text:
\section*{Introduction}
The scheme of molecular Doppler cooling (first displayed in \cite{DiRosa:04}) proved to be
efficient, robust and applicable to a large class of molecular species.
Recently highly-efficient cooling and magneto-optical trapping of diatomic molecules
was demonstrated for SrF \cite{Barry:2014}, YO \cite{Hummon:2013} and CaF \cite{Hemmerling:2016,
Anderegg:2017}.
The experiments on Doppler/Sisyphus cooling
on BaH \cite{Tarallo:2016}, MgF \cite{Liang:2016} and some other molecules and their cations
are currently conducted by different groups. Recently we have proposed a number of
polyatomic molecules containing light atoms, which may be expected
to be suitable for Doppler/Sisyphus cooling \cite{Isaev:2016}. The estimate for Doppler limit temperature for considered
molecules (CaOH, CaNC, MgCH$_3$, CaCH$_3$ and chiral MgCHDT) showed that it is quite
realistic to reach the submillikelvin temperatures with a large class of polyatomic species
(see also recent proposal by I. Kozyryev et al \cite{Kozyryev:2016b} for
a large class of polyatomic radicals amenable for laser cooling).
In 2017 J. Doyle's team at Harvard University has reported the first observation
of fast Sisyphus laser cooling of SrOH to the temperature of $\sim$750 $\mu K$ \cite{Kozyryev:2017a}.
To our knowledge the only competitive method currently allowing
to cool polyatomic (four- and bigger multi-atomic
molecules) to submillikelvin temperatures is
optoelectrical Sisyphus cooling method  \cite{Prehn:2016, Zeppenfeld:2012}. The latter method,
though having great potential,
relies on strong Stark interaction with external field and is expected to be most effective
when applied to molecules with rather large dipole moments. The method of molecular laser cooling
can be applied both to dipolar and non-dipolar species and, besides, is directly
related to very well-studied,
efficient and robust atomic Doppler cooling technique. On the one hand
electronic structure of heavy-atom molecules especially favors quasi-diagonal structure
of Franck-Condon (FC) matrix between ground and excited electronic states \cite{isaev:2010}
due to more diffuse valence electronic orbital in comparison with light-atom homologies.
On the other hand the molecular species containing
heavy atoms present considerable interest for the experiments devoted to
search for new physics outside the Standard
Model \cite{Titov:06amin, Klemperer:1993,Kozyryev:2017b},
including search for axion-like-particle candidates for dark matter
\cite{Stadnik:2014} and search for parity violation in chiral molecules (see e.g \cite{Berger:1997}).
Herein we apply the principles for identifying the laser-coolable polyatomic species
introduced in \cite{Isaev:2016} to the field of heavy-atom compounds and
propose the triatomic molecule RaOH
as a candidate for Doppler cooling and for search for
space parity violating ($\cal P$-odd~) and
also for both space parity and time-reversal violating ($\cal P,T$-odd~) interactions
with polyatomic molecules. In the first part of the article
 we calculate molecular spectroscopic parameters for
this molecule and estimate the completeness
of the cooling loop by calculating the FC matrix for vibronic transitions
between first electronic excited and ground states.
Then we apply recently developed original methodology for
calculations of electric transition dipole moments between
elaborate electronic levels in fully-relativistic framework.
Finally, we use the earlier developed by us approach to
estimate $\cal P$-odd~ and $\cal P,T$-odd~ parameters of effective molecular
spin hamiltonian in the framework of
Zero Order Regular Approximation (ZORA) \cite{Isaev:2012, Isaev:2014}
(see also \cite{berger:2005, berger:2005a}).

\section*{Relativistic electronic structure calculations}

\subsection*{Equilibrium molecular parameters}
As it was pointed out in \cite{isaev:2010} the crucial prerequisite for the closed cooling transition
loop in molecules (required for the quasi-diagonality
of the FC matrix) is the conservation of a similar molecular geometry for both ground and first excited electronic states. This happens for e.g.
transition of the valence electron between non-bonding orbitals being presented
in the leading electronic configuration for both ground end excited electronic states.
In \cite{Isaev:2016} we have proposed a
simple scheme for obtaining the molecular structures of polyatomic species which contain
non-bonding single-occupied molecular orbitals. The basic idea is to make a substitution of the halogen in the series of
MX molecules (M is the metal and X is the halogen) to pseudo-halogen
or functional groups. In our consideration in \cite{Isaev:2016} the heaviest nucleus in a molecule was calcium
(with the charge number $Z$=20) and, thus we
were able to safely neglect the relativistic effects in those
electronic structure calculations. For light
element compounds such an approximation indeed does not lead to noticeable
changes in molecular parameters (see e.g. \cite{DyallRelBook}).

In the opposite case of heavy element
compounds one has to estimate the influence of
relativistic effects on FC factors. FC factors are known to be strongly dependent on
displacements in equilibrium geometries and thus are
sensitive to both scalar and spin-dependent relativistic effects,
if such effects are
different for the considered electronic states (in our case the ground and
first excited electronic states).
We started our study from calculation of equilibrium structures and normal modes for both
ground and first excited electronic states of RaOH using spin-averaged relativistic effective
core potential ({\sc arecp}) with 10 valence electrons
treated explicitly for Ra and with all-electron description for O and H.
Multiconfiguration Self-Consistent Field method (MCSCF) is used for ARECP calculations with
17 valence electrons correlated and with
the basis sets of triple-zeta quality from Molpro program package
 library (see supplementary material for details).
The equilibrium structures and normal mode frequencies are provided in \tref{scal-fourcomp}.
It can be seen that RaOH
has essentially linear geometry in both ground ($^2\Sigma$, according to irreps of $C_{\infty v}$ group)
and first excited ($^2\Pi$) electronic states.
Very weak Renner -Teller effect in $^2\Pi$
RaOH detected within the spin-orbit-free approximation is in accord with similar
effects found
in light homologue compound CaOH \cite{Theodorakopoulos:1999,Li:1996} and should be fully suppressed due
to strong spin-orbit interaction in heavy-atom compounds.
We also would like to emphasize that in the vibrational analysis
we did not restrict symmetry of vibrational modes to the
totally-symmetric one.
To estimate the influence of the relativistic spin-orbit interaction on {\it relative displacements} in
equilibrium geometries we computed the properties for
the states of interest with scalar-relativistic four-component spin-free (SF) \cite{Dyall:1994} and
fully-relativistic four-component Dirac-Coulomb (DC) Hamiltonians.
In four-component calculations
we used Fock-Space Relativistic Coupled Cluster with Single and Double
excitations (FS-RCCSD) method  to account for electron correlations \cite{Visscher:01}.
In this approach augmented
ANO-RCC basis set on Ra and double zeta plus polarization quality
basis sets by Alrichs et al on O and H (see supplementary material)
were used.
Thus we could also directly check the stability
of the calculated FC-factors in relation to changing of the method for electron correlation accounting.
 It follows from ARECP/MCSCF calculations that the main interest
present the vibrations localized on the Ra-OH bond.
Thus one has to consider first the cross-section of the potential energy surface
along Ra-OH bond
(while relative positions of O and H nuclei can be fixed). The bond angle Ra-O-H is expected
to be very close to $180^{\circ}$ due to above-mentioned suppression of Renner-Teller effect
by spin-orbit interaction. Nevertheless to additionaly confirm this
we have also explicitly calculated dependence of the
energies of the ground and first excited electronic states on Ra-O-H bond angle (see Fig \ref{pes})
in the framework of DC/RCCSD approach.
One can see from \tref{scal-fourcomp}, that the changes in {\it displacements} of
the equilibrium geometries for ground and excited electronic states of RaOH are rather minor,
while the method of accounting for electronic correlations is changed and
simultaneously the spin-orbit interaction is taken into account. To check directly the influence of dynamic
electronic correlations and the spin-orbit interaction on FC factors we have calculated these factors for $0' -0$, $0' -1$ and $0'-2$ transition
of the quasimolecule RaX. Here $0'$, 0, 1 and 2 are the vibrational quantum numbers for the first excited electronic state (with prime)
and ground electronic state (without prime) correspondingly; mass of quasinucleus X is equal to the mass of
OH group (17 a.m.u.), while internuclear potential is equivalent to
that between Ra and O nuclei  from either ARECP/MCSCF or
SF/FS-RCCSD or DC/FS-RCCSD calculations (see supplementary material).
The calculations of FC factors were performed analogously to those from
\cite{isaev:2010} and the
results are presented in Table I in supplementary material.
Similarly to \cite{Isaev:2016} we are using here the sum of the three largest FC-factors in order to estimate the completeness of the cooling loop.
One can see from the Table I that for every calculation the sum of the three largest FC-factors
is greater than 0.99, thus it is reasonable to expect highly-closed cooling transition
$^2\Sigma_{1/2} \rightarrow ^2\Pi_{1/2}$  in RaOH.

