text large_stringlengths 384 2.05k | rank_avg float64 1 4.19k ⌀ | rank_max float64 1 8.21k ⌀ | rank_min float64 1 5.03k ⌀ | rank_median float64 1 4.21k ⌀ | rank_by_avgsim float64 1 4.19k ⌀ | avgsim_to_github float32 0.77 0.85 ⌀ | dataset large_stringclasses 1
value |
|---|---|---|---|---|---|---|---|
d $\sigma_i^2(\Delta t)$ within each group. The obtained scaling plots are shown in Fig. \[fig:scavg\].
![The normalized variance $\frac{1}{2}\log \sigma_i^2(\Delta t)-\frac{1}{2}\log \Delta t$ for the six groups of companies, with average traded values $\ev{f}\in[0,10^4)$, $\ev{f}\in[10^4,10^5)$, …, $\ev{f}\in[10^8,\... | 1,101 | 27 | 1,457 | 1,094 | 1,359 | 0.790517 | github_plus_top10pct_by_avg |
15 0.014 0.015 0.014
BLB($n^{0.6}$) 0.120 0.122 0.122 0.121 0.122 0.123 0.118
BLB($n^{0.8}$) 0.037 0.039 0.038 0.038 0.038 0.038 0.037
SDB($n^{0.6}$) 0.142 ... | 1,102 | 4,348 | 1,259 | 953 | null | null | github_plus_top10pct_by_avg |
sublinear expectation, As $\mathcal{M}_1\subset \mathcal{P}$, it is clear that On the other hand, for $\lambda_1, \lambda_2{\geqslant}0$ such that $\lambda_1+\lambda_2=1$ and $\mu_1, \mu_2\in \overline{\mathcal{M}}_1$, the closure of $\mathcal{M}_1$, Therefore, and by the choice of $\mu_k$, we have This, together with... | 1,103 | 561 | 1,648 | 1,139 | 3,801 | 0.770032 | github_plus_top10pct_by_avg |
3723 1.77 (0.50, 6.25)
**Females**^**a**^ **Females**
G/G 3 (5.7) 6 (7.3) 0.62 (0.14, 2.65) G/G 4 (4.8) 4 (16.7) 0.34 (0.08, 1.52)
... | 1,104 | 1,052 | 1,412 | 1,278 | null | null | github_plus_top10pct_by_avg |
^ -01.40 \[-5.50, 2.71\] 0.51
Family situation (single parent vs. stepfamily) 6.68 \[-6.21, 19.57\] 0.31 10.16 \[-17.43, 37.74\] 0.48
Family situation (divorced vs. s... | 1,105 | 299 | 1,002 | 1,365 | null | null | github_plus_top10pct_by_avg |
bf x}}^{\prime} \right]}{\left(-T^2+X^2 \right)^2} \nonumber \\
&& - \frac{32 \pi \epsilon^{\prime} \epsilon^{\prime\prime} |\cos\Theta_{0}| \left[ -T \dot{t}^\prime + X \dot{{\bf x}}^{\prime} \right] \left[ -T \dot{t}+X\dot{{\bf x}} \right] }{\left( -T^2+X^2 \right)^3} \nonumber \\
&& + \frac{8 \pi \epsilon^{\prime} ... | 1,106 | 4,391 | 945 | 874 | null | null | github_plus_top10pct_by_avg |
talks are invariant) For any $s\in S$ and $e\in E$, if $s\cdot e$ is defined then $\pi(s\cdot e)=\pi(e)$.
4. (universal on stalks) For any $s\in S$ and $x\in X$, $(E_x,\mu|_{S\times E_x})$ (which is well-defined by (U3)) is a universal $S$-set.
5. (continuous) The partially defined map $S\times E \to E$, $(s,x)\map... | 1,107 | 2,769 | 926 | 1,041 | null | null | github_plus_top10pct_by_avg |
{n>0} l_{a^i} \frac{1}{k+g} (B^{-1})^{ji} a^j_n
- \sum_{1 \leq i < j \leq N} l_{b^{ij}} q_{b^{ij}}
+ \sum_{1 \leq i < j \leq N} l_{c^{ij}} q_{c^{ij}} \right) | 0 \rangle,\end{aligned}$$
it can be shown that the following equations hold,
$$\begin{aligned}
& & a^i_n| l_a,l_b,l_c \rangle = b^{ij}_n| l_a,l_b,l_c \rangle
... | 1,108 | 3,440 | 1,327 | 987 | 3,526 | 0.77176 | github_plus_top10pct_by_avg |
a way that $S_j$ are assumed to be constant in subdomains.
In this example, we write out Eq. in special case of constant $S_0\geq 0$ and $\Sigma\geq 0$. Moreover, we consider a single particle CSDA transport equation only. Let $${}&P(x,\omega,E,D)u:=-{\frac{\partial (S_0u)}{\partial E}}+\omega\cdot\nabla_x u+\Sigma u... | 1,109 | 271 | 890 | 1,210 | null | null | github_plus_top10pct_by_avg |
, T., [Ellis]{}, R. S., [Liao]{}, T. X., & [van Dokkum]{}, P. G. 2005, , 622, L5
, T., [Ellis]{}, R. S., [Liao]{}, T. X., [van Dokkum]{}, P. G., [Tozzi]{}, P., [Coil]{}, A., [Newman]{}, J., [Cooper]{}, M. C., & [Davis]{}, M. 2005, , 633, 174
, I., [Conselice]{}, C. J., [Bundy]{}, K., [Cooper]{}, M. C., [Eisenhardt]{}... | 1,110 | 163 | 2,586 | 1,269 | null | null | github_plus_top10pct_by_avg |
t users and robots or the employed workers, the fake transaction records will always cause a bias or distortion of the original transaction distribution. To better observe the problem, we downloaded a real world data set containing Taobao online sellers’ transaction records and emulated the circumstances if it had been... | 1,111 | 4,649 | 1,876 | 1,120 | 3,216 | 0.773959 | github_plus_top10pct_by_avg |
\[Cor:aveGst5\] {#App:proofaveGast5}
==================================
We rewrite $G_{\bar{R}}$ as $$\label{eq:th_gain_close_alt}
G_{\bar{R}}(\Psi=i) \approx 1+\frac{\sqrt{{\sigma^2_{R_\psi}}}}{{\bar{R}_{\psi}}}E_{i}, $$ where $E_{i}$ denotes the mean of the maximum of $i$ independent standard normal random variab... | 1,112 | 1,451 | 1,469 | 1,203 | 3,390 | 0.772712 | github_plus_top10pct_by_avg |
}( \Delta_{m-n+1}+ \Delta_{n-m+1}-\Delta_{1-m-n})
+{1\over 2}( - \Delta_{m-n+2}- \Delta_{m-n-2}+\Delta_{2-m-n})$$ $$+{\alpha\over 4}( - \Delta_{m-n+3}- \Delta_{m-n-3}+\Delta_{3-m-n})
) \big]. \eqno(A14)$$
The matrix elements connecting different parities are
$$\bigg < \bar{K}^+ \bar{\nu} \bigg | -i {\tau_1 \alpha^3... | 1,113 | 3,382 | 1,428 | 1,074 | null | null | github_plus_top10pct_by_avg |
Bbb{C}^1 \ar[d]^\psi \\
Ver \ar[r]^{\iota \gamma} & Ver
}$$ Now let $\tau\in\PSL(3,\Bbb{C})$ be an element which leaves $Ver$ invariant. Define $$\begin{array}{l}
\widetilde{\tau}:\Bbb{P}_\Bbb{C}^1\rightarrow \Bbb{P}_\Bbb{C}^1 \quad.\\
\widetilde{\tau}(z)=\psi^{-1}(\tau(\psi(z))).
