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ties. Thus the net second order baryon number susceptibility is related to the second-order QNS as $\chi_B=\frac{1}{3}\chi$. The strength of the magnetic field produced in non-central heavy-ion collision can be up to $(10-20)m_\pi^2$ at the time of collision [@Bzdak:2011yy]. However, it decreases very fast being inver...
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${{\mathcal C}}$. Section 5 is a postface, or a “discussion” (as they do in medical journals) – we discuss some of the further things one might (and should) do with cyclic bimodules, and how to correct some deficiencies of the theory developed in Sections 2 and 4. Acknowledgements. {#acknowledgements. .unnumbered} --...
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not understand what is the proper cyclic bimodule context for higher-level infinitesemal extensions. Of course, if one is only interested in an $R$-deformation ${\widetilde}{A} = A_R$ over an Artin local base $R$, not in its cyclic bimodule generalizations, one can use Goodwillie’s Theorem: using the full cyclic object...
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) \cap B(O,r) \right) = 1 ~.$$ - For any $k\in \{1,\ldots,5\}$ and for all integers $n$ such that $0\leq n\leq (R-r_k-1)/2\varepsilon$: $$\hat{N}\left(B\big((r_k+1+2n\varepsilon) e^{\i (2k\pi/5\pm2\varepsilon)},\varepsilon\big) \cap V_{\varepsilon}(r_{1},\ldots,r_{5}) \right)=1 ~.$$ - The previous points are the...
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noted that the gauge parameter in this form, $\lambda_{{\mathcal{S}}\tilde{p}}=X\eta\xi_0[{\mathcal{S}},\tilde{p}]\Phi + X\eta[{\mathcal{S}},M]\Phi$, is in the restricted small Hilbert space: $\eta\lambda_{{\mathcal{S}}\tilde{p}}=0$ and $XY\lambda_{{\mathcal{S}}\tilde{p}}=\lambda_{{\mathcal{S}}\tilde{p}}$. In addition...
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” of . If *is* symmetric, then the duality $A\mapsto A\op$ extends to a self-duality of the bicategory $\cProf({\sV})$, from which the equivalence of \[item:sd1\] and \[item:sd1op\] follows formally; the proof given above shows that this equivalence remains true even in the non-symmetric case, due to this “centrality”....
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The rest of this section is devoted to the definition and basic properties of category $\mathcal{O}_c$. Since its structure depends upon the combinatorics of ${{W}}$-representations, we begin with the relevant notions from that theory. We write a partition of $n$ as $\mu = (\mu_1\geq \mu_2 \geq \cdots \geq \mu_l > 0...
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understood today. Other directions of research focus on BO in the presence of relaxation processes (spontaneous emission) [@PRA2], BO in 2D optical lattices [@PRL3], and BO in the presence of atom-atom interactions (‘BEC-regime’) [@Berg98; @Choi99; @Chio00; @Mors01]. The present Letter deals with the third problem, wh...
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ion: $$P^f (k_\parallel) = A \, {\rm exp} [- {k_\parallel^2/ {k^s_\parallel}^2}] \int_{k_\parallel}^{\infty} \Biggl[ [2-0.7(\gamma-1)] + f_{\Omega} {k_\parallel^2 \over k^2} - {{\gamma-1}\over 4} k_\parallel^2 b_{T_0}^2 \Biggr]^2 {\tilde P}^\rho (k) e^{- {k^2 / k_F^2}} {k dk \over 2 \pi} \label{Pf}$$ where $f_{\Omega} ...
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roposition are jointly distributed as $\sqrt{2}$ times the real parts of the eigenvalues of the random matrix defined in Proposition \[T:C-Ginibre-eigenvalues\], and are thus independent real standard normal random variables. Observe that in the “$G$-circulant GUE” of Proposition \[T:GUE-eigenvalues\], every element $...
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able on $\mathbb{R}$ can be solved [@boyd2004fastest]: the case where $P_{mix}$ is symmetric and the case where $P_{mix}$ is reversible for a given fixed stationary distribution. Let us first consider the case where $P$ is symmetric. The minimisation problem takes the following form: $$\label{eq:mixmix} \left\{ \beg...
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immune to systematic market fluctuations. There is an important caveat with respect to the foregoing statement. Recall that there is an inverse relationship between ${{V}}_{\mu}$, defined as the positive square root of ${{V}}_{\mu}^{2}$, and ${W}_{\mu}$, so that for highly leveraged portfolios which are characterized ...
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9 Partial response 3.2 6.2 Progressed 6.5 DUB, duodenal malignant ulcer bleeding ###### Survival of pancreatic can...
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that $F_1=4$. Indeed, there are four ways to choose a root edge in a planar cubic map with two vertices: $$\begin{picture}(340,40) \put(15,20){\oval(30,30)} \put(15,5){\vector(0,1){30}} \put(70,20){\oval(30,30)} \put(120,20){\oval(30,30)} \put(85,20){\vector(1,0){20}} \put(175,20){\oval(30,30)} \put(225,20){\oval(30,3...