\begin{figure*}[h]
\label{pes}
\caption{ (Color online)
Potential energies of the ground and first excited electronic state as functions of $R_{\rm Ra-O}$ (left) and the valence Ra-O-H angle (rigrh) with other parameter fixed at their equilibrium values
(see supplementary material for the details). Energies are given with respect to the ground state
equilibrium point. Solid black lines: DC/FS-RCCSD, dashed blue lines:  SF/FS-RCCSD.
}
\includegraphics[width=0.75\linewidth]{fig_1.eps}
\end{figure*}

\subsection*{Transition dipole moments}
Another prerequisite for the efficient molecular Doppler cooling is strongly allowed dipole transition between
working electronic states.
To estimate radiative lifetimes for the first excited $^2\Pi_{1/2}$ state on the FS-RCCSD level,
we evaluated the transition electric dipole moment (TDM) between this state and the ground
$^2\Sigma_{1/2}$ electronic state using the finite-filed method. The TDM
component values were derived from the finite-difference
approximation
for the derivative matrix elements as
\begin{eqnarray}
{\rm TDM}_\eta&=&\!\left(E_{^2\Pi_{1/2}}-E_{^2\Sigma_{1/2}}\right)
\left<\tilde{\Psi}^{\perp\perp}_{ ^2\Pi_{1/2}} (F_\eta)\left|
\frac{\partial}{\partial F_\eta}\tilde{\Psi}_{^2\Sigma_{1/2}}(F_\eta)\right.\right>
\left|\begin{array}{l}\\_{F=0}\end{array}\right. \nonumber \\
&\approx&\!\left(E_{^2\Pi_{1/2}}-E_{^2\Sigma_{1/2}}\right)
\frac{
\left<\tilde{\Psi}^{\perp\perp}_{ ^2\Pi_{1/2}} (\Delta F_\eta)\left|
\tilde{\Psi}_{^2\Sigma_{1/2}}(-\Delta F_\eta)\right.\right>}{2\Delta F_\eta}
,\quad \eta=x,\,y,\,z
\end{eqnarray}
Here $F$ is the applied uniform electric field strength and $\tilde{\Psi}^{\perp\perp}$ and
$\tilde{\Psi}$ stand for left and right eigenvectors of the field-dependent
non-Hermitian FS-RCC
effective Hamiltonian acting in the field-free ($F=0$) model space.
The chosen numerical differentiation step size $\Delta F_\eta=5\cdot10^{-5}$ atomic units corresponded approximately to the center of the interval on the logarithmic scale in which the dependence of the resulting TDM values on the step size was negligible.
Although the calculations involve only the effective Hamiltonian eigenvectors, i.\ e. the
model space projections of many-electron wavefunctions,
the resulting transition moment approximations implicitly
incorporate the bulk of the contributions from the remainder
(outer-space)
part of these wavefunctions \cite{Zaitsevskii:1998}.
The computational procedure has been implemented
within the {\sc DIRAC15} program package \cite{dirac:15}.
The lifetimes of several vibrational levels $v'$
 are estimated according to (see \cite{Matsushita:1987}):
\begin{equation}
\tau_{v'}=\frac{4.936\cdot 10^5}{|\mathrm{TDM}|^2\sum_{v}\mathrm{(FC)}_{vv'}\Delta\mathrm{E}_{vv'}^3},
\label{lifetime}
\end{equation}
where $\tau_{v'}$ is the radiative lifetime of the vibrational level $v'$ (in $s$); $|\mathrm{TDM}|^2$
is the sum of the squares of transition dipole moment moduli between one component of
the initial electronic state and both components of the final state
(in atomic units); $\mathrm{(FC)}_{vv'}$ is the FC-factor for the vibronic transition $vv'$; and
$\Delta\mathrm{E}$ is the energy interval between vibronic levels $vv'$ (in wavenumbers).
The TDM value is evaluated at the equilibrium geometry of the ground electronic state of RaOH (which is nearly coinciding with that of the excited state) from DC/FS-RCCSD calculations.
For $\tau_{0}$ we obtain the lifetime of the
excited electronic state about 40 $ns$ which corresponds to Doppler limit temperature
$T_\mathrm{D}\approx 90 \mu K$.

 We have also calculated the dependence of the transition dipole moment (TDM) on
the internuclear distance Ra-O, to check the
behavior of TDM near the equilibrium Ra-O distance and
thus control possible Herzberg-Teller contribution to the vibrational spectrum
 (see Fig. \ref{tdm}).
 This contribution is proportional to the derivation of the TDM
on the internuclear distance Ra-O.
\begin{figure*}[h]
\caption{
\label{tdm}(Color online) Absolute value of $A^2\Pi_{1/2}-X^2\Sigma^+_{1/2}$ transition dipole moment $M$ as a function of $R_\mathrm{Ra-O}$ according to DC/FS-RCCSD calculations. Dashed line: longitudinal component, $|\langle A^2\Pi_{1/2,m}\vert M_z \vert X^2\Sigma^+_{1/2,m}\rangle |$ ($|$TDM$_{\parallel}|$); dotted line: transverse component $|\langle A^2\Pi_{1/2,1/2}\vert \sqrt{1/2}\,(M_x+{\rm i} M_y )\vert X^2\Sigma^+_{1/2,-1/2}\rangle |$ ($|$TDM$_{\perp}|$); dash-dotted line: total transition dipole length ($|$TDM$|$). The solid line corresponds to the spin-orbit-free $|$TDM$|$ limit from the SF/FS-RCCSD calculations.
}
\includegraphics[width=0.75\linewidth]{fig_2.eps}
\end{figure*}
To demonstrate the influence of the spin-dependent effects we
provide on the plot with TDMs from DC/FS-RCCSD calculations also the spin-orbit-free limit
of the total TDMfrom SF/FS-RCCSD calculations and
the longitudinal component  $\vert\mathrm{M}_z\vert$, which
vanishes at the scalar relativistic limit.
Rather slow and nearly linear variation of the
 TDM near the equilibrium geometries
of the ground and first excited electronic states in RaOH
justifies the use of the approximation (\ref{lifetime}) for radiative lifetimes.

\begin{table*}[th]
\caption{ \label{scal-fourcomp} Calculated molecular parameters and FC factors for RaOH molecule.
The results of ARECP/MCSCF, SF/FS-RCCSD and DC/FS-RCCSD calculations are provided.
Internuclear distances $R_i$ are given in \AA, electric dipole moments in Debye, transition wavenumbers $T_\mathrm{e}$ and harmonic vibrational
wavenumbers $\tilde{\omega}_\mathrm{e}$ of normal mode $\nu_l$ in inverse centimeters.
For FC factors the corresponding
vibrational quantum numbers are reported, e.g 1$^{0}_{2}$ is FC factor for a vibronic transition
between the ground (0) vibrational state of the excited electronic state and the vibrational state with the first mode (1)
(Ra-O stretching) being doubly excited (2) in the ground electronic state.
The irreducible representation $\mathrm{\pi}$ is two-dimensional, but the degeneracy could be slightly lifted in the numerical calculations, so we provide vibrational wavenumbers of both components.}
\begin{tabular}{lll|llll}
\vspace{0.2cm} \\
\multicolumn{7}{c}{ARECP/MCSCF} \\
State  &  \multicolumn{2}{c}{ } & &State  &  \multicolumn{2}{c}{ }  \\
\hline
X ($^2\Sigma$)      & $R_\mathrm{(Ra-O)} $     & 2.38  &  & A ($^2\Pi$)       &  $R_\mathrm{(Ra-O)}$    & 2.35     \\
                              & $R_\mathrm{(O-H)} $        & 0.94  &    &                       & $R_\mathrm{(O-H)}$    & 0.94           \\
                              & $\angle$ Ra-O-H               &  180.0 &   &                      &  $\angle$ Ra-O-H            & 180.0     \\
                              & $|D|$                                &  2.09  &      &                      & $|D|$                            &   1.70        \\
                             &                                         &             &     &                       & $T_\mathrm{e}$            &  12.0$\times$10$^{3}$     \\
                              \hline
\multicolumn{3}{c|}{Normal modes $\nu_l$}  & & \multicolumn{3}{c}{Normal modes $\nu_l$}   \\
X ($^2\Sigma$)     &  $\nu_3(\mathrm{\sigma}^+)$        &  4243  &    & A ($^2\Pi$)      & $\nu_3(\mathrm{\sigma}^+)$     &   4248    \\
                              &  $\nu_1(\mathrm{\sigma}^+)$        & 437     &      &              & $\nu_1(\mathrm{\sigma}^+)$          &  461      \\
                              &  $\nu_2(\mathrm{\pi})$                &  366/366  &      &           &  $\nu_2(\mathrm{\pi})$               & 383/383         \\
   \multicolumn{7}{c}{FC factors ~~ 0.9050\footnote{0$^{0}_{0}$}, 0.0922\footnote{1$^{0}_{1}$ Ra$-$OH stretching}, 0.0025\footnote{1$^{0}_{2}$ Ra$-$OH stretching}}         \\
     \multicolumn{7}{c}{$\sum >$ 0.99}     \\
                             \multicolumn{3}{c|}{{\sc sf/fs-rccsd}} & &  \multicolumn{3}{c}{{\sc dc/fs-rccsd}}  \\
 X ($^2\Sigma$)      & $R_\mathrm{(Ra-O)} $     & 2.30  &    & A ($^2\Sigma_{1/2}$)       &  $R_\mathrm{(Ra-O)}$    & 2.30    \\
 A ($^2\Pi$)             & $R_\mathrm{(Ra-O)} $     & 2.29  &    & A ($^2\Pi_{1/2}$)         &  $R_\mathrm{(Ra-O)}$    & 2.29    \\
                             &    $T_\mathrm{e}$              &    13.8$\times$10$^{3}$  &     &             & $T_\mathrm{e}$            &  12.6$\times$10$^{3}$     \\
\hline

