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 |
|---|---|---|---|---|---|---|---|
ehat{\phi }^{2\kappa }}{\varepsilon (\phi )^{q(q+1)+1/p_{\ast }}}\times
(1\vee \left\Vert \phi \right\Vert _{1,q+2,\infty }^{2dq+1+2\kappa })\times
\left\Vert f\right\Vert _{q,\kappa ,p}. \label{J6} \\
&\end{aligned}$$This means that Assumption \[H1H\*1\] from Section \[sect:3.2\] hold uniformly in $z\in E$ and the co... | 1,701 | 370 | 1,060 | 1,835 | 3,845 | 0.769721 | github_plus_top10pct_by_avg |
_{C,P}$ (resp. $\nu_{D,P}$) be the $w$-multiplicity of $C$ (resp $D$) at $P$, (defined such that $\nu_{x,P}=a$ and $\nu_{y,P}=b$). Then the following equalities hold:
1. \[formula\_self-intersection1\] $\displaystyle \pi^{*}(C) = \widehat{C} + \frac{\nu_{C,P}}{e} E$,
2. \[formula\_self-intersection2\] $\displaystyl... | 1,702 | 856 | 1,644 | 1,656 | null | null | github_plus_top10pct_by_avg |
s and reduced curves in $\PP^2$ introducing ideals of quasi-adjunction \[rem:qaideals\]. Here we will introduce the analogous objects for the cyclic covers of $\PP^2_w$ ramified along non-reduced curves. These objects are not ideals in general, but modules over the local rings $\cO_{\PP^2_w,P}$ which will be called qua... | 1,703 | 1,131 | 1,830 | 1,694 | null | null | github_plus_top10pct_by_avg |
anti-parallel
vortex tube... | 1,704 | 5,468 | 384 | 1,348 | null | null | github_plus_top10pct_by_avg |
, and the Fourier-transformed emission function is defined as $\tilde S(q,K) = \int \d^4 x S(x,K) \exp(i q x).$
The measured $\lambda_*$ parameter of the correlation function is utilized to correct the core spectrum for long-lived resonance decays [@Csorgo:1994in]: $ N_1(k) = N_c(k)/{\sqrt{\lambda_{*}(k)}}. $ The em... | 1,705 | 3,455 | 2,475 | 1,672 | null | null | github_plus_top10pct_by_avg |
eparation for a given set of parameters used in the simulations. The parameters ${\epsilon_{\mathrm{SW}}=9k_{\textrm{B}}T}$, ${\Delta=0.09\sigma _{2}}$ are the depth and the width of a short-ranged attractive square well, respectively, while the parameter $\epsilon_{\textrm{Y}}=24.6k_{\textrm{B}}T$ controls the strengt... | 1,706 | 3,721 | 2,493 | 1,687 | 1,612 | 0.787644 | github_plus_top10pct_by_avg |
ents, we used the Docker virtualisation technology (Fig. [2](#Fig2){ref-type="fig"}). The docker-compose tool is used to define multi-containers, connections, and all necessary parameters.Fig. 2Deployment organization
TASKA services were developed following the characteristics and requirements of three complementary e... | 1,707 | 239 | 2,146 | 1,434 | null | null | github_plus_top10pct_by_avg |
$ \dfrac{\pi}{2} $, the conformal infinity shifts towards infinity, giving rise to the $ \sim \dfrac{1}{r^2} $ behavior which diverges only at the ring singularity at $ r=0, \theta=\dfrac{\pi}{2} $. Moreover, we observe that except for $ \theta=\dfrac{\pi}{2} $, the gravitational entropy density remains finite at $ r=... | 1,708 | 3,938 | 1,344 | 1,441 | null | null | github_plus_top10pct_by_avg |
e data.
In addition to the $L_\infty$ ball given in , we also construct a confidence set for $\beta_{{\widehat{S}}}$ to be a hyper-rectangle, with sides of different lengths in order to account for different variances in the covariates. This can be done using the set $$\label{eq:beta.hyper:CI}
\tilde C_{{\widehat{... | 1,709 | 3,859 | 1,596 | 1,417 | null | null | github_plus_top10pct_by_avg |
$i>0$, while $H^0(\operatorname{Hilb^n{\mathbb{C}}^2}, {\mathcal{P}}_1 \otimes {\mathcal{L}}_1^d) = {\mathbb{J}}^d$ by . Thus, in the notation of [@hai1 Section 3], $p({\mathbb{J}}^d, s, t)=\chi_{{\mathcal{P}}_1 \otimes {\mathcal{L}}_1^d}(s,t)$ and so, by [@hai1 Proposition 3.2], $$\label{bigr11}
p({\mathbb{J}}^d, s, t... | 1,710 | 832 | 1,146 | 1,799 | 2,601 | 0.778532 | github_plus_top10pct_by_avg |
te vectors somehow. Suppose one is given a finite vector of $P^f (k_{\parallel})$, for $k^A_\parallel \le k_\parallel \le k^B_\parallel$ say. Eq. (\[projection3\]), in component form, can be rewritten as: $$P^f (k_\parallel) - \Delta = \sum_{k=k_\parallel}^{k^B_\parallel}
A(k_\parallel,k) \, \tilde P^\rho (k)
\label{p... | 1,711 | 1,521 | 2,456 | 1,878 | null | null | github_plus_top10pct_by_avg |
ed by $\Z_m[C_r]$ and referred to as the [*group ring*]{} of the cyclic group $C_r$ with coefficients in $\Z_m$. See e.g., [@KKS13; @HH11] for some recent applications of these rings in cryptography.
