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 |
|---|---|---|---|---|---|---|---|
mportance. Let $G'\subset{\mathbb{R}}^3$ be an open bounded set such that $\ol{G'}$ is a $C^1$-manifold with boundary (i.e. $G'$ has the same regularity properties as $G$) and such that $\ol{G}\subset G'$. Let $G_{\rm e}:=G'\setminus \ol G$. Then $$\partial G_{\rm e}=\partial^1 G_{\rm e}\cup \partial^2G_{\rm e},$$ wher... | 3,501 | 1,979 | 1,983 | 3,309 | null | null | github_plus_top10pct_by_avg |
\sqrt{m} ({\widehat}{\theta}_{km} -\theta ) \notag \\
&=\frac{1}{\sqrt{K}}\sum_{k=1}^{K} W_{km}+ \frac{1}{\sqrt{K}}\sum_{k=1}^{K} R_{km},\end{aligned}$$ where $W_{km}=\frac{1}{\sqrt{m}}\sum_{i=1}^{m}\eta_{k,i}$. From Assumption \[assumption2\], we get the last term in (\[eqA1\]) is $o_{p}(1)$.
Now, we prove that ... | 3,502 | 2,770 | 2,859 | 3,147 | null | null | github_plus_top10pct_by_avg |
rages by the delta method. First, we carry out a coordinate-wise Taylor expansion of $\widehat{\theta}$ around $\theta$. We then utilize a a high-dimensional Berry-Esseen theorem for polyhedral sets established in [@cherno2] (see below for details) to derive a Gaussian approximation to the linear part in the expansion,... | 3,503 | 1,104 | 2,139 | 3,216 | null | null | github_plus_top10pct_by_avg |
trates on formal specifying/developing/modeling separation kernels and *Verification* on formally verifying separation kernels. Some work aims at these two aspects together. The “Property” indicates the policies or properties specified or verified in each work. The “Formal Language” indicates what’s the formal language... | 3,504 | 2,377 | 3,530 | 3,633 | null | null | github_plus_top10pct_by_avg |
**a member of a filter belongs to the filter: $(F\in\mathcal{F})\wedge(F\subseteq G)\Rightarrow G\in\mathcal{F}$; in particular $X\in\mathcal{F}$.
**Example A1.4.** (1) The *indiscrete filter* is the smallest filter on $X$.
\(2) The neighbourhood system $\mathcal{N}_{x}$ is the important *neighbourhood filter at $x$ ... | 3,505 | 4,141 | 2,915 | 3,189 | 1,564 | 0.788211 | github_plus_top10pct_by_avg |
ed in Section \[section1\], random graph models, in general, are not always relevant to represent the structure of a graph that has been inferred from observations. To tackle this issue, we create a new random model with an underlying structure that is a randomized version of a deterministic graph with exact cluster st... | 3,506 | 5,191 | 2,641 | 2,789 | 1,906 | 0.784522 | github_plus_top10pct_by_avg |
er $i,j$ will take values from $\{1,\dots,n\}$ and $k,l,m$ will take values from $\{1,\dots,r\}$. We simplify the above as $$\biggl(\sum_i c_i\biggr)\biggl(\sum_j\sum_{\substack{{k,l}\\k\neq l}}x_{jk}x_{jl}\biggr)
\leq c\biggl(\sum_{i,j}\sum_{\substack{{k,l}\\k\neq
l}}x_{ik}x_{jl}\biggr),$$ then we factor out and also ... | 3,507 | 1,781 | 2,841 | 3,113 | null | null | github_plus_top10pct_by_avg |
$ TeV 88 1600 760
\(2) chirally-coupled scalar
$m_S=1$ TeV, $\Gamma_S=350$ GeV 100 570 ... | 3,508 | 4,520 | 3,309 | 3,330 | 4,157 | 0.76769 | github_plus_top10pct_by_avg |
\
Weyl Spinors {#Sec3.3}
-----------------------------------------
We have seen how, on the basis of the chiral SU(2)$_+\times$SU(2)$_-$ group, it is possible to readily identify the finite dimensional representation theory of the Lorentz group SO(1,3). Let us now discuss yet another construction of its two fundamenta... | 3,509 | 4,572 | 3,126 | 3,175 | null | null | github_plus_top10pct_by_avg |
.0 573.5 48.0 340.5
Starch solution 12.4 9.3 11.4 10.6 9.9 16.2 14.4
PVA solution 7.7 16.2 10.1 13.4 15.1 19.6 17.7
Textile wastewater 40.6 52... | 3,510 | 5,814 | 1,827 | 2,436 | null | null | github_plus_top10pct_by_avg |
\psi({\widehat{S}},P)=
\left[ \begin{array}{c}
\mathrm{vech}(\Sigma_{{\widehat{S}}})\\
\alpha_{{\widehat{S}}}\\
\end{array} \right] \in \mathbb{R}^{b},$$ where $b = \frac{ k^2 + 3k}{2} $. Similarly, based on the sub-sample $\mathcal{D}_{2,n}$ we define the $n$ random vectors $$W_i =
\left[ \begin{... | 3,511 | 3,858 | 2,886 | 3,106 | null | null | github_plus_top10pct_by_avg |
ase 2* and a uniformizing element $\pi$ of $B$ and $\delta$ are fixed as explained above throughout this paper.
