${\mathbb{N}}$-graded $S$-modules $M=\bigoplus_{i\in{\mathbb{N}}}M_i$. It is immediate from the definitions that the identity map $\iota: M=\bigoplus_{i\in{\mathbb{N}}}M_i\mapsto M=\bigoplus_{i\in{\mathbb{N}}}M_i$ gives equivalences of categories $S{{\textsf}{\text{-}Grmod}}_{\geq 0}\sime... | 3,878 | 3,100 | 1,911 | 3,624 | 3,295 | 0.773392 | github_plus_top10pct_by_avg |
_i^{n-2}-+\cdots =0.$$ Thus $A[r_1,\dots, r_m]$ is integral over $A\bigl[\sigma_{ij}\bigr]$, hence also over the larger ring $A[r_1,\dots, r_m]^G$.
By assumption $R=U^{-1}A[r_1,\dots, r_m]$ where $U$ is a subgroup of units in $A[r_1,\dots, r_m]$. We may assume that $U$ is $G$-invariant. If $r/u\in R$ where $r\in A[r_1... | 3,879 | 3,363 | 3,319 | 3,411 | null | null | github_plus_top10pct_by_avg |
for U.S. Stock, U.S. Bond and world FX market participants. ? 1999-2001 Earnings.com, Inc., All rights reserved about us | contact us | webmaster | site map privacy policy | terms of service
Anna:
I know that you have been negotiating with Cheryl Nelson about the new ECI
account. I am receiving urgent cal... | 3,880 | 2,586 | 2,438 | 3,902 | null | null | github_plus_top10pct_by_avg |
left| P \right|}}$ divides ${\ensuremath{\left| \Sigma_{n-r} \right|}}$, and so ${\ensuremath{\left| \Sigma_n:\Sigma_{n-r} \right|}}= n(n-1)\cdots (n-r+1)$ should be a $p'$-number. But this is a contradiction, since $p<r$.
If $p=k=2$, then, by Lemma \[angraph\], it should be $G=\Sigma_n$, so the above reasonings work ... | 3,881 | 2,425 | 2,048 | 3,652 | 2,826 | 0.776747 | github_plus_top10pct_by_avg |
Eq. (\[eq:concentration\]) provides $$\begin{aligned}
-v\frac{dc}{d\xi} = D \frac{d^2 c}{d\xi^2}-ac+f(\xi).
\label{eq:concentration1}
\end{aligned}$$ Equation (\[eq:concentration1\]) leads to the following solutions $$\begin{aligned}
c(\xi) = \begin{cases}
\beta_1 \exp \big(\lamb... | 3,882 | 5,546 | 654 | 3,390 | null | null | github_plus_top10pct_by_avg |
tes and whose signals therefore are $\propto g_d^2$ or $\propto \frac{1}{f_a^2}$. Measuring an amplitude and not a rate makes it much easier to push the sensitivity up to high $f_a$ (low axion couplings).
Further, the actual size of the EDM is set by the product $g_d a$, where $a$ is the local dark matter, axion or AL... | 3,883 | 3,502 | 4,241 | 3,619 | 2,230 | 0.781612 | github_plus_top10pct_by_avg |
. To continue the computation we combine current conservation with the Maurer-Cartan equation to write the anti-holomorphic derivative of the $z$-component of the current in terms of a bilinear : |j\_[L,z]{}\^a = -i f\^2 [f\^a]{}\_[bc]{} :j\^c\_[L,z]{} j\^b\_[L,|z]{}:. Since all the poles in the OPE between $j^c_{L,z}$... | 3,884 | 464 | 3,440 | 3,552 | null | null | github_plus_top10pct_by_avg |
4,\ \#\#\#\#^ 3: 8.3, 4: 75.0, 5: 16.7 8.3 47.0 ± 13.4 ^\#\#\#\#^
\*^1^: Days after transplanting; \*^2^: n = 5; \*^3^: n = 9; \*^4^: n = 11; ^\#^*p* \< 0.05; ^\#\#^*p* \< 0.01; ^\#\#\#^*p* \< 0.005; and ^\#\#\#\#^*p* \< 0.001 *vs.* WT.
2.2. Alkaloid... | 3,885 | 1,767 | 2,260 | 3,582 | 2,956 | 0.775841 | github_plus_top10pct_by_avg |
distribution of energy spent per resetting event. Red disks come from experiments and the theoretical prediction of [Eq. (\[Eq:Energy\])]{} is plotted as a solid blue line. d) Normalized energy spent per resetting event at constant power vs. the normalized radial return velocity as given by [Eq. (\[minmax\])]{}. The mi... | 3,886 | 2,607 | 4,379 | 3,703 | 4,038 | 0.7685 | github_plus_top10pct_by_avg |
in Lemma \[lem:alter\_m(W)\]. Let $$M=M(W)=\int_{\Rc_r}\La f_\pi(\La;W)\dd\La.$$ Assume that $$f_\pi(\La;W)=0 \quad \textup{for all $\La\in\partial\Rc_r$}.$$ Then $\ph_H$ is minimax relative to the KL loss $(\ref{eqn:loss})$ if $\De(W;\pi_2^J)\leq 0$, where $$\De(W;\pi_2^J)=\De_1(W;\pi_2^J)-\De_2(W;\pi_2^J)-(q-3r-3)\t... | 3,887 | 2,858 | 1,567 | 3,817 | null | null | github_plus_top10pct_by_avg |
’]{} P\^b\_a\_b()\[eqn:kappagen\],\
-u\^a u\^b T\_[ab]{}\^[diss]{}+\_[j=1]{}\^[N]{}u\^a T\_[ay\_j]{}\^[diss]{} =-\[eqn:zetagen\]. Using these we can extract the viscosities $\hat\eta$, $\hat\zeta$ and the matrix of conductivities $\hat\kappa_{jj'}$. The derivative $\partial \hat P/ \partial \hat\epsilon$ is evaluated a... | 3,888 | 1,032 | 3,717 | 3,684 | null | null | github_plus_top10pct_by_avg |
rences in the appraisal of the cancer diagnosis, the perception of family functioning, cancer-related emotions and perceived quality of life across members within one family.