---
abstract: |
In this investigation we study extreme vortex states defined as incompressible velocity fields wit... | 1,712 | 265 | 1,194 | 1,794 | null | null | github_plus_top10pct_by_avg |
-----------------------
Subjects, *n* 177 73 14 29 27 3 31
Ag... | 1,713 | 4,011 | 1,699 | 1,465 | null | null | github_plus_top10pct_by_avg |
ty the isotropic case), one gets the equations $$\begin{aligned}
& \bar{a}(\bar{b}+\bar{\beta})-\bar{h}a-\bar{f}e+b\bar{h}_0+gm-q(\bar{g}+\bar{\gamma})=0 \nonumber \\
& a(b+\beta)+e(\gamma+g)+\bar{b}h_0-\bar{a}h+e_0\bar{g}+fq=0 \quad ,\label{constraintsD71braneIIB}\end{aligned}$$ where the notation for the isotropic fl... | 1,714 | 834 | 1,019 | 1,764 | null | null | github_plus_top10pct_by_avg |
,n})}{2f(t)}+\frac{D(t;h_{1,n})+b(t;h_{1,n})}{2f(t)}
\frac{f^{1/2}(t)-\hat f^{1/2}(t;h_{1,n})}{\hat f^{1/2}(t;h_{1,n})+f^{1/2}(t)}\\
&:=&\frac{D(t;h_{1,n})}{2f(t)}+\frac{b(t;h_{1,n})}{2f(t)}+\delta_4(t),\end{aligned}$$ (where $\delta_4$ depends on $n$, but we do not display this dependence) and note that (again using $... | 1,715 | 1,079 | 2,092 | 1,682 | 3,935 | 0.76918 | github_plus_top10pct_by_avg |
oup $S_{n+1}$ on $\mathcal O(n)$, which extends the given $S_n$-action, and satisfies, for $1\in\mathcal O(1)$, $\alpha\in \mathcal O(m)$, $\beta\in \mathcal O(n)$ the following relations: $$\begin{aligned}
\label{compos_cyclic1} \tau_2(1)&=&1,\\ \label{compos_cyclic2}
\tau_{m+n}(\alpha\circ_k \beta)&=&\tau_{m+1}(\alph... | 1,716 | 3,424 | 1,392 | 1,577 | 800 | 0.799832 | github_plus_top10pct_by_avg |
submanifold ${\mathbb{S}}_{2k}$ in the first jet space $J^1=J^1(X\times U)$.
####
Let us introduce a set of $p-2k$ linearly independent vectors $\xi_a:{\mathbb{R}}^q{\rightarrow}{\mathbb{C}}^p$ defined by
\[eq:3.13\] \_a(u)=[( \_a\^1(u),…,\_a\^p(u) )]{},a=1,…,p-2k,
satisfying the orthogonality conditions
\[eq:3.1... | 1,717 | 2,147 | 2,804 | 1,787 | null | null | github_plus_top10pct_by_avg |
ence\_vt\] Let $v_t$ be as defined in , initialized at $v_0$. Then for any $T=n\delta$, $$\begin{aligned}
\E{\lrn{v_T - v_0}_2^2} \leq T^2 L^2 \E{\lrn{v_0}_2^2} + T\beta^2
\end{aligned}$$ If we additionally assume that $\E{\lrn{v_0}_2^2} \leq 8 \lrp{R^2 + \beta^2/m}$ and $T \leq \frac{\beta^2}{8L^2\lrp{... | 1,718 | 1,851 | 941 | 1,542 | null | null | github_plus_top10pct_by_avg |
|\Th\sim\Nc_{r\times q}(\Th, v_yI_r\otimes I_q)$ with $(v_x,v_y)=(0.1,\, 1),\ (1,\, 1)$ and $(1,\, 0.1)$. It has been assumed that a pair of the maximum and the minimum eigenvalues of $\Th\Th^\top$ is $(0,\, 0),\ (24,\, 0)$ or $(24,\, 24)$. Note that the best invariant predictive density $\ph_U(Y|X)$ has a constant ris... | 1,719 | 649 | 1,385 | 1,641 | null | null | github_plus_top10pct_by_avg |
ing.
\[trathle2\] Assume that $\Sigma\in L^\infty(G\times S\times I)$ and that $\Sigma\geq 0$. Then $\psi$ defined by satisfies weakly in $G\times S\times I$, \[trath11\] \_x +=f, and the inflow boundary condition (\[trath8\]) is valid.
Due to (\[trath12\]) it suffices to show (\[trath11\]) only for $f\in C^1(\ol G\t... | 1,720 | 757 | 1,083 | 1,585 | null | null | github_plus_top10pct_by_avg |
this.vgap;
}
}
}
/* these 3 methods need to be overridden properly */
@Override public Dimension minimumLayoutSize(Container parent) {
return new Dimension(0,0);
}
@Override public Dimension preferredLayoutSize(Container parent) {
return ne... | 1,721 | 1,726 | 43 | 1,991 | 1,803 | 0.785591 | github_plus_top10pct_by_avg |
\tilde{\nu}_{J} (L).
\label{final-condition}\end{aligned}$$ Therefore, in the mass-basis formulation only $U$ and $W$ are involved, which is consistent with our experience in $W$ perturbation theory. An apparent contradiction to this property that one faces in the evolution equation in the flavor basis is resolved in ... | 1,722 | 1,772 | 2,044 | 1,827 | null | null | github_plus_top10pct_by_avg |
\overline{v} b \frac{\log n}{n} } \right)\\
\label{eq:Ac}
& \leq \frac{1}{n},
\end{aligned}$$ where in the third identity we have used the definition of $\epsilon_n$ in and the final inequality inequality follows from the vector Bernstein inequality and by taking the constant $C$ in appropriately large. In fa... | 1,723 | 3,235 | 2,021 | 1,518 | null | null | github_plus_top10pct_by_avg |
K}}$ and $T_{\mathrm{HII}} \simeq
7\times10^4{\,\mathrm{K}}$ are the temperature in the neutral and ionized regions, respectively. Although not very precise, this simple expression captures the qualitative features of the bipolar ionized outflows.
![The opening angle of the equatorial neutral inflow region $\theta_{\m... | 1,724 | 1,079 | 3,021 | 2,026 | 2,912 | 0.776146 | github_plus_top10pct_by_avg |
nced and size properties, with $d{\leqslant}s$. Then there exists a constant $\alpha=\alpha(\beta)$, which depends only on $\beta$, and there exists $m=\Theta(n)$ with $m < n$, such that the balanced allocation process on $({\mathcal{H}}^{(1)},\ldots, {\mathcal{H}}^{(n)})$ is $(\alpha,m)$-uniform. [Specifically, we may... | 1,725 | 931 | 1,170 | 1,561 | 1,775 | 0.78581 | github_plus_top10pct_by_avg |
haracteristics of two systems on the basis of Darboux transformations (and we obtain a construction of hierarchy of potentials as in [@Maydanyuk.2005.APNYA], see p. 443–445): $$\begin{array}{l}
H_{1} = A_{1}^{+} A_{1} =
-\displaystyle\frac{\hbar^{2}}{2m}
\displaystyle\frac{d^{2}}{dr^{2}}
+ \bar{V}_{1}(r), \\
... | 1,726 | 2,995 | 2,584 | 1,778 | null | null | github_plus_top10pct_by_avg |
es the true character of $\delta$ to allow only a view of its integral manifestation on functions. This unfortunately is not general enough in the strongly nonlinear physical situations responsible for chaos, and is the main reason for constructing the multifunctional extension of function spaces that we use. ]{}
[^10... | 1,727 | 2,719 | 2,035 | 1,676 | 2,066 | 0.783079 | github_plus_top10pct_by_avg |
d} \in \Sigma_{p,d,P}$. Hence $d|(m-n-d)$, that is, $m-n-d=td$ for some $t \in \mathbb{N}^0$ and so $m-n=(t+1)d$. Hence for any $a^ib^j \in S$ we have that $d|i-j$. By Lemma \[dimpact\], the first part of the following lemma is clear.