\end{array}$$ Clearly $\widetilde{\t... | 1,114 | 736 | 1,036 | 1,042 | 3,867 | 0.769629 | github_plus_top10pct_by_avg |
M(C^\lambda)$, since both $\cO_{X,\zeta^{\s_{\lambda,k}}}=\cO_{X}$ and the conditions on $g \in \cO_{X}$ in are independent of $k$. Moreover, if $0\leq \lambda<\frac{1}{\max\{n_i\}}$, then $\cM(C^\lambda)$ coincides with the multiplier ideal associated with the principal ideal generated by an equation of $C$ (for a de... | 1,115 | 844 | 1,467 | 1,121 | 2,739 | 0.77737 | github_plus_top10pct_by_avg |
)}H_\lambda(q)\right)^k$ is $1$ (see ). Also, the coefficient of the lowest power of $q$ in each $m_{\lambda}(\y)$ is always $1$; hence so is the coefficient of the lowest power of $q$ in $C_{\nu\mu}(\y)$.
In the course of the proof of Proposition \[maxima\] we found that when $v(\lambda)$ is minimal, and $\rho^1,\ldo... | 1,116 | 1,800 | 1,250 | 1,100 | null | null | github_plus_top10pct_by_avg |
ws the occupation probabilities $p_n = |a_n|^2$ for a defect located at the site $n = 0$ in the absence of the periodic force; the discrete values have been connected by lines to guide the eye. The lower panel shows the state under the influence of a periodic force with high frequency $\hbar\omega/W = 7.5$ and scaled a... | 1,117 | 3,691 | 1,169 | 961 | 3,620 | 0.771203 | github_plus_top10pct_by_avg |
r the Rindler trajectory, we have $z_0(\tau) =0 = x_{\perp 0}(\tau) $, hence the $u_{\omega, k_{\perp}}$ are just constants. Then $W(\tau, \tau^\prime) = W(\tau - \tau^\prime) = W(s)$ as expected for a Killing trajectory. The transition rate is straightforward to obtain and we get, $$\begin{aligned}
{\dot {\cal F}}(E) ... | 1,118 | 1,199 | 1,941 | 1,224 | null | null | github_plus_top10pct_by_avg |
eq:3.39\] v=f(z\^1,…, z\^k, |[z]{}\^1,…, |[z]{}\^k)+c.c.
for an arbitrary function $f:X{\rightarrow}U$. The expression (\[eq:3.39\]) is the general solution of the invariance conditions
\[eq:3.40\] v\_[z\^[2k+1]{}]{},…, v\_[z\^p]{}=0.
In general, the initial system (\[eq:3.1\]) described in the new coordinates $(x,v... | 1,119 | 1,058 | 1,936 | 1,216 | null | null | github_plus_top10pct_by_avg |
1.4 1.5
sensors-20-02119-t003_Table 3
######
*RMSE* and *MAE* of I--V curve obtained by equivalent circuit method.
Working Conditions 1 2 3 4
----------------------------- ------- ------- ------- -------
**Irradiance *G* (W/m^... | 1,120 | 4,854 | 796 | 521 | null | null | github_plus_top10pct_by_avg |
ection lines, which can also be added/removed through the web interface.Fig. 3Study template creation
When completed, the resulting workflow must be saved to serve as a template for workflow executions, i.e., conducting a clinical study, coordinating teamwork, or similar processes. Each execution of the template is an... | 1,121 | 138 | 1,588 | 1,264 | null | null | github_plus_top10pct_by_avg |
predecessor walks into conventional sequences.
\[D:TEST\] Let ${\mathit{w}}$ be a localized predecessor walk of $n = {\lvert{{\mathit{w}}}\rvert}$ steps, indexed from $0$ down to $-(n-1)$. Define the *test* function $\test({\mathit{w}}) = \widetilde{{\mathit{w}}}$ according to formula $\widetilde{{\mathit{w}}}_i = {\... | 1,122 | 429 | 1,161 | 1,105 | 2,593 | 0.778624 | github_plus_top10pct_by_avg |
m\] we deduce that ${\ensuremath{\left| A_s \right|}}$ divides ${\ensuremath{\left| {\operatorname}{Aut}(M) \right|}}$, and so $s^{(\delta+n)m}\cdot s^{\frac{m-1}{s-1}}$.
On the other hand, if ${\ensuremath{\left| G/N \right|}}_s=s^{\gamma}$, then ${\ensuremath{\left| G \right|}}_s={\ensuremath{\left| G/N \right|}}_s ... | 1,123 | 614 | 880 | 1,102 | null | null | github_plus_top10pct_by_avg |
as caused to age restrictions of the questionnaires, we assumed that the data are missing completely at random (MCAR). Therefore, listwise deletion was used. The ANOVA table was inspected to check for significant main and interaction effects and specific hypotheses were tested. Satterthwaite's approximation was used to... | 1,124 | 1,031 | 1,948 | 1,336 | null | null | github_plus_top10pct_by_avg |
only if one of the following occurs.
