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 |
|---|---|---|---|---|---|---|---|
\right)$, which implies ${\a^\star}$ is not optimal. Thus, ${\a^\star}(i) - {\a^\star}(j) \geq -1$. Similarly, ${\a^\star}(j) - {\a^\star}(i) \geq -1$. Therefore, ${\a^\star}(i) = {\a^\star}(j)$ or $\fabs{{\a^\star}(i) - {\a^\star}(j)}=~1$.
\[remark:hijEqual\] In Lemma \[lemma:hijEqual\], for the case where $\h(i) = \... | 1,601 | 825 | 1,799 | 1,528 | null | null | github_plus_top10pct_by_avg |
} \left| \mathbb{P}\left( \sqrt{n} \| \hat{\theta} -
\theta \|_\infty
\leq t \right) - \mathbb{P}( \| Z_n \|_\infty \leq t ) \right|,\\
A_2 & = \sup_{t>0} \left| \mathbb{P}( \| Z_n \|_\infty \leq t ) - \mathbb{P}( \|
\hat{Z}_n \|_\infty \leq t ) \right|,\\
\text{and} & \\
A_3 & = \sup_{t... | 1,602 | 2,769 | 1,566 | 1,460 | null | null | github_plus_top10pct_by_avg |
decode $\alpha\y$ as an integer linear combination, whose coefficients form $\a$, of the original codewords $\{\x_\ell\}$. The *computation rate* [@Nazer2011] is the maximum transmission rate from the associated sources to a relay such that the integer linear combinations at the relay can be decoded with arbitrarily s... | 1,603 | 298 | 1,448 | 1,758 | null | null | github_plus_top10pct_by_avg |
] We have $$\sum_{n\geq
1}\H_{(n-1,1)}(z,w)T^n=(z^2-1)(1-w^2)\frac{A_1(z,w;T)}{A_0(z,w;T)}.$$
The coefficient of the monomial symmetric function $m_{(n-1,1)}(\x)$ in a symmetric function in $\Lambda(\x)$ of homogeneous degree $n$ is the coefficient of $u$ when specializing the variables $\x=\{x_1,x_2,\dots\}$ to $\{... | 1,604 | 3,315 | 2,019 | 1,498 | null | null | github_plus_top10pct_by_avg |
f symbols $x_1, \dots, x_n, x\in \{{
\begin{pspicture}(0,0.1)(0.2,0.4)
\psline[linewidth=1pt](0.1,0)(0.1,0.4)
\end{pspicture}},{
\begin{pspicture}(0,0.1)(0.2,0.4)
\psline[linewidth=1pt, linestyle=dashed,dash=4pt 3pt](0.1,0)(0.1,0.4)
\end{pspicture}},\varnothing \}$, we have (differential graded) vector spaces $\... | 1,605 | 1,396 | 1,713 | 1,478 | 757 | 0.800722 | github_plus_top10pct_by_avg |
certain irreducible representation (irrep) of ${\ensuremath{SL(2,\mathbb{R})\times U(1)}}$ labeled by $(m,h,k)$. Then the ${\ensuremath{SL(2,\mathbb{R})\times U(1)}}$ structure factors straight through the differential operator $\mathcal{D}_{x}$, leaving a new differential operator $\mathcal{D}_{u}^{(m,h)}$ which only... | 1,606 | 2,681 | 2,004 | 1,591 | null | null | github_plus_top10pct_by_avg |
,t)$, but, for both $b=2$ and $b=3$, the function $w_c(u,t)$ for fixed $t$ is monotonically decreasing function (see figure \[fig:fdCSAWs\]). Dependence of $w_c(u,t)$ on $t$, when $u$ is fixed, is presented in figure \[fig:wcODt\], for several values of $u$.
![Critical value of the inter-chain interaction parameter $w... | 1,607 | 930 | 2,279 | 1,657 | 1,704 | 0.786621 | github_plus_top10pct_by_avg |
_{ki}\Big\|^4\\
&=O(K^{-1})\end{aligned}$$ as $K, m\to \infty$. On the other hand, from the Assumption \[assumption2\], we get $${\mathbb{P}}\Big(\max_{1\leq i\leq K} \|R_{km}\|>\epsilon K^{1/2}\Big)\to 0$$ as $K, m\to \infty$. So we can complete the proof.
\[lem-2\] Let $$S_K =\frac{1}{K}\sum_{k=1}^{K}(Y_{km}-\mu)(Y_... | 1,608 | 1,760 | 1,083 | 1,456 | null | null | github_plus_top10pct_by_avg |
his completes the proof, since that element $\bar s$ is above $s_0$ and forces that $\dot{ \mathcal{X}}\cap [Y]^\omega$ is stationary.
$(S)[S]$ implies ****.
We next need:
\[P. Larson\]\[larson\] Suppose
- ****, and
- for sufficiently large $\theta$ and stationary $E\subseteq\omega_1$, for any $X\in H(\theta)$... | 1,609 | 3,517 | 2,236 | 1,646 | null | null | github_plus_top10pct_by_avg |
rhd_{r} h := r(g)hr(g)^{-1}$, for all $g\in G$ and $h\in H$. Hence $\widehat{(\alpha_{0}, \beta_{0})} = \{(\rhd_{r}, \beta_{0})
~|~ r: G\to H ~~ {\rm ~is~ a~ morphism~ of~ groups}\}$. We restate this observation as follows: let $H$ and $G$ be two groups. Then there exists $(H, G, \alpha', \beta')$ a matched pair such t... | 1,610 | 3,022 | 1,901 | 1,608 | null | null | github_plus_top10pct_by_avg |
s then given by ${\mathbf{F}}={\mathbf{I}}_{N_s}$ with equal power allocation between the $N_s$ data streams, since the transmitter does not have the full CSI. At the receiver, the digital decoder is the joint ML decoder for maximizing the throughput.[^6] With the aforementioned transceiver architecture and CSI assumpt... | 1,611 | 575 | 1,993 | 1,552 | 3,021 | 0.775408 | github_plus_top10pct_by_avg |
:flutter_convertor/ItemBought.dart';
class task extends StatelessWidget{
@override
...
}
class taskScreen extends StatefulWidget{
@override
taskState createState() => new taskState();
}
class taskState extends State<taskScreen> {
bool isButtonEnabled = false;
//Callback function i want to call in order to c... | 1,612 | 2,372 | 62 | 928 | 82 | 0.827561 | github_plus_top10pct_by_avg |
66] implied that there is no algorithm which decides whether copies of a given finite set of polyominoes tile $\mathbb{Z}^2$. It is unknown whether the same is true for tilings by a single polyomino. For tilings of $\mathbb{Z}$ by sets of general one-dimensional tiles, such an algorithm does exist, as demonstrated by A... | 1,613 | 282 | 2,166 | 1,472 | 1,994 | 0.783758 | github_plus_top10pct_by_avg |
N$.