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ed} \nonumber K= W = 48{m}^{2} \left( \alpha r\cos \left( \theta \right) -1 \right) ^{6} \left( \left({a}^{4}\alpha+{a}^{3} \right) \cos^{3}\theta + 3{a}^{2}r \left( a \alpha-1 \right) \cos^{2}\theta - 3a {r}^{2} \left( a\alpha+1 \right) \cos \theta -{r}^{3} \left( a\alpha-1 \right) \right) \\ \times \dfrac{ \left( ...
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] \end{aligned}$$ and $$\begin{aligned} \Omega F \left[ \begin{array}{cc} - \Omega \otimes \Omega & 0 \\ 0 & I_k \end{array} \right] & = \Omega \Big[0_{k \times k^2} \;\;\;\;\; I_k\Big] \left[ \begin{array}{cc} - \Omega \otimes \Omega & 0 \\ 0 & I_k \end{array} \right] \\ & =...
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**No of interviewed (13)** --------------------------------------------------------------- ---------------------------- **Gender**   Female 8 (5 had children) Male ...
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="48.00000%"} ![image](Lren_pg_absT.eps){width="46.40000%"} Deconfinement aspects of the transition ======================================= The deconfinement phenomenon in pure gauge theory is governed by breaking of the $Z(N_c)$ symmetry. The order parameter is the renormalized Polyakov loop, obtained from the bare ...
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cdots h({\mathbf{x}}^k) \in {\mathbb{R}}[{\mathbf{y}}],$$ which is hyperbolic with respect to ${\mathbf{e}}^1\oplus \cdots \oplus {\mathbf{e}}^k$, where ${\mathbf{e}}^i$ is a copy of ${\mathbf{e}}$ in the variables ${\mathbf{x}}^i$, for all $1 \leq i \leq k$. The hyperbolicity cone of $g$ is the direct sum $\Lambda_+:=...
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19.74, \< 0.01 45.11 (42.1, 50.19) 2.08 22.18, \< 0.01 Census median centered 0.32 (0.28, 0.36) 0.02 15.62, \< 0.01 0.82 (0.73, 0.82) 0.04 19.88, \< 0.01 A2D 0.13 (0.10, 0.16) 0.02 8.08, \< 0.01 0.14 (0.10, 0.18) 0.02 6.65, \< 0.01 P...
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all even or odd antisymmetric indices, and T-duality should remove or add an index according to whether it is already there or not. As a consequence, one derives the following T-duality rules $$\begin{aligned} P_a^{b_1 ... b_p} \ & \overset{T_a}{\longleftrightarrow} \ P^{a, b_1 ... b_p a} \nonumber \\ P_a^{b_1 ... b_p...
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d takes a value of $\sim 0.01$ at $\theta = \theta_{\mathrm{shadow}}$. Although we fix the shadowing profile $f_{\mathrm{shadow}}(\theta)$ during each simulation run for simplicity, it probably depends on accretion rates in reality.[^3] In view of large uncertainties in the shadowing effect, we perform a number of simu...
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]{} AGN selection for this redshift range. One object falls into our redshift range but has $R>24$, outside our selection limits. [cccccccc]{} ID& Tile& RA (2000)& DEC (2000)& $z$& $R$ (Vega)& [F606W]{} & [F850LP]{}\ 12325 &11& 033301.7& –275819& 1.843& 20.38& 20.13& 19.65\ 19965 &23& 033145.2& –275436& 1.90 & 19.96& ...
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q is not an option. The problem, in short, is when I query with WhereGreaterThan I get zero results even though my Asset.Data has a price greater than a value. This applies to WhereGreaterThanOrEquals, WhereLessThan, and WhereLessThanOrEquals as well. public class AssetDataSearch : AbstractIndexCreationTask<Asset> { ...
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ition and multiplication) with entries in $(B\otimes_AR)/(\pi\otimes 1)(B\otimes_AR)$. Thus, the assignment $m\mapsto \mathcal{X}_{i,j}(m)$ is a polynomial in $m$. Furthermore, since $m$ actually belongs to $\mathrm{Ker~}\varphi(R)/\tilde{G}^1(R)$, we have the following equation by the argument made at the beginning of...
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[]{data-label="ATSVsPower"}](Fig3.pdf) The simulated of the reflection coefficient is shown in Fig. \[ATSVsPower\](b) with a simplified model by numerically solving Eq. (\[MasterEQ\]) in a steady state with the artificial atom parameters: $\omega_{eg}=2\pi\times3.379\,$GHz, $\omega_{fg}=2\pi\times12.173\,$GHz, $\gamma...
