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igl(\bar Y\times_Y\bar Y\bigr)$ exists. It coincides with the strict closure considered in [@lip-arf]. The curve case was introduced earlier in [@arf]. The related Lipschitz closure is studied in [@pham] and [@lip-lip]. Basic results {#basic.res.sec} ============= In this section we prove some basic existence result...
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note that for the modified system of equations to be invariant under the gauge freedom $B \to B + d \Lambda$ (where for simplicity we assume that $\mathcal{L}_I \Lambda = 0$) the “dilaton” field $\Phi$ must now transform as $\Phi \to \Phi - \iota_I \Lambda$, and hence is not unique. This can be understood by starting ...
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ar $P^\rho$ on large scales, even though the mass fluctuations have gone nonlinear on small scales. The reader is referred to Scherrer & Weinberg [-@sw97] for arguments on why that is reasonable, in the context of local-biasing (the mapping from $\delta$ to the optical depth or transmission can be seen as some kind of ...
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hen $$\tr({\mathbf{e}}_i) = \frac {d} {mk}, \ \ \rk({\mathbf{e}}_i)=1 \ \ \mbox{ and } \ \ {\mathbf{e}}_1+\cdots+{\mathbf{e}}_{mk}={\mathbf{1}},$$ for all $1\leq i \leq mk$. By symmetry, the partition $$S_1=\{1,\ldots, m\}, S_2=\{m+1, \ldots, 2m\}, \ldots, S_k=\{(k-1)m+1,\ldots, km\}$$ minimizes the bound in . Now $$\b...
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{\rm ch}^{\rm rep}(V)|_{(1)} \: = \: \oplus_{\chi} {\rm ch}(V) \otimes \chi,$$ and similarly for ${\rm ch}^{\rm rep}(TX)^{(1)}$. Now, suppose $k$ is prime. Then $\chi(g)=1$ implies $\chi = 1$. Thus, $${\rm ch}^{\rm rep}(V)|_{(g)} \: = \: {\rm ch}(V) \otimes \zeta(g),$$ $${\rm ch}^{\rm rep}(T\mathfrak{X})|_{(g)} \: = \...
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me is flat. However in the second case, as for $p$ real, $15 p^2-2 p+3 >0$, we cannot “cancel” the singularity by a proper choice of initial condition, but still, the divergence is again milder than the standard one. Now let us note that considering only the two order 8 classes $\mathcal{R}_{2,2}^0$ and $\mathcal{R}_{...
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\[-0.16, 0.77\] 0.20 2.30 \[0.79, 3.81\] 0.006^\*^ PSS -- Cancer appraisal -0.27 \[-0.42, -0.12\] \<0...
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- \partial_i \partial_j \right)A_j^a \right\} \nonumber \\ &=& \frac{1}{2} \int d\tau d^3x \ \left\{ (\vec \partial a_0)^2 - A_i^a ( \vec \partial^2 - \partial_i \partial_j) A_j^a - \right. \nonumber\\ & & \hspace{1.9cm}\left. A_i^a D_0^{ac}D_0^{cb} A_i^b \right\}, \end{aligned}$$ where we have defined $$\begin{alig...
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to calculate that $$\begin{aligned} & & :\mbox{exp} \left( X^{\alpha}(u;A,B) \right): :\mbox{exp} \left( X^{\beta}(v;C,D) \right) : \nonumber \\ & &~~~~= \mbox{exp} \left( \langle X^{\alpha}(u;A,B) X^{\beta}(v;C,D) \rangle \right) :\mbox{exp} \left( X^{\alpha}(u;A,B) \right) \mbox{exp} \left( X^{\beta}(v;C,D) \right...
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.388\*\*\*\ 0.372\*\*\*\ 0.167\ 0.223\ 0.210\ (0.058) (0.072) (0.065) (0.189) (0.168) (0.158) Amount received (*X*) -0.002\ -0.0118\ -0.003\ -0.010\ ...
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that are then used to cluster and compute similarities between images. We use a triplet network for the task of classification via an unconventional type of KNN in the embedding space. This is done by randomly sampling $50$ embeddings for each class from the training set, and then computing the similarity of these emb...
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se $n_j=\mid \{i\mid f_{i,\lambda}^*=g_j^*, 1\leq \lambda \leq r_i, 1\leq i \leq l, 1\leq j\leq s \}\mid$. Let ${\mathcal M}_j=(R/(g_j^*))^{n_j}$. Then we have [**Theorem 3.2** ]{} *Let ${\mathcal R}={\mathcal R}_1\times {\mathcal R}_2\times\cdots \times {\mathcal R}_l$, where ${\mathcal R}_i=R/(x^{m_i}-1)$ for all $i...
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Knutson71 II.3]. A simple example of a homeomorphism which is not a universal homeomorphism is ${\operatorname{Spec}}K\to {\operatorname{Spec}}L$ where $L/K$ is a finite field extension and $L\neq K$. A more interesting example is given by the normalization of the nodal curve $\bigl(y^2=x^2(x+1)\bigr)$ with one of the...
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from Eq. u\_a\^a u\_b&=&--u\_bu\_a\^a P\ &-&2u\_au\_b\_[k=1]{}\^[N]{} \_k\^a \_k-u\_b.Using Eqs., , and , this becomes \[accel\] u\_a \^au\_b=-+ . Transport coefficients ====================== Shear viscosity --------------- The first term in Eq.(\[eqn:etagen\]) is given by \[firstter\] &&P\^a\_c P\^b\_d T\_[ab]{}\^...
