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 |
|---|---|---|---|---|---|---|---|
um map is defined by the formula, $$\label{momentummapdef}
\mathbf{J} (\nu_q) \cdot \xi = \left\langle \nu_q, \xi_Q (q)
\right\rangle,$$ where $\nu_q \in T ^{\ast} _q Q $ and $\xi \in \mathfrak{g}$. In this formula $\xi _Q $ is the infinitesimal generator of the action of ${G}$ on $Q$ associated with the Lie algebra el... | 3,701 | 2,027 | 2,326 | 3,640 | null | null | github_plus_top10pct_by_avg |
\beta}\nabla^{\alpha} R^{\nu\beta}=0$. Therefore, for conformally invariant space-times, there are 1 relations coming from the corollary of the Lovelock theorem, and 7 coming from $W_{\mu\nu\alpha\beta}=0$, so there are 8 scalars less in the reduced basis, i.e. 8 scalars left.
General order 6 linear combination for FL... | 3,702 | 4,013 | 3,517 | 3,358 | null | null | github_plus_top10pct_by_avg |
( (36)(10) \: + \: 162 \right) \: + \: 20 \: = \: 281, \\
n_H - n_V & = & -12 \: \neq \: 244,\end{aligned}$$ and so we see that this cannot satisfy anomaly cancellation, mechanically verifying our previous observation that this theory cannot be consistent.
More generally, any heterotic compactification on a gerbe, in ... | 3,703 | 3,091 | 3,187 | 3,249 | 1,463 | 0.789256 | github_plus_top10pct_by_avg |
}_{\tau^{i}_D}) = u(x),\qquad \text{almost surely.}
\label{FKMC}$$ For practical purposes, since it is impossible to take the limit, one truncates the series of estimates for large $n$ and the [central limit theorem]{}gives $\mathcal{O}(1/n)$ upper bounds on the variance of the $n$-term sum, which serves as a n... | 3,704 | 4,086 | 3,800 | 3,211 | null | null | github_plus_top10pct_by_avg |
ea}}^{-1}\cap \{x_{i_j}=0\}$ for $j = 1,\cdots, n$. We denote by $\Delta_{p,\theta}$ such a hyperbolic polyhedron. Then the conditions for $\theta$ as in the definition of $\Theta_n$ ensures us that the hyperbolic polyhedron $\Delta_{p,\theta}$ has exactly $n$ facets.
Let us denote by $(i_1 i_2)i_3 \ldots i_n$ or simp... | 3,705 | 3,015 | 2,757 | 3,180 | null | null | github_plus_top10pct_by_avg |
integration conserves the total energy of the planet and $L_Z$ within 1 to 2%.
The planet is set on a circular orbit at the distance $r_p$ from the star. The initial inclination angle of the orbit with respect to the disc is $I_0$. In the simulations reported here we have taken $n=1/2$ in equation (\[sigma\]). The fun... | 3,706 | 3,040 | 4,309 | 3,429 | 3,327 | 0.773133 | github_plus_top10pct_by_avg |
ith some $a_i\in\ZZ$ and some graded prime ideals $P_i$.
The module $M$ is called a [*graded (pretty) clean module*]{}, if it admits a (pretty) clean filtration which is a graded prime filtration.
Similarly we define multigraded filtrations and multigraded (pretty) clean modules.
We denote by $(N)_i$ the $i$th grade... | 3,707 | 2,756 | 2,942 | 3,221 | 3,275 | 0.773543 | github_plus_top10pct_by_avg |
X}^{(x)}(t)\not\in B(x,\abs{x}) }\notag \\
& = |x|^{\alpha}\,\inf\Bp{|x|^{-\alpha}t> 0\colon |x| \hat{X}^{(\mathbf{i})}(|x|^{-\alpha}t)\not\in B( x,\abs{x}) }\notag \\
& = |x|^{\alpha}\,\inf\Bp{u> 0\colon \hat{X}^{(\mat... | 3,708 | 4,934 | 2,949 | 3,044 | null | null | github_plus_top10pct_by_avg |
Model \[sec:model\]
================================
The glycerol concentration $p$ of the solution was controlled in our experiments, which led to a change in the viscosity $\mu$ shown in Appendix A. In this section, we consider a viscosity dependence of the camphor boat velocity. Now, the annular glass chamber used... | 3,709 | 3,441 | 3,365 | 3,495 | 3,107 | 0.774852 | github_plus_top10pct_by_avg |
h $\Delta_{\theta}$ ($\Delta_{p}$), and zero otherwise. This choice corresponds to the so-called “water-bag" distribution which is fully specified by energy $h[f]=e$, momentum $P[f]=\sigma$ and the initial magnetization ${\mathbf
M_0}=(M_{x0}, M_{y0})$. The maximum entropy calculation is then performed analytically [@a... | 3,710 | 3,317 | 3,782 | 3,572 | null | null | github_plus_top10pct_by_avg |
lde{p}]\Psi\,,
\end{aligned}$$ and can further be rewritten in the form of a linearized gauge transformation: $$\begin{aligned}
\delta_{[\tilde{p},\tilde{p}]}\ \Phi\ =&\
\xi_0 Q [\tilde{p},\{Q, M\}]\Phi\
=\
\xi_0 Q [\tilde{p}, M]Q\Phi
\nonumber\\
\cong&\
-Q(\xi_0[\tilde{p}, M]Q\Phi)
+ \eta(\xi_0X_0[\tilde{p}, M]Q\Ph... | 3,711 | 1,881 | 1,749 | 3,750 | null | null | github_plus_top10pct_by_avg |
f the event horizon of the black hole, as in the case of the Bekenstein-Hawking entropy [@SWH1; @Bekenstein]. Here $ C=\dfrac{1}{(1+2\alpha m)} $ is the deficiency factor in the limit of $ \phi $ as it runs from $ 0\rightarrow 2\pi C $ (as mentioned earlier). In FIG. \[plot3\], we have shown the variation of the total ... | 3,712 | 837 | 1,993 | 3,628 | 3,455 | 0.772247 | github_plus_top10pct_by_avg |
,\mathcal{V})$ ***denoted by* ***$f_{\alpha}\overset{\mathbf{G}}\longrightarrow\mathscr{M}$, is the subset of $\mathcal{D}_{-}\times\mathcal{R}_{-}$that is the union of the graphs of the function $F$ and the multifunction $G^{-}$ $$\mathbf{G}_{\mathscr{M}}=\mathbf{G}_{F}\bigcup\mathbf{G}_{G^{-}}$$*
*where $$\mathbf{G}... | 3,713 | 3,407 | 3,826 | 3,315 | 1,613 | 0.787636 | github_plus_top10pct_by_avg |
breaking, $$\begin{aligned}
\nonumber
T<T_c: &\qquad \langle L(\vec x)\rangle = 0\,,\quad F_q=\infty\,, \\
T>T_c: &\qquad \langle L(\vec x)\rangle \neq 0\,, \quad F_q<\infty\,.
