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 |
|---|---|---|---|---|---|---|---|
.
The solution of (\[desol20b\]) is (cf. [@dautraylionsv6 Ch. XXI, Sec. 3.2, pp. 233-235], or [@tervo14 proof of Theorem 6.3]; replace first $\eta$ by $r_{m,j}-\eta$) $$\begin{gathered}
\label{desol20ab}
v_{2,j}(x,\omega,\eta)
\\
=H(r_{m,j}-\eta-t(x,\omega))e^{\int_0^{t(x,\omega)}-\Sigma_j(x-s\omega,\omega)ds}
\tilde{... | 3,601 | 2,107 | 918 | 3,537 | 3,905 | 0.769391 | github_plus_top10pct_by_avg |
latter differs by a total derivative.
Supergravity theories are constructed [@SUGRA] based on the YM-like theory for the gauge potential (\[usual\]). It will be interesting to consider the supersymmetrization of the gauge symmetry of diffeomorphism and to derive the supergravity theory as an alternative formulation o... | 3,602 | 1,965 | 1,609 | 3,159 | null | null | github_plus_top10pct_by_avg |
lowing result.
\[keyreduction\] Every germ as specified in §\[preamble\] is equivalent to one which, up to a parameter change, has matrix representation $$\begin{pmatrix}
1 & 0 & 0\\
q(t) & t^b & 0\\
r(t) & s(t)t^b & t^c
\end{pmatrix}$$ in suitable coordinates, with $1\le b\le c$ and $q,r,s$ polynomials such that $\de... | 3,603 | 1,681 | 2,434 | 3,270 | 4,020 | 0.768608 | github_plus_top10pct_by_avg |
nalysis [@2018osc].
Lifetime limits are computed using a Bayesian method, assuming that the SK-I through SK-IV datasets have correlated systematic uncertainties [@2018pdg]. For the nucleon decay modes, the systematic uncertainties of the “High $P_{\text{tot}}$" and “Low $P_{\text{tot}}$" search boxes are treated as in... | 3,604 | 4,137 | 3,907 | 3,365 | 2,636 | 0.778216 | github_plus_top10pct_by_avg |
$.
Again, there will be a smallest $n_{2}\in{I \kern -4.5pt N}$ such that $d(y_{n},x)-d(y_{n_{1}},x)>2$ for all $n\geq n_{2}$. Set $w_{n}=y_{0}$ for $n_{1}\leq n<n_{2}$. Thus, for $n_{1}\leq n<n_{2}$, we have that $d(y_{n},x)-d(w_{n},x)>1$ and $d(w_{n},x)\geq 0$.
Once again, there will be a smallest $n_{3}\in{I \kern... | 3,605 | 4,738 | 3,648 | 3,202 | 3,981 | 0.768823 | github_plus_top10pct_by_avg |
lux constraint*]{}.
In this section we use the positivity constraint to fix energy correlators completely in the case of extremal values of ${a \over c}$. We also show that an additional assumption of energy correlators finiteness is not consistent with the three-point function of the stress tensor being proportional... | 3,606 | 4,194 | 3,757 | 3,213 | null | null | github_plus_top10pct_by_avg |
athbf{v}}(t)= T_{k,d}(h(t{\mathbf{e}}-{\mathbf{v}}))$ where $T_{k,d}: {\mathbb{R}}[t] \rightarrow {\mathbb{R}}[t]$ is the linear operator defined by $$T_{k,d}\left(\sum_{j\geq 0} a_jt^j\right) = -\sum_{j=0}^d \left( \frac {j+1} {k+1} a_{j+1} +(d-1-j)a_j\right) (d-j)! \binom {k+1}{d-j}t^j.$$ Moreover if $f$ is a $[0,1/k... | 3,607 | 2,117 | 2,768 | 3,130 | null | null | github_plus_top10pct_by_avg |
the rate of growth of enstrophy. We also provide a comprehensive characterization of the extreme vortex states which realize estimate together with the resulting flow evolutions.
The structure of the paper is as follows: in the next section we present analytic estimates [on]{} the instantaneous and finite-time growth... | 3,608 | 1,605 | 3,344 | 3,464 | null | null | github_plus_top10pct_by_avg |
eturned adjoint form ${\mathfrak{a}}_r^*$ inherits all properties of ${\mathfrak{a}}.$
In the following we establish that ${{U}}$ can be extended to a strongly continuous evolution family on $V'.$
\[Lemma EVF on V’\] Let ${\mathfrak{a}}$ be a non-autonomous sesquilinear form satisfying (\[eq:continuity-nonaut\])-(\[s... | 3,609 | 2,834 | 1,990 | 3,311 | null | null | github_plus_top10pct_by_avg |
2_relu_v3.pdf){width="100.00000%"}
---
abstract: 'Let $X, Y$ be complete, simply connected Riemannian surfaces with pinched negative curvature $-b^2 \leq K \leq -1$. We show that if $f : \partial X \to \partial Y$ is a Moebius homeomorphism between the boundaries at infinity of $X, Y$, then $f$ extends to an isometry... | 3,610 | 2,231 | 1,056 | 3,224 | null | null | github_plus_top10pct_by_avg |
\quad \mbox{with}\quad s_{t}\in {\mathcal{S}}({%
\mathbb{R}}^{d}\times {\mathbb{R}}^{d}).$$
We define the formal adjoint operator $$S_{t}^{\ast }f(y)=\int_{{\mathbb{R}}^{d}}s_{t}(x,y)f(x)dx,\quad t>0.$$
\[H2H\*2\] If $f\in {\mathcal{S}({\mathbb{R}}^{d})}$ then $S_{t}f\in {\mathcal{S}({\mathbb{R}}^{d})}$. Moreover, th... | 3,611 | 2,465 | 1,825 | 3,397 | null | null | github_plus_top10pct_by_avg |
igraph objects, rather than the list of names of the objects. Then your current code would work as-is, and you would have functions like lapply available to you.
Update: re your assigning code.
You could do this many ways, but the common element is that instead of storing your variables in A1, ..., A100 , you store t... | 3,612 | 6,701 | 458 | 2,763 | 2,606 | 0.77849 | github_plus_top10pct_by_avg |
\colon{\sD}(B) \to {\sD}(B\times A)$. Both of these preserve colimits in both variables, on the left because colimits there are defined by postcomposition, and on the right because $F$ and $G$ preserve colimits.
