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 |
|---|---|---|---|---|---|---|---|
paired log likelihoods $$\begin{aligned}
\label{eq:likelihood_0}
\Lrb(\theta) &=&
\sum_{j=1}^n \sum_{a = 1}^{\ell_j}
\,\lambda_{j,a} \, \Big\{ \sum_{(i, \i) \in E_{j,a}}
\, \Big( \theta_{\i} - \log \Big(e^{\theta_i} + e^{\theta_{\i}}\Big) \,\Big)\, \Big\} \;,\end{aligned}$$ where $E_{j,a}$’s are... | 2,601 | 1,344 | 2,192 | 2,342 | null | null | github_plus_top10pct_by_avg |
mes 1) \underline{M}^{\prime}(R)$ of $\underline{M}^{\prime}\otimes\kappa$};\\
\textit{the subfunctor $\tilde{M}^1:R\mapsto 1+\underline{\pi M^{\prime}}(R)$ of $\mathrm{Ker~}\tilde{\varphi}$}.
\end{array} \right.$$ Here, by $1+\underline{\pi M^{\prime}}(R)$, we mean the image of $\underline{\pi M^{\prime}}(R)$ insi... | 2,602 | 2,126 | 1,589 | 2,418 | null | null | github_plus_top10pct_by_avg |
cisely, the aforesaid regular domain is taken to be the half-space that contains $D$ with boundary hyperplane that is tangent to both the current maximal sphere and $D$. It is the use of a half-space that allows us to work with unbounded domains but which forces the assumption that $D$ is convex. With a little more car... | 2,603 | 1,291 | 2,915 | 2,561 | null | null | github_plus_top10pct_by_avg |
yperbolic with respect to any vector ${\mathbf{e}}\in {\mathbb{R}}_{++}^n=(0,\infty)^n$: $$h(t{\mathbf{e}}-{\mathbf{x}}) = \prod_{j=1}^n (te_j-x_j).$$
2. Let $X=(x_{ij})_{i,j=1}^n$ be a matrix of $n(n+1)/2$ variables where we impose $x_{ij}=x_{ji}$. Then $\det(X)$ is hyperbolic with respect to $I=\diag(1, \ldots, 1)$... | 2,604 | 2,266 | 2,508 | 2,454 | null | null | github_plus_top10pct_by_avg |
with $f_\alpha\circ L_\alpha^{-1}$ on $a_{s\upharpoonright\alpha^+}\setminus n_\alpha$. Thus if $\beta\in L_\delta[a_s\setminus n_\delta]\cap L_{\alpha}[a_{s\upharpoonright\alpha^+}\setminus n_\alpha]$, then $h(\beta)=\dot{f}(\alpha)=\dot{f}(\delta)$. This completes the proof that the space is normal.
The strategy at... | 2,605 | 2,663 | 2,807 | 2,491 | 3,640 | 0.771018 | github_plus_top10pct_by_avg |
(\left\langle \mathbf{A}_{1,1}\mathbf{B}_{1,1}\right\rangle \!,\left\langle \mathbf{A}_{1,2}\mathbf{B}_{1,2}\right\rangle \!,\left\langle \mathbf{A}_{2,1}\mathbf{B}_{2,1}\right\rangle \!,\left\langle \mathbf{A}_{2,2}\mathbf{B}_{2,2}\right\rangle \right)\\
\le6-s_{1}\!\left(\left\langle \mathbf{A}_{1,1}\mathbf{A}_{1,2}\... | 2,606 | 1,435 | 2,963 | 2,470 | null | null | github_plus_top10pct_by_avg |
pha \in R_{H,+} \\ \alpha \not\perp \Delta_X}}} \frac {\langle \alpha, \mu \rangle} {\langle \alpha, \rho \rangle}
\right) k^{R_X} +
O(k^{R_X-1})
\end{aligned}$$ for the representations that occur in ${\mathbb C}[X]$. The coefficient $P(\mu) = \prod_{\alpha \in R_{H,+}, \alpha \not\perp \Delta_X} {\langle \al... | 2,607 | 3,333 | 2,445 | 2,288 | null | null | github_plus_top10pct_by_avg |
e., for any quantity $X$, the perturbation is $\delta{\tilde X} = \delta X \exp\{{i(k_rr+k_z z)-i\omega t}\}$), we will suppose that the wavevectors obey three conditions: that $k = (k_z^2 + k_r^2)^{1/2} \ll \kappa \rho$; that $k_z \gg 1/h$; and that $k_r \gg 1/r$. The first limit means that the diffusion approximation... | 2,608 | 4,821 | 1,616 | 2,121 | null | null | github_plus_top10pct_by_avg |
\Gamma'=\partial G\times S$ and $\Gamma'_{-}=\{(y,\omega)\in \partial G\times S\ |\ \omega\cdot\nu(y)<0\}$. Choose any $\eta\in C^1_0(I^\circ)$ and $\theta\in C^1(\ol G\times S)$ such that ${\rm supp}(\theta)\cap \Gamma'$ is a compact subset of $\Gamma_-'$. Then $w(x,\omega,E):=\theta(x,\omega)\eta(E)\in C^1(\ol{G}\tim... | 2,609 | 904 | 1,851 | 2,498 | null | null | github_plus_top10pct_by_avg |
} {2^{14} d\beta^4\log\lrp{\frac{2^{14} d\beta^4}{\epsilon^4L^2}}}}$, assume additionally that $n=T/\delta$ is an integer.\
Let $\bx_t$ and $\bw_t$ have dynamics as defined in and respectively, and suppose that the initial conditions satisfy $\E{\lrn{\bx_0}_2^2}\leq R^2 + \beta^2/m$ and $\E{\lrn{\bw_0}_2^2}\leq R^2 + \... | 2,610 | 2,461 | 1,955 | 2,335 | null | null | github_plus_top10pct_by_avg |
qn: lim filter}$$ and $${\textstyle \textrm{adh}(\mathcal{F})=\{ x\in X\!:(\forall N\in\mathcal{N}_{x})(\forall F\in\mathcal{F})(F\bigcap N\neq\emptyset)\}}\label{Eqn: adh filter}$$
*are respectively the sets of* *limit points* *and* *adherent* *points* *of $\mathcal{F}$*[^28]*.$\qquad\square$*
A comparison of Eqs. (... | 2,611 | 1,121 | 2,841 | 2,571 | 903 | 0.798076 | github_plus_top10pct_by_avg |
0.068
BLB($n^{0.6}$) 0.000 0.000 0.000 0.000 0.000 0.000 0.000
BLB($n^{0.8}$) 0.000 0.000 0.000 0.000 0.000 0.000 0.002
SDB($n^{0.6}$) 0.000 0.000 0.000 ... | 2,612 | 6,013 | 725 | 1,530 | null | null | github_plus_top10pct_by_avg |
ithmetic, commonly found in Prolog implementations.