\end{tabular}
\end{table*}%

\section*{Quasirelativistic calculations of P- and P,T-odd parameters}

We have previously derived the expressions for matrix elements of the $\cal P$-odd~ and $\cal P,T$-odd~ operators in
quazirelativistic Zero-Order Regular Approximation (ZORA) framework (see \cite{Isaev:2012} and
references therein) and related them to the corresponding
effective operators in polyatomic molecules with open shells.
Our previous calculations of $\cal P$-odd~ nuclear spin-dependent and $\cal P,T$-odd~ properties for diatomic molecules
within Generalized Hartree-Fock (GHF)
approach \cite{Isaev:2012} were later confirmed in
fully-relativistic four-component Dirac-Hartree-Fock (DHF) calculations \cite{borschevsky:2012, borschevsky:2013}.
It turned out that the difference between values of the $\cal P$-odd~ parameters in ZORA and four-component calculations
does not exceed 5\% (see \cite{borschevsky:2013}).
High-precision FS-RCC calculations of $\cal P$-odd~ and $\cal P,T$-odd~ molecular parameters for RaF
molecule \cite{kudashov:2014} are also in a good agreement with our previous estimates of influence of electronic correlation
on these parameters.

\begin{table*}[h]
\caption{\label{pvterms} $\cal P$-odd~ and scalar $\cal P,T$-odd~ term in ZORA Hamiltonian. The superscripts of $z$ denote
orders of the corrseponding ZORA terms on nuclear spin and $\cal P$-odd~ ($\cal P,T$-odd~) coupling constants.}
 \begin{tabular*}{12cm}{lll}
 Term         & Name  & Expression \\
  \hline
  ~\\
   \multicolumn{3}{c}{$\cal P$-odd~ terms}  \\
 $z^{(0,1)}_\mathrm{s}$       & Scalar $\cal P$-odd~ interaction &
 $\displaystyle\frac{G_\mathrm{F}}{2\sqrt{2}} Q_A \lbrace\vec{\bm{\sigma}}\cdot \vec{p},
\frac{\tilde{\omega}}{c} \rho_A(\vec{r}) \rbrace$ \vspace{2mm} \\
 $z^{(1,1)}_\mathrm{hf}$      &    Scalar $\cal P$-odd~  / hyperfine P-even interaction  &
 $\displaystyle\frac{G_\mathrm{F}}{2\sqrt{2}} Q_A \lbrace e\, \vec{\bm{\sigma}}\cdot\vec{A}_{\mu}(\vec{r}),\frac{\tilde{\omega}}{c} \rho_A (\vec{r})\rbrace$\vspace{2mm}\\
 $z^{(1,1)}_\mathrm{sd}$& Nuclear spin-dependent $\cal P$-odd~ interaction &
 $\displaystyle\frac{G_\mathrm{F}}{2\sqrt{2}} 2 k_{{\cal
A},A}\lbrace\vec{\bm{\sigma}}\cdot\vec{p}, \frac{\tilde{\omega}}{c}
 \vec{\bm{\sigma}}\cdot \vec{I}_A \rho_A (\vec{r}) \rbrace$ \vspace{2mm}\\
$z^{(2,1)}_\mathrm{sdr}$& Nuclear spin-dependent $\cal P$-odd~ / &
 $\displaystyle\frac{G_\mathrm{F}}{2\sqrt{2}} 2 k_{{\cal A},A}
\lbrace e\, \vec{\bm{\sigma}}\cdot\vec{A}_{\mu}(\vec{r}) , \frac{\tilde{\omega}}{c}
 \vec{\bm{\sigma}}\cdot \vec{I}_A \rho_A (\vec{r}) \rbrace$ \\
  & hyperfine P-even interaction & \\
 \hline
~\\
\multicolumn{3}{c}{Scalar $\cal P,T$-odd~ term}  \\
$z^{(0,1)}_\mathrm{\cal SP} $ & Scalar $\cal P,T$-odd~ interaction   & $\mathrm{i}\displaystyle\frac{G_\mathrm{F}}{2\sqrt{2}}2k_\mathrm{{\cal SP},A} Z_{A}[\vec{\bm{\sigma}}\cdot \vec{\bm{p}},\frac{\tilde{\omega}}{c}\rho_A(\vec{r})]$ \\
\end{tabular*}
\end{table*}

Here we briefly outline the fully-relativistic (four-component) operators describing nuclear spin-dependent $\cal P$-odd~ ($\cal NSD-PV$~)
and scalar $\cal P,T$-odd~ electron-nucleus
interactions and provide the corresponding expression within ZORA in \tref{pvterms} (omitting the response terms).
For detailed discussion on $\cal P$-odd~ and $\cal P,T$-odd~
terms in quasirelativistic approximation see e.g. \cite{berger:2005, nahrwold:09} and \cite{Isaev:2012, Isaev:2013}.
We use atomic units unless other is stated explicitly.

The nuclear spin-dependent $\cal P$-odd~ and scalar $\cal P,T$-odd~ operators in four-component
formalism can be written as:
\begin{eqnarray}
 H_\mathrm{\cal SD-PV}=\frac{G_\mathrm{F}}{\sqrt{2}}\sum_{A,i} k_{{\cal A},A}{\vec{\bm{\alpha}}}(i)\cdot \vec{\bf I}_A \rho_A (\vec{r_i}), \\
 H_\mathrm{\cal SP}=\mathrm{i}\frac{G_\mathrm{F}}{\sqrt{2}}\sum_{A,i} k_{\mathrm{\cal SP},A} Z_{A} \bm{\gamma}_0 (i) \bm{\gamma}_5 (i) \rho_A(\vec{r_i}),
 \label{4c-oper}
\end{eqnarray}
where $G_\mathrm{F}=2.22254\times 10^{-14}$a.u. is Fermi's constant of the weak interaction,
$k_{{\cal A},A}$ is an effective parameter describing
$\cal NSD-PV$~ interactions for nucleus $A$ (caused both by the nuclear anapole moment
\cite{zeldovich:1957,zeldovich:1958,flambaum:1980} and by weak electron-nucleon
interactions \cite{Novikov:1977}), $k_{\mathrm{\cal SP},A}$ is a dimensionless coupling constant describing scalar
 $\cal P,T$-odd~ interaction for nucleus $A$,
$\vec{\bf I}_A$ and $\rho_A$ are the spin and
normalized nuclear density distribution
of nucleus $A$, respectively,
$\bm{\gamma}_0$ and $\bm{\gamma}_5$ are the Dirac $\gamma$-matrices and $\vec{\bm{\alpha}}$ is a vector
of Dirac's $\alpha$-matricies. The summation goes over all nuclei $A$ and electrons $i$.
In \tref{pvterms}, $Q_A$ is the weak charge of nucleus $A$,
$Q_A=N_A-(1-4\sin^2\theta_\mathrm{W})Z_A$,
where $N_A$ is the number of neutrons in nucleus $A$, $Z_A$ the nuclear
charge, $\sin^2\theta_W$ the Weinberg parameter, for which we employ the
numerical value $\sin^2\theta_\mathrm{W}=0.2319$, and
$\vec{A}_{\mu}$ is the magnetic vector potential from the point-like
nuclear magnetic moments $\vec{\mu}_A = \gamma_A \vec{I}_A$ with
$\vec{A}_{\mu}(\vec{r})= \sum_A \vec{\mu}_A\times
(\vec{r}-\vec{R_A})/(|\vec{r}-\vec{R_A}|)^3$, $\gamma_A$ being the
gyromagnetic ratio,
$\lbrace x,y \rbrace = xy + yx$ is the anticommutator and $[x,y] = xy - yx$
is the commutator. The ZORA factor $\tilde{\omega}$ is also used, $\tilde{\omega}
=1/\left(2-{\widetilde{V}}/c^{2}\right)$, where $\widetilde{V}$
is the model potential (with additional damping \cite{liu:2002}) proposed
in \cite{wullen:1998}, which alleviates the gauge-dependence
of ZORA.

