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 |
|---|---|---|---|---|---|---|---|
t\{ W ^{\dagger} A (UX) \right\}_{L k}
\nonumber \\
&+&
\sum_{n} \sum_{k} \sum_{K \neq L} \sum_{m \neq k}
\biggl[
\frac{ (ix) }{ ( \Delta_{K} - h_{k} ) ( \Delta_{L} - h_{k} ) ( h_{m} - h_{k} ) }
e^{- i ( h_{k} - h_{n} ) x}
\nonumber \\
&-&
\frac{1}{ ( \Delta_{K} - h_{k} )^2 ( \Delta_{L} - h_{k} )^2 ( h_{m} - h_{k}... | 1,301 | 2,141 | 2,085 | 1,385 | null | null | github_plus_top10pct_by_avg |
because the flavor structures have different dependences in these phases, the result is that the quark and lepton EDMs become decorrelated.
Conclusion
==========
In the paper [@SmithTouati], we developped a systematic method to study the flavor structure behind the quark and lepton EDMs which can be extended easily ... | 1,302 | 1,050 | 2,695 | 1,602 | null | null | github_plus_top10pct_by_avg |
tate frequency (-energy) in the charge $+q$ sector. The dashed line denotes the charge $+q$ continuum. For $q=0$, $\omega_0\sim \sqrt{T}\ll m$. For small positive $q$, $\omega_0$ crosses zero. At some $q/m\sim\calO(1)$, $\omega_0$ crosses into the positive-charge continuum. At this point the energy of an oppositely-cha... | 1,303 | 450 | 975 | 1,429 | null | null | github_plus_top10pct_by_avg |
_{i+1}\cdot ({}^tm_{i+1,i+1}'\cdot {}^tm_{i, i+1})
=\pi m_{i,i}^{\ast\ast}+\pi \tilde{z}_i''^{\dag\dag}
\end{array} \right.$$ for some formal expansion $\tilde{z}_i''^{\dag\dag}$. Therefore, $$\delta_{i-1}v_{i-1}\cdot {}^t\tilde{m}_{i, i-1}''+\delta_{i+1}v_{i+1}\cdot {}^t\tilde{m}_{i, i+1}''=
\pi\left((... | 1,304 | 725 | 1,089 | 1,257 | 4,065 | 0.768344 | github_plus_top10pct_by_avg |
tau$ to $\cS_1$ and $\bz+t_2\bv_\tau$ to $\cS_2$ where we fix $t_1=0$ and $t_2=1$ (other choices of values would also work). $\cS_i$ then responds with the value of $F$ at the point $\bgam^{\bz+t_i\bv_\tau}$, that is with $F(\bgam^{\bz+t_i\bv_\tau})$ and the value of the ‘first order derivative’ at the same point $F^{(... | 1,305 | 3,108 | 1,374 | 1,286 | null | null | github_plus_top10pct_by_avg |
quiv \lim\limits_{\epsilon\to 0}\left[ \frac{d}{dz}\phi_j(k,\pm 1 + \epsilon) - \frac{d}{dz}\phi_j(k,\pm 1 - \epsilon)\right]$$ are the discontinuities in $d\hat{\phi}/dz$ and $d\phi_j/dz$ at $z = \pm 1$. With $\hat{\phi}$ given by Eq. and $\phi_j$ given by Eq. , one can show that $$\phi_j(k,1) = \frac{-\Delta_{+ j}}{... | 1,306 | 3,356 | 1,552 | 1,297 | null | null | github_plus_top10pct_by_avg |
[@Lecomte2007] of the modified master operator $\mathbb{W}_s$, described by $$(\mathbb{W}_s)_{ij} = e^{-s} W_{j\rightarrow i} - r_i\delta_{i,j}\,.
\label{eq:Ws}$$ This operator generates the dynamics of $s$-biased ensembles of trajectories via $\partial_t P_i(s) = \sum_j(\mathbb{W}_s)_{ij} P_j(s)$. The eigenstate of... | 1,307 | 199 | 1,926 | 1,381 | null | null | github_plus_top10pct_by_avg |
rong vertices for the $NN\pi$, $NN\pi\pi$, $\Lambda \Sigma\pi$ and $\Lambda N K$ which arise from the Lagrangians in Eq. (\[eq:str\]). \[vf1\]](lnks "fig:")
The strong vertices for the interaction between our baryonic and mesonic degrees of freedom are obtained from the strong SU(3) chiral Lagrangian [@donoghue], $$\b... | 1,308 | 581 | 1,317 | 1,409 | null | null | github_plus_top10pct_by_avg |
ip}$ in the tunneling matrix element, the general expression for $\tau^{(2)}_{\sigma}(\w)$ (Eq. ) in the inelastic current $I^{\rm (2)}_{\rm inel}$ takes on the shape as Eq. , leading to an inelastic current which for the special case of a flat DOS at the Fermi level leads to steps in the differential conductance at th... | 1,309 | 183 | 828 | 1,454 | 2,950 | 0.775867 | github_plus_top10pct_by_avg |
so that $a$ has a matrix representation $A\in\mathbb{R}^{m\times n}$ where $\mathbb{R}^{m\times n}$ is the collection of $m\times n$ matrices with real entries. The inverse $A^{-1}$ exists and is unique iff $m=n$ and $\textrm{rank}(A)=n$; this is the situation depicted in Fig. \[Fig: functions\](a). If $A$ is neither ... | 1,310 | 2,397 | 1,961 | 1,418 | 3,627 | 0.771186 | github_plus_top10pct_by_avg |
frac{\pi m}{N_\phi} \right) \right]^2.$$ Note that $\lambda^m_\phi \rightarrow -m^2/R^2$ for $m/N_\phi \ll 1$. The eigenfunction ${\cal P}^m_j$ satisfies the discrete orthogonality relation $$\frac{1}{N_\phi} \sum_{j=1}^{N_\phi}({\cal P}_j^m)^* {\cal P}^{m'}_j = \delta_{mm'}\quad\text{and}\quad\frac{1}{N_\phi} \sum_{... | 1,311 | 3,714 | 1,678 | 1,278 | null | null | github_plus_top10pct_by_avg |
and $X_2$ can be tiled with horizontal copies of $T$.
Note that $(x,x+n(k+1))+(2,k+3) = (x+2,(x+2)+(n+1)(k+1))$. Also, if $x \equiv 2n+r \pmod 8$, then $x+2 \equiv 2(n+1)+r \pmod 8$. Hence, by the definitions of $S_2$ and $S_3$, we see that $X_1$ is invariant under translation by $(2,k+3)$. To show that vertical copie... | 1,312 | 3,755 | 1,596 | 1,170 | 3,239 | 0.773822 | github_plus_top10pct_by_avg |
string has a larger number of pairs, as shown in the following example.