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========================== In this and the remining sections of the paper by $Imm^{sf}(n-k,k)$, $Imm^{\D_4}(n-2k,2k)$, $Imm^{\Z/2 \int \D_4}(n-4k,4k)$, etc., we will denote not the cobordism groups themselves, but the 2-components of these groups. In case the first argument (the dimension of the immersed manifold) is ...
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e{\sigma}_6 = \widetilde{\sigma}_7 = 0$ and $\, \widetilde{\sigma}_6^2\, =\, 4 \, \widetilde{\sigma}_3\, \widetilde{\sigma}_7 \, \;$, $\widetilde{\sigma}_1 = \widetilde{\sigma}_2 = 0$, one find the following ones : $$\begin{aligned} \begin{split} &J_2 = 2 \mathcal{L}_4+12 \mathcal{L}_6 -7 \mathcal{L}_7 = -72 \bigg( 4...
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te of the art techniques. ![Zig-zag chains formed by an incoherent superposition between a triangular lattice [@Becker2010] $V_1({\vec r}\equiv(x,y))=V_{10}\left [ \sin^2\left ({\vec b}_1\cdot{\vec r}/2\right )+\sin^2\left ({\vec b}_2\cdot {\vec r}/2\right ) +\sin^2\left (({\vec b}_1-{\vec b}_2)\cdot{\vec r}/2\right )...
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ned} S_{\alpha \beta}^{(0)} &=& \sum_{i, j} U_{\alpha i} U^*_{\beta j} \left( \sum_{k} X_{i k} X^*_{j k} e^{-i h_{k} x} \right), \label{S-alpha-beta-0th-KTY}\end{aligned}$$ and the factor in parenthesis can be calculated by the KTY technique [@Kimura:2002wd]. We want to diagonalize the Hamiltonian $$\begin{aligned} ...
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s a disjoint union of copies of $T$. We cannot tile $\mathbb{Z}^d$ with strings, as each string intersects $[k+1]^d$ in either 0 or $k$ points, and $(k+1)^d$ is not divisible by $k$. However, we could try to tile $\mathbb{Z}^d$ by using strings in $d-1$ of the $d$ possible directions, leaving holes that can be filled ...
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\hat{\rho}]} \cdot \left[\begin{array}{c}\hat{H}\\ \hat{\rho}\end{array}\right]\;, \label{eq:rho2}\end{aligned}$$ where $$\begin{aligned} \begin{array}{l} \mbox{\boldmath$\cal D$}_{\mbox{\tiny\boldmath$\cal B$},[\hat{\rho}]} =\\ \left[\begin{array}{cc} 0 & 1-\frac{\hbar}{2i} \left\{\ldots,\ln(\hat{\rho})\right\}_{\mbox...
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ht) = \left( \begin{matrix} 0&M\\ M^*&0 \end{matrix}\right)\mathbf{P}_{[0,t)},\end{aligned}$$ with $M$ and $M^*$, as in Lemma \[magneticinvertability\], respectively. Hence we interpret the operator matrix as an operator from $L^2_{2}([0,t),dx)_{\mathbb{C}}$ into itself and restrict the desired eigenfunctions from n...
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)^T\cdot\MM{\pi},\operatorname{ad}_{\MM{u}}\MM{w} \Bigg\rangle = \Bigg\langle {\frac{\delta \ell}{\delta \MM{u}}},\operatorname{ad}_{\MM{u}}\MM{w}\Bigg\rangle = -\,\Bigg\langle \operatorname{ad}^*_{\MM{u}}{\frac{\delta \ell}{\delta \MM{u}}},\MM{w}\Bigg\rangle,\end{aligned}$$ which is the (weak form of the) EPDiff equ...
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ph $({\mathcal{H}}_0^{(m)},\ldots, {\mathcal{H}}_0^{(2m)})$ results in maximum load $$\ell^*+\log_d\log n+{\mathcal{O}}(1/\varepsilon){\leqslant}2(\log_d\log n+{\mathcal{O}}(1/\varepsilon))$$ [in ${\mathcal{H}}_0^{(2m)}$]{}. Therefore, by Inequality (\[domin1\]), after using algorithm ${\mathcal{A}}$ to allocate $m$ ba...
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3^4_3$, $6^{1,1}_3$ and $5^{2,2}_3$-branes, and by including all these branes in the IIB orientifold and mapping them back to the IIA theory we arrive at a fully consistent picture in which also the allowed components of the potentials $E_{8,1}$ and $E_{10,5,2}$, corresponding to $6^1_3$ and $4^{3,2}_3$-branes, are inc...
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e generating functional obeys W=0 \[ne6b\] W\^[,a]{}=.|\_[J=0]{}=\^a \[ne6c\] Shifting the $\Phi_s^a$ fields by an amount $\phi^a$, namely $\Phi_s^a=\phi^a+\varphi_+^a$, we get e\^[iW]{}=e\^[iJ\_d\^d]{}D\_+Dq(\_+\^a-G\_[ret]{}\^[ab]{}q\_[c]{}F\^c\_b)e\^[iJ\_d\_+\^d]{} \[ne7\] This may be rewritten as e\^[iW]{}=D\_...
