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 |
|---|---|---|---|---|---|---|---|
w you would display, page, and retrieve the documents.
I would prefer embedding and updating multiple schema when there's a change, as opposed to doing a ref, for multiple reasons.
Get would be fast and easy and filter is not a problem (like you've said)
Retrieve operations usually happen a lot more often than updates... | 2,501 | 908 | 1,454 | 2,021 | null | null | github_plus_top10pct_by_avg |
49
VIII. Experiences of Others 58
IX. The American Lakes 66
X. The Happy Life 74
XI. Boy Desperadoes 82
XII. American and English Beggars 89
XIII. Beggars' Slang ... | 2,502 | 5,697 | 350 | 1,922 | null | null | github_plus_top10pct_by_avg |
is similar to that of the proof of Theorem 3.4 in [@C2] and we may skip it.
\[r35\] Let $R$ be a $\kappa$-algebra. We explain the above action morphism in terms of $R$-points. Choose an element $(m_{i,j}, s_i\cdots w_i)$ in $ \underline{M}^{\ast}(R) $ as explained in Section \[m\] and express this element formally as... | 2,503 | 1,823 | 2,582 | 2,289 | 2,089 | 0.782838 | github_plus_top10pct_by_avg |
stem of wave functions of the form $$\left|\psi(t)\right> = {{\rm e}}^{-{{\rm i}}\varepsilon t/\hbar}\left|u(t)\right>\;,$$ where $\left|u(t)\right>$ is a $T$-periodic function. The quantity $\varepsilon$ is called “quasienergy”, in analogy to the quasimomentum in solid state physics.
If there is no defect, the quasie... | 2,504 | 3,073 | 3,349 | 2,394 | 3,247 | 0.773785 | github_plus_top10pct_by_avg |
$G$-equivariantizable structure, which means that for every $g \in G$, we need a lift $\tilde{g}: {\cal E} \rightarrow {\cal E}$ such that $$\xymatrix{
{\cal E} \ar[r]^{\tilde{g}} \ar[d] & {\cal E} \ar[d] \\
X \ar[r]^{g} & X
}$$ and also such that the lifts obey the group law: $\tilde{g} \circ
\tilde{h} = \widetilde{g... | 2,505 | 3,907 | 2,511 | 2,118 | null | null | github_plus_top10pct_by_avg |
d by the ratio (w/w) of epididymal fat to liver decreased (*P*= 0.044) by 16% compared to the corresponding control group. None of the above mentioned effects were observed in the non-fasting group. Liver weight at the end of the study was 11% smaller (*P*= 0.039) among non-fasting animals in the control group, as comp... | 2,506 | 343 | 1,657 | 2,593 | null | null | github_plus_top10pct_by_avg |
,1\}$ let $N_i = N'|(A_i \cup B_i)$. Now $$\begin{aligned}
\lambda_{N'}(A_1 \cup B_1) &= r_{N'}(A_1 \cup B_1) + r_{M'}(A_0 \cup B_0 \cup X \cup Y) - r(M')\\
&= r_{N'}(A_1) + r_{M'}(A_0 \cup X) - r(M')\\
&\le |A_1| + |A_0 \cup X| - r(M') = 0,
\end{aligned}$$ Therefore $N' = N_0 \oplus N_1... | 2,507 | 1,892 | 2,091 | 2,296 | 3,597 | 0.771312 | github_plus_top10pct_by_avg |
400 1
13 7-back 19 1 2500 1 1-back 25 5 300 5
14 7-back 21 1 2500 1 1-back 25 5 300 1
15 8-back 21 1 2500 1 1-back 25 5 250 5
16 8-back 23 ... | 2,508 | 4,306 | 3,262 | 2,452 | null | null | github_plus_top10pct_by_avg |
& = & \E_0,\end{aligned}$$ which, for $\alpha \neq 0$, forces $\E({\mathbf{u}}_0) = 0$. Hence, ${\mathbf{u}}_0
\equiv 0$, $\alpha = 1/2$ and $\E({\mathbf{u}}_1) = 1$. The systems at orders $\E_0^{1/2}$ and $\E_0^1$ are given by:
\[eq:maxdEdt\_Asympt\_1\] $$\begin{aligned}
\E^{1/2}_0:\quad\qquad\qquad\qquad\qqu... | 2,509 | 2,062 | 2,568 | 2,469 | null | null | github_plus_top10pct_by_avg |
\alpha })} L_{{\sigma }_p^\chi ({\alpha })}^{-1}) q^{2(b-1)(\al
,{\alpha }_p)}\\
=&q^{2({\sigma }_p^\chi ({\alpha }),\lambda )}q^{-2({\alpha },{\alpha }_p)}
=q^{2({\alpha },{\sigma }_p^\chi (\lambda )-{\alpha }_p)},
\end{aligned}$$ which recovers the dot action of the Weyl group on the weight lattice.
If... | 2,510 | 1,972 | 2,014 | 2,245 | null | null | github_plus_top10pct_by_avg |
U^+(\chi ).$$ The vector spaces ${\mathcal{F}}^{{\underline{m}}}U^+(\chi )$, where ${\underline{m}}\in N$, are finite-dimensional, since the degrees of their elements are bounded. Moreover, $${\mathcal{F}}^0 U^+(\chi )={\Bbbk }1,\qquad
{\mathcal{F}}^{{\underline{m}}}U^+(\chi ) {\mathcal{F}}^{{\underline{m}}'}U^+(\chi... | 2,511 | 2,422 | 2,213 | 2,357 | null | null | github_plus_top10pct_by_avg |
vered by the equatorial neutral region. Note that, in our simulations, we neglect possible photoevaporation outflow coming out from the sink. We discuss it later in Sec. \[sec:mass\_loss\_inner\]. In the next section, we investigate the structure of the flow in more detail.