This construction is universal in the sense that if is a monoidal left derivator, then to make into a -modu... | 3,613 | 2,659 | 2,615 | 3,308 | 3,335 | 0.773044 | github_plus_top10pct_by_avg |
nt may be considered to be *neutral.* Appendix A3 shows the various possibilities for the derived set and boundary of a subset $A$ of $X$.$\qquad\blacksquare$
Some useful properties of these concepts for a subset $A$ of a topological space $X$ are the following.
\(a) $\textrm{Bdy}_{X}(X)=\emptyset$,
\(b) $\textrm{Bd... | 3,614 | 5,133 | 3,775 | 3,124 | 2,790 | 0.776935 | github_plus_top10pct_by_avg |
\[-0.27, 0.16\] 0.61 -0.10 \[-0.35, 0.14\] 0.40 0.006 \[-1.30, 1.31\] 0.99
FES -- FSI -0.006 \[-0.10, 0.09\] ... | 3,615 | 6,405 | 2,481 | 2,427 | null | null | github_plus_top10pct_by_avg |
tral limit theorem to show that the eigenvalues $\lambda_\chi$ are approximately distributed like uncorrelated Gaussian random variables. Even to prove asymptotic results, it is necessary here to apply some *quantitative* version of the central limit theorem, in order to achieve suitably uniform control over the $\lamb... | 3,616 | 1,990 | 3,035 | 3,351 | null | null | github_plus_top10pct_by_avg |
m_\nu \lambda^{\rm tip}_{\mu\nu}\hat X_\nu (t'))
(1 +\sum_{\nu'} \lambda^{\rm tip}_{\mu\nu'}\hat X_{\nu'} (t) )
d_{\mu\sigma} (t') d^\dagger_{\mu'\sigma}(t)
%%
\Big \rangle_0
\Big \langle
c^\dagger_{0\sigma,\rm tip}(t') c_{0\sigma,\rm tip}(t)
\Big \rangle_0
\non
&&
-
\sum_{\mu\mu'\sigma}
t_{\mu \sigma}t_{\mu'... | 3,617 | 1,989 | 3,133 | 3,380 | null | null | github_plus_top10pct_by_avg |
cO_X(D)) \simeq H^p (Y, \cO_Y( {\left \lfloor \pi^{*} D \right \rfloor} ))
\text{ and }H^p (X, \cO_X(D)) \simeq H^p (Y, \cO_Y( {\left \lceil \pi^{*} D + K_\pi \right \rceil} )).$$
Since $\cO_Y({\left \lfloor \pi^{*}D \right \rfloor})$ is acyclic for the functor $\pi_{*}$ by Lemma \[lemma:acyclic\], Leray’s spectral se... | 3,618 | 3,143 | 3,582 | 3,174 | null | null | github_plus_top10pct_by_avg |
a_i} - p_i^{a_i -1}), \, & \mbox { if }&
4\!\not|
m\\
(n,2) (n, 2^{a_0 -2}) \prod_{i=1}^k (n, p_i^{a_i} - p_i^{a_i -1}),
\, & \mbox { if }& 4|m
\end{array} \right.$$ In particular $$|\varsigma (2, m) | = \left \{\begin{array}{rcl}
2^k, \, & \mbox {\rm if }& \, a_0\leq 1\\
2^{k+1}, \, & \mbox {\rm if }& \, a_0=2\\
2^{... | 3,619 | 2,458 | 2,429 | 3,415 | null | null | github_plus_top10pct_by_avg |
every $\kappa \geq 0,q\in {\mathbb{N}}$ there exists $C\geq 1$ such that $$(A_{4})\quad \left\Vert P_{t}f\right\Vert _{q,-\kappa ,\infty }\leq
C\left\Vert f\right\Vert _{q,-\kappa ,\infty }. \label{R7}$$
For $\delta \geq 0$ we denote$$\Phi _{n}(\delta )=\varepsilon _{n}\Lambda _{n}\times \lambda _{n}^{-\theta
_{0}(a+... | 3,620 | 1,780 | 1,308 | 3,610 | null | null | github_plus_top10pct_by_avg |
etail in §\[details\].
For $a<b<c$ positive integers such that $\frac ca=C$ and $\frac ba=
\frac{C-\lambda_0}2+1$, let $$\alpha(t)=\begin{pmatrix}
1 & 0 & 0 \\
t^a & t^b & 0 \\
\underline{f(t^a)} & \underline{f'(t^a)t^b} & t^c
\end{pmatrix}$$ where $\underline{\cdots}$ denotes the truncation modulo $t^c$. The integer ... | 3,621 | 1,189 | 2,835 | 3,404 | 2,789 | 0.776938 | github_plus_top10pct_by_avg |
ned}$$ where $ w_t \in \Re^d $ is the state variable at time $t$, $\delta$ is the step size, $U:\Re^d\to\Re$ is a (possibly nonconvex) potential, $\xi:\Re^d \times \Omega \to \Re^d$ is the [*noise function*]{}, and $\eta_k$ are sampled i.i.d. according to some distribution over $\Omega$ (for example, in minibatch SGD, ... | 3,622 | 2,208 | 2,410 | 3,298 | 2,930 | 0.776006 | github_plus_top10pct_by_avg |
(cYBE and mcYBE) respectively. We adopt some notation $X\wedge Y = X\otimes Y - Y \otimes X$ and define e.g. $$r= T_1 \wedge T_2 + T_3 \wedge T_4 +\dots \ , \quad RX = {\operatorname{Tr}}_2 ( r (\mathbb{I}\otimes X)) \ .$$
We define an inner product by the matrix trace of generators, ${\operatorname{Tr}}(T_{A} T_{B})... | 3,623 | 2,793 | 3,099 | 3,313 | null | null | github_plus_top10pct_by_avg |
)+\sum_{i=1}^k\chi(G[W_i])\le|P|+\sum_{i=1}^k|Z_i|^4$$ $$\le(k-1)\omega(G)+(\sum_{i=1}^k|Z_i|)^4\le(k-1)\omega(G)+(\omega(G))^4,$$ as required.
We can turn this estimate into a polynomial time algorithm as required, using the fact that the proof of Theorem 0 is constructive. In particular, we use that, given a family ... | 3,624 | 3,744 | 3,864 | 3,280 | 4,016 | 0.768632 | github_plus_top10pct_by_avg |
S\times I)\to{\mathbb{R}}$ has an unique extension $\tilde B(\cdot,\cdot):H_1\times H_2\to{\mathbb{R}}$ which satisfies \[csda36\] |B(,v)|M\_[H\_1]{}[v]{}\_[H\_2]{}H\_1, vH\_2 and \[csda37\] B(v,v)c’[v]{}\_[H\_1]{}\^2vH\_2. We see that actually $$\begin{aligned}
\label{coex}
\tilde B(\tilde\phi,v)
={}&{\left\langle}\p... | 3,625 | 1,707 | 2,800 | 3,356 | null | null | github_plus_top10pct_by_avg |
above would be equivalent to the Jacobi identify for $n^{(3)}$ interpreted as structure constants if the terms $m_i^{(4)}$ were absent. The presence of $m_i^{(4)}$ is the evidence that $n^{(3)}$ cannot be used as structure constants.