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um_{z',x}P'_{\Lambda;o}(z',x) =O(\theta_0)\sum_{z',x}\bigg(P_{\Lambda;o}^{\prime{{\scriptscriptstyle}(0)}}(z',x) +\sum_{j\ge1}P_{\Lambda;o}^{\prime{{\scriptscriptstyle}(j)}}(z',x)\bigg).\end{aligned}$$ Similarly to [(\[eq:pi0-rthmombd\])]{} for $r=0$, the sum of $P_{\Lambda;v}^{\prime{{\scriptscriptstyle}(0)}}(z',x)$...
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the last three states are also visualized in figure \[fig:SummaryIC\]. We comment that, with the exception of the Taylor-Green vortex which was shown in §\[sec:3D\_InstOpt\_E0to0\] to be a local maximizer of problem \[pb:maxdEdt\_E\] in the limit $\E_0 \rightarrow 0$, all these initial conditions were postulated based...
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}}\, \frac{1}{(\Delta_b-\Delta_\alpha)(\frac12(\Delta_b+\Delta_\alpha)+M_N)+{\vec{p}}^2-{\vec{l}}^2} \\&=i\frac{G_Fm_\pi^2}{16\pi M_N} (C_{S(s)}^{\alpha}+C_{T(s)}^{\alpha}{\vec{\sigma}_1}\cdot{\vec{\sigma}_2})\, (C_{S(w)}^{\alpha}+C_{T(w)}^{\alpha}{\vec{\sigma}_1}\cdot{\vec{\sigma}_2})\, \\&\times \sqrt{ (\Delta_b-\Del...
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e -\langle {\mathcal{S}}\Xi(e^{-\Phi}F\Psi e^\Phi), (e^{-\Phi}F\Psi e^\Phi)^2\rangle\,. \label{I-1}\end{aligned}$$ Here the second term vanishes owing to (\[BPZ S\]) and (\[small to large\]): $$\begin{aligned} - \langle {\mathcal{S}}\Xi(e^{-\Phi}F\Psi e^\Phi), (e^{-\Phi}F\Psi e^\Phi)^2\rangle\ =&\ {\langle\!\langle}(e^...
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ise-canceling effects, as demonstrated in Study 3. Larger flocks can also be a source of individual behavioral differentiation, when a higher order of organization emerges. The key is not the size nor the amount of new information, but rather the system promoting the invention of new coordination patterns within itself...
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{qsch}\operatorname{Hom}_{\mathcal{H}_q}(Sp_q(\mu), Sp_q(\lambda)) \cong \operatorname{Hom}_{S_q}(W_q(\lambda),W_q(\mu)).$$ On the other hand, by and we have $$\label{tf} \operatorname{Hom}_{H_c}(\Delta_c(\lambda), \Delta_c(\mu)) \cong \operatorname{Hom}_{\mathcal{H}_q}(Sp_q(\lambda)^{\ast}, Sp_q(\mu)^{\ast}) \cong \o...
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s already been solved in Ref. [@konno]. For generic $N$, the desired expressions are rather complicated and our construction depend largely on the observation \[ob1\] and the result of [@sln]. One crucial difference of our construction from the one in [@sln] is that, in our case, the Yangian double $DY_\hbar(sl_N)$ sho...
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--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------...
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on between the ideal and the true estimators ==================================================== In this section we make the following assumptions on the kernel $K$, the densities $f$ and the band sequences: \[ass3\] We assume that $K$ is supported by $[-T,T]$ for some $T<\infty$ and that it has a uniformly bounded ...
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ks\right)-i\sin\left(2ks\right)=-:g_1(s)\label{f2},\quad s \in [0,t).\end{aligned}$$ [**Proof:**]{} We have to check that $$\begin{aligned} -i\left(\begin{matrix} Id&M\\ M^*&Id \end{matrix}\right) \left(\begin{matrix} f_1\vphantom{\left(A-A^*\right)}\\f_2\vphantom{\left(A-A^*\right)} \end{matrix} \right)= \left(...
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RRT\ Chronic renal failure: 38% ...
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lambda(\phi)) \right]. \label{effect}$$ In the following Section, we calculate the contributions to $V_{\hbox{\footnotesize\it \hspace{-6pt} eff\,}}$ from conformally invariant bulk fields. Massless scalar bulk fields =========================== The effective potential induced by scalar fields with arbitrary ...
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i}) (\Delta_{K} - h_{k}) } \nonumber \\ &\times& \biggl[ ( h_{k} - h_{i} ) \biggl\{(\Delta_{K} - h_{i}) (\Delta_{K} - h_{k}) e^{- i \Delta_{J} x} - (\Delta_{J} - h_{i}) (\Delta_{J} - h_{k}) e^{- i \Delta_{K} x} \biggr\} \nonumber \\ &-& (\Delta_{J} - \Delta_{K}) \biggl\{ (\Delta_{J} - h_{k}) (\Delta_{K} - h_{k})...