### Analysis of flow structure in case with ... | 2,512 | 2,535 | 3,200 | 2,550 | 3,395 | 0.772703 | github_plus_top10pct_by_avg |
ix and $\bar{A}=(\bar{a}_{nk})$ the associated matrix defined by (2.9). Then, by combining Lemmas 2.2, 2.3 and 3.1, we have the following result:
Let $1<p<\infty$ and $q=p/(p-1)$. Then we have:
\(a) If $A\in(\ell_{p}(\widehat{F}),\ell_{\infty})$, then$$0\leq \left \Vert L_{A}\right \Vert _{\chi}\leq \underset{n}{\lim... | 2,513 | 1,872 | 1,119 | 2,260 | null | null | github_plus_top10pct_by_avg |
of $\mathcal{L}^* \mathcal{L}$ and then inverting it to form the spectral density: $$S({\boldsymbol{\omega}}) = \frac{\sigma_f^2}{\mathcal{F}[\mathcal{L}^* \mathcal{L}]}.$$ In particular, the minimum norm or (classical) Tikhonov regularization can be recovered by using a white noise prior which is given by the constan... | 2,514 | 737 | 1,367 | 2,657 | 1,264 | 0.791906 | github_plus_top10pct_by_avg |
the matrix $\mathbf{M}$. The governing nonlinear PDE, Eq. has been rewritten as a system of nonlinear ODEs, Eq. . The linearized system of ODEs (Eq. with $N_{\pm} \to 0$) can be diagonalized: substituting $\hat{\Delta}_{\pm}$ for $\beta_j$ via Eq. and multiplying by $\mathbf{M}^{-1}$ on the left gives $$\label{Leig... | 2,515 | 1,698 | 2,965 | 2,396 | null | null | github_plus_top10pct_by_avg |
%
\fl A'_1&=&A_1^2 + A_1^3 + A{A_2^2} + 2A^2A_2A_3 + A{A_3^2} +
2AA_1{A_3^2} + 2AA_2A_3B_1 + 2AA_2A_3B_2 \nonumber\\
\fl &+& 4A^2A_1B_2 + 4A^2B_1B_2 +
4AA_1B_1B_2 + 2A^2{B_2^2}+ 2AA_1{B_2^2} +
{A_2^2}C + A{A_3^2}C\>, \label{eq:b2jednacinaA1}\\
%
\fl A'_2&=&AA_1A_2 + A_2^3 + A^2A_1A_3 + AA_2A_3^2 +
A^2A_... | 2,516 | 4,787 | 1,415 | 1,994 | null | null | github_plus_top10pct_by_avg |
g_{+-} & = & f_{+-}+\cdot\cdot\cdot\\
\Delta g_{--} & = & h_{--}\ r^{1-\mu l}+f_{--}+\cdot\cdot\cdot
\end{array}
\label{Asympt relaxed metric mu Neg}%$$ where $f_{\mu\nu}$ and $h_{\mu\nu}$ depend only on $x^{+}$ and $x^{-}$ and not on $r$. We use the convention that the $f$-terms are the standard deviations from AdS a... | 2,517 | 698 | 917 | 2,812 | null | null | github_plus_top10pct_by_avg |
)=g''_1(q_1)$ and $g''_1(p_1)=g''_1(q_0)$ and then $Y''_1$ consists of a connected curve with 2 nodes and 2 irreducible components.
Both of these are étale double covers of $Y_2$.
As in (\[pf.of.glue.thm.asp\]), the next lemma will be used to reduce quasi projective gluing to the affine case.
\[affine.red.lem\] Let ... | 2,518 | 2,803 | 2,326 | 2,464 | 3,077 | 0.774994 | github_plus_top10pct_by_avg |
ts in $B\otimes_AR$.
We also let $\pi^2$ be zero in $(\tilde{x}_i^j)', (\tilde{c}_i')_{\textit{$L_i$ of type $I^o$}},$ $(\tilde{f}_i', \tilde{c}_i')_{\textit{$L_i$ of type $I^e$ or free of type $I$ with $i$ odd}}$. Note that $(\tilde{x}_i^j)'$ is a diagonal entry of a formal matrix $\tilde{a}_i'$. Then these entries a... | 2,519 | 1,378 | 1,580 | 2,328 | null | null | github_plus_top10pct_by_avg |
ther with the values of $C^*$, corresponding to 2D chain, which can exist only in extended state. RG fixed point value $A_4^*$ is equal to $0.1165$ and $0.0779$, for $b=2$ and 3 respectively, and they coincide with the values of $D^*$ for $v<v_c(u<u_\theta)$ case in the ASAWs model (see table \[tab:avoiding\]).
- Fo... | 2,520 | 3,634 | 2,429 | 2,301 | 3,055 | 0.775141 | github_plus_top10pct_by_avg |
0.026 (0.054) 0.001 (0.002)
Long-term Unemployment -0.032 (0.035) -0.022 (0.023) -0.116 (0.077) ... | 2,521 | 4,935 | 2,022 | 1,360 | 1,019 | 0.795543 | github_plus_top10pct_by_avg |
mes S\times I)}$) \[trpr15\] [L\_[e,-]{}g\_[e]{}]{}\_[W\^2(G\_eSI)]{} =&\_[W\^2(G\_eSI)]{}= \_[L\^2(G\_eSI)]{}\
=& [g\_[e]{}]{}\_[T\^2(\_[e,-]{})]{}, since (cf. Remark \[changevar\]) $${\left\Vert \Psi\right\Vert}^2_{L^2(G_e\times S\times I)}
={}&\int_{\Gamma_{e,-}} \int_0^{\tau_{e,-}(x,\omega)} \big(e^{-\lambda s}g_{e... | 2,522 | 847 | 1,697 | 2,393 | null | null | github_plus_top10pct_by_avg |
t$, then clearly $g(c)\preceq t_{\leftarrow}$. Else, $t\preceq x$ for *each* $t\in C_{g}$ shows that $t_{\leftarrow}\preceq c$ because $t_{\leftarrow}$ is the smallest of all the upper bounds $c$ of $C_{g}$. Hence $t_{\leftarrow}\in C_{g}$.
Property (ST3) for $C_{g}$ follows from a small yet significant modification ... | 2,523 | 1,901 | 3,223 | 2,527 | 2,014 | 0.783512 | github_plus_top10pct_by_avg |
im$12%. By considering the forms of the effective couplings of the Higgses to the bottom quark, we can determine if this enhancement translates to a nonnegligible correction. The effective couplings are given by [@Carena:1999py] \_b\^h &=& (1 - )\
\_b\^H &=& (1 + )\
\_b\^A &=& (1 - ) , where $g^{h,H,A}_b$ are the tree ... | 2,524 | 937 | 884 | 2,587 | null | null | github_plus_top10pct_by_avg |
��j-bd\])]{} with $j\ge2$, we first note that, by applying [(\[eq:IR-xbd\])]{} and [(\[eq:psi-bd\])]{} to the definition [(\[eq:Pj-def\])]{} of $P_\Lambda^{{\scriptscriptstyle}(j)}(y,x)$, we have $$\begin{gathered}
P_\Lambda^{{\scriptscriptstyle}(j)}(y,x)\leq\sum_{\substack{v_2,\dots,v_j\\ v'_1,\dots,
v'_{j-1}}}\frac{... | 2,525 | 1,692 | 2,223 | 2,467 | null | null | github_plus_top10pct_by_avg |
ac{36 d\beta^2}{\epsilon^2L}}}, \frac{T\epsilon^4L^2} {2^{14} d\beta^4\log\lrp{\frac{2^{14} d\beta^4}{\epsilon^4L^2}}}}.