Then $\mathcal K$ admits the skew field of fractions $F(\mathcal K)$ and $F(\mathcal K)\simeq F_{n,N-n}.$
Since the action of $\mathcal M$ is trivial on $L(t_{n+1}, \ldots, t_N)$ then we have the $G$-equivariant embedding $$(L(t_1, \ldots, t_n)*\mathcal M)\otimes L(t_{n+1}, \ldots, t_N) \hookrightarrow L*\mathcal... | 1,614 | 822 | 1,458 | 1,504 | null | null | github_plus_top10pct_by_avg |
C'\subset{\mathbb{R}}^3\backslash G$ implies that for all $n$ large enough, one has $x_n-\lambda \omega_n\in y_0+\lambda_0' C'\subset{\mathbb{R}}^3\backslash G$ for all $0<\lambda\leq \lambda_0'$, hence $t(x_n,\omega_n)\leq \lambda$, from which $\limsup_{n\to\infty} t(x_n,\omega_n)\leq \lambda$, and finally $\limsup_{n... | 1,615 | 1,697 | 1,683 | 1,564 | null | null | github_plus_top10pct_by_avg |
ad {\left|\psi_2\right>}={\left|x_1^4\right>}$\
$\lambda_{max}\simeq 7,40$
- Third orbit\
${\left|\varphi_3\right>}={\left|x_0^1\right>},\quad {\left|\psi_3\right>}={\left|x_1^8\right>}$\
$\lambda_{max}\simeq 6,63$
The maximal eigenvalue of $X$:\
$\lambda_{max}(X)\simeq 17,38$.\
The corresponding sums o... | 1,616 | 2,044 | 2,518 | 1,813 | 1,910 | 0.784466 | github_plus_top10pct_by_avg |
IIA/O6 result is concerned, our expression is valid for the specific orbifold model we are considering, but it would be interesting to investigate whether the same superpotential can be derived for more general orientifolds and whether it has a natural explanation in the context of generalised geometry.
We now want to... | 1,617 | 2,644 | 1,972 | 1,607 | 1,212 | 0.792642 | github_plus_top10pct_by_avg |
correction from the approximate form. Because the approximate form of the gluino-sbottom correction is equal to the terms in the exact form proportional to the $B_0$ Passarino-Veltman functions the discrepancy must be due to the terms in the exact form proportional to the $B_1$ Passarino-Veltman functions.
![We plot ... | 1,618 | 696 | 819 | 1,313 | 1,505 | 0.788776 | github_plus_top10pct_by_avg |
ULTS {#s:tests}
============
We implement our Poisson solver in [Athena++]{} which is a state-of-art astrophysical magnetohydrodynamics (MHD) code with very flexible coordinate and grid options. Using Cartesian and uniform/logarithmic cylindrical grids, we test our solver on a few test problems to check its accuracy, ... | 1,619 | 2,010 | 2,550 | 1,745 | 3,923 | 0.769283 | github_plus_top10pct_by_avg |
i-algebraic group.
Since $\iota(\PSL(2,\Bbb{C}))$ and $\PU(2,1)$ are simple Lie groups with trivial centers, we deduce that they are semi-algebraic groups (see [@semi]). Thus the sets $$\begin{array}{l}
\{(g,h,gh): g,h\in Aut(BV)\}\\
\{(g,g^{-1}): g\in Aut(BV)\}
\end{array}$$ are semi-algebraic sets. Therefore $Aut(BV... | 1,620 | 824 | 1,422 | 1,543 | null | null | github_plus_top10pct_by_avg |
We obtain: $$\begin{aligned}
\mbox{Term 3} &=& (-i) (-1)^{ea} {f^c}_{de} (
(c_3 \kappa^{ad} \frac{1}{(\bar z - \bar w})^2 j^e_z (w)
\nonumber \\
& &
+ {f^{ad}}_g (\frac{c_4}{\bar{z}-\bar{w}} :j^e_z j^g_{\bar z}: (w) +
\frac{(c_4-g)(z-w)}{(\bar z- \bar w)^2}
:j^e_z j^g_{z}: (w)
\nonumber \\
& & + \mbox{order zero... | 1,621 | 1,929 | 1,640 | 1,665 | null | null | github_plus_top10pct_by_avg |
_j^\top(\hat\psi - \psi) +
\frac{1}{2n}\delta^\top \Lambda_j \delta, \quad \forall j \in \{1, \ldots s\}$$ where $\delta = \sqrt{n}(\hat\psi - \psi)$ and $\Lambda_j = \int_0^1 H_j( (1-t)\psi + t \hat\psi) dt \in \mathbb{R}^{b \times b}$. Hence, $$\label{eq::taylor}
\sqrt{n}(\hat\theta - \theta) = \sqrt{n}(\hat\nu - \nu... | 1,622 | 2,035 | 1,156 | 1,541 | null | null | github_plus_top10pct_by_avg |
=========
In this appendix we gather various technical results related to the current algebra .
The current algebra at order $f^2$ {#jMCOPE}
----------------------------------
In [@Ashok:2009xx] the current algebra was computed at the order of the poles. The discussion of section \[bootstrap\] shows that we can comp... | 1,623 | 1,574 | 2,103 | 1,519 | 3,203 | 0.774067 | github_plus_top10pct_by_avg |
g or dwindling) by turning the two evidence sets as sliding windows and adopting certain update strategies such as *Least Recently Used*(LRU). Time complexity for this optimization is $O(n\cdot(|\mathbb{E}_N|+|\mathbb{E}_A|)\cdot T_D)$, where $T_D$ denotes time complexity of divergence calculation.