Our ZORA/GHF values (obtained for equilibrium geometry from {\sc ARECP} RaOH calculations)
for  $|W_\mathrm{a}|$ is 1.4$\times$10$^3$ Hz and for  $W_\mathrm{s}$ is 154$\times$10$^3$ Hz.
These values are rather close to the values of the corresponding parameters for RaF from
\cite{Isaev:2013, kudashov:2014}. This is not surprising,
taking into the consideration that
the main contribution to the regarded parameters in both cases comes from the unpaired electron
located on non-bonding molecular
orbital centered on Ra.

\section*{Conclusion}
We propose RaOH as a polyatomic molecule containing
heavy nucleus, particularly suitable for highly effective cooling with lasers.
Using recently developed method for computation of transition matrix elements we calculate
transition dipole moments for cooling transitions for RaOH and estimate Doppler limit
temperature. For the first time $\cal P$-odd~ and $\cal P,T$-odd~ properties are calculated for triatomic molecule
with open electronic shells.
Some other polyatomic molecules and ions with heavy nuclei
may be also proposed for direct cooling with lasers
according to the the scheme suggested by us in previous articles.
\section*{Supplementary material}
See supplementary material for the details on electronic structure calculations (basis sets, methods etc)
and extended sets of molecular parameters.
\section*{Acknowledgements}
We are indebted to Prof. R. Berger for providing us with the code hotFCHT for calculations of Franck-Condon factors
in polyatomic molecules. T. I. is especially grateful to R. Berger for numerous insightful discussions during
joint work on calculations of $\cal P$-odd~ and $\cal P,T$-odd~ properties for molecules
with open electronic shells and implementing the routines for calculations of these properties withing tm2c code.
We are thankful for Dr. Yu. V. Lomachuk and Dr. Yu. A. Demidov for technical help.
Financial support by RFBR (grants N 16-02-01064 and N 16-03-00766) and computer time
provided by the Center for
Scientific Computing (CSC) Frankfurt is gratefully acknowledged.

