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0}\end{aligned}$$ By comparing the error bars in the key power laws and with the error bars in power-law relations , , and , we observe that there is less uncertainty in the first case, indicating that the quantities $||{\widetilde{\mathbf{u}}_{\E_0}}||_{L_\infty}$, $||{\bnabla\times}{\widetilde{\mathbf{u}}_{\E_0}}||_...
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by the expression $${{\mathcal J}_{\rm c} = C_4 + \frac{i}{2} e^{-\phi} J \wedge J = i \sum_i T_i \tilde{\omega}_i} \quad .$$ In the IIA O6-orientifold, instead, the action of the involution $\sigma_A$ is $$\sigma_A (x^i ) = x^i \qquad \sigma_A ( y^i ) = - y^i \quad .$$ This implies that the $\tau_i$’s are real. The r...
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0.781901
github_plus_top10pct_by_avg
n thus dominates the growth of galaxies. Dependence on halo mass {#sec:mass} ======================= ![image](figures/massprop_REF_L050N512_z2p0_pecvel0p1.eps) In Fig. \[fig:halomassz2\] we plot the same properties as in Fig. \[fig:haloradz2\] as a function of halo mass for gas at radii $0.8R_\mathrm{vir}<R<R_\mathr...
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s the image of a fixed element of $F_j$ under the map $\psi_j$. Since $(z_j^{\ast})_1$ can be either $0$ or $1$ by Equation (\[e42\]), $\psi_j|_{F_j}$ is surjective onto $\mathbb{Z}/2\mathbb{Z}$ and thus $\psi_j$ is surjective.\ So far, we showed that $\psi_j$ is surjective when $j$ is even. We now show that $\psi_j$ ...
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github_plus_top10pct_by_avg
)$ and $c(j)$ are rationally null-homologous. Thus their linking number is well-defined, establishing the first claim. [**B1$\Longleftrightarrow$B3**]{}: $\b^n$ is defined precisely when $[c(n)]=0$ in $H_1(M;\BQ)$ which is precisely the condition under which $c(n+1)$ can be defined. [**B1$\Longrightarrow$B4**]{}: If ...
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0.777945
github_plus_top10pct_by_avg
.FacebookClient .... Note: you can change the facebook url(because already is used 2.2) Q: Solving logarithms with different bases? How would I go about getting an exact value for a question like: $\log_8 4$ I know that $8^{2/3} = 4$ but how would I get that from the question? A: The logarit...
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702
0.802118
github_plus_top10pct_by_avg
be an $H$-set and $Y$ be an $K$-set, then: $${<}Ind_{H}^{K}X,Y{>}_{K} = {<}X,Res^{K}_{H} Y{>}_{H},$$ and $${<}Res_{H}^{K}Y,X{>}_{H} = {<}Y,Ind^{K}_{H} X{>}_{K},$$ So we have a family of linear forms $(\phi_{H})_{H\leqslant G}$ on the Burnside algebras $(RB(H))_{H\leqslant G}$ defined by: let $X\in RB(H)$, then $\phi_{...
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$X_1,\ldots,X_\ell\subset\tilde A^{e^{O(\tilde s)}}$ of size at most $\exp(e^{O(\tilde s)}\log^{O(1)}2\tilde K)$ such that $$\tilde A\subset N\prod\{A_1,\ldots,A_r,X_1,\ldots,X_\ell\},$$ with the product taken in some order. Here, and throughout this paper, given an ordered set $X=\{x_1,\ldots,x_m\}$ of subsets and/or...
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2,772
0.77707
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au D(x)+\sum_{y\ne x}\tau D(y)\,{{\langle \varphi_y \varphi_x \rangle}}_\Lambda\leq2D(x)+\sum_{y\ne x}2D(y)\,G(x-y),\end{aligned}$$ where, and from now on without stating explicitly, we use the translation invariance of $G(x)$ and the fact that $G(x-y)$ is an increasing limit of ${{\langle \varphi_y\varphi_x \rangle}}...
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lon))$, with high probability. First assume that $2m{\leqslant}n $ and suppose that the algorithm has allocated $m$ balls to ${\mathcal{H}}^{(t)}, t=1,\ldots,m$ and let $\ell^*{\leqslant}\log_d\log n +{\mathcal{O}}(1)$ denote its maximum load. We now consider two independent balanced allocation algorithms, say ${\mathc...
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0.7877
github_plus_top10pct_by_avg
$ be submodules of $M$ such that $V/U\iso R/P$ for some $P\in \Spec(R)$. Then there exists an irreducible submodule $W$ of $M$ such that $U=V\sect W$. By Noetherian induction there exists a maximal submodule $W$ of $M$ such that $U=V\sect W$. We claim that $W$ is an irreducible submodule of $M$. Indeed, suppose that $...
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github_plus_top10pct_by_avg
1}{\ensuremath{\ell k}}(c(s),c^+(t-1))\end{aligned}$$ which vanishes by our inductive assumption since $s+(t-1)<n$. [**B4$\Longrightarrow$B1**]{}: Since $\b^1$ is always defined we may assume $n>1$. It follows from B4 that ${\ensuremath{\ell k}}(c(1),c^+(n-1))=0$ if $n>1$. But we saw in the proof of B1$\Longrightarrow...