Threshold {#sec:alg... | 1,624 | 1,581 | 2,701 | 1,480 | null | null | github_plus_top10pct_by_avg |
ly that $$\begin{aligned}
\E{f(x_T - v_T) - f(x_T - y_T)} \leq 2TL\epsilon
\end{aligned}$$
\[l:non\_gaussian\_contraction\_anisotropic\] Let $f$ be as defined in Lemma \[l:fproperties\] with parameter $\epsilon$ satisfying $\epsilon\leq \frac{\Rq}{\aq\Rq^2 + 1}$. Let $x_t$, $v_t$ and $w_t$ be ... | 1,625 | 2,989 | 1,506 | 1,500 | null | null | github_plus_top10pct_by_avg |
$t \mapsto t^3$. $0 \in [-1,1]$ is the vertex of degree $2$. The other points are not in the vertex set. The map is regarded as a $D_2$-symmetric map onto $L_2$.\
\
Step 2 Around a vertex of degree $n \geq 3$.\
We consider a $C^{\infty}$ map on a $C^{\infty}$ manifold of dimension $m>1$ into the plane whose image is t... | 1,626 | 273 | 963 | 1,609 | 2,556 | 0.778885 | github_plus_top10pct_by_avg |
etting. By Jensen’s inequality, we have $$\begin{aligned}
\sum_{i = 2}^d \frac{1}{\lambda_i(L)} \geq \frac{(d-1)^2}{\sum_{i = 2}^d \lambda_i(L)} = \frac{(d-1)^2}{\Tr(L)} = \frac{(d-1)^2}{n}.\end{aligned}$$
### Proof of Lemma \[lem:cr\_lem\]
Define $\L_j(\theta)$ for $j \in [n]$ such that $\L(\theta) = \sum_{j = 1}^n ... | 1,627 | 1,396 | 1,601 | 1,517 | null | null | github_plus_top10pct_by_avg |
3}\pi^9 {\alpha '}^5} -n_{\rm short} \frac{\pi }{12} v(1 - v)~.
\label{vtotal2}$$ As above, $n_{\rm short}$ denotes the nine-dimensional bulk density of D-particles near the (moving) brane world.
As in the previous oversimplified example, the transition of the D8-brane world from a region densely populated with D-par... | 1,628 | 3,591 | 3,119 | 1,491 | null | null | github_plus_top10pct_by_avg |
use the same width was used for every target: $$TDI~ = ~{log}_{2}\left( {1 + D} \right),$$ where D is the target distance from the center in the GUI interface, and throughput was finally calculated by dividing completion time from TDI. Even though throughput contains the information of completion time, throughput and c... | 1,629 | 104 | 2,442 | 1,869 | null | null | github_plus_top10pct_by_avg |
(\chi ){\otimes }_{\Bbbk }{\mathbb{K}})v=M^\chi (\Lambda )$. Since $v$ is contained in any nonzero $U(\chi ){\otimes }_{\Bbbk }{\mathbb{K}}$-submodule of $M^\chi (\Lambda )$ by Thms. \[th:EErel\], \[th:PBWtau\], it follows that $I^\chi (\Lambda )=0$.
\[le:FFv\] Let $t\in \{1,2,\dots ,{b}-1\}$. Assume that $\Lambda (K_... | 1,630 | 1,598 | 1,511 | 1,532 | null | null | github_plus_top10pct_by_avg |
c spinor and its Dirac equation, describing massive spin 1/2 particles and antiparticles invariant under parity, which is to be discussed hereafter.
An Interlude on SU(2) Representations {#Sec3.2}
-------------------------------------
Let us pause for a moment to recall a few well known facts concerning SU(2) represe... | 1,631 | 4,439 | 1,269 | 1,233 | null | null | github_plus_top10pct_by_avg |
h_{i} )^2 }
e^{- i h_{k} x}
\nonumber \\
&-&
\frac{ 1 }{ ( \Delta_{K} - h_{i} )^3 ( h_{k} - h_{i} )^2 }
\left( \Delta_{K} + 2 h_{k} - 3 h_{i} \right)
e^{- i h_{i} x}
\biggr]
\nonumber \\
&\times&
\left\{ (UX)^{\dagger} A W \right\}_{i K}
\left\{ W ^{\dagger} A (UX) \right\}_{K k}
\left\{ (UX)^{\dagger} A W \rig... | 1,632 | 681 | 2,018 | 1,703 | null | null | github_plus_top10pct_by_avg |
een these scalars, coming from the fact that we are going to restrict our study to specific backgrounds, the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and the static spherically symmetric one, both in four dimensions.
For both of them, there are between the scalars relations coming from the Lovelock theorem (t... | 1,633 | 2,524 | 1,274 | 1,626 | null | null | github_plus_top10pct_by_avg |
f(y_t|y_{1:t-1},~s_{1:t})$ in as required; however, it is infeasible to track $\mathbb{P}\left({\mathbf{x}}_{1:t}|y_{1:t},s_{1:t}\right)$ as the dimension of the event space increases exponentially with time. Instead, combining , and gives the conditional mass function for the current firing vector given all previous f... | 1,634 | 1,223 | 2,196 | 1,650 | 4,014 | 0.768645 | github_plus_top10pct_by_avg |
e PNC will arise depending on the limit $\lim_{t\to 0}{{\mathscr C}}\circ\alpha(t)$, which we now determine.
\[quadconics\] If $C>\lambda_0$ and $B=\frac{C-\lambda_0}2+1$, then the limit $\lim_{t\to 0}{{\mathscr C}}\circ\alpha(t)$ consists of a union of quadritangent conics, with distinguished tangent equal to the ker... | 1,635 | 1,640 | 2,112 | 1,638 | null | null | github_plus_top10pct_by_avg |
ents ensures that the $\theta(a_{jm})\in {\mathcal{N}}^m$ are a free basis for the module they generate. The other conclusions of the lemma follow automatically from the construction of $\theta$.