Let $c:\{{\texttt{\textup{a}}},{\texttt{\textup{b}}},{\texttt{\textup{c}}}\}\times\{{\texttt{\textup{a}}},{\texttt{\textup{b}}},{\texttt{\textup{c}}}\}^{\leq{1}}\rightarrow\{0,1\}^{+}$ be an adaptive code of order one given as in the previous exa... | 1,313 | 2,680 | 2,781 | 1,322 | 1,054 | 0.795117 | github_plus_top10pct_by_avg |
&+& 140 A^6 B+292 A^7 B +424 A^8 B+ 332 A^9 B+12 A^3
B^2+12 A^4
B^2+ 118 A^5 B^2\nonumber\\ \fl
&+& 380 A^6 B^2+ 806 A^7 B^2+664 A^8 B^2+72 A^4
B^3 +352 A^5 B^3+704 A^6 B^3+ 1728 A^7 B^3
\nonumber\\ \fl
&+& 344 A^4 B^4+ 1568 A^5 B^4+848
A^6B^4+264 A^4 B^5+3192 A^5 B^5+ 320 A^3 B^6\, , \label{eq:Ab3} \\
\fl B'&=&A^6+... | 1,314 | 4,309 | 414 | 957 | null | null | github_plus_top10pct_by_avg |
r the classical regularization methods we can compute the variance function which gives uncertainty estimate for the solution which in the classical formulation is not available. Furthermore, the hyperparameter estimation methods outlined in the next section provide principled means to estimate the parameters also in t... | 1,315 | 4,487 | 1,098 | 883 | 4,049 | 0.76845 | github_plus_top10pct_by_avg |
) \right\},$$ where, for $j=1,\ldots,s$, $t_{2j-1} = t_{2j} = \frac{t}{\|G_j\|}$.
Recalling that $\widehat{\nu} = G \widehat{\psi}$, we have that $$\left\| \sqrt{n}(\hat{\nu} - \nu ) \right\|_\infty \leq t \quad
\text{if and only if } \quad
\sqrt{n} (\hat{\psi} - \psi) \in P(G,t).$$ Similarly, if $\tilde{Z}_n \si... | 1,316 | 3,086 | 1,286 | 1,108 | null | null | github_plus_top10pct_by_avg |
�(\[eq.3.1.4\]) for calculation of a new reflectionless potential $V_{2}(r)$ with a barrier on the basis of the known reflectionless inverse power potential $V_{1}(r)$. Let’s assume, that these potentials are connected with one superpotential $W_{2}(r)$. Let’s consider the wave function for the reflectionless inverse p... | 1,317 | 3,741 | 1,241 | 1,234 | 2,778 | 0.777044 | github_plus_top10pct_by_avg |
A$ of size at most $\exp(\log^{O(1)}2\tilde K)$ such that $$\label{eq:induction.step}
\tilde A\subset X\tilde A_1\cdots\tilde A_r.$$ Since $G/N_0$ is generated by the $K$-approximate group $\rho(A)$, we may apply the induction hypothesis to each approximate subgroup $\rho(\tilde A_i)$ of $G/N_0$ to obtain, for each $i=... | 1,318 | 1,019 | 1,726 | 1,242 | null | null | github_plus_top10pct_by_avg |
\left \{
% \frac{1}{\bar z-\bar x}\left(
%-\frac{c_+}{c_++c_-} t^a \phi(w) 2\phi \delta^{(2)}(x-w) + :\bar \p j^a_{L,z} \phi:(w) \right. \right. \cr
%&\qquad \qquad \qquad \left.
%+ {A^a}_c \frac{1}{\bar x-\bar w} :j^c_{L,z} \phi:(w) + {B^a}_c \frac{1}{x-w} :j^c_{L,\bar z} \phi:(w) + \mathcal{O}(f^4)
%\right) \cr
%&... | 1,319 | 2,845 | 1,679 | 1,312 | null | null | github_plus_top10pct_by_avg |
\alpha}\lambda_{q'\beta}U_{\beta 1}
U_{\alpha 1}^{*} = \xi_{q1}^{*} \xi_{q'1}$ with $(q,q'=d,s,b)$, and ${\cal B} = \kappa_{\alpha \beta}U_{\beta 1} U_{\alpha 1}^{*}$. For flavor changing processes, ${\cal A}_{qq'}$ plays the main role, with ${\cal B}$ its counterpart in flavor conserving processes.
Before continuing,... | 1,320 | 715 | 1,821 | 1,460 | 2,620 | 0.778377 | github_plus_top10pct_by_avg |
y $$\frac{1}{2^m}q : L\longrightarrow A, x\mapsto \frac{1}{2^m}h(x,x).$$ Then $\frac{1}{2^m}q$ mod 2 defines a quadratic form $L/\pi L \longrightarrow \kappa$. It can be easily checked that $\frac{1}{2^m}q$ mod 2 on $L/\pi L$ is an additive polynomial. We define a lattice $B(L)$ as follows.
- $B(L)$ is defined to be... | 1,321 | 2,346 | 1,260 | 1,222 | null | null | github_plus_top10pct_by_avg |
egin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(2*.25,0);\end{tikzpicture}}};{b\!\!+\!\!2},;1_2{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(2*.25,0);\end{tikzpicture}}};1;1;1)$}};\\
B&=
{\text{\footnotesize$\gyoungx(1.2,;1_2{{\begin{tikzpicture}[baseline=0cm]\draw[thic... | 1,322 | 1,463 | 1,204 | 1,325 | 1,525 | 0.788624 | github_plus_top10pct_by_avg |
sin^2(\theta)(a^2\cos^2(\theta)+r^2)^2}{(r\alpha\cos(\theta)-1)^8}}(a^2\cos^2(\theta)+r^2)^5(r\alpha \cos(\theta)-1)^3} \nonumber\\
&\bigg(\sin(\theta)\Big(((2a^{10}\alpha^{3} m^{2} r-2a^{8}\alpha m^{2}r)\cos^{8}(\theta)-4(a^{4}m^{2}\alpha^{2}+(9\alpha^{2}r^{2}-1)m^{2}a^{2})a^{6}\cos^{7}(\theta)-10(m^{2}(\frac{34}{5}r^... | 1,323 | 1,577 | 991 | 1,428 | null | null | github_plus_top10pct_by_avg |
\[Sec:Nz\] we present the results on a stack of bilayers along the same lines as for the bilayer. Finally, in Sec. \[sec:dis\] we discuss the implications of our analytical and numerical results and also provide an alternative model for the SP.