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3,659
3,609
0.771246
github_plus_top10pct_by_avg
ed curve) in the curve complex. Hence, any superinjective simplicial map is induced by the identity homeomorphism. If $(g, n) = (1, 2)$, there are only two elements in the curve complex (see [@Sc]). They are the isotopy classes of $a$ and $b$ as shown in Figure \[figure1\]. We see that $i([a], [b]) = 1$. So, the super...
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by $A_{j,\alpha} = \alpha^{j-1}$ is a $\GF(q)$-representation of $U_{s,q}$; see Section 6.5 of \[\[oxley\]\] for more detail. \[localrep\] There is a function $f_{\ref{localrep}}\colon \bZ^3 \to \bZ$ so that, for all integers $s,t,n \ge 2$, if $q$ is a prime power, and $M$ is a matroid with a $\PG(r(M)-1,q)$-restrict...
4,114
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x,\hs{2ex}b_y=x\bar{h}_y+w_y.$$ The conservation law reads, $$\partial_y b_x+\partial_x b_y=0,\hs{2ex}\partial_x\bar{h}_y+\partial_y\bar{h}_x=0$$ which allows us to write the current $\bar{h}_y$ as, $$\bar{h}_y=-\partial_x w_y-\partial_y w_x.$$ From the commutation relations, we learn that $w_x$ is invariant under the ...
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0.773472
github_plus_top10pct_by_avg
)}. \label{u1charges}$$ In the light–cone gauge, the free fermionic heterotic–string models in four dimensions require $20$ and $44$, left–moving and right–moving real world–sheet fermions respectively, to cancel the conformal anomaly. In the usual notation these are denoted as: $\psi^\mu, \chi^{1,\dots,6},y^{1,\dots...
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ta_Y} d\operatorname{DH}_Y(\mu') \, g(\mu')$$ for any test function $g$. In particular, this inequality would hold for $g$ the indicator function of $\Delta_X$. But this is clearly impossible, since $\operatorname{DH}_Y$ is absolutely continuous with respect to Lebesgue measure on $\Delta_Y$, for which $\Delta_X$ is a ...
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3,741
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l p}{\partial x}+\Gamma p+ [\Gamma v-\bar{\omega}_{b}^{2}x]\frac{\partial p}{\partial v}+ A\frac{\partial^{2} p}{\partial v^{2}}+B\frac{\partial^{2} p}{\partial v \partial x}\hspace{0.2cm},$$ where we have used the following abbreviations; $$A=J_{ee}-\Gamma(0)I_{ee}+[g'(0)]^{2}J_{nn}-\Gamma(0)[g'(0)]^{2}I_{nn}$$ and $$...
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tant $L>0$, $H_{3}(\frac{t}{L})+dt^2$ on $S^{4k-1}\times [0,L]$ has positive scalar curvature. Now we have a desired $4k$-ball to be glued to the part made previously out of $M'$. After the gluing, what we get is just $M$ with a specially devised smooth metric which we denote by $\bar{g}$. Remember that the scalar cur...
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ground for the formation of expressions (\[2\]). Since the experiments indicate absence of definite values of $CP$-parity of the decaying neutral $K$-mesons, one should consider the case when the mass term in Lagrangian (\[1\]) does not possess the mentioned $SU(3)$-invariance. Then the first step of the appropriate p...
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operatorname}{O}_{p}(H)}^P\leq P$. This contradicts the fact ${{\operatorname}{O}_{p}(G)}=1$ and it proves the claim. \[new\] The subgroup $\langle y \rangle$ does not normalise $N_i$, for each $i \in\{1, \ldots, r\}$. In particular, $r > 1$. Assume that $\langle y \rangle$ normalises some $N_i$ with $i \in\{1, \ldo...
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3,946
3,999
0.768718
github_plus_top10pct_by_avg
\begin{aligned} \mathbb{E}[d_{\mathcal{P}}(\overline{X}_n)]&\le& \mathbb{E}_m[d_{\mathcal{P}}(\overline{X}_n)]\\ &\le& \mathbb{E}_m[d_{P_m}(\overline{X}_n)]+r_m-R\\ &\le& r_m-R+\sqrt{\frac{m}{n}}\sqrt{\overline{\sigma}^2+4r^2_m}.\end{aligned}$$ By setting $m=n^{\frac{1}{5}}$, we have $$\mathbb{E}[d_{\mathcal{P}}(\overl...
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github_plus_top10pct_by_avg
6,60 (4,84) Sex ill child, boys, *n (%)* 69 (60%) Diagnosis, *n (%)* Acute lymphoblastic leukemia (ALL) 85 (73,9%) ...
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peliotopoulos' date: 'November 30, 2007' title: 'Connecting the Galactic and Cosmological Scales: Dark Energy and the Cuspy-Core Problem' --- Introduction ============ The recent discovery of Dark Energy [@Ries1998; @Perl1999] has not only broadened our knowledge of the universe, it has brought into sharp relief the ...
