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 |
|---|---|---|---|---|---|---|---|
ference operators $D_\alpha$ corresponds to multiplication by $\left(e^{-\alpha} - 1 \right)$. Therefore, the left-hand side of is identified with $\left( \prod_{\alpha \in R_{G,+}} - D_\alpha \right) m_{T_G,V_{G,\lambda}}$.
Now consider the right-hand side of . Since $\lambda + \rho$ is a strictly dominant weight, it... | 2,401 | 1,724 | 1,398 | 2,243 | null | null | github_plus_top10pct_by_avg |
i) \in {\prod{\Phi}}$. Hence ${\mathbf{f}}\,' = (\psi', \phi') \in {\prod{\Psi}} \times {\prod{\Phi}}$, and ${\mathbf{f}}\,'$ is a frame.
Finally, definition \[D:ITERATIVE\_TRANSFORM\] calls for the succeeding locus as $\lambda' = \Delta(\lambda, \psi)$. Definition \[D:JUMP\_FUNCTION\] specifies the jump function as a... | 2,402 | 2,304 | 2,906 | 2,211 | null | null | github_plus_top10pct_by_avg |
o masses are naturally explained without assuming the triplet fields to be heavy. The Yukawa sector is then the same as the one in the HTM, so that its predictions for the LFV processes are not changed. See Refs. [@Babu:2001ex; @Chun:2003ej] for some discussions about two-loop realization of the $\mu$-term[^1].
This p... | 2,403 | 1,445 | 2,876 | 2,423 | 2,795 | 0.776917 | github_plus_top10pct_by_avg |
insists that this total reshuffling of physical interpretation should leave the basic mathematical building blocks (a certain generating set of algebras and the symmetry group structure) untouched, then there is only one answer: an associated anti De Sitter (AdS) theory [@Wit]. The nontrivial reprocessing leads to a m... | 2,404 | 839 | 2,667 | 2,179 | null | null | github_plus_top10pct_by_avg |
elta\E}$ at the next enstrophy level for some sufficiently small $\Delta\E > 0$. As will be demonstrated in §\[sec:3D\_InstOpt\_E0to0\], in the limit $\E_0 \rightarrow 0$ optimization problem \[pb:maxdEdt\_E\] admits a discrete family of closed-form solutions and each of these vortex states is the limiting (initial) me... | 2,405 | 444 | 1,692 | 2,505 | null | null | github_plus_top10pct_by_avg |
al correlations and fluctuation scaling, let us repeat here Eqs. and : $$\begin{aligned}
\alpha(\Delta t)=\alpha_0^\pm + \gamma^\pm \log \Delta t, \nonumber \\
H_i=H_0^\pm + \gamma^\pm \log \ev{f_i}. \nonumber\end{aligned}$$ Beyond the obvious symmetry of these two logarithmic laws, notice that the prefactors a... | 2,406 | 836 | 2,670 | 2,239 | null | null | github_plus_top10pct_by_avg |
\right\vert},
\end{aligned}$$ so by and , $$\mu^{(n)} (f) \to \bigl[(1-p) \gamma_{\mathbb{C}}+ p \gamma_\alpha\bigr](f)$$ in $L^2$, and hence in probability.
The proof is analogous to that of Theorem \[T:circular-law-correlated\], setting $\alpha = 0$. In that case $\operatorname{Cov}(\lambda_\chi)$ no longer depen... | 2,407 | 4,221 | 2,264 | 1,743 | null | null | github_plus_top10pct_by_avg |
and post-quench Hamiltonians are different in the limit $\eta\to 0$, only when $m=0$. The process becomes then reversible in such a limit, provided $m\neq 0$. Now, we investigate the role of the classical Rabi frequency $\Omega$ on the irreversibility. The result is depicted in Fig. \[fig2L2\], where one can see that ... | 2,408 | 2,045 | 3,278 | 2,333 | null | null | github_plus_top10pct_by_avg |
\lambda_q)) \: = \: {\rm ch}(d( \sum_i (-)^i \wedge^i N^*)
\: = \: (1, \vec{0}, 0; 4, \cdots, 4).$$ In addition, $${\rm ch}^{\rm rep}({\rm Td}(TI_{\mathfrak{X}})) \: = \:
(1, \vec{0}, 0; 1, \cdots, 1),$$ hence $${\rm Td}(\mathfrak{X}) \: = \:
\alpha_{\mathfrak{X}}^{-1} {\rm Td}(T I_{\mathfrak{X}})
\: = \:
(1, \vec{0},... | 2,409 | 2,771 | 2,460 | 2,174 | null | null | github_plus_top10pct_by_avg |
.
Let $\Sigma$ and $\Delta$ be two alphabets, and let ${c:\Sigma\times\Sigma^{\leq{n}}\rightarrow\Delta^{+}}$ be a function. If $C_{{\sigma_{1}\sigma_{2}\ldots\sigma_{h}}}$ is a prefix code, for all ${\sigma_{1}\sigma_{2}\ldots\sigma_{h}}\in\Sigma^{\leq{n}}$, then $c\in{{\it AC}(\Sigma,\Delta,n)}$.
**Proof** Let us a... | 2,410 | 4,070 | 2,059 | 2,248 | null | null | github_plus_top10pct_by_avg |
g*, [2014](#grl53099-bib-0038){ref-type="ref"}; *Chung and Soden*, [2015](#grl53099-bib-0005){ref-type="ref"}\], for example, to be decomposed into correctable parameterization errors and legitimate differences in model climatology.
Highly accurate calculation of radiative fluxes is of primary interest to the climate ... | 2,411 | 180 | 1,949 | 2,903 | 1,576 | 0.788078 | github_plus_top10pct_by_avg |
vec
x)\rangle$, or $L[\langle A_0\rangle]$, is used to determine the phase transition temperature $T_c$ as well as critical exponents. The temperature-dependence of the Polyakov loop two-point function relates to the string tension. In the confining phase, for $T<T_c$, and large separations $|\vec x-\vec y|\to\infty$, ... | 2,412 | 3,152 | 1,846 | 2,123 | 3,226 | 0.7739 | github_plus_top10pct_by_avg |
appearance of $b_{gz}$ with $g>G$ is in the third sum. Since the $b_{uz}$ are a ${\mathbb{C}}[{\mathfrak{h}}]^{{W}}$-basis of ${\mathcal{N}}$, that third term $\sum_{g>G} c'_{gz}b_{gz}$ is actually zero.