\label{eq:orderdisorder}\end{aligned}$$ The expectation value of the Polyakov loop can be deduced from the equations of motion of its effe... | 3,714 | 3,327 | 3,411 | 3,241 | 2,997 | 0.775538 | github_plus_top10pct_by_avg |
trial 1/0 indicator) and *treat* ~*ij*~ (treatment group 1/0 indicator) value for each of 100 participants in each of 10 trials.
Next, based on the previous meta‐analysis,[22](#sim7930-bib-0022){ref-type="ref"} we set the true parameter values for this simulation to be as follows: θ = −9.66 (summary treatment effect; ... | 3,715 | 1,981 | 3,981 | 3,583 | 1,480 | 0.789047 | github_plus_top10pct_by_avg |
atement for the case when $\Phi$ is a word. If $\Phi=z$ then the claim is evident. If $\Phi=uv$ then $z$ can belong to either $u$ or $v$. Let $z$ belongs to $u$. Then using Lemma \[lemma2\] we obtain $$\begin{gathered}
\Psi^z_{{\mathrm{As}}}(\mathcal{J}(\Phi))=\Psi^z_{{\mathrm{As}}}(\frac{1}{2}[\mathcal{J}(u)\mathcal{J... | 3,716 | 1,689 | 2,476 | 3,598 | null | null | github_plus_top10pct_by_avg |
tal derivative $B$-field constructed from a 2-cocycle on the isometry group with respect to which we dualise and then dualising.
In this note we develop this line of reasoning. We begin by outlining the essential features of Yang-Baxter $\sigma$-models and the technology of non-abelian T-duality in Type II supergravit... | 3,717 | 2,278 | 2,129 | 3,404 | null | null | github_plus_top10pct_by_avg |
inite paths, say $\gamma$ and $\gamma'$, respectively below and above the horizontal axis, and satisfying the following property: there is no semi-infinite path in the RST, different from $\gamma$ and $\gamma'$, and trapped between them (in the trigonometric sense). Parts $(i)$ and $(ii)$ of Theorem \[HN1\] force $\gam... | 3,718 | 2,428 | 2,407 | 3,318 | 3,373 | 0.772794 | github_plus_top10pct_by_avg |
{true_inequality}$$ A superficial look at the instance (\[prop17\]) of Proposition 17 can induce the idea that, for [*every*]{} D-strategy ${\cal S}$ (in particular for $S_6$), the inequality $$EqLv(E(L_1),E(L_1)) \leq EqLv(E(\bot),E(\bot),{\cal S})
\label{false_inequation}$$ holds. In fact, what shows Proposition 17, ... | 3,719 | 797 | 3,667 | 3,510 | null | null | github_plus_top10pct_by_avg |
$X$, and $G/K \cong H$ acts effectively. In this case, $\mathfrak{X} = [X/G]$ is a $K$-gerbe. A vector bundle on $\mathfrak{X}$ is a $G$-equivariant vector bundle on $X$, and as such, the $K$ action is defined by a representation of $K$ on the fibers of that vector bundle. This is the more general picture of the second... | 3,720 | 3,127 | 2,332 | 3,418 | null | null | github_plus_top10pct_by_avg |
k} - h_{m} ) (\Delta_{L} - h_{k} )^2 (\Delta_{L} - h_{m} )^2 }
\nonumber \\
&\times&
\biggl\{
(\Delta_{L} - h_{m} )^2
e^{- i ( h_{k} - h_{n} ) x}
- (\Delta_{L} - h_{k} )^2
e^{- i ( h_{m} - h_{n} ) x}
+ ( h_{k} - h_{m} )( h_{k} + h_{m} - 2 \Delta_{L} ) e^{- i ( \Delta_{L} - h_{n} ) x}
\biggr\}
\biggr]
\nonumber ... | 3,721 | 1,085 | 2,977 | 3,626 | null | null | github_plus_top10pct_by_avg |
e classification of tissue degeneration {#Sec11}
--------------------------------------------------
Variable reduction and classification based on PCA show that the samples can be grouped into two linearly separable classes based on variations in their NIR spectral data using the 1^st^ and 2^nd^ principal components s... | 3,722 | 2,185 | 2,730 | 2,766 | null | null | github_plus_top10pct_by_avg |
r in Krakow, to the effect that the need for ethical approval is waived for the experiments.
During all experiments we manipulated one main variable, namely the visibility level (amount of smoke was increasingly greater in consecutive experiments). Additionally, during experiment 3 we asked participants to obtain *the... | 3,723 | 1,343 | 3,546 | 3,144 | null | null | github_plus_top10pct_by_avg |
ion parameters do not require linear estimators. For example we can define $$\gamma_{{\widehat{S}}}(j) = \mathbb{E}_{X,Y}\Biggl[ |Y-\hat\mu_{{\widehat{S}}(j)}(X_{{{\widehat{S}}}(j)})| -
|Y-\hat\mu_{{\widehat{S}}}(X_{{\widehat{S}}})|\ \Biggr], \quad j \in {\widehat{S}},$$ where $\hat\mu_{{\widehat{S}}}$ is any regre... | 3,724 | 2,912 | 3,358 | 3,503 | 1,729 | 0.786328 | github_plus_top10pct_by_avg |
neral one-dimensional tiles, Gruslys, Leader and Tan [@gltan16] conjectured that there is a bound on the dimension in terms of the size of the tile:
For any positive integer $t$, there exists a number $d$ such that any tile $T \subset \mathbb{Z}$ with $|T| \leq t$ tiles $\mathbb{Z}^d$.