{#step-1}
As happens with many questions about ${{W}}$-invariants, it is easy to prove that $\Theta$ is surjective on ${\... | 1,636 | 1,197 | 983 | 1,615 | null | null | github_plus_top10pct_by_avg |
i y_i\\ \pi v_i&1+\pi z_i \end{pmatrix}$ and $\tilde{m}_{i,i}$ as $\begin{pmatrix} \tilde{s}_i&\pi \tilde{y}_i\\ \pi \tilde{v}_i&1+\pi \tilde{z}_i \end{pmatrix}$ such that $\tilde{s}_i=\mathrm{id}$ mod $\pi \otimes 1$. Then $$\label{ea25'}
\sigma({}^t\tilde{m}_{i,i})h_i\tilde{m}_{i,i}=(-1)^{i/2}\begin{pmatrix}\sigm... | 1,637 | 1,297 | 1,774 | 1,567 | 3,456 | 0.772228 | github_plus_top10pct_by_avg |
adherent* *to* *$A$ is given by* *is the union* ***of $A$ with its boundary.*
*The* *interior of $A$* $$\textrm{Int}(A)\overset{\textrm{def}}=\{ x\in X\!:(\exists N\in\mathcal{N}_{x})\textrm{ }(N\subseteq A)\}\label{Eqn: Def: Interior}$$ *consisting of those points of $X$ that are in $A$ but not in its boundary,* $\te... | 1,638 | 2,669 | 1,907 | 1,569 | 2,107 | 0.782691 | github_plus_top10pct_by_avg |
_n$, given in , can be bounded, on an event of probability at least $1 - \frac{1}{n}$ and using again , by $$\label{eq:new.aleph}
C \frac{k^{5/2}}{u_n^3 u^2} \overline{v} \sqrt{ \frac{ \log n}{n}},$$ for each $P \in \mathcal{P}_n^{\mathrm{OLS}}$ and some $C>0$ dependent on $A$ only. (In light of the bounds derived ne... | 1,639 | 3,984 | 1,096 | 1,182 | null | null | github_plus_top10pct_by_avg |
psilon\Big)\to 0$$ as $K,m\to \infty$. It remains to consider $$\label{eqA2}
(Km)^{-1} \sum_{k=1}^K\Big(\sum_{i=1}^m \eta_{kij}\Big)\Big(\sum_{i=1}^m \eta_{kil}\Big)=(Km)^{-1} \sum_{k=1}^K\sum_{i=1}^m \eta_{kij}\eta_{kil}+(Km)^{-1} \sum_{k=1}^K\sum_{1\leq i_1\not=i_2\leq m}\eta_{ki_1j}\eta_{ki_2l}.$$ The second sum on ... | 1,640 | 1,561 | 1,830 | 1,674 | null | null | github_plus_top10pct_by_avg |
-547ins+275 *MX1* Interferon-induced GTP metabolizing enzyme, antiviral properties Indel 275 bp Promoter SSC13 \[[@B12-viruses-11-00706]\]
-1533G\>A *USP18* Ubiquitin-specific proteases, Downregulation of interfer... | 1,641 | 5,569 | 1,266 | 551 | null | null | github_plus_top10pct_by_avg |
linewidth=1pt, linestyle=dashed,dash=4pt 3pt](0.1,0)(0.1,0.4)
\end{pspicture}})=k$.
Graphically, we represent $\mathcal P(x_1,\dots,x_n;x)$ by a tree with $n$ inputs and one output of the given color. Since the color $\varnothing$ cannot appear as an input, we may use the following convention: we represent the output... | 1,642 | 469 | 1,896 | 1,836 | 672 | 0.802639 | github_plus_top10pct_by_avg |
tars can populate (again assuming solar metallicity.) For maximum effective temperatures of $^{MS}=50,000$ K, $^{WN}=120,000$ K, and $^{WC}=150,000$ K, for [@pauldrach01] model O stars and @hillmill WR stars, we find the following:
- Main sequence O stars can only produce $[{\hbox{{\rm Ar}\kern 0.1em{\sc iii}}}]/[{\... | 1,643 | 2,206 | 2,750 | 1,938 | null | null | github_plus_top10pct_by_avg |
C}}$ are tangent to the line $y=0$, leaving to the reader the necessary adjustments in the presence of such branches. We write the generator $F$ for the ideal of ${{\mathscr C}}$ as a product of formal branches $F =\prod_{i=1}^m (z-f_i(y))$. We will focus on the formal branches that are tangent to the line $z=0$, whic... | 1,644 | 1,268 | 1,251 | 1,470 | 3,072 | 0.775028 | github_plus_top10pct_by_avg |
e downsampled sinogram with $140$ rays and 15 projections from $360^\circ$ angle of view. In the computations, the size of the target is set to $120 \times 120$.
Figure \[CheeseRec\](c) shows the GP reconstruction (Matérn covariance function) of the cross section of the carved cheese slice using 15 projections (unifor... | 1,645 | 80 | 1,805 | 1,856 | 1,082 | 0.794633 | github_plus_top10pct_by_avg |
farming behaviours: Centralized and Equalized. Centralized click farming refers to the scenarios that transactions are randomly generated throughout the day. A significant feature of this approach is that the cheating transactions usually assemble together in a short period of time since most workers work at the same ... | 1,646 | 3,189 | 1,706 | 1,601 | null | null | github_plus_top10pct_by_avg |
heorem \[t1\] we are therefore motivated to look closer at the following problem.
\[central\] Let $h$ be a polynomial of degree $d$ which is hyperbolic with respect to ${\mathbf{e}}$, and let $\epsilon >0$ and $m \in {\mathbb{Z}}_+$ be given. Determine the largest possible maximal zero, $\rho=\rho(h,{\mathbf{e}},\epsi... | 1,647 | 934 | 2,126 | 1,448 | null | null | github_plus_top10pct_by_avg |
{and}\ t\in F^{n-s}R,$ as required.
\(2) Here, $rF^{n}I \subseteq F^n(rI)$ whence $rF^{n}I = r^2F^{n}I \subseteq rF^n(rI)
\subseteq rF^nI$. Since $rF^n(rI) = F^n(rI) $ this implies that $rF^n(I)=F^n(rI)$.
[**Example**]{}. It is easy to check that some hypotheses are required for the lemma to hold. For example, filte... | 1,648 | 1,114 | 1,412 | 1,557 | 2,818 | 0.776773 | github_plus_top10pct_by_avg |
^d, \|v\|_2 =1} \lrn{Gv}_2.
$.