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\alpha}^{\beta}f_{k}^{(-m)}\varphi^{m}\end{aligned}$$ where $f_{k}^{(-m)}(x)=\pi_{k}(x)+\int_{c}^{x}dx_{1}\int_{c}^{x_{1}}dx_{2}\cdots\int_{c}^{x_{m-1}}dx_{m}f_{k}(x_{m})$ is an $m$-times arbitrary indefinite integral of $f_{k}$. If now it is true that $\int_{\alpha}^{\beta}f_{k}^{(-m)}\rightarrow\int_{\alpha}^{\beta}...
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ox{5pt}{${\scriptscriptstyle}{{\bf n}}$}} {\overset{}{\longleftrightarrow}}}y}\leq P_{\Lambda;y}^{\prime{{\scriptscriptstyle}(0)}}(o,x),\end{aligned}$$ which will be used in Section \[ss:pijbd\] to obtain the bounds on $\pi_\Lambda^{{\scriptscriptstyle}(j)}(x)$ for $j\ge1$. Since the inequality is trivial if $x=o$, w...
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{E}[||\hat \beta - \beta||_\infty]$. Let $P_0$ be multivariate Normal with mean $(0,\ldots, 0)$ and identity covariance. For $j=1,\ldots, D$ let $P_j$ be multivariate Normal with mean $\mu_j=(0,\ldots,0,a,0, 0)$ and identity covariance where $a = \sqrt{ \log D/(16n)}$. Then $$\begin{aligned} \inf_{\hat\beta}\sup_{w\in ...
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ac{n}{2}+32}/i \times \RP^{95}, \dots$, $X_j = S^{\frac{n}{2} - 32(j-2)-1}/i \times \RP^{32(j+2)-1}, \dots$, $X_{\frac{n+2}{64}} = S^{63}/i \times \RP^{\frac{n}{2}+64}$. The embedding of the corresponding manifold in $Z$ is defined by the Cartesian product of the two standard embeddings. The union of the submanifolds ...
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ng in $y_\chi$. These ingredients are difficult to consistently implement in other model constructions without violating constraints on light force carriers. The effect of strong differences between proton and neutron coupling to DM have been explored by [@Feng:2011vu]. To concentrate on the kinematics we shall theref...
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ntity corresponds to the momentum distribution $P(k)=\rho(k,k)$ of the atoms, directly measured in the experiment. It is seen in Fig. \[fig1\] that, around $v=15$, there is a qualitative change in the momentum distribution, in close analogy with that observed in the experiment [@Grei02]. It should be noted, however, th...
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M(1)={\mathbb{C}}[{\mathfrak{h}}\oplus {\mathfrak{h}}^*]\delta e$. On the other hand, for the given decomposition Lemmas \[thetainjA\] and \[abstract-products\] imply that $\operatorname{{\textsf}{tgr}}H_c$ is a homomorphic image of $ T=\operatorname{{\textsf}{ogr}}H_{c+1}e\otimes_{U_{c+1}}\operatorname{{\textsf}{ogr}}...
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p\left(-i\frac{W}{2F}\sum_{l=1}^L\langle {\bf n}| \hat{n}_l(\hat{n_l}-1)|{\bf n}\rangle \right) \;.$$ Finally, by noting that the quantity $\langle {\bf n}|\hat{n}_l(\hat{n_l}-1)|{\bf n}\rangle$ is always an even integer, one comes to the conclusion that, besides the Bloch period, there is additional period, $$\label{7...
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acities. Since an extended cf Petri net $N_z$, $z\in\{h, c, s\}$, has two kinds of places, i.e., places labeled by nonterminal symbols and *control* places, it is interesting to consider two types of place capacities in the Petri net: first, we demand that only the places labeled by nonterminal symbols are with capacit...
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preliminaries on Moebius maps and the circumcenter extension, and then in section 3 we prove the main theorem. Preliminaries ============= For details and proofs of the assertions made in this section we refer to [@biswas3], [@biswas5], [@biswas6], [@biswas7]. Moebius metrics and visual metrics ---------------------...
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hen $H_y$ satisfies the hypotheses (H2). If ${\ensuremath{\left| H_y \right|}}<{\ensuremath{\left| G \right|}}$, by minimality we obtain that $H_y$ has a normal Sylow $p$-subgroup, and so $[y, {{\operatorname}{O}_{p'}(G)}]=1$. If this holds for every $y\in (P\cap A)\cup (P\cap B)$, then $[P, {{\operatorname}{O}_{p'}(G)...
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urbations, Teukolsky adopted the Newman-Penrose (NP) formalism [@Newman:1961qr] and obtained a separable wave equation for Weyl curvature tensor components $\Psi_0$ and $\Psi_4$. The spin-weighted version of this equation, known as the Teukolsky equation, not only works for gravitational perturbations, i.e. tensor fiel...