Often the relation between YM and GR indicated by the double-copy procedure is symbo... | 3,626 | 2,988 | 3,646 | 3,385 | null | null | github_plus_top10pct_by_avg |
ely poor since it considers only the largest gap between two distributions, which provides little information.
Discussion
----------
MGoF’s learning procedure of anomalous probability hypothesis is inefficient. To maintain a comprehensive knowledge of anomalies, MGoF has to reserve a single hypothesis entry for every... | 3,627 | 3,135 | 1,328 | 2,929 | null | null | github_plus_top10pct_by_avg |
$\delta j_\mu (x)/\delta A^t_\nu
(x^{\prime\prime})|_{A^t=A^{ext}}=\Pi_{\mu\nu}(x,x^{\prime\prime}\vert
A_\mu^{ext})$. The external (constant and homogeneous) classical magnetic field is described by $A_\mu^{ext}(x)=1/2F_{\mu\nu}^{ext}x^\nu$, where the electromagnetic field tensor $F_{\mu \nu}^{ext}=\partial_\mu
A_\nu^... | 3,628 | 2,336 | 3,674 | 3,360 | null | null | github_plus_top10pct_by_avg |
Next
.Save
End With
End Sub
coupled with a Custom Document Property named 'Counter', whose value you initially set to 0. Should you need to re-set the counter for some reason, simply edit the 'Counter' Custom Document Property accordingly.
Then, wherever you want the count to appear, add a DOCPROPERTY field that r... | 3,629 | 385 | 4,437 | 3,471 | 1,125 | 0.794037 | github_plus_top10pct_by_avg |
clusion $D\subset V(x)$. The formula for $p(\alpha,d)$ uses the coordinate system and scaling property of stable processes in Lemma \[scaled\] as well as the identity for the first exit from a sphere given by Theorem \[BGR\].
We are now ready to prove our main result.
Suppose we condition on the previous positions of... | 3,630 | 1,921 | 2,255 | 3,557 | 2,717 | 0.777613 | github_plus_top10pct_by_avg |
tilde {\bf P}_{C,0})$.
We assume that the stopping powers for $j=2,3$ satisfy $$\begin{aligned}
{}& S_j\in C^2(I, L^\infty(G)), \label{Sj-ass:1} \\[2mm]
{}& \kappa_j:=\inf_{(x,E)\in \ol{G}\times I}S_j(x,E)>0, \label{Sj-ass:2} \\[2mm]
{}& \nabla_x S_j\in L^\infty(G\times I). \label{Sj-ass:3}\end{aligned}$$
We give her... | 3,631 | 1,650 | 1,558 | 3,528 | null | null | github_plus_top10pct_by_avg |
lpha-\beta)\beta^{-1}\tau}I(\theta)^{1/2} \left(\int \theta {\left\verte^{d\tau}{\nabla}{\mathcal{K}}(e^{\tau}\cdot)\ast\theta\right\vert}^2 d\eta \right)^{1/2} \\
& \leq (1-e^{-\delta\tau})I(\theta) + Ce^{(2-2\alpha-2\beta)\beta^{-1}\tau + \delta\tau}. \end{aligned}$$ The rest of the proof follows similarly to the cas... | 3,632 | 2,374 | 500 | 3,766 | null | null | github_plus_top10pct_by_avg |
mma < d$, $$\begin{aligned}
{\|e^{d\tau}{\nabla}{\mathcal{K}}(e^{\tau}\cdot)\ast \theta\|}_\infty & \leq \left( {\| e^{d\tau}{\nabla}{\mathcal{K}}(e^{\tau}\cdot)\mathbf{1}_{B_1(0)} \ast \theta\|}_\infty + {\| e^{d\tau}{\nabla}{\mathcal{K}}(e^{\tau}\cdot)\mathbf{1}_{{\mathbb R}^d \setminus B_1(0)} \ast \theta\|}_\infty ... | 3,633 | 2,319 | 1,793 | 3,683 | null | null | github_plus_top10pct_by_avg |
airs $(H, G, \alpha, \beta)$ and classify up to an isomorphism all bicrossed products $H\, {}_{\alpha}\!\! \bowtie_{\beta} \,
G$.*
The motivation for the above problem is triple: first of all, the problem presents an interest in itself in group theory. On the other hand the construction of the bicrossed product provid... | 3,634 | 1,143 | 3,052 | 3,343 | null | null | github_plus_top10pct_by_avg |
}=0,\quad
\psi(\cdot,\cdot,E_{\rm m})=0.\end{gathered}$$ For simplicity we denote ${1\over{S_0(E)}}f$ and ${1\over{S_0(E)}} K$ again by $f$ and $K$. Assume that $I=[0,\infty[{}=:{\mathbb{R}}_+$ and that $K$ is of the *Volterra type operator* (cf. [@engelnagel pp. 447-452]) $$(K\psi)(x,\omega,E)=\int_0^E\int_S
\sigma(x,... | 3,635 | 1,996 | 2,458 | 3,359 | null | null | github_plus_top10pct_by_avg |
stributing the colloidal dumbbells in the simulation box and with random orientations. The initial distance between the colloid-1 and colloid-2 in a dumbbell is set smaller than $\lambda+\Delta$. In contrast, the initial distance between any two colloidal species that belongs to different dumbbells is larger than ${\si... | 3,636 | 2,190 | 1,645 | 3,808 | 2,977 | 0.77565 | github_plus_top10pct_by_avg |
s-box ones. Direct box diagrams usually present a pinch singularity. This is because the poles appearing in the baryonic propagators get infinitesimally close to one another. In our integrals the denominators appearing in the baryonic propagators also contain terms proportional to $M_\Lambda-M_N$ and $M_\Sigma-M_\Lambd... | 3,637 | 1,228 | 2,534 | 3,511 | null | null | github_plus_top10pct_by_avg |
er surface whose Kodaira dimension is not equal to $- \infty$, then $$Y(M)=-4\sqrt{2}\pi\sqrt{(2\chi+3\sigma)(\tilde{M})},$$ where $\sigma$ denotes the signature and $\tilde{M}$ is the minimal model of $M$. Now based on this evidence, one can ask if the blowing-up does not change the Yamabe invariant of a closed orient... | 3,638 | 2,046 | 2,436 | 3,326 | null | null | github_plus_top10pct_by_avg |
Wigner tomography measurements. (b) and (c) The measured joint Wigner function $W_{12}$ of the Bell states ${\ensuremath{\left|\Phi_{+}\right\rangle}}$ and ${\ensuremath{\left|\Phi_{-}\right\rangle}}$ on the Re-Re and Im-Re planes, respectively. (d) and (e) Real parts of the density matrices of the states ${\ensuremath... | 3,639 | 1,117 | 2,526 | 3,515 | 2,210 | 0.781834 | github_plus_top10pct_by_avg |
(1,2)
+\frac{{\mbox{\boldmath $p$}}_1\cdot{\mbox{\boldmath $p$}}_2}{A_cm},
\label{3bh}$$ where $A_c$ is the mass number of the core nucleus, $m$ is the nucleon mass, and $\hat{h}_{nC}$ is the single-particle (s.p.) Hamiltonian for a valence neutron interacting with the core. The last term in Eq. (\[3bh\]) is the two-b... | 3,640 | 1,480 | 2,958 | 3,422 | 2,233 | 0.781588 | github_plus_top10pct_by_avg |
$e^{O(n^2)}\log^{O(n)}2K$ and step at most $n$ such that $A$ is contained in the union of at most $\exp(K^{O_n(1)})$ left translates of $P$.