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cal K}$, which implies that $\rho={\mathcal K}$. $\Box$ If $C$ is a $1$-generator skew GQC code of block length $(m_1, m_2, \ldots, m_l)$ and length $\sum_{i=1}^lm_i$ over $\mathbb{F}_q$, then by Theorem 3.5, each $C_i$, $i=1,2,\ldots,s$, is either trivial or an $[l, 1]$ linear code over $R/(g_i^*)$. Conversely, any l...
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\times I)$. \(ii) Suppose that additionally the assumption ${\bf TC}$ holds (p. ). Then a solution $\phi$ of the equations (\[cosyst1\]), (\[cosyst2\]) obtained in part (i) is a solution of the problem -. \(iii) Under the assumptions imposed in part (ii), any solution $\phi$ of the problem - that further satisfies \[...
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er (initial) condition holding for a.e. $(x,\omega)\in G\times S$. \[csdale1a\] Assume that the conditions (\[ass1\]), (\[ass2\]) and (\[ass3\]) are valid. Then $$\Sigma-K_C:L^2(G\times S\times I)\to L^2(G\times S\times I)$$ is a bounded operator and it satisfies the following accretivity condition \[se7\] (-K\_C),\...
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ibutions. STM tunnel current {#sec:tunnel-current} ------------------ Since in the tunneling limit $\hat H_{T}$ defines the smallest energy scale of the system, we proceed in the interaction picture. We assume that the tunnel Hamiltonian $\hat H_{T}$ is switched on at time $t_0$. Then, the current evaluated at time $...
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bin it chose, as part of the balanced allocation procedure, had load at least $h$. Starting from bin (vertex) $r$, let us recover all $\ell$ edges corresponding to the balls that were placed in $r$ with height at least $c$. Thus, the alternative bin choices have loads at least $\ell+c-1,\ldots,c$, respectively. These $...
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characterizing the pulsation of LP 133-144 and list them in Table \[table:lp133freq\]. The Rayleigh frequency resolution of the whole dataset is $0.09\,\mu$Hz. --------- -------------------- ------- ----- ------ ------- ...
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e number of walkers reached on replica 1 are given in table \[tab:-energies-xyl\]. With this procedure the obtained number are in agreement with the MPS-LCC results, there are usually a bit more negative since this is a fully uncontracted technique. However this approach is not really practical since the number of walk...
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fulfilled in the region of the super-inflation $( \tau \in [ \sim -6 , \sim -4 ] )$ . In the right panel we can see the evolution of $\Gamma$ for three different values of $k$. $\begin{array}{cc} \includegraphics[width=6cm,angle=270]{plot2.eps} & \includegraphics[width=6cm,angle=270]{plot3.eps} \end{array} $...
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k{a}}(t,u,v)-{\mathfrak{a}}(s,u,v)| \le\omega(|t-s|) \Vert u\Vert_{V_\gamma} \Vert v\Vert_{V_\gamma}\quad \ (t,s\in[0,T], u,v\in V),$$ with $$\label{eq 2:Dini-condition}\sup_{t\in[0,T]} \frac{\omega(t)}{t^{\gamma/2}}<\infty \quad \text{ and } \int_0^T\frac{\omega(t)}{t^{1+\gamma/2}}<\infty$$ where $V_\gamma:=[H,V]$ is...
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g. It has been reported that *Clostridium difficile* \[[@B18-ijerph-09-03330]\] spores can survive temperatures and chemical treatment of typical hospital laundering cycles and that cross-contamination of *Clostridium difficile* spores can occur on bed linen during a wash cycle. Therefore the persistent nature of this...
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ependence of the equatorial inflow rate $\dot{M}_{\mathrm{inflow}}(r)$ (solid blue) and bipolar outflow rate $\dot{M}_{\mathrm{outflow}}(r)$ (solid red), defined in equation . The blue arrow marks the estimated value of the inflow rate at the inner boundary $\dot{M}_{\mathrm{inflow}}(R_{\mathrm{in}})$ (equation \[eq:17...
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t $F'=\{F'_1,F'_2,\dots ,F'_k\}$ be a basis of $U^-(\chi )_{-{\alpha }}$, and let $d(F')=\det {\mathrm{Sh}}(F'_i,F'_j)_{i,j\in \{1,\dots ,k\}} \in {{\mathcal{U}}^0}$. Then $d(A'F')=(\det A')^2d(F')$ for all $A'\in \mathrm{GL}(k,{\Bbbk })$, and hence $\det ^\chi _{\alpha }=d(F')/{{\Bbbk }^\times }$ does not depend on th...
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er-base* $_{\textrm{F}}\mathcal{B}$; alternatively $_{\textrm{F}}\mathcal{B}$ is the filter-base of $\mathcal{F}$. The entire neighbourhood system $\mathcal{N}_{x}$, the local base $\mathcal{B}_{x}$, $\mathcal{N}_{x}\bigcap A$ for $x\in\textrm{Cl}(A)$, and the set of all residuals of a directed set $\mathbb{D}$ are amo...