This conjecture remains unresol... | 3,725 | 3,632 | 3,741 | 3,634 | null | null | github_plus_top10pct_by_avg |
J}_\Omega$ with the vector field $X \in
\mathfrak{X}(\Omega)$ yields $$\begin{aligned}
\left\langle \MM{J}_\Omega (\MM{l}, \MM{\pi} ), X \right\rangle & =
-\,\langle\, \MM{\pi} \cdot {\mathrm{d}}\MM{l} \,, X \,\rangle
\\& =
-\,\int_S
\pi_kl_{k,j}X_j (\MM{x})
\,{\mathrm{d}}V(\MM{x})
\\& =
-\,\left\langle (\MM{l}, \MM{\p... | 3,726 | 1,609 | 3,081 | 3,444 | null | null | github_plus_top10pct_by_avg |
egrees of freedom, the naive choice for the supercharges would be $Q=-i\partial_\eta$ and $Q^\dagger=i\partial_{\eta^\dagger}$. However, a quick check then finds that all anticommutators $\left\{Q,Q,\right\}$, $\left\{Q^\dagger,Q^\dagger\right\}$ and $\left\{Q,Q^\dagger\right\}$ vanish, thus not reproducing the supersy... | 3,727 | 3,883 | 3,628 | 3,361 | null | null | github_plus_top10pct_by_avg |
tilde{\varphi}/\tilde{M}^1$ by using points of the scheme $(\underline{M}'\otimes\kappa)/ \underline{\pi M}'$, based on Lemma \[la3\]. To do that, we take the argument in pages 511-512 of [@C2].
Recall from two paragraphs before Lemma \[la3\] that $(1+)^{-1}(\underline{M}^{\ast})$, which is an open subscheme of $\unde... | 3,728 | 2,970 | 2,467 | 3,506 | null | null | github_plus_top10pct_by_avg |
H \delta(g\cdot f)-\delta(f)d\mu(f)\\
&=\int_H \Big(\delta(g\cdot f\cdot h)-\delta(h)\Big)-\Big(\delta(f\cdot h)-\delta(h)\Big)d\mu(f)\\
&=\int_H \delta(g\cdot f\cdot h)-\delta(f\cdot h)d\mu(f\cdot h)=P(\delta(g)),\end{aligned}$$ which finishes the claim.
Let $X$ denote the range of $P$ and let us show that it is line... | 3,729 | 2,566 | 3,122 | 3,169 | null | null | github_plus_top10pct_by_avg |
igma}_n^2\partial^2_{xx} v_n&=&0, \ (t,x)\in (0,1]\times\mathbb{R},\\
v_n(0,x)&=& \varphi (x).\end{aligned}$$ As $\varphi$ vanishes at infinity, $$\mathbf{M}(R):=\mathop{\max_{|x|\ge R;}}_{1\ge t\ge 0}\big\{|u(t,x)|, |v_n(t,x)|: \ n\in\mathbb{N} \big\}$$ approaches zero as $R$ approaches $+\inft... | 3,730 | 3,081 | 1,559 | 3,402 | null | null | github_plus_top10pct_by_avg |
} &=&-\frac{v_{x}}{u}AG(\phi )sin\phi +\varepsilon
\left[ u\left( \frac{d^{2}v_{z}}{d\phi ^{2}}-v_{z}Q\right) +\frac{v_{x}}{\gamma }\frac{dv_{x}}{d\phi }\frac{dv_{z}}{d\phi }-\left( 1-\frac{v_{z}}{\gamma }\right) \left( \frac{dv_{z}}{d\phi }\right) ^{2}\right] \label{52}\end{aligned}$$
From the above equations we de... | 3,731 | 5,194 | 1,604 | 3,246 | null | null | github_plus_top10pct_by_avg |
od}}$;
- the associated graded ${\mathbb{Z}}$-algebra $\operatorname{gr}B$ has $\operatorname{gr}B{\text{-}{\textsf}{qgr}}\simeq \operatorname{{\textsf}{Coh} }\operatorname{Hilb(n)}$, the category of coherent sheaves on the Hilbert scheme of points in the plane.
This can be regarded as saying that $U_c$ sim... | 3,732 | 3,394 | 711 | 3,504 | null | null | github_plus_top10pct_by_avg |
or which we can have singularities (irregularities) that integrate to a finite number . In other words, we think about energy correlators as if they are regular functions up to a set of isolated points $\{ \xi^*_i \}$ where they are defined only in the functional sense.