This compares with the bound of $K^{O_n(1)}$ on the rank of $P$ obtained by Gill, Helfgott, Pyber and Szabó using \[thm:old\].
If $K<2$ then $A$ is a finite subgroup and the co... | 3,641 | 2,539 | 1,880 | 3,419 | 2,254 | 0.781406 | github_plus_top10pct_by_avg |
derset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf m}}$}}
{\overset{}{\longleftrightarrow}}}x\text{ in }{{\cal A}}{^{\rm c}}\}$}}}{\nonumber}\\
&=\sum_{{{\cal A}}\subset\Lambda}\;\sum_{{\partial}{{\bf n}}=o{\vartriangle}{\underline{b}}}\frac{w_\Lambda({{\bf n}})}
{Z_\Lambda}\,{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle ... | 3,642 | 2,078 | 1,914 | 3,445 | null | null | github_plus_top10pct_by_avg |
55 6.4$\pm$0.6 68.2$\pm$6.8 100.9$\pm$5.3 76.4$\pm$3.8 32.6$\pm$2.3 14.5$\pm$1.0 5.8$\pm$0.4 1.1$\pm$0.1
11 05 38 45.73 -69 27 53.10 55 3.7$\pm$0.4 45.2$\pm$4.5 78.0$\pm$4.2 65.0$\pm$3.3 30.1$\pm$2.1 14.2$\pm$1.0 5.9$... | 3,643 | 4,653 | 2,079 | 3,126 | null | null | github_plus_top10pct_by_avg |
imate equalities in assume that there is no accidental degeneracy among the sterile state masses. That is, we assume that the relation $|\Delta m^2_{JK}| \gg |\Delta m^2_{31}|$ always holds.
After averaging out the fast oscillations, $P(\nu_\beta \rightarrow \nu_\alpha)$ is given to second order in $W$ by $$\begin{ali... | 3,644 | 2,617 | 3,326 | 3,486 | null | null | github_plus_top10pct_by_avg |
cr{C}}}(X|\mathcal{O}, H)$, which is evaluated through a set of matrix operations [@rasmussen_gaussian_2006] (see Appendix). As we are using a GP, we can also get the variance of the functions conditioned on $\mathcal{O}$ and $H$: $\sigma_{\hat{\mathscr{C}}}(X|\mathcal{O}, H)$ [@rasmussen_gaussian_2006]. Both of these ... | 3,645 | 3,156 | 3,969 | 3,646 | 2,181 | 0.781956 | github_plus_top10pct_by_avg |
hrm{SJ}}\,\langle X\rangle$ is a subalgebra in ${{\mathrm{As}}\,\langle
X\rangle}^{(+)}$ generated by the set $X$. Similarly, ${\mathrm{Di}}{\mathrm{SJ}}\,\langle X\rangle\hookrightarrow {{\mathrm{Di}}{\mathrm{As}}\,\langle
X\rangle}^{(+)}$.
An element from ${\mathrm{As}}\,\langle X\rangle$ is called a *Jordan polynom... | 3,646 | 1,589 | 2,472 | 3,420 | null | null | github_plus_top10pct_by_avg |
is convenient to use the Landau gauge. In this gauge neither $\Sigma_n$ ($n=0,1,2...$) nor the contribution of Fig.1f contain the large logarithm $\ln(\lambda_C/r_0)$. Therefore, after the renormalization, taking zero momentum transfer as a reference point, the contribution of Fig.1f is of the form $\delta_f \sim Z\al... | 3,647 | 2,160 | 3,434 | 3,446 | null | null | github_plus_top10pct_by_avg |
e o so that 2/9*o**2 - 2/9 - v*o**3 + 2/3*o = 0.
-1, 1/3, 1
Let n(i) be the first derivative of 3*i**5/20 + i**4/16 - i**3/4 - i**2/8 - 1. Factor n(x).
x*(x - 1)*(x + 1)*(3*x + 1)/4
Suppose -4*h = f + 4, 58*h + f + 4 = 57*h. Factor -2/7 + 2/7*b**2 + h*b.
2*(b - 1)*(b + 1)/7
Let r(b) be the third derivative of b**7/1120... | 3,648 | 2,725 | 2,201 | 3,348 | null | null | github_plus_top10pct_by_avg |
48
28/10/2006 4037.0438 1800 149 2039
28/10/2006 4037.0836 1800 135 1849
28/10/2006 4037.1051 1800 127 1741
28/10/2006 4037.1758 1800 106 1448
28/10/2006 4037.1968 1800 112 1530
29/10/2006 4037.9357 1800 85 1162
29/10/2006 4037.9568 1... | 3,649 | 3,227 | 2,832 | 3,657 | null | null | github_plus_top10pct_by_avg |
s ratio becomes $\xi = {1 - n^3 \over 2}$ and we keep it fixed. This allows us to think of $f(\xi)$ as constant numbers. We consider then all possible polarization tensors and $n^{1,2}$ components. One can check that the solution to is given by We are left with one functional degree of freedom given by $f_5$. Indeed, ... | 3,650 | 2,521 | 3,653 | 3,346 | null | null | github_plus_top10pct_by_avg |
“Reality of Superstring Field Theory Action,” JHEP [**1611**]{}, 014 (2016) doi:10.1007/JHEP11(2016)014 \[arXiv:1606.03455 \[hep-th\]\]. A. Sen, “Unitarity of Superstring Field Theory,” arXiv:1607.08244 \[hep-th\]. A. Sen, “Wilsonian Effective Action of Superstring Theory,” arXiv:1609.00459 \[hep-th\]. A. Sen, “Equiva... | 3,651 | 1,580 | 3,018 | 3,344 | null | null | github_plus_top10pct_by_avg |
=\diag(\la_1,\ldots,\la_r)$. Denote by $\Ga=(\ga_{ij})$ an $r\times r$ orthogonal matrix such that $\Ga^\top\Si \Ga=\La$. Assume that $g(\Si)$ is orthogonally invariant, namely, $g(\Si)=g(P\Si P^\top)$ for any orthogonal matrix $P$. Then, we can assume that $g(\Si)=g(\La)$ without loss of generality.