\end{aligned}$$
If we assume that $\bx_0 = \bw_0$, then there exists a coupling between $\bx_t$ and $\bw_t$ such that for any $k$, $$\begin{aligned}
\E{\lrn{\bx_{k\delta} - ... | 2,526 | 3,269 | 1,923 | 2,261 | null | null | github_plus_top10pct_by_avg |
,\frac{w_{\tilde{{\cal D}}{^{\rm c}}}({{\bf k}})}{Z_{\tilde{{\cal D}}{^{\rm c}}}}\bigg(\prod_{i=1}^j{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{z_i{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf m}}+{{\bf k}}$}}
{\overset{}{\longleftrightarrow}}}z'_i\}$}}}\bigg)\bigg(
\prod_{i\ne l}{\mathbbm{1}{\raisebox{-2pt}{... | 2,527 | 1,333 | 2,555 | 2,568 | null | null | github_plus_top10pct_by_avg |
a _{\tau (n)}}^{m_{\tau (n)}}\,&|\,
0\le m_\nu <{b^{\chi}} (\beta _\nu )
\text{ for all $\nu \in \{1,2,\dots ,n\}$} \big\}
\end{aligned}$$ form vector space bases of $U ^+(\chi )$, and the sets $$\begin{aligned}
\big\{ F_{\beta _{\tau (1)}}^{m_{\tau (1)}} F_{\beta _{\tau (2)}}^{m_{\tau
(2)}}\cdots F_{... | 2,528 | 4,152 | 1,994 | 2,184 | null | null | github_plus_top10pct_by_avg |
$Here also we will work with weighted Sobolev norms. And a similar hypothesis is supposed to hold for the adjoint $P_{t}^{\ast ,n}$ (see Assumption [A2A\*2]{} for a precise statement).
Finally we assume the following regularity property: for every $t\in (0,1]$, $P_{t}^{n}(x,dy)=p_{t}^{n}(x,y)dy$ with $p_{t}^{n}\in C^{... | 2,529 | 1,028 | 1,457 | 2,607 | null | null | github_plus_top10pct_by_avg |
ered.
Moore and Russell [@MR01] analyzed both the discrete and the continuous quantum walk on a hypercube. Kendon and Tregenna [@KT03] performed a numerical analysis of the effect of decoherence in the discrete case. In this article, we extend the continuous case with the model of decoherence described above. In parti... | 2,530 | 4,686 | 2,809 | 1,957 | 2,788 | 0.776938 | github_plus_top10pct_by_avg |
,\mathbf{C},\mathbf{D}\in\mathbb{C}^3$ suitably chosen so that $\mathbf{A}\cdot[1,1,1] = 0$, $\mathbf{B}\cdot[-1,1,1]
= 0$, $\mathbf{C}\cdot[1,-1,1] = 0$ and $\mathbf{D}\cdot[1,1,-1] = 0$, which ensures that incompressibility condition is satisfied, and that $\E({\mathbf{u}}_1) = 1$; in this case, $|{\mathbf{k}}|^2... | 2,531 | 2,998 | 3,647 | 2,474 | 3,490 | 0.771992 | github_plus_top10pct_by_avg |
sing restrictions on an adversary it was shown by Lo in [@Lo97] and and Buhrman et al. in [@Buhrman12] that these constructions are impossible, even in a quantum setting. As a consequence, constructions for generic unrestricted adversaries in the quantum setting are doomed to failure.
All in all, the necessity for aut... | 2,532 | 1,825 | 3,274 | 2,232 | null | null | github_plus_top10pct_by_avg |
hbf{e}}+ \left(1-\frac 1 m + \frac t m \right) {\mathbf{1}}\in \Gamma_+.$$
Hence by (the homogeneity of $\Gamma_+$ and) Remark \[hypid\], the maximal zero is at most $$\inf \left\{ \frac {\epsilon t+ \left(1-\frac 1 m\right)\frac t {t-1}} {1-\frac 1 m + \frac t m } : t >1\right\}.$$ It is a simple exercise to deduce ... | 2,533 | 1,372 | 2,067 | 2,277 | null | null | github_plus_top10pct_by_avg |
------ -------
\(1\) Weekly -- 7428.08 3197.22 1.13 1.49
\(2\) Weekday 0.96\*\*\* -- 8295.71 3585.12 1.30 2.44
\(3\) Weekend 0.71\*\*\* 0.49\*\* -- 5187.05 3375.77 0.61 −0.22
\*\*p \< 0.01, \*\*\*p \< 0.001; M = mean; SD = standard deviatio... | 2,534 | 1,033 | 2,916 | 2,710 | null | null | github_plus_top10pct_by_avg |
s n_i}(B\otimes_AR)$. This equation should be interpreted as follows. We formally compute the right hand side then it is of the form $\pi\cdot X$, where $X$ involves $\tilde{m}_{i,i}^{\ast}$ and $\tilde{m}_{i,i}^{\ast\ast}$. The left hand side $\mathcal{X}_{i,i}^{\ast}(\tilde{m})$ is then defined to be $X$. Then by usi... | 2,535 | 1,235 | 1,384 | 2,644 | 2,495 | 0.779339 | github_plus_top10pct_by_avg |
eta_{{\widehat{S}}})\leq t)$. There is no uniformly consistent estimator of $\psi_n(\beta)$.
[**Prediction Accuracy.**]{} Now we discuss prediction accuracy which is where splitting pays a price. The idea is to identify a population quantity $\theta$ that model selection is implicitly targeting and compare splitting v... | 2,536 | 3,348 | 2,604 | 2,225 | null | null | github_plus_top10pct_by_avg |
neered the research in this field by presenting a new epidemic model called *Susceptible-Infected-Disabled* (SID), which relates each state with a specific functionality of a node in the network [@calle2010multiple]. The state diagram of the SID model (*Susceptible$\leftrightarrows$Infected$\rightarrow$Disabled$\righta... | 2,537 | 1,201 | 3,747 | 2,445 | 3,000 | 0.775513 | github_plus_top10pct_by_avg |
\sum_{N_{A},N_{B},N_{C},N_{D}}
d(N_{A},N_{B},N_{C},N_{D})\,
A^{N_A}B^{N_B}C^{N_C}
D^{N_{D}}
\>,
\label{eq:RGA4}\end{aligned}$$ where we have used the prime symbol as a superscripts for $(r+1)$-th restricted partition functions and no indices for the $r$-th order partition functions. These relations can be consi... | 2,538 | 173 | 1,834 | 2,869 | 2,206 | 0.781847 | github_plus_top10pct_by_avg |
rametric, of order $\frac{1}{\sqrt{n}}$.