Even though the terms like $\delta(1-\xi)$ do ap... | 3,733 | 3,995 | 3,863 | 3,339 | null | null | github_plus_top10pct_by_avg |
gned}$$
Similarly, we observe that from Lemmas \[lem:diff1\] and \[lem:diff3\] $$\begin{aligned}
\tr[\Dc_\La\{f_\pi(\La;W)\La\}M]
&=\tr[\La M\Dc_\La f_\pi(\La;W)]+f_\pi(\La;W)\tr[M\Dc_\La\La]\\
&=\frac{1}{2}\Big[(q+r+1)\tr M+\frac{2}{\pi_2^J(\La)}\tr[\La M\Dc_\La \pi_2^J(\La)] \\
&\qquad -\frac{1}{v}\tr(MWW^\top\La)\B... | 3,734 | 1,998 | 1,507 | 3,696 | null | null | github_plus_top10pct_by_avg |
n $M_0''$ is *free of type II* and so we have a morphism from $G_{j-1}$ to the even orthogonal group associated to $M_0^{\prime\prime}$. Here, $G_{j-1}$ is the special fiber of the smooth integral model associated to $Y(C(L^{j-1}))$. Thus, the Dickson invariant of this orthogonal group induces the morphism $$\psi_j : \... | 3,735 | 2,964 | 1,755 | 3,679 | 2,327 | 0.780836 | github_plus_top10pct_by_avg |
from the bracket equation for the quantum-classical density matrix (\[eq:rhoW\]), by dealing in a suitable manner with the Poisson bracket terms, the most simple way to find the representation of the wave equations (\[eq:fckrk\]) in the adiabatic basis is to first represent Eq. (\[eq:rhoW\]) in such a basis and then de... | 3,736 | 1,405 | 2,479 | 3,715 | null | null | github_plus_top10pct_by_avg |
nfalling gas remains $\sim10^2$, and while the cold-mode temperature remains $\sim 10^4~$K, the temperature of infalling gas increases with halo mass. Both of these differences can be explained by noting that, around the virial radius, hot-mode gas accounts for a greater fraction of the infall in higher mass haloes (se... | 3,737 | 786 | 2,056 | 3,804 | 3,931 | 0.769218 | github_plus_top10pct_by_avg |
conformal Field Theories from Principal 3-Bundles over Twistor Space,” arXiv:1305.4870 \[hep-th\]. S. Palmer and C. Sämann, “Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory,” J. Math. Phys. [**54**]{}, 113509 (2013) \[arXiv:1308.2622 \[hep-th\]\]. S. Palmer, “Higher Gauge Theory and M-Theory,” arXi... | 3,738 | 3,008 | 831 | 3,414 | null | null | github_plus_top10pct_by_avg |
}{{\mathbb S}}={\varnothing},~{{\mathbb S}}_{{\cal A}}={\varnothing}\}.\end{aligned}$$ We note that $|{\mathfrak{S}}|$ is zero when there are no paths on ${{\mathbb G}}_{{\bf N}}$ between $v$ and $x$ consisting of edges whose endvertices are both in ${{\cal A}}{^{\rm c}}$, while $|{\mathfrak{S}}'|$ may not be zero. The... | 3,739 | 1,529 | 2,771 | 3,625 | 2,910 | 0.776148 | github_plus_top10pct_by_avg |
$ for all $t\in [0,\ol{\tau}]$.
We write this solution as $\gamma(x,\omega,E,t)$, and write $\ol{\tau}(x,\omega,E)$ for the end-point of its maximal interval of existence. Because $S_0\geq \kappa>0$ on $G\times I$ (by ), we have $$\begin{aligned}
\label{eq:inequality_gamma}
\gamma(x,\omega,E,t')\geq \gamma(x,\omega,E,... | 3,740 | 2,097 | 2,508 | 3,682 | null | null | github_plus_top10pct_by_avg |
ete.
Shapovalov determinants for bicharacters with finite root systems {#sec:shapdetgen}
=================================================================
In Sect. \[sec:shapdet\] we mainly considered bicharacters $\chi \in {\mathcal{X}}_5$. Here we extend our results to all $\chi \in {\mathcal{X}}_3$ with $\chi (\be... | 3,741 | 2,610 | 902 | 3,694 | null | null | github_plus_top10pct_by_avg |
e interval. An example would be : *Usain Bolt won the gold medal at the 2008 summer Olympics in Bejing*. With the availability of annotators that can provide us with accurate semantic annotations in form of named entities, geographic locations, and temporal expressions; we can leverage the growing number of knowledge r... | 3,742 | 5,894 | 3,474 | 2,661 | null | null | github_plus_top10pct_by_avg |
ee effective interactions have been tested and compared in RHB plus proton-neutron relativistic QRPA calculations of $\beta$-decay half-lives for the isotopic chains: Fe, Ni, Zn, Cd, Sn and Te. The nuclear ground-states have been calculated in the RHB model with the DD-ME1, D$^{3}$C, and D$^3$C effective interactions i... | 3,743 | 2,316 | 3,503 | 3,393 | null | null | github_plus_top10pct_by_avg |
hbar \omega_{ge}\sigma _{ee} \\ \nonumber
&&+\hbar g_{0}\left( a^{\dag}\sigma _{ef}+a\sigma _{fe}\right) + 2\hbar \Omega(\sigma_{fg}+\sigma_{gf}) \cos\omega_p t.\end{aligned}$$ Here, the atomic operator $\sigma_{jk}$ is defined as $\sigma_{jk}=|j\rangle\langle k|$ with $\{|j\rangle,|k\rangle\}=\{|g\rangle,|e\rangle, |... | 3,744 | 2,338 | 3,739 | 3,627 | 2,939 | 0.775967 | github_plus_top10pct_by_avg |
=\bigoplus \operatorname{{\textsf}{ogr}}^n H_c$, where $\operatorname{{\textsf}{ogr}}^n H_c = \operatorname{{\textsf}{ord}}^n H_c/\operatorname{{\textsf}{ord}}^{n-1}H_c$. Then is equivalent to the assertion that $\operatorname{{\textsf}{ogr}}H_c$ is isomorphic to the skew group ring ${\mathbb{C}}[{\mathfrak{h}}\oplus {... | 3,745 | 2,629 | 1,268 | 3,508 | 3,547 | 0.77162 | github_plus_top10pct_by_avg |
=0}^{\infty}f^{-i}(\textrm{Per}(f))$ (where $\textrm{Per}(f)$ denotes the set of periodic points of $f$) are totally disconnected, it is expected that at any point on this complement the behaviour of the limit will be similar to that on $\mathcal{D}_{+}$: these points are special as they tie up the iterates on $\textrm... | 3,746 | 2,628 | 3,361 | 3,376 | 2,845 | 0.776566 | github_plus_top10pct_by_avg |
rder of $\vert W \vert^4 \sim 10^{-4}$, except for the $\mathcal{O} (W^2)$ difference in normalization constant in the disappearance probability. It is practically the limit of order of magnitude that can be explored by the next generation neutrino oscillation experiments.