Now consider where the specific term $b_{Gw}$ appears on the right hand side of . For $g<G$, implies that $\operato... | 2,413 | 1,012 | 1,132 | 2,540 | 3,653 | 0.77089 | github_plus_top10pct_by_avg |
em$11$}}/ {\hbox{{\rm Br}\kern 0.1em$10$}}]_{case B}$. We assumed the value $[{\hbox{{\rm Br}\kern 0.1em$11$}}/ {\hbox{{\rm Br}\kern 0.1em$10$}}]_{case B} = 0.75$, which is appropriate for $n = 10^2$ and $T_e = 5,000$ K [@chad; @hs87]. For each galaxy, we computed both these ratios for both realizations of the continu... | 2,414 | 1,625 | 2,795 | 2,495 | null | null | github_plus_top10pct_by_avg |
space ${{{\mathbb P}}}^d, \; d\ge 3.$ Then we have $\;\; \chi(G)\le(\omega(G))^2.$
In both cases, there are polynomial time algorithms that, given the lines corresponding to the vertices of $G$, find complete subgraphs $K\subseteq G$ and proper colorings of $G$ with at most $|V(K)|^3$ and $|V(K)|^2$ colors, respecti... | 2,415 | 633 | 2,719 | 2,282 | null | null | github_plus_top10pct_by_avg |
many cardinals $\d=\d(\Gamma)$ where $\Gamma$ has strong closure properties. In fact, we expect that it can be used to prove Theorem 1.1 of [@KKMW] but we certainly haven’t done so. We now start proving [Theorem \[main theorem\]]{}.\
Let $\kappa=\utilde{\delta}^2_1$. By Martin’s theorem (see Theorem 2.31 and Definiti... | 2,416 | 2,368 | 2,526 | 2,206 | 4,106 | 0.768077 | github_plus_top10pct_by_avg |
ypes of size $n$. We denote by $m_{d,\lambda}(\omega)$ the multiplicity of $(d,\lambda)$ in $\omega$. As with partitions it is sometimes convenient to consider a type as a collection of integers $m_{d,\lambda}\geq 0 $ indexed by pairs $(d,\lambda)\in \Nstar\times \; \calP^*$. For a type $\omega=(d_1,\omega^1)(d_2,\omeg... | 2,417 | 1,402 | 2,590 | 2,279 | 2,948 | 0.775886 | github_plus_top10pct_by_avg |
s an example of a neighbourhood base at that point,* an observation that has often led, together with Eq. (\[Eqn: TB\]), to the use of the term “neighbourhood” as a synonym for “non-empty open set”. The distinction between the two however is significant as neighbourhoods need not necessarily be open sets; thus while no... | 2,418 | 4,386 | 3,410 | 2,314 | 2,641 | 0.778199 | github_plus_top10pct_by_avg |
defined above is a very general mesh/partition on $\Omega$, as we do not specify the shape and conformal property of $K\in \mathcal{T}_h$. The interior penalty discontinuous Galerkin (IPDG) method can be extended to such a general mesh, without any modification of the formulation. However, to ensure its approximation ... | 2,419 | 1,641 | 2,306 | 2,208 | 3,795 | 0.770055 | github_plus_top10pct_by_avg |
on the different particles from the general expressions Eqs. (\[eq:fp\_unperturb\])-(\[eq:fp\_perturb\]) and from the approximate expressions of Sects. \[sec:inertial\] and \[sec:drag\].
Numerical evaluation of the inertial force {#sec:numerical-inertial}
------------------------------------------
We consider a test... | 2,420 | 688 | 870 | 2,642 | null | null | github_plus_top10pct_by_avg |
A W \right\}_{k K}
\left\{ W ^{\dagger} A (UX) \right\}_{K k}
\nonumber \\
&+&
\sum_{n} \sum_{k} \sum_{K} \sum_{m \neq k}
\biggl[
\frac{ (ix) }{ ( \Delta_{K} - h_{k} )^2 ( h_{m} - h_{k} ) }
e^{- i ( h_{k} - h_{n} ) x}
\nonumber \\
&-&
\frac{ (ix) }{ ( \Delta_{K} - h_{k} )^2 ( \Delta_{K} - h_{m} ) }
e^{- i ( \D... | 2,421 | 1,558 | 2,598 | 2,458 | null | null | github_plus_top10pct_by_avg |
e without the CKM factors, respectively. We emphasize that the SM parametrization in Eqs. (\[eq:decomp-1\])–(\[eq:decomp-4\]) is completely general and independent from U-spin considerations. For example, further same-sign contributions in the CF and DCS decays can be absorbed by a redefinition of $t_0$ and $t_2$, see ... | 2,422 | 2,130 | 2,682 | 2,252 | null | null | github_plus_top10pct_by_avg |
sed $\hat{A}$ as \_[ab]{} = \_[ab]{}/2 + \_[ab]{}, where $\hat{h}_{ab}$ is symmetric and $\hat{B}_{ab}$ is anti-symmetric. The trace part of $\hat{h}_{ab}$ is denoted [^4] \_a\^a.
The effective metric (\[metric\]) is \_ = \_\^a\_[ab]{}\_\^b \_ + \_[ab]{} + 2 \_[ab]{} + [O]{}(A\^2). We also have \_\^[a]{}\_a\^ = D (1 +... | 2,423 | 971 | 2,906 | 2,483 | null | null | github_plus_top10pct_by_avg |
o, there is no way to rank the relative importance of hazards of mixed type. Loss of the ability to compare risks of all hazards is a flagrant omission. Under correct physics, risks of multiple hazards are additive. This is not the case under MIL-STD-882.