Bilayer model of SP {#Sec:I}
===================
Here we introduce a mode... | 1,324 | 352 | 1,470 | 1,275 | 1,399 | 0.790055 | github_plus_top10pct_by_avg |
erline{u}}_1({\overline{E}},{\vec{p}\,'}) \gamma_\mu ({\cancel{k}_N}+M_N)
u_1(E_p^\Lambda,{\vec{p}}) \nonumber\\
&\times&
{\overline{u}}_2({\overline{E}}_p,-{\vec{p}\,'})
\gamma_\nu
u_2(E_p,-{\vec{p}})\,.\end{aligned}$$ Using heavy baryon expansion, $$\begin{aligned}
V_a
&=&\ \frac{G_Fm_\pi^2h_{\Lambda N}}{8\Delta Mf_... | 1,325 | 240 | 749 | 1,508 | null | null | github_plus_top10pct_by_avg |
and
may
not
be
relied on by anyone as the basis of a contract by estoppel
or
otherwise.
Thank you.
**********************************************************************
---------------------- Forwarded by Vince J Kaminski/HOU/ECT on ... | 1,326 | 274 | 947 | 2,024 | null | null | github_plus_top10pct_by_avg |
lpha }_p)
=(q_{pj}q_{jp})^{-c_{pj}^\chi },\\
\xi _1({\alpha }_j)=q_{pj}^{{b}-1} q_{jp}^{{b}-1}
=(q_{pj}q_{jp})^{-c_{pj}^\chi }.
\end{gathered}$$ Hence $\xi _1({\alpha }_j)=\xi _2({\alpha }_j)$ also in this case. This proves the lemma.
Multiparameter Drinfel’d doubles {#sec:DD}
===========================... | 1,327 | 780 | 1,538 | 1,235 | 3,475 | 0.772078 | github_plus_top10pct_by_avg |
t we can easily check the validity of the result. We have checked that if we substitute $ e=0 $ in these calculations, then we get back the result for the accelerating rotating black hole.
In FIG. \[fig6\] we find that the gravitational entropy density is not smooth, but contains several singularities. The above analy... | 1,328 | 1,084 | 1,689 | 1,379 | null | null | github_plus_top10pct_by_avg |
parents change jobs 0.89 times more often (*p* \< .01) than nontransnational parents. Thus, the first condition for mediation is only met for job instability and not for job absenteeism. Therefore, we only continue with the next steps of the mediation analysis for job instability.
######
Results of Mediation Analys... | 1,329 | 2,424 | 1,910 | 1,238 | null | null | github_plus_top10pct_by_avg |
D-19
Baloxavir marboxil COVID-19
Thymosin α1 MERS
Nucleotide reverse transcriptase inhibito... | 1,330 | 5,884 | 314 | 612 | null | null | github_plus_top10pct_by_avg |
i _{\kappa }(x)=(1+\left\vert x\right\vert ^{2})^{\kappa },\quad \kappa
\in {\mathbb{Z}} . \label{NOT2}$$The following properties hold:
- for every $\kappa\geq \kappa^{\prime }\geq 0$, $$\psi _{\kappa }(x) \leq \psi _{\kappa ^{\prime }}(x); \label{NOT3a}$$
- for every $\kappa\geq 0$, there exists $C_{\kappa }>0... | 1,331 | 1,755 | 1,237 | 1,263 | null | null | github_plus_top10pct_by_avg |
**Sliding window (SW)** **Most significant result**
------------------------- ----------------------------- -------- -------- -------------- --------------
**SNPs/SW** **No. of SW** **SW** **SW** ***P*value** ***P*value**
1 ... | 1,332 | 2,048 | 1,973 | 1,512 | null | null | github_plus_top10pct_by_avg |
addition, there is another functor $$\pi_1^* \: \equiv \: \pi^* \otimes {\cal O}_{\Lambda}(1): \:
\mbox{Coh}({\mathbb P}^n) \: \stackrel{\sim}{\longrightarrow} \:
\mbox{Coh}({\mathbb P}^n, \chi(\alpha) ).$$ (In fact, there is an analogue of $\pi_1^*$ for every ${\cal O}_{\Lambda}(
\mbox{odd})$.)
To determine $\pi^* {\... | 1,333 | 1,160 | 1,528 | 1,185 | null | null | github_plus_top10pct_by_avg |
PTSD symptom clusters and CSB among those with a PTSD diagnosis. The results of this model are displayed in [Table 3](#T3){ref-type="table"}. The re-experiencing symptom cluster was the only cluster significantly associated with CSB (*p* \< 0.05). A 1-standard-deviation increase in the re-experiencing symptoms was ass... | 1,334 | 39 | 2,262 | 1,731 | null | null | github_plus_top10pct_by_avg |
the binary probability estimates along the path from the root node to the leaf node corresponding to the class.
For non-trivial multi-class problems, the space of potential nested dichotomies is very large. An ensemble classifier can be formed by choosing suitable decompositions from this space. In the original formul... | 1,335 | 1,133 | 2,070 | 1,135 | 1,715 | 0.786496 | github_plus_top10pct_by_avg |
orphisms $${\sD}^{[1]}\stackrel{(i_1)_\ast}{\to}{\sD}^{A_1}\stackrel{(i_2)_!}{\to}{\sD}^{A_2}\stackrel{(i_3)_!}{\to}{\sD}^{A_3}\stackrel{(i_4)_\ast}{\to}{\sD}^\boxbar.$$ The first two functors add a cofiber square and homotopy (co)finality arguments (for example based on [@groth:ptstab Prop. 3.10]) show that the remain... | 1,336 | 1,076 | 861 | 1,258 | 1,717 | 0.786487 | github_plus_top10pct_by_avg |
T transformation $i \leftrightarrow j$, $U \rightarrow U^*$, $W \rightarrow W^*$, etc. as $$\begin{aligned}
\left\{ (UX)^{\dagger} A W \right\}_{i K} &\rightarrow &
\left\{ W^{\dagger} A (UX) \right\}_{K j},
\nonumber \\
\left\{ W^{\dagger} A (UX) \right\}_{K j} &\rightarrow &
\left\{ (UX)^{\dagger} A W \right\}_{i ... | 1,337 | 4,045 | 1,380 | 1,067 | null | null | github_plus_top10pct_by_avg |
d only if $\ltheta^*_{i} > \ltheta^*_{\j}$.
Recall that $\gamma_{\beta_1} \equiv \ld (\kappa-2)/(\lfloor \ell\beta_1 \rfloor+1 )(d-2) $ and $\eta_{\beta_1} \equiv (\lfloor \ell \beta_1 \rfloor +1)^2/2(\kappa-2)$. Construct Doob’s martingale $(Z_2,\cdots,Z_{\kappa})$ from $\{Y_{\k}\}_{ 3 \leq \k \leq \kappa}$ such that... | 1,338 | 722 | 1,470 | 1,279 | null | null | github_plus_top10pct_by_avg |
}\subset\cdots\subset E^1\subset E^0=(\F_q)^n$$such that ${\rm dim}(E^{i-1}/E^i)=\lambda_i$.