redpajama_set_name: RedPajamaArXiv


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text:
0 Introductory Material
0.1 Inverse Trigonometric Functions
0.2 Derivatives of Inverse Trigonometric Functions
0.3 L'Hôpital's Rule
1 Integration
1.1 Approximating Areas
1.2 The Definite Integral
1.3 The Fundamental Theorem of Calculus
1.4 The Net Change Theorem and Integrals of Symmetric Functions
1.5 Substitution
2 Applications of Integration
2.1 Areas between Curves
2.2 Determining Volumes by Slicing
2.3 Volumes of Revolution: Cylindrical Shells
2.4 Arc Length of a Curve and Surface Area
3 Techniques of Integration
3.1 Integration by Parts
3.2 Trigonometric Integrals
3.3 Trigonometric Substitution
3.4 Partial Fractions
3.7 Improper Integrals
7 Parametric Equations and Polar Coordinates
7.1 Parametric Equations
7.2 Calculus of Parametric Curves
7.3 Polar Coordinates
7.4 Area and Arc Length in Polar Coordinates
Table of Derivatives
Review of Pre-Calculus
Calculus: Volume 2 (Second University of Manitoba Edition)
Determine the length of a curve with equation between the two given points.
Find the surface area of a surface of revolution.
In this section, we use definite integrals to find the arc length of a curve. We can think of arc length as the distance you would travel if you were walking along the path of the curve. Many real-world applications involve arc length. If a rocket is launched along a parabolic path, we might want to know how far the rocket travels. Or, if a curve on a map represents a road, we might want to know how far we have to drive to reach our destination.
We begin by calculating the arc length of curves defined as functions of then we examine the same process for curves defined as functions of (The process is identical, with the roles of and reversed.) The techniques we use to find arc length can be extended to find the surface area of a surface of revolution, and we close the section with an examination of this concept.
Arc Length of the Curve y=f(x)
In previous applications of integration, we required the function to be integrable, or at most continuous. However, for calculating arc length we have a more stringent requirement for Here, we require to be differentiable, and furthermore we require its derivative, to be continuous. Functions like this, which have continuous derivatives, are called smooth . (This property comes up again in later chapters.)
Let be a smooth function defined over We want to calculate the length of the curve from the point to the point We start by using line segments to approximate the length of the curve. For let be a regular partition of Then, for construct a line segment from the point to the point Although it might seem logical to use either horizontal or vertical line segments, we want our line segments to approximate the curve as closely as possible. Figure 1 below depicts this construction for
Figure 1. We can approximate the length of a curve by adding line segments.
To help us find the length of each line segment, we look at the change in vertical distance as well as the change in horizontal distance over each interval. Because we have used a regular partition, the change in horizontal distance over each interval is given by The change in vertical distance varies from interval to interval, though, so we use to represent the change in vertical distance over the interval as shown in Figure 2 below. Note that some (or all) may be negative.
Figure 2. A representative line segment approximates the curve over the interval
By the Pythagorean theorem, the length of the line segment is We can also write this as Now, by the Mean Value Theorem, there is a point such that Then the length of the line segment is given by Adding up the lengths of all the line segments, we get
This is a Riemann sum. Taking the limit as we have
We summarize these findings in the following theorem.
Arc Length for y=f(x)
Let be a smooth function over the interval Then the arc length of the portion of the graph of from the point to the point is given by
Note that we are integrating an expression involving so we need to be sure is integrable. This is why we require to be smooth. The following example shows how to apply the theorem.
Calculating the Arc Length of a Function of x
Let Calculate the arc length of the graph of over the interval
We have so Then, the arc length is
Substitute Then, When then and when then Thus,
Use the process from the previous example. Don't forget to change the limits of integration.
Although it is nice to have a formula for calculating arc length, this particular theorem can generate expressions that are difficult to integrate. We study some techniques for integration in the subsequent chapters of this text. Before we know them, we may have to stop after setting up the integral.
Setting Up the Integral for the Arc Length of a Function of x
Let Set up the integral for the arc length of the graph of over the interval
We have so Then the arc length is given by
Use the process from the previous example.
Arc Length of the Curve x=g(y)
We have just seen how to approximate the length of a curve with line segments. If we want to find the arc length of the graph of a function of we can repeat the same process, except we partition the y-axis instead of the x-axis. Figure 3 below shows a representative line segment.
Figure 3. A representative line segment over the interval
Then the length of the line segment is which can also be written as If we now follow the analogous steps to what we have done before, we get a formula for arc length of a function
Arc Length for x=g(y)
Let be a smooth function over an interval Then, the arc length of the graph of from the point to the point is given by
Setting up the Integral for the Arc Length of a Function of y
We have so Then the arc length is
Area of a Surface of Revolution
The concepts we used to find the arc length of a curve can be extended to find the surface area of a surface of revolution. Surface area is the total area of the outer layer of an object. For objects such as cubes or bricks, the surface area of the object is the sum of the areas of all of its faces. For curved surfaces, the situation is a little more complex. Let be a nonnegative smooth function over the interval We wish to find the surface area of the surface of revolution created by revolving the graph of around the x-axis as shown in the following figure.
Figure 4. (a) A curve representing the function (b) The surface of revolution formed by revolving the graph of around the x-axis.
As we have done many times before, we are going to partition the interval and approximate the surface area by surface areas of simpler shapes. We start by using line segments to approximate the curve, as we did earlier in this section. For let be a regular partition of Then, for construct a line segment from the point to the point Now, revolve these line segments around the x-axis to generate an approximation of the surface of revolution as shown in the following figure.
Figure 5. (a) Approximating with line segments. (b) The surface of revolution formed by revolving the line segments around the x-axis.
Notice that when each line segment is revolved around the axis, it produces a band. These bands are actually pieces of cones (think of an ice cream cone with the pointy end cut off). A piece of a cone like this is called a frustum of a cone.
To find the surface area of the band, we need to find the lateral surface area, of the frustum (the area of just the slanted outside surface of the frustum, not including the areas of the top or bottom faces). Let and be the radii of the wide end and the narrow end of the frustum, respectively, and let be the slant height of the frustum as shown in the following figure.
Figure 6. A frustum of a cone can approximate a small part of surface area.
We know the lateral surface area of a cone is given by
where is the radius of the base of the cone and is the slant height (see the following figure).
Figure 7. The lateral surface area of the cone is given by
Since a frustum can be thought of as a piece of a cone, the lateral surface area of the frustum is given by the lateral surface area of the whole cone less the lateral surface area of the smaller cone (the pointy tip) that was cut off (see the following figure).
Figure 8. Calculating the lateral surface area of a frustum of a cone.
The cross-sections of the small cone and the large cone are similar triangles, so we see that
Solving for we get
Then the lateral surface area (SA) of the frustum is
Let's now use this formula to calculate the surface area of each of the bands formed by revolving the line segments around the x-axis. A representative band is shown in the following figure.
Figure 9. A representative band used for determining surface area.
Note that the slant height of this frustum is just the length of the line segment used to generate it. So, applying the surface area formula, we have
Now, as we did in the development of the arc length formula, we apply the Mean Value Theorem to select such that This gives us
Furthermore, since is continuous, by the Intermediate Value Theorem, there is a point such that so we get
Then the approximate surface area of the whole surface of revolution is given by
This almost looks like a Riemann sum, except we have functions evaluated at two different points, and over the interval Although we do not examine the details here, it turns out that because is smooth, if we let the limit works the same as a Riemann sum even with the two different evaluation points. This makes sense intuitively. Both and are in the interval so it makes sense that as both and approach Those of you who are interested in the details should consult an advanced calculus text.
Taking the limit as we get
As with arc length, we can conduct a similar development for functions of to get a formula for the surface area of surfaces of revolution about the These findings are summarized in the following theorem.
Surface Area of a Surface of Revolution
Let be a nonnegative smooth function over the interval Then, the surface area of the surface of revolution formed by revolving the graph of around the x-axis is given by
Similarly, let be a nonnegative smooth function over the interval Then, the surface area of the surface of revolution formed by revolving the graph of around the y-axis is given by
Calculating the Surface Area of a Surface of Revolution 1
Let over the interval Find the surface area of the surface generated by revolving the graph of around the x-axis.
The graph of and the surface of rotation are shown in the following figure.
Figure 10. (a) The graph of (b) The surface of revolution.
We have Then, and Then,
Let Then, When and when This gives us
Let Consider the portion of the curve where Find the surface area of the surface generated by revolving the graph of around the y-axis.
Notice that we are revolving the curve around the y-axis, and the interval is in terms of so we want to rewrite the function as a function of . We get The graph of and the surface of rotation are shown in the following figure.
We have so and Then
Let Then When and when Then
Let over the interval Find the surface area of the surface generated by revolving the graph of around the y-axis.
The arc length of a curve can be calculated using a definite integral.
The arc length is first approximated using line segments, which generates a Riemann sum. Taking a limit then gives us the definite integral formula. The same process can be applied to functions of
The concepts used to calculate the arc length can be generalized to find the surface area of a surface of revolution.
The integrals generated by both the arc length and surface area formulas are often difficult to evaluate.
Key Equations
Arc Length of a Function of x
Arc Length of a Function of y
Surface Area of a Function of x
For the following exercises, find the length of the curve with the given equation over the specified interval.
4. Pick an arbitrary linear function over any interval of your choice Determine the length of the corresponding curve with calculus and then verify the answer is correct by using geometry.
5. Find the surface area of the surface generated when the curve from to revolves around the x-axis, as shown below.
6. Find the surface area of the surface generated when the curve from to revolves around the y-axis.
For the following exercises, find the lengths of the given curves. If you cannot evaluate the integral, leave your answer in the integral form (set up).
7. from
(Hint: rewrite the equation of the curve in the form .)
10. from to
11. [Set Up] on to
12. from
16. [Set Up] from
20. [Set Up] from to
For the following exercises, find the surface area of the surface generated when the given curve revolves around the x-axis. If you cannot evaluate the integral, leave your answer in the integral form (set up).
For the following exercises, find the surface area of the surface generated when the given curve revolves around the y-axis. If you cannot evaluate the integral, leave your answer in the integral (set up) form.
43. The base of a lamp is constructed by revolving a quarter circle around the y-axis from to as shown below. Set up an integral for the surface area of the base of the lamp and compute it.
44. A light bulb is a sphere with radius in. with the bottom sliced off to fit onto a cylinder of radius in. and hight in., as shown below. The sphere is cut off at the bottom to fit exactly onto the cylinder, so the radius of the cut is in. Find the surface area of the light bulb (not including the top or bottom of the cylinder).
45. [Set Up] A lampshade is constructed by rotating a curve around the y-axis from to as shown below. Set up an integral for the amount of material you would need to construct this lampshade, that is, its surface area.
46. [Set Up] An anchor drags behind a boat according to the function where represents the depth beneath the boat and is the horizontal distance to the anchor from the back of the boat. If the anchor is 23 ft below the boat, set up the integral to determine how much rope you have to pull to reach the anchor.
47. [Set Up] You are building a bridge that will span 10 ft. You intend to add decorative rope in the shape of where is the distance in feet from one end of the bridge. Set up the integral to determine how much rope you need.
48. Find the arc length of the curve from to
(Hint: Recall trigonometric identities.)
the arc length of a curve can be thought of as the distance a person would travel along the path of the curve
a portion of a cone; a frustum is constructed by cutting the cone with a plane parallel to the base
the surface area of a solid is the total area of the outer layer of the object; for objects such as cubes or bricks, the surface area of the object is the sum of the areas of all of its faces
Previous: 2.3 Volumes of Revolution: Cylindrical Shells
Next: Introduction
Calculus: Volume 2 (Second University of Manitoba Edition) by Gilbert Strang and Edward 'Jed' Herman, modified by Varvara Shepelska is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

redpajama_set_name: RedPajamaCommonCrawl


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JasonBourne had the most liked content!
Is there anything like this for Air?
It is nice to know and see that community suggested features can make it into new releases. I, in particular, am very satisfied that the app is now aware of concurrent VPN use. I have tested with OpenVPN for Android and Adguard and the OS correctly revokes from any already running VPN application the permission to operate the VPN connection. The developers had considered this for a future Eddie version since 2.0 and have now delivered with 2.1. Bravo. Well done!
Hello! We can't reproduce the issue: we see no difference between "Quick" and "Server" connection views reports. However we are not sure we have understood correctly what you mean. Would you like to elaborate? Kind regards This has now been resolved in version 2.0.1. Correct profiles now showing in "Quick" and "Server" connection views reports and is correct even in the account "Client Area"
For your consideration [i know I am sweating the small stuff now ] Are the following pop-ups entirely necessary? For me this is what the CONNECTION -tab is already giving me. It saves another finger-press acknowledging the popup OK-button. Besides for those who like the extra acknowledgement; that's what Eddie Notifications can do for you already. Urgent Make sound and pop up on screen I'll admit this is just cosmetics. Or is it?
Two devices (profiles): - Laptop - Mobile Phone The Profile drop-down box on QUICK CONNECT -tab is correct: I choose Mobile Phone --> Quick Connect --> Profile: Mobile Phone on CONNECTION -tab BUT The Profile drop-down box under cogwheel on AIRVPN SERVER -tab reverses the values: I choose Mobile Phone --> Connect Server --> Profile: Laptop on CONNECTION -tabI choose Laptop --> Connect Server --> Profile: Mobile Phone on CONNECTION -tabMinor cosmetic error, perhaps some string parameter(s) got reversed in code. The behaviour described above is also observed in on-line Client Area of the AirVPN website.
Profile option within 'AirVPN Server Settings' values are reversed when connecting from AIRVPN SERVER -tab However the QUICK CONNECT -tab Profile option shows correctly in CONNECTION -tab. For example: when set to 'Mobile Phone' it shows up as 'Laptop' in CONNECTION -tab. And when set as 'Laptop' it shows as 'Mobile Phone'. The values are reversed.
Nice! Thank you, signed up for 2 more years. Best VPN service on the planet.
I concur, thank you to the development team for progress made till date. Compatibility with AdGuard is an issue as it does not get paused automatically or incorrectly when the 'Connect' -button in Eddie is pressed. Through some testing of my own AdGuard gets paused - when Eddie application opens or takes the focus however - when the 'Connect' -button is pressed AdGuard resumes and Eddie reports VPN has been locked. In comparison OpenVPN for Android does not pause AdGuard any earlier than when VPN profile gets selected. I.e. just opening the OpenVPN for Android does not pause AdGuard; selecting a profile for connection does.
I am wondering about the exact same behaviour too (Linux Mint 18.3 x86_64 | Eddie 2.15.2) And I am also fairly sure Eddie did not show this behaviour previously. This is unusual, maybe a bug? Thank you.
Hello! Thank you for addressing this security 'flaw' affecting Windows firefox, chrome and opera web browsers. And also thank you for the quick addition of the WebRTC detection check to ipleak.net. Alternatively, Chrome users can install the ScriptSafe extension and Firefox users could block the request with the NoScript addon, which both reportedly block the vulnerability. Opera users can download this plugin that will allow them to download and use Google Chrome add-ons.
Apologies Air, my bad. I am new to AirVPN and Eddie, I wrongly believed RC3 and 2.8.6 to be the same. I was already on 2.8.6. Hence the minor bug and my question remain the same as per my previous post. Any one who can comment on how to use 'Routes' to put hosts by zone name in 'Outside tunnel'. Is this possible? Or some one can advise how I can put all my e-mail traffic (imap, imaps, pop3, smtp) in 'Outside tunnel'. I thought that this could be done in 'Routes' but maybe I am not understanding correctly. Thank you.