The formal sense of *assurance* is lost by these definitional v... | 2,424 | 321 | 3,234 | 2,655 | null | null | github_plus_top10pct_by_avg |
}_{t}f(x)={\mathbb{E}}(P_{t}^{N,Z}f(x))=\sum_{m=0}^{\infty
}I_{m}(f)(x)$$with$$I_{0}(f)(x)={\mathbb{E}}(1_{\{N(t)=0\}}P_tf(x)) =e^{-\rho t}P_tf(x)$$ and for $m\geq 1$, $$\begin{aligned}
I_{m}(f)(x) &={\mathbb{E}}\Big(1_{\{N(t)=m\}}\frac{m!}{t^m}%
\int_{0<t_{1}<...<t_{m-1}<t_{m}\leq
t}P_{t-t_{m}}\prod_{i=0}^{m-1}U_{Z_{m... | 2,425 | 1,061 | 1,095 | 2,368 | null | null | github_plus_top10pct_by_avg |
enstrophy in finite time might be to increase its kinetic energy by allowing for a smaller instantaneous rate of growth (i.e., with an exponent $2 < \alpha \le 3$ instead of $\alpha = 3$). This can be achieved by prescribing an additional constraint in the formulation of the variational optimization problem, resulting... | 2,426 | 1,038 | 2,391 | 2,310 | 3,951 | 0.769035 | github_plus_top10pct_by_avg |
bda}\,, &
\phi &= \Phi + \frac{T}{\lambda}\,, &
r &= 1 + \lambda R\,.\end{aligned}$$ We also introduce a new coordinate $u$ for the polar angle via $u=\cos\theta$. The NHEK limit is then obtained by taking the $(a\to M, \lambda \to 0)$ limit of the Kerr metric in these coordinates, which yields the line element $$\... | 2,427 | 5,076 | 858 | 1,930 | null | null | github_plus_top10pct_by_avg |
olume $\text{(fm}^4\text{)}$ Configurations
---- ----------------- --------- ---------- ------------------------------- ----------------
1w $16^3\times 32$ 5.70 0.179 $2.87^3 \times 5.73$ 100
1i $16^3\times 32$ 4.38 0.166 $2.64^3 \times 5.28$ 100
... | 2,428 | 934 | 2,300 | 2,287 | null | null | github_plus_top10pct_by_avg |
X\_a=\_[i\_a]{}-\_[i\_a]{}\^A\_[i\_A]{}-|\_[i\_a]{}\^A\_[i\_A]{},A=1,…,k.
Substituting expressions (\[eq:3.28\]) into (\[eq:3.31\]) or (\[eq:3.32\]) and simplifying gives the unified form
\[eq:3.34\] [( \^[( + )]{}\_[(a\_1.]{}[( + )]{}…\_[[a\_s]{})]{}[( + )]{})]{}=0.
The index $s$ is either $\max(s)=q-1$ or $\max(s... | 2,429 | 3,183 | 3,839 | 2,374 | null | null | github_plus_top10pct_by_avg |
}{2} + l) \hbar ) \right. \nonumber\\
& & ~~~~ + \hat{a}^i_\pm (u \mp \frac{1}{4} k \hbar ) \nonumber \\
& &~~~~ + \left. \sum_{l=i+1}^N \hat{b}^{il}_{\pm}
( u \pm \frac{1}{2} (\frac{k}{2} + l) \hbar )
- \sum_{l=i+2}^N \hat{b}^{i+1,l}_{\pm}
( u \pm \frac{1}{2} (\frac{k}{2} + l -1) \hbar ) \right\}:~, \label{hpn}\end{al... | 2,430 | 1,623 | 2,904 | 2,366 | null | null | github_plus_top10pct_by_avg |
=(z_x,z_y)\in {{\mathbb Z}}^2$ and $r$ sufficiently large, we have that $\card(N\cap \Lambda(z(X),r))\leq \card(N\cap B(O,|X|)\cap B(X,|X-\mathcal{A}(X)|)),$ the latter quantity being 0 since $[\mathcal{A}(X),X]$ is an edge of the RST, implying that there is no point of $N$ in $\Lambda(z(X),r)$. Thus, for $r\geq \sqrt{... | 2,431 | 1,626 | 1,361 | 2,273 | null | null | github_plus_top10pct_by_avg |
y_{d-1}-\frac{\epsilon}{\triangle},\
y_{d}+\epsilon+\delta,\
y_{d+1},\ \cdots, \\ \\
y_{n-m-1},\ y_{n-m}-\epsilon-\delta,\ \displaystyle
y_{n-m+1}+\frac{\epsilon}{m}, \ \cdots,\ y_n+\frac{\epsilon}{m}).
\end{array}$$ Now define $x$ as the direct sum of the vectors $(y_1,\dots,y_{t})$ and $\bar{x}'^{\da}$, that is $$x=... | 2,432 | 1,153 | 1,477 | 2,340 | 3,886 | 0.769523 | github_plus_top10pct_by_avg |
/n')
To:
password = word.strip("\n")
But you might as well just:
password = word.strip()
See the strip documenation:
Return a copy of the string with leading and trailing characters
removed. If chars is omitted or None, whitespace characters are
removed. If given and not None, chars must be a string; the charac... | 2,433 | 2,209 | 284 | 1,892 | null | null | github_plus_top10pct_by_avg |
th $1/5$ solar abundances (“the low–Z models”); neither abundance set includes depletion onto dust grains. (We address the effects of dust in § \[sec:caveats\].) Because Cloudy does not predict the intensity of [ $1.7$ ]{}, we scaled the intensity from [ $4471$]{} Å, which shares the same upper level. For Case B and T$... | 2,434 | 2,881 | 2,803 | 2,356 | null | null | github_plus_top10pct_by_avg |
=1pt](0.1,0)(0.1,0.4)
\end{pspicture}},{
\begin{pspicture}(0,0.1)(0.2,0.4)
\psline[linewidth=1pt, linestyle=dashed,dash=4pt 3pt](0.1,0)(0.1,0.4)
\end{pspicture}})$. Let us first show the validity of equation . The map $\textbf{D} (\widehat{\mathcal O^!}) (\vec X;\varnothing)\to \widehat{ \mathcal O}(\vec X;\varnot... | 2,435 | 2,254 | 2,108 | 2,158 | 3,465 | 0.772168 | github_plus_top10pct_by_avg |
sociated channel matrices may be correlated. Thus, taking the dependent reconfiguration states into consideration is an interesting future work, where we can have correlated and non-identically distributed $R_{\psi}$. While this paper has adopted the VCR as the analytical channel model, as mentioned earlier, there are ... | 2,436 | 1,120 | 877 | 2,558 | 2,426 | 0.779849 | github_plus_top10pct_by_avg |
ed}$$ where $a(t)$ is the scale factor and $d\Omega^2 = d\theta ^2 + \sin ^2\theta \, d\phi ^2 $ is the metric of the 2-sphere. This metric is conformally invariant to Minkowski space-time, and from the relations written in the first Appendix, we can choose the following reduced basis of all independent order 6 scalar ... | 2,437 | 4,316 | 2,081 | 2,045 | null | null | github_plus_top10pct_by_avg |
he action is free, it is also a bijection. It is easy to check that a bijective quasi-isometry between two uniformly discrete metric spaces is in fact a bi-Lipschitz equivalence. This finishes the proof.