Let $G$ acts on $\calF_\lambda$ in the natural way. Fix an element $$X_o=\left(\{0\}=E^r\subset E^{r-1}\subset\cdots\subset E^1\subset E^0=(\F_q)^n\right)\in\calF_\lambda$$ and denote by $P_\lambda$ the stabilizer of $X_o$ in ... | 1,339 | 1,442 | 1,076 | 1,246 | null | null | github_plus_top10pct_by_avg |
e{{\scriptscriptstyle}(4)}}(f,x)$ to $\sum_{z,x}|x-y|^2|x|^t\tau_{y,z}Q'_{\Lambda;o}(z,x)$: $$\begin{aligned}
{\label{eq:IRSchwarz}}
\text{(i)}\quad\raisebox{-1.5pc}{\includegraphics[scale=0.14]
{IRnonSchwarz}}\hspace{5pc}
\text{(ii)}\quad\raisebox{-1.5pc}{\includegraphics[scale=0.14]
{IRSchwarz}}\end{aligned}$$ wher... | 1,340 | 971 | 1,677 | 1,343 | 1,053 | 0.795181 | github_plus_top10pct_by_avg |
Empty}}}(H_t){\geqslant}{\textsc{{Empty}}}(H'_t){\geqslant}{s}/2.$$
[Fix $m=m(n)$ to equal the $m$ provided by Lemma \[lem:empty\].]{} For $t=1,\ldots, m$, let $D_t$ be the $d$-element subset of $H_t$ that is chosen by the $t$-th ball. Define the indicator random variable ${\mathbb{I}}_t$ as follows: $${\mathbb{I}}_t:... | 1,341 | 2,598 | 1,152 | 1,314 | null | null | github_plus_top10pct_by_avg |
$ in the orthogonal group associated to $M_0''/\pi M_0''$ is $$T_1=\begin{pmatrix} \begin{pmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0& (x_j)_1 &1& (x_j)_1+1/\sqrt{b+b'}(z_j^{\ast})_1\\0&0& 0 & 1 \end{pmatrix} &0 \\ 0 & id \end{pmatrix}.$$ Since $(x_j)_1=0$ by Equation (\[e42\]), the Dickson invariant of $T_1$ is the same as tha... | 1,342 | 838 | 1,366 | 1,349 | 3,331 | 0.773077 | github_plus_top10pct_by_avg |
with $\bfun{\chi '}({\alpha }_i)<\infty $. This follows from Lemma \[le:Eheight\](i).
\[th:PBW\] Assume that $\chi \in {\mathcal{X}}_3$. Let $n=|R_+^\chi |\in {\mathbb{N}}$. Both sets $$\begin{aligned}
\label{eq:LusztigPBW+}
\big\{ E_{\beta _1}^{m_1} E_{\beta _2}^{m_2}\cdots E_{\beta _n}^{m_n}\,&|\,
0\le ... | 1,343 | 1,462 | 1,208 | 1,338 | null | null | github_plus_top10pct_by_avg |
xt{$q$ is a root of $1$, $m_{ij}\in {\mathbb{Z}}$ for all $i,j\in I$,}$$ such that the set $$\begin{aligned}
V^\chi _{\underline{n}}=\{\chi '\in {\overline{{\mathcal{X}}}}\,|\,&
R^{\chi '}_+ =R^\chi _+ ,\,
{b^{\chi '}}(\beta )={b^{\chi}} (\beta ) \text{ for all }
\beta \in R^\chi _{+{\mathrm{fin... | 1,344 | 2,646 | 1,353 | 1,292 | null | null | github_plus_top10pct_by_avg |
nd Novartis; Marta S. Figueroa is a consultant for Bayer, Alcon, Allergan, and Novartis; IMS Health received funding from Bayer HealthCare for the conduct, analysis, and reporting of the study; Jordi Farrés Martí is a salaried employee of Bayer HealthCare.
![Changes in visual acuity over the follow-up period compared ... | 1,345 | 4,957 | 1,120 | 448 | null | null | github_plus_top10pct_by_avg |
in this section. The differences between the present calculation and that in Ref. [@kha02] are the mesh size, the boundary condition, the cutoff energy for the QRPA calculation, and the treatment of the spin-dependent interaction ($G_{0}$ and $G_{0}^{\prime}$) in Eq. (\[eq:res\_ph\]). In the present calculation, the s... | 1,346 | 115 | 2,378 | 1,335 | 2,685 | 0.77787 | github_plus_top10pct_by_avg |
ot involve the collision operator $K=(K_1,K_2,K_3)$, and $u$ contains a direct contribution from the external (boundary) sources $g$ (through ). On the other hand, the field $u$ *right after collision* as modelled by the term $Ku$, acts as an internal source in the equation for the secondary field $w$, while external s... | 1,347 | 405 | 956 | 1,435 | 2,600 | 0.778541 | github_plus_top10pct_by_avg |
n the time-scale associated with mean shear ($S$). In other words, $$\frac{1}{\sqrt{\kappa^2E(\kappa)}} \ll \frac{1}{S}.$$ Using the “-5/3 law” of Kolmogorov [@kolmogorov41a] and Obukhov [@obukhov41a; @obukhov41b], this equation can be re-written as: $$\frac{1}{\sqrt{\kappa^{4/3} \overline{\varepsilon}^{2/3}}} \ll \fra... | 1,348 | 2,640 | 2,288 | 1,423 | 1,619 | 0.787523 | github_plus_top10pct_by_avg |
on the right into $M$ completes the proof of Lemma \[faber\].
The matrices $H$, $M$ appearing in Lemma \[faber\] may be omitted by changing the bases of $W$ and $V$ accordingly. Further, we may assume that $b>0$, since we are already reduced to the case in which $\alpha(0)$ is a rank-1 matrix. This concludes the proof... | 1,349 | 2,712 | 1,777 | 1,260 | 2,571 | 0.778793 | github_plus_top10pct_by_avg |
nctor is in fact a map from $RB(X^2)$ to $RB(G)$. Here we use Green’s notation for $RB(G)$.