Prediction/Accuracy Tradeoff: Comparing Splitting to Uniform Inference {#section::splitornot}
======================================================================
There is a price to pay for sample splitting: the selected model may be less accurate because only part of the d... | 2,539 | 913 | 2,546 | 2,299 | 1,007 | 0.795862 | github_plus_top10pct_by_avg |
{Var}}$.
The simplest example of a conformal algebra can be constructed as follows. Let $A$ be an ordinary algebra, then a conformal product is uniquely defined on $\Bbbk[T]\otimes A$ by the following formulas for $a,b\in
A$: $$a{\mathbin{{}_{(n)}}}b=\begin{cases}ab, & n=0,\\ 0, & n>0.\end{cases}$$
The conformal alge... | 2,540 | 1,538 | 797 | 2,770 | 3,342 | 0.773004 | github_plus_top10pct_by_avg |
se from ten dimensions have been classified. Typically, from the point of view of the ten-dimensional theory these solutions are locally well-defined only in the presence of isometries, and are dubbed ‘exotic branes’ in the literature [@Elitzur:1997zn]. Denoting with $p+1$ the world-volume directions and with $n$ the n... | 2,541 | 340 | 3,023 | 2,513 | null | null | github_plus_top10pct_by_avg |
on_{n,j}^{\pm}$ on $\tilde{A_{n}}$ such that $\varepsilon_{n,j}^{\pm}(x_i)=\tau_j^{\pm}(x_i)$, $$\varepsilon_{n,j}^{\pm}(\partial_j)=\mp x_j^{2}\partial_j \, \mbox{ and }
\, \varepsilon_{n,j}(\partial_i)=\partial_i \, \mbox{ if } i\neq j \, ,$$ $i,j=1, \ldots, n$. We show it for $n=1$. Suppose we have a group actio... | 2,542 | 2,659 | 2,585 | 2,302 | null | null | github_plus_top10pct_by_avg |
au^2 +(\delta_{ij}+h_{ij} )dx^i dx^j \right]
\label{metric1}$$ where $|h_{ij}|\ll 1$. Using constraints $h^i_i=\nabla_ih^i_j=0 $ we can see that tensor $h_{ij}$ have only two independent components $h^1_1=-h^2_2=h_+$ and $h^2_1=h^1_2=h_{\times}$. These components correspond to two different polarisations of gravitation... | 2,543 | 3,979 | 2,837 | 2,315 | null | null | github_plus_top10pct_by_avg |
0\\
t^2 & 0 & 0\\
0 & 0 & 1
\end{pmatrix}\quad{\rm and}\quad
{\rm V}:
\begin{pmatrix}
1 & 0 & 0\\
t^4 & t^5 & 0\\
t^8 & 2t^9 & t^{10}
\end{pmatrix}$$ and the corresponding limits of ${{\mathscr C}}_2$ are given by $$z(y^2z-x^3)\quad{\rm and}\quad(y^2-xz+x^2)(y^2-xz-x^2),$$ respectively: a cuspidal cubic with its inflec... | 2,544 | 1,034 | 1,896 | 2,501 | 1,580 | 0.788036 | github_plus_top10pct_by_avg |
ad
O^{R,L}_{\Delta S=2} =\bar s \gamma_\mu (1\pm\gamma_5) d \,
\bar s \gamma^\mu (1\pm\gamma_5) d \ .$$ The $W$-boson diagrams yield a purely real Wilson coefficient $C^L_{\Delta S=2}(\mu)$; CP violation in kaon matrix elements is due solely to the operator $O^R_{\Delta S=2}$ rather than $O^L_{\Delta
S=2}$, in contras... | 2,545 | 2,385 | 2,914 | 2,414 | null | null | github_plus_top10pct_by_avg |
, $$\begin{aligned}
& \ddt \E{\lrn{x_t}_2^2} \\
=& 2\E{\lin{\nabla U(x_t), x_t - x_0}} + \E{ \tr\lrp{M(x_t)^2}}\\
\leq& 2L \E{\lrn{x_t}_2 \lrn{x_t - x_0}_2} + \beta^2\\
\leq& 2L \E{\lrn{x_t - x_0}_2^2} + 2L\E{\lrn{x_0}_2\lrn{x_t - x_0}_2} + \beta^2\\
\leq& 2L ... | 2,546 | 3,178 | 1,308 | 2,263 | null | null | github_plus_top10pct_by_avg |
}\,, \\
\mathcal{BR}(D^0\rightarrow K^- \pi^+ ) &= (3.89\pm 0.04)\cdot 10^{-2}\,,\end{aligned}$$ we obtain the normalized combinations $$\begin{aligned}
R_{K\pi} &= -0.11 \pm 0.01\,, \\
R_{KK,\pi\pi} &= 0.534 \pm 0.009\,, \\
R_{KK,\pi\pi,K\pi} &= 0.071 \pm 0.009\,.\end{aligned}$$
- ... | 2,547 | 3,225 | 3,231 | 2,511 | 1,350 | 0.79063 | github_plus_top10pct_by_avg |
0}\right)$ matrix is positive definite. In particular the DE for the first order perturbation is $$\frac{\partial\Ket{\Psi_{1}}}{\partial\tau}=-\left(\hat{H}_{0}-E_{0}\right)\Ket{\Psi_{1}}-V\Ket{\Psi_{0}}.\label{eq:psi1diffeq}$$
This equation is similar to the one used for $\Ket{\Psi_{0}}$ , with the addition of a sou... | 2,548 | 2,022 | 647 | 2,427 | 1,139 | 0.793706 | github_plus_top10pct_by_avg |
teq S=F_D \cup F \cup \Lambda_{I,p,d}\cup \Sigma_{p,d,P}$. Then, $d|(n-m)$. For, as $0\in P$, $a^pb^{p+d}\in S$ and we have that $a^pb^{p+d}a^mb^n=a^pb^{n-m+p+d} \in \Sigma_{p,d,P}$, so that $d|(m-n-d)$, that is, $m-n=(t+1)d$ for some $t\in \mathbb{N}^0$. Hence for any $a^ib^j \in S$ we have that $d|i-j$. By Lemma \[... | 2,549 | 2,935 | 2,637 | 2,338 | null | null | github_plus_top10pct_by_avg |
l m)\leq T$. This is because the numerator in the middle expression in (\[eqpoi2\]) is a finite sum of polynomials. However, there is no universal lower bound.