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\\ & & - \pi_k{\frac{\partial \xi_k(\MM{l})}{\partial l_j}}{\frac{\partial }{\partial \pi_j}} - \left(\pi_k{\frac{\partial \xi_k(\MM{l})}{\partial l_j}}\right)_{,t}{\frac{\partial }{\partial \pi_{j,t}}} - \left(\pi_k{\frac{\partial \xi_k(\MM{l})}{\partial l_j}}\right)_{,i}{\frac{\partial }{\partial \pi_{j,i}}}.\end{a...
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Fleet/Inventory\* Quantitative ------------- ------- ----------------------------------------------------------------------------------------- --------------------------------------------------- ----------------------------------------------------------------------------...
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Tangent method; V1 45 (14) 57 (73) 22 (28) 17 (22) Spontaneous VT/VF VT/VF/aborted SCD vs asymptomatic/syncope 22/54/29/‐ -- ...
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zdec1}}~~\leq~~ \Bigg(~~\raisebox{-2pc}{\includegraphics[scale=0.12]{IRSchwarzdec2}} ~~\Bigg)^{1/2}~\Bigg(~~\raisebox{-1.5pc}{\includegraphics[scale=0.12] {IRSchwarzdec3}}~~\Bigg)^{1/2},\end{aligned}$$ where the two weighted arcs between $o$ and $v$ in the second term is $|v|^tG(v)^2\equiv(|v|^{t/2}G(v))^2$. By tran...
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R^{\mu\nu}R_{\nu\alpha}R^{\alpha}_{\;\,\mu} + 2 \, R R^{\mu\nu} R_{\mu\nu} \;\Big) \;\bigg] + \curv{L}_m \Bigg),\end{aligned}$$ where $\curv{L}_m$ is the Lagrangian density for matter, one find the acceleration equation : $$\begin{aligned} 3 H(t)^2+2 \dot{H}(t)-36\, \nu \, H(t)^4 \big(H(t)^2+2 \dot{H}(t)\big) = -8...
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e{\sigma},\overline{\sigma}]}E[\varphi(\lambda X_i)]=:\mathcal{N}[\varphi],$$ i.e., $\xi_1, \cdots, \xi_n$ are identically distributed under $\mathbb{E}$. Set $W_{i,n}=\frac{\xi_1+\cdots+\xi_i}{\sqrt{n}}$. We next prove that, for any function $\varphi\in lip(\mathbb{R})$, $$\begin{aligned} \label {se2} \mathbb{E}[\var...
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leq \Theta \times \theta _{q,t}(m),\qquad and \label{j3} \\ %\theta _{q,t}^{1/q}(m) &\leq &\frac{Q^{m}}{(\lambda t)^{\theta _{0}(1+\delta)}} \theta _{q,t}(m) & \leq \frac{Q^{m q}}{(\lambda t)^{\theta _{0}(q+d+2\theta_1)}} . \label{j4}\end{aligned}$$ We define now $$\phi _{t}^{m_{0}}(x,y)=\sum_{m=0}^{m_{0}}\int...
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\mathbf{h}}_{c+t}e_-\delta) \ =\ e ([{\mathbf{h}}_{c+t}, m]) \delta e.$$ By $H_{c+t}$ is diagonalisable under the adjoint ${\mathbf{h}}_{c+t}$-action and so the result for $B_{ij}$ follows. The same argument works for the modules $N(i)$ and $M(i)$ if one uses the decompositions $N(i)=(B_{i0})(eH_c)$ and $M(i)=(H_{...
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ses there is a chiral phase transition which is expected to be of second order and in the $O(4)$ universality class [@rob_o4]. However, universal scaling allows to define pseudo-critical temperatures for the chiral transition even for non-zero light quark masses, provided they are small enough. For staggered fermions t...
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isotopic to identity on $c$, ${h_1}^{-1} h_2$ is isotopic to identity on $T$. This implies that $(h_1)_{\#}^{-1} (h_2)_{\#} = t_c^m$ for some $m \in \mathbb{Z}$. Since $(h_1)_{\#}^{-1} (h_2)_{\#}$ also fixes $[d]$, we have $m=0$, so $(h_1)_{\#}^{-1} (h_2)_{\#} = [id]$. Let $h=h_1$. If $x$ is a 1-sided simple closed cu...
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mes$ 10$^{5}$ 126 11 28.5 1.42 $\times$ 10$^{2}$ (3.87 $\times$ 10$^{2}$) 0.60 2.43 3.2 1.0 $\times$ 10$^{7}$ 151 12 26.8 1.08 $\times$ 10$^{2}$ (2.47 $\times$ 10$^{2}$) 0.86 2.50 2.3 5.5 $\times$ 10$^{2}$ 164 1...
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\,\,\, 3\,\,\, 4$} \rput[b](4,2){$\rightsquigarrow$} \end{pspicture} \begin{pspicture}(0,0.8)(4,3.4) \psline[linestyle=dashed](2,2)(1.2,3) \psline(2,2)(1.6,3) \psline(2,2)(2,3) \psline(2,2)(2.4,3) \psline[linestyle=dashed](2,2)(2.8,3) \rput[b](2,3.2){$1\,\,\, 2\,\,\, 3\,\,\, 4\,\,\, 5$} \end{pspicture}$$ We defi...
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atent patterns for each part template. - It is important to maintain the generality of the pre-trained CNN during the learning procedure. *I.e.* we do not change/fine-tune the original convolutional weights within the CNN, when we grow new AOGs. This allows us to continuously learn new semantic parts from the same C...