\[dequal1l\] If a two-sided subsemigroup $S=F_{D}\cup \widehat{F}\cup \widehat{\Lamb... | 1,728 | 2,208 | 1,806 | 1,629 | 3,340 | 0.773006 | github_plus_top10pct_by_avg |
def}(\Omega_{\rm c})_{d[ab}(J_{\rm c}^2)_{c]def} \Big) \nonumber \\
& (P_1^5\cdot\Omega_{\rm c}\cdot J_{\rm c}^2)_{abc} =\tfrac{1}{3} \Big( \tfrac{1}{16} P^{d_1...d_5}_{[a}(\Omega_{\rm c})_{bc]d_1}(J_{\rm c}^2)_{d_2...d_5}+\tfrac{1}{8}P^{d_1...d_5}_{[a}(\Omega_{\rm c})_{| d_1 d_2 d_3}(J_{\rm c}^2)_{d_4 d_5|bc]}\nonum... | 1,729 | 1,676 | 1,631 | 1,598 | 3,808 | 0.769987 | github_plus_top10pct_by_avg |
aybreaks \\
&= 2 \sum_{k = n + 1}^{2n} \frac{1}{k} \allowdisplaybreaks \\
&= 2 \sum_{k = 1}^{n} \frac{1}{k + n}. \end{aligned}$$ Therefore, we find $$\begin{aligned}
\lim_{n \rightarrow \infty} S_{n}
&= 2 \lim_{n \to \infty} \sum_{k = 1}^{n} \frac{1}{k + n} \allowdisplaybreaks \\
&= 2 \lim_{n \to \infty} \frac{1}{n} \... | 1,730 | 3,874 | 2,264 | 1,470 | null | null | github_plus_top10pct_by_avg |
h between this and alternatives such as the logistic curve will arise, chiefly, from tail events. Moreover, the Gaussian assumption allows a small, albeit potentially negligible, probability of a spurious firing event when no stimulus is applied. Given this contradiction with the experimental design, the following log-... | 1,731 | 2,067 | 3,194 | 1,774 | 3,457 | 0.772227 | github_plus_top10pct_by_avg |
a^{-1}\int_{0}^{1}\int_{-\pi}^{\pi} {f}(\rho_n+r_n r(\cos\theta,\sin\theta)) \\
& \hspace{7cm}\times\left(1-I(r^2;1-\alpha/2,\alpha/2)\right)\frac{{\rm d}\theta}{2\pi}\times \alpha r^{\alpha-1}\,{\rm d}r.
\end{aligned}$$ We used the Monte Carlo approach for evaluating this integral. Consider independen... | 1,732 | 1,603 | 2,063 | 1,686 | null | null | github_plus_top10pct_by_avg |
d currents realization of $U_q(\widehat{sl_N})$
------------------------------------------------------
$U_q(\widehat{sl_N})$ is an associative algebra generated by the Drinfeld generators $E^{\pm,i}_n~(n\in {\Bbb Z})$, $H^i_n~(n\in {\Bbb Z})~
(i=1,~2,~...,~N-1)$ and the center $\gamma$. Let
$$K_i = \mbox{exp}\left((q... | 1,733 | 1,197 | 1,602 | 1,596 | null | null | github_plus_top10pct_by_avg |
interested in the representation $V_{\operatorname{U}(abc),(k)} = \operatorname{Sym}^k({\mathbb C}^{abc})$, not in arbitrary irreducible representations of $\operatorname{U}(abc)$. By specializing the construction described in to this one-parameter family of representations, we obtain the following result:
\[optimize... | 1,734 | 3,323 | 1,770 | 1,545 | null | null | github_plus_top10pct_by_avg |
f $f$ is indispensable.
The fiber product $X\times_YX\subset X\times X$ defines an equivalence relation on $X$, and one might hope to reconstruct $Y$ as the quotient of $X$ by this equivalence relation. Our main interest is in the cases when $f$ is not flat. A typical example we have in mind is when $Y$ is not normal ... | 1,735 | 3,354 | 2,043 | 1,627 | 1,907 | 0.78451 | github_plus_top10pct_by_avg |
thcal{B}$. Then $$q=a^mb^n=(a^0b^m)^{-1}(a^0b^n),$$ so that $R_1$ is a straight left I-order in $\mathcal{B}$. In fact, it is a special case of Clifford’s result, mentioned in the Itroduction.
\[rems\] Any subsemigroup of $\mathcal{B}$ that contains $R_1$ is a straight left I-order in $\mathcal{B}$.
\[identity\] Let ... | 1,736 | 3,877 | 1,990 | 1,681 | null | null | github_plus_top10pct_by_avg |
}}\left[(1-p/\alpha) + e^{\frac{-\alpha d \log n}{2}}(1+p/\alpha)\right].$$ Suppose we choose $d$ such that $d > (p - \alpha)^{-1}$. Then $\gamma = o(n^{-1/2})$, which implies that $\|P^n - U^n\| = o(1)$. On the other hand, if $d < (p - \alpha)^{-1}$, then $\gamma = \omega(n^{-1/2})$ and there exists a constant $\epsil... | 1,737 | 521 | 1,439 | 1,705 | 3,045 | 0.775234 | github_plus_top10pct_by_avg |
property due to the input restrictions.
One can easily verify that the while loop in algorithm **** is iterated $$|u|-\sum_{i=1}^{h}(|c(w_{i},P_{n}(w_{1}w_{2}\ldots w_{i-1}))|-1)$$ times, where $w=w_{1}w_{2}\ldots w_{h}$, and $P_{n}$ is the function given in Theorem 2.1.