3. For any $g_0$, the number of $a_{g\ell m}$ with $g=g_0$ equals the number of $b_{gu}$ with $g=g_0$. This is simply because $\sum v^{a(g\ell m)} = \sum v^{b... | 2,550 | 1,203 | 1,645 | 2,320 | null | null | github_plus_top10pct_by_avg |
rtial_y d_y+d h_y,\ee
\be
[\bar{H},b_x]=\partial_y b_x,\hs{2ex}[\bar{H},b_y]=\partial_yb_y,$$ $$[D,h_x]=(c x\partial_x+d y\partial_y)h_x+2c h_x,\hs{2ex}[D,h_y]=(c x\partial_x+d y\partial_y)h_y+(c+d) h_y,$$ $$[D,\bar{h}_x]=(c x\partial_x+d y\partial_y)\bar{h}_x+(c+d) \bar{h}_x,\hs{2ex}[D,\bar{h}_y]=(c x\partial_x+d y\pa... | 2,551 | 788 | 880 | 2,580 | null | null | github_plus_top10pct_by_avg |
r{\kappa}, \bar C>0$ such that $P_t\psi_\kappa(x)\leq \bar C\psi_{\bar \kappa}(x)$, for all $x\in \R^d$ and $t>0$. Then $%
P_{t}(x,y)=p_{t}(x,y)$ with $p_{t}\in C^{\infty }(\R^{d}\times \R^{d})$ and for every $\kappa \in \N$, $\varepsilon >0$ and for every multi-indexes $\alpha $ and $\beta $ there exists $%
C=... | 2,552 | 914 | 2,046 | 2,438 | 4,160 | 0.767674 | github_plus_top10pct_by_avg |
2.67 ± 0.52 X10^6^/µl - p-value 0.833) between the two groups. The mean post-transplant hemoglobin (8.39 ± 0.91 gm/dl vs 8.37 ± 0.85 gm/dl - p-value 0.85), hematocrit (26.54 ± 2.96 % vs 26.34 ± 2.93 % - p-value 1), and RBC count (3.24 ± 0.41 X10^6^/µl vs 3.09 ± 0.54 X10^6^/µl - p-value 0.571) were comparable in group ... | 2,553 | 301 | 2,946 | 2,849 | null | null | github_plus_top10pct_by_avg |
el{450}$$ $${\check{V}}^{crv}_{1} = {{[{\bar{{\alpha}^{2}}} {\sin}^{2} (\theta)]}^{1
\over 2} \over {N}^{-{1 \over 2}}[{r}^{av} -{\cos}^{2}
(\theta){R}^{crv}_{N}] }.
\label{451}$$
The results just derived demonstrate the powerful volatility reduction effect of diversification coupled with short sales for the market-or... | 2,554 | 2,101 | 2,632 | 2,504 | null | null | github_plus_top10pct_by_avg |
al A}}}\,\sum_{{\partial}{{\bf N}}=y{\vartriangle}x}\frac{w_\Lambda({{\bf N}})}
{Z_\Lambda^5}\sum_{\substack{{\partial}{{\bf n}}=y{\vartriangle}x\\ {\partial}{{\bf m}}_i={\varnothing}~
{{}^\forall}i=1,\dots,4\\ {{\bf N}}={{\bf n}}+\sum_{i=1}^4{{\bf m}}_i}}{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{y{\underset{\rais... | 2,555 | 1,002 | 1,639 | 2,616 | null | null | github_plus_top10pct_by_avg |
or each }N\in\mathcal{N}_{x}\}\label{Eqn: TBx}$$ *determines the full neighbourhood system* $$\mathcal{N}_{x}=\{ N\subseteq X\!:x\in B\subseteq N\textrm{ for some }B\textrm{ }\in\,\mathcal{B}_{x}\}\label{Eqn: TBx_nbd}$$
*reciprocally as all supersets of the basic elements.$\qquad\square$*
The entire neighbourhood sys... | 2,556 | 4,484 | 3,586 | 2,389 | 4,002 | 0.768693 | github_plus_top10pct_by_avg |
, ... _I ever_ ... _ever I_.
... ... 97, ... _wage-pasty_ ... _way-pasty_.[100]
... ... 99, ... _he_ ... _ye_.
... ... _ib._ ... _ield_ ... _yelde_.
... ... 105, ... _to please_ ... _it please_.
... .... | 2,557 | 5,785 | 938 | 1,588 | null | null | github_plus_top10pct_by_avg |
ollowing relation: $$\Lambda = - \Lambda_5 .$$ We will find the solution by construction. Assume the ansatz in Eqn. (7) for the warp factor $f(z)$. Then its derivatives are given by Eqns. (8,9). $$\begin{aligned}
f(z) = {\alpha}
{\displaystyle Sinh[g(z)]^{-1} }
& & \\
f'( z) = -{\alpha} \displaystyle \fr... | 2,558 | 4,088 | 2,508 | 2,318 | 3,047 | 0.775227 | github_plus_top10pct_by_avg |
. For a massless representation, one has $\hat{P}^2=0$ and $\hat{W}^2=0$. Such representations are characterised by the helicity $s$ of the state, namely a specific representation of the helicity group SO(2), the rotation subgroup of the Wigner little group for a massless particle.[^9] For instance, for a light-like en... | 2,559 | 4,513 | 3,630 | 2,387 | null | null | github_plus_top10pct_by_avg |
gR \left( \h, \a \right) = \bigR \left( \S\h, \S\a \right)$ always holds. Therefore, $\S{\a^\star}$ is optimal for $\S\h$ with the same power constraint $P$.
(Nonnegative Ordered Vector) A vector $\h$ is said to be nonnegative ordered if its elements are nonnegative and in nondecreasing order according to their indice... | 2,560 | 1,101 | 1,856 | 2,292 | 3,205 | 0.77404 | github_plus_top10pct_by_avg |
onnected* *if it has no separation, that is if it cannot be partitioned into two open or two closed nonempty subsets. $X$ is* *separated (disconnected)* *if it is not connected.$\qquad\square$*
It follows from the definition, that for a disconnected space $X$ the following are equivalent statements.
\(a) There exist ... | 2,561 | 4,336 | 3,346 | 2,284 | 2,525 | 0.77918 | github_plus_top10pct_by_avg |
lta_{ij}L
\right)_{,j}=0,$$ which amounts to the momentum conservation law $$m_{i,t}+\left(\lambda^2u_{k,i}u_{k,j}-u_jm_i-\delta_{ij}\left(\frac{1}{2}u_ku_k+\frac{\lambda^2}{2}u_{k,l}u_{k,l}\right)\right)_{,j}.$$
Conservation of vorticity
-------------------------
Next, consider the coefficient of each ${\mathrm{d}}x... | 2,562 | 623 | 1,992 | 2,516 | null | null | github_plus_top10pct_by_avg |
that the determinant of the matrix $M$ (Eq. \[determinant\]) doesn’t vanish under this homomorphism.