Let $X$ and $Z$ be finite $G$-sets, let $a$ and $b$ be maps of $G$-sets from $Z$ to $X$. Let $$f=\xymatrix{
& Z \ar[dl]_{b}\ar[dr]^{a}&\\
X && X
}$$ The Burnside trace $Btr : RB(X^2)\to RB(G)$ is defined on $f$ by: $$Btr(f):=\{... | 1,350 | 2,373 | 1,531 | 1,270 | null | null | github_plus_top10pct_by_avg |
use of certain symmetries of the problem for a hollow charge distribution, @james77 devised a formulation that uses sine and cosine transforms to expresses the potential on the each surface as the sum of seven terms. We refer the reader to Equations (4.7)–(4.20) of @james77 for the description of this formulation, whi... | 1,351 | 3,372 | 1,913 | 1,399 | 3,514 | 0.771844 | github_plus_top10pct_by_avg |
type $I$}}(4n_i-4)$$ with variables $(m_{i,j})_{i\neq j}, (y_i, v_i, z_i, z_i^{\ast})_{\textit{i:even and $L_i$:of type $I^o$}},
(r_i, t_i, y_i, v_i, x_i, z_i, u_i, w_i, z_i^{\ast})_{\textit{i:even and $L_i$:of type $I^e$}}$, $ (r_i, t_i, y_i, v_i, x_i, z_i, u_i, w_i)_{\textit{i:odd and $L_i$:free of type I}}$, $ (m_... | 1,352 | 628 | 1,212 | 1,363 | 1,113 | 0.794239 | github_plus_top10pct_by_avg |
rved value of the “hierarchy”, $\lambda_{obs}$, and the observed value of the effective four-dimensional cosmological constant, which we take to be zero. Thus, we take as our renormalization conditions $$V_{\hbox{\footnotesize\it \hspace{-6pt} eff\,}}(\lambda_{obs})
={dV_{\hbox{\footnotesize\it \hspace{-6pt} eff\,}}\ov... | 1,353 | 3,016 | 1,864 | 1,354 | null | null | github_plus_top10pct_by_avg |
ity follows form equation , $\alpha\in \widehat{\mathcal O}(\vec X;\varnothing) =\mathcal O(m)$ has $m+1$ inputs, and $\beta\in\widehat{\mathcal
O}(\vec Y;{
\begin{pspicture}(0,0.1)(0.2,0.4)
\psline[linewidth=1pt, linestyle=dashed,dash=4pt 3pt](0.1,0)(0.1,0.4)
\end{pspicture}})=\mathcal O(n)$ (or similarly $\beta\i... | 1,354 | 2,328 | 1,536 | 1,315 | 1,819 | 0.785442 | github_plus_top10pct_by_avg |
(z\^[\*]{}), with $\Psi(z)$ is the digamma function (z) , and $z=1/2 -i\hat{\mu}$. At small chemical potential, $\aleph(z)$ can be expanded as (z)&=&-2\_E-4 2+14(3)\^2-62(5)\^4+254(7)\^6+[ O]{}(\^8).\[aleph\] In addition to the renormalized quark free-energy in Eq , the renormalized gluon free-energy is given as &=&-\
... | 1,355 | 1,003 | 253 | 1,386 | null | null | github_plus_top10pct_by_avg |
0.5941 (2) 0.3709 (3) 0.26080 (18) 0.0201 (10)
H25 0.5678 0.3462 0.2785 0.024\*
C26 0.57227 (19) 0.1766 (3) 0.36167 (16) 0.0112 (8)
C27 0.5416 (2) 0.2602 (3) 0.36530 (18) 0.0173 (9)
H27 0.5... | 1,356 | 3,929 | 1,159 | 1,131 | null | null | github_plus_top10pct_by_avg |
[${\bf Q}(y\!=\!+1|I)\!=\!0$]{}. Then, our approach selects and asks about an object $\hat{I}$ based on Equation (\[eqn:select\]). We use the answer to update ${\bf P}$. If a new object part is labeled during the QA process, we apply Equation (\[eqn:LossAOG\]) to update the AOG. More specifically, if people label a ne... | 1,357 | 142 | 1,544 | 1,405 | 1,655 | 0.787129 | github_plus_top10pct_by_avg |
Eq. (\[eq:DeltaACPdirParameter\]) as $$\begin{aligned}
\Delta a_{CP}^{\mathrm{dir}} &=
4\, \mathrm{Im}\left(\frac{\lambda_b}{\Sigma}\right) \left|\tilde{p}_0 \right| \sin( \delta_{\mathrm{strong}})\,,\end{aligned}$$ with the unknown strong phase $$\begin{aligned}
\delta_{\mathrm{strong}} &= \mathrm{arg}(\tilde{p}_0)\... | 1,358 | 960 | 1,791 | 1,309 | 1,557 | 0.788279 | github_plus_top10pct_by_avg |
trol the signals emitted on two distinct channels, which are propagated through the environment to the agents within a neighboring radius set to $50$. The choice for two channels was made to allow for signals of higher complexity, and possibly more interesting dynamics than greenbeard studies [@gardner2010].
The recei... | 1,359 | 1,107 | 2,700 | 1,171 | null | null | github_plus_top10pct_by_avg |
$ [@DF96] are fixed to reproduce the experimental data of the corresponding hyperon decays, while the ones involving kaons, $C_K^{PC}=-18.9$, $D_K^{PC}=6.63$, $C_{K}^{PV}=0.76$ and $D_K^{PV}=2.09$, are derived using SU(3) symmetry.
![Weak vertices corresponding to the $\Lambda N\pi\pi$, and $\Lambda N$ interactions. T... | 1,360 | 936 | 224 | 1,565 | 1,492 | 0.788895 | github_plus_top10pct_by_avg |
section \[integrability\] we comment on the classical and quantum integrability of the model, and its consistency with the conformal current algebra. We conclude in section \[conclusions\].
We have gathered many technical details in the appendices. In appendix \[compositeOPEs\] we give a prescription to compute OPEs ... | 1,361 | 827 | 615 | 1,334 | 3,816 | 0.769923 | github_plus_top10pct_by_avg |
learns from objects without part annotations. $$\begin{split}
S^{\textrm{unant}}_{\textrm{AOG}}&={\sum}_{u\in Child(v^{*})}S^{\textrm{unant}}_{u}\\
L^{\textrm{unant}}({\boldsymbol\Lambda}_{\textrm{AOG}})&={\sum}_{u\in Child(v^{*})}\lambda^{\textrm{close}}\Vert\Delta{\bf p}_{u}\Vert^2
\end{split}
\label{sec:unsuper}$$ ... | 1,362 | 205 | 1,012 | 1,406 | 2,362 | 0.780526 | github_plus_top10pct_by_avg |
2\to V$ of $p$, $X_2\to X$ of $g^{-1}(p)$ and an open embedding $ Z\times_XX_2\into Z_2:=Z\times_VV_2$. Our only remaining problem is that $Z_2\neq Z\times_XX_2$, hence $Z_2$ is not a subscheme of $X_2$. We achieve this by further shrinking $V_2$ and $X_2$.