In practice, we can use only adaptive codes s... | 1,738 | 4,179 | 2,247 | 1,525 | 1,522 | 0.788651 | github_plus_top10pct_by_avg |
depends on the thermal drag such that it vanishes at zero temperature. But it also depends non-trivially on the size of the impurity and it diverges in the limit of point-like particle. Faxén corrections involving derivatives of the unperturbed flow are not present here because of the decoupling between $\delta\psi_0$ ... | 1,739 | 793 | 2,027 | 2,015 | null | null | github_plus_top10pct_by_avg |
s the energy of two monomers in contact, it turns out that the two chains cannot exist independently, even for extremely weak attraction ($|\epsilon_c|\ll k_BT$). Therefore, we define additional weight factor $t=e^{-\epsilon_t/k_BT}$, where $\epsilon_t>0$ is the energy associated with two sites, visited by different SA... | 1,740 | 341 | 1,747 | 2,033 | 2,375 | 0.78042 | github_plus_top10pct_by_avg |
ation of the PSF-DW and HI-MI transition we have additionally analyzed the energy-level-crossings with, respectively, periodic and twisted-boundary conditions. The KT transitions from SF to MI and HI have been determined by the extraction of the Luttinger parameter $K$ [@commentLuttinger].](bh3_pd.eps){width="8.0cm"}
... | 1,741 | 870 | 1,854 | 1,840 | 2,073 | 0.783032 | github_plus_top10pct_by_avg |
[Energy Bounds]{} \[ss:energy\_bounds\]
\[l:energy\_x\] Consider $x_t$ as defined in . If $x_0$ satisfies $\E{\|x_0\|_2^2} \leq R^2 + \frac{\beta^2}{m}$, then Then for all $t$, $$\begin{aligned}
\E{\|x_t\|_2^2} \leq 6\lrp{R^2 + \frac{\beta^2}{m}}\\
\end{aligned}$$ We can also show that $$\begin{aligne... | 1,742 | 3,368 | 1,435 | 1,422 | null | null | github_plus_top10pct_by_avg |
its from the Configuration Element class.
UPDATE:
The above code sample I pasted in allows you to edit what already exists in the config file inside your custom section. In order to add a new item for example like the following:
FavsSection favconfig = (FavsSection)config.GetSection("FavouritesMenu");
... | 1,743 | 2,595 | 73 | 1,495 | null | null | github_plus_top10pct_by_avg |
$\begin{aligned}
\label{eq:outthsin}
R_{{\widehat{\psi}}}^{{\mathrm{out}}}=\max~R,~~\mathrm{s.t.}~~{\mathbb{P}}(R_{{\widehat{\psi}}}<R)\le\epsilon\end{aligned}$$ and $$\begin{aligned}
\label{eq:outthrec}
R_{\psi}^{{\mathrm{out}}}=\max~R,~~\mathrm{s.t.}~~{\mathbb{P}}(R_{\psi}<R)\le\epsilon,
\end{aligned}$$ respective... | 1,744 | 647 | 1,910 | 1,673 | null | null | github_plus_top10pct_by_avg |
------ -- -- -- --
Buda-Lund
v1.5
0 - 30 % ... | 1,745 | 559 | 1,712 | 1,947 | null | null | github_plus_top10pct_by_avg |
after a new part annotation as $$\begin{split}
\tilde{\bf Q}(y=+1|I')=&\frac{1}{Z}\exp[\beta S_{top,I'}^{\textrm{new}}|_{\tilde{I}}]\\
S_{top,I'}^{\textrm{new}}|_{\tilde{I}}=&S_{top,I'}+\Delta S_{top,\tilde{I}}e^{-\alpha\cdot dist(I',\tilde{I})}\!\!\!\!\!\!\!\!\!\!
\end{split}
\label{eqn:predict}$$ where $S_{top,I'}$ ... | 1,746 | 852 | 1,686 | 1,874 | 2,170 | 0.782054 | github_plus_top10pct_by_avg |
\]. We take $\eta >\kappa +d$ and, using $(A_{4})$ (see ([R7]{})) we obtain $$\left\vert \mu ^{\eta ,\kappa }\right\vert =\int_{{\mathbb{R}}^{2}}\frac{%
\psi _{\eta }(x)}{\psi _{\kappa }(y)}P_{t}(x,dy)dx\leq C\int_{{\mathbb{R}}}%
\frac{dx}{\psi _{\kappa -\eta }(x)}<\infty .$$Then, $A(\delta )<C$ (see (\[reg12’\])). One... | 1,747 | 864 | 1,406 | 1,864 | null | null | github_plus_top10pct_by_avg |
se set in $QP(3,\Bbb{C})=(M(3,\Bbb{C})\setminus\{0 \})/\Bbb{C}^*$ called in [@CS] the space of pseudo-projective maps. Let $\widetilde{M}:\mathbb{C}^{3}\rightarrow\mathbb{C}^{3}$ be a non-zero linear transformation. Let $Ker(\widetilde M)$ be its kernel and $Ker([[\widetilde M]])$ denote its projectivization. Then $\wi... | 1,748 | 1,286 | 1,398 | 1,635 | null | null | github_plus_top10pct_by_avg |
}(v_1,v'_2)=\raisebox{-9pt}{\includegraphics[scale=.1]
{P1}}\qquad
P_\Lambda^{{\scriptscriptstyle}(3)}(v_1,v'_3)=\raisebox{-15pt}{\includegraphics[scale=.1]
{P2}}\\[5pt]
P_{\Lambda;u}^{\prime{{\scriptscriptstyle}(1)}}(v_1,v'_1)=\raisebox{-7pt}{\includegraphics
[scale=.1]{P0p}}\hspace{5pc}
P_{\Lambda;u,v}^{\prime\pri... | 1,749 | 2,735 | 1,825 | 1,768 | 1,648 | 0.787241 | github_plus_top10pct_by_avg |
ltaV_FRGeq}
\beta\, \partial_{t} {\Delta V}_{k} =
\frac{1}{2} \int \0{d^3 p}{(2 \pi)^3} \frac{ \partial_{t}
R_{0,k}}{Z_0\vec p{\,}^2 +
\partial^2_{A_0}( \Delta V_{k} + V_{\bot,k}) +
R_{0,k}} \,.$$ With the specific regulator $R_k$ in we can perform the momentum integration analytically. We also introduce the s... | 1,750 | 3,825 | 2,031 | 1,482 | 3,210 | 0.77401 | github_plus_top10pct_by_avg |
) \le t' k_2$. Let $M'= M \con (F \cup E(S))$. By the maximality of $h$, every restriction of $M'$ with rank at most $t'$ is $\GF(q)$-representable. In particular, every rank-$(s-1)$ restriction of $M'$ is $\GF(q)$-representable and every nonloop $f$ of $M'$ is spanned by a $\PG(s-2,q)$-restriction $P_f$ of $M'$ contai... | 1,751 | 1,528 | 783 | 1,707 | null | null | github_plus_top10pct_by_avg |
11 (37%) 28 (36%) 73 (42%)
Withdrawal by sponsor/ lack of funding 0 5 (23%) 0 5 (17%) 3 (4%) 2 (1%)
Benefit 0 0 0 ... | 1,752 | 3,210 | 2,151 | 1,814 | null | null | github_plus_top10pct_by_avg |
\widetilde{\Phi}_{i+1}^{mn} = 4\pi G \rho^{mn}_i$$ in uniform cylindrical coordinates, and $$\label{eq:tridiagonal_log}
\frac{1}{(R_i\ln f)^2} \widetilde{\Phi}_{i-1}^{mn} + \left[ \lambda_\phi^m + \lambda^n_z - \frac{2}{(R_i\ln f)^2} \right] \widetilde{\Phi}_i^{mn} + \frac{1}{(R_i\ln f)^2} \widetilde{\Phi}_{i+1}^{... | 1,753 | 919 | 1,713 | 1,939 | 3,545 | 0.771637 | github_plus_top10pct_by_avg |
ate as claimed.