For example, we can work over the ring $\Z_6$ and use the element $-1$ as a substitute for $\gamma$. Since $(-1)^6 = 1$ all of the calculations we did with $\gamma$ carry through. In addition, the resulting determinant... | 2,563 | 4,334 | 3,348 | 2,376 | 3,380 | 0.772757 | github_plus_top10pct_by_avg |
thbb{Z}})$ such that $m'_{1i}=m_i/m_0$ for all $i\in \{1,2,\dots ,k\}$. Then $(X_1^{(M')})^{m_0}-q\in J$, and hence $J$ is the intersection of the (finite number of) ideals $J+(X^{(M')}_1-q')$, where $q'\in {\bar{{\Bbbk }}}$, ${q'}^{m_0}=q$. By assumption, $J+(X^{(M')}_1-q')$ is generated by $X^{(M')}_1-q'$ and by elem... | 2,564 | 1,641 | 2,741 | 2,324 | null | null | github_plus_top10pct_by_avg |
m{on}\quad\mathcal{D}_{-}=\{0\}=\mathcal{D}_{+},\qquad G(y)=0\quad\mathrm{on}\quad\mathcal{R}_{-}=[0,1]=\mathcal{R}_{+}.$$
The graphical limit is $(0,[0,1])$.$\qquad\blacksquare$
[1.4]{} In these examples that we consider to be the prototypes of graphical convergence of functions to multifunctions, $G(y)=0$ on $\math... | 2,565 | 1,963 | 2,846 | 2,528 | 2,221 | 0.781736 | github_plus_top10pct_by_avg |
a_{3k}\}\setminus\{a_{n-3k}\}$ (size $k-1$).
The reasoning behind this lemma is that there exist sets $X \subset \mathbb{Z}_{k+1}^{2} \times \mathbb{Z}$ that are missing exactly $k+1$ points in every $\mathbb{Z}_{k+1}^{2}$ layer and can be tiled with strings. If we take $d = 2$ in Lemma \[otherlemma\], we would like ... | 2,566 | 3,267 | 2,913 | 2,398 | 2,134 | 0.782494 | github_plus_top10pct_by_avg |
\sim \Sigma (1,0) - \frac{\lambda_b}{2} (0,0)\,,\end{aligned}$$ where $(i,j) = \mathcal{O}^{\Delta U=i}_{\Delta U_3=j}$, and the appearing combination of CKM matrix elements are $$\begin{aligned}
\Sigma &\equiv \frac{V_{cs}^* V_{us} - V_{cd}^* V_{ud}}{2}\,, \qquad
-\frac{\lambda_b}{2} \equiv -\frac{V_{cb}^* V... | 2,567 | 2,314 | 2,758 | 2,364 | null | null | github_plus_top10pct_by_avg |
gamma^{\mu}\ell)+B^{'}q_{\mu}(\bar{\ell}\gamma^{\mu}\ell)
+C^{'}P_{\mu}(\bar{\ell}\gamma^{\mu}\gamma_5\ell)\nonumber\\&+&
D^{'}q_{\mu}(\bar{\ell}\gamma^{\mu}\gamma_5\ell)+A(\bar{\ell}\ell)
+B(\bar{\ell}\gamma_5\ell)+iC(P_{\mu}q_{\nu}-P_{\nu}q_{\mu})(\bar{\ell}\sigma^{\mu\nu}\ell)
\nonumber\\&+&D(P_{\mu}q_{\nu}-P_{\nu}q... | 2,568 | 1,827 | 2,503 | 2,459 | null | null | github_plus_top10pct_by_avg |
sure the number of unbounded subtrees of different colors is exactly $m$, an additional precaution must be taken. Precisely, a fourth condition is added to the event $\hat{N}\in B_{\varepsilon}$:
- For any $k\in\{1,\dots,m\}$, the argument of the point $Y_{k}$ of $\hat{N}\cap B(r e^{\i 2k\pi/m},\varepsilon)$ belongs... | 2,569 | 2,506 | 2,954 | 2,321 | 2,573 | 0.778782 | github_plus_top10pct_by_avg |
s to prove the statements resumed in Section \[sect:results\]: in Section \[sect:3.1\] we give an abstract regularity criterion, in Section \[sect:3.2\] we prove a regularity result for iterated integrals.
A regularity criterion based on interpolation {#sect:3.1}
---------------------------------------------
Let us f... | 2,570 | 1,062 | 769 | 2,736 | 3,255 | 0.773746 | github_plus_top10pct_by_avg |
)_R$ model[^1] was discussed in ref. [@su421]. The SU421 class of heterotic–string models differs from the HSPSM models in the breaking of $SU(2)_R\rightarrow U(1)_R$ directly at the string level. Similar to the HSPSM, the SU421 heterotic–string models admit the $SO(10)$ embedding and the chiral states are obtained fro... | 2,571 | 1,015 | 3,609 | 2,694 | null | null | github_plus_top10pct_by_avg |
tinuing from above, and using item 2 and 3 of Lemma \[l:N\_is\_regular\], $$\begin{aligned}
\circled{5}
\leq& q'(g(z_t)) \cdot \lrp{\frac{8\beta^2 \LN}{\cm} + \frac{\LN^2\|y_t-y_0\|_2^2}{\epsilon}}\\
\leq& q'(g(z_t)) \cdot \lrp{\frac{m}{2} \|z_t\|_2}
+ q'(g(z_t)) \cdot \lrp{ \frac{\LN^2\... | 2,572 | 2,941 | 1,934 | 2,295 | null | null | github_plus_top10pct_by_avg |
a certain tree can be found as a subgraph of ${\mathcal{C}}_m$.