We must note, however, that this conclusion i... | 3,747 | 2,389 | 3,649 | 3,417 | null | null | github_plus_top10pct_by_avg |
es}. \end{aligned}$$ If $J$ is a $p$-perfect subgroup of $G$ such that $p\mid |N_{G}(J)/J|$, then there are two conjugacy classes of subgroups $L$ of $G$ such that $O^{p}(L)=J$. We denote by $S_{J}$ a subgroup of $G$ such that $J\subset S_{J}$ and $O^{p}(S_{J})=J$. The block matrix indexed by $J$ is of size $2$. The f... | 3,748 | 2,265 | 2,827 | 3,352 | null | null | github_plus_top10pct_by_avg |
o make it a global and standardised therapy to treat COVID-19 infection.
RECOMMENDATIONS
===============
Through this review, we recommend a few guidelines which could help to speed up the process of viral deactivation and production of the vaccine. Also, these recommendations will help the COVID-19 patients to recov... | 3,749 | 1,241 | 3,924 | 3,300 | null | null | github_plus_top10pct_by_avg |
}-[E]{}=0,U(0)=f. The solution of can be written in the form (cf. Example \[desolex1\] below) $$\begin{gathered}
U(x,\omega,E,t)
=
(U(t))(x,\omega,E) \\
=
H(R_x(E_m)-R_x(E)-t)
{{S_0(x,R_x^{-1}(R_x(E)+t))}\over{S_0(x,E)}} f(x,\omega,R_x^{-1}(R_x(E)+t)),\end{gathered}$$ where $H$ is the Heaviside function and $$R_x(E):=\... | 3,750 | 2,880 | 1,874 | 3,530 | null | null | github_plus_top10pct_by_avg |
analogous argument it is easy to prove that the element $\aleph= \sum_{j=1}^{j_0} \alpha_j$ is $\Z/2 \int \D_4$-framed cobordant to the manifold obtained by gluing the union $-OP[\tilde L^{n-4k}_x] \cup 2^j(-OP)^{j-1}[\tilde L^{n-4k}_y]$ by an $\I_3$-manifold along the boundary. Moreover, this cobordism is relative wi... | 3,751 | 3,150 | 1,713 | 3,466 | 3,937 | 0.769147 | github_plus_top10pct_by_avg |
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$ \lambda_{i} \bigl((A+H... | 3,752 | 3,885 | 236 | 3,709 | 1,024 | 0.795493 | github_plus_top10pct_by_avg |
rdered by $\sqsubseteq$, then the set $$S := \bigcup_{s \in P} s$$ is still a D-q-strategy and fulfills: $$\forall s \in P, s \sqsubseteq S.$$ Hence the extension ordering over the set of D-q-strategies w.r.t. $(T,T')$ is inductive.
Let $S \subseteq ({\cal R}\times{\cal R})^*$ be finite and let $n:= \max\{ |\alpha| \m... | 3,753 | 1,262 | 2,690 | 3,442 | 3,225 | 0.773905 | github_plus_top10pct_by_avg |
}
For either model (stratified or random intercept), under any given scenario and data generating mechanism, using ML always produced more downwardly biased estimates than REML (Table [3](#sim7930-tbl-0003){ref-type="table"}), as expected.([14](#sim7930-bib-0014){ref-type="ref"}, [15](#sim7930-bib-0015){ref-type="ref"... | 3,754 | 653 | 4,444 | 3,293 | 1,888 | 0.784669 | github_plus_top10pct_by_avg |
as a product of pairwise coprime t.s.m elements in $R$. Since ${\rm gcd}(\widehat{f}_i^*, f_i^*)=1$, there exist polynomials $b_i, c_i \in R$ such that $b_i\widehat{f}_i^*+c_if_i^*=1$. Let $e_i=b_i\widehat{f}_i^* \in R$. Then\
(i) $e_1, e_2, \ldots, e_t$ are mutually orthogonal in $R$;\
(ii) $e_1+e_2+\cdots +e_t... | 3,755 | 4,319 | 3,972 | 3,412 | 2,964 | 0.775793 | github_plus_top10pct_by_avg |
25 1
**Flexibility of multiplexing** Low---requires manual dispensing bioreagents High---Printing nL/µL size dots or multi-line ... | 3,756 | 7,465 | 1,330 | 1,527 | 2,008 | 0.78357 | github_plus_top10pct_by_avg |
tions in consideration of predictions errors. Actually, in some cases, it is best not to act as predicted because of prediction errors. For example, the paper [@Yamaguchi2018] formulates a method for minimizing the expected value of the procurement cost of electricity in two popular spot markets: [*day-ahead*]{} and [*... | 3,757 | 3,287 | 3,301 | 3,341 | null | null | github_plus_top10pct_by_avg |
Recruiting University of Hong Kong, Queen Mary Hospital
2\. Ribavirin ... | 3,758 | 5,617 | 2,989 | 2,632 | null | null | github_plus_top10pct_by_avg |
rovided is a step‐by‐step guide to our simulation study. For simplicity, and to considerably speed up the many simulations, we removed the baseline adjustment term in models (1) and (2), such that it does not exist in any of the data generating mechanisms or models fitted in our simulations. In other words, we generate... | 3,759 | 587 | 3,638 | 3,556 | null | null | github_plus_top10pct_by_avg |
hcal{V},\mathcal{E})}}_0 \rangle}=\bigotimes_{\{i,j\} \in \mathcal{E}} CZ_{ij}{| {g_{(\mathcal{V})}}_0 \rangle}.$$
![\[Graph\] (Color online) Example of a mathematical graph associated to a physical graph state. We have displayed a possible partition of this graph, splitting the system in three parts $\mathcal{A}$, $\... | 3,760 | 1,141 | 2,250 | 3,735 | 3,274 | 0.773549 | github_plus_top10pct_by_avg |
ft\{ W ^{\dagger} A (UX) \right\}_{K k}
\biggr]
\nonumber \\
&+&
\sum_{K}
e^{- i \Delta_{K} x}
W_{\alpha K} W^*_{\beta K}.