For the original problem we get
\[m-d-co1\] Suppose that the assumptions (\[ass1\]), (\[ass2\]), (\[ass3\]), (\[evo16\]), (\[evo8-a\]) and (\[evo9-a\]) are valid with $C=\frac{\max\{q,0\}}{\kappa}$ and $c>0$. Furthermore, suppose that ${f}\in L^2(G\times S\times I)$, and $g\in H^1(I,T^2(\Gamma_-'))$ i... | 1,754 | 378 | 852 | 1,846 | null | null | github_plus_top10pct_by_avg |
v\in {\mathcal{U}}(\chi )$.}
\label{eq:Shfprop}\end{aligned}$$ Moreover, by definition of ${\mathrm{Sh}}$ and ${\theta ^{\chi}} $, $$\begin{aligned}
{\mathrm{Sh}}(u,v)=0 \quad \text{if $u\in \sum _{i\in I}{\mathcal{U}}(\chi )E_i$ or
$v\in \sum _{i\in I}{\mathcal{U}}(\chi )E_i$.}
\label{eq:Shfprop2}\end{aligned... | 1,755 | 1,443 | 941 | 1,772 | null | null | github_plus_top10pct_by_avg |
, ${\mathbb C}^{\times}$ invariants only exist in the case that $k$ divides $m$, and in that case, are counted by degree $m/k$ polynomials in $n+1$ variables.
Now, let us compare to the original claim. It is a standard result that for $\ell > 0$, $$H^i({\mathbb P}^n, {\cal O}_{{\mathbb P}^n}(\ell)) \: = \:
\left\{ \be... | 1,756 | 1,115 | 1,834 | 1,727 | 2,809 | 0.776817 | github_plus_top10pct_by_avg |
ence between the wave functions for the same energy levels of two systems. The coefficients $N_{1}$ and $N_{2}$ can be calculated from a normalization conditions for the wave functions (for the continuous energy spectra), and boundary condition are defined by scattering or decay process.
The interdependence between am... | 1,757 | 2,715 | 2,754 | 1,772 | 2,867 | 0.776433 | github_plus_top10pct_by_avg |
aligned}
\rho_{\sigma,\rm tip}(\w) = \lim_{\delta\to 0^+} \frac{1}{\pi} \Im G_{c_{0\sigma,\rm tip}, c^\dagger_{0\sigma,\rm tip}}
(\w-i\delta).\end{aligned}$$ As usual, $G_{A,B}(z)$ refers to the equilibrium Green’s function [@Rickayzen1980] defined in the complex frequency plane $z$ except on the real axis. Throughout... | 1,758 | 957 | 2,158 | 1,719 | null | null | github_plus_top10pct_by_avg |
in appendix \[sec:spectral\], assuming familiarity with standard methods of the spectral theory of automorphic forms.
[**Acknowledgements:**]{} We thank Peter Sarnak for his comments on an earlier version and for alerting us to Good’s work.
A geometric argument {#sec:Geom}
====================
We start with a basis ... | 1,759 | 3,495 | 2,121 | 1,593 | 1,908 | 0.784508 | github_plus_top10pct_by_avg |
x)}
(1 + \Delta_i)^{3/2}(1 + \Delta_j)^{3/2}
\exp[-x(\Delta_i + \Delta_j)]~,
\nonumber \\
\langle\sigma_{ij}v\rangle
&=&
\left(\frac{m}{4\pi T}\right)^{3/2}
\int 4\pi v^2dv~\left(\sigma_{ij}v\right)
\exp\left(-\frac{mv^2}{4T}\right)~,
\label{effective CS}\end{aligned}$$ where $i,j = \DM$, $\CP$ and $\CPC$, $\... | 1,760 | 2,959 | 2,699 | 1,751 | 2,064 | 0.783104 | github_plus_top10pct_by_avg |
(M_\infty)$. Since $[\tl c_{1}]\in{\operatorname{image}}\p_*$, it is $(t-1)$-torsion so $\b$ is $(t-1)^{N+1}$-torsion. Moreover $\b$ lies in the submodule $A\subset
H_1(M_\infty,\BQ)$ consisting of elements annihilated by some power of $t-1$, so, by choice of $N$, $(t-1)^N\b=0=[\tl c_{1}]=0$ as desired. This completes ... | 1,761 | 626 | 933 | 1,685 | 1,861 | 0.784953 | github_plus_top10pct_by_avg |
h compositions, and it is well-defined since for any $v \in V([n])$, its preimage $f^{-1} \subset V([m])$ carries a natural linear order induced by the orientation of the circle $S^1$.
\[alg.def\] For any associative unital algebra $A$ over $k$, its Hochschild, cyclic and periodic cyclic homology $HH_{{\:\raisebox{1pt... | 1,762 | 1,230 | 1,691 | 1,664 | 2,723 | 0.777553 | github_plus_top10pct_by_avg |
ions in vacuum can be found in Christodoulou’s work [@Chr] on the formation of black holes.