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\sigma (\phi )(x)\geq \varepsilon (\phi )>0 \label{ip11}$$Then, for $\kappa, q\in{\mathbb{N}}$ and $p> 1$, $$\left\Vert \psi _{\kappa }V_{\phi }^{\ast }(\frac{1}{\psi _{\kappa }}% f)\right\Vert _{q,p} \leq C \psi _{\kappa }(\phi (0))\times \frac{1\vee \left\Vert \phi \right\Vert _{1,q+2,\infty }^{2dq+1+2\kappa }}{ \v...
4,125
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can be applied in this context. The organization of our paper is as follows: Sec. II deals with the definition of gravitational entropy and Sec. III enlists the metrics of accelerating black holes considered by us. Sec. IV provides the main analysis of our paper where we evaluate the gravitational entropy and the corre...
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4,010
3,905
2,979
0.775642
github_plus_top10pct_by_avg
to the electron (neutron) electric dipole moment are non-zero beginning at the three (two) loop level. Surprisingly similar to the Standard Kobayashi-Maskawa Model, our model is of milliweak character but with seemingly superweak phenomenology.' --- 6.5in -1cm **A Simple Charged Higgs Model of Soft CP Violation** *...
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\int_{-R}^R f({\mathbf x}_i^0+s\hat{{\mathbf u}}_i) ds + \varepsilon_i,$$ where $i$ corresponds to the data point index. The corresponding inverse problem is given the noisy measurement data $\{y_i\}_{i=1}^n$ in to reconstruct the object $f$. Gaussian processes as functional priors {#functional priors} ---------------...
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0.794726
github_plus_top10pct_by_avg
} \in A_{\varepsilon} \} \cap \{ \hat{N} \in B_{\varepsilon} \} \subset \{ \widetilde{N}+\hat{N} \in A_{3\varepsilon} \cap B_{\varepsilon} \} ~,$$ where $\widetilde{N}+\hat{N}$ denotes the superposition of the two processes $\hat{N}$ and $\widetilde{N}$. These two processes can also be assumed independent. In this case...
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an inverse length scale corresponding to the typical distance diffused by the particle in the time between two resetting events, and $D$ is the diffusion constant. The steady state radial density of the particle can also be extracted from the experimental trajectories by looking at the steady-state distribution of the...
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0.786763
github_plus_top10pct_by_avg
BA ansatz is written as $$\begin{aligned} \frac{d\sigma(\Omega_{^9\text{He}})}{dE \,d \Omega_{^8\text{He}}} \sim \frac{v_{f}}{v_{i}}\,\sqrt{E} \, \sum \nolimits_{MM_S} \left| \sum \nolimits_J\langle \Psi^{JMM_S}_f \left| V \right| \Psi_i \rangle \right|^2 \label{eq:sigma}\\ % = \frac{v_f}{v_i} \sum _{MM_S} \sum _{JJ'...
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x{\boldmath $r$}},{{\mbox{\boldmath $b$}}_p}) = \left\{ \begin{array}{ll} {\mathcal N}_0\, \left(\frac{ r \, Q_{s,p}}{2}\right)^{2\left(\gamma_s + \frac{\ln (2/r Q_{s,p})}{\kappa \,\lambda \,Y}\right)} & \mbox{$r Q_{s,p} \le 2$} \\ 1 - \exp \left[-A\,\ln^2\,(B \, r \, Q_{s,p})\right] & \mbox{$r Q_{s,p} > 2$} ...
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github_plus_top10pct_by_avg
apse in the bilayer.[]{data-label="fig:phase_diag"}](glow_compare_phase-diagr.pdf){width="\linewidth"} We determine the density instabilities of the bilayer system by analyzing the divergences of the static response function matrix $\chi_{ij} ({{\mathbf q}},0)$. Specifically, we search for zeros of the largest inverse...
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3,998
3,351
0.772972
github_plus_top10pct_by_avg
0.7 Hb (gr/dL) 11.6 ± 1.3 11.9 ± 1.4 0.3 Cholesterol (mg/dL) 158.5 ± 47.3 165.2 ± 44....
4,134
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1,011
3,610
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ots w_kS' {\Rightarrow}w_1w_2\cdots w_k$$ where the subwords $w_i$ are derived from $S$ as in $G$. As regards closure under intersection with regular sets and under inverse homomorphisms, the constructions to show closure of $\mathbf{CF}$ cannot be extended, since they do not keep the capacity bound. We suspect that $...
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hat{\psi},V}}\left(i,j\right)\right]_{i\in{{\mathcal{M}_{r}},j\in\mathcal{I}_t}}$; $\mathcal{I}_r:=\mathcal{I}_r-\left\{J\right\};$ $J:=\arg\max_{j\in \mathcal{I}_r}{\mathbf{h}}_j\left({\mathbf{I}}_{N_t}+\frac{\rho}{N_t}{\widetilde{\mathbf{H}}_{\widehat{\psi},V}}^H{\widetilde{\mathbf{H}}_{\widehat{\psi},V}}\right)^{-1...