\[prp:condition2\... | 3,652 | 2,622 | 2,061 | 3,359 | null | null | github_plus_top10pct_by_avg |
\hat{\epsilon}}$, then $$\begin{aligned}
W_1\lrp{p^*, p^y_{n\delta}} \leq 2\hat{\epsilon}
\end{aligned}$$ where $p^y_t := \Law(y_t)$.
Note that $m,L,R$ are from Assumption \[ass:U\_properties\], $L_N$ is from , $\cm, \beta,L_\xi$ are from Assumption \[ass:xi\_properties\]).
Finding a suitable $y_0$ ca... | 3,653 | 3,247 | 3,109 | 3,145 | null | null | github_plus_top10pct_by_avg |
ft( \sup_{x\in Q}\left \Vert
(I-P_{m})(x)\right \Vert _{\ell_{p}}\right) ,$$ where $I$ is the identity operator on $\ell_{p}.$
Let $X$ and $Y$ be Banach spaces. Then, a linear operator $L:X\rightarrow Y$ is said to be $\mathit{compact}$ if the domain of $L$ is all of $X$ and $L(Q)$ is a totally bounded subset of $Y$... | 3,654 | 1,914 | 2,279 | 3,577 | 3,837 | 0.769762 | github_plus_top10pct_by_avg |
}_\#)
= H_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(\Delta^{opp},\gamma_{n!}\gamma^*_nE_n^{\Delta}) =
H_{{\:\raisebox{1pt}{\text{\circle*{1.5}}}}}(\Delta^{opp},E_n^{\Delta} \otimes \gamma_{n!}k),$$ where we have used the projection formula in the right-hand side. The homology of the category $\Delta^{opp}$ can be comp... | 3,655 | 3,203 | 2,923 | 3,203 | 3,386 | 0.772734 | github_plus_top10pct_by_avg |
59.35 58.56 56.34 65.68 58.15 60.30 58.00 52.20 57.61 53.42
18 months 63.46 55.91 56.43 58.95 58.02 55.56 59.95 41.67 54.66 57.49
24 months 57.13 56.58 53.89 61.26 56.96 55.55 56.83 47.92 55.44 ... | 3,656 | 6,560 | 907 | 2,040 | null | null | github_plus_top10pct_by_avg |
ows from Proposition \[qisom\] that $F : X \to Y$ is an isometry. $\diamond$
Proof of main theorem
=====================
Let $X, Y$ be complete, simply connected Riemannian surfaces of pinched negative curvature $-b^2 \leq K \leq -1$, and let $f : \partial X \to \partial Y$ be a Moebius homeomorphism with circumcente... | 3,657 | 2,800 | 1,798 | 3,428 | 4,075 | 0.768253 | github_plus_top10pct_by_avg |
{B}$, where $$\label{eq3}
\mathbf{B}=\mathbf{X}^T\mathbf{X}-\frac{\mathbf{d}\mathbf{d}^T}{2m}.$$ Under the assumptions in Lemma \[thm3\], let $$\mathbf{m}_i^T=\mathbf{b}_i^T\mathbf{X}^\dagger=\sum_{j=1}^k\frac{\gamma_{ij}}{\sigma_j}\mathbf{u}_j^T.$$ The $i$-th modularity component is defined to be $$\mathbf{c}_i=\frac{... | 3,658 | 3,435 | 3,395 | 3,480 | 3,787 | 0.770092 | github_plus_top10pct_by_avg |
thbf{Q}_{3,2}\right\rangle \right)\\
+s_{1}\left(\left\langle \mathbf{Q}_{1,2}\mathbf{Q}_{1,3}\right\rangle ,\left\langle \mathbf{Q}_{2,1}\mathbf{Q}_{2,3}\right\rangle ,\left\langle \mathbf{Q}_{3,1}\mathbf{Q}_{3,2}\right\rangle \right)\le4,
\end{array}$$ $$\begin{array}{l}
s_{1}\left(\left\langle \mathbf{Q}_{1,2}\mathb... | 3,659 | 2,981 | 2,580 | 3,406 | null | null | github_plus_top10pct_by_avg |
rresponds to the one of (at least) two semi-infinite paths, as in Part (iii) of Theorem \[HN1\].