Finally, we define a few useful constants which will be used throughout the paper: $$\begin{aligned}
&\LN := \frac{4\beta L_\xi}{\cm}, \ \ \aq:=\frac{\LR+L_N^2}{2\cm^2}, \\ &\Rq:=\max\lrbb{R,{\frac{16\beta^2 L_N}{m\cdot \cm}}} \\
&\lambda :=\min\lrbb{\f... | 1,649 | 954 | 1,455 | 1,574 | null | null | github_plus_top10pct_by_avg |
(\nu_\beta \rightarrow \nu_\alpha) &=&
\mathcal{C}_{\alpha \beta} +
\left| \sum_{j=1}^{3} U_{\alpha j} U^{*}_{\beta j} \right|^2
\nonumber\\
&-&
2 \sum_{j \neq k}
\mbox{Re}
\left[ (UX)_{\alpha j} (UX)_{\beta j}^* (UX)_{\alpha k}^* (UX)_{\beta k} \right]
\sin^2 \frac{ ( h_{k} - h_{j} ) x }{ 2 }
\nonumber\\
&-&
\s... | 1,650 | 2,025 | 2,316 | 1,800 | null | null | github_plus_top10pct_by_avg |
irst attempt to control the value of that plateau the initiator approximation has been implemented for walkers that belong to replica 1. We allow the initiator threshold to be different in replica 0 and replica 1. As an illustration we studied the carbon dimer molecule with the cc-pVQZ basis set[@jr_gaussian_1989], wit... | 1,651 | 1,284 | 964 | 1,324 | null | null | github_plus_top10pct_by_avg |
v_{\eta'} v_{\eta'}^T}}}
\end{aligned}$$
For any fixed $\eta$ and $\eta'$, let’s further simplify notation by letting $u,u',v,v'$ denote $u_\eta, u_{\eta'}, v_\eta, v_{\eta'}$. Thus $$\begin{aligned}
&\tr\lrp{\lrp{uu^T - vv^T} \lrp{u'u'^T - v'v'^T}}\\
=& \tr\lrp{ \lrp{(u-v)v^T + v(... | 1,652 | 2,943 | 1,555 | 1,529 | null | null | github_plus_top10pct_by_avg |
------------------------------------------------------------------------- --
Using strong and weak LO contact interactions and two baryonic propagators one can also build three diagrams that enter at NLO. These caramel-like diagrams are shown in Fig. \[fig:caramels\]. They only differ in the position of the strong and... | 1,653 | 492 | 2,238 | 1,709 | 2,113 | 0.78264 | github_plus_top10pct_by_avg |
erms are for $J'\leqslant K \leqslant S_{J}$ and since $|S_{J}|/|J'|=p$ either $K=J'$ or $K=S_{J}$. If $K=S_{J}$, then $O^{p}(K)=J'$ is $H$-conjugate to $O^{p}(S_{J})=J$, that is $J'$ is $H$-conjugate to $J$. If $K=J'$ and $J\neq J'$, then there we have the following situation: $$\xymatrix{
& S_{J} &\\
J\ar@{=}[ur]^{p}... | 1,654 | 1,167 | 1,422 | 1,467 | null | null | github_plus_top10pct_by_avg |
some”.
Suppose that $t-1$ is injective. Note that the injectivity of $t-1$ is equivalent to $\p_*:H_2(M)\to H_1(M_\infty)$ being the zero map. Then, for [**any**]{} $[V_y]$ as above, $\p_*([V_y])=0$. But we claim that $\p_*([V_y])$ is represented by $[\tl c(x,y)]$, since $V_x$ is Poincaré Dual to the class $x$ defini... | 1,655 | 524 | 1,462 | 1,720 | 2,654 | 0.778107 | github_plus_top10pct_by_avg |
ith entries in $B\otimes_AR$. Here, $\dag$ is a polynomial of $m_{i-1,i-1}', m_{i-1,i}', m_{i,i-1}', m_{i,i}', m_{i,i+1}', m_{i+1,i}', m_{i+1,i+1}'$. Thus $$\label{ea3'}
(f_{i, i}^{\ast})'=\pi\left((m_{i,i}^{\ast})'-(m_{i,i}^{\ast\ast})'h_i+\dag\right).$$ Since this is an equation in $B\otimes_AR$, it is of the form $X... | 1,656 | 560 | 1,173 | 1,688 | 2,706 | 0.777712 | github_plus_top10pct_by_avg |
\,c\ .$$
The chiral point
================
Asymptotic behavior
-------------------
Hereafter we only consider $\mu l=1$, since the case of $\mu l=-1$ just corresponds to the interchange $x^{+}\longleftrightarrow x^{-}$.
In the case of $\mu l=1$, the appropriate asymptotic behavior for $\Delta
g_{\mu\nu}$ reads $$%... | 1,657 | 744 | 1,294 | 1,715 | null | null | github_plus_top10pct_by_avg |
a}_j = \sqrt{ \hat{\Gamma}_{j,j}}$ and $\hat{t}_j = z_{\alpha/(2s)} \hat{\gamma}_j$ We use the same arguments and notation as in the proofs of and . Thus, let $\mathcal{E}_n$ be the event that $ \frac{\overline{H} ||\delta||^2}{2\sqrt{n}} < \epsilon_n$, where $\frac{\overline{H} ||\delta||^2}{2\sqrt{n}}$ is an upper bo... | 1,658 | 3,671 | 1,343 | 1,382 | null | null | github_plus_top10pct_by_avg |
e because the two set-theoretic defining requirements of $fGf=f$ and $GfG=G$ for the generalized inverse are satisfied, as Fig. \[Fig: GenInv\] shows, in the following forms $$jf_{\textrm{B}}Gf=f\qquad Gjf_{\textrm{B}}G=G.$$ In fact the commutativity embodied in these equalities is self evident from the fact that $e=if... | 1,659 | 4,505 | 2,764 | 1,643 | 1,713 | 0.786503 | github_plus_top10pct_by_avg |
abel{eigval+}
\begin{aligned}
\mu_{+}^{(n,m)} & =
\hbar\nu\left(n+\frac{m}{2}\right)-
\frac{\hbar}{2}\sqrt{\omega_{L}^{2}+
\Omega^{2}\left|f_n^m\right|^{2}}, \\
\gamma_{+}^{(n,m)} & = \hbar\nu\left(n+\frac{m}{2}\right)+
\frac{\hbar}{2}\sqrt{\omega_{L}^{2}+\Omega^{2}\left|f_n^m\right|^{2}},
\end{aligned}$$ respectivel... | 1,660 | 2,051 | 2,080 | 1,684 | null | null | github_plus_top10pct_by_avg |
^\dag
L_q)=1$. Then we obtain that the probability is $$p_q = \left[ {\mathrm{tr}}_B \left( (L^\dag L)^{-1} \right) \right]^{-1}.
\label{eq:p_q2}$$
For an arbitrary entangled shared pair described by invertible $L$, the set of measurement outcomes providing fidelity 1 conditional teleportation is given by the set $${\... | 1,661 | 4,443 | 801 | 1,091 | 2,146 | 0.782285 | github_plus_top10pct_by_avg |
ong\_T\] for two different temperatures.