1. $\mu$ or $\mu'$ equals $(u,v)$, where $v\equiv3\ppmod4$ and $\mbinom{u-v}{a-v}$ is odd.
2. $\mu$ or $\mu'$ equals $(u,v,2)$, where $\mbinom{u-v}{a-v}$ is odd.
Using this result, we can show that most of the Specht modules under consideration are decomposable. Specifically, w... | 1,125 | 718 | 782 | 1,110 | 1,421 | 0.789802 | github_plus_top10pct_by_avg |
res \[fig:fg\](a) and \[fig:fg\](b) we observe that for a short period of time $f(\tau)$ exhibits a very similar growth to the upper bound $g(\tau)$, but then this growth slows down and $f(\tau)$ eventually starts to decrease short of ever approaching the limit $1/\E_0$.
We further characterize the time evolution by s... | 1,126 | 1,216 | 1,521 | 1,212 | 2,953 | 0.775857 | github_plus_top10pct_by_avg |
)) \leq D$, $d(x_i, x_{i+1}) \leq K$, and $d(g\circ f(x_i), g\circ f(x_{i+1})) \leq L$, the unioned sequence is an $L$-sequence. Further, because the two sequences ${x_n}$ and ${g\circ f(x_n)}$ are visited in order, we can say that ${x_n}$ and ${g\circ f(x_n)}$ are both subsequences of this union. Thus, the diagram com... | 1,127 | 2,198 | 2,540 | 1,184 | 4,090 | 0.768179 | github_plus_top10pct_by_avg |
`
`SRR022865_71442` `3` `ctgagtaacga`
`cttaata... | 1,128 | 4,367 | 2,898 | 1,013 | null | null | github_plus_top10pct_by_avg |
on $A$ and $U$, and since $U \leq A$, we can reduce the dependence of such constant on $A$ only.
$\Box$
Appendix 6: Anti-concentration and comparison bounds for maxima of Gaussian random vectors and Berry-Esseen bounds for polyhedral sets {#app:high.dim.clt}
===========================================================... | 1,129 | 609 | 1,339 | 1,085 | 3,639 | 0.771027 | github_plus_top10pct_by_avg |
a continuous measure, coded (1) not at all, (2) once or twice a month, (3) once a week, (4) a few times a week, and (5) everyday (mean is 3.43). Results of the regression analysis are presented in [Table 4](#table4-0192513X17710773){ref-type="table"}. This analysis reveals that especially poor functioning transnationa... | 1,130 | 275 | 1,670 | 1,369 | null | null | github_plus_top10pct_by_avg |
omplete action (\[complete action\]). If this is in fact space-time supersymmetry, the commutator of two transformations should satisfy the supersymmetry algebra $$[\delta_{{\mathcal{S}}_1},\,\delta_{{\mathcal{S}}_2}]\ =^{\hspace{-2mm} ?}\ \delta_{p(v_{12})}\,,
\label{susy alg}$$ up to the equations of motion (\[equati... | 1,131 | 739 | 2,066 | 1,237 | null | null | github_plus_top10pct_by_avg |
de of is defined via Theorem \[thm:intersection\]. It is easily seen that and match with Sakai’s definition ([@Sakai84]) of intersection multiplicity assuming $\pi$ is a resolution, not a $\Q$-resolution.
\[ex:QNC:pullback\] Following Example \[ex:QNC:resolution\] note that $\pi_1^*D_1=\hat D_1+mE$ and the equation ... | 1,132 | 610 | 858 | 1,096 | null | null | github_plus_top10pct_by_avg |
EA~ clade dissemination in east Africa.\
We provide snapshots of the dispersal pattern for the years 1960, 1965, 1970, 1975, 1980, 1985, 1990 and 2000. Lines between locations represent branches in the Bayesian MCC tree along which location transition occurs. Location circle diameters are proportional to square root of... | 1,133 | 1,229 | 2,718 | 1,367 | null | null | github_plus_top10pct_by_avg |
frac{\Phi_{i-1,j,k}-2\Phi_{i,j,k}+\Phi_{i+1,j,k}}{(\delta x)^2}, \\
\Delta_y^2\Phi_{i,j,k} &= \frac{\Phi_{i,j-1,k}-2\Phi_{i,j,k}+\Phi_{i,j+1,k}}{(\delta y)^2}, \\
\Delta_z^2\Phi_{i,j,k} &= \frac{\Phi_{i,j,k-1}-2\Phi_{i,j,k}+\Phi_{i,j,k+1}}{(\delta z)^2}.
\label{eq:delz2}\end{aligned}$$
Uniform Cylindrical Grid
-... | 1,134 | 4,035 | 1,528 | 996 | null | null | github_plus_top10pct_by_avg |
ibution of . From Lemma \[l:energy\_x\], we know that $\bx_0$ satisfies the required initial conditions in this Lemma. Continuing from , $$\begin{aligned}
& \E{\lrn{\bx_{i\delta} - \bw_{i\delta}}_2}\\
\leq& 2\exp\lrp{\frac{7\aq\Rq^2}{3}}\lrp{2e^{-\lambda i\delta} \E{\lrn{\bx_0}_2^2 + \lrn{\bw_0... | 1,135 | 1,408 | 687 | 1,063 | null | null | github_plus_top10pct_by_avg |
File file = new File(name);
if (file.exists()) {
this.keyStore = KeyStore.getInstance(KeyStore.getDefaultType());
try (FileInputStream fileInputStream = new FileInputStream(name)) {
this.keyStore.load(fileInputStream, password.toCharArray());
... | 1,136 | 6,289 | 97 | 805 | 218 | 0.817801 | github_plus_top10pct_by_avg |
$.