\label{S-alpha-beta-2nd}\end{aligned}$$
The oscillation probability to second order in $W$ {#sec:probability-2nd}
--------------------------------------------------
In this section, we discuss... | 3,761 | 3,051 | 3,253 | 3,405 | null | null | github_plus_top10pct_by_avg |
behavior at large distances ($r\sim a_B$) [@Kh]. In the leading approximation the PNC interaction
=8.cm
related to the weak charge is due to Z-bozon exchange, see Fig.1a. Calculation of the corresponding weak interaction matrix element gives [@Kh] $$\label{pnc}
<p_{1/2}|H_{W}|s_{1/2}>_0=M_0\propto (F_sG_p-G_sF_p)|_{r... | 3,762 | 2,387 | 3,723 | 3,641 | null | null | github_plus_top10pct_by_avg |
^2(\alpha r cos\theta-1)^6}{r^6}.$$ The Weyl scalar is defined by $$W=C_{abcd}C^{abcd},$$ where the $C_{abcd} $ is the Weyl curvature tensor. For the $C$-metric (non-rotating black hole) the Weyl scalar is evaluated as $$\label{non-rot_Wscalar}
W_{c}=\dfrac{48m^2(\alpha r cos\theta-1)^6}{r^6}.$$ This result is expected... | 3,763 | 4,472 | 3,736 | 3,476 | null | null | github_plus_top10pct_by_avg |
of the form $I_{n!}E$, $[n] \in \Lambda$, $E \in {\operatorname{Shv}}({{\mathcal C}}^n)$ admissible, and to prove the first claim, it suffices to consider $M_\#=I_{n!}E$ of this form. In degree $0$, is the definition of the functor ${\operatorname{\sf tr}}_\#$, and the higher degree terms in the right-hand side vanish... | 3,764 | 3,201 | 1,253 | 3,578 | 2,848 | 0.776548 | github_plus_top10pct_by_avg |
anyway. Of course, this concern applies to the scalar ALP model we have considered, other fields or models could change this. Having ALP dark matter with the coupling we are considering changes the status of the nucleon EDM from a fundamental constant of nature to a parameter dependent on the local field value. Thus we... | 3,765 | 1,763 | 3,433 | 3,596 | null | null | github_plus_top10pct_by_avg |
Since $\langle W \rangle = 0$, the second moment is also the variance of the work distribution. The third moment is given by $$\label{3mom}
\left\langle W^{3}\right\rangle = \frac{\hbar^{3}\Omega^{2}}{4}
\left[\nu\eta^{2} +
\omega_{0}
... | 3,766 | 4,302 | 3,368 | 3,382 | null | null | github_plus_top10pct_by_avg |
r dimensions, by taking the coordination number sufficiently large.
Organization
------------
In the rest of this paper, we focus our attention on the model-dependent ingredients: the lace expansion for the Ising model (Proposition \[prp:Ising-lace\]) and the bounds on (the alternating sum of) the expansion coefficie... | 3,767 | 2,653 | 1,321 | 3,491 | 503 | 0.807716 | github_plus_top10pct_by_avg |
8.57cm"}
Plotted in Fig. \[fig1\] are snapshots at different times of three trajectories at different disorder strengths $d$, all prepared in the same local initial state. At small $d$ it is clear that the exciton moves almost uniformly in space and time, with the lattice having been occupied uniformly after short tim... | 3,768 | 2,210 | 4,112 | 3,581 | null | null | github_plus_top10pct_by_avg |
W14] also considered balanced allocation on graphs where the number of balls $m$ can be much larger than $n$ (i.e., $m\gg n$) and the graph is not necessarily regular and dense. Then, they established upper bound ${\mathcal{O}}(\log n/\sigma)$ for the gap between the maximum and the minimum loaded bin after allocating ... | 3,769 | 1,128 | 2,734 | 3,314 | 1,355 | 0.790548 | github_plus_top10pct_by_avg |
$, $Y_2(k) =
\RP^{31} \ast \dots \ast \RP^{31}$ the joins of the $k$ copies of the standard projective space $\RP^{31}$. Let us define $J_j
=Y_1(\frac{n+2}{64}-j+2)) \times Y_2(j+2)$ $Q =
Y_1(\frac{n+2}{64}+2) \times Y_2(\frac{n+2}{64}+2)$. For a given $j$ the natural inclusions $J_j \subset Q$ are well-defined. Let us... | 3,770 | 1,791 | 3,303 | 3,342 | 3,964 | 0.768934 | github_plus_top10pct_by_avg |
to examine whether [Fe [i]{} ]{}abundances show any trend with line strength for different values of $\xi$. Since $\xi$ for the samples of OAO, [Fran[ç]{}ois ]{}, and Clegg et al. were estimated using the empirical relation of Edvardsson et al. (1993), the uncertainty of $\Delta\xi \simeq 0.22$ [${\rm km \: s^{-1}}$]{... | 3,771 | 1,501 | 3,235 | 3,644 | null | null | github_plus_top10pct_by_avg |
3.18 2.35 0--10 22,602 (122)
Trust in the Legal System: 0 = No trust at all; 10 = Complete trust 4.47 2.65 0--10 22,461 (122)
Trust in the Parliament: 0 = No trust at... | 3,772 | 7,202 | 1,402 | 1,132 | null | null | github_plus_top10pct_by_avg |
een the layers has immediate implication for the windings along $z$-direction – the minimal length $M$ of the element $J_i$ must be $M=2$ in Eq.(\[GenM\]). Thus, the stiffness $u_r$ in the limit $u<<1$ becomes u\_r = 4[e]{}\^[-1/u\_V]{}= u\^2, \[UR3\] where the asymptotic expression $ u_V=\frac{1}{2 \ln (2/u)}$ [@Villa... | 3,773 | 1,690 | 1,080 | 3,795 | 1,699 | 0.786657 | github_plus_top10pct_by_avg |
1 290 0
S4 86.43 1316 1 729 1
MEAN 89.09 534 \<1 278 \<1
**NINAPRO data** **COMPLETE** **REDUCED**
**Accuracy** **SVs... | 3,774 | 2,639 | 3,463 | 3,685 | null | null | github_plus_top10pct_by_avg |
0.001
MCP-1 (pg/mL) 51.3 41.04 0.1
TNF-α (pg/mL) 50.06 ... | 3,775 | 5,541 | 1,049 | 3,309 | null | null | github_plus_top10pct_by_avg |
s $2$-complete with joint-set $B'$. Now, for each $i \in \{1,2,3\}$ we have $M' \con (B'-B_i')|(B_i' \cup X') \cong m'U_{1,2}$ and $B_i'$ is a basis of $M \con (B-B_i')$, so for each $x \in X'$, there exists a unique $b_i(x) \in B_i'$ such that $\{x,b_i(x)\}$ is a parallel pair of $M \con (B'-B_i')$. Let $B(x) = \{b_1(... | 3,776 | 3,185 | 1,621 | 3,662 | null | null | github_plus_top10pct_by_avg |
Other modifications we have added are summarized as follows.