![Variation of the transverse part of the second-order QNS scaled with that of free field value in presence of strong magnetic field with temperature (left panel) and magnetic field (right panel) strength for $N_f=3$.[]{data-label="QNS_sfa_trans_T"}](chi2_sfa_trans.pdf "fig:") ... | 1,662 | 1,342 | 362 | 1,442 | 3,201 | 0.774078 | github_plus_top10pct_by_avg |
}} & := & \{(\varepsilon,\varepsilon), (r_{12},r_{12}), (r_{13},r_{13}),(r_{12}r_{14},r_{12}r_{14}), (r_{13}r_{14},r_{13}r_{14})\}).\end{aligned}$$ One can check that ${\rm Id_{C,1}}$ is a prefix of the strategy, for the game with initial position $(C,C)$, $${\rm Id}_{C,\infty}:=\{(u,u) \mid u \in {\cal R}^*, C(L_1) {\... | 1,663 | 912 | 2,100 | 1,669 | 3,192 | 0.774128 | github_plus_top10pct_by_avg |
t $x_0$ be a basepoint in $X$ and $y_0 = f(x_0)$ be a basepoint in $Y$. Because $g\circ f$ is close to ${\text{id}}_X$, we can say that there is a $D$ such that ${\text{d}}(x,g\circ f(x))\leq D$ for all $x \in X$. Let $K$ be the integer provided by $X$ being $\sigma$-stable and $K'$ be the integer provided by $Y$ being... | 1,664 | 3,179 | 2,292 | 1,624 | 2,841 | 0.776626 | github_plus_top10pct_by_avg |
al{R}_s$, we change the coordinates such that $x_0$ is the origin and regard $\mathbb{R}^d$ as $s^\perp \bigotimes s$, where $s^\perp$ is the orthogonal space of $s$. Suppose that $s^\perp$ is $d_1$-dimensional. Then, under this new coordinate system and for $y\in \mathcal{R}_s$, we have Hence $D^2 \varphi(y)$ is a dia... | 1,665 | 2,565 | 1,771 | 1,649 | null | null | github_plus_top10pct_by_avg |
raints\] for a possible application of $c_1^{\rm rep}$).
For any stack $\mathfrak{X}$, let $V$ be a vector bundle over $\mathfrak{X}$, and $I_{\mathfrak{X}}$ the inertia stack of $\mathfrak{X}$. Let $q: I_{\mathfrak{X}} \rightarrow \mathfrak{X}$ denote the natural projection operator onto one component.
We define Che... | 1,666 | 1,213 | 2,028 | 1,611 | 1,539 | 0.788516 | github_plus_top10pct_by_avg |
)\Xi\Psi)\,.\end{aligned}$$ Using the fact that ${\mathcal{S}}$ is BPZ odd, $$\langle {\mathcal{S}}A, B\rangle\ =\ -\langle A, {\mathcal{S}}B\rangle\,,
\label{BPZ S}$$ it is easy to see that the quadratic terms of the action (\[complete action\]), $$S^{(0)}\ =\ - \frac{1}{2} \langle\Phi, Q\eta\Phi\rangle
- \frac{1}{2} ... | 1,667 | 1,348 | 2,027 | 1,576 | null | null | github_plus_top10pct_by_avg |
{f\rho}_\ell k dk/2\pi$ (which is restricted to its upper, or lower depending on one’s convention, triangular entries by the limits of integration), treating $\Delta$ as a free parameter or ignoring it altogether.
Instead of doing so, we will rewrite eq. (\[split\]) into a form that is closer to the original analysis ... | 1,668 | 2,919 | 2,287 | 1,675 | 1,681 | 0.786837 | github_plus_top10pct_by_avg |
e coupling variation in the channel $c$ amounts then to replacing in this expression $T_c$ with $T_c^{\mathrm{eff}}$. This suggests the following heuristic formula for the coupling fidelity $$\label{eq:app2}
F_{\mathrm{surm}}(t) = \left[\frac{(1+2T_c t/\beta)(1+2T'_c t/\beta) }{
|1+2T^{\rm eff... | 1,669 | 604 | 1,772 | 1,659 | null | null | github_plus_top10pct_by_avg |
ete gamma functions, respectively, defined by $$\begin{aligned}
\G(a, x) := \int_{x}^{+\infty} t^{a - 1} e^{-t} dt, \qquad
\g(a, x) := \int_{0}^{x} t^{a - 1} e^{-t} dt, \end{aligned}$$ where $\text{Re}(a) > 0$ and $x \geq 0$. These functions have the following properties:
\[lem:3.0\] For ${\rm Re}(a) > 0$ and $x \geq... | 1,670 | 4,091 | 1,999 | 1,390 | null | null | github_plus_top10pct_by_avg |
eq p, \;\Omega^{-1}(\i) \geq p \big\} \label{eq:cr83} \\
-B_2 & \;\; \text{if} \; i \neq \i, \; \big\{\Omega^{-1}(i) \geq p, \; \Omega^{-1}(\i) < p \big\} \label{eq:cr84} \\
-B_2 & \;\; \text{if} \; i \neq \i, \; \big\{\Omega^{-1}(i) < p, \; \Omega^{-1}(\i) \geq p\big\} \label{eq:cr85} \\
-(B_3 + B_4 - A_3^2) & \;... | 1,671 | 1,306 | 1,876 | 1,679 | null | null | github_plus_top10pct_by_avg |
a (4 years, inclusive). Incidences include 95% CI
Junior Senior Combined
----------------------------- --------------------- ------------------------- ---------------------
Permanent (ND+Quad.+Fatal) 0.24 (0 to 0.65) **4.52 (0.74 to 8.30)** ... | 1,672 | 3,268 | 1,696 | 1,718 | null | null | github_plus_top10pct_by_avg |
e invariant subspaces in $\Bbb{P}^2_\Bbb{C}$.