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mplexes. Then the following conditions are equivalent: 1. $\Gamma=\bar{\Gamma}$; 2. for each $a\in\Gamma$ there exists $m\in{\mathcal M}(\Gamma)$ with $a\leq m$. (a)(b): We proceed by induction on $n-|\ip a|$. If $n-|\ip a|=0$, then $a(i)=\infty$ for all $i$, and hence $a\in {\mathcal M}(\Gamma)$. Suppose now that...
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0.27 -0.05 \[-1.44, 1.33\] 0.94 -0.60 \[-2.18, 0.98\] 0.46 0.85 \[-0.56, 2.26\] 0.24 T...
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$\alpha$ of the inertia stack, the $\langle \alpha \rangle$-equivariant line bundle $$K_{\alpha} \otimes \det {\cal E}^{\alpha}_0$$ admit a square root. We defer further discussion of this condition to appendix \[app:spectra:fockconstraints\]. One of the original goals of this project was to find a suitable generaliza...
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ure constant and $n^{(3)}_{\lam\m\n}(p, q, -(p+q))$ the kinematic factor n\^[(3)]{}\_(p, q, r) (p-q)\_\_ + (q-r)\_\_ + (r-p)\_\_. \[n\] Here $(p, q, r)$ are the momenta of the 3 external legs, and $\lam, \m, \n$ are Lorentz indices labelling the polarizations of the vector fields. The origin of this factor (\[n\]) is t...
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rontier Research Institute for Interdisciplinary Sciences of Tohoku University. This work is supported in part by MEXT/JSPS KAKENHI Grant Number 15J03873 (KS), 25800102, 15H00776 and 16H05996 (TH), 15H06022 (HY) and 25287040 (KO). natexlab\#1[\#1]{} , T., [Anninos]{}, P., [Zhang]{}, Y., & [Norman]{}, M. L. 1997, New ...
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gned} \label{eq:preVbot} V_{\bot,k} &=& V_{\bot,\Lambda_{\rm UV}} +\left. \012 {\mathrm{Tr}}\, \left[\ln (S_{YM}^{(2)} + R_{A})\right]_{ii} \right|^k_{\Lambda_{\rm UV}} \\\nonumber &=& V_W + T \sum_{n} \int \frac{d^3p}{(2\pi)^3} \theta (k_\bot ^2 - \vec p^2) \ln ( k_\bot ^2 + D_0^2)\,.\end{aligned...
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0.769749
github_plus_top10pct_by_avg
jection $p:\X_\lambda(\F)\rightarrow \mathfrak{g}(\F)$, $(X,gP_\lambda)\mapsto X$ is the Zariski closure $\overline{\calO}_{\lambda'}$ of the nilpotent adjoint orbit $\calO_{\lambda'}$ of $\gl_n(\F)$ whose Jordan form is given by $\lambda'$, and that $p$ is a desingularization. Put $$\mathbb{V}_\muhat:=\left\{\left(a...
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x;{{\cal A}}}[{\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle L$}}}]=\Theta_{y,x;{{\cal A}}}[{\mathbbm{1}{\scriptstyle\{y{\underset{\raisebox{5pt}{${\scriptscriptstyle}$}} {\overset{}{\longleftrightarrow}}} v\}}}]-\Theta''_{y,x,v;{{\cal A}}}$. First we recall [(\[eq:EE’-dec\])]{}, in which $b$ is the last pivotal bond for...
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{\mathbf{v}}_j)-1}\right)\\ &\geq \xi_i[h]({\mathbf{v}}_j) \left( \delta - \frac { \delta/(\delta-1)}{ \delta/(\delta-1)-1}\right) =0, \end{aligned}$$ where the last inequality follows from , and the concavity of ${\mathbf{z}}\rightarrow \xi_j[h]({\mathbf{z}})$. Consider ${\mathbb{R}}^{n+m}={\mathbb{R}}^n\oplus {\mat...
2,360
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github_plus_top10pct_by_avg
0.25 0.25 *Penicillium* species (1) Efinaconazole 0.016 0.016 Itraconazole 0.13 0.13 *Alternaria* species (1) ...
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github_plus_top10pct_by_avg
and the Ore Polynomial ring $F_q[Y^{q_0}, \circ]$.* $\Box$ For a skew cyclic code over $\mathbb{F}_q$, it can also be described in terms of the $n$-th root of unity. By the above mapping $\phi$, one can verify that $\phi(x^n-1)=Y^{q_0^n}-Y$. Since $\sigma=\theta^d$, the fixed subfield is $\mathbb{F}_{p^d}=\mathbb{F}_...
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vert_A}} \bigr). \end{split}$$ In particular, for $\chi \in \widehat{G}$, $$\operatorname{Var}(\lambda_\chi) = 1 + \alpha {\mathbbm{1}_{\chi = \overline{\chi}}} + p_2 (\beta - \alpha - 1).$$ Denoting $$\nu^{(n)} = (1-p_2^{(n)}) {\mathcal{N}}\bigl(0,1 + p_2^{(n)}(\beta - \alpha - 1)\bigr) + p_2^{(n)} {\mathcal{N}}...