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nd{aligned}$$ comprising an elastic and an inelastic current. This naturally defines the terminology used throughout the rest of the paper. In summary, we have related the total current to products involving a greater Green’s function $G^>\sim \langle C(\lambda^{\rm tip}) d^\dagger_{\mu\sigma}(t') d_{\mu'\sigma}(t)...
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a monoidal left derivator, then any shift ${\sV}^A$ is also a -module. We also have the following universal construction: For any left derivators ${\sD},{\sE}$, define ${\mathsf{HOM}}({\sD},{\sE})$ by $${\mathsf{HOM}}({\sD},{\sE})(A) = \cDER({\sD},{\sE}^A)$$ where a functor $u:A\to B$ induces the restriction functor ...
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-7.66); *p-*value \<0.01), and only 26% (4 of 15) of LTR were alive at the conclusion of the study. ***Conclusion.*** CDI is associated with increased mortality in LTR. LTR have many risk factors that predispose them to development of CDI. Strategies to decrease the risk of CDI are needed to improve survival in this p...
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. In atomic and molecular physics (Clebsch–Gordan series), as well as in high-energy physics, this problem has been studied extensively [@weyl50; @wigner59; @wigner73], perhaps most famously in Ne’eman and Gell-Mann’s eight-fold way of elementary particles [@neeman; @gellmann2; @gellmann]. In pure mathematics, the comb...
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i}\phi_{\varepsilon}(\mu,\nu_{i})=\psi_{+}(\mu)+\psi_{-}(\mu),\qquad\mu\in[-1,1],\textrm{ }\nu_{i}\geq0\label{Eqn: HRFR_Discrete}$$ of the discretized boundary condition Eq. (\[Eqn: BC\]), where $\psi_{+}(\mu)$ is by definition the incident flux $\psi(\mu)$ for $\mu\in[0,1]$ and $0$ if $\mu\in[-1,0]$, while $$\psi_{-}...
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\ -1/4\\ 3/4\end{array}\right)\begin{array}{rr} -2 & 1\\ 0 & -1\\ 1 & 0\\ 0 & 1\end{array}\right)=\left(\begin{array}{rrrr} 1 & 0 & 0 & 0\\ -3 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 3/2 & -1/4 & 0 & 0\\ 1/2 & 3/4 & 0 & 0\end{array}\right).$$ The second matrix on the left is invertible as its rank is $4$. This gives $${\display...
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--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------...
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uestion is: what is $C$? As at this time no method is available in order to calculate $C$ with a well-defined theoretical uncertainty, we do not employ here a dynamical calculation in order to provide a SM prediction for $C$ and $\Delta a_{CP}^{\mathrm{dir}}$. We rather show the different principal possibilities and ho...
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r, thereby counteracting the effect of the unstable modes. One may similarly expect that stable modes can affect other transport channels such as matter entrainment and heat transport. This line of inquiry will be left for future investigations. The authors would like to thank F. Waleffe for valuable discussions and i...
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_y.$$ The conditions are simply $$\bar{h}_y=0,\ \ h_y=-d\bar{h}_x,$$ which are exactly the relations and . The other condition is the conservation of the currents[@Hofman:2014loa] $$D_\mu J^\mu_a=0.$$ With $$J^\mu=q^aJ^\mu_a,\ \ \ \bar{J}^\mu=\bar{q}^aJ^\mu_a,$$ we have $$\nabla_\mu J^\mu=0,\ \ \ \nabla_\mu\bar{J}^\mu...
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]{}, . , , , , , & (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , , , , , , , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . , , & (). . , [ ** ]{}, . , & (). . , [**]{}, . , & (). . , [ ** ]{}, . (). . , [ ** ]{}, . , , , & (). . , [ ** ]{}, . ,...
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ned} \nonumber \hspace{-.5cm}Z[J]&=&\int dA_0\,dA_{\bot,i} \,\exp\Bigl\{-S_{\rm eff}[A]\\ & &\hspace{.3cm} +\int d^3 x\,J_0 A_0+\int_T d^4 x \, J_{\bot,i} A_{\bot,i} \Bigr\}\,. \label{eq:Zpol}\end{aligned}$$ In we have normalised the temporal component $J_0$ of the current with a factor $\beta$. The classical action...
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s problem has been recently discussed in the literature Ref. [@Hart], which provided numerical solutions of the Lorentz-Dirac equation. The integration was performed backwards in time so that the unphysical, exponentially growing homogeneous solutions of LD would damp out, resulting in a numerical stable solution. We ...
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0.30 (0.14)[\*](#table-fn11-0192513X17710773){ref-type="table-fn"} 0.25 Years in the Netherlands 0.11 (0.05)[\*](#table-fn11-0192513X17710773){ref-type="table-fn"} 0.28 Housing^[e](#table-fn9-0192513X17710773){ref-t...