Let us assume that there is a complex line $\ell$ invariant under $\iota(\Gamma)$. By Bézout’s theorem $Ver\cap \ell$ has either one or two points. From the following commutative diagram $$\xymatrix{
\Bbb{P}_\Bbb{C}^1 \ar[r]^{ \tau}\ar[d]^\psi & \Bbb{P}_\Bbb{C}^1 \... | 1,673 | 1,192 | 790 | 1,756 | null | null | github_plus_top10pct_by_avg |
j})}\prod_j p_{ij}^{\alpha_{ij} - 1} d\theta_k\\
\nonumber &=& p(x_1)\prod_i\frac{\Gamma(\sum_j \alpha_{ij})}{\prod_j \Gamma(\alpha_{ij})} \int \prod_j p_{ij}^{n_{ij}} \prod_j p_{ij}^{\alpha_{ij} - 1} d\theta_k\\
\nonumber &=& p(x_1)\prod_i\frac{\Gamma(\sum_j \alpha_{ij})}{\prod_j \Gamma(\alpha_{ij})} \int \prod_j p_... | 1,674 | 4,019 | 2,255 | 1,540 | null | null | github_plus_top10pct_by_avg |
is conjugate to a subgroup of $Mob(\hat{\Bbb{R}})$, therefore $ \Lambda_{Gr}\iota^{-1}Aut(BV)$ is a circle in the Riemann sphere and $\Lambda_{Gr}\iota^{-1}Aut(BV) = \psi^{-1}C$.\
In order to prove part (\[l:6\]), observe that after a projective change of coordinates we can assume that $\psi^{-1}C=\hat{\Bbb{R}}$. Thus ... | 1,675 | 2,692 | 2,421 | 1,549 | 4,074 | 0.768254 | github_plus_top10pct_by_avg |
\leq e^{(1-\alpha-\beta)\beta^{-1}\tau}\left( {\| e^{d\tau}{\nabla}{\mathcal{K}}(e^{\tau}\cdot)\mathbf{1}_{B_1(0)} \ast \theta\|}_q + {\| e^{d\tau}{\nabla}{\mathcal{K}}(e^{\tau}\cdot)\mathbf{1}_{{\mathbb R}^d \setminus B_1(0)} \ast \theta\|}_q \right) \\
& \leq e^{(1-\alpha-\beta)\beta^{-1}\tau}\left( {\|e^{d\tau}{\n... | 1,676 | 557 | 595 | 1,808 | null | null | github_plus_top10pct_by_avg |
$(f,\Xi_M,\kappa) \in Imm^{sf}(n-k,k)$ be an arbitrary element, where $f: M^{n-k} \looparrowright \R^n$ is an immersion of codimension $k$ with the characteristic class $\kappa \in H^1(M^{n-k};\Z/2)$ of the skew-framing $\Xi_M$. We say that the pair $(M^{n-k},\kappa)$ admits a retraction of order $q$, if the mapping $\... | 1,677 | 662 | 366 | 1,781 | 3,432 | 0.77243 | github_plus_top10pct_by_avg |
=\bigcup_u\big\{\{y{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}}
{\overset{}{\longleftrightarrow}}}u\}\circ I_1(u,z',x)\big\},
{\label{eq:I12-def}}\\
I_3(y,z,z',x)=\bigcup_u\Big\{\{I_2(y,z,u)\circ I_2(u,z',x)\}\cup\big\{
\{y{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}}
{\overset{}{\longl... | 1,678 | 811 | 1,502 | 1,714 | null | null | github_plus_top10pct_by_avg |
W\^[,(AB)]{}= to distinguish it from
W\^[,AB]{}= The 2PI CTP EA is the full Legendre transform
=W-J\_A\^A-12K\_[AB]{}Therefore the mean field equations of motion are
\_[,A]{}=-J\_A-K\_[AB]{}\^B
\_[,(AB)]{}=-12K\_[AB]{}
One further variation yields the identities
\^[C,E]{}+\_[,A(CD)]{}G\^[CD,E]{}=-\_[A]{}\^E
\^[C... | 1,679 | 3,739 | 3,079 | 1,317 | null | null | github_plus_top10pct_by_avg |
/v) \;.$$
If we replace $v'$ by adding to it an integer multiple of $v$, then ${\operatorname{sk}}(v,v')$ changes by $${\operatorname{sk}}(v,v'+nv) = {\operatorname{sk}}(v,v') + n \;.$$ In particular, since $v'$ is unique up to addition of an integer multiple of $v$, looking at the fractional part, that is in $\R/\Z... | 1,680 | 3,402 | 2,084 | 1,621 | 2,729 | 0.777455 | github_plus_top10pct_by_avg |
the dependence on the topology of the data, and $C_b'$ and $C_b$ are constants that only depend on $b$. Putting these together, we will show that there exists a $\theta\in\Omega_b$ such that $$\begin{aligned}
\|\widehat\theta -\theta^* \|_2 &\leq& \frac{2\|\nabla \cL_{\rm RB}(\theta^*)\|_2 }{-\lambda_2(H(\theta))}... | 1,681 | 1,579 | 1,806 | 1,563 | 3,035 | 0.775313 | github_plus_top10pct_by_avg |
frac{1}{2}u_iu_i -\frac{\lambda^2}{2}W_{ij}W_{ij}\right) = -\left(\frac{1}{2}|\MM{u}|^2 -\frac{\lambda^2}{2}|W|^2\right).$$
One-form quasi-conservation law
-------------------------------
For our multisymplectic formulation of EPDiff($H^1$), the independent variables are $$q^j = x_j, \quad j=1,\ldots n, \qquad q^{n+1... | 1,682 | 1,357 | 2,319 | 1,632 | 4,052 | 0.768438 | github_plus_top10pct_by_avg |
ration.
**AND nodes:** Each part template is an AND node, which uses its children (latent patterns) to represent its constituent or contextual regions. We use $v$ and $Child(v)=\{u_{1},u_{2},\ldots,u_{m}\}$ to denote the part template and its children latent patterns. We learn the average displacement from $\Lambda_{u... | 1,683 | 1,272 | 2,344 | 1,839 | 582 | 0.805145 | github_plus_top10pct_by_avg |
isor-Ck}
{\left \lfloor \pi_{*} D' \right \rfloor} = {\left \lfloor \pi_{*}(K_Y-L^{(k)}) \right \rfloor} = K_X + k H
- \sum_{j=1}^r {\left \lfloor \frac{k n_j}{d} \right \rfloor} \mathcal{C}_j,$$ which has $w$-degree $$\label{eq:degree-sk}
k - |w| - \sum_{j=1}^r {\left \lfloor \frac{kn_j}{d} \right \rfloor} d_j = \sum_... | 1,684 | 1,134 | 899 | 1,559 | null | null | github_plus_top10pct_by_avg |
Meropenem 8 (6) 1--10
Ampicillin-sulbactam 6 (4) 1--37
Ceftazidime 6 (4) 1--9
Ampicillin 4 (3) 2--7
Azithromycin 4 (3) 1--6
Fluconazole 4 (3) ... | 1,685 | 4,577 | 862 | 1,014 | null | null | github_plus_top10pct_by_avg |
K)$, the group $L$ canot be equal to $K$. So $G/K f_{J}^{G}$ is a $R$-linear combination of transitive $G$-set $G/L'$ where $|L'|<|K|$. By induction, $G/K$ is a $R$-linear combination of elements of the form $G/I f_{J}^{G}$.
Following [@deiml], let us consider the linear form $\phi_{G}$ on $RB(G)$ defined on a basis e... | 1,686 | 1,725 | 1,761 | 1,457 | null | null | github_plus_top10pct_by_avg |
V}}$. Then, we compare the obtained ${\widehat{\widetilde{\mathbf{H}}}_{\psi,V}}$ among all reconfiguration states to complete the selection of optimal ${\widetilde{\mathbf{H}}_{\psi,V}}$, denoted by ${\widehat{\widetilde{\mathbf{H}}}_{\widehat{\psi},V}}$. Since there are $\Psi$ reconfiguration states and $\binom{N_t}{... | 1,687 | 1,468 | 1,817 | 1,647 | 1,764 | 0.785887 | github_plus_top10pct_by_avg |
M_N}
\label{eq:vnlo}
+ \,C_1^1 \; \displaystyle\frac{{\vec \sigma}_2{\vec q}}{2 M_N}
+ {\im} \, C_1^2 \; \displaystyle
\frac{({\vec \sigma}_1 \times {\vec\sigma}_2)\;{\vec q}}{2 M_N}
\\
&+ C_2^0 \; \displaystyle\frac{{\vec \sigma}_1{\vec q}
\;{\vec\sigma}_2{\vec q}}{4 M_N^2}+
C_2^1 \; \displaystyle\frac{{\vec \sigma}... | 1,688 | 359 | 936 | 1,956 | null | null | github_plus_top10pct_by_avg |
le cell. Even if both inputs are ‘1’ the Physarum cells have no space to avoid collision and therefore the merge and propagate into the output channel.
