text:
\section{Introduction}
\setlength{\parskip}{0em}
\begin{figure*}
		\includegraphics[width=1.0\textwidth]{Fig1.png}
		\caption{\label{struc} Description of BTCPO unit cell with up and down Cu$_{4}$O$_{12}$ square cupola (blue), PO$_{4}$ tetrahedra (green), and TiO$_{5}$ pyramids (brown), and Ba ions as large grey spheres along the $c$ (left panel) and $a$ (middle panel) axis. Two possible arrangements of the spins $\varGamma_3(1)$ and $\varGamma_3(2)$ (right panel).}
\end{figure*}

Recently, an interesting class of compounds,$AE$(TiO)Cu$_4$(PO$_4$)$_4$ ($AE$TCPO; $AE$ = Ba, Sr, or Pb), was newly synthesized~\cite{Kimura2016magneto,Kimura2018a} .
The structure of $AE$TCPO is tetragonal with the space group $P$42$_1$2 and consists of the layers of up and down square cupola Cu$_{4}$O$_{12}$  (FIG.~\ref{struc}). Each square cupola is made of four corner sharing CuO$_{4}$ plaquets. The layers are separated by $AE$ ions and TiO$_{5}$ pyramids.
These compounds undergo an antiferromagnetic (AF) transition at low temperatures. For example,  \BTCP/ (BaTCPO) exhibits an AF ordered  state at temperatures below the N\'{e}el temperature T$_N$~=~9.5~K. Below T$_N$
the arrangement of magnetic moments of coppers shows an antiferroic quadrupolar order. Because of the antiferroic order, BaTCPO does not exhibit a magnetoelectric effect where an electric (magnetic) field causes magnetization (electric polarization).
Instead, this compound exhibits a remarkable magnetodielectric effect. Sr(TiO)Cu$_4$(PO$_4$)$_4$ (SrTCPO) also shows similar magnetic and magnetodielectric properties below T$_N$~=~6.2~K~\cite{SrPRRB2019}, while Pb(TiO)Cu$_4$(PO$_4$)$_4$ (PbTCPO) exhibits a ferroic quadrupolar order resulting in a linear magnetoelectric effect  below  T$_N$~=~6.5~K ~\cite{PbPRMat2018,PbJPSJ2019}.

Magnetic structure of BaTCPO was carefully studied by neutron scattering experiments ~\cite{Kimura2016magneto}.
These studies yielded two possible arrangements of the spins: one, denoted $\varGamma_3(1)$, where the moments are confined approximately in the CuO$_{4}$ planes; and the other, $\varGamma_3(2)$, where the moments are approximately perpendicular to the CuO$_{4}$ planes forming two-in-two-out-type structure (FIG.~\ref{struc}). The latter arrangement had smaller R-factor, thus being the most probable arrangement. Later Babkevich \textit{et al.}~\cite{Babkevich2017} confirmed the two possible structures using spherical neutron polarimetry, inclining by a discernible, albeit small advantage towards the $\varGamma_3(2)$ spin structure.

In the present report we will use $^{31}$P NMR techniques to study the local magnetic fields in a single crystal of BaTCPO. Phosphorus ions in PO$_{4}$ tetrahedra see four coppers in two cupolas as next-nearest-neighbours. Therefore, the local field at phosphorus is definitely influenced by the magnetic arrangement of coppers. Previous NMR studies of SrTPCO~\cite{Islam2018} and BaTPCO~\cite{Kumar2019} have used powder samples where detailed information about the magnetic structure is difficult to get.

\section{Experimental details}
Single crystals of \BTCP/ were grown with the flux method by Kimura \textit{et al.}~\cite{Kimura2018a,Kimura2016inorganic}. The sample crystal used in the experiments sized 1.9~x~2.0~x~3.9~mm and weighed 61.84~mg. NMR measurements were conducted using the spectrometer MAGRes2000 attached to a B = 4.7~T superconducting magnet, $^{31}$P resonance frequency 80.97~MHz. He-flow cryostat (JANIS Research Inc.) allowed measurements in the temperature range of 4.5 to 300~K. The NMR probe was our own made and had a single-axis goniometer. LakeShore CERNOX  calibrated sensors and  Model 332 temperature controller were used for temperature regulation. Spin-lattice relaxation T$_1$ was measured using inversion-recovery method. The magic angle spinning (MAS) room temperature spectrum was recorded using a home-built probe with the $1.8$~mm O.D. rotor spinning $25$~kHz. The magnetic shifts are given relative to the resonance of H$_3$PO$_4$.