The complement $B_2:=Z_2\setminus Z\times_XX_2$ is closed, th... | 1,363 | 1,065 | 977 | 1,283 | 2,767 | 0.777149 | github_plus_top10pct_by_avg |
The first containment is by Lemma \[l:qproperties\].\[f:q(r)\_bounds\]: $\frac{1}{2}\exp\lrp{-\frac{7\aq\Rq^2}{3}}\cdot g(z) \leq q(g(z)) \leq g(z)$. THe second containment is by Lemma \[l:gproperties\].4: $g(\|z\|_2) \in [\|z\|_2-2\epsilon, \|z\|_2]$.
\[l:hproperties\] Given a parameter $\epsilon$, define $$\begin{... | 1,364 | 4,399 | 671 | 988 | null | null | github_plus_top10pct_by_avg |
meet and join on $(\mathcal{L(S)},\subset )$ by the same symbols $^{\bot }$, $\Cap $, and $\Cup $, respectively, that we have used in order to denote the corresponding operations on $(\mathcal{L(H)},\subset )$ and $(\mathcal{E},\prec )$, and call $(\mathcal{L(S)},\subset )$ *the lattice of closed subsets of* $\mathcal... | 1,365 | 2,813 | 1,532 | 1,396 | 1,723 | 0.786392 | github_plus_top10pct_by_avg |
w_T}_2^2} \leq 32 \lrp{T^2 L^2 + TL_\xi^2} T\beta^2
\end{aligned}$$
Using the fact that conditioned on the randomness up to step $k$, $\E{\xi(v_0,\eta_{k+1}) - \xi(w_{k\delta}, \eta_{k+1})}=0$, we can show that for any $k\leq n$, $$\begin{aligned}
& \E{\lrn{v_{(k+1)\delta} - w_{(k+1)\delta}}_2^... | 1,366 | 2,788 | 1,366 | 1,337 | null | null | github_plus_top10pct_by_avg |
artial_{-}^{3}T^{-}\right)
. \label{delta2h--}%\end{aligned}$$ As $\beta_{+}\,\delta_{\eta}\int f_{++}Y^{+}d\phi\sim\lbrack Q_{+}%
(Y^{+}),Q_{+}(T^{+})+Q_{-}(T^{-})]$ (with $\beta_{\pm}=2l^{-1}\left( 1\pm(\mu
l)^{-1}\right) $) and $\beta_{-}\,\delta_{\eta}\int f_{--}Y^{-}d\phi
\sim\lbrack Q_{+}(Y^{+}),Q_{+}(T^{+})+Q_... | 1,367 | 320 | 891 | 1,359 | null | null | github_plus_top10pct_by_avg |
}$$ For all $i \in [d]$, we have, $$\begin{aligned}
\label{eq:hess_posl_12}
\E\Bigg[\sum_{\i = 1}^d \big(\big(A^{(j)}\big)^2\big)_{i\i} \Bigg] & \leq & \E\Bigg[ \bigg(\sum_{\i =1 }^d A^{(j)}_{i\i} \bigg) \max_{i \in [d]} \bigg\{ \sum_{\i =1 }^d A^{(j)}_{i\i}\bigg\} \Bigg] \nonumber\\
&\leq & \E\bigg[ D^{(j)}_{ii} \de... | 1,368 | 2,761 | 1,408 | 1,281 | null | null | github_plus_top10pct_by_avg |
0, 150\}$ and $n=10^5$. We report empirical sizes and powers for different distributions. Each experiment is repeated 500 times at the nominal level $\alpha=0.05$.
\[example1\] We consider the linear model: $Y=X^\top\beta + \varepsilon$. Here $\beta$ is a $7\times 1$ vector with all coordinates 0.2 and $X$ comes from ... | 1,369 | 3,737 | 1,842 | 1,230 | null | null | github_plus_top10pct_by_avg |
ies);
var allReporterFiles = files1.Union(files2);
var sw = Stopwatch.StartNew();
var fileCount = allReporterFiles.Count(); // <--- takes ~3.5 seconds
sw.Stop();
Trace.WriteLine($"KillChromeSoftwareReporterTool completed in: {sw.Elapsed.TotalMilliseconds}ms or {sw.Elapsed.TotalSeconds}sec");
A:
Is this a ... | 1,370 | 5,071 | 158 | 1,371 | 941 | 0.797176 | github_plus_top10pct_by_avg |
fig2\]. The collapse of the data from different runs, on to seemingly universal curves, is remarkable for all the cases except for $Ri_g > 0.2$. We would like to mention that similar scaling behavior was not found if other normalization factors (e.g., $h$) are used.
Both normalized $L_{OZ}$ and $L_b$ decrease monotoni... | 1,371 | 4,112 | 2,043 | 1,346 | 830 | 0.799171 | github_plus_top10pct_by_avg |
e, $$\begin{aligned}
\circled{1} + \circled{2} + \circled{4} + \circled{5}
\leq& \lrp{\LR + L_N^2} q'(g(z_t)) g(z_t) + 2\cm^2 q''(g(z_t)) + \frac{L_N^2\|y_t-y_0\|_2^2}{2\epsilon} + 2 \lrp{L + \LN^2}\epsilon\\
\leq& - \frac{2\cm^2\exp\lrp{-\frac{7\aq\Rq^2}{3}}}{32\Rq^2} q(g(z_t)) + \frac{L_N^2\... | 1,372 | 1,762 | 1,503 | 1,298 | null | null | github_plus_top10pct_by_avg |
e are extra factors of $\eta$ coming from the initial splitting of the photon into two open string states. When these are taken into account, the constraints from Crab Nebula [@crab] can be satisfied for much larger values of $\eta$. We postpone a more detailed discussion of D3-foam phenomenology for future work.
---... | 1,373 | 337 | 1,712 | 1,157 | null | null | github_plus_top10pct_by_avg |
ntical within machine precision to the potential from the full $2\pi$ domain. This confirms that our Poisson solver in a restricted $\phi\in[0,2\pi/P]$ domain correctly deals with mass distributions under $P$-fold azimuthal symmetry.