- Set $$\xi:=\pi\cdot\sigma(\pi).$$
- We consider a $B$-lattice $L$ with a hermitian form $$h : L \times L \rightarrow B,$$ where $h(a\cdot v, b \cdot w)=\sigma(a)b\cdot h(v,w)$ and $h(w,v)=\sigma(h(v,w... | 3,512 | 4,689 | 3,432 | 2,963 | null | null | github_plus_top10pct_by_avg |
Y)$ is the smallest closed topological extension of $M=\textrm{Map}(X,Y)$ is the following, refer Thm. A1.4 and its proof. Let $(M,\mathcal{T}_{0})$ be a topological space and suppose that$${\textstyle \widehat{M}=M\bigcup\{\widehat{m}\}}$$
is obtained by adjoining an extra point to $M$; here $M=\textrm{Map}(X,Y)$ and... | 3,513 | 2,999 | 3,690 | 3,236 | 2,781 | 0.777024 | github_plus_top10pct_by_avg |
d antibody incubation conditions are shown in [Table 2](#pone.0214536.t002){ref-type="table"}. The Western blots were also incubated with secondary antibodies only for detecting non-specific signals. For the chemiluminescence detection of immunocomplexes by ChemiDoc, the membranes were treated with Supersignal West Fem... | 3,514 | 106 | 3,410 | 3,585 | null | null | github_plus_top10pct_by_avg |
, \label{a2}$$where $p_\ast$ is the conjugate of $p$. So, does not matter the value of $\theta _{1},$ one may replace it by $\frac{d%
}{p_{\ast }}.$
**Proof** We take $n_{\ast }\in \N$ and we define $f_{n}=0$ for $n\leq
n_{\ast }$ and $f_{n}=\varphi p_t$ for $n>n_{\ast }.$ Notice that $d_{0}(\varphi p_{t},0)\leq m.$ T... | 3,515 | 1,747 | 2,310 | 3,212 | null | null | github_plus_top10pct_by_avg |
s filed on or about August 25, 2003, recorded under document
number 2003053083 of the Official Public Records of Brazoria County, Texas (See
Exhibit "A" attached hereto and incorporated herein for all purposes);
2. Notice of Lis Pendens filed on or about September 19, 2005, recorded unde... | 3,516 | 4,475 | 2,759 | 2,489 | null | null | github_plus_top10pct_by_avg |
}\psi)(x,\omega,\cdot,E)\big)(E)$. We have by , \[csda5\] & [H]{}\_1((\_[22,1]{})(x,,,E))(E) = \_E\^[E\_m]{}[1]{}(\_[22,1]{})(x,,E’,E)dE’\
=& \_E\^[2E]{}[1]{}(\_[22,1]{})(x,,E’,E)dE’+ \_[2E]{}\^[E\_m]{}[1]{}(\_[22,1]{})(x,,E’,E)dE’\
& \_E\^[2E]{}[1]{}\_1(x,E’,E)(x,,E’)dE’+ \_[2E]{}\^[E\_m]{}[1]{}(\_[22,1]{})(x,,E’,E)dE... | 3,517 | 674 | 3,722 | 3,443 | null | null | github_plus_top10pct_by_avg |
ainties in the anisotropic shadowing effect (Sec. \[sec:direction\_dep\]), we study the cases with different shadow opening angles $\theta_{\mathrm{shadow}}$ by reducing it from $45^\circ$ in “Dds run” (here we also call it “s100 run”) to $33.75^\circ$ (“s075 run”), $22.5^\circ$ (“s050 run”) and $11.25^\circ$ (“s025 ru... | 3,518 | 1,385 | 2,872 | 3,375 | 2,317 | 0.780891 | github_plus_top10pct_by_avg |
n [(\[eq:Theta’-evdec\])]{} to $\Theta'_{y,x;{{\cal A}}}$ and $\Theta''_{y,x,v;{{\cal A}}}$, respectively.
**(a)** First we investigate the contribution to $\Theta'_{y,x;{{\cal A}}}$ from ${\mathbbm{1}{\scriptstyle\{y{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}}
{\overset{}{\Longleftrightarrow}}}x\}}}$:... | 3,519 | 2,344 | 2,392 | 3,198 | null | null | github_plus_top10pct_by_avg |
ns with left-sided pleural-based focus of confluent fluid attenuation that extends through the anterior chest wall and insinuates between the pectoralis major and minor muscles representing empyema necessitans (arrows) are shown.](CRIID2018-4906547.001){#fig1}
![Arterial-phase axial computed tomographs of the lower th... | 3,520 | 601 | 3,688 | 3,524 | null | null | github_plus_top10pct_by_avg |
er
iB(-2I_{21}-q_0I_{11}+2I_{10}+q_0I){\vec{\sigma}_1}({\vec{q}}\times{\vec{p}})
\Big]\,.\end{aligned}$$ We have used the master integrals with $q_0=-\frac{M_\Lambda-M_N}{2}$, $q_0'=-M_\Lambda+M_N$ and ${\vec{q}}={\vec{p}}'-{\vec{p}}$.
![Second type of down-triangle involving the intermediate exchange of a $\Sigma$.[]... | 3,521 | 1,557 | 836 | 3,719 | null | null | github_plus_top10pct_by_avg |
iv\,
\frac{1}{i}
{\int\frac{d^4l}{(2\pi)^4}}\frac{1}{l^2-m^2+i\epsilon} \,,$$ $$\begin{aligned}
A_{;\mu;\mu\nu}(q,q')\equiv\,&
\frac{1}{i}{\int\frac{d^4l}{(2\pi)^4}}\frac{1}{(l+q)^2-m^2+i\epsilon}
\\&\times
\frac{1}{-l_0-q_0'+i\epsilon}(1;l_\mu;l_\mu l_\nu) \,,\end{aligned}$$ $$\begin{aligned}
C_{;\mu;\mu\nu;\mu\nu\rho... | 3,522 | 1,208 | 1,542 | 3,645 | null | null | github_plus_top10pct_by_avg |
f(y)\right\vert dy\leq \frac{C}{(\lambda t)^{\theta_0(q+\theta_1)}}\int
\frac{\psi _{\pi (q,\kappa +d)}(y)}{\psi _{\kappa +d}(x-y)}\times \left\vert
f(y)\right\vert dy.$$By (\[NOT3b\]) $\psi _{\kappa +d}(x)/\psi _{\kappa +d}(x-y)\leq C \psi
_{\kappa +d}(y)$ so that$$\begin{aligned}
\psi _{\kappa +d}(x)\left\vert \part... | 3,523 | 1,304 | 2,105 | 3,473 | null | null | github_plus_top10pct_by_avg |
ed transport system (\[intro10a\])-(\[intro12\]), which has not been studied in the literature, in $L^2(G\times S\times I)^3$-based spaces. We also show certain a priori estimates (needed e.g. in section \[irtpre\]) which in particular show (under specific assumptions) that the solution depends continuously on the data... | 3,524 | 1,980 | 918 | 3,407 | 3,929 | 0.769226 | github_plus_top10pct_by_avg |
d event $\xi \in \Xi$. Frame $\mho_{\mathbf{F}}({\mathit{s}})$ conjoins frame $\mho_{\mathbf{F}}({\mathfrak{A}}_\xi({\mathit{s}}))$.