It is worth pointing out here that our proofs strongly rely on the planarity of the RST and the non-crossing property of its branches (see Lemma \[lemm:croisement\] in appendix). They cannot be carried to an arbitrary dime... | 3,660 | 2,388 | 1,515 | 3,434 | 3,997 | 0.768727 | github_plus_top10pct_by_avg |
0 --physdev-is-bridged
ACCEPT all -- anywhere 192.168.122.0/24 state RELATED,ESTABLISHED
ACCEPT all -- 192.168.122.0/24 anywhere
ACCEPT all -- anywhere anywhere
REJECT all -- anywhere anywhere reject-with icmp-port-u... | 3,661 | 7,448 | 283 | 1,563 | 2,517 | 0.779204 | github_plus_top10pct_by_avg |
ite (\[X1\]) and the corresponding $n$-direction symmetry in the potential variables (\[eq:dLP-gen-ph-1\]), we obtain
\[eq:phi-sys-sym\] $$\begin{gathered}
\partial_t \phi^{(i)}_{m,n} = \alpha^{-1} q^{(i-\ell_1)}_{m,n} \phi_{m-1,n}^{(i+k_1)} -\frac{\phi^{(i)}_{m,n}}{N\alpha^{N}} , \label{eq:phi-sys-sym-1} \\
\partial_... | 3,662 | 1,750 | 3,218 | 3,513 | 2,639 | 0.77821 | github_plus_top10pct_by_avg |
. This curve has only one singular point at $P = [0:0:1]$ and does not pass through the singular points of $\PP^2_{w}$. Resolving the singularity of the curve with a $(3,2)$-blow up gives rise to one exceptional divisor $E$ with self-intersection number $-1/6$ and $\pi^* \mathcal{C} = \hat{\mathcal{C}} + 6 E$, $K_{\pi}... | 3,663 | 2,042 | 2,521 | 3,183 | null | null | github_plus_top10pct_by_avg |
tely. In the following, we review the fact that metric compatibility and the torsion free condition cannot determine the affine connection uniquely. The covariant derivative acts on the tensor as $$D_\mu V^\nu_\rho=\partial_\mu V^\nu_\rho+\Gamma^\nu_{\sigma\mu}V^\sigma_\rho-\Gamma^\sigma_{\rho\mu}V^\nu_\sigma.$$ The to... | 3,664 | 2,115 | 3,667 | 3,240 | null | null | github_plus_top10pct_by_avg |
$\alpha $ and $\beta $ such that $$\begin{aligned}
\label{eq:lambda2_L2}
\alpha \equiv \frac{\lambda_2(L )(d-1)}{\Tr(L)} = \frac{\lambda_2(L)(d-1)}{ \sum_{j = 1}^n \tau_{j}\ell_j} \;\; \text{and} \;\; \beta \equiv \frac{\Tr(L)}{d D_{\max}} = \frac{ \sum_{j = 1}^n \tau_{j}\ell_j}{d D_{\max}} \;.
\end{aligne... | 3,665 | 2,217 | 3,000 | 3,352 | null | null | github_plus_top10pct_by_avg |
y caused by metallicity variations from SN to SN). An uncertainty of $\pm$0.3 mag can be assigned to this technique based on the reddening difference yielded by both colors.
The ejecta velocities come from the minimum of the Fe II $\lambda$5169 lines interpolated to day 50, which is good to $\pm$300 km s$^{-1}$ [@hamu... | 3,666 | 2,712 | 4,004 | 3,668 | 3,875 | 0.769592 | github_plus_top10pct_by_avg |
for $j = i,f$. More details about the statistical meaning of work can be found in [@WGF] and references therein. One of the most important results of nonequilibrium statistical mechanics is the Jarzinsky equality [@jarzinsky], from which one can directly obtain a fundamental inequality involving average work $\left\lan... | 3,667 | 4,337 | 3,701 | 3,497 | null | null | github_plus_top10pct_by_avg |
matroids of smaller rank. Let $e \in B$. We may assume that $M \con e$ has no $U_{a+1,b}$-minor $U$ in which $E(U) \cap (B-\{e\})$ is a basis, so $\tau_{a}(M \con e) \le \binom{b}{a}^{r-a-1}$. Let $\cF$ be a cover of $M \con e$ with $\binom{b}{a}^{r-a-1}$ rank-$a$ sets. Since $\binom{b}{a}^{r-a} \le \tau_{a}(M) \le \su... | 3,668 | 2,696 | 2,317 | 3,449 | 3,687 | 0.770681 | github_plus_top10pct_by_avg |
ays identify a probability vector with the bipartite pure state represented by it.
Deterministic case
==================
In this section, we study the relation between catalyst-assisted transformation and multiple-copy transformation in deterministic case. First, we introduce some notations.
Denote by $V^n$ the set ... | 3,669 | 3,299 | 3,510 | 3,373 | 1,779 | 0.785787 | github_plus_top10pct_by_avg |
e $x_i=y_i$. Let $\pi$ be the stationary distribution of the following random walk on $\Gamma(n, R)$: at each step, the walker stays at the current vertex with probability $p$, and otherwise chooses a neighbour randomly and moves to that neighbour. The transition probability from vertex $u$ to a neighbouring vertex $w$... | 3,670 | 1,290 | 2,754 | 3,440 | 1,696 | 0.78669 | github_plus_top10pct_by_avg |
e define a map $P':G\rightarrow {\mathcal{F}}(G)$ by setting for any $g\in G$ $$\begin{aligned}
P'(g):=\int_H \delta(g\cdot h)-\delta(h)d\mu(h).
\label{P'}\end{aligned}$$In case only (i) holds, we define for any $g\in G$ $$P'(g):=\int_H \delta(h\cdot g)-\delta(h)d\mu(h).$$ We will treat only the case where (ii) or (iii... | 3,671 | 2,305 | 2,591 | 3,302 | null | null | github_plus_top10pct_by_avg |
428.7 ± 6.5 417.5 ± 5.2 275.4 ± 13.5 298.3 ± 4.1 290.8 ± 21.3 279.2 ± 6.4 271.5 ± 18.6 298.1 ± 7.9 67.5 ± 3.9 67.3 ± 1.5 98.6 ± 7.2 99.8 ± 4.1
Hyb 18 483.9 ± 4.8 406.2 ± 8.3 273.9 ± 4.0 ... | 3,672 | 5,229 | 2,221 | 3,037 | null | null | github_plus_top10pct_by_avg |
r) = \alpha.$$
Output: $\hat{C}^*_{{\widehat{S}}} = \{ \beta\in\mathbb{R}^k:\ ||\beta-\hat\beta_{{\widehat{S}}}||_\infty\leq \hat{t}_\alpha/\sqrt{n}\}$.
For $\gamma_{{\widehat{S}}}$:
Get $\hat\beta_{{\widehat{S}}}$ from ${\cal D}_{1,n}$. This can be any estimator. For $j\in \hat{S}$ let $\hat\gamma_{\hat{S}}(j) = \f... | 3,673 | 2,227 | 2,088 | 3,395 | null | null | github_plus_top10pct_by_avg |
e $Z_2$.