Moreover, depending on the values of $K_{\pm}$ bosonization opens the possibility of two consecutive phase transitions with increasing $U$ starting from the CSF phase [@Supplementary], which we have confirmed with our DMRG calculations (Fig. \[fig:2\](a)). First a KT transition occurs from CSF to chiral-Mott (CMI),... | 1,137 | 194 | 1,951 | 1,276 | 2,211 | 0.781834 | github_plus_top10pct_by_avg |
verline{g(a)},$$ and $\ell^2(\widehat{G})$ is defined analogously. The Fourier transform of $f \in \ell^2(G)$ is the function $\widehat{f} \in
\ell^2(\widehat{G})$ given by $$\widehat{f}(\chi) = {\left\langle f, \overline{\chi} \right\rangle}
= \sum_{a \in G} f(a) \chi(a).$$ This includes as special cases both the clas... | 1,138 | 4,415 | 1,302 | 842 | 3,942 | 0.769088 | github_plus_top10pct_by_avg |
chi (\Lambda )$. Then Eq. follows from Thm. \[th:PBWtau\].
Assume now that $\nu \in \{2,3,\dots ,n\}$ and that the lemma holds for $\nu -1$. Let $\chi _\mu =r_{i_{\mu -1}}\cdots
r_{i_2}r_{i_1}(\chi )$ and $\Lambda _\mu ={t}_{i_{\mu -1}}\cdots {t}_{i_2}
{t}_{i_1}^\chi (\Lambda )$ for all $\mu \in \{1,2,\dots ,\nu ... | 1,139 | 845 | 926 | 1,143 | null | null | github_plus_top10pct_by_avg |
cause the tableaux involved are not semistandard.
\[sigmanz\] With the notation above, $\sigma\neq0$.
The version of this paper published in the Journal of Algebra includes a fallacious proof of Proposition \[sigmanz\]; the proof below replaces it. The authors are grateful to Sinéad Lyle for pointing out the error.
... | 1,140 | 777 | 1,060 | 1,127 | 375 | 0.811673 | github_plus_top10pct_by_avg |
$ is defined in . To prove the lower bound on $\lambda_2(\E[\lM])$, notice that $$\begin{aligned}
\label{eq:bottoml_hess2}
\E\big[\lM\big] &=& \sum_{j = 1}^n \sum_{i<\i \in [\ld]} \E\Bigg[ \sum_{a = 1}^{\ell} \I_{\big\{(i,\i) \in G_{j,a}\big\}} \Big| (i,\i \in S_j) \Bigg] \P\Big[i,\i \in S_j\Big] (\le_i - \le_{\i... | 1,141 | 821 | 1,433 | 1,030 | null | null | github_plus_top10pct_by_avg |
complex integral elements. {#sec:2}
============================================================
The methodological approach assumed in this section is based on the generalized method of characteristics which has been extensively developed (*e.g. in* [@Burnat:1972; @DoyleGrundland:1996; @Grundland:1974; @GrundlandTaf... | 1,142 | 214 | 2,261 | 1,255 | null | null | github_plus_top10pct_by_avg |
eratorname{ss}}} \rightarrow \Lambda^*_H$ and $C_z \colon \Lambda^*_{Z(G)} \rightarrow \Lambda^*_H$.
Let us now choose group homomorphisms $A \colon {\mathbb Z}^s \rightarrow {\mathbb Z}^t$ and $B = B_1 \oplus B_2 \colon \Lambda^*_{G_{\operatorname{ss}}} \oplus \Lambda^*_{G_{\operatorname{ss}}} \rightarrow {\mathbb Z}... | 1,143 | 3,130 | 1,337 | 1,136 | null | null | github_plus_top10pct_by_avg |
in S$*,* $\pi _{S}(\delta _{1})=J$* implies* $\pi
_{S}(\delta _{2})=J$*.*
The binary relation $\prec $ can then be characterized as follows.
*For every* $\delta _{1}$*,* $\delta _{2}\in \psi _{A}^{Q}$*,* $\delta _{1}\prec $* *$\delta _{2}$* iff* $S_{\delta _{1}}\subset S_{\delta _{2}}$*.*
The relation $\prec $ is ob... | 1,144 | 224 | 1,654 | 1,227 | 4,093 | 0.768157 | github_plus_top10pct_by_avg |
& \quad +P{\left(a_7=2,b_8=2\right)}+P{\left(a_8=0,b_4=2\right)}+P{\left(a_8=1,b_5=1\right)}+P{\left(a_8=2,b_7=2\right)}+\\
& \quad +P{\left(a_1=0,b_6=1\right)}+P{\left(a_1=1,b_3=0\right)}+P{\left(a_1=2,b_2=2\right)}
+P{\left(a_2=0,b_6=0\right)}+\\
& \quad +P{\left(a_2=1,b_1=0\right)}+P{\left(a_2=2,b_3=1\right)}+P{\lef... | 1,145 | 1,083 | 1,358 | 1,290 | null | null | github_plus_top10pct_by_avg |
use this method to detect the pair for $(a,b) = (2,2)$, since $H^1(\tilde{X}_\lambda,\CC) = 0$ for $\lambda = 1,\zeta$.
Assume from now on that $(a,b) = (1,3)$. The curve $\mathcal{C}_{\lambda}$ has only three singular points at the origins of the projective plane, $P_1 = [1:0:0]$, $P_2=[0:1:0]$, $P_3=[0:0:1]$ and no... | 1,146 | 597 | 599 | 1,141 | 2,883 | 0.776338 | github_plus_top10pct_by_avg |
x_\mu )\in U^+(r_{i_1}(\chi ))$ for all $\mu \in \{0,1,\dots
,m\}$ by [@p-Heck07b Prop.5.19,Lemma6.7(d)]. Since ${T}^-_{i_1}(E_{\beta _\nu })\in U^+(r_{i_1}(\chi ))$, triangular decomposition of $U(r_{i_1}(\chi ))$ implies that $x_\mu =0$ for all $\mu >0$. Hence $E_{\beta _\nu }=x_0\in \ker {\partial ^K}_{i_1}$. Then... | 1,147 | 2,701 | 996 | 1,028 | null | null | github_plus_top10pct_by_avg |
\max_{j \in [n]} \ell_j$ and $\kappa_{\max} = \max_{j \in [n]} \kappa_j$. The second inequality follows from the Jensen’s inequality.
Consider a case when the comparison graph is an expander such that $\alpha$ is a strictly positive constant, and $b=O(1)$ is also finite. Then, the Cramér-Rao lower bound show that the ... | 1,148 | 605 | 205 | 1,216 | null | null | github_plus_top10pct_by_avg |
}}^I$.