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ly given by $$\label{eq:gammadef} \begin{aligned} ds^2 & = ds^2_{AdS}+ \sum_{i= 1\dots 3} ( dr_i^2 + G r_i^2 d\phi_i^2) + G r_1^2 r_2^2 r_3^2 \Big( \sum_{i= 1\dots 3} \nu_i dr_i \Big)^2 \ ,\\ B & = G ( r_1^2 r_2^2 \nu_3 d\phi_1 \wedge d\phi_2 + r_1^2 r_3^2 \nu_2 d\phi_3 \wedge d\phi_1 + r_2^2 r_3^2 \nu_1 d\phi_2 \wedge...
4,137
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xpressions – are approximated pseudo-spectrally using standard dealiasing of the nonlinear terms and with resolutions varying from $128^3$ in the low-enstrophy cases to $512^3$ in the high-enstrophy cases, which necessitated a massively parallel implementation using the Message Passing Interface (MPI). As regards the c...
4,138
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4,205
3,843
0.769726
github_plus_top10pct_by_avg
rox - \alpha /2R^4$ at large distances and differ in the short-range limit due to the “cut-off” parameters or functions which contain parameters estimated on some reasonable assumptions. Effects of the NN interaction on the scattering process can be investigated by solving the Schrödinger equation for the Hamiltonian ...
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0.776749
github_plus_top10pct_by_avg
$\partial_\nu$ is the weak normal derivative. Thus the domain of $A(t)$ is the set $$D(A(t))=\Big\{ u\in H^1(\Omega_{ext}) {\, \vert \,}{\mathop{}\!\mathbin\bigtriangleup}u\in L^2(\Omega_{ext}), \partial_\nu u(t)+\beta(t,\cdot){{u}{_{|\Gamma}}}=0 \Big\}$$ and for $u\in D(A(t)), A(t)u:=-{\mathop{}\!\mathbin\bigtriangle...
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sc surfaces in vertical directions [see e.g., @Abramowicz:1988aa; @Watarai:2000aa; @Ohsuga:2005aa; @Jiang:2014aa; @Sc-adowski:2016aa]. The first term $2 L_{\mathrm{E}}$ corresponds to the luminosity from the outer standard disc in $r > r_{\mathrm{tr}}$ (see Fig. \[fig:acc\_whole\]a), given approximately by the energy g...
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github_plus_top10pct_by_avg
tion of motion for test particles can be accounted for in $T_{\mu\nu}$, and we still have $R=4\Lambda_{DE}G/c^2+8\pi GT/c^4$ in Eq. $(\ref{extendL})$. For massless particles, $v^\nu\nabla_\nu \left(\mathfrak{R}[4+8\pi T/\Lambda_{DE}c^2]v^\mu\right)=0$ instead. With the reparametization $dt \to \mathfrak{R} dt$, t...
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3,318
0.773186
github_plus_top10pct_by_avg
1 (N159) 34.7 3.08 $\times$ 10$^{3}$ (8.67 $\times$ 10$^{3}$)$^a$ 0.37 2.38 6.9 1.2 $\times$ 10$^{5}...
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Eq.(74) in the form $$F(u,t)=F_{s}(u)e^{-\phi(t)}\hspace{0.2cm},$$ where $F_{s}(u)$ is the steady state solution obtained in the earlier section, i.e., it satisfies $$\alpha u \frac{\partial F_{s}}{\partial u}+KT\frac{\partial^{2}F_{s}} {\partial u^{2}}=0\hspace{0.2cm}\hspace{0.2cm}.$$ We require further $$\left.{\c...
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usion\] contains concluding remarks. Extra results, proofs and a discussion of another version of the bootstrap, are relegated to the Appendices. Notation -------- Let $Z=(X,Y)\sim P$ where $Y\in\mathbb{R}$ and $X\in \mathbb{R}^d$. We write $X = (X(1),\ldots, X(d))$ to denote the components of the vector $X$. Define ...
4,145
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0.784114
github_plus_top10pct_by_avg
. Out of 27,678 IRs in MG1655 we were able to identify 914 IRs that appear in at least 10 species. These orthologs reside in 234 NC regions and were further analyzed. For each of these 234 regions, we computed a conservation score (see [fig. 4*A* and *B*](#evy044-F4){ref-type="fig"} and Materials and Methods for full d...
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s controlled by these Petri nets (for details, see [@das:tur; @tur]). Let $G=(V, \Sigma, S, R)$ be a context-free grammar with its corresponding cf Petri net $$N=(P, T, F, \phi, \beta, \gamma, \iota).$$ Let $T_1, T_2, \ldots, T_n$ be a partition of $T$. 1\. Let $\Pi=\{\rho_1, \rho_2, \ldots, \rho_n\}$ be the set of d...
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ore generally, for any finite linearly ordered set $S$ with $n$ elements, we have a product functor $m_S:{{\mathcal C}}^S \to {{\mathcal C}}$, where ${{\mathcal C}}^S = {{\mathcal C}}^n$ with multiples in the product labeled by elements of $S$. Then for any $[n],[n'] \in \Lambda$, and any $f:[n'] \to [n]$, we can defin...