The Yukawa interactions are the same as those in the HTM. The Higgs potential is given as $$\begin{aligned}
V
&=&
\frac{1}{\,2\,} m_{s_2^0}^2 (s_2^0)^2
+ \left\{
\mu_\eta^{}\, \eta^T\, i\sigma_2\, \Delta^\dagger\, \eta
+ \text{h.c.}
\right\}
+ \left\{
\lambda_{s\Phi\eta}\, s_1^0\, s_2^0\, (\... | 3,674 | 1,663 | 2,515 | 3,494 | null | null | github_plus_top10pct_by_avg |
the horizontal axis on $W_r$. On the right: The segment $[X,\mathcal{A}(X)]$ crosses $I_{r}$ (in bold) on $J(X)$. On this picture, $X$ is outside $I_{r}\oplus B(0,c)$.*]{}](Chi_r-c.eps "fig:"){width="6.5cm" height="5cm"}
-------------------------------------------------------------------------------------------------... | 3,675 | 1,995 | 968 | 3,830 | null | null | github_plus_top10pct_by_avg |
ke inference on parameters of population without assuming the form of the underlying distribution, such as mean, quantiles and regression parameters. We will take advantage of DAC and EL. Compared with BLB and SDB, we not only take full data information, but also save the cost computation. Our method is very simple and... | 3,676 | 1,616 | 3,089 | 3,364 | 3,100 | 0.774883 | github_plus_top10pct_by_avg |
{(4)} [3]
\nonumber \\
&=&
- \sum_{K}
\biggl[
\frac{ 1 }{ ( \Delta_{K} - h_{i} )^2 }
\{ (ix) e^{- i \Delta_{K} x} + (ix) e^{- i h_{i} x} \}
+
\frac{ 2 }{ ( \Delta_{K} - h_{i} )^3 }
\left( e^{- i \Delta_{K} x} - e^{- i h_{i} x} \right)
\biggr]
\nonumber \\
&\times&
\left\{ (UX)^{\dagger} A W \right\}_{i K}
\left... | 3,677 | 1,569 | 3,242 | 3,563 | null | null | github_plus_top10pct_by_avg |
me $\delta>0$. Let $\rho$ be the maximal zero in Problem \[central\]. Then the function $$(-\delta, 1+\delta) \ni s \mapsto \chi[{\mathbf{v}}_1(s),{\mathbf{v}}_2(s), {\mathbf{v}}_3, \ldots, {\mathbf{v}}_m](\rho)$$ is a degree at most two polynomial which has local minima at $s=0$ and $s=1$. Hence this function is ident... | 3,678 | 2,155 | 1,824 | 3,538 | null | null | github_plus_top10pct_by_avg |
bda(u_1,u_2)^2}.{\label{eq:nsum-2ndbd}}\end{gathered}$$ We repeat this computation until all indicators for ${{\bf k}}$ are used up. We also apply the same argument to the sum over ${{\bf h}}$ in [(\[eq:Psi-def\])]{}. Summarizing these bounds with [(\[eq:psi-delta\])]{} and [(\[eq:psi-delta-G2\])]{}, and replacing $u_0... | 3,679 | 1,549 | 3,405 | 3,526 | null | null | github_plus_top10pct_by_avg |
oor \pi^* D \right \rfloor} \geq 0$ is equivalent to $(\tilde h) + \pi^{*} D \geq 0$ because $(\tilde h)$ is an integral divisor. Writing $\tilde h = \pi^{*} h$ where $h \in K(X)$, one can split the previous condition $(\pi^{*} h) + \pi^{*} D \geq 0$ into two different ones, $$\label{eq:global_sections}
(h) + D \geq 0 ... | 3,680 | 2,364 | 3,219 | 3,288 | 2,408 | 0.780049 | github_plus_top10pct_by_avg |
dition (\[eq:3\]) says that, for any $\epsilon > 0$, there exists an $n_0$ such that for all $n > n_0$, $P^B_c - \frac{1}{2} <
\epsilon$ and $P^A_c < \epsilon$, to which we may refer as $\epsilon$-[*concealing*]{} and $\epsilon$-[*binding*]{}. These cheating probabilities are to be computed purely on the basis of logic... | 3,681 | 3,303 | 3,571 | 3,347 | 2,312 | 0.780927 | github_plus_top10pct_by_avg |
uniform linear acceleration. We find that the transition rate is non-thermal, and angle dependent. Thermality is however restored in the low and high frequency regimes, and also in the regime of high acceleration compared with the inverse of the detector’s spatial extent.
In section \[rindlerframesection\] we analyse ... | 3,682 | 4,187 | 4,083 | 3,368 | null | null | github_plus_top10pct_by_avg |
A^2D_s}{16\sqrt{3}M_N^2f_\pi^3}
{\int\frac{d^4l}{(2\pi)^4}}\frac{1}{(l+q)^2-m_\pi^2+i\epsilon}
\nonumber\\\times&\,
\frac{1}{l^2-m_\pi^2+i\epsilon}\,
\frac{1}{r_N^2-M_N^2+i\epsilon}
\\\times&\nonumber\,
\frac{(l^\rho+{\vec{q}}^\rho)(l^\nu+q^\nu)(l^\mu)}{k_N^2-M_\Sigma^2+i\epsilon}
\\\times&\nonumber\,
{\overline{u}}_1(... | 3,683 | 2,771 | 2,800 | 3,332 | null | null | github_plus_top10pct_by_avg |
f $a_n$ is just a high probability bound on the maximal element-wise difference between $V$ and $\hat{V}$, valid for each $ P \in \mathcal{P}_n^{\mathrm{OLS}}$.
Next, recall that $\beta_S = g(\psi_S)$. Now define $$C_n = \Biggl\{ g(\psi) :\ \psi \in H_n \Biggr\}.$$ We call $C_n$ the [*image bootstrap confidence set*]{... | 3,684 | 2,587 | 3,392 | 3,251 | 2,010 | 0.783555 | github_plus_top10pct_by_avg |
chi \coloneqq {g}(\rho_{N}) + \sum_{n=0}^{N-1} r_n^{\alpha}\, V_{1}(0, {f}(\rho_n + r_n\cdot))
, \qquad x\in D,$$ which is again justified by an obvious [strong law of large numbers]{}and the [central limit theorem]{}in the spirit of Corollary \[rate1\].
\[rate2\] When $D$ is bounded and convex, ${g}$ is conti... | 3,685 | 2,245 | 3,036 | 3,371 | null | null | github_plus_top10pct_by_avg |
h x\in \dot{ \mathcal{X}}$. It is clear that $\mathcal{X}$ is a stationary subset of $[\kappa]^\omega$ because $s_0$ forces that $\mathcal{X}$ meets every cub. Now apply **Axiom R** to choose $Y\in \mathcal{C}$ so that $\mathcal{X}\cap [Y]^\omega$ is a stationary subset of $Y$.
