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asymptotic quantum numbers $[Nn_{3}\Lambda]\Omega$. Only components with $X_{\alpha\beta}^{2}-Y_{\alpha\beta}^{2} > 0.001$ are listed. Two-quasiparticle excitation energies are given by $E_{\alpha}+E_{\beta}$ in MeV and two-quasiparticle transition matrix elements $Q_{10,\alpha\beta}$ in $e \cdot$fm. In the row (i), th...
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ots,v\},\quad X^{12}=\{1,\dots,v\},\quad X^{i1}=T^i\text{ for }i\gs2.$$ Thus we have ${\hat\Theta_{T}}\circ{\hat\Theta_{A}}={\hat\Theta_{D}}$. In the case $S=B$, let $y$ be the $(2,3)$-entry of $T$. Then $y>x$. $X^{22}$ must contain either $x$ or $y$, so if $x>v$ then we cannot possibly achieve ($\dagger$). So we get ...
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} = {\bf 32_2} \oplus {\bf 32_0} \oplus {\bf 32_{-2}} \nonumber \\ & {\bf (220,2)} = {\bf 220_1} \oplus {\bf 220_{-1}} \\ & {\bf (12,2)} = {\bf 12_1} \oplus {\bf 12_{-1}} \quad ,\nonumber\end{aligned}$$ where the subscript denotes the $\mathbb{R}^+$ weight. The representation ${\bf 32_2}$ corresponds to the R...
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not quite so obvious as the following examples which are significantly useful in dealing with convergence questions in topological spaces, amply illustrate. The neighbourhood system $$_{\mathbb{D}}N=\{ N\!:N\in\mathcal{N}_{x}\}$$ at a point $x\in X$, directed by the reverse inclusion direction $\preceq$ defined as $$M...
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rt{r_1}, \qquad x\in D.$$ The result now follows by taking logarithms. Exact simulation of stable paths {#stable_paths} ================================ The key ingredient to the walk-on-spheres in the Brownian setting is the knowledge that spheres are exited continuously and uniformly on the boundary of sphe...
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${{X}^{crv}}_{\mu}=0 $ for $2 \leq \mu \leq N-1$, since the corresponding inverse variances ${{Z}^{crv}}_{\mu}$ all vanish. The three components of the efficient frontier are the riskless asset together with ${{\bf e}^{crv}}^{1}$ and ${{\bf e}^{crv}}^{N}$. Furthermore, the latter portfolio will be strongly disfavored ...
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alent. 1. $f_1(x), \ldots, f_m(x)$ have a common interleaver. 2. for all $p_1, \ldots, p_m \geq 0$, $\sum_{i}p_i=1$, the polynomial $$p_1f_1(x)+ \cdots+ p_mf_m(x)$$ is real–rooted. \[largestz\] Let $f_1,\ldots, f_m$ be real–rooted polynomials that have the same degree and positive leading coefficients, and suppose...
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}({\mathcal{W}}(\chi ))$, then $R^\chi _+=R^{\chi '}_+$. By Thm. \[th:rschi\], ${\mathcal{R}}(\chi )$ is a root system of type $\cC (\chi )$. \(i) Assume that $R^\chi _+=R^{\chi '}_+$. Then $C^{\chi }=C^{\chi '}$ by Lemma \[le:cm\]. Therefore ${\sigma }_i^\chi ={\sigma }_i^{\chi '}$ in ${\mathrm{Aut}}({\mathbb{Z}}^...
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exes. Let $\Delta$ be a simplicial complex on the vertex set $[n]$. To each facet $F\in \Delta$ we associate the element $a_F\in\NN^n_\infty$ with $$a_F(i)=\left\{ \begin{array}{lll} \infty, & \text{if} & i\in F\,\\ 0, & \mbox{if} & i\not\in F, \end{array} \right.$$ Then $\{a_F\: F\in \Delta\}$ is the set of facets of ...
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X(j)$ (in both the model selection and estimation steps). Of course, it is possible to extend the definition of this parameter by leaving out several variables from ${\widehat{S}}$ at once without additional conceptual difficulties.\ The parameter $\gamma_{{\widehat{S}}}$ has several advantages over the projection ...
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probability, $r<c_2\cdot d$. Now suppose that after allocating $m$ balls, there is a ball at height $\ell+c_1+c_2+1$. This implies that there is a $d$-choice, denoted by $R$, whose minimum load is at least $\ell+c_1+c_2+1$. Let us consider all balls placed in the bins contained in $R$ with height at least $\ell+c_1+1$...
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----------+ | Capital investment costs | 10‐40 | Million USD | Production scale, grade and containment level of the facility | β ...
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now ready to put these observations together to prove the hard part of Proposition \[pre-cohh\]. \[grsameA\] Fix $k\geq 0$ and set ${\mathcal{J}}= eJ^k\delta^k$ and ${\mathcal{N}}=N(k)$. Then the map $\theta:{\mathcal{J}}\to{\mathcal{N}}$ is an isomorphism. Set $\mathfrak{m}= {\mathbb{C}}[{\mathfrak{h}}]^{W}_+$ and n...