[^3]: The notation $A\lesssim B$ means $A\le cB$ for some universal constant $c$.
[^4]: Because is used very frequently in a similar manner, we will not point it out again when we use in the rest of the paper. Because $\mathsc... | 1,763 | 212 | 1,118 | 1,489 | 750 | 0.800809 | github_plus_top10pct_by_avg |
ed to describe the relevant quasienergy splitting when the periodic force is turned on. Sec. \[sec:twodefs\] explains in detail the strategy for achieving controlled population transfer between the two defects. Conclusions are drawn in the final Sec. \[sec:conclusion\].
Localization at a single defect {#sec:single}
==... | 1,764 | 3,631 | 2,254 | 1,697 | 3,207 | 0.774026 | github_plus_top10pct_by_avg |
he infinite equivalent set [\[]{}0[\]]{}. While Fig. \[Fig: tent4\] was a comparison of the first four iterates of the tent and absolute sine maps, Fig. [\[Fig: tent17\]]{} following shows the “converged” graphical limits for after 17 iterations.
***4.1. The chaotic attractor***
One of the most fascinating characteri... | 1,765 | 3,219 | 2,492 | 1,834 | 1,433 | 0.789655 | github_plus_top10pct_by_avg |
f monoid schemes. Namely, we claim the following commutative diagram of schemes: $$\xymatrixcolsep{5pc}\xymatrix{
\underline{M}^{\prime}\times \underline{M}^{\prime} \ar[d]^{\star} \ar[r]^{(1+)\times (1+)} &\underline{M}\times
\underline{M}\ar[d]^{multiplication}\\
\underline{M}^{\prime} \ar[r]^{1+} &\underline{M}}$$ S... | 1,766 | 1,773 | 1,490 | 1,584 | null | null | github_plus_top10pct_by_avg |
ome (32% for males and 47% for females).
{#pone.0153583.t003g}
------------------------- ------------------------- -------------------
**Males (N = 69)**
**4-MA4-MM** \<0.6 m/s (dismobility) ≥0.6 m/s (normal)
\<0.6 m/s (dismobility) 6 (8... | 1,767 | 57 | 2,144 | 2,086 | null | null | github_plus_top10pct_by_avg |
ac{\mu(s)\Psi(s)}{\psi(s)}ds}
\end{aligned}$$
For $r\in[0,\Rq]$, $\tau'(r) = r$, so that $\psi'(r) = \psi(r)(-\aq r)$. Thus $$\begin{aligned}
q'(r)
=& \psi(r) \nu(r)\\
q''(r)
=& \psi'(r) \nu(r) + \psi(r) \nu'(r)\\
=& \psi(r) \nu(r) (-\aq r) + \psi... | 1,768 | 4,264 | 1,283 | 1,292 | null | null | github_plus_top10pct_by_avg |
and accuracy of the variant algorithm in Section \[section5\] through experiments on simulated and real medical dataset (Section \[section6\]).
New random graph model {#section2}
======================
Notations
---------
This work considers the framework of an unweighted undirected graph $G(V,E)$ with no self-loop... | 1,769 | 318 | 1,081 | 1,924 | 1,271 | 0.791793 | github_plus_top10pct_by_avg |
ith uniform weights by a constant factor. We fix $\kappa = 128$ and $n=128000$. As illustrated by a figure on the right, the position of the separators are chosen such that there is one separator at position one, and the rest of $\ell-1$ separators are at the bottom. Precisely, $(p_{j,1},p_{j,2},p_{j,3},\ldots,p_{j,\el... | 1,770 | 342 | 927 | 1,917 | 1,769 | 0.785853 | github_plus_top10pct_by_avg |
-------------------- -------------- -------------- -------------- ---------
Sex Girls 1863 37.5 48.2 8.4 5.9 \<0.001
Boys 1765 28.4 53.4 ... | 1,771 | 6,354 | 895 | 368 | null | null | github_plus_top10pct_by_avg |
(6)$ $0.43(1)$
CTTP $0.64(1)$ $0.78(3)$ $1.55(5)$ $0.43(1)$
Manna $0.64(1)$ $0.78(2)$ $1.57(4)$ $0.42(1)$
DP $0.583(4)$ $0.80(1)$ $1.766(2)$ $0.451(1)$
$\tau_s... | 1,772 | 4,146 | 2,215 | 1,699 | null | null | github_plus_top10pct_by_avg |
polynomial $f$ so that $f(x)=\sum_{i=1}^q \alpha_{i}x^{i-1}$. Since we defined $t_i=i-1$, we have $f(x)=\sum_{i=1}^q \alpha_{i}x^{t_i}$. Define $\beta_i=-\alpha_i$ for all $i\in [q]$. Our final construction of $h$ is thus $$h(\ell)=f(\gamma^\ell)-\ell f(\gamma^\ell)$$
$h(\ell)=0\ \forall \ell\in S$
Since $0\notin S$,... | 1,773 | 4,156 | 2,369 | 1,709 | null | null | github_plus_top10pct_by_avg |
\end{aligned}$$ as $n\to\infty$. This, together with (\[rem\]) and (\[rem2\]) prove the proposition.
.1truein This proposition is similar to Theorem 3.1 of Hall, Hu and Marron (1995) and to Theorem 1 of Novak (1999), who do not consider uniformity in $t$ or $f$, and our proof is somewhat adapted from the latter refere... | 1,774 | 1,172 | 1,916 | 1,723 | 3,747 | 0.770382 | github_plus_top10pct_by_avg |
only the case $n=1$. The significance of this Corollary is that it has been previously shown by Ivanov and Katz (\[IK, Theorem 9.2 and Cor.9.3\]) that the conclusion of Corollary \[systole\] is sufficient to guarantee a certain optimal systolic inequality for $M$. The interested reader is referred to those works.