\section{Results and analysis}
\subsection{Magnetization}
The temperature dependence of magnetic susceptibility was measured with the applied magnetic field B = 4.7~T along the [001] and [100] directions as shown in FIG.~\ref{susc}. At temperature region T$^{\text{max}}\approx$~17~K there is a broad maximum of $\rchi$ vs T curve, which indicates onset of short range order
\begin{figure}[!]
	    \centering
		\includegraphics[width=0.5\textwidth]{Fig2.png}
		\caption{\label{susc}Temperature dependence of magnetic susceptibility $\rchi(T)$ in an applied magnetic field B~=~4.7~T, measured in two different directions: B$\parallel$[100] (black, filled) and B$\parallel$[001] (red, empty). The cyan line represents the Curie-Weiss fit. The inset shows a detailed behavior of susceptibilities below T$_N~=~9.5$~K.}
\end{figure}

At high temperature $\rchi(T)$ followed the Curie-Weiss law:
\begin{align}
	\rchi(T)=\rchi_0+\frac{C}{T-\theta_\text{CW}}.
\end{align}
Here $\rchi_0$ is temperature-independent susceptibility.
At T~$ > $~100~K the fitting gives the following parameters: for the magnetic field along the [001] direction:
$\rchi_{0}~=~-7.3(4) \times 10^{-5}$~cm$^3$/mole per Cu,
$C~=~0.460(1)$~cm$^3$~K  per mole Cu,
$\theta_{\text{CW}}~=~-29.0(4)$~K; and for the field along the [100] direction:
$\rchi_{0}~=~-3.5(2) \times 10^{-5}$~cm$^3/$mole-Cu,
$C~=~0.454(7)~\times10^{-4}$~cm$^3$~K $/$mole-Cu,
and $\theta_{\text{CW}}~=~-29.3(2)$~K. From the Curie constant one gets the effective copper magnetic moment as  $\mu_{\text{eff}}=\sqrt{3k_BC/N_A}$, where $k_B$ is the Boltzmann factor, and $N_A$ is Avogadro's number. We get $\mu_{\text{eff}}~=~1.920~\mu_B$ and 1.911~$\mu_B$ for  [001] and [100] directions, respectively.
Here, $\mu_B~$ is the Bohr magneton. Using $g~=~\sqrt{S(S+1)}\mu_{\text{eff}}$ we get almost equal Lande $g$-factor values as $g~=~2.22$ and $g~=~2.20$ for  [001] and [100], respectively, which are common for Cu$^{2+}$ ions.

Here we note, that in regular, collinear antiferromagnets the $\rchi$ vanishes in the direction where the local magnetic moments are aligned parallel or antiparallel to an external magnetic field and stays constant in the directions where the external field is perpendicular to the local magnetic moments~\cite{Singer1956}. Thus the local moments here may prefer the [001] direction, but the non-vanishing $\rchi$  could also just be a signature of the non-collinear order.

\subsection{$^{31}$P Knight shift}
\setlength{\parskip}{0em}
\begin{figure}[!]
	\includegraphics[width=0.40\textwidth]{Fig3.png}
	\caption{\label{Knight}Temperature dependence of $^{31}$P Knight shift as measured when the single crystal is oriented with $a$ axis parallel to the external field $B$ (a, filled blue dots) and with $c$ axis parallel to $B$ (b, empty circles). The insets show the Clogston-Jaccarino plots giving quite close values to the hyperfine field in both the directions.}
\end{figure}

Temperature dependence of $^{31}$P Knight shift is presented in FIG.~\ref{Knight}.  Above the N\'{e}el temperature T$_N$~=~9.5~K, the Knight shift $K$(T) follows perfectly the magnetic susceptibility curve $\rchi$(T), as given~\cite{Clogston1961} by Eq.(\ref{C-J}):
\begin{equation} \label{C-J}
K(T)=K_0+\frac{\textit{H}_{\text{hf}}}{N_A\mu_B}\rchi.
\end{equation}
\noindent
Here, $K_0$ is the temperature-independent shift, the chemical shift, and \textit{H}$_{\text{hf}}$ is the hyperfine coupling constant.
From the $K $vs $\rchi$ plots (insets of  FIG.~\ref{Knight}) we found the hyperfine field values as \textit{H}$_{\text{hf}}$~=~7.65(5) kOe/$\mu_B$ for $a\parallel B$ direction and slightly smaller value,  \textit{H}$_{\text{hf}}$~=~7.40(5) kOe/$\mu_B$ for direction $c\parallel B$.
\begin{figure}[!]
		\includegraphics[width=0.40\textwidth]{Fig4a.png}
		\includegraphics[width=0.40\textwidth]{Fig4c.png}
	\caption{\label{Tn}Temperature development of the splitting of the resonance lines below the ordering temperature in the orientation $a\parallel B$ (upper panel) and $a\parallel B$ (lower panel). The solid lines are fittings by Eq.~\ref{power} .}
\end{figure}