By hypothesis $\xi \in {\prod{\Xi}}$ and ${\mathit{s}} \in {\mathbb{S}}$. By definition \[D:STEP\_SPACE\] of step space, there exist locus $\lambda \in \Lambda$, frame ${\mathbf{f}} = (\... | 3,525 | 2,080 | 2,546 | 3,184 | null | null | github_plus_top10pct_by_avg |
exists a random variable $\hat{\Gamma}$ such that $N\leq \hat{\Gamma}$ almost surely and $$\mathbb{P}(\hat{\Gamma} = k) = (1-\hat{q})^{k-1}\hat{q}, \qquad k\in \mathbb{N},$$ for some $\hat{q}=\hat{q}(\alpha, D)$.
Reviewing the proof of Theorem \[main\], we note that it suffices to prove that, in the context of Corol... | 3,526 | 3,840 | 3,034 | 3,046 | null | null | github_plus_top10pct_by_avg |
re trained to obtain the optimal training models. After the test set verification of the optimal training model, the results obtained are shown in [Figure 5](#sensors-20-02119-f005){ref-type="fig"}. [Figure 5](#sensors-20-02119-f005){ref-type="fig"}a,b indicate the linear fitting effect of I--V curves predicted by MLP ... | 3,527 | 1,925 | 1,690 | 3,284 | 2,144 | 0.782309 | github_plus_top10pct_by_avg |
ften used Henyey-Greenstein kernel.
The *dose* $D(x)=(D\psi)(x)$ is calculated from the solution of the problem $$\begin{gathered}
\omega\cdot\nabla_x\psi_1+\Sigma_1\psi_1-K_1\psi=f_1, \label{intro10a}\\
-{{\frac{\partial (S_{j,r}\psi_j)}{\partial E}}}+\omega\cdot\nabla_x\psi_j+\Sigma_{j,r}\psi_j-K_{j,r}\psi=f_j,\quad... | 3,528 | 1,193 | 1,799 | 3,482 | 2,149 | 0.782264 | github_plus_top10pct_by_avg |
3|\geq 28$. Since $28=(4-1)^3+1$, we can use Theorem \[kflemma\] to conclude that $\cI_3$ contains a $4$-flower. Let $k\geq 4$ be maximum such that $\cS$ is a $k$-flower in $\cI_3$, and let $C$ be the core of $\cS$. As $\cI_3$ is $3$-uniform and intersecting, every subfamily $\cG\sse \cI$ has $\tau(\cG)\leq 3$, which i... | 3,529 | 1,935 | 1,685 | 3,299 | null | null | github_plus_top10pct_by_avg |
{pspicture}};\varnothing), \\ G\subset \mathcal
F(\widehat{E})({
\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}},{
\begin{pspicture}(0,0.1)(0.2,0.4... | 3,530 | 2,557 | 1,421 | 3,328 | 1,449 | 0.789405 | github_plus_top10pct_by_avg |
gerbe with rank 8 bundle. Nearly the same analysis applies as in the Spin$(32)/{\mathbb Z}_2$ case. At the level of SCFT, before imposing the left GSO projections, the same duality argument we have just given suggests the gerbe theory should be dual to an $E_8$ bundle, as above. The left GSO for the corresponding bundl... | 3,531 | 2,322 | 2,114 | 3,394 | 3,818 | 0.769916 | github_plus_top10pct_by_avg |
The proof of Theorem \[morrat\] will be through a series of lemmas and we begin with the first equality in . Set $d=c+1$; thus $d\in {\mathbb{R}}_{\geq 1}$, with $d\notin \frac{1}{2}+{\mathbb{Z}}$.
Reduction to Category ${\mathcal{O}}$ {#subsec-4.2}
-------------------------------------
If $H_de_-H_d$ is a *proper* ... | 3,532 | 2,512 | 1,146 | 3,585 | 2,112 | 0.782654 | github_plus_top10pct_by_avg |
to view this structure is the following. One checks easily that for any cyclic $A$-bimodule $M_\#$, the restriction $j^*M_\# \in {\operatorname{Fun}}(\Delta^{opp},k)$ is canonically isomorphic to the simplicial $k$-vector space $M^\Delta_\#$ associated to the underlying $A$-bimodule $M$ as in . By adjunction, we have a... | 3,533 | 2,119 | 2,650 | 3,222 | 1,777 | 0.785799 | github_plus_top10pct_by_avg |
gma}_K^2}{\sigma_K^2}\right)\mathcal{N}_K\notag\\
=&-2(\gamma-1)\sigma_K\int_M\left[|\nabla\nabla v|^2+({\rm Ric}+Kg)(\nabla v,\nabla v)+(\gamma-1)(\Delta v)^2\right]vu\,dV\notag\\
&+2(\gamma-1)\sigma_K\int_MK|\nabla v|^2vu\,dV+2\frac{\dot{\sigma}_K}{\sigma_K}\frac{d}{dt}\mathcal{N}_K
+\left(\frac{\ddot{\sigma}_K}{\sig... | 3,534 | 2,564 | 3,226 | 3,279 | null | null | github_plus_top10pct_by_avg |
shielding effect.