Supp... | 1,775 | 762 | 1,734 | 1,689 | 2,801 | 0.776844 | github_plus_top10pct_by_avg |
g Equation , but we only keep four 3D arrays ${\cal G}^m_{i,i'}({\rm top \to top}) = {\cal G}^m_{i,i',0}$, ${\cal G}^m_{i,i'}({\rm top \to bot}) = {\cal G}^m_{i,i',-N_z-1}$, ${\cal G}^m_{k,i'}({\rm top \to inn}) = {\cal G}^m_{0,i',k-N_z-1}$, and ${\cal G}^m_{k,i'}({\rm top \to out}) = {\cal G}^m_{N_R+1,i',k-N_z-1}$, co... | 1,776 | 1,390 | 2,306 | 1,916 | 3,470 | 0.77211 | github_plus_top10pct_by_avg |
ming from the Lagrangians in Eq. (\[eq:weakl\]). The weak vertex is represented by a solid black circle. \[vf2\]](nspw "fig:") ![Weak vertices for the $\Lambda N\pi$, $\Sigma N\pi$ and $NNK$ stemming from the Lagrangians in Eq. (\[eq:weakl\]). The weak vertex is represented by a solid black circle. \[vf2\]](nnkw "fig:"... | 1,777 | 431 | 1,512 | 1,862 | null | null | github_plus_top10pct_by_avg |
\
b(j) \approx \max_{j} g(\hat\psi_j).$$
[**Proof of .**]{} We will establish the claims by bound the quantity $\left\|
\hat\beta_{S} - \beta_{S}
\right\| $ uniformly over all $\beta_S \in H_n$.\
Our proof relies on a first order Taylor series expansion of of $g$ and on the uniform bound on the norm of the ... | 1,778 | 2,551 | 1,376 | 1,660 | null | null | github_plus_top10pct_by_avg |
ral static bubble. We also see from the Hamiltonian constraint that for small $Q/L^2$, curvatures near the bubble are of order $1/Q$. Therefore there is a minimum $Q$, controlled by the cutoff, for which we can study this geometry classically.
Adding Charged Matter
---------------------
We would like to study the sta... | 1,779 | 785 | 1,950 | 1,903 | null | null | github_plus_top10pct_by_avg |
- e^{- i h_{k} x} \right)
\left( e^{+ i \Delta_{L} x} - e^{+ i h_{l} x} \right)
\nonumber \\
&\times&
\biggl[
(UX)_{\alpha k} W^*_{\beta K}
\left\{ (UX)^{\dagger} A W \right\}_{k K}
+
W_{\alpha K} (UX)^*_{\beta k}
\left\{ W ^{\dagger} A (UX) \right\}_{K k}
\biggr]
\nonumber \\
&\times&
\biggl[
(UX)_{\alpha l}^... | 1,780 | 1,877 | 2,206 | 1,806 | null | null | github_plus_top10pct_by_avg |
, etc..);
Foo foo(bar);
But if bar is a big object (for example, contains an array), then it would be inefficient to pass bar by value. The only way is to have bar passed by reference or pointer, but I also want the user to be able to use bar with parameterized constructor, and hence my confusion began.
Regarding to t... | 1,781 | 2,099 | 708 | 1,351 | 858 | 0.798823 | github_plus_top10pct_by_avg |
um_{ij\in \text{C}}\sum_n
\left|\left[\hat{g}_0(i\w_n)\right]_{ij}
-\left[\hat{g}_{0,N_{\text{B}}}(i\w_n)\right]_{ij}\right|^2
e^{-\w_n/t},
\label{eq:distance}\end{aligned}$$ where $\hat{g}_{0,N_{\text{B}}}$ is the non-interacting Green’s function for the effective Hamiltonian and we have introduced th... | 1,782 | 3,916 | 2,062 | 1,424 | 3,104 | 0.77486 | github_plus_top10pct_by_avg |
18}\cap[G,G]\right)\\
&\subset\left(A^{18}\cap\pi^{-1}(H)\right)\prod_{i=1}^r\left(A^{24}\cap\pi^{-1}(\langle x_i\rangle)\right).\end{aligned}$$ Since $a$ was an arbitrary element of $\pi^{-1}(HP)\cap A^6$, the proposition then follows from .
It is at this point that we diverge from the original proof of \[thm:old\]... | 1,783 | 1,103 | 1,180 | 1,850 | 4,170 | 0.767605 | github_plus_top10pct_by_avg |
})$ would be a good target for PINGU extensions of IceCube and KM3NeT-ORCA [@TheIceCube-Gen2:2016cap; @Adrian-Martinez:2016zzs]. $P(\nu_{\mu} \rightarrow \nu_{\tau})$ and $P(\nu_{\mu} \rightarrow \nu_{\mu})$ would be explored by them, with possibility of seeing anticorrelation between $\mu$ and $\tau$ yields. Although ... | 1,784 | 1,940 | 3,123 | 1,950 | 1,928 | 0.784326 | github_plus_top10pct_by_avg |
_\mathrm{vir}$), whereas it suddenly drops to below $10^5$ K around $0.2 R_{\rm vir}$ when metal-line cooling is included. Thus, the catastrophic cooling flow of the diffuse, hot component in the inner haloes is due to metals. Indeed, while the median hot-mode radial peculiar velocity within $0.2 R_{\rm vir}$ is positi... | 1,785 | 958 | 1,976 | 1,877 | null | null | github_plus_top10pct_by_avg |
a$ is generated by the one-loop diagram to which $Z_2$-odd particles contribute. The lightest $Z_2$-odd scalar boson can be a candidate for the dark matter. We briefly discuss a characteristic signal of our model at the LHC.'
author:
- Shinya Kanemura
- Hiroaki Sugiyama
title: |
Dark matter and a suppression mecha... | 1,786 | 200 | 2,703 | 1,868 | null | null | github_plus_top10pct_by_avg |
nerally become sparser the higher the order. Hence, we come up with many more ties and the chance is higher that we assign higher ranks for observed transitions in the testing data. The most extreme case happens when we do not have any information available for observations in the testing set (which frequently happens ... | 1,787 | 6,575 | 976 | 592 | null | null | github_plus_top10pct_by_avg |
- C(A) - R(A) + J\end{aligned}$$ First note that the rank of $\breve{A}$ and that of $A$ can differ by at most 3. Now, consider the case where $A$ is the Gram matrix of some vectors $v_1,...,v_n \in R^d$. Then all diagonal entries of $\breve{A}$ equal one, and the $(i,j)$ entry is 2$<v_i,v_j> - <v_i,v_i> - <v_j,v_j> +... | 1,788 | 3,935 | 2,387 | 1,636 | 3,677 | 0.770774 | github_plus_top10pct_by_avg |
{Q-1}
\end{pmatrix}.\end{aligned}$$
Definition of $\rho_{{\mbox{\boldmath $\alpha$}}}(f_i)$
-------------------------------------------------------
Next, we define a linear map for $f_i$.