We now recall the definition of the real hyperbolic $n$-space. There are many definitions and we refer the reader t... | 2,438 | 975 | 2,450 | 2,250 | null | null | github_plus_top10pct_by_avg |
13(522): 829-844.
Zhang, Y., Duchi, J. C. and Wainwright, M. J. (2013). Communication-efficient algorithms for statistical optimization. Journal of Machine Learning Research, 14, 3321-3363.
[^1]: School of Mathematical Sciences, Soochow University, 215006, Suzhou, China, stamax360@outlook.com
[^2]: School of Mathema... | 2,439 | 1,171 | 2,151 | 2,198 | 2,395 | 0.780216 | github_plus_top10pct_by_avg |
T - w_T) (v_T - w_T)^T} ds dt}\\
\leq& \int_0^1 \int_0^s \E{\lrn{\nabla^2 f(x_T - v_T + s(v_T-w_T))}_2\lrn{v_T - w_T}_2^2} ds \\
\leq& \frac{1}{\epsilon} \E{\lrn{v_T - w_T}_2^2}\\
\leq& \frac{32}{\epsilon} \lrp{T^2 L^2 + TL_\xi^2} T\beta^2
\end{aligned}$$ wehere the second inequality is ... | 2,440 | 3,060 | 2,026 | 2,154 | null | null | github_plus_top10pct_by_avg |
-1}X^{(x)}_{\sigma_{B_1}} \in C_{0, r/|x|} \}}\geq\mathbf{1}_{\{|x|^{-1}X^{(x)}_{\sigma_{B_1}} \in C_{0, r/\eta} \}}\eqqcolon \hat{J},$$ where $\hat{J}$ is a Bernoulli random variable with parameter $\hat{q}$. Stochastic dominance, $N\leq \hat{\Gamma}$ almost surely, follows by the same line of reasoning as in the pr... | 2,441 | 1,183 | 2,203 | 2,309 | 3,129 | 0.77467 | github_plus_top10pct_by_avg |
({\rm rk}\, {\cal E}^{\alpha}_n)
\left( \frac{ \theta^{{\cal E},\alpha}_n }{\pi} \right)^2
\: - \: \frac{1}{8} \sum_n ( {\rm rk}\, T^{\alpha}_n )\left(
\frac{ \theta^{T,\alpha}_n }{\pi} \right)^2.\end{aligned}$$ In all cases the right-moving vacuum energy vanishes, since the right-moving bosons and fermions make equal... | 2,442 | 1,298 | 2,427 | 2,304 | null | null | github_plus_top10pct_by_avg |
uation shows that indeed $G_1$ is twice the stochastic propagator $G_s^{ab}$ defined in eq. \[ne21\].
Remarks
-------
In this Section we have shown that the 1PI EA derived from a quantum field theory, cut off at terms quadratic in the difference field $\phi_-$, is identical in form to the effective action derived fro... | 2,443 | 1,271 | 3,645 | 2,424 | null | null | github_plus_top10pct_by_avg |
one of the regions $U$ or $V$ is included in the ball $B(X,|X-\A(X)|)$. So, one of the two points $Y$ and $\A(Y)$ belongs to the ball $B(X,|X-\A(X)|)$. This contradicts the fact that $\A(X)$ is the ancestor of $X$.
![\[fig:croisement2\] [*The hatched area corresponds to the one of the two sets $U$ and $V$ which is inc... | 2,444 | 196 | 3,155 | 2,644 | null | null | github_plus_top10pct_by_avg |
$. The advantage of this grading is that it is simply given by the left multiplication of ${\mathbf{h}}_{c+i}$. Thus, as is an isomorphism of left $U_{c+i}$-modules and hence of left ${\mathbb{C}}[{\mathbf{h}}_{c+i}]$-modules, it is automatically a graded isomorphism under the canonical grading.
Since ${\mathfrak{h}}^... | 2,445 | 1,814 | 2,073 | 2,111 | 3,973 | 0.768884 | github_plus_top10pct_by_avg |
(b) + 3*f(b).
-4*b**2 - b
Let c(j) = j + 1. Let s(v) = -2*v**2 + v + 2. Let u(q) = 2*q - 1. Let y be u(1). Give y*c(o) - s(o).
2*o**2 - 1
Let f(h) = 22*h. Let q(i) be the first derivative of -7*i**2/2 + 8. Give 5*f(y) + 16*q(y).
-2*y
Let t(k) = -22*k**2 + 50*k**2 + 6*k - 22*k**2 + 6*k**3. Let q(j) = -j**3 - j**2 - j. G... | 2,446 | 813 | 1,566 | 2,169 | null | null | github_plus_top10pct_by_avg |
} {f}\left(\rho_n + X^{(n+1)}_s\right)\,\mathrm{d}s\right],
\qquad x\in D,
\label{withrho}$$ where $X^{(n)}$ are independent copies of $(X, \mathbb{P}_0)$. Applying Fubini’s theorem, then conditioning each expectation on $\mathcal{F}_{n}\coloneqq \sigma(\rho_k\colon k\leq n)$ followed by Fubini’... | 2,447 | 4,114 | 1,947 | 1,818 | null | null | github_plus_top10pct_by_avg |
e process probabilistic [@pra61_034301].
The main part of our paper is based on the formalism summarized in Section \[sec:formalism\]. Our description is completely independent of the dimensions of the Hilbert-spaces involved, and we do not even need to fix a basis. In Section \[sec:teleport\] we give a general condit... | 2,448 | 4,109 | 2,831 | 2,286 | 1,210 | 0.792662 | github_plus_top10pct_by_avg |
f there is a failover.
The thing is that none of the dependencies are distributed in the same way, and can therefore be expected to be running everywhere.