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=H^{-1}\cdot h_0(t)$, and $K=k(0)$, this shows that $\alpha(t)$ is equivalent to $$H\cdot h_1(t) \cdot \begin{pmatrix} 1 & 0 & 0 \\ 0 & t^b & 0 \\ 0 & 0 & t^c \end{pmatrix} \cdot K$$ with $h_1(0)=I$, and $K$ constant and invertible. By Corollary \[MPIcorol\], this matrix is equivalent to $$\beta(t)=H\cdot \begin{pmatr...
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ta\not\supset\xi$ for any $\xi\in\tilde\Omega_{z_1\to z'_1}^{{\bf N}}$ earlier than $\omega_1$. Then, we define $\tilde\Omega_{z_2\to z'_2}^{{{\bf N}};\omega_1}$ to be the set of paths $\zeta\in\Xi_{z_2\to z'_2}^{{{\bf N}};\omega_1}$ such that there are $k-2$ edge-disjoint paths on ${{\mathbb G}}_{{{\bf N}}}\setmin...
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eroth-order terms are rewritten in a familiar way. However, the expression in (\[P-beta-alpha-2nd-averaged\]) does not mean a great simplification. That is, the matter dependent terms with sterile sector model-dependence remain. Suppression by the energy denominator {#sec:energy-denominator} -------------------------...
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morphism is represented by an affine group scheme which is isomorphic to $\underline{G}_j$. Note that $T$ preserves the hermitian form attached to the lattice $M_0^{\prime}\oplus C(L^j)$. We claim that $\begin{pmatrix} 1&0 \\ 0&m \end{pmatrix}$ is contained in $\underline{G}_j'(R)$. If this is true, then the above mat...
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tion whether we can improve the bootstrap rates. For example, the remainder term in the Taylor approximation of $\sqrt{n}(\hat\beta(j) - \beta(j))$ is $$\frac{1}{2n}\int \int \delta^\top H_j((1-t)\psi + t \hat\psi) \delta\, dt$$ where $\delta=\sqrt{n}(\hat\psi - \psi)$. By approximating this quadratic term it might be...
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proof for ${\hat{T}}^-_p$ is analogous. Let $\chi '=r_p(\chi )$ and $\Lambda '={t}_p^\chi (\Lambda )$. By Lemma \[le:MLiso\] and Thm. \[th:PBWtau\], $$M^{\chi }(\Lambda )_{{\alpha }_j+a{\alpha }_p}=0= M^{\chi }(\Lambda )_{-{b}{\alpha }_p} \quad \text{for all $a\in {\mathbb{Z}}$.}$$ Thus, since $\deg {T}_p(E_j)={\...
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) is true under the Euler specialization $(z,w)\mapsto\left(\sqrt{q},1/\sqrt{q}\right)$; namely, we have $$\H_{(n-1,1)}(z,z^{-1}) =\H^{[n]}(z,z^{-1}). \label{CV=HS1}$$ Equivalently, the two varieties $\M_{(n-1,1)}$ and $X^{[n]}$ have the same $E$-polynomial. Consider the generating function $$F:=(1-z)(1-w)\sum_\lambda...
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TB 1.000 1.000 1.000 1.000 1.000 1.000 1.000 3 K=50 1.000 1.000 1.000 1.000 1.000 1.000 1.000 K=100 1.000 1.000 1.000 1.000 1.00...
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actly equal to the relative entropy between the thermal state used to evaluate $F(\lambda_f, \beta)$ and the postwork state [@daffner]. It is important to remark that the relative entropy is zero for identical states and it diverges for orthogonal states [@vedral]. Short Review on Trapped Ions Interacting with Classic...
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G allele 77 (72.6) 126 (75.9) 0.5465 1 G allele 121 (72.9) 38 (79.2) 0.3809 1 **rs6603797** **rs6603797** C allele 94 (88.7) ...
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Vert _{\chi}\leq \underset{n}{\lim \sup}{\displaystyle \sum \limits_{k}} \left \vert \bar{a}_{nk}\right \vert$$ and$$L_{A}\text{ is compact if }\underset{n}{\lim}{\displaystyle \sum \limits_{k}} \left \vert \bar{a}_{nk}\right \vert =0.$$ \(b) If $A\in(\ell_{\infty}(\widehat{F}),c_{0})$, then $$\left \Vert L_{A}\right ...
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ct that the gauge algebra involves kinematic factors is also the reason why it is possible for higher-form gauge symmetries to be non-Abelian. Higher-form global symmetries are always Abelian [@Gaiotto:2014kfa]. Hence an ordinary procedure of “gauging” the global symmetry by introducing space-time dependence to the gen...
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nt to specifying an initial joint prior on ${\bar{\nu}}$ and $\nu$). Letting ${\bar{\nu}}_{\tau-1}^{\mbox{\scriptsize med}}$ denote the posterior median of ${\bar{\nu}}$ at time $\tau-1$, tuning parameters $\epsilon<<1$ and $\delta<<1$ are chosen such that $\mathbb{P}(\nu>\epsilon{\bar{\nu}})\approx \delta$ is desired....