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3,727
2,946
0.775929
github_plus_top10pct_by_avg
(x_1A_1+ \cdots+x_nA_n).$$ Thus we cannot directly derive an analog of Proposition \[lowprop\] for Theorem \[MSSmain\]. Consequences for strong Rayleigh measures and weak half-plane property matroids =============================================================================== A discrete probability measure, $\mu$,...
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by more than an order of magnitude when more effective supernova feedback or AGN feedback is included (not shown). For $M_\mathrm{halo}>10^{12.5}$ M$_\odot$ the hot-mode inflow rate is slightly stronger than the cold-mode inflow rate. The grey, dashed curve indicates the accretion rate a halo with a baryon fraction $...
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0.779785
github_plus_top10pct_by_avg
=Z_B^0 \int \mathcal{D}(\bar{\psi}_{\sigma},\psi_{\sigma}) e^{-S_F^{eff}} \label{Z2}\end{aligned}$$ where the effective action for fermions is $$\begin{aligned} S_F^{eff}&=&\int_{k,\tilde{\omega}} \sum_{\sigma}\bar{\psi}_{\sigma}(k,\tilde{\omega}) \Big[-i\tilde{\omega}+\frac{k^2}{2m}-\mu\Big]\psi_{\sigma}(k,\tilde{\ome...
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github_plus_top10pct_by_avg
left( \bar{e} \gamma_5 \gamma^{\mu} e \right).$$ This coupling is very similar to the nucleon coupling in Eqn  and leads to similar effects. The QCD axion generally has this coupling with $g_{aee} \sim \frac{1}{f_a}$, though it can be fine-tuned to zero. Astrophysics constrains $g_{aee} \lessapprox 10^{-10} \text{ GeV}...
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the KM mechanism is inoperative. Tree-level flavor changing neutral currents are automatically absent, and the neutral Higgs sector is CP conserving at tree level. As in the KM Model, the quark and electron EDMs are severely suppressed. The electron EDM vanishes at the two-loop level, while the first non-zero contribut...
4,153
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ir paper: > [*When fitted models are approximations, conditioning on the regressor is no longer permitted ... Two effects occur: (1) parameters become dependent on the regressor distribution; (2) the sampling variability of the parameter estimates no longer derives from the conditional distribution of the response alo...
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}{\varepsilon }\frac{dv_{x}}{d\phi }-\frac{v_{x}}{\gamma }\left( \frac{dv_{x}}{d\phi }\right) ^{2}+\left( 1-\frac{v_{z}}{\gamma }\right) \frac{dv_{x}}{d\phi }\frac{dv_{z}}{d\phi }+\frac{A}{\varepsilon }G(\phi )sin\phi \right) \label{34} \\ \frac{d^{2}v_{z}}{d\phi ^{2}} &=&v_{z}Q+\frac{1}{u}\left( \frac{1}{\varepsilon }...
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s $H_d$-module homomorphisms of degree zero. A [*graded standard module*]{} \[graded-standard-defn\] $\widetilde{\Delta}_d(\mu)$, isomorphic to $\Delta_d(\mu)$ as an ungraded module, is given by setting $\widetilde{\Delta}_d(\mu)_r = {\mathbb{C}}[{\mathfrak{h}}]_r\otimes \mu$. By local nilpotence and finite generation,...
4,156
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4,064
3,601
0.771293
github_plus_top10pct_by_avg
states are - $H^m(X, \wedge^{\rm even} {\cal E})$, charge $({\rm even}-2, m-n/2)$, giving spacetime states valued in a spinor of $so(8)$. In the (NS,R) sector, the vacuum energy $E_{{\rm Id}} = -1$. The massless charged states are - $H^m(X, {\cal E}^* \otimes {\cal E})$, charge $(0,m-n/2)$, spacetime gauge neutr...
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in the set of solutions $\{ {{\bar{\a}}^\dagger}_k \}$ to the QPs in . Fortunately, to obtain the solution set $\{ {{\bar{\a}}^\dagger}_k \}$, it is sufficient to solve merely one QP in with $k = 1$, according to the following theorem. \[theorem:aLinear\] Denote the solution to the QP in with the constraint $\a(L) = k...
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1392180.1588220.049102HV AlgorithmHEIA\*cMLSGANSGA-II\*MOEA/DMTS Average0.1748460.1744750.1744610.1740940.168158 (S.D.)0.0000270.0000390.0002880.0002140.000464\*indicates if the results are significantly different to the next lowest rank, using the Wilcoxon's rank sum with a 0.05 confidence In order to better understa...
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Initiated \- Norwegian Coronavirus Disease 2019 Study Hydroxychloroquine Sulfate ...
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n then find $\S^{**}$ which is a suitable correct iterate of both $\S$ and $\S^*$. Notice that since $\S^{**}$ is suitable, the iteration embeddings $i : \S|(\l_\S^+)^\S\rightarrow \S^{**}|(\l_{\S^{**}}^+)^{\S^{**}}$ and $j: \S^*|(\l_{\S^*}^+)^{\S^*}\rightarrow \S^{**}|(\l_{\S^{**}}^+)^{\S^{**}}$ exists. Suppose now t...