You should only need to expand on that config file to get it to work. Here I've done it and reindented it to show its structure better:
[{kernel,
[{distributed, [... | 2,449 | 1,075 | 1,863 | 2,022 | 3,253 | 0.773749 | github_plus_top10pct_by_avg |
otential was already considered in [@Aldazabal:2006up] and arises from the Chern-Simons term $$\int D_8 \wedge (Q \cdot H_3 +P_1^2 \cdot F_3 )_2 \quad . \label{D8tadpole}$$ By imposing absence of sources for this potential, this leads to the quadratic constraint $$Q^{cd}_{[a}H_{b]cd}+P^{cd}_{[a}F_{b]cd}=0 \quad . \l... | 2,450 | 808 | 2,234 | 2,180 | 2,099 | 0.782737 | github_plus_top10pct_by_avg |
\ .$$ The dominant contributions should be the gluon and electroweak penguins mediated by $H$ and $Q$. In contrast to the KM Model, the vector coupling of the vector quark means that the $Z$ boson penguin will be suppressed by $O(m_K^2/m_Z^2)$ due to vector current conservation. The gluon penguin contributes only to $... | 2,451 | 2,021 | 3,050 | 2,206 | 3,945 | 0.769081 | github_plus_top10pct_by_avg |
this also gives $\mbinom{u'-v'}{u'-a'+1}$ odd.
We let $u=2u'-2$ and $v=2v'-3$. Then $u+v=n$, and we have $$u-v=2(u'-v')+1\equiv-1\ppmod{2^{l(v')+1}}$$ and $l(v)\ls l(v')+1$. So $S^{(u,v)}$ is irreducible. Furthermore, $v\gs7$, $v\equiv3\ppmod4$ and $$\binom{u-v}{u-a}=\binom{2u'-2v'+1}{2u'-2a'(+2)}\equiv\binom{u'-v... | 2,452 | 1,833 | 2,217 | 2,109 | 2,393 | 0.780236 | github_plus_top10pct_by_avg |
tation theory [@gst:basic; @gst:tree; @gst:Dynkin-A; @gst:acyclic] which will be continued in [@gst:acyclic-Serre]. The perspective from enriched derivator theory offers additional characterizations of stability, and these together with a more systematic study of the stabilization will appear in [@gs:enriched]. It is w... | 2,453 | 826 | 2,351 | 2,431 | null | null | github_plus_top10pct_by_avg |
imate, parameter inference is also available to assist in assessing the quality of fit. The deterministic map to the sufficient statistics from the set of firing events and responses permits the transformation from the final particle set $\{X_{1:T}^{(i)}\}_{i=1}^{N}$ to an $N$-component Gaussian-gamma mixture approxima... | 2,454 | 611 | 2,078 | 2,428 | 1,762 | 0.785898 | github_plus_top10pct_by_avg |
rbation $\delta\rho_1 =
\delta\psi_1^*+\delta\psi_1$ then follows as $$\delta\hat\rho_1 = \frac{e^{-\frac{k^2a^2}{2}} (4 k^2(1+\gamma^2)-8i\gamma{\boldsymbol{k}}\cdot {\boldsymbol{V}}_p)}{4{\boldsymbol{k}}\cdot{\boldsymbol{V}}_p({\boldsymbol{V}}_p \cdot {\boldsymbol{k}}+i\gamma k^2 +2i\gamma)- k^2(4+k^2)(1+\gamma^2)}.
... | 2,455 | 3,320 | 2,636 | 2,270 | null | null | github_plus_top10pct_by_avg |
a_{\hat{S}} + t/\sqrt{2n}]$$ Both confidence intervals satisfy (\[eq::honest\]).
We now compare $\hat\beta_{{\widehat{S}}}$ and $\hat{C}_{{\widehat{S}}}$ for both the splitting and non-splitting procedures. The reader should keep in mind that, in general, $\hat{S}$ might be different between the two procedures, and he... | 2,456 | 4,097 | 2,386 | 1,977 | 2,882 | 0.776347 | github_plus_top10pct_by_avg |
led introduction to the topics missing from Ref. but necessary to understand supersymmetric field theories is of greater use and interest to most readers of this Proceedings volume. With these notes, our aim is thus to equip any interested reader with a few handy concepts and tools to be added to the backpack to be ca... | 2,457 | 391 | 3,141 | 2,614 | null | null | github_plus_top10pct_by_avg |
standard Gaussian random variable. If $\varphi$ is concave, then we have
Corollary \[t0\] follows directly from Theorem \[t6\] by and the fact that $1+\dots+\frac{1}{n}{\leqslant}\log n+1.$
For the general case where the mean of $X_1$ is uncertain (that is, $\underline{\mu}\ne \overline{\mu}$) and $\varphi$ may not b... | 2,458 | 1,315 | 851 | 2,465 | 3,811 | 0.769973 | github_plus_top10pct_by_avg |
a})} + 2\delta^2L^2 \E{\lrn{w_{k\delta}}_2^2} + 2\delta \beta^2\\
\leq& \E{a(w_{k\delta})} -m\delta \E{a(w_{k\delta})} + 2\delta^2L^2 a(w_{k\delta}) + 2\delta^2 L^2 R^2 + 2\delta \beta^2\\
\leq& (1-m\delta/2)a(w_{k\delta}) + {m\delta} R^2 + 2\delta \beta^2
\end{aligned}$$
Where the first inequa... | 2,459 | 3,452 | 1,796 | 2,267 | null | null | github_plus_top10pct_by_avg |
equences \[Sec:consequences\]
=================================
In the previous section, we compared the magnitude of the SUSY threshold corrections to the bottom quark mass. Particularly, we have shown that the various approximations made to obtain the common form in \[Eq:common-app\] all seem to be valid approximati... | 2,460 | 847 | 2,342 | 2,451 | null | null | github_plus_top10pct_by_avg |
t {{W}}$ and its subrings from . Since $e$, $e_-$ and $\delta$ are homogeneous under this action, each $Q_{c+\ell}^{c+\ell+1}$ and hence each $B_{ij}$ and $N(k)$ is also graded under this action. As in , this induces a graded structure, again called $\operatorname{{\mathbf{E}}\text{-deg}}$, on $\operatorname{{\textsf}{... | 2,461 | 2,623 | 2,632 | 2,214 | 4,183 | 0.767494 | github_plus_top10pct_by_avg |
95), 133–164.