### Chemical and thermal processes {#sec:chemistry}
To solve the chemical and thermal processes, we use the same methods developed in [@Hosokawa:2016aa] with several modifications. Unlike in [@Hosokawa:2016aa], we omit ${\mathrm{H}}_2$ chemistry assuming th... | 3,777 | 2,745 | 4,293 | 3,767 | 3,674 | 0.770782 | github_plus_top10pct_by_avg |
een the RCTs approved in Freiburg and RCTs approved in Canada (Hamilton) and Switzerland (Basel, Lausanne, Zurich, and Lucerne) at the same time period. Details about this cohort of 1017 RCTs were reported earlier \[[@pone.0165605.ref001], [@pone.0165605.ref012]\].
Results {#sec008}
=======
Included studies {#sec009}... | 3,778 | 2,276 | 1,227 | 3,488 | null | null | github_plus_top10pct_by_avg |
oduction functional by $$I(\theta) = \int \theta {\left\vert{\nabla}\log \theta + \eta\right\vert}^2 d\eta. \label{def:I_linear}$$ In the nonlinear case $m > 1$, the corresponding quantities are, $$H(\theta) = \frac{1}{m-1}\int \theta^m d\eta + \frac{1}{2}\int {\left\vert\eta\right\vert}^2 \theta d\eta, \label{def:H}$... | 3,779 | 2,230 | 1,758 | 3,630 | 2,019 | 0.783472 | github_plus_top10pct_by_avg |
^k-B^k_j)$ for all $j \in \{k+1,\dotsc,3\}$, and so that $M^k \con (B^k-B^k_j)|(B^k_j \cup X^k) \cong m_kU_{1,2}$ for all $j \in \{1, \dotsc, k\}$. This clearly holds for $k = 0$, and setting $k = 3$ will give the claim. The argument essentially consists of three aplications of Theorem \[selfdual\].
Suppose that these... | 3,780 | 2,742 | 2,161 | 3,287 | null | null | github_plus_top10pct_by_avg |
and (c) $\rho_{d_{0\sigma},c^\dagger_{0\sigma}}(\w)$. The spectral functions have been calculated with NRG. We set $U/\Gamma_0=10$, $\omega_0/\Gamma_0=0.1$ and different colors indicate various unconventional Holstein couplings $\lambda_c$. []{data-label="NRG_fig2"}](fig17-Elastic-Lc){width="50.00000%"}
The elastic pa... | 3,781 | 1,179 | 3,218 | 3,797 | 3,921 | 0.769288 | github_plus_top10pct_by_avg |
\quad x{\mathbin\vdash}y{\mathbin\vdash}z + y{\mathbin\vdash}x{\mathbin\vdash}z,\ x>y; \quad x{\mathbin\vdash}x{\mathbin\vdash}y; \quad x{\mathbin\dashv}y{\mathbin\dashv}y$$ is a Gröbner-Shirshov basis. Reduced words are of the form $$\dot x_1x_2\dots x_k,\ k\ge 1,\ x_2<x_3<\dots < x_k,$$ and the set of all reduced wor... | 3,782 | 1,708 | 3,326 | 3,523 | null | null | github_plus_top10pct_by_avg |
of the complement of the ramification locus (a projective curve) and their influence on the topology of the original surface as a branched covering of the projective plane. He realized that not only the type of singularities of the branched locus was relevant, but their position as well ([@Zariski-irregularity]). In pa... | 3,783 | 1,087 | 4,081 | 3,484 | null | null | github_plus_top10pct_by_avg |
ons, they have turned to theorem proving approach and used the PVS theorem prover to analyze the DEOS scheduler [@Ha04]. They model the operations of the scheduler in PVS and the execution timeline of DEOS using a discrete time state-transition system. Properties of time partitioning (TP) are formulated as predicates o... | 3,784 | 5,051 | 3,799 | 3,463 | null | null | github_plus_top10pct_by_avg |
^2-2b^2=1\}$ for a flat $A$-algebra $R$. Thus we cannot guarantee that $a-1$ is contained in the ideal $(2)$, which should be necessary in order that $(a, b)$ is an element of $\underline{G}(R)$.
The special fiber of the smooth integral model {#sf}
==============================================
In this section, we wi... | 3,785 | 3,400 | 903 | 3,571 | null | null | github_plus_top10pct_by_avg |
prob(b>\{c,d\})\, \,\prob(c>d) \nonumber \\
&=& \frac{e^{\theta_a}}{(e^{\theta_a}+e^{\theta_b}+e^{\theta_c}+e^{\theta_d} ) } \,
\frac{e^{\theta_b}}{(e^{\theta_b}+e^{\theta_c}+e^{\theta_d} )} \,
\frac{e^{\theta_c}}{(e^{\theta_c}+e^{\theta_d})} \, \;.\end{aligned}$$ We use the notation $(a>b)$ ... | 3,786 | 4,489 | 3,099 | 3,398 | null | null | github_plus_top10pct_by_avg |
directions as well so that the two-point energy correlator cannot be identically zero at non-coincident points. Thus, we have a contradiction and we are compelled to conclude that in CFTs with finite energy correlators the three-point function of the stress tensor cannot be purely bosonic.