Given a program, containing integer arithmetics, and a class of queries, described using modes, we infer a subset of these queries for which we prove existential non-termination (i.e. the derivation tree for these queries contains an infinite path). The inference and... | 2,613 | 791 | 1,726 | 2,003 | null | null | github_plus_top10pct_by_avg |
'}(G)}\cap A}(y)}={{\operatorname}{C}_{{{\operatorname}{O}_{p'}(A)}}(y)}$ and $A_0:=\langle y \rangle \times C$. Then $A=(N\cap A)A_{0}$ and $G=AN=A_{0}N$.
By the minimal choice of $G$, we deduce that $G/N\cong A/A\cap N$ is $p$-decomposable. Hence $[{{\operatorname}{O}_{p'}(G)}\cap A, \langle y\rangle ]\leq N\cap A$... | 2,614 | 1,817 | 2,277 | 2,293 | null | null | github_plus_top10pct_by_avg |
o $L_n \subset {\mathbb{R}^2}$. Suppose that for a transformation ${\phi}_{n}$ on $L_n$ defined as $${\phi}_{n}(r \cos \frac{2k\pi}{n}, r \sin \frac{2k\pi}{n})=(r \cos \frac{2(k+1)\pi}{n}, r \sin \frac{2(k+1)\pi}{n})$$ there exists a $C^s$ diffeomorphism ${\Phi}_{n}$ satisfying ${\phi}_n \circ q=q \circ {\Phi}_n$ and t... | 2,615 | 988 | 1,839 | 2,355 | null | null | github_plus_top10pct_by_avg |
\\
\mathcal{D}_{Ru} & \frac{i m u \left(u^4+6 u^2-3\right)}{4 \left(u^2-1\right) \left(u^2+1\right)^2} & -\frac{i h m \left(u^4+6 u^2-3\right)}{8 \left(u^4-1\right)} \\
\mathcal{D}_{uu} & -\frac{i (h+1) m \left(u^4+6 u^2-3\right)}{4 \left(u^2-1\right)^2 \left(u^2+1\right)} & \frac{i m u \left(u^2+3\right)}{2 \left(... | 2,616 | 2,442 | 2,207 | 2,403 | null | null | github_plus_top10pct_by_avg |
ions are twofold: firstly, the choice of prior is necessary for certain tractable operations but does not reflect true prior belief; secondly, prior specification does not lead conveniently and efficiently to sequential inference yet a simple approximation achieves this goal. An overview of the methodology is first pro... | 2,617 | 938 | 2,623 | 2,475 | 1,133 | 0.79385 | github_plus_top10pct_by_avg |
B2‐A1** −0.41 −0.43 −0.37 −0.41 0.46 0.52 0.05 −0.17
**B2‐A2** −0.45 −0.41 −0.44 −0.42 −0.45 −0.37 −0.3... | 2,618 | 4,446 | 2,770 | 2,415 | 2,225 | 0.781668 | github_plus_top10pct_by_avg |
rt of particles in $G_{\rm e}$ is governed by the system of equations on $G_{\rm e}\times S\times I$, $$\begin{gathered}
\omega\cdot\nabla_x\Psi_1+\Sigma_{{\rm e},1}\Psi_1-K_{{\rm e},1}\Psi=0,\label{ref2a}\\
-{{\frac{\partial (S_{{\rm e},j}\Psi_j)}{\partial E}}}+\omega\cdot\nabla_x\Psi_j+\Sigma_{{\rm e},j}\Psi_j-K_{{\r... | 2,619 | 1,665 | 1,153 | 2,696 | null | null | github_plus_top10pct_by_avg |
2 + {\mathbf{k}}_3, {\mathbf{k}}_2 - {\mathbf{k}}_3 \}$; the most general solution can be then constructed as $$\begin{aligned}
{\mathbf{u}}_1({\mathbf{x}}) & = & \mathbf{A}{\textrm{e}^{2\pi i[1,1,0]\cdot{\mathbf{x}}}} +
\mathbf{B}{\textrm{e}^{2\pi i[1,-1,0]\cdot{\mathbf{x}}}} +
... | 2,620 | 5,301 | 524 | 1,966 | null | null | github_plus_top10pct_by_avg |
proof of Theorem \[mult-thm\] for $\v_\muhat$ is indivisible is given in [@hausel-letellier-villegas] by expressing $\langle
\Lambda\otimes R_\muhat,1\rangle$ as the Poincaré polynomial of a comet-shaped quiver variety. This quiver variety exists only when $\v_\muhat$ is indivisible.
In [@Hiss] the authors discusses s... | 2,621 | 2,186 | 2,240 | 2,186 | null | null | github_plus_top10pct_by_avg |
c connective $N$ in $\mathcal{L}_{Q}^{P}$ (it has already been proved in Ref. 27 that this principle does not hold in the general language $\mathcal{L}^{P}$).
It is also interesting to note that the justification values of different elementary afs, say $\vdash E(x)$ and $\vdash F(x)$, must be different for some state ... | 2,622 | 3,201 | 2,600 | 2,455 | null | null | github_plus_top10pct_by_avg |
$\ker\alpha(0)$. Fans and stars are studied in [@MR2002d:14084], and are the only kinds of curves with small orbit that consist of lines; they are items (1) through (5) in our classification of curves with small orbit, see §\[appendix\].
For types II—V we choose coordinates so that $p=(1:0:0)$ is a point of ${{\mathsc... | 2,623 | 1,272 | 2,481 | 2,468 | 892 | 0.798194 | github_plus_top10pct_by_avg |
\times {\mathbb Z}_2$ partition functions are very different, despite the fact that the theories differ by a trivially-acting gauged ${\mathbb Z}_2$.
In fact, in the example above, one can show that the partition function of the $D_4$ orbifold is the same as the partition function of a disjoint union of two ${\mathbb... | 2,624 | 961 | 2,333 | 2,377 | null | null | github_plus_top10pct_by_avg |
e additional non-trivial constraints that survive the orientifold projection but are not such that the upstairs and downstairs indices are all different. In the IIB case, from eq. one gets the components $(Q \cdot H_3-P_1^2 \cdot F_3)^{x^j}_{x^i y^i x^j}$ and $(Q \cdot H_3-P_1^2 \cdot F_3)^{y^j}_{x^i y^i y^j}$, which i... | 2,625 | 1,054 | 3,053 | 2,450 | 2,368 | 0.780458 | github_plus_top10pct_by_avg |
particular, the bounds are valid unconditionally with respect to the joint distribution of the entire sample and of the splitting outcome.