S. Kojima and Y. Yamashita, [Shapes of stars]{}, Proc. Amer. Math. Soc., 117 (1993), 845–851.
S. Kojima, H. Nishi and Y. Yamashita, [Configuration spaces of points on the circle and hyperbolic Dehn fillings]{}, to appear in Topology.
W. Neumann and D. Zagier, [*Volumes of hyperbolic 3-manifolds*]{}, To... | 2,462 | 393 | 1,663 | 2,091 | null | null | github_plus_top10pct_by_avg |
]{} on that side. Such polynomials are of the form $$G=x^{\overline e}y^fz^e \prod_{j=1}^S(y^c+\rho_j x^{c-b}z^b)
\quad.$$
For the first assertion, simply note that under the stated hypotheses only one monomial in $F$ is dominant in $F\circ\alpha(t)$; hence, the limit is supported on the union of the coordinate ax... | 2,463 | 888 | 2,312 | 2,385 | 1,644 | 0.787277 | github_plus_top10pct_by_avg |
the single vector meson production, which is determined by the photon flux and the $\gamma h \rightarrow V h$ cross section.
In what follows we will consider the color dipole formalism to describe the diffractive vector meson photoproduction, which successfully describe the HERA data and recent LHC data [@amir; @brun... | 2,464 | 2,627 | 2,653 | 2,272 | 2,496 | 0.779336 | github_plus_top10pct_by_avg |
7.6 1.24 0.14 2.79 0.82 2.46
Combined (1393) 172.1 1.6 11.82 0.30 0.68 0.11 0.70
: The $v_H^{*}$ (km/... | 2,465 | 2,369 | 2,702 | 2,449 | 694 | 0.802256 | github_plus_top10pct_by_avg |
defect states start to overlap significantly, and the particle initially tied to one defect oscillates to the other. If the amplitude then rises again and reaches the “collapse” value $$F_{\rm collapse} = j_{0,1} \frac{\hbar\omega}{ed}$$ at $t = T_{\rm pulse}$, and is kept constant thereafter, the particle has been tra... | 2,466 | 4,795 | 1,932 | 2,092 | 2,115 | 0.78261 | github_plus_top10pct_by_avg |
ekar variables the full Hamiltonian for general relativity is a sum of constraints $$H_{\text{G}}^{\text{tot}}= \int d^3 {\bf x} \, (N^i G_i + N^a C_a + N h_{\text{sc}}),$$ where $$\begin{aligned}
C_a &= E^b_i F^i_{ab} - (1-\gamma^2)K^i_a G_i ,\nonumber \\
G_i &= D_a E^a_i\end{aligned}$$ and the scalar constraint has ... | 2,467 | 4,219 | 2,150 | 2,103 | null | null | github_plus_top10pct_by_avg |
}\,}+ \langle \mathcal{L}_{L_+}{\bf u}^{(k)}, {\bf v}^{(k^\prime-1) } \rangle,\end{aligned}$$
where in the last line we used the fact that $\overline{L_+}=-L_-$. Note that this relationship does not hold between $H_{\pm}$, so this type of proof will not work in Poincaré coordinates.
We would like to discard the first... | 2,468 | 2,205 | 2,917 | 2,341 | null | null | github_plus_top10pct_by_avg |
, and hence 1-balanced, and it satisfies the 1-size property as $|\mathcal{E}_t|= n$. Suppose that $\{\beta_1, \beta_2\}\subset H_t(\alpha)$ for some $\alpha\in \mathbb{Z}_n$, [with $\beta_1\neq \beta_2$]{}. Then there exists $j_1,j_2\in \{0,\ldots, s-1\}$ such that $\beta_1 = \alpha + j_1 k_t\, (\operatorname{mod}\, ... | 2,469 | 2,956 | 2,072 | 2,349 | null | null | github_plus_top10pct_by_avg |
as the defining relations of new local operators $s_x$ and $s_y$, taking into account of the fact that $$\bar{h}_x=\bar{h}_x(x),\hs{2ex}\bar{h}_y=0.$$ The canonical commutation relations are still valid, as well as the conservation laws. Considering the conservation laws of $d_\m$ and $h_\m$ $$\partial_y d_x+\partial_... | 2,470 | 3,586 | 2,819 | 2,231 | null | null | github_plus_top10pct_by_avg |
} }
],
"DO" : [
{ "commerce_order_update_status" : { "commerce_order" : [ "commerce_order" ], "order_status" : "completed" } }
]
}
}
In short as soon as the balance is 0 I want the order to be complete.
A:
In the end I created a new rule:
{ "rules_complete_order" : {
"LABEL" : "Complete Orde... | 2,471 | 2,630 | 69 | 2,442 | 924 | 0.797569 | github_plus_top10pct_by_avg |
) (y_T - v_T)^T} ds dt}\\
=& \E{f(x_T - y_T)+ \underbrace{\lin{\nabla f(x_0 - y_0), y_T - v_T}}_{\circled{1}} + \underbrace{\lin{\nabla f(x_T - y_T) - \nabla f(x_0 - y_0), y_T - v_T}}_{\circled{2}} }\\
&\quad + \E{\underbrace{\int_0^1\int_0^s \lin{\nabla^2 f(x_T - y_T + s(y_T-v_T)), (y_T - v_T) ... | 2,472 | 2,910 | 1,691 | 2,230 | null | null | github_plus_top10pct_by_avg |
f Specht modules in our family.
In fact, we speculate that every Specht module has a filtration in which the factors are isomorphic to indecomposable Specht modules; this would imply in particular that every indecomposable summand has a Specht filtration. This speculation is certainly true in the case of Specht module... | 2,473 | 1,966 | 1,110 | 2,390 | 568 | 0.805448 | github_plus_top10pct_by_avg |
below Eq. \[e.2to2operator\]. The *upper dotted orange line* is for $y^{\phi_1}_\chi = y^{\phi_2}_\chi/20$, in which case the vertical axis is understood to be $(y_\chi^{\phi_2}/\Lambda)^2$. **Right:** Direct detection bounds on the $2\rightarrow2$ regime of $n_\phi = 1$ dmDM, same labeling as the left plot. The verti... | 2,474 | 1,009 | 1,619 | 2,406 | 380 | 0.811601 | github_plus_top10pct_by_avg |
xtrm{if}\ (x_0,\omega_0,E_0)\in \Gamma_-.