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\psi _{\mu }\partial ^{\rho }g_{z})\big\Vert_{q_{2},\infty } \\ & \leq C\psi _{\eta ^{\prime }}(x)\sup_{z\in {\mathbb{R}}^{d}}\big\Vert % Q_{1}(\psi _{\mu }\partial ^{\rho }g_{z})\big\Vert_{q_{2},-\eta ,\infty }.\end{aligned}$$Using (\[h\]) $j-1$ times and (\[B2\]) (with $\kappa =\mu )$ we get $$\begin{aligned} \left\V...
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valent to $\left( B^\top \otimes A\right) \mathrm{vec}(X) = \mathrm{vec}(C)$, with $B=C = \Omega$ and $X = A = I_k$. We now bound $\sigma_1 \Big([I_{k^2}\otimes \alpha^\top \otimes I_k] \; J \; [ \Omega\otimes\Omega \;\;\;\; 0_{k^2\times k}] \Big)$, the second matrix in the upper block in . We have th...
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$} for cavity $S_2$. The corresponding process fidelity $F_\mathrm{CNOT\_ED}$ ($F_\mathrm{ED}$) is 0.829 (0.857).[]{data-label="fig:fig3"}](Figure3_final.pdf) The experiments presented in this work are based on two circuit quantum electrodynamics (QED) devices [@Wallraff; @Clarke2008Superconducting; @You2011Atomic; @S...
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{t\})$ and maximal tori $T_1$ and $T_2$ of $N$, of orders divisible by $r$ and $s$, respectively, with $( |T_1|, |T_2|)=1$, as stated in Table 3. In the cases denoted by $(\star)$, $r$ and $s$ denote the largest prime divisor of $|T_1|$ and $|T_2|$, respectively. The Tits group $N=F_4(2)'$ contains a Sylow 13-subgrou...
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formReady(); //ERROR: The method formReady is not defined for the class _addImageState }, ) ); } } How do i call the function formReady from the widget addImage ? EDIT: I tried this code, and removed all compile errors however still not getting the desired result: in addImage.dart ...
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times S$ \[et\] \_[(x,)(y,),(x,)GS]{}t(x,)=y,+|y,|. For $(y,\omega)\in \Gamma'_+$ the projection ${\left\langle}y,\omega{\right\rangle}$ is non-negative (and then the limit (\[et\]) is $\tau_+(y,\omega)$) and for $(y,\omega)\in \Gamma'_-$ it is non-positive and then the limit (\[et\]) is $0$). Hence $\ol t:\ol G\times ...
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athbb{C}}} W_{\alpha}(M).$ This observation has two useful consequences. First, if $\theta:M_1\rightarrow M_2$ is an $H_c$-module homomorphism with $M_i\in {\mathcal{O}}_c$, then $\theta (W_{\alpha}(M_1)) \subseteq W_{\alpha}(M_2)$ for each $\alpha\in{\mathbb{C}}$. Secondly, if $p\in H_c$ has $\operatorname{{\mathbf{E...
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\quad K_{2,n} = C A \sqrt{ k U \frac{\log k + \log n}{n} },$$ with $C = C(\eta)>0$ the constant in . Assume that $n$ is large enough so that $v_n = v - K_{1,n}$ and $u_n = u -K_{2,n}$ are both positive. Then, for a constant $C = C(A)>0$, $$ \inf_{w_n \in \mathcal{W}_n} \inf_{P\in {\cal P}^{\mathrm{OLS}}_n}\math...
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}, \overrightarrow{F(x)f(\xi_3)} > \\ c_1 = < \overrightarrow{x\xi_2}, \overrightarrow{x\xi_3} > \ , & \ c_2 = < \overrightarrow{F(x)f(\xi_2)}, \overrightarrow{F(x)f(\xi_3)} > \\\end{aligned}$$ Taking inner products of the left-hand side of equation (\[no1\]) above with the vectors $\overrightarrow{x\xi_i}, i = 1,2,3$,...
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_N=\c[t_1, \ldots, t_N]*\mathbb Z^N$, where the group $\mathbb Z^N$ is generated by the elements $\sigma_i$, $i=1, \ldots, N$ as above. For each $i=1, \ldots, N$ and any $c\in k$ consider the involutions $\epsilon_{R_N,c,i}^{\pm}$ on $R_N$ defined by $\epsilon_{R_N,c,i}^{\pm}(\sigma_i)=\pm\,\sigma_i^{-1}$, $\epsilon_{R...
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t take into account the change of angle for the (new) primary electron during transport. Hence the angular derivative ($\nabla_\omega$) is missing from it. On the other hand, CSDA-Focker-Plank approximation contains also second order partial derivatives (with respect to angle) which do not show up in (\[n2k-6\]). As a...
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ic Oxide Gas Not yet recruiting \- Efficacy and Safety of IFN-a2b in the T...