Also, in the proof $C$ denotes a positive positive that may depend on $A$ only but not on any other variable, and whose value may change from line to line.
[**Proof of .**]{} As ... | 2,626 | 1,905 | 2,469 | 2,238 | null | null | github_plus_top10pct_by_avg |
ec{p}\,'}}{E'+M_N}
\end{array}\right)\,.\end{aligned}$$ The relativistic propagator of a baryon with mass $M_B$ and momentum $p$ reads $$\frac{i}{\cancel{p}-M_B+i\epsilon}
=\frac{i(\cancel{p}+M_B)}{p^2-M_B^2+i\epsilon} \,.$$ Making the heavy baryon expansion with these spinors and propagators introduces mass difference... | 2,627 | 1,556 | 974 | 2,517 | null | null | github_plus_top10pct_by_avg |
It is useful to derive a closed analytic expression for the self-energy of the molecular orbital GF [@Kolodzeiski2017] which is used to increase the precision of the NRG GF [@BullaHewsonPruschke98] as well as analyze the results. We consider the system Hamiltonian $H_S$ $$\begin{aligned}
H_S&=& \sum_{\k\sigma} \e_{\k\... | 2,628 | 1,491 | 2,574 | 2,515 | null | null | github_plus_top10pct_by_avg |
{\v \in \Gamma_P} (\nu_\v-1) E_\v.
\end{aligned}$$ Clearly one has the relations $\hat{\mathcal{C}} = \sum_{j=1}^r n_j \hat{\mathcal{C}}_j$ and $m_\v = \sum_{j=1}^r n_j m_{\v j}$. Finally consider the divisor $L^{(k)}$ corresponding to the covering $\rho_Y$, see Theorem \[thm:Esnault\].
\[thm:h2Lk\] The dual space $H^... | 2,629 | 2,018 | 2,296 | 2,241 | null | null | github_plus_top10pct_by_avg |
revious papers that the coherence between active and sterile, and sterile and sterile states are not maintained for sterile mass differences larger than $0.1$ eV$^2$. The effect of decoherence is taken into account by making average over the fast oscillations. We feel it desirable for the current treatment be replaced ... | 2,630 | 1,245 | 2,208 | 2,705 | null | null | github_plus_top10pct_by_avg |
hermore, assume that the stopping powers $S_j$, where $j=2,3$, satisfy $$\begin{aligned}
& S_j\in C^2(I,L^\infty(G)), \label{ass5} \\[2mm]
& \nabla_x S_j\in L^\infty(G\times I), \label{ass5n} \\[2mm]
& \kappa_j:=\inf_{(x,E)\in \ol{G}\times I} S_j(x,E) > 0. \label{ec4}\end{aligned}$$
Let $f\in C^1(I,L^2(G\times S)^3)$ ... | 2,631 | 1,813 | 1,025 | 2,637 | null | null | github_plus_top10pct_by_avg |
0$ sites keeping per block on average $400$ states for gapped phases and $600$ states for gapless ones), and bosonization techniques to unveil the low-energy behavior of model . For $j<1/4$, we employ standard bosonization transformations [@Giamarchi], with an additional oscillating factor $b_i\to (-1)^ie^{i\sqrt{\pi}\... | 2,632 | 1,772 | 2,770 | 2,433 | 2,027 | 0.783356 | github_plus_top10pct_by_avg |
X,k}(k \mu) \, \dim V_{k \mu}
\geq~\sum_{\mathclap{\mu \in K \cap \frac 1 k \Lambda^*_{H,+}}} m_{H,X,k}(k \mu) \, \dim V_{k \mu} \\
\geq~&D \, k^{R_X} \sum_{\mathclap{\mu \in K \cap \frac 1 k \Lambda^*_{H,+}}} m_{H,X,k}(k \mu)
\sim D \, k^{R_X + d_X} \int_K d\operatorname{DH}_X.
\end{aligned}$$ We conclud... | 2,633 | 2,453 | 2,670 | 2,205 | null | null | github_plus_top10pct_by_avg |
corresponding to the $i$-th element of ${\bf f}_{I'}$.
[^3]: It is the “forehead” part for birds in the CUB200-2011 dataset.
[^4]: Two latent patterns may select the same neural unit
[^5]: We used part boxes annotated during the QA process to learn a fast-RCNN for part detection. Given the inference result $\Lambda... | 2,634 | 2,062 | 892 | 1,944 | 3,412 | 0.772575 | github_plus_top10pct_by_avg |
critical assumption in their model is that the ion and electron densities can be written as a function of the local electrostatic potential alone. Although this assumption sounds reasonable for instance in the collisionless limit where OML theory should apply, its validity must be tested carefully. On the other hand, ... | 2,635 | 2,747 | 3,732 | 2,746 | 3,366 | 0.77285 | github_plus_top10pct_by_avg |
abelian group $G$ in a way that naturally generalizes the relationship between circulant matrices and cyclic groups. It is shown that, under mild conditions, when the size of the group $G$ goes to infinity, the spectral measures of such random matrices approach a deterministic limit. Depending on some aspects of the st... | 2,636 | 977 | 1,213 | 2,518 | null | null | github_plus_top10pct_by_avg |
ever, it is impossible that a mapping $\xi ^{\prime }$ exists such that $\xi ^{\prime }(x)\in S^{\prime }$, with $S\neq S^{\prime }$ and $\sigma (\xi )=\sigma (\xi ^{\prime })$, since $\sigma (\xi )$ and $\sigma
(\xi ^{\prime })$ are defined on different domains ($\mathcal{E}_{S}\cup
\mathcal{E}_{S}^{\bot }$ a... | 2,637 | 2,262 | 747 | 2,326 | null | null | github_plus_top10pct_by_avg |
s for the problem considered remains an open question.
Single Continuous Slowing Down Equation {#single-eq}
=======================================
Preliminaries {#presingle-eq}
-------------
At first we consider a [*single CSDA transport equation*]{} given by \[se1\] -[E]{}+\_x+- K= f GSI, where the solution satisf... | 2,638 | 312 | 2,447 | 2,732 | null | null | github_plus_top10pct_by_avg |
ned}
\label{equ:49-Gamma-eff}
\Gamma_\text{eff} &=&\Gamma_0 + \Im[\Sigma_\sigma(-i0^+)] \end{aligned}$$ must hold using the general property $G_{d_{0\sigma}, d^\dagger_{0\sigma} }(z)=[ z-\e_{d \sigma} -\Delta(z) -\Sigma_\sigma(z)]^{-1}$, where we have divided the total self-energy of the molecular orbital $\Sigma_{\rm... | 2,639 | 1,175 | 1,800 | 2,496 | null | null | github_plus_top10pct_by_avg |
$S_j$ and $S_k$ are the other geodesics besides $S_i$.