Now we obtain a contradiction (and thus ... | 3,686 | 3,702 | 3,160 | 3,337 | null | null | github_plus_top10pct_by_avg |
tate at 8.9 MeV in $^{28}$Ne has a similar structure to that in $^{26}$Ne and $K^{\pi}=0^{-}$ state in $^{28}$Ne, corresponding mainly to the neutron two-quasiparticle excitation of $\nu(2s^{-1}_{1/2}2p_{3/2})$, with 64.0% contribution. In addition to this neutron p-h like excitation, the following excitations have an ... | 3,687 | 1,684 | 2,323 | 3,014 | null | null | github_plus_top10pct_by_avg |
get the following: In the complement of $a'$ there can be at most a $3(r-1) + (n+ 2) - 4 = 3r + n -5$ dimensional simplex. Hence, there can be at most a $3r + n - 4$ dimensional simplex containing $a'$ on $N$. Since dim $\lambda(\Delta) = 4r + n -4 > 3r + n - 4$, we get a contradiction (since $r \geq 1$).
[**(ii)**]{}... | 3,688 | 1,548 | 2,636 | 3,441 | null | null | github_plus_top10pct_by_avg |
ation. We define as $\mathcal{T}_{X}$ the subtree of $\mathcal{T}$ consisting of $X\not=O$ and all its descendants, i.e. all the vertices of $\mathcal{T}$ that have $X$ in their ancestry. This tree is naturally rooted at $X$.\
If $\mathcal{T}_X$ is unbounded, then we can construct two particular semi-infinite paths tha... | 3,689 | 1,540 | 1,389 | 3,569 | 3,089 | 0.774937 | github_plus_top10pct_by_avg |
of $H(\theta)$, e.g. $S$) such that for all $\alpha$, $N_\alpha\cap\kappa\in S$ if and only if there is a countable $M\prec H(\theta)$ such that $N_\alpha\subseteq M$, $M\cap\omega_1=N_\alpha\cap\omega_1$, and $M\cap\kappa\in S$.
Let $\mathcal{S}$ and $\mathcal{C}$ be as in **Axiom R**. Choose $\theta$ sufficiently la... | 3,690 | 1,578 | 1,890 | 3,440 | null | null | github_plus_top10pct_by_avg |
onal file [2](#MOESM2){ref-type="media"}).
During July and August from 2006 to 2013, 17,017 emergency hospitalizations due to cardiovascular diseases registered by SIDIAP fulfilled the inclusion criteria. The mean age at study entry was 70.1 years (sd = 13.9), 7,615 (45%) were women, 11,508 (68%) had one single cardio... | 3,691 | 590 | 2,395 | 3,403 | null | null | github_plus_top10pct_by_avg |
the metric has the form $$\begin{aligned}
-2\Omega^2({\mathrm{d}}\ub\otimes{\mathrm{d}}u+{\mathrm{d}}u\otimes{\mathrm{d}}\ub)+r^2{\mathrm{d}}\sigma_{\mathbb{S}^2}\end{aligned}$$ where the area radius function $r=r(\ub,u)$ is defined by $$\begin{aligned}
\text{Area}(S_{\ub,u})=4\pi r^2,\end{aligned}$$ and ${\mathrm{d}}... | 3,692 | 1,534 | 3,126 | 3,472 | null | null | github_plus_top10pct_by_avg |
h_{i} )^2 ( \Delta_{K} - h_{j} )^2 ( \Delta_{K} - h_{k} ) }
\left( h_{i} + h_{j} - 2 \Delta_{K} \right)
e^{- i \Delta_{K} x}
\nonumber \\
&+&
\frac{ 1 }{ ( \Delta_{K} - h_{j} )^2 ( \Delta_{K} - h_{k} ) ( h_{j} - h_{i} ) }
e^{ - i h_{j} x}
-
\frac{ 1 }{ ( \Delta_{K} - h_{i} )^2 ( \Delta_{K} - h_{k} ) ( h_{j} - h_... | 3,693 | 3,364 | 3,040 | 3,494 | null | null | github_plus_top10pct_by_avg |
), with $N_z=1$. This leads to Eq.(\[GenM\]) with $M=1$: u\_r= . \[urXY\] Later we will present the numerical evidence that the stiffness perpendicular to the layers of a simple XY layered model in the asymptotic limit can well be described by the above equation. Below we will show that for the case of the two asymmetr... | 3,694 | 1,599 | 3,720 | 3,494 | 3,913 | 0.769312 | github_plus_top10pct_by_avg |
and $x{\mathbin{{}_{(\dashv)}}}y:=x\circ
y$ is an exceptional Jordan dialgebra.
Assume the opposite. Let $J\hookrightarrow D^{(+)}$ where $(D,\vdash,\dashv)$ is an associative dialgebra and the product in $D^{(+)}$ is given by the formula (\[eq:QuasiJordanProduct\]). Consider $I={\mathop{\mathrm{Span}}\nolimits}\{a{\m... | 3,695 | 2,220 | 1,058 | 3,587 | 2,629 | 0.778295 | github_plus_top10pct_by_avg |
for $(\mu, \sigma^2)\in \mathcal{M}_2$ in [18]{}. It is straightforward to show, by checking the values of the supremum in [14]{} at the boundary points below and by the fact that $\sup_{(\mu, \sigma^2)\in \mathcal{M}_2} [f_{i-1, b}(\mu, \sigma^2) ]$ is continuous for $b$ in a compact set in $(0,\infty)$, that in [14]... | 3,696 | 1,731 | 2,351 | 3,376 | null | null | github_plus_top10pct_by_avg |
ct of dimension and the eigenvalues of $\Sigma$, while leveraging results from [@cherno1; @cherno2] on high dimensional central limit theorems for simple convex sets.
We derive a general result on the accuracy of the Normal approximation over hyper-rectangles for nonlinear parameters. We make use of three findings fro... | 3,697 | 2,300 | 1,725 | 3,600 | 2,640 | 0.778206 | github_plus_top10pct_by_avg |
disorder (past yr.) 87 (40.7) 24 (55.8) 1.83 0.067
No
Yes 140 (66.2) 27 (62.8) Ref.
... | 3,698 | 7,001 | 960 | 1,106 | null | null | github_plus_top10pct_by_avg |
ion (\[explota\]) is obtained.
Proof of the *third requirement* as a consequence of Properties 1 and 2
=======================================================================
The purpose of this section is to show that Property 1 and Property 2 given above imply the *third requirement*. This leads to the conclusion t... | 3,699 | 1,660 | 2,876 | 3,544 | null | null | github_plus_top10pct_by_avg |
e anticommutator of a supersymmetry generator with its adjoint gives the Hamiltonian of the system. In a certain sense thus, making a system supersymmetric amounts to taking a square-root of its Hamiltonian. Put differently, the square-root of the Klein–Gordon equation is the Dirac equation, when this correspondence is... | 3,700 | 1,956 | 2,951 | 3,291 | null | null | github_plus_top10pct_by_avg |
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