For a tableaux $P = ({\mbox{\boldmath $\alpha$}}^{(0)}, {\mbox{\boldmath $\alpha$}}^{(1/2)}, \ldots, {\mbox{\boldmath $\alpha$}}^... | 1,789 | 1,911 | 1,903 | 1,605 | 2,278 | 0.781193 | github_plus_top10pct_by_avg |
ametricstable}
\dot{\beta}_2(k) = i\omega_2(k)\beta_2(k) + \int \limits_{-\infty}^{\infty}\frac{dk'}{2\pi}D_1(k,k')\beta_1(k')\beta_1(k'').$$ Note that for these times $\beta_2 \ll \beta_1$ therefore the $D_1$ terms are the largest of the $D_j$ terms. Since the $C_j$ nonlinearities have not reached the amplitudes of th... | 1,790 | 1,778 | 3,191 | 1,932 | 2,101 | 0.782718 | github_plus_top10pct_by_avg |
hat \in
\P^k$ as above define $$a_\muhat:=a_{\mu^1}(\x_1)\cdots a_{\mu^k}(\x_k).$$ Let $\langle\cdot ,\cdot \rangle$ be the Hall pairing on $\Lambda(\x),$ extend its definition to $\Lambda(\x_1,\ldots,\x_k)$ by setting \[extendedhall\] a\_1(\_1)a\_k(\_k), b\_1(\_1)b\_k(\_k)= a\_1, b\_1 a\_k, b\_k , for any $a_1,\ldots,... | 1,791 | 930 | 1,895 | 1,739 | 3,908 | 0.769355 | github_plus_top10pct_by_avg |
to test the hypothesis: $\beta_{j}=\beta_{j0}$ for some $1\leq j\leq p$, or $\beta=\beta_{0}$.
We let $\beta$ be a $7\times 1$ vector with all coordinates equal to 0.2. $Z_i$ comes from seven distributions which were used in [@Shi2018].
- $N(0, \Sigma)$, $\Sigma=(\rho_{ij})$ with $\rho_{ij}=0.5^{I(i\neq j)}$, where... | 1,792 | 1,456 | 1,811 | 1,690 | null | null | github_plus_top10pct_by_avg |
can be identified with a (weighted) *colimit* functor, then of course it commutes with all other colimits. It also explains the left-right duality in the first theorem as due to the fact that the class $\mathsf{FIN}$ of finite categories is closed under taking opposites. Thus we can say:
**Answer \#2:** The homotopy t... | 1,793 | 437 | 2,338 | 1,926 | null | null | github_plus_top10pct_by_avg |
es the Randall-Sundrum brane world model [@20]. These two corrections are regular cosmological solutions and allow to avoid the Big-Bang singularity [@19; @16]. One should also note that the above equation may be obtained within other approches (see [@21; @22]).
Static Spherically Symmetric Space-times
===============... | 1,794 | 3,050 | 2,473 | 1,757 | null | null | github_plus_top10pct_by_avg |
mponents indicators are solution of some specific problem.
\[prop2\] The minimization problem ($\mathcal{P}_0$)
$\underset{v\in \mathcal{V}_{1,k}^0 \backslash\{0\}}{\arg\min} {\|v\|}_0 $
has a unique solution (up to a constant) given by $\textbf{1}_{C_{n-k+1}}$.
In other words, $\textbf{1}_{C_{n-k+1}}$ is the spar... | 1,795 | 2,984 | 1,527 | 1,666 | null | null | github_plus_top10pct_by_avg |
= \kappa$, are chosen uniformly at random from the set of $d$ items for all $j \in [n]$. The rank-breaking log likelihood function $\Lrb(\ltheta)$ for the set of items $[\ld]$ is given by $$\begin{aligned}
\label{eq:likelihood_bl_0}
\Lrb(\ltheta) &=&
\sum_{j=1}^n \sum_{a = 1}^{\ell_j}
\,\lambda_{j,a} \,... | 1,796 | 2,895 | 1,640 | 1,641 | null | null | github_plus_top10pct_by_avg |
u))}\,{\rm d}u\notag\\
& \eqqcolon\Lambda({\varepsilon}/{\zeta_0})\,\sqrt{\zeta_0},
\label{ineq}
\end{aligned}$$ where $\mathbf{1}_S$ denotes the indicator function on the set $S$. Using the primitive ${\displays... | 1,797 | 1,524 | 1,348 | 1,619 | null | null | github_plus_top10pct_by_avg |
1/2 \\ 0 \\ \frac{1}{4}(-1 + \frac{p}{\alpha}) \\ \frac{1}{4}(-1 - \frac{p}{\alpha}) \end{matrix} \right]$$ and thus at time $t$ we have $$\rho_t = e^{\mathbf{A}}\rho_0 = \left[\begin{matrix} 1/2 \\ 0 \\
\frac{1}{4}e^{\frac{-p t - \alpha t}{2n}}(-1 + \frac{p}{\alpha})
\\ \frac{1}{4}e^{\frac{-p... | 1,798 | 5,293 | 909 | 1,079 | null | null | github_plus_top10pct_by_avg |
n: R+}$$
It is to be noted that the conditions $\mathcal{D}_{+}=\mathcal{D}_{-}$ and $\mathcal{R}_{+}=\mathcal{R}_{-}$ are necessary and sufficient for the Kuratowski convergence to exist. Since $\mathcal{D}_{+}$ and $\mathcal{R}_{+}$ differ from $\mathcal{D}_{-}$ and $\mathcal{R}_{-}$ only in having cofinal subsets o... | 1,799 | 474 | 2,492 | 1,793 | 1,976 | 0.783952 | github_plus_top10pct_by_avg |
I*. If $L_i$ is *free of type I*, then $\pi^i f_{i,i}$ is of the form $$\xi^{(i-1)/2}\cdot \pi\begin{pmatrix} a_i&\pi b_i& e_i\\ -\sigma(\pi \cdot {}^tb_i) &\pi^3f_i&1+\pi d_i \\
-\sigma({}^te_i) &-\sigma(1+\pi d_i) &\pi+\pi^3c_i \end{pmatrix}.$$ Here, the diagonal entries of $a_i$ are are divisible by $\pi^3$, wh... | 1,800 | 2,449 | 1,684 | 1,586 | null | null | github_plus_top10pct_by_avg |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.