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t and right products. Then $\bar J\in{\mathcal{H}}{\mathrm{SJ}}$ and $\widehat J=\bar J\oplus J=\bar J\oplus\bar J\in{\mathcal{H}}{\mathrm{SJ}}$, so $J\in{\mathrm{Di}}{\mathcal{H}}{\mathrm{SJ}}={\mathcal{H}}{\mathrm{Di}}{\mathrm{SJ}}$. We obtain $J\vDash f$, hence $\bar J\vDash \bar f$. Therefore, ${\mathcal{H}}{\mathr...
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1,488
0.78893
github_plus_top10pct_by_avg
qbezier[20](60,25)(60,10)(75,10) \qbezier[20](75,40)(90,40)(90,25) \qbezier[20](75,10)(90,10)(90,25) \qbezier[30](20,5)(20,25)(20,45) \qbezier[20](180,25)(180,40)(195,40) \qbezier[20](180,25)(180,10)(195,10) \qbezier[20](195,40)(210,40)(210,25) \qbezier[20](195,10)(210,10)(210,25) \qbezier[20](120,25)(120,45)(140,45) ...
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Superantigen-like protein 5 1633215 A:5 C:83 C:37 5 18.4 28 ...
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_1(x)=h_2(x)=\cdots =h_l(x)$. Therefore, from the discussion above, we have if $h_1(x)=h_2(x)=\cdots =h_l(x)$, then $d_{\rm H}(C)=\sum_{i=1}^ld_i\geq \sum_{i=1}^l(\delta_i+1)$. $\Box$ From Theorems 4.2 and 4.3, we have the following corollary immediately. [**Corollary 4.4**]{} *Let $C$ be a $1$-generator skew QC code...
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thbb{E}}{\left\Vert M \right\Vert}}{\sqrt{\log{\left\vert G \right\vert}}} \le C \sqrt{\max_{a \in G} {\mathbb{E}}{\left\vert Y_a \right\vert}^2},$$ where $c, C > 0$ are constants, independent of $G$ and the distributions of the $Y_a$. The rest of this paper deals mainly with infinite sequences of finite abelian gr...
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[Baseline attack success rates and transfer success rates for an IGS attack with an epsilon of 1.0 on LeNet models trained on MNIST. 8 pairs of models were trained for the parallel Jacobian goal, and 8 pairs of models were trained for the perpendicular goal to obtain error bars around attack success rates.[]{data-label...
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lace operator ($-k^2$). The discrete analog of the Sturm-Liouville theory (e.g., @hil68 [chap. 1.10–1.16]; see also, @atk64) guarantees that the eigenfunctions given in Equation – satisfy discrete orthogonality relations, for example, $$\label{eq:orthogorel} \frac{2}{N_x+1} \sum_{i=1}^{N_x}{\cal X}_i^l{\cal X}_i^{l'...
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patterns to obtain a spare AOG. Besides, for each part template $v$, we estimated $n_{k}$ latent patterns in the $k$-th conv-layer. We assumed that scores of all latent patterns in the $k$-th conv-layer follow the distribution of [$Score(u)\sim\alpha\exp[-(\xi\cdot{rank})^{0.5}]+\gamma$]{}, where $rank$ denotes the sco...
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mrc; @Miranda:2016wdr; @Ge:2016xya; @Dutta:2016vcc; @Dutta:2016czj; @Rout:2017udo]. [^5]: To understand the formulas presented in this section, minimal explanation of definitions of the quantities may be helpful. Let the flavor mixing matrix $\bf{U}$ in $(3+N) \times (3+N)$ space that connect the flavor and mass eigen...
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)(1.5,3) \psline(0.4,2.6)(0.4,3) \psline(0.7,2.3)(0.7,3) \rput(1.4,1.3){\tiny $\alpha_1$} \rput(0.2,2.4){\tiny $\alpha_2$} \rput(0.6,2.1){\tiny $\alpha_3$} \rput(1,2.3){\tiny $\alpha_4$} \pscircle[linestyle=dotted](1,2.2){1.4} \rput(5.2,1){$\psi$} \psline(3.5,1.5)(3,3) \psline(3.5,1.5)(4,3) \psline(4.5,2.5)(...
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e impurity Anderson model plus unusual Holstein coupling $\lambda_c$ for a single vibrational mode $\omega_0$. Renormalized hybridization $\Gamma_0\rightarrow\Gamma_{\rm eff}(\lambda_c)$ as function of $\lambda_c$ for two different values for $\omega_0$ at $U/\Gamma_0=10$. The inset depicts the same quantity for $\omeg...
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the electric charge.[^17] In contradistinction, the quanta associated to a Dirac spinor may be distinguished in terms of particles and their antiparticles carrying opposite values of a conserved quantum number, such as for instance the electric charge (or baryon or lepton number), associated to a symmetry under arbitr...
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.Experience, ethics, planning and selection, ethic education, thought leaders.Protocols (4 mentions).Truthfulness, exclusion criteria, diagnostic criteria, treatment design, patient selection, patient follow-up.Sites (4 mentions).Certifications, requirements, screening by authorities, proceedings and operation.Declarat...
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har.sec\] for details. \[quot.norm.lem\] Let $p_1,p_2:R\rightrightarrows X$ be a finite, set theoretic equivalence relation such that $(X/R)^{cat}$ exists. 1. If $X$ is normal and $X, R$ are pure dimensional then $(X/R)^{cat}$ is also normal. 2. If $X$ is seminormal then $(X/R)^{cat}$ is also seminormal. Proof. I...