\[lem:col\] [Let $({\mathcal{H}}^{(1)},\ldots, {\mathcal{H}}^{(n)})$ be a dynamic $s$-uniform hypergraph which satisfies the $\beta$-balanced, $\varepsilon$-visibility and $c_0$-size properties.]{} Suppose that $c>0$ is an arbitrary constant and $k=C\log... | 2,573 | 655 | 1,737 | 2,546 | 1,112 | 0.794264 | github_plus_top10pct_by_avg |
\; \Bigg( \frac{1}{16 \pi}\bigg[ R +\nu
\sqrt{
-5 R^4 -9 \Big( 8 R^{\mu\nu}R^{\alpha\beta}R^{\sigma\rho}_{\;\,\;\,\,\mu\alpha}R_{\sigma\rho\nu\beta} - 32 R\,R^{\mu\nu\alpha\beta}R_{\mu\;\,\alpha}^{\;\,\sigma\;\,\rho}R_{\nu\sigma\beta\rho}
} \nonumber\\
& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ov... | 2,574 | 4,995 | 745 | 2,019 | null | null | github_plus_top10pct_by_avg |
proof of Theorem \[sequentially\], and induction on the length of the pretty clean filtration it follows easily that $$\Hilb(\Ext_S^i(M,\omega_S))=\sum_{j\atop \dim S/P_j=n-i}\Hilb(\omega_{S/P_j})t^{-a_j} \quad\text{for}\quad i=0,\ldots, \dim M.$$
In particular we have
\[hilbert\] With the assumptions and notation of... | 2,575 | 1,464 | 1,982 | 2,379 | 3,293 | 0.773395 | github_plus_top10pct_by_avg |
the coefficients $\gamma_{\lambda_0}$, $\gamma_{\frac {\lambda_0+C}2}$ for these $S$ branches agree. Let $\gamma_C^{(1)},\dots,\gamma_C^{(S)}$ be the coefficients of $y^C$ in these branches (so that at least two of these numbers are distinct, by the choice of $C$). Then the limit is defined by $$x^{d-2S}\prod_{i=1}^S\... | 2,576 | 514 | 1,736 | 2,629 | null | null | github_plus_top10pct_by_avg |
Normal 0.8-1.4 ml EDTA & ACT tubes 2-8°C To confirm the viral infection RT-PCR
RDT ... | 2,577 | 5,421 | 548 | 1,753 | null | null | github_plus_top10pct_by_avg |
$& 21.9& 1.6\
05498&01& 22.91& 25.5& 25.2$\pm0.2$ & 23.1& 7.1& 22.28& 25.0?& 24.4 $\pm1.2$& 22.5& 6.0\
51835&55& 23.01& 26.0& 25.7$\pm0.3$ & 23.1& 11.2& 22.41& 23.8 & 23.4 $\pm0.2$& 23.0& 1.6\
00784&05& 23.28& 25.0& 24.7$\pm0.2$ & 23.6& 2.8& 22.80& 24.0 & 23.7 $\pm0.2$& 23.4& 1.2\
05696&02& 22.73& 24.7& 24.4$\pm0.2$ & ... | 2,578 | 254 | 3,300 | 2,876 | null | null | github_plus_top10pct_by_avg |
a\|}_p^p + C(M,p),$$ which immediately concludes the lemma with ${\|\theta\|}_p^p \leq \max({\|\theta_0\|}_p^p, C(M,p)\delta^{-1})$.
We now turn to proving that implies something analogous to Lemma \[lem:finite\_p\_bounded\]. Let $u(t)$ be as in *(ii)* of Theorem \[thm:Decay\]. One can verify that is equivalent to $$\... | 2,579 | 1,974 | 501 | 2,685 | null | null | github_plus_top10pct_by_avg |
mathbb{Z}_{k+1}^2$ have size $(k+1)^2-mk$ for some $m$, and this is always odd, so we cannot use Lemma \[biglemma\]. The same is true if we replace 2 with a larger dimension, or if, as in [@gltan16], we use strings in which every $(2k+1)$th point, rather than every $(k+1)$th point, is removed. We will therefore need a ... | 2,580 | 4,656 | 2,784 | 2,170 | 1,586 | 0.787937 | github_plus_top10pct_by_avg |
; @penas; @shukla1; @andriot; @shukla2]. By S-duality, the $Q$ flux is mapped to $P_a^{bc}$, and in [@Aldazabal:2006up] it was indeed shown that the second constraint in eq. is modified by the addition of the term $-P^{ae}_{[b}F_{cd]e}$, while the fourth constraint, which is the only other one that is relevant in the c... | 2,581 | 1,246 | 1,500 | 2,544 | null | null | github_plus_top10pct_by_avg |
xplicit formulas for them were obtained. Subbarao and Sitaramachandrarao, Huard, Williams and Zhang, and Tsumura researched the explicit formulas for $T(a,b,c)$ for $a,b,c \in{\mathbb{N}}$. The value $T (0, a, b \,; x,y)$ and their multiple sum versions have been already defined in Arakawa and Kaneko [@AraKa] for the c... | 2,582 | 1,332 | 2,241 | 2,413 | null | null | github_plus_top10pct_by_avg |
{-1} j)^{-1} (j^{T}R^{-1} r(X) - 1)^2 ) \label{eqn:varC}\end{aligned}$$ where $\sigma_{\mathcal{C}}^2$ is the variance of the costs $\mathcal{C}$, and we define the constant $\beta \equiv (j^{T}R^{-1} j)^{-1} j^{T}R^{-1} Y$, the $N \times 1$ vector $r(X)$ such that $\{r(X)\}_{1,i} = K(X,X_i,H)$, the $N \times 1$ vector... | 2,583 | 4,573 | 2,119 | 1,985 | null | null | github_plus_top10pct_by_avg |
States of
the far West:
PLACE. RECEIPTS. EXPENSES. BALANCE.
California Red Cross State $22,119.74 $10,472.63 $11,647.11
Association, Cal.
Red Cross Society, San Francisco, Cal. 55,408.83 33,434.18 21,974.65
" " " San Jose, Cal. ... | 2,584 | 5,207 | 1,002 | 1,776 | null | null | github_plus_top10pct_by_avg |
-hand side is the normalized outer potential. An analytic solution to this equation is given by $$\label{sol}
r_{{\rm c}}=\lambda_{{\rm D}} W\left(\frac{\alpha}{4\pi \Lambda}\frac{q}{e}\right),$$ where $W\left(x\right)$ is the inverse function of $x=W\exp\left(W\right)$, which is also known as the Lambert W-functio... | 2,585 | 3,587 | 3,038 | 2,529 | null | null | github_plus_top10pct_by_avg |
eta)}{\partial\theta_i \partial \theta_{\i}}$ is given by $$\begin{aligned}
H(\theta) = - \sum_{j = 1}^n \sum_{i<\i \in S_j} (e_i - e_{\i})(e_i - e_{\i})^\top \sum_{m = 1}^{\ell_j} \frac{\exp(\theta_i+ \theta_{\i})\I_{\{\sigma_j^{-1}(i),\sigma_j^{-1}(\i) \geq m\}}}{[\exp(\theta_{\sigma_j(m)})+\exp(\theta_{\sigma_j(m+1)... | 2,586 | 2,214 | 2,107 | 2,384 | null | null | github_plus_top10pct_by_avg |
for decay estimates. Indeed, is simply the requirement that the solution of the rescaled system remain uniformly equi-integrable. The proofs of Theorems \[thm:Decay\],\[thm:IA\] and \[thm:IA2\] are outlined in more detail in §\[sec:outline\]. Remarks on the limitations and possible extensions are made after the statem... | 2,587 | 1,968 | 690 | 2,618 | null | null | github_plus_top10pct_by_avg |
12.1 ± 2.0 0.001
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
jcdd-05-00035-t003_Table 3
######
Logistic regression an... | 2,588 | 4,703 | 2,215 | 2,173 | null | null | github_plus_top10pct_by_avg |
ngle layer case, RPA is never accurate for dipolar interactions, since it neglects exchange correlations [@babadi2011; @sieberer2011] which are important even in the long-wavelength limit [@parish2012].