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n particular, if $\mathfrak{n}=\sum y_iR+q_jR$, then $\Sigma$ is an r-sequence for the $R_{\mathfrak{n}}$-module $N(k)_\mathfrak{n}$. By the Auslander-Buchsbaum formula [@matsumura Ex. 4, p.114], $N(k)_\mathfrak{n}$ is therefore free as a $R_{\mathfrak{n}}$-module. Finally, consider $\overline{N(k)}=N(k)/\sum q_jN(k)$...
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are as follows, $$\label{eq3} \begin{array}{r@{}l@{\qquad}l} &m{{\ddot{x}}_{m}}={{F}_{2}}-{{F}_{1}}, \\ %\label{eq4} &m{{\ddot{y}}_{m}}=2{{F}_{s1y}}=2{{F}_{s2y}}, \\ %\label{eq5} &mg=2{{F}_{s1z}}=2{{F}_{s2z}}, \end{array}$$ where $$\begin{aligned} \begin{array}{r@{}l@{\qquad}l} {{\dd...
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es. In Sec.\[HigherGauge\], we comment on extensions of the generalized notion of gauge symmetry to higher form gauge theories. Gauge Symmetry Algebra {#GaugeSymm} ====================== In a naive textbook introduction to non-Abelian gauge symmetry, the gauge transformation parameter $\Lam(x) = \sum_a \Lam^a(x)T_a$ ...
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in\] may be applied to any given plane curve, producing a list of its limits. In practice, one needs to find the marker germs for the curve; these determine the components of the PNC. The two examples in §\[twoexamples\] illustrate this process, and show that components of all types may already occur on curves of degre...
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}}\}}}\equiv1$ for any ${{\bf n}}''\in{{\mathbb Z}_+}^{{{\mathbb B}}_{{{\cal B}}{^{\rm c}}}}$ with ${\partial}{{\bf n}}''={\overline{b}}{\vartriangle}x$. As in the derivation of [(\[eq:0th-summand3\])]{} from [(\[eq:0th-summand2\])]{}, we can omit “off $b$” and ${\mathbbm{1}{\scriptstyle\{m_b,n_b \text{ even}\}}}$ in [...
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vide a business reason on a Direct Cash Flow basis for an item buried within the Indirect Cash Flow format. Call me if you have any further questions. -----Original Message----- From: Hayslett, Rod Sent: Wednesday, November 14, 2001 6:45 AM To: Kleb, Steve Cc: Geaccone, Tracy Subject: FW: Fw: Undel...
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ed by E. Getzler [@getz] is that we have an analog of the Gauss-Manin connection: if ${\operatorname{Spec}}R$ is smooth, the $R$-module $HP_i(A_R/R)$ carries a canonical flat connection for every $i$. Consider now the case when $R$ is not smooth but, on the contrary, local Artin. Moreover, assume that ${{\mathfrak m}}...
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-)} =F(v)=\tilde{B}(\tilde{\phi},v) \\[2mm] ={}& {\left\langle}\phi, P'(x,\omega,E,D)v{\right\rangle}_{L^2(G\times S\times I)}+{\left\langle}CS_0\phi,v{\right\rangle}_{L^2(G\times S\times I)}+{\left\langle}(\Sigma-K_C)\phi,v{\right\rangle}_{L^2(G\times S\times I)} \\ {}&+{\left\langle}q_{|\Gamma_+},\gamma_+(v){\right\...
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it is a right action of the group $H$ on the set $G$ and $(g_1 g_2) \lhd h = (g_1 \lhd h) (g_2 \lhd h)$ for all $g_1$, $g_2 \in G$ and $h\in H$. ${{\rm Aut}\,}(H)$ is the group of automorphisms of $H$ and $C_n$ is the cyclic group of order $n$. Let $H$ and $G$ be two groups with the multiplications $m_{H}: H \times H...
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versus no abortion probabilities during a PRRSV outbreak by marker genotype. Only markers showing different abortion rates by genotype are shown. Marker Gene Contrast Odds Ratio *p* -------------- --------- ---------- ------------ ---------- rs80800372 *GBP1* AA/AG 2.69 0.00...
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nd a primary field $\phi$: $$\begin{aligned} j^a_{L,z}(z) \phi(w) = & -\frac{c_+}{c_++c_-} \frac{t^a \phi(w)}{z-w} + :j^a_{L,z} \phi:(w) \cr & + {A^a}_c \log|z-w|^2 :j^c_{L,z} \phi:(w) + {B^a}_c \frac{\bar z - \bar w}{z-w} :j^c_{L,\bar z} \phi:(w) + \mathcal{O}(f^4) \cr j^a_{L,\bar z}(z) \phi(w) = & -\frac{c_-}{c_++c_-...
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ms contains the initial fluctuation of energy density $\Delta {\cal U}$ \[$\Delta {\cal U}={\cal U}(\omega,0)-\frac{1}{2} KT$\] due to excitation of the system at $t=0$ \[see Eq.(15)\]. $$\begin{aligned} p(x,v,t)\stackrel{t\rightarrow 0} {\longrightarrow} N\left(\frac{2\pi KT}{\alpha}\right)^{\frac{1}{2}} e^{-2D\frac{...