2,363
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1,612
1,805
3,888
0.769508
github_plus_top10pct_by_avg
0.172^a^ 51.62 ± 10.89 51.08 ± 10.92 53.89 ± 10.62 0.095^a^ BMI (mean ± SD) 24.6 ± 3.1 24.6 ± 3.0 24.6 ± 3.2 0.971^a^ 24.5 ± 3.5 24.5 ± 3.7 24.5 ± 3.1 0.933^a^ Degree of inflammatory activity (A0/A1-3) 3...
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github_plus_top10pct_by_avg
omega,E',E)$. It has a decomposition ([@duclous], [@lorence], [@boman], [@hensel]) \[i-e-e1\] \_[22]{}(x,’,,E’,E) =\^p\_[22]{}(x,’,,E’,E)+\^s\_[22]{}(x,’,,E’,E). where $\sigma^p_{22}(x,\omega',\omega,E',E)$ is corresponding to the (new) primary electrons and $\sigma^s_{22}(x,\omega',\omega,E',E)$ is corresponding to th...
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SM instead of restricting ourselves to a particular model. For each point, we calculate both the full, exact one-loop radiative corrections to the bottom quark and compare with the value obtained from the approximate form of the corrections as given in \[Eq:common-app\]. For each point in the pMSSM scan, we additionall...
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] u=[( + )]{}[( M\^1+M\^2| )]{}+c.c., where c.c. means the complex conjugate of the previous term. The $k\times k$ matrices $M^1$ and $M^2$ are defined by \[eq:3.7b\] M\^1=&\^[-1]{},\ M\^2&=-M\^1 [( + )]{}[( I\_k- )]{}\^[-1]{}, \[eq:3.8\] =[( )]{}\^[qk]{},=[( )]{}\^[qk]{},=(\_i\^A)\^[kp]{}, \[eq:3.9\] =[( )]{}=[( x...
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2,981
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2,874
0.776389
github_plus_top10pct_by_avg
------------- To avoid a proliferation of superscripts and subscripts, we adopt the following convention for the various power spectra, $P$, discussed in this paper. We use $\tilde{}$ to distinguish between one-dimensional and three-dimensional power spectra: $P$ is 1-D and $\tilde P$ is 3-D (i.e. $P$ has a dimension ...
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- V)G_l^\top \right| \leq B^2 \| \hat{V} - V \|_{\mathrm{op}} \leq C B^2 \sqrt{ b \overline{v} \frac{ \log b + \log n }{n} },$$ with probability at least $ 1- \frac{1}{n}$, where $C$ depends only on $A$ and we have used the fact that $\max_j \| G_j (\psi(P))\|^2 \leq B^2$ uniformly over $P \in\mathcal{P}_n$. Thus,...
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od simply from the matter representations: a spinor in the worldvolume theory can be represented mathematically in the form [@lawson-m] $$\left( \wedge^{\bullet} TB \right) \otimes \sqrt{K_B}.$$ In terms of the worldsheet RNS formalism, perturbative modes realize the $TB$ factors, and the $\sqrt{K_B}$ is implemented by...
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rs_p-conf-ece.pdf "fig:"){width="\linewidth"} [.4]{} ![Proportion of times each classifier is already calibrated with different p-tests.[]{data-label="fig:uncal:p:ece"}](figures/results/p_table_classifiers_p-cw-ece.pdf "fig:"){width="\linewidth"} Figures \[fig:uncal:p:cw:ece\] and \[fig:uncal:p:conf:ece\] show the pr...
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261
0.815615
github_plus_top10pct_by_avg
-280*a**3*f**3*z + 12*a**3*f**3 - a**2*f**3 + 2*a**2*f*z + 225*a*f**3*z - 3*f**3*z wrt a. -1680*f**3*z + 72*f**3 What is the second derivative of -j**2*s**2 + 26*j**2*s - j*s**2 + 35*j*s wrt j? -2*s**2 + 52*s What is the derivative of 2*j**2*s - 63*j**2 + 2*j*s + 5*j - 345*s + 4 wrt j? 4*j*s - 126*j + 2*s + 5 What is t...
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github_plus_top10pct_by_avg
a\] be expressed as Jordan dipolynomial $\Phi$ in $x$, $y$, $u_i$ and dotted tetrads involving this variables. Since $f$ is linear in the $u$’s so is $\Phi$ and therefore no dotted tetrad can involve more than one $u$, but it must involve at least one. By permutation of variables any such tetrad can be reduced to the f...
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2,071
3,613
0.771223
github_plus_top10pct_by_avg
ert G \right\vert}}{2} \bigl( \alpha {\mathbbm{1}_{\chi_1 = \overline{\chi_2}}} + {\mathbbm{1}_{\chi_1 = \chi_2}}\bigr). \end{aligned}$$ Similarly, it follows that the off-diagonal blocks of $\operatorname{Cov}\bigl((\lambda_{\chi_1}, \lambda_{\chi_2})\bigr)$ are $0$ unless $\chi_1 = \chi_2$ or $\chi_1 = \overl...
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482
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github_plus_top10pct_by_avg
the high vitamin C group (*p*=0.01) ([Table 5](#T0005){ref-type="table"}). In the mixed model, there was a significant interaction between maternal vitamin A intake and age in terms of head circumference when adjusting for confounding variables ([Fig. 2](#F0002){ref-type="fig"}). This denotes that these indices increas...