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h{\operatorname{\mathbf{Pr}}\left[{\mathbb{I}}_t=0 \mid (i\in D_t) \text{~and~} \neg {\mathcal{F}}\right]}}\cdot{\ensuremath{\operatorname{\mathbf{Pr}}\left[\neg {\mathcal{F}}\right]}}\nonumber\\ &{\leqslant}{\ensuremath{\operatorname{\mathbf{Pr}}\left[{\mathbb{I}}_t=0 \mid (i\in D_t) \text{~and~} {\mathcal{F...
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ned}$$ \[c:clt\_sum\] Let $X_1...X_n$ be random vectors with mean 0, covariance $\Sigma$, and $\lrn{X_i}\leq \beta$ almost surely for each $i$. let $Y$ be a Gaussian with covariance $n\Sigma$. Then $$\begin{aligned} W_2\lrp{\sum_i X_i, Y}\leq 6\sqrt{d}\beta \sqrt{\log n}\end{aligned}$$ This is simply taking the resul...
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github_plus_top10pct_by_avg
erent entering end exiting vertices from $P_3$ chain) cross $M$ times and have $K$ pairs of sites belonging to different chains and neighboring the crossing sites. Functions $A_i^{(r)}$ and $B_i^{(r)}$ satisfy the following recursion relations $$\begin{aligned} A'_i&=& \sum_{\cal{N}} a_i({\cal{N}})\, A^{N_A}B...
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mily in July and October. N = 3 ± SE. Statistics show two‐way [anova]{.smallcaps} with genotype and date as factors *P* = ≤ 0.05 Mixed Population Acid digestible carbohydrate Enzymatic carbohydrate release \% Digestibility ...
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\]](oke "fig:") ![One-pion and one-kaon exchange contributions to the transition.\[fig:loc\]](contactw0 "fig:") ------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------- --------------------...
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oung(;1;1;1_5{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(5*.25,0);\end{tikzpicture}}};1;2;3;\star;{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--++(1*.25,0);\end{tikzpicture}}};\star,;2;3;\star_3{{\begin{tikzpicture}[baseline=0cm]\draw[thick,densely dotted](0,.13)--...
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github_plus_top10pct_by_avg
he optical potential at 1 GeV nucleon energy has been constrained to 50 MeV. With the increase of the effective nucleon mass from DD-ME1 to D$^3$C and D$^3$C$^*$, we also note the corresponding decrease of the nuclear matter compression modulus $K_{\infty}$ . This correlation between $K_{\infty}$ and $m^*$ is also well...
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difference plots for bagging. Both subset selection methods improve when utilising multiple subset selection. In the case when class-balanced selection is used, as was observed for single nested dichotomies, the average ranks across all datasets closely correspond to the integer values, showing that increasing the num...
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/g) \cosh (g\tau) $ and $y = z = 0$ in Eqs.(\[Tdef\]) and (\[Xdef\]), we have $$\begin{aligned} -T^2+X^2 & = \frac{2}{g^2} \bigg\{ 1 - \sqrt{1-{c^{\prime}}^2} \sqrt{1-{c^{\prime\prime}}^2} \cosh \bigl[ g(\tau-\tau^{\prime})-i(\alpha_{c^{\prime\prime}}+\alpha_{c^{\prime}} ) \bigr] \notag \\ & \hspace{8ex} - \left( \fra...
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messageProperty: 'message' }, writer: { type: 'json', encode: true, root: 'details' }, fields: ['id','document', 'date'], }, });`. I...
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15
0.839742
github_plus_top10pct_by_avg
7 15.28 40 repressor ...
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ms and by the indicator of $|X_i-t|\le h_{2,n}B$). The three terms from $\delta_3$ involve, instead of $\delta_4$, respectively $\delta_2$, $\delta^2$ and $\delta_2\delta$ (see (\[e1\])-(\[e3\])). We have from (\[delta\]), (\[classic1\]) and (\[classic2\]) that $$\sup_{t\in D_r^\varepsilon}\delta^2_n=O_{\rm a.s.}\left(...
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t $$(\bar{L} \bar{\beta})_{i j} = \psi^4 (L \beta)_{i j} \; ; \qquad (\bar{L} \beta)^{i j} = \psi^{-4} (L \beta)^{i j} \; .$$ Next, we note, perhaps surprisingly, that the lapse function $\bar{N}$ has essential non-trivial conformal behavior. Furthermore, this is [*the*]{} new element in the IVP analysis. In [@Teitel;...
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0.788827
github_plus_top10pct_by_avg
dagger} A W \right\}_{k K} \left\{ W^{\dagger} A (UX) \right\}_{K m} \left\{ (UX)^{\dagger} A W \right\}_{m L} \biggr\}. \label{P-beta-alpha-W4-H3-First} \end{aligned}$$ $$\begin{aligned} && P(\nu_\beta \rightarrow \nu_\alpha)^{(4)}_{5th-2nd} \equiv 2 \mbox{Re} \left[ \left( S^{(0)}_{\alpha \beta} \right)^{*} ...