\end{cases}$$ where $(x,\omega,E)\in G\times S\times I$ when taking the limits.
Define $$z_0=\begin{cases}
x_0-t(x_0,\omega_0)\omega_0,\ & \textrm{if}\ (x_0,\omega_0,E_0)\in G\times S\times I \\
x_0-\tau_+(x_0,\omega_0)\omega_0,\ & \textrm{if}\ (x_0,\omega_0,E_0)\in \Gamma_+ \... | 2,475 | 1,209 | 1,558 | 2,249 | null | null | github_plus_top10pct_by_avg |
inside another vacuous ball, thereby requiring the algorithm to continue. In that case, the comparison with the case of exiting a single sphere breaks down.
{ref-type="table"}. Patients with isolated SSc tendon repai... | 2,477 | 156 | 2,461 | 2,782 | null | null | github_plus_top10pct_by_avg |
y $v\in C^1(\ol G\times S\times I)$, \[csda25\] &-,v\_[L\^2(GSI)]{}+\_x,v\_[L\^2(GSI)]{}+CS\_0,v\_[L\^2(GSI)]{}\
&+,v\_[L\^2(GSI)]{}-K\_C,v\_[L\^2(GSI)]{}\
=& ,S\_0[E]{}\_[L\^2(GSI)]{}- \_[GS]{} S\_0v|\_[E=0]{}\^[E=E\_[m]{}]{} dx d\
&-,\_x v\_[L\^2(GSI)]{} +\_[GSI]{}()v dddE\
&+,CS\_0v\_[L\^2(GSI)]{} +,\^\* v\_[L\^2(GS... | 2,478 | 569 | 2,549 | 2,564 | null | null | github_plus_top10pct_by_avg |
st(site1);
getPageURLList(site2);
}
Calls the same method that gets called when there is only one link
private void getPageURLList(string site)
{
webBrowser.DocumentCompleted += createList;
webBrowser.Navigate(site);
}
I'm pretty sure the issue is "Navigate" is getti... | 2,479 | 1,777 | 519 | 1,300 | null | null | github_plus_top10pct_by_avg |
are equivalent but the second one is a bit more convenient to handle in practice. The quantitative equivalence of the two definitions as well as the existence of the limit could be seen using the global conformal transformations explained in . We review it in appendix A.
Energy correlators are defined as follows In ... | 2,480 | 3,496 | 2,874 | 2,280 | null | null | github_plus_top10pct_by_avg |
g \triangleright h_2$ that can be written as $${\label{eq:KS4'}}
g^{-1}(g\triangleleft {h_1}) \in {\rm Stab}_G (h_2)$$ for any $g\in G$, $h_1$, $h_2\in H$. Thus if $\alpha$ is an action as automorphisms then $(H, G, \alpha, \beta)$ is a matched pair if and only if [(\[eq:3\])]{} and [(\[eq:KS4’\])]{} hold. The conditio... | 2,481 | 4,389 | 1,953 | 1,941 | 2,286 | 0.781151 | github_plus_top10pct_by_avg |
YM theory of the gauge symmetry of Sec.\[GaugeSymm\] can be interpreted as a gravity theory. This will be the main issue to focus on below.
Nevertheless, motivated by this potential identification, we denote the covariant derivative as D\_[a]{} = \_[a]{}\^\_, where we used the notation \_[a]{}\^ \_[a]{}\^ + A\_[a]{}\^... | 2,482 | 371 | 2,294 | 2,446 | null | null | github_plus_top10pct_by_avg |
thbb{G}}}_a$; this fact was mentioned in §\[germlist\]. The following picture represents schematically the curves described above.
 
[^1]: [**Acknowledgments.**]{} Work on this paper was made possible by support from Mathematisches Forschungsinstitut Oberwolfa... | 2,483 | 1,608 | 1,439 | 1,752 | 2,988 | 0.775588 | github_plus_top10pct_by_avg |
measurement errors and the expected variation of helium abundance. Thus, these starburst regions appear to contain massive stars ($> 39,000$ K if main sequence stars.) By contrast, NGC 253, NGC 4102, and the nucleus of M82 have [ $1.7$ ]{}/$<0.15$, and thus are inferred to have softer ionizing continua ($\lesssim 37,0... | 2,484 | 2,325 | 3,626 | 2,747 | null | null | github_plus_top10pct_by_avg |
een $V'$ and $V.$ As usual, by identifying $H$ with $H'$ we have $V\underset d\hookrightarrow H\cong H'\underset d\hookrightarrow V'$ see e.g., [@Bre11].
Let ${\mathfrak{a}}:[0,T]\times V \times V \to {\mathbb{C}}$ be a *non-autonomous sesquilinear form*, i.e., ${\mathfrak{a}}(t;\cdot,\cdot)$ is for each $t\in[0,T]$ a... | 2,485 | 2,022 | 2,586 | 2,160 | 3,237 | 0.773823 | github_plus_top10pct_by_avg |
athbb E}}\big(\widetilde{\chi}_r^{2}\big)} \sqrt{{{\mathbb P}}(\widetilde{\chi}_{r}\geq 1)} ~,$$ the desired limit follows from (\[step1\]) if we prove that $\limsup_{r\rightarrow+\infty}{{\mathbb E}}(\widetilde{\chi}_{r}^{2})$ is finite, which is the result of Lemma \[lemme:moment2\]. $\Box$
The section ends with the... | 2,486 | 1,301 | 459 | 2,739 | null | null | github_plus_top10pct_by_avg |
eq \mathbb{P}(\Gamma >n ) = (1-p)^n, \qquad n\in\mathbb{N}.$$
- The randomness in the geometric random variables $\Gamma$ is heavily correlated to $N$. The fact that each of the $\Gamma$ are geometrically distributed has the advantage that $$\sup_{x\in D}\mathbb{E}_x[N] \leq \sup_{x\in D}\mathbb{E}_x[\G... | 2,487 | 2,288 | 2,138 | 2,265 | null | null | github_plus_top10pct_by_avg |
$. Let $a_j$, $j=1,2,\ldots$ be an ascending sequence in $\Gamma$. Since $\Gamma_i=\bar{\Gamma}_i$ for all $i\in I$, it follows that $\lim a_j\in \Gamma_i$ for all $i$, and hence $\lim a_i\in \Gamma$, as desired.