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_gamma\], we show a case where the inversion $\gamma$ is chosen to be slightly different from the known input $\gamma$. (The actual value for $\gamma$ in the real universe is likely to have a narrow range $1.3 \, {\mbox{$^{<}\hspace{-0.24cm}_{\sim}$}}\, \gamma \, {\mbox{$^{<}\hspace{-0.24cm}_{\sim}$}}\, 1.6$ c.f. ). Th...
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github_plus_top10pct_by_avg
G. Rodrigo, L. Martin-Moreno, A. Yu. Nikitin, A. V. Kats, I. S. Spevak, and F. J. Garcia-Vidal, Opt. Lett. **34**, 4 (2009). A commercial software <span style="font-variant:small-caps;">comsol</span> has been used. E. H. Hwang, S. Adam, and S. D. Sarma, Phys. Rev. Lett. **98**, 186806 (2007). K. I. Bolotin, K. J. Sikes...
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github_plus_top10pct_by_avg
ic perturbation $g^\prime_{ab} = g_{ab} + \epsilon h_{ab}+\mathcal{O}(\epsilon^{2})$, where $g_{ab}$ is the NHEK metric and $h_{ab}$ is a perturbation. The linearized Einstein equations (i.e. at order $\epsilon^{1}$) are $$G^{(1)}_{ab}[ h ] = 8 \pi T_{ab} \,,$$ where $T_{ab}$ is the stress-energy tensor of a source te...
2,378
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github_plus_top10pct_by_avg
y} \right. $ Now in terms of $H(t)$ and its derivatives, considering only the scalars of the reduced FKWC basis : $$\begin{aligned} \begin{split} J=&\sum\limits_{i=4, 6, 7} v_i \mathcal{L}_i + \sum\limits_{j=1, 3, 5, 8} x_j \curv{L}_j =3 \Bigg( \widetilde{\sigma}_1(v_i,x_i) \; H(t)^6 + \widetilde{\sigma}_2(v_i,x_i) ...
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coefficient $m_{d-i}$ can be computed recursively (starting with $i=0$) as the unique integer $m_{d-i} \ge -1$ such that $$\rho_q(d-i,m_{d-i}) \le N-\sum_{j=d-i+1}^{d}\rho_q(j,m_j) <\rho_q(d-i,m_{d-i}+1).$$ From the existence-part of the proof of Theorem \[thm:genrepMac\] it follows directly that the given greedy alg...
2,380
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1,733
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0.773774
github_plus_top10pct_by_avg
\], \[\]/\[\] is *underproduced* in starburst galaxies with respect to the predictions of a Salpeter IMF extending to $100$ . Testing Optical  Indicators {#sec:optical} --------------------------- How well do optical forbidden and recombination line ratios estimate  in starbursts? Figures 9 and 10 of @kbfm show that ...
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k}}}{^{\rm c}}}({{\bf m}}'')}{Z_{{{\cal A}}{^{\rm c}}\cap\,{{\cal S}}_{{{\bf m}}+{{\bf k}}}{^{\rm c}}}}\, \frac{w_{\tilde{{\cal D}}{^{\rm c}}\cap\,{{\cal S}}_{{{\bf m}}+{{\bf k}}}{^{\rm c}}}({{\bf k}}'')}{Z_{\tilde{{\cal D}}{^{\rm c}}\cap\,{{\cal S}}_{{{\bf m}}+{{\bf k}}}{^{\rm c}}}}\,{\mathbbm{1}{\raisebox{-2pt}{$\sc...
2,382
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A:29 G:391 G:192 29 15.13 40 putative transposase 1857109 A:162 G:12 ...
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github_plus_top10pct_by_avg
$ due to channel $a$ by writing $H_{\mathrm{eff}}=H_{\mathrm{eff}}^{a}-i\lambda_a V_a V_a^{\dag}$, and then treat $V_aV_a^{\dag}$ as a rank 1 perturbation to the term $H_{\mathrm{eff}}^{a}=H-i\sum_{k\neq a}\lambda_k V_k V_k^{\dag}$. The upper index “$a$” for $H_{\mathrm{eff}}^{a}$ denotes that the contributions of all ...
2,384
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github_plus_top10pct_by_avg
$ As a special case we obtain the following result about the general linear groups of the string topology spectrum. \[string\] If $G \to P \to M$ is a principal bundle over a manifold and ${\mathcal{L}}= \Sigma^\infty_M (P_+)$, there is a homotopy equivalence $$BGL_n ({\mathcal{S}}(P)) \simeq Map_{\oplus_n{\mathcal{L...
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ism as a weighted colimit if it is naturally isomorphic to $\colim^W$ for some $W$. In a dual way, if ${\sD}$ is a -opmodule, one defines **weighted limits** $$\mathrm{lim}^W=(-\lhd_{[A]}W)\colon{\sD}^A\to{\sD}^B,$$ Moreover, if is a closed -module, then weighted colimits and weighted limits are always adjoint to each ...
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github_plus_top10pct_by_avg
hcal{P}}_1\otimes {\mathcal{L}}_1^d).$$ It is not true, however, that the natural ${{W}}$-action on the two sides agrees. Indeed, thanks to the proof of [@hai2 Proposition 4.2] the isomorphism written ${{W}}$-equivariantly is $$\label{cohj1} {\mathbb{J}}^d \otimes {\epsilon}^{\otimes d} \cong H^0(\operatorname{Hilb^...