By Eq. , the claim is equivalent to the equation $$\begin{aligned}
{\zeta ^{\chi}} \Big(-\sum _{k=1}^{m-1}({b^{\chi}} (\beta _k)-1)\beta _k\Big )
(K_{\alpha }L_{\alpha }^{-1})=
\frac{{\rho ^{\chi}} ({\alpha })}{{\rho ^{\chi '}}(w({\alpha }))}.
\label{eq:Fhweight}
\end{aligned}$$ For each $k\in... | 1,149 | 2,482 | 1,121 | 1,125 | null | null | github_plus_top10pct_by_avg |
ow \pi^+\pi^-)}{A_{\Sigma}(D^0\rightarrow \pi^+\pi^-)} \right) &=
2\, \mathrm{Re}(2 \tilde{p}_0 \tilde{s}_1 + \tilde{p}_1 ) {\nonumber}\\
&= 2 \left[ 2\, \mathrm{Re}(\tilde{p}_0) \tilde{s}_1 + \mathrm{Re}(\tilde{p}_1)\right] \,. \label{eq:retildep1}\end{aligned}$$ As $\tilde{s}_1$ is already in principle determined fro... | 1,150 | 305 | 1,479 | 1,226 | 287 | 0.81473 | github_plus_top10pct_by_avg |
geometrical/combinatorial explanation.
In [@Mu] a nice formula was proposed for the number tree-rooted planar maps, i.e. edge-rooted planar maps with distinguished spanning tree: the number of such maps with $n$ edges is $C_n\cdot
C_{n+1}$, where $C_k$ is $k$-th Catalan number. An elegant proof of this formula see in ... | 1,151 | 3,981 | 1,057 | 909 | 1,873 | 0.784818 | github_plus_top10pct_by_avg |
Consider the following two bootstrap confidence sets: $$\label{eq:ci.boot.loco}
\hat{D}^*_{{\widehat{S}}} = \left\{ \gamma \in \mathbb{R}^{{\widehat{S}}} \colon \|
\gamma - \hat{\gamma}_{{\widehat{S}}}
\|_\infty \leq \frac{ \hat{t}^*_{\alpha}}{\sqrt{n}} \right\} \quad
\text{and} \quad
... | 1,152 | 3,330 | 1,278 | 1,016 | null | null | github_plus_top10pct_by_avg |
nd analysis of all examined cases.
**Clinicopathological features** **OS**
---------------------------------- ------------ -------------------- --------- --------- ---------- -----------
**N (%)** **Median, months*... | 1,153 | 5,599 | 476 | 372 | null | null | github_plus_top10pct_by_avg |
tive curves.
In this paper we extend the above results in three directions: first, the theory is extended to surfaces with quotient singularities, second the ramification locus can be partially resolved and need not be reduced, and finally global and local conditions are given to describe the irregularity of cycli... | 1,154 | 386 | 1,371 | 1,151 | null | null | github_plus_top10pct_by_avg |
egion between 0.1 and 1.0[ $(\text{GeV}\! / c)^2$]{} was selected for the analysis (see [[Fig. \[fig:tPrime\]]{}]{}).
![[${\ensuremath{\pi^-}}{\ensuremath{\pi^+}}{\ensuremath{\pi^-}}$]{} invariant mass distribution of the selected data sample for $t' \in [0.1, 1.0]{~\ensuremath{(\text{GeV}\! / c)^2}}$.[]{data-label="f... | 1,155 | 562 | 1,349 | 1,294 | 1,026 | 0.795479 | github_plus_top10pct_by_avg |
(solid lines) and theoretical results for the experimental parameter $\lambda_W$ (dotted line) and the fit parameter $\lambda_{\rm fit}$ (dashed line) for two openings $d=\rm 6.5\,mm$ with $\lambda_W=0.05$ and $\lambda_{\rm fit}=-0.18i$ (black), and $d=\rm 11.2\,mm$ with $\lambda_W=0.52$ and $\lambda_{\rm fit}=-0.55i$... | 1,156 | 706 | 2,593 | 1,308 | null | null | github_plus_top10pct_by_avg |
eta complaining about low quality first user questions. And there's always suggestions about how to tweak the question wizard... Have you thought that maybe you're inviting bad post by being a little more difficult to use than you should?
A:
Tour
Open https://webapps.stackexchange.com/tour.
Help menu
Website foote... | 1,157 | 1,653 | 595 | 744 | 251 | 0.816016 | github_plus_top10pct_by_avg |
note that the low-frequency part of the all spectral functions in Fig. \[NRG\_fig2\] is governed by the same energy scale $T_{K}$ that is reduced with increasing $\lambda_c$.
![Contributions to the inelastic spectrum due to tunneling into the molecular orbital $d_{0\sigma}$, the local surface orbital $c_{0\sigma}$ an... | 1,158 | 280 | 1,472 | 1,305 | null | null | github_plus_top10pct_by_avg |
ft(A^{18}\cap\pi^{-1}(H)\right)\prod_{i=1}^r\left(A^{24}\cap\pi^{-1}(\langle x_i\rangle)\right)\right|\ge\frac{|A|}{\exp(\log^{O(1)}2K)}.$$
We prove \[prop:pre-chang.tor.free\] shortly.
\[lem:x\[G,G\]\] Let $s\ge2$. Let $G$ be an $s$-step nilpotent group, write $\pi:G\to G/[G,G]$ for the quotient homomorphism, and le... | 1,159 | 810 | 1,307 | 1,137 | 2,421 | 0.779882 | github_plus_top10pct_by_avg |
defect to the other, or to create superposition states with well-defined weights. This might open up new perspectives for the design of quantum logical devices.
I would like to thank M. Holthaus for his continuous support and insightful discussions.
\[sec:eigen\]Eigenfunction for a single defect
=====================... | 1,160 | 4,626 | 340 | 875 | null | null | github_plus_top10pct_by_avg |
|
| | 25‐250 for mRNA | | | ... | 1,161 | 204 | 1,539 | 1,225 | null | null | github_plus_top10pct_by_avg |
0.084 0.084 0.083 0.083 0.084 0.083
mVC 0.103 0.103 0.103 0.103 0.103 0.103 0.103
mMSE 0.096 0.095 0.096 0.096 0.096 0.096 0.095
... | 1,162 | 5,112 | 420 | 786 | null | null | github_plus_top10pct_by_avg |
^!})(\vec X;\varnothing)$ with “dashed” first and last inputs, can uniquely be written in the form $\varphi *_\sigma\psi$ or $\varphi\#_\sigma\psi$ for some $\varphi,\psi$ and $\sigma$.