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C \left( \frac{\sqrt{k}}{\hat{u}_t ^2} + \frac{1}{\hat{u}_t} \right),$$ where $\hat{u}_t \geq (1 - t) \lambda_{\min}(\Sigma_{S}) + t \lambda_{\min}(\hat{\Sigma}_{S})$. By in and Weyl’s theorem, and using the fact that $ u > u_n$, on an event with probability at lest $1 - \frac{1}{n}$, $$\left\| G\left( 1-t)\psi_{S} + ...
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github_plus_top10pct_by_avg
mplete hyperbolic structure. Then $\overline{X_{6,\theta}}$ can be regarded as the resultant of the hyperbolic Dehn filling of the complete hyperbolic 3-manifold $\overline{X_6}$, which lies in ${\cal H}(\overline{X_6})$ (for more detail, see [@KojimaNishiYamashita]). Thus we have a map $\Phi_6: \Theta_6 \to {\cal H}(\...
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we warn the reader that the homomorphism ${\psi_{d,t}}$ is called $\psi_{d,\la_{d+1}-t}$ in \[*loc. cit.*\]. The importance of the homomorphisms ${\psi_{d,t}}$ is in the following. [ ]{}\[kit\] Suppose $\la$ is a partition of $n$. Then $$S^\la=\bigcap_{\begin{smallmatrix}d\gs1\\1\ls t\ls\la_{d+1}\end{smallmatrix}}\ke...
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interior of an edge, consider a small closed interval $C_p$ including the point, $q {\mid}_{q^{-1}(C_p)}:q^{-1}(C_p) \rightarrow C_p$ is $C^r$-PL equivalent to a $C^r$ trivial bundle, appearing locally around a closed interval in the interior of an edge in the Reeb graph of a map of the class $\mathcal{C}$. 2. At ea...
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4271.345 10 1173 4.89 10 Jun 20 4272.454 30 198 2.23 11 Jul 06 4288.389 30 184 2.42 12 Jul 07 4289.347 10 1417 5.18 13 Jul 08 4290.337 10 1449 5.60 14 Jul 09 4291.351 30 ...
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of the central accretion disc, given by $\dot{N}_{\mathrm{ion}}=L/3h\nu_{\mathrm{T}}$ for the assumed spectral shape of $L_\nu\propto \nu^{-1.5}$. Equating this supply rate with the recombination rate, we have $$\frac{L}{3h \nu_{\mathrm{T}}}\frac{\mathcal{F}(\theta)}{4 \pi} = \int_{R_{\mathrm{in}}}^{r_{\mathrm{HII}}}(\...
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---------------------------------------------- $\bar{f}'_i$ & $P^{y^i, y^i y^j y^k x^i}$ & $P^{y^i, y^i x^j x^k y^j y^k}$\ It is straightforward to deduce the rule for the $P$ fluxes that survive the orientifold projection in the IIA theory. With respect to $\Omega_P (-1)^{F_L}$, the fluxes $P^{a,b}$, $P_a^{b_1 b_2 ...
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_0,\dots,v_j\\ v_l\ne v_{l'}\,{{}^\forall}l\ne l'\\ v_j=v}}{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{y{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}} {\overset{}{\longleftrightarrow}}}u\\}$}}}\,\circ\,\{u{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}} {\overset{}{\longleftrightarrow}}} x\...
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into $L_{i+1}\oplus L_{i+2}\oplus\dots$. This completes the inductive step, and thus produces the wanted derivation $d$ on $F_{\mathcal Lie}(C[1])$. In a similar way, we may produce the derivation $g$ of $F_{\mathcal Lie,\,C[1]}C[1]$ over $d$, by decomposing $F_{\mathcal Lie, C[1]} C[1]=L'_1\oplus L'_2\oplus\dots$, wh...
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github_plus_top10pct_by_avg
(\Gamma(G))}$. Moreover, if $r \in \pi(G) \setminus \pi(G/N)$, then $r$ is adjacent to $p$ in $\Gamma(N)$. By our hypotheses, for any prime $r \in \pi(G) \setminus \{p\}$ there exists an element $x \in A \cup B$ of order $r$ such that $x \in C_G(P)$, for some $P \in {{\operatorname}{Syl}_{p}\left(G\right)}$. Hence the...
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first term if the source constraints for ${{\bf m}}$ and ${{\bf n}}$ are exchanged. Next, we consider the second term of [(\[eq:WZ-num\])]{}, whose exact expression is $$\begin{gathered} {\label{eq:2ndterm-expl}} \sum_{\substack{{\partial}{{\bf m}}=\{v,x\},\,{\partial}{{\bf n}}={\varnothing}\\ {{\bf m}}|_{{{\mathbb B...
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ome about $~10^{-10}$. In this way, the number of terms kept in the sum may vary in different plots as it is clearly depends on the specific set of parameters used to produce the plot. We indicate the truncation number in the caption of each figure. --- abstract: 'We review the stabilization of the radion in the Rand...