Organizers hope to raise $200,000 after once-separate Relay for Life events merged in Canton, Plymouth.
The merger of cancer-fighting Relay for Life events in Canton and Plymouth appears to have spurred renewed interest in forming teams to raise money, officials say.
More than 50 teams aiming to raise $200,000 have surpassed the $80,000 mark. They are ahead of their collective fundraising efforts compared to last year, when Canton and Plymouth had separate events.
"They are tracking ahead, year over year," said Megan Schaper, Relay for Life community manager. "The fundraising is going really well. Things feel really good. There's a lot of energy we haven't felt in a long time. We have momentum."
Teams hope to raise as much money as possible by the time Relay for Life happens 10 a.m. to midnight Saturday, May 20, in Canton's Heritage Park. However, Schaper said fundraising will continue through fall, when the Plymouth-Canton Educational Park has its event.
Hundreds of area residents are expected to attend Relay and raise money for the American Cancer Society. It is free to attend and open to the public.
"Relay For Life is a chance to make the greatest impact in the fight to end cancer," said Denise Staffeld, co-chair of Relay for Life of Canton and Plymouth. "Many participants are loved ones who have faced cancer themselves, as well as groups coming together to fight back in memory of those they have lost.
"Each new team brings us one step closer to saving more lives and we simply cannot finish the fight without every dedicated cancer fighter," she added.
Relay, founded in 1985 by Dr. Gordy Klatt in Washington, is the world's largest fundraising event to save lives from cancer. Organizers say it unites communities across the globe, celebrating survivors, remembering lost loved ones and spurring action for change.
On May 20, Relay participants will take turns walking around the pond in Heritage Park. They already had begun their fundraising months leading up to the event. The local Relay is sponsored by Adient, Canton Township and Meijer.
The money helps the American Cancer Society provide free information and support for people facing the disease and also helps to pay for cancer research. The ACS has invested more than $4.3 billion in research since 1946 and funded more than 20,000 scientists at more than 1,000 institutions nationwide, officials say.
Organizers are inviting cancer survivors, their families and caregivers to kick off the Canton-based Relay with an opening lap at 10 a.m. May 20. Registration begins at 9 a.m. Afterward, cancer survivors and one guest are invited to a complimentary luncheon by Outback Steakhouse of Canton.
Event parking is available at nearby locations, including St. Joseph Mercy Health System's cancer center in Canton, the Canton Public Library, Summit on the Park and the Canton Administration Building. A shuttle service for survivors who need assistance will be provided by St. Joseph at 1600 S. Canton Center.
Relay will include family friendly entertainment, activities and food. A "kids zone" will be happening from noon to 3 p.m., with a tinkering workshop by Home Depot, photo opportunities with fire trucks and police cars and trick-or-treating 2-3 p.m. Attendees are encouraged to dress up as their favorite superhero.
For more information, go to RelayForLife.org/CantonPlymouthMI or contact Megan Shaper at 248-663-3417 or by email at Megan.Schaper@cancer.org.


text:
layout: page
title: "Amanda Kathy Johnson"
comments: true
description: "blanks"
keywords: "Amanda Kathy Johnson,CU,Boulder"
---
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<script src="https://dl.dropboxusercontent.com/s/pc42nxpaw1ea4o9/highcharts.js?dl=0"></script>
<!-- <script src="../assets/js/highcharts.js"></script> -->
<style type="text/css">@font-face {
	font-family: "Bebas Neue";
	src: url(https://www.filehosting.org/file/details/544349/BebasNeue Regular.otf) format("opentype");
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		font-family: "Bebas Neue", Verdana, Tahoma;
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#### TEACHING INFORMATION

**College**: College of Architecture and Planning

**Classes taught**: ENVD 1052, ENVD 1102, ENVD 2120

#### ENVD 1052: Design and Communication 1

**Terms taught**: Fall 2011, Fall 2012, Fall 2013

**Instructor rating**: 4.68

**Standard deviation in instructor rating**: 0.66

**Average grade** (4.0 scale): 3.11

**Standard deviation in grades** (4.0 scale): 0.24

**Average workload** (raw): 4.67

**Standard deviation in workload** (raw): 0.48

#### ENVD 1102: Design and Communication 2

**Terms taught**: Spring 2013, Spring 2013

**Instructor rating**: 4.82

**Standard deviation in instructor rating**: 0.1

**Average grade** (4.0 scale): 3.0

**Standard deviation in grades** (4.0 scale): 0.03

**Average workload** (raw): 5.07

**Standard deviation in workload** (raw): 0.7

#### ENVD 2120: Environmental Design Studio 1

**Terms taught**: Fall 2013, Fall 2015

**Instructor rating**: 4.54

**Standard deviation in instructor rating**: 0.79

**Average grade** (4.0 scale): 3.28

**Standard deviation in grades** (4.0 scale): 0.12

**Average workload** (raw): 5.5

**Standard deviation in workload** (raw): 0.14

redpajama_set_name: RedPajamaGithub


text:
Q: How to rename SWIGTYPE_p... to something more friendly? I have a c++ function returning an uint8_t* array like:
uint8_t* getData();

Swig maps this to a SWIGTYPE_p_unsigned_char. I would like a more friendly name. In my .i file I have simply included my h file containing the code above. I have tried %rename but it doesnt work:
%rename (SWIGTYPE_p_unsigned_char) u8_t;
%include "myhfile.h"

How do I force Swig to rename my type (or solve it some other way)?

A: In the general case you can rename SWIGTYPE_p_... using an empty definition to get it wrapped as an opaque "handle".
This specific instance looks like you've got one of the standard typedefs. You can still do as in the linked answer, e.g.:
%module test

%{
#include <stdint.h>
%}

typedef struct {
} uint8_t;

%inline %{
  uint8_t *getData() {
    static uint8_t d[5];
    return d;
  }
%}

Which loses the SWIGTYPE_ prefix and can be used as:
public class run {
  public static void main(String[] argv) {
    System.loadLibrary("test");
    test.getData();
  }
}

However that's not ideal:

*

*There's no access to the array being returned (you probably want to access that data in Java rather than just pass it around)

*More seriously it will interfere with any other arrays you have  in the same interface and possibly even with string handling

A better solution might be to use the SWIG carrays.i interface to wrap it and use an unbounded array class to exactly replicate the behaviour you would have in C++:
%module test

%{
#include <stdint.h>
%}

%include <stdint.i>
%include <carrays.i>

%array_class(uint8_t, U8_Array);

%typemap(jstype) uint8_t *getData "U8_Array"
%typemap(javaout) uint8_t *getData {
  return new $typemap(jstype,uint8_t *getData)($jnicall,$owner);
}

%inline %{
  uint8_t *getData() {
    static uint8_t d[5];
    return d;
  }
%}

Your return type will now come from carrays.i and have a getitem and setitem method.
You can actually use the jstype and javaout typemaps to map the result (the pointer cast to a long) onto any Java type, it doesn't have to come from carrays.i just that happens to be quite a useful case. Or you could write come JNI code that returns it as a Java array directly if you're so inclined.
If you know a priori the size of the array you can take steps to wrap it as a bounded instead of unbounded array in Java, e.g. by implementing AbstractList.

redpajama_set_name: RedPajamaStackExchange


Long lost WWII diagrams of … exploding chocolate bars?
You're more likely to die from a selfie than a shark attack.
Surreal pond installation by Belgian duo.
Powerful images of women boxers in NYC.
For your inner Type A: food arranged in perfect pyramids.
Creative duo Ciurej and Lochman create fantastical landscapes made of everyday processed foods.
Get lost in this hypnotic dream world set to soothing electronic music.
Mesmerizing geometric paintings by Pavel Hayek.
A breathtaking labyrinth home, four decades in the making.
Swedish design studio Tomorrow Machine is pushing the boundaries of package design.