Let us now relax the finite... | 3,787 | 2,889 | 3,307 | 3,215 | null | null | github_plus_top10pct_by_avg |
\- -0.020 (0.022)
Age Median \- -0.042 (0.032) \- ... | 3,788 | 5,772 | 865 | 3,060 | 3,992 | 0.768748 | github_plus_top10pct_by_avg |
o feel lonely. This was the case for all family members. Finally, there was also a significant effect of the *age of the ill child at diagnosis* \[χ^2^(1) = 4.58, *p* = 0.03\]: the older the ill child was at diagnosis, the less all family members reported to feel lonely. None of the other variables were significantly r... | 3,789 | 1,273 | 3,928 | 3,637 | null | null | github_plus_top10pct_by_avg |
field, of the form $$B \: \mapsto \: B \: + \: d \Lambda,$$ the Chan-Paton gauge field must necessarily transform as $$A \: \mapsto \: A \: - \: \Lambda$$ in order to preserve gauge-invariance on the open string worldsheet, and such affine translations correspond, in terms of transition functions, to the modified over... | 3,790 | 2,463 | 3,503 | 3,438 | null | null | github_plus_top10pct_by_avg |
ve where and
Theorem \[t2\] is a direct consequence of the following multivariate version, which will be proved in Section 5.1.
\[t4\] Let $X_1, X_2, \dots$ be an i.i.d. sequence of $d$-dimensional random vectors under a sublinear expectation $\E$ such that for a family of linear expectations $\{E_\theta: \theta\in ... | 3,791 | 2,117 | 1,142 | 3,674 | null | null | github_plus_top10pct_by_avg |
& & \lim(\mathcal{F})\subseteq\lim(\mathcal{G})\\
\textrm{adh}(\zeta)\subseteq\textrm{adh}(\chi) & & \textrm{adh}(\mathcal{G})\subseteq\textrm{adh}(\mathcal{F});\end{aligned}$$
a filter $\mathcal{G}$ finer than a given filter $\mathcal{F}$ corresponds to a subnet $\zeta$ of a given net $\chi$. The implication of thi... | 3,792 | 3,989 | 3,478 | 3,381 | 1,526 | 0.788619 | github_plus_top10pct_by_avg |
c sigma model on the Hitchin moduli space ${\cal M}_H(G,C)$, with a twisted bundle over that moduli space, twisted by an element of $H^2(Z(G))$. Since the Hitchin moduli space is defined by modding out the adjoint action of $G$, the center is trivial, and so one could naturally replace the Hitchin moduli space with a m... | 3,793 | 2,979 | 3,490 | 3,226 | 2,821 | 0.776768 | github_plus_top10pct_by_avg |
d_{\mathcal{P}}(\overline{X}_n)]\le \frac{\big(7\pi^2R+\sqrt{\overline{\sigma}^2+16R^2}\big)}{n^{\frac{2}{5}}}.$$
Statistical inference for uncertain distributions
-------------------------------------------------
The upper bound in Theorem \[t7\] provides us with a quantitative version of the fact that for large $n$... | 3,794 | 2,681 | 1,024 | 3,706 | 3,791 | 0.770068 | github_plus_top10pct_by_avg |
they are the positivity sets of functions from the linear space of functions of the two variables $u$ and $x$ spanned by $f^{1/2}(x)$, $xf^{1/2}(x)$ and $K_1^{-1}(u/f^{1/2}(x))$. Hence, by a result of Dudley (e.g. Proposition 5.1.12 in de la Peña and Giné (1999)) the subgraphs of ${\cal K}_1$ are VC of index 4. If the ... | 3,795 | 2,816 | 1,943 | 3,547 | null | null | github_plus_top10pct_by_avg |
−0.55 0.41 −1.36, 0.26
Daily 90 −0.58 0.84 −2.23, 1.08 90 −0.004 0.006 −0.016, 0.008 91 −0.37 0.54 −1.43, 0.69
BFP, body fat percentage; SE: standard error; CI: confidence interval; OR: odds ratio; SSB, sugar-sweetened beverage; WC, waist circumference; WHR,... | 3,796 | 4,776 | 3,011 | 3,272 | null | null | github_plus_top10pct_by_avg |
Thurston’s polyhedralization is constant, that is $n$. Under this assumption, the topology of a deformation will be almost constant.
In [@KojimaNishiYamashita], we discussed local behavior of the deformations appeared in our setting near the equal weight. When $n = 5$, the deformations are topologically a connected s... | 3,797 | 1,636 | 3,064 | 3,396 | null | null | github_plus_top10pct_by_avg |
gned}$$
Combining with , one has $$\label{BERic}
{\rm \overline{Ric}}(\overline{\nabla} v,\overline{\nabla} v)={\rm Ric}^m_f(\nabla v,\nabla v),$$ and $$\label{WLaplacian}
\bar{\Delta}v=\Delta_{f}v.$$ Put , and into , we can get the desired result .
Differential Harnack estimates and applications
=================... | 3,798 | 3,276 | 1,869 | 3,683 | null | null | github_plus_top10pct_by_avg |
ions are dualised the coset representative is fully fixed to $\hat{g}=1$ leaving three further gauge fixings to be made on the dynamical Lagrange multipliers. We parametrise these as $$v_1= \frac{x_0}{\eta} \ , \quad v_2= \frac{-1+z}{\eta} \ , \quad v_3 = \frac{x_1}{\eta} \ , \quad v_5 + i v_7 = \frac{r e^{i\theta}}{\e... | 3,799 | 3,188 | 3,056 | 3,283 | null | null | github_plus_top10pct_by_avg |
theorem can also be found in [@wilkinson1965algebraic].
\[thm1\] Let $\mathbf{C}=\mathbf{D}+\rho\mathbf{vv}^T$, where $\mathbf{D}$ is diagonal, $\|\mathbf{v}\|_2=1$. Let $d_1\le d_2\le \cdots\le d_n$ be the eigenvalues of $\mathbf{D}$, and let $\tilde{d}_1\le \tilde{d}_2\le \cdots\le \tilde{d}_n$ be the eigenvalues o... | 3,800 | 4,285 | 3,898 | 3,390 | null | null | github_plus_top10pct_by_avg |
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