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0$ since the propagator is of order $f^0$. Now let us assume that the statement has been proven for $p <n+2$, and consider a Feynman diagram with $n+2$ external lines. We isolate $m$ of these external legs that are contracted on the same vertex with $m+1$ legs. This piece is of order $f^{m-1}$. The other piece of the F...
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github_plus_top10pct_by_avg
have closed structure and for $k=0.5$ a variety of intermediate structures can be found. These observations are in good agreement with our results for colloid-droplet radial distribution functions, as discussed above. ![image](fig7a){width="5.9cm"} ![image](fig7b){width="5.9cm"} ![image](fig7c){width="5.9cm"} Symmetr...
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0.782605
github_plus_top10pct_by_avg
^3 \det H_0.\end{aligned}$$ The adjugate of $H_{0}$ is defined as $\text{Adj} H_{0} \equiv (H_{0})^{-1} \text{det} H_{0}$. Notice that $T$, $A$ and $D$ are invariant under unitary transformation of $ H_0\to K H_0 K^{\dagger}$ with $K$ any unitary matrix and so are $\lambda_i$. Following the notation in [@Kimura:2002wd...
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0.767793
github_plus_top10pct_by_avg
\overset{\delta}{\rightarrow} X)$ is given by (the isomorphism class of ) the pullback along $\beta$ and $\gamma$. $$\xymatrix{ & & P\ar@{..>}[dr]\ar@{..>}[dl] & & \\ & Y\ar[dl]_{\alpha}\ar[dr]^{\beta} & & Z\ar[dl]_{\gamma}\ar[dr]^{\delta} & \\ X & & X & &X }$$ The identity of this $R$-algebra is (the isomorphism class...
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github_plus_top10pct_by_avg
epair protein MutS `Sbjct: 754 ASAGKKSSISN` `764` ...
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ulated periods fitted with our observed ones in Table \[table:g207params\]. We also list the $\sigma_\mathrm{{rms}}$ values of the models. The $T_{\rmn{eff}}=12\,000$K solutions are in agreement with the spectroscopic value. The $T_{\rmn{eff}}=12\,400$K model seems somewhat too hot comparing to the $\sim12\,100$K spect...
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D. P., [Strand]{}, N. E., [Hall]{}, P. B., [Blomquist]{}, J. A., & [York]{}, D. G. 2008, , 678, 635 , A. D. [et al.]{} 2006, , 638, 622 , T., [Johansson]{}, P. H., & [Ostriker]{}, J. P. 2009, , 699, L178 , T., [Johansson]{}, P. H., [Ostriker]{}, J. P., & [Efstathiou]{}, G. 2007, , 658, 710 , T., [Khochfar]{}, S., ...
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ga}-\xi_{k_2-k}) \nonumber \\ &\times& (i\tilde{\omega}_1+i\tilde{\omega}_2-i\tilde{\omega}_3-i\tilde{\omega}-\xi_{k_1+k_2-k_3-k}) \nonumber \\ &\times& (-i\tilde{\omega}_2+i\tilde{\omega}_3+i\tilde{\omega}-\xi_{-k_2+k_3+k}) \Big]^{-1}\end{aligned}$$ with $\xi_k\equiv k^2/2m - \mu$. Using again the condition characteri...
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d at the hadronic supercolliders and $e^+e^-$ colliders. The advantages of the processes in Fig. \[one\] are that the $W_LW_L$ scattering is no longer on loop level, and additional vector bosons in the final state can be tagged on to eliminate the large $W_T W_T$ and $Z_T Z_T$ backgrounds. In addition, both the $W_L^+ ...
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2,850
0.776537
github_plus_top10pct_by_avg
_{i}f(x)=\int_{{\mathbb{R}}^{d}}U_{i}^{\ast }s_{t}^{x}(y)f(y)dy.$$As a consequence, one gets the kernel in (\[h6\]): $$\tilde{p}_{\delta_{1},\ldots ,\delta_{m}}(x,y)=\int_{{\mathbb{R}}^{d\times (m-1)}}U_{1}^{\ast }s_{\delta_{1}}^{x}(y_{1})\Big(\prod_{j=2}^{m-1}U_{j}^{% \ast }s_{\delta_{j}}^{y_{j-1}}(y_{j})\Big)s_{\delt...
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w $\varepsilon (\delta )=\frac{h\delta }{1+\delta }$ which gives $% \frac{2h}{2(h-\varepsilon (\delta ))}=1+\delta .$ And we take $l(\delta )\geq 1$ such that $2^{l\delta /(1+\delta )}\geq l$ for $l\geq l(\delta ).$ Since $h\geq 1$ it follows that $\varepsilon (\delta )\geq \frac{\delta }{% 1+\delta }$ so that, for $l\...
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site $\gamma > 0$ be sufficiently strong that its amplitudes in the left half of the lattice are negligible. One then has $$\widetilde{\left<\psi_1\right|}\left.{\psi}_0\right>\simeq \frac1{\sqrt{2}}\widetilde{\left<\psi_0\right|}\left.{\psi}_0\right> = \frac1{\sqrt{2}} \; ,$$ leading to $$\begin{aligned} E_0...