A straightforward and physically motivated way of incorporating correlations beyond RPA is by means of local field f... | 2,589 | 3,136 | 3,326 | 2,436 | 1,126 | 0.794036 | github_plus_top10pct_by_avg |
mathrm{e}} \rightarrow {\mathrm{He^{2+}}} + 2{\mathrm{e}}$ $k_3=$ 2
$4^{a}$ ${\mathrm{H^+}}+{\mathrm{e}} \rightarrow {\mathrm{H}} + h\nu$ $k_4=2.753\times10^{-14} (T_{\math... | 2,590 | 4,798 | 803 | 2,203 | null | null | github_plus_top10pct_by_avg |
heta_{j_2})}\cdots \nonumber\\
&& \sum_{\substack{j_{\ell-1} \in S \\ j_{\ell-1} \neq i,\i, \\ j_1,\cdots,j_{\ell-2}}} \Bigg( \frac{\exp(\ltheta_{j_{\ell-1}})}{\widetilde{W}-\sum_{k=j_1}^{j_{\ell-1}}\exp(\ltheta_{k})} \Bigg)\Bigg)\Bigg) \nonumber\\
&\geq& \frac{e^{-4b} \exp(\ltheta_i)}{\widetilde{W}} \sum_{\substack{... | 2,591 | 1,524 | 1,868 | 2,365 | null | null | github_plus_top10pct_by_avg |
etilde{\sigma}_9(v_i,x_i) \; \dot{H}(t) H^{(3)}(t) \Bigg).
\end{split}\end{aligned}$$
To find squares, we use the following general procedure that is usefull for FLRW space-time, and necessary for spherical symmetry : Take the higher order perfect square $\ddot{H}(t)^2$. In the expansion of our square, each term will ... | 2,592 | 3,990 | 1,972 | 2,139 | 4,070 | 0.768289 | github_plus_top10pct_by_avg |
B''$.
{#app-to-main}
Analogues of Theorem \[main\] also hold for certain important $U_{c+k}$-modules and we will derive the theorem from one of these. The module in question is the $(U_{c+k},H_c)$-bimodule $N(k)=B_{k0}eH_c$ with the induced $\operatorname{{\textsf}{ord}}$ filtration coming from the inclusion $N(k)\s... | 2,593 | 1,072 | 932 | 2,606 | 1,732 | 0.786284 | github_plus_top10pct_by_avg |
b P}}^1\cong C_1\cong C_2\subset X$ such that $C_1+C_2$ is homologous to $0$. Let $g:C_1\cong C_2$ be an isomorphism and $R$ the corresponding equivalence relation.
We claim that there is a no quasi projective open subset $U\subset X$ which intersects both $C_1$ and $C_2$. Assume to the contrary that $U$ is such. The... | 2,594 | 1,359 | 1,499 | 2,377 | 2,586 | 0.77867 | github_plus_top10pct_by_avg |
}$ and $\E{\lrn{y_0}_2^2} \leq 8 \lrp{R^2 + \beta^2/m}$, we can verify that $$\begin{aligned}
& \int_0^T \frac{L_N^2}{\epsilon} \E{\lrn{y_s - y_0}_2^2} ds \leq \frac{1}{4} TL_N^2 \epsilon + TL_N^2 \epsilon\\
& L \E{\lrn{y_s - y_0}_2} \leq \frac{1}{2} TL\epsilon + TL\epsilon
\end{aligned}... | 2,595 | 3,131 | 2,500 | 2,300 | null | null | github_plus_top10pct_by_avg |
GP17 CA 67 7 (3 + 4) T3A 7.4 \+ 7 (3 + 4) 95 80
######
Characteristics of the analyzed prostate tumor and matched normal blood whole genomes.
Characteristics of the analyzed prostate tumor and matched normal blood whole genomes ... | 2,596 | 5,430 | 1,031 | 1,653 | null | null | github_plus_top10pct_by_avg |
)}{\ell_j}\label{eq:tau_def}\\
\delta_{j,1} & \equiv & \bigg\{ \max_{a \in [\ell_j]} \Big\{\lambda_{j,a}(\kappa_j - p_{j,a})\Big\} + \sum_{a = 1}^{\ell_j} \lambda_{j,a} \bigg\} \;\;, \;\text{and}\;\;\;\;\;\; \delta_{j,2} \equiv \sum_{a = 1}^{\ell_j} \lambda_{j,a} \label{eq:delta12_def} \\
\delta & \equiv & \ma... | 2,597 | 3,890 | 2,383 | 2,285 | null | null | github_plus_top10pct_by_avg |
((\tau+2)/3)} - \frac{27\eta'(3\tau)}{\eta(3\tau)} \right), \nonumber \\
y_{2}(\tau) &=& \frac{-i}{\pi}\left( \frac{\eta'(\tau/3)}{\eta(\tau/3)} +\omega^2\frac{\eta'((\tau +1)/3)}{\eta((\tau+1)/3)}
+\omega \frac{\eta'((\tau +2)/3)}{\eta((\tau+2)/3)} \right) , \label{eq:Yi} \\
y_{3}(\tau) &=& \frac{-i}{\pi}\left( ... | 2,598 | 3,157 | 2,312 | 2,343 | null | null | github_plus_top10pct_by_avg |
,0],[0,1]\notin \Lambda(\Gamma)$. Then there are $k,r,s\in \Bbb{C}$ such that
$$\begin{array}{l}
\psi(x)=[1,2k,k^2] \\
\psi(y)=[1,2r,r^2] \\
\psi(z)=[1,2s,s^2].
\end{array}$$ From Lemma \[l:ltanver\] we know $$\begin{array}{l}
T_{\psi(x)} Ver=\{
[x,y,z]
\in \Bbb{P}^1_\Bbb{C} \vert z=ky-k^2x\} \\
T_{\psi(y)} Ver=\{
[x... | 2,599 | 1,104 | 1,077 | 2,656 | null | null | github_plus_top10pct_by_avg |
\wedge^{\ell_n} T_n^{\alpha}
\otimes \wedge^{k_n} T_n^{\alpha *} \right) \otimes
{\cal F}
\right) ,$$ where $${\cal F}^{\alpha} \: = \: \sqrt{ K_{\alpha} \otimes \det {\cal E}^{\alpha}_0 }
\otimes_{n>0} \left( \left( \det {\cal E}^{\alpha}_n \right) \left(
\det T^{\alpha}_n \right)^{-1}\right)^{- \frac{n}{t_{\alpha}} ... | 2,600 | 1,753 | 2,021 | 2,462 | null | null | github_plus_top10pct_by_avg |
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