Below T$_N$, due to the  onset of local magnetic fields, the resonance line splits into four lines in the orientation $a\parallel B$ and into two lines when the crystal is oriented with $c\parallel B$.
Following the approach given in Ref.~\cite{Islam2018} we will estimate the critical order parameter $\beta$ of the phase transition from the growth of the internal field $B_{int}$ in the vicinity of the ordering temperature. As a measure of the internal field we use the frequency difference between the most shifted resonance lines instead of the internal ones, which is proportional to the internal field by gyromagnetic ratio $^{31}\gamma/2\pi$~=~17.237~MHz/T. The temperature dependences of the frequency differences in the two orientations of the single crystal are given in FIG.~\ref{Tn}.

The temperature dependence of the frequency difference is fitted by the formula
\begin{equation}\label{power}
\Delta F(T)=\Delta F_0\left(1-\frac{T}{T_n}\right)^\beta.
\end{equation}

The best fit was obtained with  T$_N$~=~9.48~K, $\beta$~=~0.26 for the orientation $a\parallel B$,  and  T$_N$~=~8.82~K, $\beta$~=~0.20 for  $c\parallel B$.  The critical exponent $\beta$ values, if compared to some theoretical values (as given \textit{e. g.} in Ref.~\cite{Nath2009}), indicate that the ordering scheme is the closest to the 2D XY case.
\subsection{$^{31}$P NMR of powder sample}
\begin{figure}[!]
	\includegraphics[width=0.40\textwidth]{Fig5.png}
	\caption{\label{powder}(a): $^{31}$P MAS NMR of BaTCPO powder sample at T~=~305~K with a spinning frequency $\nu$~=~25~kHz.
The NMR spectrum of rotating sample consists of a center band at isotropic Knight shift K$_{\text{iso}}$~=~0.1643~\%, and of a number of spinning sidebands denoted by asterisks at multiples of the spinning frequency from the center band. (b): $^{31}$P NMR of a static powder sample at slightly lower temperature T~=~295~K. The red line is a fit to the powder line with the eigenvalues of nearly axially symmetric Knight shift tensor: K$_{11}~=~0.1952$~\%, K$_{22}~=~0.1832$~\%, K$_{33}~=~0.1298$~\%.}
\end{figure}

Before starting $^{31}$P analysis of single crystal we recorded the spectrum of a powder sample.
FIG.~\ref{powder}(a) shows $^{31}$P NMR spectrum recorded with magic angle spinning~\cite{MAS-NMR_reference} of the sample. The spectrum shows a single sharp line at isotropic magnetic shift. The spectrum of a static sample (FIG.~\ref{powder}(b)) shows a typical powder line shape with singularities at the principal values of the Knight shift tensor:
\begin{equation}\label{PAS}
	K_{PAS}=
	\begin{pmatrix} 1+K_{11} & 0 & 0 \\ 0 & 1+K_{22} & 0 \\ 0 & 0 & 1+K_{33} \end{pmatrix},
\end{equation}
with K$_{11}=0.1952$ \%, K$_{22}=0.1832$ \%, K$_{33}=0.1298$ \%.  These values give us  the reference for the interpretation of the rotation patterns of the single crystal.