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}}$, $\chi(i) \in \Psi(i)$. Since $R \subseteq {{\operatorname{dom}{\Psi}}}$, then for each $r \in R$, $\xi(r) \in \Psi(r)$. Consider ${{\Psi}\negmedspace\mid\negmedspace{R}}$, for which ${{\operatorname{dom}{({{\Psi}\negmedspace\mid\negmedspace{R}})}}} = R$. By definition of restriction, for $r \in R$, $({{\Psi}\negme...
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w[thick,densely dotted](0,.13-1*.125)--++(0,1*.25);\end{tikzpicture}}},;{\hat\imath},;{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13-1*.125)--++(0,1*.25);\end{tikzpicture}}},;{b\!\!+\!\!2})$}}\tag*{for $v<i\ls b+2$;}\\ U[i]&={\text{\footnotesize$\gyoungx(1.2,;1;2;3_2{{\begin{tikzpicture}[baseline=...
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github_plus_top10pct_by_avg
times k}$, and $D_0\in B[x]^{k\times k}$ such that $\det D_1,\det D_2\not=0$ and Eq.  holds. Let $V$ be a non-empty Zariski open subset of the affine variety of $B\simeq B[x]/(x)$ such that $(\det D_1)_p,(\det D_2)_p, b_p\not=0$ and $\mathrm{rk}\,X(0)_p\le r$ for all $p\in V$. This exists by the assumption on $r$ and...
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v \text{ if either }|w|<|v|, \text{ or }|w|=|v|\text{ and }w\preceq' v.$$ For an element $g\in G$, by $W_g$ we denote the set $\{w\in W\colon w_G=g\}$ and by $w_g$ the minimal element of the set $W_g$, which is easily verified to exist, in $\preceq$. If there is no danger of confusion, for an element $g\in G$ we shal...
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underlying Newton-Cartan geometry has been studied in [@Hofman:2014loa]. For the case at hand, we need to introduce a Newton-Cartan geometry with a different scaling structure however. Flat Geometry ------------- We start with the geometry similar to the flat Euclidean geometry. Such geometry admits the following sy...
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otation implicitly contains the assumption that the identity of Alice’s measurements as random variables does not depend on Bob’s settings, and vice versa. It is well known [@fine_hidden_1982] that under the no-signaling conditions the existence of the jpd is equivalent to the CHSH inequalities being satisfied. Applyin...
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*)=\max_{i=1}^k\alpha(G[W_i])\le\alpha(G)\le m.$$ By our assumption, $G^*$ has at most $f(m)$ vertices, so that $\sum_{i=1}^k|W_i|\le f(m).$ As we have seen in the proof of Theorem 3.1, the total number of piercing points is at most $(k-1)\sum_{i=1}^k|Z_i|\le(k-1)\omega(G)<km$, and each segment in $V_0$ contains at le...
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by cell $x$ is going to change the state of cell $y$, the change in the state of $y$ depends only on the states of $x$ and $y$. In other words, the new state of $y$ is a function of the previous states of $x$ and $y$. - ED Data Separation Properties To provide evidence for a CC evaluation of the ED (Embedded Devic...
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---------- The average throughput gain of employing the reconfigurable antennas is given by $$\label{eq:th_gain} G_{\bar{R}}={\bar{R}_{{\widehat{\psi}}}}/{\bar{R}_{\psi}}, $$ where $\bar{R}_{{\widehat{\psi}}}=\mathbb{E}\{R_{{\widehat{\psi}}}\}$, $\bar{R}_{\psi}=\mathbb{E}\{R_{\psi}\}$, and the expectation is over dif...
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chieved in our model as soon as $v$ is different from zero. We shall in the following solve the generalized $BFM$ in the atomic limit (i.e., putting the second term in Eq.(2) equal to zero) for a grand canonical ensemble. In this case the eigenstates of the Hamiltonian are $$\begin{aligned} |0,l \rangle& =& |~0\rangle...
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{1}$ and since $A\in(\ell_{1}(\widehat{F}),\ell_{p})$, we obtain from Lemma 2.3 that $\bar{A}\in(\ell_{1},\ell_{p})$ and $Ax=\bar{A}y.$ Thus, we have for every $m\in\mathbb{N} $ that$$\begin{aligned} \left \Vert (I-P_{m})(Ax)\right \Vert _{\ell_{p}} & =\left \Vert (I-P_{m})(\bar{A}y)\right \Vert _{\ell_{p}}\\ & =\le...
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on to the Planck energy scale relevant to quantum gravity, $10^{19}$ GeV) and yet not exactly vanishing cosmological constant of our universe.[@Lambda] If only from that perspective, dynamical spontaneous symmetry breaking of supersymmetry is thus an extremely fascinating issue in the quest for a fundamental unificatio...