![Comparison between simulation results and theoretical models including the OML correction for the electric field acting on the grain. Only results with $\Lambda\simeq16$ are shown.[]{data-label="com"}](comcom.eps){width="90mm"}
To determine the value of $\alpha$, Figure \[com\] compares the simula... | 3,535 | 3,111 | 4,143 | 3,593 | null | null | github_plus_top10pct_by_avg |
ies $V_m(z,s)$ satisfies $$\label{straightforward}
(\Delta-s(1-s))V_m(z,s)=(2\pi m)^2V_m(z,s+2) \textrm{ when } {\operatorname{Re}}(s)>1,$$ since $f_s(z)=y^s e^{2\pi i m {\operatorname{Re}}z}$ satisfies this equation and because the Laplacian commutes with isometries, so does $V_m(z,s)$, being a sum of translates of ... | 3,536 | 2,327 | 2,589 | 3,120 | 3,499 | 0.771899 | github_plus_top10pct_by_avg |
> 0$ and $x \geq 0$, we define $$\begin{aligned}
y_{2} (a, x) &:= a \g(a, x)^{2} - a \G(a)^{2} + 2 e^{-x} \G(2a, x); \\
y_{3} (a, x) &:= a x^{a - 1} \g(a, x) - \G(2a, x) - x^{2a - 1} e^{-x}; \\
y_{4} (a, x) &:= a (a - 1) \g(a, x) + x^{a} e^{-x} (2x + 1 - a). \end{aligned}$$ Then, we have $$\begin{aligned}
\frac{d}{dx} ... | 3,537 | 1,393 | 1,742 | 3,492 | null | null | github_plus_top10pct_by_avg |
9.2\rm\,GHz$. Solid lines show the experimental results and the theoretical curves are dotted for experimental parameter (available only for the 50$\Omega$ load case) and dashed for fitting parameter. The corresponding parameter and the transmission coefficient for the measuring antenna $a$ are listed in Tab. \[tab:01\... | 3,538 | 1,897 | 827 | 3,665 | null | null | github_plus_top10pct_by_avg |
nction $f_{\textrm{C}}$ such that $$g(x)=f_{\textrm{C}}(\mathscr{M}(x))\in\mathscr{M}(x)$$ is an immediate successor of $x$ chosen from the many possible in the set $\mathscr{M}(x)$. The basic idea in the proof of the first of the three-parts is to express the existence of a maximal element of a partially ordered set $... | 3,539 | 4,378 | 4,349 | 3,225 | 1,502 | 0.788802 | github_plus_top10pct_by_avg |
35} {\vec{q}}^2
\nonumber\right.\\+&\left.\nonumber
(4-\eta) K_{22}+(5-\eta) K_{34}\right)
{\vec{\sigma}_1}\cdot\left({\vec{p}}\times {\vec{q}}\right)
+2 i B K_{22}
{\vec{\sigma}_2}\cdot\left({\vec{p}}\times {\vec{q}}\right)
\nonumber\\-&\nonumber
2 B \Big(K_{11}{\vec{q}}^2
\left({\vec{p}}\cdot {\vec{q}}+2 q_0{}^... | 3,540 | 3,619 | 2,482 | 3,237 | null | null | github_plus_top10pct_by_avg |
im \mathcal{O} (1),
\label{assumption}\end{aligned}$$ where $L$ denotes baseline, $\Delta m^2_{ji} \equiv m_j^2 - m_i^2$, and $$\begin{aligned}
\frac{ a L }{2E}
&=& \sqrt{2} G_F N_e L
= 0.58
\left(\frac{\rho}{3 \text{g/cm}^3}\right)
\left(\frac{L}{1000 \mbox{km}}\right).
\label{aL-2E}\end{aligned}$$ They probably ... | 3,541 | 3,371 | 3,733 | 3,337 | 3,387 | 0.772732 | github_plus_top10pct_by_avg |
m in the potential comes from the exchange of photons, while the second one is from the exchange of $Z$ bosons. In the calculation of $\Gamma$, we consider only the final states of SM particles, and neglect their masses, since they are light enough compared to the wino-like neutralino we are discussing.
In both cases ... | 3,542 | 3,785 | 3,518 | 3,416 | 3,988 | 0.768756 | github_plus_top10pct_by_avg |
downarrow}_n$, we have $T^{\lambda}(y)=S^{\lambda}(y)$ (Theorem 10 of [@FD05a]), then $T^{\lambda}(y)= T^{\lambda-}(y)$ follows from the continuity of $S^{\lambda}(y)$ for any $0<\lambda<1$ (Theorem 3 of [@FD05a]).
Now we prove 3). The relation $T^{\lambda+}(y)\subseteq
T^{\lambda}(y)^{\circ}$ is easy from 1) and 2). ... | 3,543 | 2,553 | 1,426 | 3,431 | 2,884 | 0.776323 | github_plus_top10pct_by_avg |
on of the intergrain distance $d$. Note that the distance is normalized by the Debye length defined with the kinetic energy measured at the equilibrium states rather than the initial temperature. The red and green lines are the theoretical curves expected from the standard Yukawa potential and the ODS attractive potent... | 3,544 | 1,178 | 3,287 | 3,615 | 1,788 | 0.785693 | github_plus_top10pct_by_avg |
one the same in the CbD approach as well: we could have defined $\text{\ensuremath{\Delta}}$ directly based on the joint of all eight variables without explicitly defining the connection correlations –, and then we would have obtained the result directly from the half-space representation, as we do in the negative prob... | 3,545 | 748 | 2,483 | 3,383 | null | null | github_plus_top10pct_by_avg |
=&K\left(\frac{t-X_i}{h_{2,n}}f^{1/2}(X_i)\right)+L_1\left(\frac{t-X_i}{h_{2,n}}f^{1/2}(X_i)\right)
\delta (X_i)+\delta_2(t,X_i),\end{aligned}$$ where $$\label{delta2}
\delta_2(t,X_i)=\frac{K^{\prime\prime}(\xi)}{2}
\frac{(t-X_i)^2}{h_{2,n}^2}f(X_i)\delta^2(X_i),$$ $\xi$ being a (random) number between $\frac{t-X_i}{h_... | 3,546 | 863 | 2,409 | 3,565 | null | null | github_plus_top10pct_by_avg |
y the definition of $C$ and assumption , we have $$C=\frac{\max\{q,0\}}{\kappa}\geq \frac{\max\{q,0\}}{S_0}\geq \frac{q}{S_0}$$ a.e. and hence $$C{\left\langle}\phi,S_0\phi{\right\rangle}_{L^2(G\times S\times I)}\geq q{\left\Vert \phi\right\Vert}_{L^2(G\times S\times I)}^2.$$
Taking Lemmas \[csdale0\] and \[csdale1a\]... | 3,547 | 1,645 | 1,117 | 3,590 | null | null | github_plus_top10pct_by_avg |
variant constant implies $$q_a\partial_\mu q^a=0,\ \ \ \bar{q}^a\partial_\mu \bar{q}_a=0,$$ which means that $$q_aq^a=\mbox{const.}, \ \ \ \bar{q}_a\bar{q}^a=\mbox{const.}$$ As at different points, the normalization should be the same, one can choose the constants to be unit.
The scaling structure is covariantly cons... | 3,548 | 1,266 | 2,803 | 3,227 | null | null | github_plus_top10pct_by_avg |
(E',E))\psi(x,\omega',E')d\omega'
=
\int_{0}^{2\pi}
\psi(x,\gamma_{\mu_{11}(E',E)}(s),E')ds,$$ as desired, since $\gamma_{\mu_{11}(E',E)}(s)=\gamma(s)$ ($=\gamma_{11}(E',E,\omega)(s)$).