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eta} \right| \sim \frac{ \lambda_{s\Phi\eta}^2 v_s^2 } { 64 \pi^2 ({\mathcal M}_0)_{\eta\eta}^2 } \sim 10^{-3} \text{-} 10^{-7} .\end{aligned}$$ Thus, even if the value of $\mu_\eta$ is in the TeV scale, we can obtain $\mu \sim 0.1\,{{\text{MeV}}}$ although we need further suppression with $h_{\ell{{\ell^\prime...
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0.777128
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-> android -> existing android code into workspace Browse to the unzipped folder of ZXing 2.1 You will have two projects in the list. Select both and click OK. They will be imported into your workspace and you will have errors. For the first Project (CaptureActivity in my case), you have to add the core.jar file presen...
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+b$ for integers $a$ and $b$ satisfying $a \ge 0$ and $1 \le b \le q-1$. With this notation, we obtain that for any $0 \le j \le a-1$ and $0 \le \ell \le q-2$ we have that $$n_{d-j(q-1)-\ell} \le n_d-j \le m_d-j-1.$$ In particular choosing $j=a-1$ and $\ell=0$, this implies that $m_d \ge a+n_{q-1+b} \ge a+1+n_b \ge a$...
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ntary consequence is: If $\overline{m_1}$ has a well-defined critical exponent $\beta_1^{\text{dis}}$ in the sense that [@Sta71] $$\label{defce} \beta_1^{\text{dis}}=\lim_{\tau\to 0^-} \frac{\ln \overline{m_1}(\tau)}{\ln \tau}$$ exists, then we have $$\label{ordeq} \beta_1^{\text{dis}}=\beta_1^{\text{ord}}\,.$$ Two fu...
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2,036
0.783287
github_plus_top10pct_by_avg
g the decreasingly nested filter-base associated with $\textrm{Orb}(x_{0})$. The so-called *$\omega$-limit set of* $x_{0}$ given by $$\begin{array}{ccl} \omega(x_{0}) & \overset{\textrm{def}}= & \{ x\in X\!:(\exists n_{k}\in\mathbb{N})(n_{k}\rightarrow\infty)\textrm{ }(f^{n_{k}}(x_{0})\rightarrow x)\}\\ & = & \{ x\in ...
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0.790676
github_plus_top10pct_by_avg
{- i ( \Delta_{K} - h_{n} ) x} - \frac{ 1 }{ (\Delta_{K} - \Delta_{L} ) (\Delta_{L} - h_{k} ) (\Delta_{L} - h_{l} )^2 } e^{- i ( \Delta_{L} - h_{n} ) x} \nonumber \\ &+& \frac{ 1 }{ (\Delta_{K} - h_{k} ) (\Delta_{L} - h_{k} ) ( h_{l} - h_{k} )^2 } e^{- i ( h_{k} - h_{n} ) x} \nonumber \\ &-& \frac{ 1 }{ (\Delta_{...
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)=\_[I’]{}\_[S’]{}(x,’,,E’,E)(x,’,E’)d’ dE’. The simplest case is where $\sigma=\sigma_0(x,\omega',\omega,E',E)$ is a measurable non-negative function $G\times S'\times S\times (I'\times I\setminus D)\to{\mathbb{R}}$, where $D=\{(E,E)\ |\ E\in I=I'\}$ is the diagonal of $I'\times I$, obeying for $E\neq E'$ the estimate...
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lies that $x=y$. The constructed functor $\Phi(X,\mu)\colon L(S)\to {\mathsf{Sets}}$ is torsion-free. This follows from the definition of $\sim$ since $$\Phi(X,\mu)(e',e)(x)=e'\cdot x=e\cdot x=x$$ for any $e'\geq e$ in $E$ and any $x\in X$ such that $e\cdot x$ is defined. We have therefore assigned to $(X,\mu)$ a t...
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github_plus_top10pct_by_avg
}^k u_iv_i$. For a commutative ring $\cR$ we will denote by $\cR[{x_1,\cdots,x_k}]$ the ring of polynomials in formal variables $x_1,\ldots,x_k$ with coefficients in $\cR$. We will use the notation $\bx^\bz$ with $\bx=({x_1,\cdots,x_k}),\ \bz=({z_1,\cdots,z_k}) \in \Z^k$ to denote the monomial $\prod_{i=1}^k x_i^{z_i}$...
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4,009
0.768663
github_plus_top10pct_by_avg
various Freiman-type theorems in non-nilpotent groups. As in \[sec:details\], at various points we separate the trivial case $K<2$ from the meaningful case $K\ge2$ so as to avoid the need for multiplicative constants. Our first corollary improves an earlier result of the author for residually nilpotent groups [@resid...
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2,012
0.783544
github_plus_top10pct_by_avg
enever the null model is nested within the alternative model the likelihood ratio approximately follows a $\chi^2$ distribution with degrees of freedom specified by $(|S|^m-|S|^k)(|S|-1)$. If the p-value is below a specific significance level we can reject the null hypothesis and prefer the alternative model [@bartlett...
2,277
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1,741
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github_plus_top10pct_by_avg
230 1 1 1 1 1 0 0 0 270 1 1 1 1 1 1 0 0 270 1 1 1 1 1 1 0 0 320 1 1 1 1 1 1 1 0 300 1 1 1 1 1 1 1 0 360 1 1 1 1 1 1 1 1 350 1 1 1 1 ...