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j)$ are respectively defined as the infimum and the supremum of the set $\{r>0 , \theta_r(i,j) \mbox{ exists} \}$. ![\[fig:angle\_ij\] [*On the unit sphere, the black squares are points of $\mathbf{T}_{r}(i)$ while black circles are points of $\mathbf{T}_{r}(j)$. The arc $a(\theta,\theta')$ is divided in two equal par...
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other confusing issue that had to be straightened out to make sense of strings on stacks. Briefly, the answer is that the theory decomposes into a union of theories on ordinary spaces, see [*e.g.*]{} [@summ; @cdhps; @sugrav-g] for discussions in two and four-dimensional theories. We will return to this in section \[sec...
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(\[h6\]) we obtain$$I_{n}^{m}f(x)=\int_{0}^{t}dt_{1}...\int_{0}^{t_{m-1}}dt_{m}\int p_{t-t_{1},t_{1}-t_{2},...,t_{m}}^{n,m}(x,y)f(y)dy.$$We denote$$\phi _{t}^{n,m_{0}}(x,y)=p_{t}^{n}(x,y)+\sum_{m=1}^{m_{0}-1}\int_{0}^{t}dt_{1}...% \int_{0}^{t_{m-1}}dt_{m}p_{t-t_{1},t_{2}-t_{1},...,t_{m}}^{n,m}(x,y)$$so that (\[R2\]) re...
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on evolves through a set of stochastic processes that mimic the projector of Eq.\[eq:projector\]: 1. A cloning/death step, in which the walker population on each determinant is increased/reduced with a probability $\left(H_{ii}-S\right)\Delta\tau$. $S$ is a shift parameter that is used to control the total walker pop...
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\leftrightarrow u_2) = 0 ~\mbox{for}~|i-j|=1, \label{y7}\\ & & E^{\pm}_i(u) E^{\pm}_j(v) = E^{\pm}_j(v) E^{\pm}_i(u) ~~\mbox{for}~|i-j|>1, \label{y8}\end{aligned}$$ where $$u_\pm = u \pm \frac{1}{4} \hbar c$$ and $$B_{ij} = \frac{1}{2} a_{ij}.$$ $q$-affine-Yangian double correspondence ---------------------------...
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###### **Four single nucleotide polymorphisms in the*GNB1*gene in 265 HCV-1 and 195 HCV-2 infected patients receiving PEG-IFNα-RBV therapy with or without a RVR in a Chinese population in Taiwan** **SNP** **Position in*GNB1*** **Chromosome position**^**a**^ **Alleles** **HCV-1** **HCV-2** ...
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converges to $x\in X$ with all such $x$ defining the closure $\textrm{Cl}(A)$ of $A$. Furthermore taking the directed set to be $${\textstyle _{\mathbb{D}}N_{t}=\{(N,t)\!:(N\in\mathcal{N}_{x})(t\in N\bigcap A-\{ x\})\}}\label{Eqn: Der_Directed}$$ which, unlike Eq. (\[Eqn: Closure\_Directed\]), excludes the point $x$ t...
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tic c-number kernel $G_s^{AB}=G^{AB}+\gamma^{AB}$. We assume the identity \_s\^A\_s\^B=\^A\^B+G\^[AB]{}+\^A\^B+\^A\^B+\^[AB]{} The required expectation values are \_H\^C\_H\^E=\^C\^E+\^C\^E \_H\^C\_H\^D\_H\^E&=&\_H\^C(\_H\^D\_H\^E)&=&\^C\^D\^E+\^CG\^[DE]{}+\^DG\^[CE]{}+\^EG\^[CD]{}+\^C\^[DE]{}Observe that this impli...
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n: IT\]) and (\[Eqn: FT’\]) are in terms of inverse images (the first of which constitutes a direct, and the second an inverse, problem) the image $f(U)=\textrm{comp}(V)$ for $V\in\mathcal{V}$ is of interest as it indicates the relationship of the openness of $f$ with its continuity. This, and other related concepts ar...
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, W. C. [Stwalley]{}, and P. L. [Gould]{}, , 9689 (1996). K. [Aikawa]{} [*et al.*]{}, Physical Review Letters [**105**]{}, 203001 (2010), 1008.5034. A. Wakim, P. Zabawa, M. Haruza, and N. P. Bigelow, Opt. Expr. [**20**]{}, 16083 (2012). M. [Zeppenfeld]{}, M. [Motsch]{}, P. W. H. [Pinkse]{}, and G. [Rempe]{}, , 04140...
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G \rightarrow H$ are not morphisms of groups. We will fix two groups $H$, $G$ and $\beta: G \times H \rightarrow G$ a right action of the group $H$ on the set $G$. We define $${\rm Ker}(\beta):= \{h \in H ~|~ g \lhd h = g, \forall g \in G\}$$ We denote by $MP_{\beta}(H,G):= \{\alpha ~|~ (H, G, \alpha, \beta) {\rm~is~...
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