It thus follows that (K\_[11]{})(x,,E) =&\_[I’]{} (\_[11]{} )(x,,E’,E)dE\
=& \_[I’]{}\_[11]{}(E’,E)\_[11]{}(x,E’,E) \_[0]{}\^[2]{}(x,... | 3,549 | 751 | 3,136 | 3,387 | null | null | github_plus_top10pct_by_avg |
rs. The panels of Fig. \[fig:ccd\] show the variable and the comparison stars in the CCD fields. We applied low-order polynomial fits to the light curves to correct for the instrumental trends and for the atmospheric extinction. This method did not affect the pulsation frequency domains. Figure \[fig:lcshort\] shows tw... | 3,550 | 479 | 2,403 | 3,531 | 1,578 | 0.788057 | github_plus_top10pct_by_avg |
any finite field with $q$ elements $A_{\Gamma,\v}(q)=\#{\rm A}_{\Gamma,\v}(\F_q)$. We call $A_{\Gamma,\v}$ the *$A$-polynomial* of $(\Gamma,\v)$.
Let $\Phi(\Gamma)\subset \Z^I$ be the root system associated with the quiver $\Gamma$ following Kac [@kacconj] and let $\Phi(\Gamma)^+\subset \left(\N\right)^I$ be the subse... | 3,551 | 2,556 | 3,018 | 3,117 | 3,672 | 0.770807 | github_plus_top10pct_by_avg |
0.42 \[-2.74, 3.57\] 0.80 -0.67 \[-4.28, 2.95\] 0.72 0.50 \[-2.71, 3.70\] 0.76
Family situation (married vs. stepfamily) 2.50 ... | 3,552 | 6,319 | 2,166 | 2,017 | null | null | github_plus_top10pct_by_avg |
ned. So we propose to use EL as follows.
Since the blocks are disjoint, ${\widehat}{\theta}_{1m}, \dots, {\widehat}{\theta}_{Km}$ are independent. We can regard them as one sample and apply EL to make inference on $\theta$. For notational convenience, let $Y_{km}={\sqrt{m}}{\widehat}{\theta}_{k m}$ and $\mu=\sqrt{m}\t... | 3,553 | 1,197 | 2,846 | 3,334 | 4,088 | 0.768181 | github_plus_top10pct_by_avg |
by means of the trace. This is not at all trivial. Indeed, if for instance $M_\# \in {\operatorname{Shv}}({{\mathcal C}}_\#)$ is cocartesian, then, while $L^{{\:\raisebox{3pt}{\text{\circle*{1.5}}}}}{\operatorname{\sf tr}}^\#M_\#$ lies in the subcategory ${{\mathcal D}}_{const}(\Lambda,k) \subset {{\mathcal D}}(\Lambd... | 3,554 | 2,489 | 2,118 | 3,226 | null | null | github_plus_top10pct_by_avg |
he peak subtraction method.
Detection sensitivity {#sec:detection}
---------------------
To determine the limits for detecting host galaxies we constructed a sample of 200 randomly selected unsaturated stars, 100 in each observed band, to mimic unresolved quasars. This way we could investigate how our nucleus-removal... | 3,555 | 289 | 3,777 | 3,518 | null | null | github_plus_top10pct_by_avg |
e force, describing correspondingly the collapse or the indefinite separation of the branes, just as happened in the Appelquist and Chodos calculation [@ac]. In this case, then, the stabilization of the interbrane distance cannot be due to quantum fluctuations of fields propagationg into the bulk.
AdS Spacetime
-----... | 3,556 | 3,538 | 3,930 | 3,252 | null | null | github_plus_top10pct_by_avg |
23}$. This shows that $\dim H^1(\tilde{X}_{1},\CC) = 2$ while $\dim H^1(\tilde{X}_{\zeta},\CC) = 0$. Note that the expected dimension of the cokernel is 0 since both spaces have the same dimension. The existence of the special curve $\{F=0\}$ whose equation is in the kernel of this map, satisfying certain local propert... | 3,557 | 2,401 | 3,171 | 3,295 | null | null | github_plus_top10pct_by_avg |
from the space covered by the training data. The joint distribution of $\mathbf{Y}$ is then $$\label{joint}
\begin{bmatrix} \mathbf{Y}_t \\ \mathbf{y}_* \end{bmatrix} \sim\mathcal{N}\left(0,
\begin{bmatrix} \mathbf{K}(\mathbf{X}_t,\mathbf{X}_t)+\mathbf{E} & \mathbf{K}(\mathbf{x}_*,\mathbf{X}_t)^T \\ \mathbf{K}(\mathbf... | 3,558 | 3,206 | 3,254 | 3,198 | null | null | github_plus_top10pct_by_avg |
iv \: \rho(\tilde{h}^{-1} g \tilde{h} )$$ for all $g \in K$. If $K$ is abelian, this is well-defined. If $K$ is not abelian, then it can be shown (see [@summ]\[section 4\]) that there exists an operator intertwining the representations $h \cdot \rho$ defined by any two lifts, hence $h \cdot \rho$ is well-defined in $\h... | 3,559 | 1,826 | 3,020 | 3,279 | null | null | github_plus_top10pct_by_avg |
re equivalent, are the wave equation: $$\begin{aligned}
\label{DbLphi}{\underline{D}}(rL\phi)=&-\Omega^2h\Lb\phi,\\
\label{DLbphi}D(r\Lb\phi)=&-{\underline{h}}L\phi.\end{aligned}$$ Finally, we have the following equation about the mass function $m$: $$\begin{aligned}
\label{Dm}Dm=&-\frac{1}{2}{\underline{h}}\Omega^{-2}... | 3,560 | 1,607 | 2,355 | 3,401 | null | null | github_plus_top10pct_by_avg |
on $\theta$ in the RST.
The idea of the proof of Proposition \[prop:<2\] is classical: see [@howardnewman2] for first passage percolation models defined from homogeneous PPP on $\mathbb{R}^{2}$ and [@FP] for a directed last passage percolation model on the lattice $\mathbb{Z}^{2}$. Thanks to Fubini’s theorem, we ge... | 3,561 | 1,523 | 1,859 | 3,498 | null | null | github_plus_top10pct_by_avg |
anks to the boundedness of $D$). In the inequality, we have used the fact that, on $\{\sigma_D <\sigma_{B^*}\}$, we have $X_{\sigma_D}\in B^*\backslash D$, moreover, that, as a continuous function on $\mathbb{R}^d$, ${g}$ is bounded in $B^*\backslash D$. In the second equality, we have used spatial homogeneity and the ... | 3,562 | 2,602 | 2,042 | 3,153 | null | null | github_plus_top10pct_by_avg |
ceivable that the constraints from measurements using probes in the charged lepton sector play a dominant role. On the other hand, in the case of low-scale unitarity violation, neutrino oscillation experiments will play key role in constraining unitarity violation.