On the other hand, suppose $J=\{1,\ldots,k\}$ and let $\Gamma=\Union_{i=1}^k\Gamma_i$. Then $\Gamma$ satis... | 2,488 | 3,464 | 1,988 | 2,192 | null | null | github_plus_top10pct_by_avg |
+ 36 = 0, a - t - 2*t - 10 = i. What is the un
- 0 - 8/(-2). Suppose 1251 = -2*b + 1307. Calculate b*z(i) + h*f(i).
-4*i
Let p(h) = 4*h - 3. Suppose b - 4 = -0*u - 2*u, 2*b - 5*u = 53. Let t(s) = 9*s - 7. Calculate b*p(g) - 6*t(g).
2*g
Let w(n) = -5*n**2 + 4*n + 4. Let d(v) = -6*v**2 + 3*v + 3. Suppose 32 + 36 = 17*y.... | 2,489 | 516 | 763 | 2,510 | null | null | github_plus_top10pct_by_avg |
wards new stimuli. It was implemented on a Fischer Technik mobile robot, which uses a Motorola 68HC11 microcontroller. The robot has a two wheel differential drive system and four light sensors facing in the cardinal directions.
{width=".3\textwidth"}
In the experiments described be... | 2,490 | 4,319 | 3,059 | 2,122 | null | null | github_plus_top10pct_by_avg |
r-order expansion coefficients are more involved, due to the above item (c). This will also be explained in detail in Section \[s:bounds\].
Bounds on $\Pi_\Lambda^{{\scriptscriptstyle}(j)}(x)$ for the ferromagnetic models {#s:reduction}
=================================================================================
... | 2,491 | 1,624 | 408 | 2,482 | 1,238 | 0.792193 | github_plus_top10pct_by_avg |
re is the orbit $Gp = \{ \phi_{g}(p) | g\in G\}$, all points which are related to $p$ by an ${\ensuremath{SL(2,\mathbb{R})\times U(1)}}$ transformation. $Gp$ is a 3-dimensional submanifold of $\mathcal{M}$, and the collection of all the orbit spaces forms a foliation. In this case, each leaf $\Sigma_{u}$ is a surface o... | 2,492 | 4,403 | 2,442 | 2,145 | null | null | github_plus_top10pct_by_avg |
tivity of an NMR style experiment using Xe, the blue line is the sensitivity using $^3\text{He}$. The dashed lines show the limit from magnetization noise for each sample. These lines assume the parameters in Table \[Tab: experiments\]. The ADMX region shows the part of QCD axion parameter space which has been covered ... | 2,493 | 3,751 | 3,387 | 2,537 | null | null | github_plus_top10pct_by_avg |
rst, **generic information**: the latent patterns in the AOG were pre-fine-tuned using massive object images in a category, instead of being learned from a few part annotations. Thus, these patterns reflected generic part appearances and did not over-fit to a few part annotations.
Second, **less model drifts:** Instea... | 2,494 | 400 | 2,887 | 2,476 | null | null | github_plus_top10pct_by_avg |
times
K(\Z/2,1)$ is given by the composition $L^{62}_{\I_3} \to
K(\I_3,1) \stackrel{\pi_{b,\ast}}{\longrightarrow} K(\I_b,1)
\subset K(\Z/4,1) \times K(\Z/2,1)$, where $\kappa_1 \in
K(\I_b;\Z/2)$ determines the inclusion $K(\I_b,1) \subset
K(\Z/2,1) \subset K(\Z/4,1)$.
Let us formulate the results in the following lem... | 2,495 | 1,137 | 2,023 | 2,226 | null | null | github_plus_top10pct_by_avg |
)\end{array}$$
with the last two being disjoint unions, and $A$ is closed iff $A$ contains all its cluster points, $\textrm{Der}(A)\subseteq A$, iff $A$ contains its closure. Hence $$\begin{gathered}
A=\textrm{Cl}(A)\Longleftrightarrow\textrm{Cl}(A)=\{ x\in A\!:((\exists N\in\mathcal{N}_{x})(N\subseteq A))\vee((\foral... | 2,496 | 3,716 | 3,496 | 2,421 | null | null | github_plus_top10pct_by_avg |
\], which we restate here in a stronger form.
\[bigmatroid\] Let $s \ge 0$ be an integer and $M$ be a matroid. Either
- $M$ has a $U_{s,2s}$-minor,
- $M$ has an $s U_{1,2}$-minor, or
- $M$ has a minor $N$ so that $|M| - |N| \le 4^{4^{2s^2}}$ and every element of $N$ is a loop or a coloop.
The result is trivi... | 2,497 | 840 | 1,811 | 2,278 | null | null | github_plus_top10pct_by_avg |
y Theorem \[mixhyp\] (since ${\mathbb{E}}{\mathbf{v}}_i \in \Lambda_+$ for all $i$ by convexity). In particular the polynomial ${\mathbb{E}}f({\mathsf{X}}_1,\ldots, {\mathsf{X}}_m;t)$ is real–rooted.
The second assertion is an immediate consequence of the first combined with Lemma \[rk1le\].
Bounds on zeros of mixed ... | 2,498 | 857 | 1,345 | 2,563 | null | null | github_plus_top10pct_by_avg |
-1 \right) E_i \cdot E_j.$$ Following the Hirzebruch-Jung method, one obtains two exceptional divisors $E_1$ and $E_2$ and the following numerical data: $$A = \begin{pmatrix} -2 & 1 \\ 1 & -3 \end{pmatrix},
\quad \nu_1 = \dfrac{4}{5}, \quad \nu_2 = \dfrac{3}{5},
\quad \b_1 = -\dfrac{11}{5}, \quad \b_2 = -\dfrac{2}{5},$... | 2,499 | 1,461 | 2,289 | 2,228 | null | null | github_plus_top10pct_by_avg |
1}}{a_{t-1}}\left({\mathbf{x}}_{t}^\top C_{t-1}{\mathbf{x}}_{t}+{\mathbf{x}}_{t}^\top{\mathbf{1}}\right),
~2 a_{t-1}\right] \quad & \mathrm{otherwise}.\\
\end{array}
\right.\label{eq:ObsMarginal}\end{aligned}$$ Here, $\mathsf{t}(y; m, v, n)$ denotes the Student’s t-density function on $n$ degrees of freedom... | 2,500 | 2,783 | 2,434 | 2,240 | 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.