The versatility and elegance of the diamond bracelet design makes it a must for any jewelry wardrobe. These twenty five sparkling round brilliant cut diamonds of 0.24 ct. (Tw.) are prong set in lustrous 10k yellow gold and finished with a secure safety clasp.


text:
Q: Upload more than 4 GB file into .net Core 5 API What i have  tried :
<system.webServer>
< security >
  < requestFiltering >
    < requestLimits maxAllowedContentLength="4294967295" / >
  </ requestFiltering >
</ security>

</system.webServer>
and
services.Configure<FormOptions>(o =>
        {o.ValueLengthLimit = int.MaxValue;
            o.MultipartBodyLengthLimit = 4294967295;
            o.MemoryBufferThreshold = int.MaxValue;
        });
        services.Configure<IISServerOptions>(options => {
            options.MaxRequestBodySize = 4294967295;
        });

but its limited to 4 gb.. but my client wan to transfer file of 16 gb through this Rest API. i doubt that. is it possible ?


Interested in saving time and money for your district?
Three members of the ASBSD Board of Directors appeared on this weekend's Inside Keloland to discuss the teacher shortage. Director Tom Farrell of Madison, Director Kathy Greeneway of Yankton and Past President Denise Lutkemier of Wilmot shared information on how the shortage has impacted their district. You can watch the segment here.