The notion of hyperbolicity makes sense even for metric spaces which are not literally geodesic, but when a reasonable notion of geodesic segment can be defined. This is the case e.g. for finitely generated groups with word metrics, where a geodesic segment betwe... | 2,640 | 4,279 | 2,699 | 2,214 | 4,104 | 0.768083 | github_plus_top10pct_by_avg |
ory as a generalized YM theory.
The translation symmetry implies that the commutators are of the form = \_[\_3]{} f(\_1, p\_1, \_2, p\_2, \_3) T(\_3, p\_1 + p\_2), \[ansatz\] and the Lorentz symmetry implies that the structure constants are Lorentz-invariant functions of the vectors $\teps_1, \teps_2, \teps_3, p_1, p_... | 2,641 | 1,461 | 1,417 | 2,585 | null | null | github_plus_top10pct_by_avg |
.$$ Let us prove the reverse inclusion.\
Let $\alpha \in S' \cap ({\cal R}\times{\cal R})^{\leq n}$. Let $\beta$ be the longuest word in ${{\rm PREF}}(\alpha) \cap S$.\
If $\beta = \alpha$, then $\alpha \in S$, as required.\
Otherwise $\alpha \in S'-S$. By condition E2 of definition \[def-extension\], there exists some... | 2,642 | 1,606 | 389 | 2,922 | 1,990 | 0.78378 | github_plus_top10pct_by_avg |
\hat{\mathcal{H}}_{+}^{[2]}$$ with $$\label{hblocks+}
\begin{aligned}
& \hat{\mathcal{H}}^{[1]}_{+} =
\bigoplus_{n = 0}^{m - 1} \langle n , g |\hat{\mathcal{H}}^{(m)}_{+} | n , g \rangle
= \hbar
\bigoplus_{n = 0}^{m - 1} \left( \nu n - \tfrac{\omega_0}{2} \right), \\
& \hat{\mathcal{H}}... | 2,643 | 5,212 | 246 | 2,142 | null | null | github_plus_top10pct_by_avg |
tSQLvar = 0;
string strSeperator = string.Empty;
foreach (KeyValuePair<int, string> benefit in benefits)
{
sb.AppendFormat(" {0} BenefitID=@benerfit{1}", strSeperator, intSQLvar);
intSQLvar++;
strSeperator = "OR";
}
SqlConnection con = new Sq... | 2,644 | 3,652 | 42 | 2,130 | 45 | 0.832029 | github_plus_top10pct_by_avg |
0\sigma},d^\dagger_{0\sigma}}(z)$ [@BullaHewsonPruschke98].
As shown by Hewson and Meyer [@HewsonMeyer02], the self-energy $\Sigma_\sigma(z)= [UF_\sigma(z) +\lambda_d M_\sigma(z)] /G_{d_{0\sigma},d^\dagger_{0\sigma}}(z)$ maintains Fermi liquid properties and its imaginary part vanishes for $T,\w\to 0$ for a coupling o... | 2,645 | 1,024 | 2,868 | 2,441 | 3,859 | 0.769669 | github_plus_top10pct_by_avg |
e convenient than from the computational point of view and will be used in the present study. We note, however, that since the RHS of this inequality cannot be expressed entirely in terms of properties of the initial data, this is [*not*]{} in fact an a priori estimate. Estimate also allows us to obtain a condition on ... | 2,646 | 1,170 | 2,968 | 2,565 | 2,075 | 0.783013 | github_plus_top10pct_by_avg |
ines (including those without fine-tuning). *Fast-RCNN (1 ft)* and *CNN-PDD* used the cropped objects as the input of the CNN; *SS-DPM-Part*, *PL-DPM-Part*, *Part-Graph*, and *Interactive-DPM* used object boxes and part boxes to learn models. *CNN-PDD-ft*, *Fast-RCNN (2 fts)*, and methods based on *fc7* features used o... | 2,647 | 1,541 | 1,423 | 1,821 | null | null | github_plus_top10pct_by_avg |
which gives a contradiction.
- Since $k=p>1$, then $A\cap M_{\Delta}=1={{\operatorname}{C}_{{{\operatorname}{O}_{p'}(A)}}(M_{\Delta})}$.
Let $x\in A\cap M_{\Delta}$ of prime power order, which is a $p$-regular element. Then by hypotheses there exists $n\in N$ with $x\in{{\operatorname}{C}_{G}(\langle y\rangle^... | 2,648 | 1,493 | 2,042 | 2,478 | null | null | github_plus_top10pct_by_avg |
\tau \; \langle \nabla\cdot F_1(t) \;
\exp(-\tau \nabla\cdot F_0) \; \nabla\cdot F_1(t-\tau) \rangle
\nonumber \\
\exp(\tau\nabla\cdot F_0) \} \; p(u,t) \; \; .\end{aligned}$$
The operator $\exp(-\tau\nabla\cdot F_0)$ in the above equation provides the solution of the equation $$\frac{\partial f(u,t)}{\partial t} = -... | 2,649 | 3,175 | 2,646 | 2,440 | null | null | github_plus_top10pct_by_avg |
ap.
I was wondering, why can it be caused? I posted another post a while ago because I wanted to include this problem in a JSFiddle but I couldn't work out how to include the fonts files in the JSFiddle so the icons don't appear there.
Does anyone has a slight idea about what can I do to fix it?