Essence of the present and the previous papers {#sec:... | 3,563 | 735 | 3,230 | 3,408 | null | null | github_plus_top10pct_by_avg |
comp-dd\] [**g**]{}(,,E\_[m]{})=0 holds. Then the problem $$\begin{gathered}
-{{\frac{\partial (S_0\phi)}{\partial E}}}+\omega\cdot\nabla_x\phi+CS_0\phi+\Sigma\phi -K_C\phi={\bf f},\ \nonumber\\
{\phi}_{|\Gamma_-}={\bf g},\quad \phi(\cdot,\cdot,E_{\rm m})=0, \label{co3aa-dd}\end{gathered}$$ has a unique solution \[soli... | 3,564 | 573 | 2,387 | 3,536 | null | null | github_plus_top10pct_by_avg |
ss of stock $H^-\approx 0.51-0.52$. This means that intraday fluctuations of traded value are nearly uncorrelated.
2. For long time fluctuations the data are correlated, but the strength of correlations depends strongly on the liquidity of the stock. As one moves to groups of larger $\ev{f}$, the strength of correlat... | 3,565 | 1,593 | 1,376 | 3,726 | 661 | 0.802986 | github_plus_top10pct_by_avg |
ted entanglement transformation is strictly more powerful than multiple-copy one in either deterministic or probabilistic setting. For purely probabilistic setting, however, we can prove that these two kinds of transformations are geometrically equivalent in the sense that the two sets $T^{\lambda}(y)$ and $M^{\lambda}... | 3,566 | 2,057 | 2,470 | 3,302 | null | null | github_plus_top10pct_by_avg |
s paper I use these four objects to improve the calibration of the Hubble diagram, and solve for the value of the Hubble constant.
The Luminosity-Velocity Relation {#lv_sec}
================================
The SCM is based on the luminosity-velocity relation, which permits one to standardize the relative luminositie... | 3,567 | 3,091 | 4,180 | 3,548 | null | null | github_plus_top10pct_by_avg |
Phys. A [**49**]{} (2016) no.44, 445403 \[[[arXiv:1607.00795](http://arxiv.org/abs/1607.00795)]{}\].
[^1]: A more precise field theoretic explanation of what this limit means has been proposed in [@Lozano:2016kum].
[^2]: In some cases it can be that this doesn’t fully fix the gauge and additional fixing should be imp... | 3,568 | 2,682 | 1,649 | 2,970 | null | null | github_plus_top10pct_by_avg |
\textrm{sup}}$ with $x_{1}\in C_{1}$ and $x_{2}\in C_{2}$, then from the $\subseteq$-comparability of $C_{1}$ and $C_{2}$ we may choose $x_{1},x_{2}\in C_{1}\supseteq C_{2}$, say. Thus $x_{1}$ and $x_{2}$ are $\preceq$-comparable as $C_{1}$ is a chain in $(X,\preceq)$; $C_{*}\in\mathcal{X}$ is therefore a chain in $(X,... | 3,569 | 2,175 | 3,355 | 3,235 | 2,877 | 0.776382 | github_plus_top10pct_by_avg |
ghput from adding reconfiguration states becomes small when the number of reconfiguration states is already large. Comparing the limiting behaviors of the average throughput gain and the outage throughput gain, we further find that the growth rate of the average throughput and the growth rate of the outage throughput h... | 3,570 | 1,837 | 1,267 | 3,527 | 3,751 | 0.770325 | github_plus_top10pct_by_avg |
Yes Yes
The proband underwent a series of genetic tests including oligo array, fragile X, *MECP2*, *CDKL5*, *SLC9A6*, and *COH1*, all of which were negative. The sibling also underwent genetic testing (*ZEB2* and *MECP2*). Both sisters had metabolic studies... | 3,571 | 520 | 3,193 | 3,559 | null | null | github_plus_top10pct_by_avg |
js; @Li:2012cfa; @Atwood:2012ac; @Grossman:2012ry; @Brod:2011re]. Another example for category (3) is the $\Delta I=1/2$ rule in the kaon sector which is further discussed in sections \[sec:DeltaI12inKDB\] and \[sec:UandIrules\].
The current data, Eq. (\[eq:mainresult\]), is consistent with category (2). In the SM pic... | 3,572 | 1,166 | 3,073 | 3,289 | 1,346 | 0.790664 | github_plus_top10pct_by_avg |
is to generalize this result to normal surfaces, see Theorem \[thm:Esnault\].
Cyclic coverings of P2 branched along a curve
---------------------------------------------
In the particular case when $X=\PP^2$ the complex projective plane and $\mathcal{C}$ is a reduced projective plane curve of degree $n$, the descrip... | 3,573 | 2,502 | 2,238 | 3,353 | 2,059 | 0.783146 | github_plus_top10pct_by_avg |
y the same, as in the case of the surface-interacting polymer chain in a poor solvent in Euclidean spaces [@r1; @r2; @r3]. On the other hand, the obtained phase diagrams for CSAWs model, resemble the phase diagrams of the same surface-interacting chain problem, in fractal containers [@EZM]. This similarity is not surpr... | 3,574 | 2,670 | 3,680 | 3,248 | null | null | github_plus_top10pct_by_avg |
gg(\frac{1}{R_\Lambda(\lambda')}-\frac{1}{R_0(\lambda')}\bigg)\bigg[-\theta_\Lambda(\lambda_i)-c+\frac{c}{2}(e^{-c\lambda_i}-e^{-c \lambda'})+\int_{\lambda_i}^{\lambda'} e^{-c\xi} p_\Lambda(\xi)d\xi\bigg]$$ $$+\frac{1}{R_0(\lambda')}\bigg[-\theta_\Lambda(\lambda_i)-c+\frac{c}{2}(e^{-c\lambda_i}-e^{-c \lambda'})+\int_{\... | 3,575 | 853 | 2,599 | 3,537 | null | null | github_plus_top10pct_by_avg |
to the degree of $h(x)$.* $\Box$
Let $h_1(x)$ and $h_2(x)$ be the parity-check polynomials of $1$-generator skew GQC codes $C_1$ and $C_2$, respectively. If $C_1=C_2$, then $h_1(x)=h_2(x)$, which implies that ${\rm deg }(h_1(x))={\rm deg}(h_2(x))$. It means that $R/(h_1(x))_r=R/(h_2(x))_r$. Conversely, suppose $h_1(x... | 3,576 | 1,495 | 2,331 | 3,323 | 2,148 | 0.782266 | github_plus_top10pct_by_avg |
rn hidden inside a neural unit. Lots of visualization methods have been used in the literature.