Materials and Methods {#s1}
=====================
Participants
------------
The sample consisted of 115 families where one child has been diag... | 3,889 | 1,157 | 3,188 | 3,725 | null | null | github_plus_top10pct_by_avg |
$v_{50}$
(km s$^{-1}$) (km s$^{-1}$)
$\pm$187 $\pm$0.06 $\pm$0.3
1968L 321 0.219 0.00 12.03(08) ... 4020(300)
1969L 784 ... | 3,890 | 5,658 | 1,460 | 3,269 | null | null | github_plus_top10pct_by_avg |
providers operating SDNTNs. As observed, the CP can be either centralized (providers A and B) or distributed (provider C) [@Gringeri2013SDNTN; @distributed2013sdtns]. As shown in the bottom left, the SDN-controller might host different applications that run on a Network Operating System (NOS). In addition, there is a ... | 3,891 | 408 | 4,061 | 3,349 | null | null | github_plus_top10pct_by_avg |
efan-Boltzmann law for the neutrino flux at the resonance surface, a neutrino emitted in a direction ${\bf \hat{p }}$ has a momentum $p=E_{o}(1+4h_{T}^{-1}\delta r)$, where $E_{o}=E(r_{o})$. Therefore it carries an angular momentum $${\bf l=}r_{o}E_{o}({\bf \hat{r}}\times {\bf \hat{p})}\left[
1+4h_{T}^{-1}\delta r\righ... | 3,892 | 4,315 | 3,540 | 3,618 | null | null | github_plus_top10pct_by_avg |
er she want to bind or to reject the contract. In the former case she measures all unmeasured qubits in the Accept basis, in the latter in the Reject base. Both parties then report Trent for each respective qubit whether they measured it in the Accept or Reject basis, and submit respective measurement outcomes. Trent v... | 3,893 | 1,375 | 3,519 | 3,642 | null | null | github_plus_top10pct_by_avg |
Cleft( of District Court~a Co., Texas
BY DEPUlY
JAS FAMILY LIMITED PARTNERSHIP § IN THE DISTRICT COURT .
#4LTD §
... | 3,894 | 830 | 3,198 | 3,941 | null | null | github_plus_top10pct_by_avg |
---------------------- ---------------------------- --------- ------ --------------------
1 31 Female None Negative Fever Disturbance of consciousness Bacterial meningitis Sacroiliitis Blood culture Cerebrospina fluid l Positive None Penicillin... | 3,895 | 5,653 | 2,274 | 2,744 | null | null | github_plus_top10pct_by_avg |
atisfy reflection positivity, their mean-field behavior cannot necessarily be established, even in high dimensions. If we believe in universality, we expect that finite-range models exhibit the same mean-field behavior as soon as $d>4$. Therefore, it has been desirable to have approaches that do not assume reflection p... | 3,896 | 2,652 | 3,811 | 3,388 | 2,615 | 0.778417 | github_plus_top10pct_by_avg |
tal magnitudes of $m_{\mathrm{{F606W}},\mathrm{tot}}=21.5$ and $m_{\mathrm{{F850LP}},\mathrm{tot}}=21.6$, respectively. This image is shown in Figure \[fig:unresplot\]. With the higher sensitivity we now indeed find a host galaxy component in the [F606W]{}-band image after PSF subtraction of 4.4% of the total flux. The... | 3,897 | 2,258 | 4,197 | 3,787 | 1,085 | 0.794585 | github_plus_top10pct_by_avg |
integrate to $\langle \hat X_\nu\rangle \delta_{\mu,\mu'}$. Hence, for a vanishing displacement $\langle\hat X_\nu \rangle=0$, either the Green’s function $G^{(1)}_{d\sigma}$ is identically zero, or its spectrum (i.e., the transmission function $\tau^{(1)}_{\sigma}(\w)$) has equal positive and negative spectral contri... | 3,898 | 2,526 | 2,655 | 3,558 | null | null | github_plus_top10pct_by_avg |
}(\omega) \; d\theta \; d{{\mathbb P}}(\omega)\end{aligned}$$ ($N$ is a.s. countable). For a given point $X\in N$ and a given $\omega\in \Omega$, the indicator function $${{\bf 1}}_{{\scriptstyle \underline{\gamma}_{X} \;\mbox{\small{or}}\; \overline{\gamma}_{X} \;\mbox{\small{admits}}\; \theta \;\mbox{\small{as}}} \at... | 3,899 | 2,406 | 1,802 | 3,669 | 3,290 | 0.773419 | github_plus_top10pct_by_avg |
{\left \lfloor{\ell\beta_1} \right \rfloor} \}$. Since set $S$ is chosen randomly, $i,\i$ and $j \in \Omega$ are random. Throughout this section, we condition on the random indices $i,\i$ and the set $\Omega$ such that event $E_{\beta_1}$ holds. To get a lower bound on $\P[\sigma^{-1}(i),\sigma^{-1}(\i) > \kappa - \ell... | 3,900 | 1,971 | 1,938 | 3,755 | null | null | github_plus_top10pct_by_avg |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.