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github_plus_top10pct_by_avg
data at RHIC at the maximum, $\sqrt{s_{\NN}} = 200$ GeV bombarding energies. The emission function of the Buda-Lund hydro model ================================================== The Buda-Lund hydro model was introduced in refs. [@Csorgo:1995bi; @Csorgo:1995vf]. This model was defined in terms of its emission functi...
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github_plus_top10pct_by_avg
particles and the boundary dissipation. In the limit in which the particle addition is infinitely slow with respect to the spreading of activity, the system reaches a critical state with density $n_c$ (in the thermodynamic limit)[@braz]. The infinitely slow drive is implemented by adding a new active particle only whe...
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ussed in [@footnote2], this limit is finite. This finite behavior is illustrated with the case $m=0$ in Fig. \[fig5L5\]. Other choices of $m$ will lead to conclusions alike since the asymptotic behavior of $|f_n^m|$ with $n$ and $\eta$ does not depend on $m$ in any fundamental way [@footnote2]. To finish the analysis ...
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lary \[poincare-S2A\] and is related to the standard modules $\Delta_{c+k}(\mu)$. The key observation is that these factors have the same Poincaré series and so they are naturally isomorphic as graded vector spaces. The proof of the theorem then amounts to lifting this isomorphism to give the desired equality $eJ^k\del...
2,391
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1,789
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2,578
0.778721
github_plus_top10pct_by_avg
Q: Term for law workarounds Let's imagine there is some law (for example, gambling prohibition law) and malefactors try to find some workarounds to continue their business (for example, pretend like this is not gambling but lottery). What are these law workarounds called in general? A: They're called loopholes or ...
2,392
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971
1,438
155
0.822317
github_plus_top10pct_by_avg
for $i=2,\dots,j$, and ${\overline{e}}_j\ne x$; otherwise, the following argument can be simplified. We consider each event $I_i$ in [(\[eq:fin-ind:=1\])]{}–[(\[eq:fin-ind:geq2\])]{} individually, and to do so, we assume that $y$ and ${\underline{e}}_1$ are the only sources for $I_1(y,z_1,{\underline{e}}_1)$, that ${\...
2,393
2,748
2,108
2,311
1,782
0.785753
github_plus_top10pct_by_avg
set $A\subseteq X$ is nowhere dense in $X$ iff it is contained in its own boundary, iff it is contained in the closure of the complement of its closure, that is $A\subseteq\textrm{Cl}(X-\textrm{Cl}(A))$. In particular a closed subset $A$ is nowhere dense in $X$ iff $A=\textrm{Bdy}(A)$, that is iff it contains no open ...
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2,370
1,256
0.791988
github_plus_top10pct_by_avg
* Here is where the error keeps returning, blueJ keeps pointing * me to this line of code and it has to be the variables I am using * in the array that are causing the issue. The only issue is I * don't know what to insert for that. ...
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,2.2){1.4} \rput(-0.2,1){$\varphi$} \psline(2.5,0.5)(2,3) \psline(2.5,0.5)(1.3,3) \psline(1.7,2.2)(1.7,3) \psline(0.4,2.6)(0.4,3) \psline(0.7,2.3)(0.7,3) \rput(0.2,2.4){\tiny $\alpha_2$} \rput(0.6,2.1){\tiny $\alpha_3$} \rput(1.4,2.1){\tiny $\alpha_4$} \psccurve[linestyle=dotted](0.5,0.8)(-0.5,3)(1,3.6)(2.4,3...
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0.770955
github_plus_top10pct_by_avg
\, .$$ Since $W_H$ is a cyclic group of order $n_H$, this is a complete set of orthogonal idempotents in $\c W_H$. Now, for $H\in \mathcal{A}$, we fix a sequence of non-negative integers $k_H=\{k_{H,i}\}_{i=0}^{n_H-1}$ so that $k_H=k_{H'}$ if $H$ and $H$ are on same orbit of $W$ on $\mathcal{A}$. The *rational Cheredni...
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detail, applying the $\Lambda$ bound Eqn. \[e.NScoolingbound\] and with the understanding that the full realization of dmDM requires a slightly non-minimal spectrum. The dark matter yukawa coupling is constrained from observations on large scale structure and (under certain assumptions) from cosmology: - Dark matt...
2,398
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2,775
2,362
1,489
0.788925
github_plus_top10pct_by_avg
mathbb Z}_+}^{{{\mathbb B}}_{{\cal A}}}$, we omit “in ${{\cal A}}$” and simply write $x{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}} {\overset{}{\longleftrightarrow}}}y$. We also define $$\begin{aligned} {\label{eq:incl/excl}} \{x{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf n}}$}} ...
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2,365
2,217
4,163
0.767658
github_plus_top10pct_by_avg
check the DNS records A,PTR seem to be ok. And netbios resolution does also work. So how does kerberos lookup the hostname. Does it extract the hostname out of the UNC-Path? Writing the Hostname into /etc/hosts does not work neither. Nevertheless another server with the same windbind, samba, cifs.upcall and kerberos Ve...
2,400
5,979
806
1,710
70
0.828854
github_plus_top10pct_by_avg