For each $r\geq 1$, we show that the $(-r)$th homology of $\textbf{D}(\widehat{\mathcal O^!})(\vec X;\varnothing)$ vanishes by decomp... | 1,163 | 4,076 | 760 | 733 | 2,891 | 0.776269 | github_plus_top10pct_by_avg |
le qubit energy $k/n$, resulting in a system with energy $k$. This choice will allow us to precisely describe the behavior of the walk in terms of the relationship between the energy of the system and the rate of decoherence.
We can write each of the terms in the exponent of the superoperator from (\[superop-soln\]) a... | 1,164 | 2,690 | 1,383 | 1,147 | null | null | github_plus_top10pct_by_avg |
'
- 'Primož Škraba, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana, SLOVENIA '
author:
- Ganna Kudryavtseva
- Primož Škraba
title: The principal bundles over an inverse semigroup
---
Introduction
============
The classifying topos ${\mathcal{B}}(S)$ of an inverse semigroup $S$ has recently begun to be investigat... | 1,165 | 226 | 1,707 | 800 | null | null | github_plus_top10pct_by_avg |
\end{pmatrix}\quad.$$ By (\[refMPI\]) in Lemma \[MPI\], $\ell(t)$ has entries in ${{\mathbb{C}}}[[t]]$ and is invertible; in fact, $L=\ell(0)$ is lower triangular, with 1’s on the diagonal. Therefore Lemma \[MPI\] gives $$h_1(t)\cdot
\begin{pmatrix}
t^a & 0 & 0 \\
0 & t^b & 0 \\
0 & 0 & t^c
\end{pmatrix}=
\begin{pmatri... | 1,166 | 427 | 916 | 1,221 | 4,141 | 0.76782 | github_plus_top10pct_by_avg |
S {#sec-lambda-0}
In order to make the connection to the literature and also to point out the major difference of our theory in comparison with earlier ones, we consider the limit of vanishing electron-phonon coupling in the system S, but maintain a small but non-zero $\lambda^{\rm tip}_{\mu\nu}$. Then, $\langle\hat ... | 1,167 | 2,462 | 1,470 | 1,118 | 4,050 | 0.768449 | github_plus_top10pct_by_avg |
6]), so provision was made for the elimination of data recorded on days when conditions were especially adverse (e.g., intense rain or cold). However, no data were required to be removed on these grounds.
In addition to calculating the average number of steps taken by participants, the analysis also grouped results ac... | 1,168 | 433 | 2,711 | 1,070 | null | null | github_plus_top10pct_by_avg |
O(s)}}}$; finite $K^{e^{O(s)}}$-approximate groups $A_1,\ldots,A_r\subset A^{e^{O(s)}}$ such that, writing $\pi:G\to G/N$ for the quotient homomorphism, each group $\langle\pi(A_i)\rangle$ is abelian; and sets $X_1,\ldots,X_t\subset A^{e^{O(s)}}$ of size at most $\exp(e^{O(s)}\log^{O(1)}2K)$ such that $$A\subset N\prod... | 1,169 | 640 | 1,239 | 1,099 | 2,928 | 0.776015 | github_plus_top10pct_by_avg |
<!-- <thead class="thead-dark"> -->
<tr>
<th>Item</th>
<th>Quantity</th>
<th>Rate</th>
<th>Subtotal</th>
... | 1,170 | 704 | 154 | 522 | 1,735 | 0.786257 | github_plus_top10pct_by_avg |
omega_2$ the stable one. Because $b$ depends on $\omega$ through Eq. and the eigenmode structure $\phi(z)$ depends on $b$ through Eq. , the two solutions $\omega_j$ correspond to two different eigenmodes $\phi_j(z)$. We identify $b_j$ and $\phi_j$ as the $b$ and $\phi$ corresponding to $\omega_j$. The eigenmodes are t... | 1,171 | 713 | 1,654 | 1,377 | 3,715 | 0.770528 | github_plus_top10pct_by_avg |
\Q$-resolution as defined in section \[sec:h2\]. Recall that $$H^1(\tilde X,\CC)=H^1(\tilde Y,\CC)=H^1(Y,\cO_Y)\oplus H^0(Y,\Omega^1_Y)=H^1(Y,\cO_Y)\oplus \overline{H^1(Y,\cO_Y)}.$$ In this section the dimension of the $e^{\frac{2\pi ik}{d}}$-eigenspace of $H^1(Y,\mathcal{O}_Y)$ will be computed using the tools develop... | 1,172 | 974 | 1,030 | 1,223 | null | null | github_plus_top10pct_by_avg |
g Theorem \[theorem:aLinear\].
5. \[item:outline:Quantize\] Quantize $\{ {{\bar{\a}}^\dagger}_k \}$ to integer-valued vectors $\{ {{\bar{\a}}^\diamond}_k \}$ with Algorithm \[agorithm:SuccessiveQuantization\].