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t_1} \mu_1 \xrightarrow{t_2} \ldots \xrightarrow{t_k} \mu_k$. For each $1\leq i\leq k$, marking $\mu_i$ is called *reachable* from marking $\mu$. $\mathcal{R}(N, \mu)$ denotes the set of all reachable markings from a marking $\mu$. A *marked* Petri net is a system $N=(P, T, F, \phi, \iota)$ where $(P, T, F, \phi)$ is ...
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){width="85.00000%"} ### $P(\nu_{\mu} \rightarrow \nu_{e})$ In figure \[fig:Pmue\_energy\_dist\]-(a) (upper panel) and (b) (lower panel), presented are the iso-contours of $P(\nu_{\mu} \rightarrow \nu_{e})_{ \text{non-unitary} }^{(0)}$ and $\Delta P (\nu_{\mu} \rightarrow \nu_{e}) \equiv P(\nu_{\mu} \rightarrow \nu...
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/*! * Bootstrap Grunt task for generating raw-files.min.js for the Customizer * http://getbootstrap.com * Copyright 2014-2015 Twitter, Inc. * Licensed under MIT (https://github.com/twbs/bootstrap/blob/master/LICENSE) */ 'use strict'; var fs = require('fs'); var btoa = require('btoa'); var glob = require('glob');...
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de <networkit/community/PLM.hpp> #include <networkit/sparsification/LocalDegreeScore.hpp> #include <networkit/sparsification/RandomEdgeScore.hpp> #include <networkit/sparsification/GlobalThresholdFilter.hpp> #include <networkit/auxiliary/Timer.hpp> #include <networkit/auxiliary/Random.hpp> #include <iostream> #inclu...
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axentStress maxentStressAlgo(graph, 2, 1, 0.001, MaxentStress::LinearSolverType::CONJUGATE_GRADIENT_IDENTITY_PRECONDITIONER, true, MaxentStress::GraphDistance::ALGEBRAIC_DISTANCE); maxentStressAlgo.run(); t.stop(); runtime = t.elapsedMicroseconds(); if (graph.numberOfNodes() < 1e5) { ...
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se); Aux::Timer t; t.start(); PivotMDS pivotMds(graph, 2, 30); pivotMds.run(); MaxentStress maxentStressAlgo(graph, 2, pivotMds.getCoordinates(), 1, 0.001, MaxentStress::LinearSolverType::CONJUGATE_GRADIENT_IDENTITY_PRECONDITIONER, false, MaxentStress::GraphDistance::ALGEBRAIC_D...
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ngle-line triple-quoted string rules << Rule("'''.*?'''", quote_format); rules << Rule("\"\"\".*?\"\"\"", quote_format); // Beginning of multiline string rules << Rule("'''.*$", quote_format, BASE, MULTILINE_SINGLE); rules << Rule("\"\"\".*$", quote_format, BASE, MULTILINE_DOUBLE); // End of mul...
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if (!match.hasMatch()) continue; auto index = match.lastCapturedIndex(); if (match_start == -1 || match.capturedStart(index) < match_start) { match_start = match.capturedStart(index); match_length = match.capturedLength(index); ...
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File; /** True if the file was successfully copied to the remote location */ private boolean succeeded; /** An optional error message if the remote file copy was not successful */ private String errorMessage; /** An optional exception describing why this attempt failed */ private ...
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this.succeeded = wasSuccessful; } /** * @return True if the file was successfully copied to the remote file * location. */ public boolean isSucceeded() { return succeeded; } /** * @param error the error to set */ public void setError(Exception error) { ...
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: 0} m_GameObject: {fileID: 3691887641913671224} m_Enabled: 1 m_EditorHideFlags: 0 m_Script: {fileID: -405508275, guid: f70555f144d8491a825f0804e09c671c, type: 3} m_Name: m_EditorClassIdentifier: m_Padding: m_Left: 0 m_Right: 0 m_Top: 0 m_Bottom: 0 m_ChildAlignment: 0 m_Spacing: 10 ...
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s: 0 m_CorrespondingSourceObject: {fileID: 0} m_PrefabInstance: {fileID: 0} m_PrefabAsset: {fileID: 0} m_GameObject: {fileID: 4153264261330621392} m_LocalRotation: {x: 0, y: 0, z: 0, w: 1} m_LocalPosition: {x: 0, y: 0, z: 0} m_LocalScale: {x: 1, y: 1, z: 1} m_Children: - {fileID: 7335350715391774470} ...
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60445797975860} - component: {fileID: 4901496528780876147} m_Layer: 5 m_Name: Divider m_TagString: Untagged m_Icon: {fileID: 0} m_NavMeshLayer: 0 m_StaticEditorFlags: 0 m_IsActive: 0 --- !u!224 &4050628322365125319 RectTransform: m_ObjectHideFlags: 0 m_CorrespondingSourceObject: {fileID: 0} m_Pref...
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90, guid: f70555f144d8491a825f0804e09c671c, type: 3} m_Name: m_EditorClassIdentifier: m_IgnoreLayout: 0 m_MinWidth: -1 m_MinHeight: -1 m_PreferredWidth: -1 m_PreferredHeight: 2 m_FlexibleWidth: 1 m_FlexibleHeight: -1 m_LayoutPriority: 1 --- !u!1 &8164632549414063899 GameObject: m_ObjectHideFlags...
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