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USD 339.00 PER NIGHT GUARANTEE GIVEN NONSMOKING KING ENRON CORP TO AVOID BILLING CANCEL 24 HOURS PRIOR TO ARRIVAL HOTEL TIME CONTINENTAL AIRLINES 11SEP NEW YORK NY HOUSTON TX 745P 1033P CO 1963 A MON LA GUARDIA G.BUSH INTERCO ...
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r\\ &-\frac{13}{24}e^4)a^2 -\frac{1}{48}e^2r^4\alpha^2(e^2-2mr))\cos^2(\theta)+60(((\frac{1}{30}r^3\alpha^2-r)m+e^2)ma^2+\frac{1}{10}r(e^4-\frac{1}{3}e^2mr-\frac{1}{3}m^2r^2)) \times \nonumber\\ &\alpha r^5\cos(\theta) -4a^2\alpha^2m^2r^7+6e^4r^5-10e^2mr^6+4m^2r^7)\sin(\theta)+(a^2\cos^2(\theta)+r^2)(a^2(a^2\alpha m+...
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mmetric in the indices $c,b$. Moreover the double contraction of the structure constant vanishes since the dual Coxeter number of the Lie super algebra vanishes. This concludes the proof of equation up to terms of order $f^4$. Let us mention that the same equation also guaranties the quantum integrability of the model ...
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$}} {\overset{{{\cal A}}}{\longleftrightarrow}}}x\}}}$, we have $$\begin{aligned} {\label{eq:Theta''-1stindbd}} {\mathbbm{1}{\raisebox{-2pt}{$\scriptstyle \{y{\underset{\raisebox{5pt}{${\scriptscriptstyle}{{\bf m}}+{{\bf n}}$}} {\overset{{{\cal A}}}{\longleftrightarrow}}}x\\}$}}}\,\cap\,\{y{\underset{\raisebox{5pt}{$...
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q:posl_expec1a} \E[M] &=& \sum_{j = 1}^n \sum_{a =1}^{\ell_j} \lambda_{j,a} \sum_{i<\i \in S_j} \P\Big[(i,\i) \in G_{j,a} \Big| (i,\i \in S_j) \Big] (e_i - e_{\i})(e_i - e_{\i})^\top\;.\end{aligned}$$ The following lemma provides a lower bound on $\P[(i,\i) \in G_{j,a} | (i,\i \in S_j)]$. \[lem:posl\_lowerbound\] ...
2,283
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1,906
2,067
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github_plus_top10pct_by_avg
{{\frac{\partial (S_0\phi)}{\partial E}}}+\omega\cdot\nabla_x\phi+CS_0\phi +\Sigma\phi -K_C\phi ={\bf f}, \nonumber\\ {\phi}_{|\Gamma_-}=0,\quad\ \phi(\cdot,\cdot,E_{\rm m})=0. \label{co3-d}\end{gathered}$$ Let (for clarity, we have included here the subscript $C$ into $P$) P\_C(x,,E,D):=& -[E]{}+\_x+CS\_0\ =& -S\_0[E]...
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1,457
2,317
4,027
0.768577
github_plus_top10pct_by_avg
s $k$ times, i.e. $${\xi}^{(m\,h\,k)} = (\mathcal{L}_{H_-})^k\,{\xi}^{(m\,h\,0)}.$$ #### Lifting to the whole manifold. Finally, we promote the basis functions living on $\Sigma_u$ to functions living on the whole manifold $\mathcal{M}$ by sending all unknown constant coefficients $c_{\beta}$ (from the end of step b)...
2,285
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github_plus_top10pct_by_avg
C_{q}}\sum_{0\leq \left\vert \alpha \right\vert \leq q}\left\vert \partial ^{\alpha }(\psi _{k}f)\right\vert \leq \sum_{0\leq \left\vert \alpha \right\vert \leq q}\psi _{k}\left\vert \partial ^{\alpha }f\right\vert \leq C_{q}\sum_{0\leq \left\vert \alpha \right\vert \leq q}\left\vert \partial ^{\alpha }(\psi _{k}f)\rig...
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992
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github_plus_top10pct_by_avg
le $J$ over the special Jordan algebra $\bar J$ is special. The bimodule $J$ is embedded into $D$ and $D$ is a $\bar J$-bimodule too. Consider mappings $\sigma_1,\,\sigma_2\colon\bar J\to\mathrm{Hom}(D,D)$ defined by the rule $$\sigma_1(\bar a)\colon d\mapsto a{\mathbin\vdash}d\in D,\, \sigma_2(\bar a)\colon d\mapsto d...
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2,252
2,187
2,284
0.781154
github_plus_top10pct_by_avg
x_i^{a(i)}$ and $Z=\{x_i\: i\in\ip a\}$. Then $(u,Z)\in\mathcal A$ and $a=\log u+c(Z)$. Since $a\in\Gamma$ it follows that $u\cdot K[Z]\sect I=\{0\}$. Suppose that $(u,Z)$ is not minimal with this property. Then there exists $(v,W)\in \mathcal A$ with $v\cdot K[W]\sect I=\{\ 0\}$ and $(v,W)<(u,Z)$, and we have 1. $b=...