Gradient-based visualization [@CNNVisualization_1; @CNNVisualization_2; @CNNVisualization_3] estimates the input image that maximizes the activation score of a neural unit. Dosovitskiy *et al.* [@FeaVisual] proposed up-conv... | 3,577 | 650 | 3,817 | 3,301 | 3,379 | 0.772763 | github_plus_top10pct_by_avg |
null and satisfying the normalization (\[norma\]).
The null geodesic corresponding to the element $\Lambda=(p, k^\mu)$ will be denoted as $\gamma_\Lambda(\lambda)$ in the following. All the quantities depending on this curve such as $G_\gamma(\lambda)$ will be subsequently denoted as $G_\Lambda(\lambda)$ and so on. T... | 3,578 | 2,481 | 2,959 | 3,319 | null | null | github_plus_top10pct_by_avg |
a^2}\over Z} \sum_{l,m,s=\pm} \left| \sum_{n \leq l}
v_{m,s}^n
\sqrt{{l! \over n!}}\sum_{n'=0}^n {n \choose n'}
{\alpha^{n-n'}(-\alpha)^{l-n'} \over(l-n'!)} \right| ^2 \nonumber \\
&&(e^{-\beta \varepsilon_{m,s}}+
e^{-\beta(\varepsilon_0+E_0+l\hbar\omega_0-\varepsilon_{BP})})
\delta(\omega+\varepsilon_{m,s}-\varepsi... | 3,579 | 3,477 | 3,633 | 3,298 | null | null | github_plus_top10pct_by_avg |
\alpha$" prescription to local fluctuations, one might expect that ${\cal Q}_p \simeq \alpha$.
The Dispersion Relation
=======================
General considerations
----------------------
In terms of these dimensionless quantities, the dispersion relation is: $$\begin{aligned}
\lefteqn{3\omega_{*}^5
+ \left[i k_{*... | 3,580 | 3,594 | 3,588 | 3,325 | null | null | github_plus_top10pct_by_avg |
f\right\Vert _{q,p}. \label{A38}$$
**Proof**. We will prove (\[A38\]) first. Let $\alpha $ with $%
\left\vert \alpha \right\vert \leq q.$ By (\[A36\]) $$\begin{aligned}
\left\vert \partial ^{\alpha }(\psi _{k}P_{t}^{\ast }(f/\psi
_{k})(x))\right\vert &\leq &C\psi _{k}(x)\sum_{\left\vert \gamma \right\vert
\leq q}\le... | 3,581 | 1,367 | 1,707 | 3,562 | null | null | github_plus_top10pct_by_avg |
bility density $p(x,v)$ and the current $j_{s}$ as $$p(x,v,\infty)=
N\left[\left(\frac{\pi KT}{2 \alpha}\right)^{\frac{1}{2}}
+\int_{0}^{v-|a|x}dz \exp\left(-\frac{\alpha z^{2}}{2KT}\right)\right]
\exp\left[ -\frac{\frac{v^{2}}{2}+\tilde{V}(x)}{KT}\right]$$ with $$\begin{aligned}
F_{s} =
N\left[\left(\frac{\pi KT}{2 \... | 3,582 | 3,466 | 3,388 | 3,248 | null | null | github_plus_top10pct_by_avg |
-contrbd\])]{}, we easily obtain $$\begin{aligned}
{\label{eq:EE'E''predec3}}
\Theta_{y,x;{{\cal A}}}\big[{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle R_1(b)$}}}\big]&=\sum_{\substack{{\partial}{{\bf m}}={\varnothing}\\ {\partial}{{\bf n}}={\overline{b}}{\vartriangle}x}}\frac{w_{{{\cal A}}{^{\rm c}}}({{\bf m}})}{Z_{
{{\... | 3,583 | 1,492 | 2,187 | 3,465 | null | null | github_plus_top10pct_by_avg |
to multi-partitions: $\muhat=
(\mu^1,\ldots,\mu^k) \in \left(\calP_n\right)^k$ is rectangular if each $\mu^i$ is (the $\mu^i$’s are not required to be of the same length). Note that $\muhat$ is rectangular if and only if the associated dimension vector $\v$ satisfies $(\e_{[i,j]},\v)= 0$ for all $[i,j]$ by .
\[sigma-... | 3,584 | 1,901 | 3,219 | 3,217 | 3,468 | 0.772153 | github_plus_top10pct_by_avg |
ctly the one of a bicrossed product on the set $ H \times (G,
*)$ associated to the actions $\alpha'$ and $\beta'$. In other words, we have to prove that $$\bigl( h( g \rhd' h'), \, (g \lhd' h')g'\bigl) = \psi^{-1}
\Bigl(\psi(h,g) \cdot \psi(h',g')\Bigl)$$ for all $h$, $h' \in H$, $g$, $g' \in G$ or equivalently, as $\... | 3,585 | 2,041 | 3,109 | 3,306 | null | null | github_plus_top10pct_by_avg |
Soft Markers (N = 19) Control (N = 19) *p*
---------------------------------------------------------------------------------------------------- ----------------------- ---------------------- ----------
*Socio-demographic Characteristics* ... | 3,586 | 4,752 | 3,104 | 2,678 | null | null | github_plus_top10pct_by_avg |
------------------------
Let $D$ be an associative dialgebra. If we define on the set $D$ new operations $$\label{eq:QuasiJordanProduct} a{\mathbin{{}_{(\vdash)}}}b=\frac{1}{2}(a{\mathbin\vdash}b+b{\mathbin\dashv}a),\ a{\mathbin{{}_{(\dashv)}}}b=\frac{1}{2}(a{\mathbin\dashv}b+b{\mathbin\vdash}a)$$ then we obtain a new... | 3,587 | 1,994 | 3,539 | 3,173 | 1,322 | 0.791025 | github_plus_top10pct_by_avg |
mpling using the starspot model and revealed that the variations of the shape of light curves are mainly accounted for by spot evolution and migration on the K star of SZ Psc. @eaton2007 suggested that the cooler component have many small starspots rather than a few large ones, because its line profiles lack large dist... | 3,588 | 4,557 | 3,313 | 3,517 | null | null | github_plus_top10pct_by_avg |
text of the main neutrinosphere models proposed.