[^1]: <http://www.fftw.org/>
[^2]: <https://www.sandia.gov/~sjplimp/docs/fft/README.... | 1,374 | 277 | 657 | 1,525 | 3,199 | 0.77409 | github_plus_top10pct_by_avg |
+10450 Intron 26 \-
\* The position of the polymorphisms was calculated over the genomic DNA sequence taking the position of the start codon as a reference.
viruses-11-00706-t003_Table 3
######
Functional predictions in the missense mutations of the *HDAC6* g... | 1,375 | 4,039 | 1,534 | 851 | null | null | github_plus_top10pct_by_avg |
$\mathrm{Sp}(B_i/Y_i, h_i)$).}$$ This equation will be proved in Appendix \[App:AppendixA\]. Thus $\mathrm{Im~}\varphi$ contains the identity component of $\prod_{i:even} \mathrm{O}(B_i/Z_i, \bar{q}_i)_{\mathrm{red}}\times \prod_{i:odd} \mathrm{Sp}(B_i/Y_i, h_i)$. Here $\mathrm{Ker~}\varphi$ denotes the kernel of $\var... | 1,376 | 476 | 866 | 1,374 | null | null | github_plus_top10pct_by_avg |
Omega-expand\]) and $\hat{S}$-$\Omega$ relation in (\[hatS-Omega\]) as $$\begin{aligned}
\hat{S}_{i i}^{(2)} [2] &=&
\sum_{K} \left[
(ix) e^{- i h_{i} x} + \frac{e^{- i \Delta_{K} x} - e^{- i h_{i} x} }{ ( \Delta_{K} - h_{i} ) }
\right]
\left\{ (UX)^{\dagger} A W \right\}_{i K}
\frac{ 1 }{ \Delta_{K} - h_{i} }
\le... | 1,377 | 886 | 1,754 | 1,416 | null | null | github_plus_top10pct_by_avg |
\sigma(h')\bigl) \lhd r(g')\bigl]v(g') =
\bigl(v(g) \lhd (\sigma(h')r(g'))\bigl)v(g')$$
It follows that [(\[eq:c2\])]{} and hence [(\[eq:def4\])]{} holds and we are done.
\(3) Follows from (2) and the [Proposition \[pr:1\]]{}.
Schreier type theorems for bicrossed products
===========================================... | 1,378 | 996 | 1,239 | 1,474 | 3,827 | 0.76984 | github_plus_top10pct_by_avg |
abel{tilde-H0+H1} \end{aligned}$$ Therefore, what we mean by “expansion by unitarity violation effect” is an expansion by the $W$ matrix elements.[^9] We assume, for simplicity, that all the $W$ matrix elements are small and have the same order $\epsilon_{s}$. Then, $3 \times N$ ($N \times 3$) sub-matrix elements in $\... | 1,379 | 1,011 | 1,527 | 1,329 | null | null | github_plus_top10pct_by_avg |
monin], ideally one would like to solve the $N$-electron case, but the single particle problem is generally an important first step, and while the $N$ electron system on flat and spherical surfaces has been studied [@lorke2; @bulaev; @goker; @bellucci; @tempere; @ivanov], the torus presents its own difficulties. In an ... | 1,380 | 4,453 | 1,154 | 1,251 | null | null | github_plus_top10pct_by_avg |
the superscripts indicates generic formulas that are valid for all three meson systems.
In order to understand better the anatomy of the $\Delta I=1/2$ rule we use again the form $$\begin{aligned}
\frac{A_0}{A_2} &= B + C e^{i\delta}\,, \label{eq:DeltaI12-generic}\end{aligned}$$ analogously to Eq. (\[eq:defC\]) in Sec... | 1,381 | 949 | 2,054 | 1,407 | 1,307 | 0.791335 | github_plus_top10pct_by_avg |
\mathcal{C}(N)$ be a superinjective simplicial map. If $a$ is a 1-sided simple closed curve on $N$ whose complement is nonorientable, then $\lambda(a)$ is the isotopy class of a 1-sided simple closed curve whose complement is nonorientable.
Let $a$ be a 1-sided simple closed curve on $N$ whose complement is nonorient... | 1,382 | 970 | 2,407 | 1,347 | null | null | github_plus_top10pct_by_avg |
$$ Theorem \[unif dist of rho\] states that for any fixed subinterval $[\alpha,\beta]\in (-1/2,1/2]$, $$\frac 1{\#L_{prim}(T)} \{v\in L_{prim}(T): \alpha<\rho(v)<\beta \}
\to \beta-\alpha$$ as $T\to \infty$.
Equidistribution of real parts of orbits
----------------------------------------
We will reduce Theorem \[uni... | 1,383 | 2,466 | 1,700 | 1,289 | 3,476 | 0.772076 | github_plus_top10pct_by_avg |
j} U^{*}_{\beta j} \right|^2 -
2 \sum_{j \neq k}
\mbox{Re}
\left( U_{\alpha j} U_{\beta j}^* U_{\alpha k}^* U_{\beta k} \right)
\sin^2 \frac{ ( \Delta_{k} - \Delta_{j} ) x }{ 2 }
\nonumber\\
&-&
\sum_{j \neq k} \mbox{Im}
\left( U_{\alpha j} U_{\beta j}^* U_{\alpha k}^* U_{\beta k} \right)
\sin ( \Delta_{k} - \De... | 1,384 | 4,175 | 884 | 1,090 | 3,040 | 0.775284 | github_plus_top10pct_by_avg |
n see the least sensitive parameter appears to have no effect on the production of a BEC. This parameter corresponds to an intentionally added 7th parameter of the system that controls nothing in the experiment. Fig. 4(a) shows the learner successfully identified this, even with such a small data set. After making this... | 1,385 | 1,188 | 3,330 | 1,552 | null | null | github_plus_top10pct_by_avg |
d* *P*
------------ -------- ----- ------------------- ------ ------ ------
Weekly Female 60 7494.09 (3268.83) 0.23 0.04 0.07
Male 57 7358.60 (3147.58)
Weekdays Female 60 8301.11 (3721.95) 0.02 0.00 0.05
Male 57 8290.0... | 1,386 | 812 | 3,035 | 1,524 | null | null | github_plus_top10pct_by_avg |
bb Z}^u$ and $\mathcal B \colon \Lambda^*_G \oplus \Lambda^*_H \rightarrow {\mathbb Z}^u$ with the following property: For every irreducible representation $V_{G,\lambda}$ of $G$ and $V_{H,\mu}$ of $H$, the multiplicity $m^\lambda_\mu$ of the latter in the former is given by $$m^\lambda_\mu =
\sum_{\gamma \in \Gamm... | 1,387 | 1,035 | 1,000 | 1,236 | null | null | github_plus_top10pct_by_avg |
uality is by item 1 of Assumption \[ass:U\_properties\], the fourth inequality uses Lemma \[l:divergence\_vt\].
Substituting the above two equation blocks into , and applying recursively for $k=0...n-1$ gives $$\begin{aligned}
& \E{\lrn{v_{T} - w_{T}}_2^2} \\
=& \E{\lrn{v_{n\delta} - w_{n\delta... | 1,388 | 2,378 | 972 | 1,316 | null | null | github_plus_top10pct_by_avg |
f $\Q$, $Lp(\Q|\xi)\inseg\Q$.