.containerOfSites {
... | 2,650 | 5,731 | 96 | 1,884 | 88 | 0.826977 | github_plus_top10pct_by_avg |
aystyle\frac{\epsilon}{m}, \ \cdots,\ \lambda
y_{m}-\frac{\epsilon}{m},\ \lambda y_{m+1}+\epsilon+\delta,\\ \\
&&\lambda y_{m+2}, \ \cdots,\lambda y_{d-1},\ \lambda
y_{d}-\epsilon-\delta,\ \displaystyle \lambda
y_{d+1}+\frac{\epsilon}{\triangle}, \\ \\
&& \cdots,\ \lambda
y_{n-t}+\displaystyle\frac{\epsilon}{\triangle}... | 2,651 | 1,845 | 2,270 | 2,352 | null | null | github_plus_top10pct_by_avg |
ion 4, we compute the entropy bounds for this algorithm. A natural generalization of adaptive codes is presented in Section 5. Finally, the last section contains a few concluding remarks. Before ending this introductory section, let us present some useful notation used throughout the paper [@rs1; @as1], and then review... | 2,652 | 3,154 | 3,368 | 2,577 | 981 | 0.796431 | github_plus_top10pct_by_avg |
(UX)^*_{\alpha n} (UX)_{\beta n}
\nonumber \\
&\times&
\left\{ (UX)^{\dagger} A W \right\}_{k K}
\left\{ W ^{\dagger} A (UX) \right\}_{K k}
\left\{ (UX)^{\dagger} A W \right\}_{k K}
\left\{ W ^{\dagger} A (UX) \right\}_{K l}
\nonumber \\
&+&
\sum_{n}
\sum_{k \neq l }
\sum_{K}
\biggl[
-
\frac{ (ix) }{ ( \Delt... | 2,653 | 3,025 | 2,932 | 2,671 | null | null | github_plus_top10pct_by_avg |
lem:3.1}$, we have the following: $$\begin{aligned}
\operatorname{{E}}[\Pe(Z)]
&= \frac{(k_{1} + k_{2}) b}{2 \G(a)}
\G\left( 2a \right), \label{E[L(Z)]} \\
\operatorname{{V}}[\Pe(Z)]
&= \frac{(k_{1}^{2} + k_{2}^{2}) b^{2} \G(3a)}{2 \G(a)}
- \frac{(k_{1} + k_{2})^{2} b^{2} \G(2a)^{2}}{4 \G(a)^{2}}. \label{V[L(Z)]}... | 2,654 | 4,723 | 1,682 | 2,179 | null | null | github_plus_top10pct_by_avg |
e other hand, $$\begin{aligned}
\label{wkpment2}
(\gamma-1)\left|\nabla_i\nabla_jv+\frac{\eta_K(t)}{n(\gamma-1)}g_{ij}\right|^2
=&(\gamma-1)|\nabla\nabla v|^2+\frac{2\eta_K}{n}\Delta v+\frac{\eta_K^2}{n(\gamma-1)}.\end{aligned}$$ Putting into , we get
$$\begin{aligned}
\label{wkpment3}
&\frac{d}{dt}\mathcal{W}_K(t)\no... | 2,655 | 2,534 | 2,740 | 2,521 | null | null | github_plus_top10pct_by_avg |
grightarrow \underline{H} .$$
We start with any $m\in \underline{M}^{\ast}(R)$ and $f\in \underline{H}(R)$. In order to show that $\underline{M}^{\ast}(R)$ acts on the right of $\underline{H}(R)$ by $f\circ m = \sigma({}^tm)\cdot f\cdot m$, it suffices to show that $f\circ m$ satisfies conditions (a) to (e) given in t... | 2,656 | 2,787 | 2,411 | 2,386 | 3,371 | 0.772823 | github_plus_top10pct_by_avg |
bel{eq:Bmarginal}$$ for $i,j\in\text{\{1,2\}}.$
Writing the inequalities and in terms of these expectations rather than in terms of probabilities is the most economic way of presenting the 128 non-trivial inequalities of the system, as the marginal probabilities $a_{1},a_{2},b_{1},b_{2}$ (or expectations $\left\langle... | 2,657 | 3,154 | 3,449 | 2,646 | null | null | github_plus_top10pct_by_avg |
Typical program for hospital bed linen 50 ppm Chlorine, 54 ppm peracid, 100 ppm peroxid *Clostridium difficile* spores Hellickson & Owens, 2007... | 2,658 | 3,813 | 2,485 | 2,429 | null | null | github_plus_top10pct_by_avg |
g.
\[prop:normalize\] A crank form expression of a seat-plan is moved to its standard expression.
Now we prove that any word in the alphabet ${\cal L}_n^1$ is moved to a crank form expression. By the above proposition, we will find that any word can be moved to its standard expression.
If ${\cal C}(\mathbb{M},\sigma... | 2,659 | 1,159 | 1,966 | 2,361 | 3,831 | 0.769798 | github_plus_top10pct_by_avg |
tively. A label [$y\in\{+1,-1\}$]{} indicates whether $I$ contains the target part. The AOG estimates the probability of object $I$ containing the target part as [${\bf Q}(y\!=\!+1|I)\!=\!\frac{1}{Z}\exp[\beta S_{top}]$]{}, where $Z$ and $\beta$ are parameters for scaling (see Section \[sec:implement\] for details); [$... | 2,660 | 2,467 | 2,553 | 2,553 | 2,981 | 0.775625 | github_plus_top10pct_by_avg |
d}}_\#)$ are taken pointwise: for every $n$, we have an exact sequence $$0 \to ({\operatorname{{\sf Ker}}}\phi)([n]) \to M_\#([n]) \overset{\phi}{\to}
M'_\#([n]) \to ({\operatorname{{\sf Coker}}}\phi)([n]) \to 0.$$ The transtition maps $\iota_f$ for ${\operatorname{{\sf Ker}}}\phi$ are obtained by restriction from tho... | 2,661 | 2,110 | 2,225 | 2,417 | 2,340 | 0.780741 | github_plus_top10pct_by_avg |
e each potential is expressed through one function $W_{1}(r)$: $$\begin{array}{ll}
\bar{V}_{1}(r) =
W_{1}^{2}(r) - \displaystyle\frac{\hbar}{\sqrt{2m}}
\displaystyle\frac{d W_{1}(r)}{dr} + C_{1}, &
\bar{V}_{2}(r) =
W_{1}^{2}(x) + \displaystyle\frac{\hbar}{\sqrt{2m}}
\displaystyle\frac{d W_{1}(r)}{dr} + C_{1... | 2,662 | 2,952 | 3,046 | 2,507 | 2,428 | 0.779831 | github_plus_top10pct_by_avg |
or instance, the situation where there is no background cosmological constant ($\Lambda=0$). In this case we easily obtain $$a^3(z)={6\pi G A \over (z_- -z_+)^5}(C-z)^2
={{3\over 4}\pi^3 \zeta'_R(-4) G_5 }{(z_0-z)^2\over(z_- -z_+)^5},$$ where the brane tensions are given by $$2\pi G \sigma_{\pm}=\pm (C-z_{\pm})^{-1}$$ ... | 2,663 | 4,273 | 2,674 | 2,307 | 3,803 | 0.770014 | github_plus_top10pct_by_avg |
s in this context, in accordance with section \[m-d\].