The gate [and]{} looks like distorted ‘H’: $
\begin{smallmatrix}
& & \, & \downarrow & & \downarrow\\ \hline
\downarrow & & \, & & ... | 1,689 | 3,453 | 2,493 | 1,702 | null | null | github_plus_top10pct_by_avg |
such ethical approval is not mandatory for experimental studies that do not involve any risk or discomfort for the participants as long as anonymity is preserved (Spanish Law 15/1999 for Personal Data Protection) and participants are fully informed about the procedures of the study and give written informed consent to ... | 1,690 | 314 | 1,820 | 1,695 | null | null | github_plus_top10pct_by_avg |
unction doSomething(macguffin: any) {
//todo: implement doSomething
}
}
export class MyCollection {
public static doSomething(macguffin: any) {
//todo: implement doSomething
}
}
A:
It's probably best to use modules instead of namespaces or static class methods. From the TypeScript officia... | 1,691 | 2,315 | 1,479 | 1,165 | 1,219 | 0.792505 | github_plus_top10pct_by_avg |
le unitarity violation poses highly nontrivial features such as non-Hermitian Hamiltonian [@Antusch:2006vwa], or the evolution equation $i \frac{d}{dx} \nu_{\alpha} = \sum_{j} \left[ U \left( {\bf \Delta_{a} } + U^{\dagger} A U \right) U^{\dagger} \right]_{\alpha \beta} \nu_{\beta}$ [@Escrihuela:2016ube]. The latter is... | 1,692 | 875 | 2,371 | 1,763 | null | null | github_plus_top10pct_by_avg |
sider $D_1, D_2 \in \operatorname{Weil}_\QQ(X)$. The *intersection number* $(D_1 \cdot D_2)_X$ is defined as $$(D_1 \cdot D_2)_X :=
\frac{1}{k_1 k_2} (k_1 D_1 \cdot k_2 D_2 )_X \in \QQ,$$ where $k_1, k_2 \in \ZZ$ are chosen so that $k_1 D_1\in \text{Weil}(X)$, $k_2 D_2\in \text{Cart}(X)$ and either the divisor $D_1$ i... | 1,693 | 1,769 | 1,674 | 1,513 | 2,607 | 0.778487 | github_plus_top10pct_by_avg |
==
In this section we show an upper bound for maximum load attained by the balanced allocation on [regular]{} dynamic graphs (i.e., Theorem \[thm:s2c\]). Suppose that the balanced allocation process has allocated $n$ balls to the dynamic regular graph $(G^{(1)},\ldots, G^{(n)})$. Define the *conflict graph* ${\mathcal... | 1,694 | 216 | 854 | 1,779 | 1,737 | 0.786219 | github_plus_top10pct_by_avg |
l area and volume. The Bayesian linear results show notable bias in $N$, $\mathit{BA}$, and $V$.
{width="\textwidth"}
The CI coverages of GPR and the reference Bayesian inference method are compared in Figure \[fig:ci\]. The numerical CI% value is shown above each bar; the ideal value is here ... | 1,695 | 204 | 3,373 | 1,698 | null | null | github_plus_top10pct_by_avg |
{R}}%
^{d})\}.$$Then $\overline{\pi }_{k,q,h,p}$ is equivalent with the interpolation norm of order $\rho =\frac{k+q+d/p_{\ast }}{2h}$ between the spaces $W_{\ast
}^{k,\infty }$ (the dual of $W^{k,\infty })$ and $W^{2h+q,2h,p}=\{f:$ $%
\left\Vert f_{n}\right\Vert _{2h+q,2h,p}<\infty \}$. This is proved in [\[BC\]]{}, s... | 1,696 | 1,078 | 852 | 1,668 | null | null | github_plus_top10pct_by_avg |
odate, for example, the following term. $$\begin{aligned}
&&\langle \pi|N^*(t_{\rm snk})|N\rangle
\langle N| \bar N^*(t_{\rm src})|\pi\rangle \nonumber \\
&\times&e^{-E_N(t_{\rm snk}-t_{\rm src})}\times
e^{-E_\pi (N_t-t_{\rm snk}+t_{\rm src})}.\end{aligned}$$ Here, $N_t$ denotes the temporal extent of a lattice. Such a... | 1,697 | 697 | 1,826 | 1,696 | 1,403 | 0.790034 | github_plus_top10pct_by_avg |
ces {#sec:RR}
----------------------------------------
For a given $X$ a normal projective surface and $D\in \operatorname{Weil}(X)$, the following formula is a generalization of the classical Riemann-Roch formula from the smooth case.
\[thm:RR\] There is a rational map $R_{X,P}:\operatorname{Weil}(X,P)/\operatorname... | 1,698 | 1,308 | 1,707 | 1,618 | null | null | github_plus_top10pct_by_avg |
tional problem (\[vareqcoad\]) and vice versa.
The method founded on the $m$-dissipativity (see sections \[m-d\] and \[mdiss-op\]) can be applied also to the adjoint problem. Define $$P_{1}^*(x,\omega,E,D)\psi_1^*:={}&-\omega\cdot\nabla_x\psi_1^*, \\[2mm]
P_{j}^*(x,\omega,E,D)\psi_j^*:={}&S_j{{\frac{\partial \psi_j^*}... | 1,699 | 570 | 1,048 | 1,716 | null | null | github_plus_top10pct_by_avg |
pha\beta}W_{\mu\sigma\rho\beta}W_{\;\;\;\nu\alpha}^{\sigma\;\,\;\,\,\;\rho}\end{aligned}$$ are the two independent cubic contractions of the Weyl tensor in four dimensions.
From the relations of Ref [@25], we have found the following geometrical identities : $$\begin{aligned}
L_{\mu\nu}R^{\mu\nu}=-(2 \mathcal{L}_3 + \... | 1,700 | 1,303 | 1,931 | 1,566 | 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.