If $\Q$ is good then it has a unique $(\omega, \omega_1)$-iteration strategy with Dodd-Jensen property. We let $\Sigma_\Q$ be this strategy. Also, let $\eta_\Q$ be the largest cardinal of $\Q$. Given an iteration tree $\T$ on $\Q$ according to $\Sigma_{\Q}$ with last model $\R$ such that ... | 1,389 | 1,443 | 1,274 | 1,330 | null | null | github_plus_top10pct_by_avg |
with ${\mathcal{L}}_{X}$ where $X$ is one of $\{ L_{0}, L_{\pm}, W_{0} \}$.
The highest- (lowest-) weight method {#sec:high-lowest-weight}
====================================
In this section we construct the scalar, vector, and symmetric tensor bases for NHEK’s isometry group ${\ensuremath{SL(2,\mathbb{R})\times U(... | 1,390 | 1,140 | 2,025 | 1,475 | null | null | github_plus_top10pct_by_avg |
hm:new.gen\], noting that $H\lhd G$. Let $\pi:G\to G/H$ be the quotient homomorphism, and note that $$\begin{aligned}
\frac{|\pi(AP)|}{|\pi(P)|}&=\frac{|APH|}{|PH|}\\
&\le\exp(e^{O(s^2)}\log^{O(s)}2K)\frac{|APH|}{|AH|}\\
&=\exp(e^{O(s^2)}\log^{O(s)}2K)\frac{|\pi(AP)|}{|\pi(A)|}\\
&\le\exp(e^{O(s^2)}\log^{O(s)}... | 1,391 | 433 | 992 | 1,501 | 3,252 | 0.773749 | github_plus_top10pct_by_avg |
nd $\psi^{(1)}_{m,n} = \psi_{m,n}$ in (\[eq:M-red-sys-5\]) and (\[eq:M-sys-5\]), then they will reduce to equations (\[eq:MX2a\]) and (\[eq:Bog\]), respectively.
The reduced systems for $\boldsymbol{N>5}$ {#the-reduced-systems-for-boldsymboln5 .unnumbered}
------------------------------------------
It can be easily c... | 1,392 | 896 | 1,436 | 1,617 | 2,663 | 0.778036 | github_plus_top10pct_by_avg |
2)(\kappa+\alpha_{i,i',\ell,\theta}-3)\cdots(\kappa-1)} \nonumber\\
&=& \frac{e^{-2b}}{(\kappa-1)} \frac{(\kappa-\ell + \alpha_{i,i',\ell,\theta}-2)(\kappa -\ell +\alpha_{i,i',\ell,\theta}-3)\cdots (\kappa -\ell)}{(\kappa+\alpha_{i,i',\ell,\theta}-2)(\kappa+\alpha_{i,i',\ell,\theta}-3)\cdots(\kappa)}\nonumber\\
&\geq& ... | 1,393 | 2,905 | 1,045 | 1,273 | null | null | github_plus_top10pct_by_avg |
tems [@Perad:1985], we have to find the necessary and sufficient conditions for the existence of solutions of type (\[eq:2.4\]). These conditions are called involutivity conditions.
####
First we derive a number of necessary conditions on the vector fields $(\gamma,\lambda)$ and their complex conjugate $(\bar{\gamma... | 1,394 | 1,736 | 2,182 | 1,485 | null | null | github_plus_top10pct_by_avg |
n and represents the Ito product rule. The same equations as and were presented in Refs. [@hufnagel2004forecast; @colizza2006modeling]. In this description, the fraction of the infected population is given by $$\rho=1-s(\infty).$$ In Fig. \[fig-sy\_lgv-pm3d\], we show the result of numerical simulations of the Langevin... | 1,395 | 3,740 | 1,367 | 1,211 | 2,142 | 0.782329 | github_plus_top10pct_by_avg |
$+$ $+$ $+$ $+$ $+$ $0$
: Case of $a \geq 1$
Calculation of the expected value and the variance of the loss
==============================================================
Here, we calculate the expected value and the variance of t... | 1,396 | 3,390 | 978 | 1,356 | null | null | github_plus_top10pct_by_avg |
ave that $\binom{[4]}{\le 3}_h\cup\{H\}$ is a star in $\cH$ of size $8>7$, a contradiction. Hence there is no such $H$, which is case (\[case:1\]) of the theorem.\
### $\cIt$ is a triangle
We may assume that $\cIt= \{\{1,2\},\{1,3\},\{2,3\}\}$.\
Relabel, if necessary, so that $0\le|C(\oone)|\le |C(\otwo)|\le |C(\othr... | 1,397 | 651 | 490 | 1,593 | null | null | github_plus_top10pct_by_avg |
4} & -\frac{2 u \left(u^4-4 u^2+3\right)}{\left(u^2+1\right)^4} & -\frac{4 (h+1) \left(u^2-1\right)^2}{\left(u^2+1\right)^3} \\
\mathcal{D}_{RR} & -\frac{u \left(u^2-3\right)}{\left(u^2+1\right)^2} & \frac{2 u \left(u^2-3\right)}{\left(u^2+1\right)^2} & \frac{u \left(u^2-3\right)^3}{8 \left(u^2-1\right) \left(u^2+1\ri... | 1,398 | 1,896 | 1,311 | 1,384 | null | null | github_plus_top10pct_by_avg |
n/R^n\bigr)^{(q)}.$$ Here $X\to \bigl(X^n/R^n\bigr)^{(q)}$ is finite and $R$ is an equivalence relation on $X$ over the base scheme $\bigl(X^n/R^n\bigr)^{(q)}$. Hence, by (\[quot.X/S.finite.lem\]), the geometric quotient $X/R$ exists.
Some of the scheme theoretic aspects of the purely inseparable case are treated in [... | 1,399 | 656 | 1,140 | 1,306 | 1,513 | 0.788718 | github_plus_top10pct_by_avg |
sigma(\pi)\pi\begin{pmatrix} {}^ts_i'a_is_i'+\pi^2X_i & \pi Y_i & Z_i
\\ \sigma( \pi \cdot {}^tY_i) &\pi^2X_i'&\pi Y_i' \\ \sigma({}^tZ_i)&\sigma(\pi\cdot {}^tY_i') &{}^tt_i'a_it_i'+\pi^2 Z_i' \end{pmatrix}$ for certain matrices $X_i, Y_i, Z_i, X_i', Y_i', Z_i'$ with suitable sizes. Here, the diagonal entries of... | 1,400 | 4,482 | 467 | 1,058 | null | null | github_plus_top10pct_by_avg |
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