For a hard neutrinosphere model in thermal equilibrium as considered in Refs. [@kusegre; @kusegref; @qian], the momentum asymmetry in the ${\bf v}$ direction is generated by the emission at points with different temperatures on the resonance surface: $\Delta p/p\approx ... | 3,589 | 3,283 | 3,808 | 3,469 | null | null | github_plus_top10pct_by_avg |
e to generate three-dimensional GS states.
[**Acknowledgments**]{}
The author would like to thank B. Etemadi for useful discussions and F. Sales-Mayor for a careful reading of the text.
[**Appendix**]{}
This appendix gives closed form expressions for the matrix elements needed to construct the matrix $H_{\tau \bar{... | 3,590 | 4,119 | 2,622 | 3,091 | null | null | github_plus_top10pct_by_avg |
up to logarithmic corrections as $q^2\to\infty$ because of asymptotic freedom. The continuum tree-level propagator is $1/q^2$. We also expect asymptotic freedom on the lattice despite finite lattice spacing artefacts. We [*define*]{} the lattice $q_\mu$ such that the lattice $D^{\rm tree}(q)\equiv 1/q^2$, and use this ... | 3,591 | 2,008 | 3,488 | 3,210 | null | null | github_plus_top10pct_by_avg |
with similar $T_\mathrm{eff}$ (about 1 dex), combined with the large error bars on theoretical predictions.
Since in most of the cases the models with $\alpha_\mathrm{PMS}=\alpha_\mathrm{MS}$ disagree with the data, and given the high sensitivity of $^7$Li surface abundance predictions to the convection efficiency, it... | 3,592 | 1,109 | 3,549 | 3,663 | 1,011 | 0.795809 | github_plus_top10pct_by_avg |
o [n']}\bigotimes_{v' \in V([n'])}
A^{opp} \otimes A^{\otimes f^{-1}(v')}$$ for any $[n'] \in \Lambda$. Then $L^p{\operatorname{\sf tr}}_\#I_{n!}E = 0$ for $p \geq 1$, and one checks easily that $${\operatorname{\sf tr}}_\# I_{n!}E = i_{n!}{\operatorname{\sf tr}}E = i_{n!}A^{\otimes n} \in {\operatorname{Fun}}(\Lambda,... | 3,593 | 3,355 | 2,677 | 3,190 | 2,771 | 0.777091 | github_plus_top10pct_by_avg |
of this blow-up. We have the following commutative diagram: $$\xymatrix@M=10pt{
E \ar@{->>}[d] \ar@<-.5ex>@{^(->}[r] & {{{{\widetilde{{{\mathbb{P}}}}}}}}^8 \ar@{->>}[d]^\pi
\ar@<-.5ex>@{^(->}[r] & {{\mathbb{P}}}^8\times {{\mathbb{P}}}^N \ar@{->>}[d] \\
{{\mathscr S}}\ar@<-.5ex>@{^(->}[r] & {{\mathbb{P}}}^8 \ar@{-->}... | 3,594 | 2,675 | 3,085 | 3,132 | null | null | github_plus_top10pct_by_avg |
the fidelity decay.
Derivation of EQ. (\[eq:Teff\]) and qualitative discussion {#app:theo}
==========================================================
The calculation of Eq. (\[eq:ss\_ft\]) proceeds along the same lines as in [@ver85a], hence we indicate below only the main steps and essential differences. First, we ... | 3,595 | 1,630 | 1,543 | 3,275 | 3,029 | 0.775351 | github_plus_top10pct_by_avg |
the auxiliary field $G^{--}$, keeping only the physical degrees of freedom.
For simplicity, and as in [@CalHu99], let us assume a symmetric scalar field theory, meaning that the background fields vanish and also $\Gamma_{,A\left(BC\right)}=0$. Then the 2PI EA can be written as
=12S\_[AB]{}\^[AB]{}-i2+\_Q
The first ... | 3,596 | 1,485 | 3,032 | 3,447 | null | null | github_plus_top10pct_by_avg |
Furthermore, when implemented with many particles, the learner can be used to make estimates of the cost landscape to determine what parameters most contributed to BEC production and aid better experimental design. In future work we will apply MLOO to atomic species with more exotic scattering properties [@altin_collap... | 3,597 | 2,780 | 3,947 | 3,433 | 2,374 | 0.780429 | github_plus_top10pct_by_avg |
$ if and only if $\mu=\nu^1+\cdots+\nu^s$ up to permutation of the parts of each $\nu^p$ for $p=1,\ldots,s$.
It follows immediately from the definition of the monomial symmetric function.
Let $\v$ be the dimension vector associated to $\muhat$.
\[connectedness1\] If $\v$ is in the fundamental set of imaginary roots ... | 3,598 | 3,224 | 2,750 | 3,168 | 4,015 | 0.768644 | github_plus_top10pct_by_avg |
nd to Inwon Kim for helpful discussions as well suggesting the problem. This work was in part supported by NSF grant DMS-0907931.
Appendix
========
\[lem:GNS\] Let $d \geq 2$ and $f:{\mathbb R}^d \rightarrow {\mathbb R}$ satisfy $f \in L^p\cap L^q$ and ${\nabla}f^k \in L^r$. Moreover let $1 \leq p \leq rk \leq dk$, $... | 3,599 | 2,717 | 2,194 | 3,317 | null | null | github_plus_top10pct_by_avg |
of a conformal generator $R_{\mu }$ with pure discrete spectrum. The perturbative reading of $R_{0\text{ }}$as a Hamiltonian in its own right i.e. associated with an action in a functional integral setting naturally leads to the AdS formulation. The formal service role of AdS in order to access CQFT by a standard pertu... | 3,600 | 950 | 3,199 | 2,991 | null | null | github_plus_top10pct_by_avg |
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