Given ${\bf f}=({\bf f}_1, {\bf f}_2, {\bf f}_3)\in L^2(G\times S\times I)^3$, and ${\bf g}\in T^2(\Gamma_-)\times H^1(I,T^2(\Gamma_-'))^2$, find $\phi=(\phi_1,\phi_2,\phi_3)\in L^2(G\times S\times I)^3$ which satisfies the system of equations of $G\times S\times ... | 2,664 | 1,600 | 2,458 | 2,555 | null | null | github_plus_top10pct_by_avg |
}-D \delta^{ij} \partial_i u \partial_j u -m^2_{\text{eff}}u^2 ]$$ where $$m^2_{\text{eff}} = - \frac{\sqrt{D}}{a} \left( \frac{a}{\sqrt{D}} \right)^{''} .$$ Till now the considerations of the gravitational waves has been purely classical. The next step is the quantisation of the classical gravitational waves what bri... | 2,665 | 4,080 | 2,540 | 2,298 | null | null | github_plus_top10pct_by_avg |
of $(\textrm{Map}(X,Y),\mathcal{T})$ to be $$\begin{gathered}
B((x_{i}),(V_{i});(y_{i}),(U_{i}))=\{ g\in\mathrm{Map}(X,Y)\!:\\
(g(x_{i})\in V_{i})\wedge(g^{-}(y_{i})\bigcap U_{i}\neq\emptyset)\textrm{ },i=1,2,\cdots,I\},\label{Eqn: func_bi}\end{gathered}$$
where $(x_{i})_{i=1}^{I},(V_{i})_{i=1}^{I}$ are as in that exa... | 2,666 | 1,602 | 2,474 | 2,494 | 2,296 | 0.781099 | github_plus_top10pct_by_avg |
ement at time $t$, and $U$ the uniform distribution: $$P(0) = \frac{1}{2}+ \gamma, \qquad P(1) = \frac{1}{2}- \gamma, \qquad U(0) = U(1) = \frac{1}{2},$$ where $$\gamma = \frac{1}{4}\left[e^{\frac{(-p-\alpha)t}{2n}}(1-p/\alpha) + e^{\frac{(\alpha-p)t}{2n}}(1+p/\alpha)\right].$$ For $x = (x_1, \dots, x_n) \in \mathbb{Z}... | 2,667 | 4,292 | 2,691 | 2,345 | null | null | github_plus_top10pct_by_avg |
mathcal R}, k=1,2,\ldots,s$. Then $\phi$ is an $R$-module isomorphism from ${\mathcal R}$ onto ${\mathcal M}_1\times\cdots\times{\mathcal M}_s$. For any left $R$-module $M_j$, it is obvious that $M_1\times\cdots\times M_s$ is a left $R$-submodule of ${\mathcal M}_1\times\cdots\times{\mathcal M}_s$. Therefore there is a... | 2,668 | 1,412 | 2,429 | 2,411 | 1,784 | 0.785711 | github_plus_top10pct_by_avg |
detected in Energy Import/Export schedule.
Variances detected in SC Trades schedule.
LOG MESSAGES:
PARSING FILE -->> O:\Portland\WestDesk\California Scheduling\ISO Final
Schedules\2001041523.txt
---- Energy Import/Export Schedule ----
$$$ Variance found in table tblINTCHG_IMPEXP.
Details: (Hour: 23 / Pref... | 2,669 | 1,380 | 1,944 | 2,996 | null | null | github_plus_top10pct_by_avg |
us turn to an example which does not have such a realization, but which is relevant to (0,2) GLSMs. Take $\mathfrak{X} = {\mathbb P}^4_{[1,1,1,2,2]}$, with bundle $$0 \: \longrightarrow \: {\cal E} \: \longrightarrow \:
\oplus_a {\cal O}(n_a) \: \stackrel{F_a}{\longrightarrow} \: {\cal O}(m)
\: \longrightarrow \: 0$$ ... | 2,670 | 1,744 | 2,634 | 2,362 | 1,457 | 0.789324 | github_plus_top10pct_by_avg |
artial (S_0L\tilde{{\bf g}})}{\partial E}}}+CS_0(L\tilde{{\bf g}})\in L^2(G\times S\times I),$$ where the equality $\omega\cdot\nabla_x(L \tilde{{\bf g}})=0$ has been used again.
We additionally obtain the following a priori estimate.
\[cdd\] Under the assumptions of Theorem \[coth3-dd\] the solution $\phi$ of the pr... | 2,671 | 650 | 2,534 | 2,567 | null | null | github_plus_top10pct_by_avg |
e diagrams for the averaged ranking results of the metric Log-loss.](figures/results/crit_diff_loss_v2 "fig:"){width="\linewidth"}
The same process is applied to each of the $11$ classifiers for every metric. Table \[table:loss\] shows the final average results of all classifiers. Notice that the row corresponding to ... | 2,672 | 2,066 | 483 | 2,359 | null | null | github_plus_top10pct_by_avg |
mall. Taking the matter potential of CC reaction and the earth diameter, $AL = 6.2 \left(\frac{\rho}{5 \text{g/cm}^3}\right) \left(\frac{L}{6,400 \mbox{km}}\right)$. Therefore, $ALW^2$ can be order unity for $|W| \simeq 0.4$.
[^24]: This statement applies also to the original expression (\[P-beta-alpha-0th+2nd\]).
[... | 2,673 | 3,954 | 3,765 | 2,679 | null | null | github_plus_top10pct_by_avg |
bar \chi \chi \bar N N$ contact operator, but with an additional $1/E_r$ suppression in the cross section. This gives a similar phenomenology as a light mediator being exchanged at tree-level with derivative coupling.
Note that the relative importance of these two scattering processes is highly model dependent. For ex... | 2,674 | 603 | 2,054 | 2,520 | null | null | github_plus_top10pct_by_avg |
ons $$\label{qu}
{\cal Q}_n:=\left\{Q(x)=L\left(\frac{t-x}{h_{2,n}}f^{1/2}(x)\right)
f^{-1/2}(x)b(x;h_{1,n})I(|t-x|<h_{2,n}B):t\in D_r\right\}$$ are of VC type with the same characteristics $A$ and $v$, for envelopes of the order of $M(K,r)\|f''\|_\infty h_{1,n}^2$, where $M$ depends on $r$ and $K$ only (in particular,... | 2,675 | 1,876 | 2,617 | 2,360 | null | null | github_plus_top10pct_by_avg |
=\frac{\left\langle \sum_{j\in{\cal H}_{1}}N_{j}\left[\sum_{i\in{\cal H}_{0}}N_{i}H_{ij}\right]\right\rangle }{\left\langle \sum_{i\in{\cal H}_{0}}N_{i}^{2}\right\rangle },\label{eq:E2}$$
through the spawning process, this strategy has already been used for the calculation of reduced density matrices[@overy_unbiased_2... | 2,676 | 439 | 2,107 | 2,724 | 687 | 0.802339 | github_plus_top10pct_by_avg |
]_T
\,
\sigma_{d d}({\mbox{\boldmath $r$}}_1, {\mbox{\boldmath $r$}}_2,Y)
\, ,
\label{sigmatot}\end{aligned}$$ where $\Psi^{\gamma}$ and $\Psi^{V_i}$ are the light-cone wave functions of the photon and vector meson, respectively, and $T$ the transverse polarization. The variable ${\mbox{\boldmath $r$}}_1$ defines the ... | 2,677 | 599 | 1,920 | 2,523 | null | null | github_plus_top10pct_by_avg |
alization of the latter. In this subsection we shall review two early attempts in this direction and point out their shortcomings. The proper stochastic formulation shall be presented in next Section.