6. \[item:outline:Select\] Select a vector from $\{ {{\bar{\a}}^\diamond}_k \}$ to be a suboptimal coeffic... | 1,173 | 328 | 1,361 | 1,287 | null | null | github_plus_top10pct_by_avg |
\
[ letellier.emmanuel@math.unicaen.fr]{}
- |
Fernando Rodriguez-Villegas\
[*University of Texas at Austin*]{}\
[ villegas@math.utexas.edu]{}\
\
[with an appendix by Gergely Harcos]{}
title: |
Arithmetic harmonic analysis on\
character and quiver varieties II
---
Introduction
==========... | 1,174 | 566 | 729 | 1,155 | 2,202 | 0.781855 | github_plus_top10pct_by_avg |
riangleleft {(b\triangleright a^2)}) (b\triangleleft {a^2})
\stackrel{ {(\ref{eq:2.4.750})} } =( b\triangleleft a)( b\triangleleft
{a^2}) = b^{2(l + t + 1 )}$$ $$\beta (b^3, a^2) = (bb^2)\triangleleft {a^2} \stackrel{{(\ref{eq:3})}
}= (b\triangleleft {(b^2\triangleright a^2)}) (b^2 \triangleleft
{a^2}) \stackrel{ {(\re... | 1,175 | 3,642 | 857 | 1,035 | 3,941 | 0.769123 | github_plus_top10pct_by_avg |
re also linearly independent. Then (\[eq:linfq2\]) implies that their coefficients are zero, that is, the probability (\[eq:p\_q\]) of the outcome $q$ is independent of the input state $|\Phi\rangle_A$. Reversely, if (\[eq:p\_q\]) is independent of $|\Phi\rangle_A$, then $LL_q^\dag$ is injective and $f_q$ is linear. We... | 1,176 | 1,051 | 2,276 | 1,362 | 1,877 | 0.784777 | github_plus_top10pct_by_avg |
\;\leq\; \frac{e^{6b}\ell_j}{\max\{ \ell_j, \kappa_j - p_{j,\ell_j}\}} \leq \frac{e^{6b}\eta \ell_j}{ \kappa_j}\,,\end{aligned}$$ where we used $\eta$ defined in Equation . Define a diagonal matrix $D^{(j)} \in \cS^{d}$ and a matrix $A^{(j)} \in \cS^d$, $$\begin{aligned}
A^{(j)}_{i\i} &\equiv & \I_{\big\{i,\i \in S_... | 1,177 | 831 | 1,108 | 1,156 | null | null | github_plus_top10pct_by_avg |
_i+4c_i \end{pmatrix}$ as explained in Section \[h\] and thus we have $$\label{ea12}
\begin{pmatrix} a_i'&\pi b_i'\\ \sigma(\pi\cdot {}^t b_i') &1 +2\bar{\gamma}_i+4c_i' \end{pmatrix}=
\sigma(1+\pi\cdot {}^tm_{i,i}')\cdot\begin{pmatrix} a_i&\pi b_i\\ \sigma(\pi\cdot {}^t b_i) &1 +2\bar{\gamma}_i+4c_i \end{pma... | 1,178 | 3,468 | 1,438 | 1,062 | null | null | github_plus_top10pct_by_avg |
her partitioned into smaller regions, corresponding to various phases of the system (see figure \[fig:fdCSAWs\]).
![Phase diagrams in the space of interaction parameters for CSAWs model in the case of $b=2$ and $b=3$ SG fractal, for $t=0.5$. In both cases the critical line $w=w_c(u,t)$ separates the $u-w$ plane into ... | 1,179 | 263 | 1,566 | 1,288 | 1,326 | 0.790965 | github_plus_top10pct_by_avg |
p\times q$ matrix functions of $u$ ([*i.e.* ]{}$\mathcal{A}^\mu=(\mathcal{A}^{\mu i}_\alpha(u))\in
{\mathbb{R}}^{p\times q}, \mu=1,\ldots, m$). For the given initial system of equations (\[eq:3.1\]), the matrices $\mathcal{A}^\mu$ are known functions of $u$ and the trace conditions (\[eq:3.22\]) or (\[eq:3.23\]) are co... | 1,180 | 308 | 1,760 | 1,404 | 3,719 | 0.770519 | github_plus_top10pct_by_avg |
oreover, one sees that every strong solution with homogeneous inflow boundary conditions is a weak solution of $P(x,\omega,E,D)\phi=f$, that is $$\begin{aligned}
\label{eq:P_0_in_P-dot-star}
\tilde P_{0}\subset P'^*.\end{aligned}$$
Since $\tilde P_{0}$ is a closed operator, the space \[eq:H\_tilde-P\_0\_is\_D-tilde-P\... | 1,181 | 565 | 1,430 | 1,180 | null | null | github_plus_top10pct_by_avg |
$$\partial_t\hat\psi({\boldsymbol{k}},t) = \hat\omega({\boldsymbol{k}})\hat\psi({\boldsymbol{k}}, t) + \hat N({\boldsymbol{k}} ,t),
\label{eq:DecompositionGPE}$$ which can be solved by an operator-splitting and exponential-time differentiating method [@cox2002exponential]. It means that we exploit the fact that th... | 1,182 | 1,331 | 2,054 | 1,280 | 1,464 | 0.789252 | github_plus_top10pct_by_avg |
ntegral model associated to $C(L^j)$ to the smooth integral model associated to $M_0'\oplus C(L^j)$ explained in Remark \[r410\], the image of a fixed element of $F_j$ in the special fiber of the smooth integral model associated to $M_0'\oplus C(L^j)$ is $$\begin{pmatrix}\begin{pmatrix}1&\frac{-2a}{a+2b} z_j^{\ast} &0 ... | 1,183 | 1,516 | 849 | 1,149 | 4,036 | 0.768514 | github_plus_top10pct_by_avg |
ries) was proved by Bose and Mitra in [@BoMi].
We will not attempt to deal thoroughly with the question of when the convergence in probability in the results above can be strengthened to almost sure convergence. However, the following result gives some sufficient conditions. Each of the conditions stated automatically... | 1,184 | 680 | 1,104 | 1,116 | null | null | github_plus_top10pct_by_avg |
\delta_t}, {\boldsymbol \omega} \rangle$, $t\geq 0$.
Another useful corollary of Theorem \[charthm\] concerns integration of a family of generalized functions, see [@PS91; @HKPS93; @KLPSW96].
\[intcor\] Let $(\Lambda, {\mathcal{A}}, \nu)$ be a measure space and $\Lambda \ni\lambda \mapsto \Phi(\lambda) \in (S)'$ a ma... | 1,185 | 3,228 | 1,171 | 1,083 | null | null | github_plus_top10pct_by_avg |
uses . Substituting these observations into Corollary \[gr\] gives the second equality in .
Proof of proposition \[app-c-prop\] {#subsec-6.21C}
-----------------------------------
We first show that the map $\theta:J^{k-1}\delta^ke \to M(k)$ is an isomorphism for all $k\geq 1$. This is analogue of Proposition \[grsam... | 1,186 | 507 | 785 | 1,321 | 3,321 | 0.773172 | github_plus_top10pct_by_avg |
s no longer appropriate to model the channel for each reconfiguration state as a full-rank matrix with i.i.d. entries due to the sparse nature of mmWave channels.[^4] In the following, we present the channel model of mmWave MIMO systems with reconfigurable antennas.
### Physical Channel Representation
The physical ch... | 1,187 | 1,428 | 1,639 | 1,252 | 3,188 | 0.774163 | github_plus_top10pct_by_avg |
,l}) =
E^{(1)}_{k,l} (A_{1} \chi^{(1)}_{k,l}).