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1,823
0.785388
github_plus_top10pct_by_avg
+ R_{2} e^{ikr}), & \chi_{tr}^{(2)}(k, r \to +\infty) \to \bar{N}_{2} T_{2} e^{ikr}, \end{array} \label{eq.2.4.2}$$ where the coefficients $\bar{N}_{1}$ and $\bar{N}_{2}$ can be found from the normalization conditions. Using (\[eq.2.4.2\]) for the wave functions in asymptotic region, taking into account the inte...
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0.778248
github_plus_top10pct_by_avg
on}(\overline{D})$ enters. Note in particular that Theorem \[corr\] follows as a corollary. We can develop the expression in in terms of the walk-on-spheres $(\rho_n, n\leq N)$, providing the basis for a Monte Carlo simulation. What will work to our advantage here is another explicit identity that appears in [@BGR]. D...
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ication map $\phi: E\to (A^1\delta)^{i-j}$ is surjective and its kernel is the largest torsion $A^0$-submodule of $(A^1\delta)^{i-j}$. On the other hand $\operatorname{{\textsf}{ogr}}B_{ij}\subseteq e{\mathbb{C}}[{\mathfrak{h}}\oplus{\mathfrak{h}}^*]^{{W}}$ is a torsion-free $A^0$-module and so $\mathrm{ker}(\phi) \sub...
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0.77498
github_plus_top10pct_by_avg
eq:split.hom\] for every $x,y\in G/N$ with $x,y,xy\in\pi(A)$ we have $\varphi(xy)\in\varphi(x)\varphi(y)\left(A^3\cap N\right)$. This is essentially just an observation: by definition of $\varphi$ we have $a\varphi(\pi(a))^{-1}\in A^2\cap N$ and $\varphi(y)^{-1}\varphi(x)^{-1}\varphi(xy)\in A^3\cap N$. \[lem:pullback...
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\Omega) } {d \Omega} = \Big[ (I_k \otimes \Omega) \otimes I_{k^2} \Big] \frac{d (\Omega \otimes I_k)}{d \Omega} + \Big[ I_{k^2} \otimes( \Omega \otimes I_k) \Big] \frac{d (I_k \otimes \Omega)}{d \Omega}.$$ Next, $$\frac{d (\Omega \otimes I_k)}{d \Omega} = \Big( I_k \otimes K_{k,k} \otimes I_k \Big) \Big( ...
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1,674
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I}_{\space\text{n}}=-\int\frac{1}{\sqrt{1-\text{u}^2}}\space\text{d}\text{u}=\text{C}-\arcsin\left(\text{u}\right)=\text{C}-\arcsin\left(\frac{\cot\left(x\right)}{\sqrt{\text{n}}}\right)\tag3$$ Q: PHP: Does password_hash() check if the hash generated is unique? (Understanding!) Simple question because i did not fi...
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755
0.800755
github_plus_top10pct_by_avg
y such constraint one wished to impose on individual twisted sectors. [^25]: For $m>0$. The total spaces of line bundles of positive degree over projective spaces do not seem to admit a GLSM description, even though they are toric varieties – they can be described as GIT quotients of open subsets of ${\mathbb C}^{n+2}...
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evel 1 list so maintaining parent child relationship. Normalized structure would be cumbersome for now but it would have long term benefits and flexibility Step 2 : Drawing Chart Method 1 : Jquery Charts Fetch data from SharePoint List using Rest API or CSOM on client side. CRUD-Operation-to-List-Using-SharePoint-Rest-...
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1,876
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0.781896
github_plus_top10pct_by_avg
rt}{2 \G(a)^{2}} \g\left(a, \left\lvert \frac{c}{b} \right\rvert^{\frac{1}{a}} \right) \G\left(2a, \left\lvert \frac{c}{b} \right\rvert^{\frac{1}{a}} \right) \nonumber \\ &\quad - \frac{(k_{1} + k_{2})^{2} c^{2}}{4 \G(a)^{2}} \g\left(a, \left\lvert \frac{c}{b} \right\rvert^{\frac{1}{a}} \right)^{2} - \frac{(k_{1} + k_...
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})$ a root system of type ${\mathcal{C}}$. Let ${\mathcal{W}}$ be the abstract groupoid with ${\mathrm{Ob}}({\mathcal{W}})=A$ such that ${\mathrm{Hom}}({\mathcal{W}})$ is generated by abstract morphisms $s_i^a\in {\mathrm{Hom}}(a,{r}_i(a))$, where $i\in I$ and $a\in A$, satisfying the relations $$\begin{aligned} s_...
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ever we point out that this is *not the same as the mapping space to the group completion, which would be the zero space of the mapping spectrum $Map_0 (M, K(\Sigma^\infty (G_+))$. This spectrum calculates the ${K(\Sigma^\infty (G_+))}$-cohomology of $M$. However, as we will show below, we can define a homomorphism of ...
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eduling in the real-time specification for java. In: [*Proceedings of the 4th international workshop on Java technologies for real-time and embedded systems*]{}, 2006, 20–29. Alves-Foss J. Multiple independent levels of security. In: [ *Encyclopedia of Cryptography and Security*]{}, Springer US, 2011, 815–818. Clarks...
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616
0.803903
github_plus_top10pct_by_avg