As we have said in Section II, the peculiar structure of the 1PI EA allows to associate to a field theory problem an e... | 2,678 | 3,375 | 3,511 | 2,435 | null | null | github_plus_top10pct_by_avg |
ectral gap is larger, as evidenced in previous learning to rank results in simpler settings [@NOS14; @SBB15; @HOX14]. This is made precise in , and in the main result of Theorem \[thm:main2\], we appropriately rescale the spectral gap and use $\alpha\in[0,1]$ defined as $$\begin{aligned}
\label{eq:lambda2_L1}
\... | 2,679 | 1,459 | 2,013 | 2,544 | 1,730 | 0.786315 | github_plus_top10pct_by_avg |
and let $P_{\mathcal{L}}\to M$ denote the principal $GL_1R$-bundle defined by the classifying map of ${\mathcal{L}}$, $\gamma_{\mathcal{L}}: M \to BGL_1(R)$. Let $\oplus_n P_{\mathcal{L}}$ denote the principal bundle classified by $$M {\xrightarrow}{\Delta} \prod_n M {\xrightarrow}{\gamma_{\mathcal{L}}^n } \prod_n BG... | 2,680 | 2,259 | 2,532 | 2,247 | null | null | github_plus_top10pct_by_avg |
\{4,5\}\}$. Denote $\cR^*=\{R\in\cR\mid R\subseteq X^*\}$. Since $|\cR^*|\le 4<|Y|+5$, we know that $\cR\setminus\cR^*\ne\emptyset$.\
For each $x\in X^*$ we set $\hat{x}$ to be the integer and $C_x$ to be the $2$-set such that $\{\{x,\hat{x}\},C_x\}=\{\{2,3\},\{4,5\}\}$ (so, in particular, $C_x=C_{\hat{x}}$). Also defi... | 2,681 | 1,839 | 1,592 | 2,456 | null | null | github_plus_top10pct_by_avg |
dictive densities with superharmonic priors.
Let $\ph_\pi=\ph_\pi(Y|X)$ be a Bayesian predictive density with respect to a prior $\pi(\Th)$, where $\pi(\Th)$ is twice differentiable and the marginal density $m_\pi(X;v_x)$ is finite. All the results in this section are based on the following key lemma.
\[lem:superharm... | 2,682 | 1,389 | 2,225 | 2,543 | null | null | github_plus_top10pct_by_avg |
gebra $\C[\gl_n(\F_q)]$.
If $\mu=(\mu_1,\mu_2,\dots,\mu_r)$ is a partition of $n$, an irreducible character of $\GL_n(\F_q)$ is said to be of type $\mu$ if it is of the form $R_{L_\mu}^{GL_n}(\alpha)$ where $L_\mu=\GL_{\mu_1}\times\GL_{\mu_2}\times\cdots\times\GL_{\mu_r}$ and where $\alpha$ is a *regular* linear chara... | 2,683 | 1,237 | 2,258 | 2,539 | 1,607 | 0.787657 | github_plus_top10pct_by_avg |
Gâteaux differential with the $H^2$ inner product , integrating by parts and using , we obtain the required $H^2$ gradient $\nabla\R$ as a solution of the following elliptic boundary-value problem $$\begin{aligned}
&\left[ {\operatorname{Id}}\, - \,\ell_1^2 \,\Delta + \,\ell_2^4 \,\Delta^2 \right] \nabla\R
= \nabla^{L_... | 2,684 | 1,090 | 2,027 | 2,572 | null | null | github_plus_top10pct_by_avg |
{k}}\partial
^{\alpha }f+\sum_{\substack{ (\beta ,\gamma )=\alpha \\ \left\vert \beta
\right\vert \geq 1}}c(\beta ,\gamma )\partial ^{\beta }\Big(\frac{1}{\psi
_{k}}\Big)\partial ^{\gamma }f.$$This, together with (\[n2\]) implies $$\Big\vert \partial ^{\alpha }\Big(\frac{f}{\psi _{k}}\Big)\Big\vert \leq
C\sum_{0\leq \... | 2,685 | 1,196 | 1,482 | 2,601 | null | null | github_plus_top10pct_by_avg |
\mathcal{O}_{S_3}$, and $\mathcal{O}_{S_3,\zeta^2} = \langle x_3^2, x_3y_3, y_3^2 \rangle\mathcal{O}_{S_3}$.
For $P_2 = [0:1:0]$ one uses the change of coordinates on $G_\lambda(x,1,z)$, $(x, z) = (x_2, z_2-x_2)$ to get a polynomial of the form $\beta_\lambda x_2^4 + z_2^3 + \sum_{ij} b_{\lambda ij} x_2^i z_2^j$ with ... | 2,686 | 2,291 | 2,216 | 2,344 | null | null | github_plus_top10pct_by_avg |
d:1985] for hyperbolic systems of equations (\[eq:2.1\]) allows the construction of certain classes of $k$-wave solutions admitting $k$ arbitrary functions of one variable. The replacement of the matrix of derivatives $u_i^\alpha$ in the system of equations (\[eq:2.1\]) by the simple real element $L_i^\alpha$ allows us... | 2,687 | 3,639 | 3,304 | 2,811 | null | null | github_plus_top10pct_by_avg |
mathcal{A}^{c \bar a}(w) \right. \cr
& \qquad + \left. j^b_{L,z}(x)
\left( \frac{c_+}{c_++c_-} \frac{i{f^{ac}}_d
\mathcal{A}^{d \bar a}(w)}{z-w} + ... \right) \right] \cr
%
& = -\frac{c_-}{c_+} \left[ \frac{c_1 \mathcal{A}^{a \bar a}(w)}{(z-w)^2} + \left(-c_2 + \frac{i c_+}{c_++c_-} \right) \frac{{f^a}_{bc}:j^b_{L,z}... | 2,688 | 1,978 | 3,084 | 2,446 | 2,982 | 0.775615 | github_plus_top10pct_by_avg |
y Eq. , ${\mathrm{ch}\,M}^\chi (\Lambda )$ does not depend on $\Lambda $. Hence by Prop. \[pr:VTMiso\] we may assume that ${\hat{T}}_p$ is an isomorphism. Then Eq. follows from Eq. .
\[le:chsub\] Let $\Lambda \in {{\mathrm{Hom}}({\mathcal{U}}^0,{{\mathbb{K}}^\times })}$ and $t\in \{1,2,\dots ,{b}-1\}$. Assume that $\... | 2,689 | 1,408 | 2,156 | 2,486 | null | null | github_plus_top10pct_by_avg |
g the two parts, we now have ${\mathit{u}}_{i - n} = {\mathit{v}}_{i - n}$ for each $i$. In other words, the two localized predecessor walks are actually the same walk: ${\mathit{u}} = {\mathit{v}}$. Thus $\test$ is a bijection.