\label{eq.2.3.2}$$ We see, that the function $f(r)=A_{1} \chi^{(1)}_{k,l}(r)$ is the eigen-function of the operator $\hat{H}_{2}$ with quantum number $l$ to a constant factor, i. e. it represents the wave function $\chi^{(2)}_{k^{\prime},l}(r)$ of the hamiltonian $H_{2}$... | 1,188 | 3,600 | 1,114 | 1,119 | null | null | github_plus_top10pct_by_avg |
\widehat{S}}} = \mathbb{E}[X({\widehat{S}}) X({\widehat{S}})^\top].$$ We will be studying the ordinary least squares estimator $\hat{\beta}_{{\widehat{S}}}$ of $\beta_{{\widehat{S}}}$ computed using the sub-sample $\mathcal{D}_{2,n}$ and restricted to the coordinates ${\widehat{S}}$. That is, $$\label{eq:least.squares}... | 1,189 | 738 | 1,078 | 1,178 | null | null | github_plus_top10pct_by_avg |
rements, say $X = (X_t, t\geq 0)$ with probabilities $(\mathbb{P}_x, x\in\mathbb{R}^d)$, whose semi-group is represented by the Fourier transform
$$\mathbb{E}_0\bp{{\rm e}^{{\rm i}\langle\theta ,X_t\rangle}} = {\rm e}^{-|\theta|^\alpha t}, \qquad \theta\in \mathbb{R}^d, \;t\geq 0,$$ where $\langle \cdot,\cdot \rang... | 1,190 | 1,323 | 685 | 1,145 | null | null | github_plus_top10pct_by_avg |
s crucial to distinguish between low-energy and high-energy unitarity violation, is of order $W^4$. The other normalization term, the second term in (\[P-beta-alpha-ave-vac\]), also deviates from the one in unitary case by a quantity of order $W^4$ in the appearance channels, but in an implicit way. The resulting expre... | 1,191 | 1,947 | 1,869 | 1,332 | 1,658 | 0.787103 | github_plus_top10pct_by_avg |
17.99 37.74 11.3 7.24
Q08380 Galectin-3-binding protein 17.44 15.73 65.3 5.27
P01876 Immunoglobulin heavy constant alpha 1 17.06 25.78 37.6 6.51
P35443 Thrombospondin-4 9.76 ... | 1,192 | 2,710 | 1,793 | 1,219 | null | null | github_plus_top10pct_by_avg |
-bottom: as shown in Fig. \[fig:sdntn\_prop2\], an attacker launches a DoS attack against an OpenFlow switch, which is connected to a primary SDN-controller. In order to increase the resilience of the system, the switch has been assigned a secondary SDN-controller. The switch needs to contact the SDN-controller for eve... | 1,193 | 2,902 | 2,038 | 1,203 | null | null | github_plus_top10pct_by_avg |
tive to LINQ you can use operations over the array with Array.FindLastIndex + AsSpan + ToArray (note that all solutions here forward assume that it's possible for your array to be all nulls):
string[] strings = { "Hello", null, "World", null, null, null, null, null, null };
var idx = Array.FindLastIndex(strings, c => c... | 1,194 | 6,328 | 35 | 688 | 90 | 0.826928 | github_plus_top10pct_by_avg |
sidered in this work.
Heating and cooling rates {#sec:heat_cool}
-------------------------
[lllc]{} No. & Process & Rate \[${\mathrm{erg\, cm^{-3}\, s^{-1}}}$\] & Ref.\
\
1 & ${\mathrm{H}}$ photoionization & $\Gamma_1$ (see text)&\
2 & ${\mathrm{He}}$ photoionization & $\Gamma_2$ (see text)&\
3 & ${\mathrm{He^+}}$ ph... | 1,195 | 1,847 | 2,455 | 1,312 | null | null | github_plus_top10pct_by_avg |
he different aspects of the optical processes raised by the selection of distinct sidebands.
We proceed to apply the NL in Eq. (\[nl1\]) to reveal the irreversibility of the work protocol. Just like what happened with the full Hamiltonian (\[hf\]), the first moment of the work distribution or simply the average work i... | 1,196 | 3,832 | 1,168 | 1,026 | null | null | github_plus_top10pct_by_avg |
{\bigcup\{\dot{Z}(\xi,C_{\zeta(\xi)}):\xi\in f_\gamma^{-1}(n)\}}
\subseteq\dot{W}(\gamma,n).$$ Then we can get a $\zeta(\gamma)$ that works for all $n$.
By recursion on $\gamma\in\omega_2$, we can choose $\zeta(\gamma)\geq\gamma$ as above, so that the sequence $\{\zeta(\gamma):\gamma\in\omega_2\}$ is strictly increasi... | 1,197 | 1,115 | 950 | 1,152 | null | null | github_plus_top10pct_by_avg |
-(\[csda3\]), and related operators. Write &T\_1:=\_x\_1+\_1\_1-K\_1,\
&T\_j:=-[E]{}+\_x\_j+ \_j\_j - K\_j,j=2,3,and define a (densely defined) linear operator $T:L^2(G\times S\times I)^3\to L^2(G\times S\times I)^3$ by D(T):=&{L\^2(GSI)\^3 | T\_jL\^2(GSI), j=1,2,3},\
T:=&(T\_1,T\_2,T\_3). Let $f\in L^2(G\times S\times... | 1,198 | 201 | 1,162 | 1,218 | null | null | github_plus_top10pct_by_avg |
he Standard Model parameters, we use the measured values of the top quark, W, Z, and Higgs masses. Note that we use $m_h=125.3$ GeV for all points when calculating threshold corrections. After running through , the points that survive all have a Higgs mass within 3 GeV of this value. This is at most a $\sim$2% differen... | 1,199 | 3,233 | 2,137 | 1,296 | null | null | github_plus_top10pct_by_avg |
vation by Idea program \[VIREPAP 19104\]. EIT Health is supported by the European Institute of Innovation and Technology (EIT), a body of the European Union that receives support from the European Union' s Horizon 2020 Research and innovation program.
The corresponding author (A.M. (Albert Mihranyan)) is the inventor ... | 1,200 | 4,953 | 823 | 591 | null | null | github_plus_top10pct_by_avg |
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