text:
« How Wenger Used the Doom and Gloomers to his advantage
"A towel has immense psychological value" (Douglas Adams)* »
Arsenal should be more like Man U
by Simon Bailey
My mum hates football.
She loves racing, athletics, tennis, snooker, rugby, just not football. But within her dislike of football is her loathing of anything Manchester United.
Even as a dedicated non supporter of football, my mum, I am proud to say, is an ABU. Anyone but united. Whilst they were capturing the Asian markets and building their global brand and bank balance, back home they were the team we all wanted to see lose. Except for the United fans themselves of course.
But while the groundswell of public opinion was undeniably anti-United, the press were always friendly to the point of obsequiousness. United and their British manager and players could do no wrong. The water had been walked on.
Now that United are in decline in terms of global brand and bank balance, Arsenal have emerged as a club with a very good global profile, and a very healthy financial situation. The appointment of Gazidis was inspired and things are so finely tuned that the current membership of the board and shareholders are poised to rebuff any potential hostile takeover.
As United were building their brand, they inevitably did it on the back of good performances on the field and league tables. This is the yeast that rose their bread. Sold out fixtures every week and a unified fan base that loved everything about their club completed the list of ingredients.
If we visit the United bakery today, we can see that many of the ingredients needed are out of stock. There is no doubting their position in the league right now, but their onfield performances have been nothing short of woeful. Rooney aside. Yes, the measure of a good team is to grind out results regardless of how well the game was played, but there is no doubt that they are a shadow of their former selves.
As for sold out grounds and fan unity and complacency, it's all too obvious that the fans really hate the Glazers and tickets at United have never been so easy to get hold of. There's a report in the press today that they are now doing telephone selling of unsold tickets to fans.
Back in London, things are looking rosier . It's true that there are empty seats at the Emirates sometimes, and that there is a section of our support who do not support, but unlike at United our lot are the minority and they're wrong. Whilst our D and Gers are unquestionably lunatics, the equivalent bunch at Manchester United have plenty of reasons to be worried. 710 million to be precise.
The British press have a long tradition of building up celebrity only to knock it down at the most unfortunate moment. Almost every famous person or organisation has been held on the pedestal until a suitably juicy story comes along.
They are also fiercely patriotic. The Scottish press slagging the English, the Welsh press slagging the English, the Irish press slagging the English, and the English slagging everybody especially if you have to go by boat or plane to get there.
So the pendulum has swung. Arsenal are now the football model to be envied and emulated. Our refusal to waste untold cash, our resistance to boardroom change coupled with exquisite on field performances and positive results have made Arsenal the latest darling of the press. No hint of financial doping, transfer irregularities, tax avoidance or off field embarrassment. The spot on that pedestal is ours.
Except that it isn't. And never will be.
The way things have been going, and they look set to continue, it looks like the Arsenal aren't going to put a foot wrong. We may lose a few, get knocked out of some competitions, and not be top the league, but this is no longer enough for the press to whip us with. After all, it's been their line for years now.
And this is the point. Where was our build up? All I can remember is the press knocking chunks out of us for years now. This season it's been Eduardo diving, Chelsea leading us by 11 points and now Gallas and his evil boots.
We have to face the reality that the reality that the press portrays is not our reality. They are never going to like us, especially while we balance the books, employ so many foreigners and play such beautiful football.
The answer then is simple. Let's be more like United.
OFFICIAL ANNOUNCEMENT. You should also read the article on www.emiratesstadium.info, and it would do you no harm to read the Making the Arsenal blog either.
Just do it will you?
(Sorry I read the article and started to morph into a Man U steward. – Tony)
January 26th, 2010 | Category: Arsenal stories, Finances, Football & club strategies | 30 comments - (Comments are closed)
30 comments to Arsenal should be more like Man U
Uffffff… Imagine you wake up in morning and you suddenly find you are Manure fan. Imagine to date girl who have Rooney poster in room (hm I would really doubt what she id doing with me).
Imagine day in which they teach you God have wear number 7 on shirt, and imagine next morning you wake with image God leaving for Spain.
Imagine you 10 years believe you are best on earth and one day they jsut tell you, there is no money, and you have to leave your house…
Hm maybe we could organize some concert on Emirates for raising funds for saving Traford. Be a Gooner be a giver :):):)
Long live the mums of this world, Simon. 😉
You raise some very pertinent questions in your article holding a mirror where some people (from the press) can look at themselves.
The problem that the press is giving a false image of reality upon Arsenal wouldn't be a problem but helas so many fans really believe what the press is telling.
Some of those unfortunate souls end up in the D&G brigade not realising how much they are decieved by the press.
It is a handicap we have to live with and which can work against us but the way I know The Arsenal we will walk our way, undisturbed by the words in the press.
That is why I like this club so much. Apart from the trophy-side, but for the rest: Let us never be more like United.
Great article! I wonder what the press have left to turn to if/when Arsenal win the league this season. It'll probably be a media black-out, in terms of EPL news that is.
Arsesession
Armin – your imagination worries me. ….. wearing #7; hilarious stuff!
Simon, wonderful write up. Its easy to influence people – fans when they lack an understanding of the issue, combined with a media who use a formula for creating and controlling the talking points. Facts aren't relevant. (a big part of Rupert's marketing strategy)
The current media pundits, not likely to change. We must patiently wait for a other writers to elbow their way to the foreground.
Aniruddh
I live in India and until recently (last two years) I have not been up to date with the british press and articles that have been posted, was it the same back then when we were the invincibles or when we did the double? or has the anti-arsenal brigade a recent thing?
Interesting question Aniruddh. Though I am not most experienced gooner here, let me say as far as my remembrance goes back (and that's somewhere 1984), last 25 years sow some fierce anti-arsenalsiam as branch of sport journalism. From accusing us to play boring football (and forgive me God we did, at some point, but who didn't at that time)till being cheaters, week, foreigners, sellers and so and so.
But I guess explosion of blogging make it too obvious, because as we all know journalists and pundits aren't nothing else than "tribunes" telling what people like to hear or talking between each other.
Now you would have to go in psychological research to find why there is so many blogs "against" Arsenal. But it can be generalized as phenomena which came with generation grown on Instant Success made by Chelsea and Manure.
Of course there is lot to blame different Football manager games, in which players can post Clichy as CF and make him best scorer of league, and that such player take right to question Wenger logic because on computer he proved Clichy can be Forward. And make it crown evidence that Arsene is dilettante..
gunners lover
arsenal only pretends to play beautiful football, more often than not they are thrashed by more than ordinary physical teams..so no big deal about beautiful stuff.. as for the financial stability, it hardly matters as it is not brining in the quality we all demand. where s the keeper? silvestre as 3rd choice left back? no forward for the next 4 crucial games?
its all hypocritical nothing else.. arsenal has fooled us into believing in them..
but yet am a gooner.. call me fake but thats the truth!
Is "gunners lover" for real or just a joke post? I assume a joke post since it is hard to imagine stupidity like that revealing itself intentionally. But if it is a joke post, and surely it is, I had a chuckle at that.
Sir Tony
Now then, Gunners Lover… You said, and it is on the screen as I write this…
"more often than not they are thrashed by more than ordinary physical teams"..
They, refers to the Arsenal.
So, let's look at this "more often than not" bit. Arsenal are currently second in the league, and the top scorers.
Now I am not a mathematician, but I was fairly decent at maths at school, and it seems to me that if we where "thrashed" as you say, we would have a terrible goal difference, to balance out the goals we have scored making us second in the league. And yet, it seems, our goal difference is the same as Chelsea.
Let's try it another way. If Arsenal were thrashed more often than not then we would have lost more games than we won. So how could we even be in the top half of the league, let along be second?
No, no matter how I work this out, I reach the same conclusion. You are talking nonsense. Or maybe it is sense but as seen from a different part of north London.
And by the way, if we didn't have a keeper or centre forward, how come we moved from being way behind to second in the league?
(Actually I was going to point out that Bendtner is back but I suspect you equate him with Silvertre (who is actually 4th choice, not 3rd choice left back.
I think gunners lover is right. We only make our selves believe that we are in the top. Arsenal.com are just a bunch of lying cheets, as is all the other sites who keep the league table up to date.
In fact gunners lover is the only one in the universe that knows we are in the bottom 3 of the league… oh wait a minute, he held it upside down like you told us Tony… 😉
Darius Stone
Simon. Great article.
Speaking of family allegiances, I don't know whether to rejoice at the fact that my wife hates Man United with all her guts, or hide my face in shame because she's a die hard Chelsea supporter.
I guess it's true what they say about marriage being a compromise and finding common ground to work with and stuff like that.
Yeahhhhh! Lets be MORE like Man Utd!
http://www.telegraph.co.uk/finance/newsbysector/banksandfinance/7073774/Goldman-star-Jim-ONeill-attacks-Man-United-fund-raising.html
abiodun
"Arsenal has fooled us into believing in them"? And this from someone who claims to be gunnerslover? Please someone tell me this makes sense to them!
Are you all watching this so-called battle for Smalling unfold? Man Utd claim to have a bid accepted from Fulham but the word over at Young Guns is that we are willing to match their offer and are trying to gazump Fergie. The further fruitiness to this juice is that Smalling is a 'allegedly' a lifelong Arsenal fan.
Will this be a Ramsey situation all over again? I have never seen Smalling but I'd LMAO if Fergie got beaten to the punch again. TBH it'd be worth offering 2 million more than them, just to bump the price on poor cash-strapped Man Utd and see how they respond!
The bids are allegedly at about £8Million which does seem a lot but if both Arsene and Fergie say he is good the chances are he is good.
I can smell Lajic all over again tbh.. Manu bying some young prospect, postponing his arrival and "suddenly" deciding he is not good enough and deal. The deal is off. How anyone can conduct big buissness(because purchases in the region of 7m definitely is) with such an unreliable economical power as Man U is at the moment is beyond my understanding. Looking back at the Lajick deal one should think twice before doing long term agreements with Man U. I did not even know it was leagal to break deals like they did. or have i missed something?
darius, i can empathise with your position, my missus goes on and on about rafa and gerrard like they were gods.
its tricky when were both on telly at the same time, but as she says, i'm more computer literate so i can watch a stream. unless were both on different sky sports channels and then we can both sit in different rooms and cheer our respective teams.
gunners lover, i would argue your point that our financial stability isnt bringing in the quality. well last year we bought 2 players, arshavin and vermaelen. with that simple statement i know i have won the arguement, but theres more. a lot of our money is spent on scouting and youth development. the list of 'quality' players that have come through this direction rather than the multi-million direction is too long to list. also, our stadium has cost us a fair few quid, but it will be the magic porridge pot when the mortgage is paid off. more money for youth development, scouting and even a few astute purchases.
More good news – Ferdinand banned! Should miss the Arsenal game too.
http://www.telegraph.co.uk/sport/football/leagues/premierleague/manutd/7079119/Manchester-United-defender-Rio-Ferdinand-charged-with-violent-conduct-following-return.html
don't believe the hype
He has been charged, not found guilty yet Jonny.
Yeah sure, I know.
Nonetheless it was clear as day. I'd say if he appeals, he will lose and I think most would agree – even Man Utd. I doubt they will appeal as it's hard to see on 'what grounds' and they surely won't want to risk a longer ban.
Hmm, Simon, I'm the opposite of you here. My mum loves United with a passion. Heck, out of four kids, I'm the only one who supports Arsenal. My kid brother was also able to resist the Borg conditioning, though he ended up at Liverpool, yikes!
Back home, cruising the internet always gave one a sense that that MSM had it in for Arsenal. Back then, you could only rely on very few blogs for a positive outlook on the Arsenal life. Nowadays, it seems even supposedly pro-Arsenal blogs, have taken to bashing the team, the manager, the players, etc. Myles Palmer, who I once read with some respect, suddenly morphed into this snide, sniping, prick who used every opportunity to slag off the team, the manager, everything, and a lot of bloggers out there probably followed his lead.
I remain eternally grateful to Sir Tony for creating this sea of calm amid the raging oceans of negativity one has to put up with out there, and to Walter and you Simon for your capable assistance to the big man.
'gunners lover', I guess your 'points' up there must explain why we are second from bottom, musn't we? Our points on the PL table must be fake as well, musn't it? Yeah, It's all a mirrage; some sort of 'Abrakadabra', isn't it?
Wow, I definitely underestimated the power of ignorance. 'gunners lover' is the mighty ignoramus itself.
Good piece Simon.
Gooner lover today, neutral fan yesterday, and others before them making claims without merit and disappear. Is this what they call rotational fouling? It's fine with me as they get the best out of everyone. We tend to get more history about the Arsenal and detailed explanation. I'm enjoying this.
Simon great write up there. I'm a rehablitated Arsenal fan came back from the brink of distruction with ManIOU. Long time ago, that is.
LRV, is that really you?
Simon — excellent, well-written article.
Getty — I agree w/ you about posters like "neutral fan" and "gunners lover." It's good to have different voices, even if most of us completely disagree with them. Like you say, it gives people here a chance to make better arguments.
Armin — your comment about video games and the ability of fans to be manager is sharp. I think you are on to something.
I think these games and simulations have probably played a role in the "spend, spend, spend" philosophy. Take EA's FIFA Soccer, for example, which I played maybe 8-9 years ago while in college. I've always wondered how games like these could give players such exact ratings for things like "tenacity" and "vision." How the f&ck do you measure that?
In these games, you always want to play with the fasted, most-skilled players because that makes the game more fun. But players' "ratings" don't change. Which means the only way to improve your team is to "Buy, buy, buy." So you go out and buy a player like Luis Figo (who in the version I played was God-like).
In these video games, long-term development means nothing. And there is always an allure to get the biggest names in football all on your team.
Man City, Chelsea, and Real Madrid run their clubs like video games.
It's all a fu^king illusion.
(Sorry Simon and others…quite off topic…)
Well now we are off topic: What has Ferdinand done to get charged ? I haven't seen the game and haven't seen any higlights so I really don't know what he is charged for.
About the video game I think it would be intresting to see if there is a difference between the video game generation and the older generation ? I have never played such games but I can imagine that if you win the league time after time you could imagine that you know better than Wenger. In the game that is, not in real life.
And on topic: I was just wondering Simon, if we would be more like ManU would your mother not start hating us ?
No surprises there, a Brittish ManUre player commits a foul which he is being charged with and no media uproar… Tisk tisk. If that had been an arsenal player…
The way I see it, it's all Tony's fault that people like 'gunners lover' thinks we're 2nd from bottom. Quit asking us to read the table upside-down Tony!
There's quite a few infants here among the readers lately. They'll get the joke as they grow up. I certainly hope so.
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