#### Volatile variables preservation {#S:VOLATILE_VARIABLES}
The danger in reversed think... | 2,690 | 6,086 | 2,746 | 1,870 | 3,038 | 0.775295 | github_plus_top10pct_by_avg |
chouk polynomial of order $s$ over $\Z_2^k$. For simplicity we assume that $k$ is odd.
1. For any $x \in \Z_2^k$ with $|x|=i$, $\sum_{z \in \Z_2^k\\|z|=s}(-1)^{<x,z>} = K_s^{(k)}(i)$.
2. $\sum_{s=0}^l K_s^{(k)}(i) = K_l^{(k-1)}(i-1)$.
3. For any $s$ and $k$, $\max_{i=0,\dots,n} |K_s^{(k)}(i)| = K_s^{(k)}(0) = {k ... | 2,691 | 2,026 | 2,989 | 2,595 | 3,171 | 0.774311 | github_plus_top10pct_by_avg |
rm a $K^G$-basis of $K$. Then any $r\in R$ can be written as $$r=\sum_i a_i r_i{\quad\mbox{where $a_i\in K^G$.}\quad}$$ Applying any $g\in G$ to it, we get a system of equations $$\sum_i g(r_i)a_i= g(r){\quad\mbox{for $g\in G$.}\quad}$$ We can view these as linear equations with unknowns $a_i$. The system determinant i... | 2,692 | 2,216 | 2,504 | 2,432 | 2,557 | 0.778884 | github_plus_top10pct_by_avg |
xpression as that valid for the standard asymptotic behavior. The Virasoro charges are then easily integrated to yield $$\label{once}Q_{\pm}[T^{\pm}]=\frac{2}{l}\left( 1\pm\frac{1}{\mu l}\right)
\int T^{\pm}f_{\pm\pm}d\phi\$$ (up to additive constants). The details will be given in [@HMTfuture]. What happens is that t... | 2,693 | 986 | 2,520 | 2,557 | null | null | github_plus_top10pct_by_avg |
\in{\mathfrak S}_p$ such that $\{M_{i_{\sigma(k)}}\sqcup F_{j_{k}}\ ;\ k = 1, \ldots, p \}
= \pi(w)$. Then the product $${\cal C}(\mathbb{M},\sigma,\mathbb{F})
=
x_{\mathbb{\overline{M}}}
{C}[\mathbb{M}]C^{\mathbb{M}}_{\mathbb{F}}[\sigma]C^*[\mathbb{F}]
x^*_{\overline{F}}$$ becomes a presentation of $w$... | 2,694 | 4,172 | 3,005 | 2,457 | 1,824 | 0.785383 | github_plus_top10pct_by_avg |
e normalized distribution was universal, then the ratio of the standard deviation and the mean would have to obey $\sigma_i/\ev{f_i}=h$, where $h$ is a constant independent of the stock. Equivalently, a relationship $$\sigma_i \propto \ev{f_i}^\alpha
\label{eq:alpha_first}$$ would have to hold with an exponent $\alpha ... | 2,695 | 422 | 983 | 2,777 | 2,370 | 0.780445 | github_plus_top10pct_by_avg |
tandard model of particle interactions to include an extra $U(1)_A$ gauge symmetry and an extra $U(1)_{PQ}$ global symmetry. All standard-model particles are trivial under these two new symmetries. We then introduce a new heavy quark singlet $\psi$ and two scalar singlets $\sigma$ and $\eta$ with $U(1)_A$ and $U(1)_{PQ... | 2,696 | 917 | 1,884 | 2,945 | null | null | github_plus_top10pct_by_avg |
s forced to be a $G_\delta$ containing $(\delta,x_g)$. There is a cub $C_1$ such that for each $\alpha\in C_0$ and each $s\in S_{\alpha^+}$ (again, $\alpha^+$ is the minimal element of $C_1$ above $\alpha$), $s$ forces that $\dot{Z}_\alpha$ contains $\{\alpha\}\times a_s^*$. Since $S$ is ccc, the cub $C_1$ can be chose... | 2,697 | 1,200 | 1,982 | 2,592 | 3,986 | 0.76879 | github_plus_top10pct_by_avg |
more information on the inertia stack.) In general, points in the inertia stack are pairs $(x,\alpha)$, where $x$ is a point of $\mathfrak{X}$, and $\alpha$ is an automorphism of $x$, which for an orbifold $[Y/G]$ by $G$ a finite group, would define the twisted sectors. In the $[{\mathbb C}^3/{\mathbb Z}_3]$ example, i... | 2,698 | 2,487 | 2,530 | 2,323 | 2,603 | 0.778523 | github_plus_top10pct_by_avg |
= (\lambda^{(1)}, \lambda^{(2)}, \lambda^{(3)},
\lambda^{(4)}, \lambda^{(5)})$$ to mean the tableau $p$ goes through $\lambda^{(1)}$, $\lambda^{(2)}$, $\lambda^{(3)}$, $\lambda^{(4)}$, $\lambda^{(5)}$ at the 1-st, the $(2-\frac{1}{2})$-th, the 2-nd, the $(3-\frac{1}{2})$-th and the 3-rd coordinates respectively.
Supp... | 2,699 | 1,232 | 2,519 | 2,648 | null | null | github_plus_top10pct_by_avg |
hcal{L}}, \oplus_n {\mathcal{L}})$, where $Mor^R$ refers to the $R$-module morphisms in the category of parameterized spectra over $X$. Thus when $S = End^R({\mathcal{L}})$, we have a natural equivalence $$End^S(\vee_n S) \simeq \prod_n(Mor^R({\mathcal{L}}, \oplus_n {\mathcal{L}}) = End^R (\oplus_n {\mathcal{L}}).$$ Fu... | 2,700 | 1,840 | 1,519 | 2,634 | 4,112 | 0.768028 | github_plus_top10pct_by_avg |
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