\subsection{Orientation of the $^{31}$P Knight shift tensor}

Determination of tensor orientation in a single crystal is not very easy task~\cite{Mehring1976}. For that, in general case, one needs to record resonance frequencies rotating the sample around three different axes. Depending on symmetry or having some principal values of the shift tensor pre-determined, the number of necessary rotation patterns may be smaller. After obtaining those rotation patterns, one needs to find unitary transformation that will transform the principal axis system (PAS) into the crystal frame.
As usual, the Hamiltonian of spin-$\frac{1}{2}$ nucleus consists of the Zeeman and the Knight shift interaction
\begin{equation} \label{H}
\mathcal{H}=\mathcal{H}_Z+\mathcal{H}_K=\gamma \textbf{H}_0\cdot \textbf{K} \cdot \textbf{I},
\end{equation}
where $\textbf{I}=(I_x,I_y,I_z)^T$, $\textbf{H}_0 = (0,0,H_0)$, and $I_x,I_y,I_z$ are Pauli matrices:
\begin{equation}
I_x=\frac{\hbar}{2}\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix};
I_y=\frac{\hbar}{2}\begin{pmatrix} 0 & i \\ -i & 0 \end{pmatrix};
I_z=\frac{\hbar}{2}\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}.\\
\end{equation}
Three successive rotations, each characterized by three Euler angles,
transform the Hamiltonian from the principal axes frame (PAS) into the laboratory frame:
\begin{eqnarray*} \label{H}
 \begin{array}{c}K_{\scriptstyle PAS}\\ \scriptstyle(1,2,3)\end{array}\underrightarrow{ \scriptstyle R_p(a_1,a_2,a_3)}\begin{array}{c}K^*\\ \scriptstyle(a,b,c)\end{array}\scriptstyle \underrightarrow{R_i(b_1,b_2,b_3)}\begin{array}{c} K_g\\ \scriptstyle (x_g,y_g,z_g) \end{array}\scriptstyle \underrightarrow{R_g(c_1,c_2,c_3)}\begin{array}{c} K\\ \scriptstyle(x,y,z)\end{array}
\end{eqnarray*}
 There are four frames of reference: PAS with diagonal tensor ($ K_{PAS} $), crystal frame ($ K^* $), goniometer frame ($ K_g $), and laboratory frame (K). The transformations between them are $R_p$, $R_i$, $R_g$ with the corresponding Euler angles. We used the conventional Euler ZYZ rotation of the Hamiltonian~\cite{easyspin}.

In BaTCPO there are eight different positions of the phosphorus ions in the unit cell, each giving the resonance corresponding to different transformation $R_p$.
The rotation patterns around the $c$ and $a$ axis at temperatures T~=~295~K and T~=~18~K are shown in FIG.~\ref{rotation}.
The angles $b_1$, $b_2 $, $b_3$ and $c_1$, $c_2 $, $c_3$ are unique for each experiment; $a_1$, $ a_2 $, $a_3$ are desired eight sets of the Euler angles transforming the tensor in PAS to the crystal frame for each phosporus site. It turns out that the principal axis $K_{33}$ of the Knight shift tensor is tilted by 45 degrees from the crystal $c$ axis.
Schematics of the Knight tensor's eight orientations are presented in Fig.~\ref{BTCP_295K}.

\begin{figure*}[!]
	\begin{center}
		\includegraphics[width=0.75\textwidth]{Fig6.png}
		\caption{\label{rotation} $^{31}$P NMR resonance frequencies by rotating BaTCPO single crystal around the $a$ (a) and $c$ axis (b) at T=295~K (upper panels) and T=18~K (lower panels). The full lines correspond to the angle dependencies according to the parameters given in Table~\ref{details}. Due to symmetry, eight different sites in the unit cell contribute only to two different rotation patterns. The red lines in panel (a) correspond to the sites 1, 3, 6 and 7 (see Table~\ref{details}), and to the sites 2, 3, 6 and 8 in panel (b), the rest of the sites are given by blue lines.}
		\vspace{5mm}
	\end{center}
\end{figure*}

\begin{figure}[ht!]
		\includegraphics[width=0.4\textwidth]{Fig7.png}
		\caption{\label{BTCP_295K} Orientations of the Knight shift tensor at eight phosphorus locations of the unit cell
at temperature T~=~295~K. The tensors have three principal vectors - green, orange, dark-violet, which correspond to the $K_{PAS}$ values $K_{11}$, $K_{22}$, $K_{33}$, respectively.}
\end{figure}

\begin{table*
	\caption{\label{tab:18K}(a) and (b): the Euler angles for transforming BaTCPO single crystal shift tensors from crystal frame to the laboratory frame. Tables (c) and (d) show the Euler angles for transforming the tensors from PAS to the crystal frame. Tensor components of PAS ($ K_{11} $,$ K_{22} $,$ K_{33} $) are in $\%$ units of $\omega_L$.}
	\label{details}
	\begin{ruledtabular}
	\begin{tabular}{|c|c c c|c c c|c|c c c|c c c|c c c|}
		\multicolumn{7}{|c|}{(a) T=295K} & T & & (c) 295K & & & (d) 18K & & \multicolumn{3}{c|}{T=295K} \\%[0.5ex]
		\hline
		& $c_1$ & $c_2 $ & $c_3$ &$b_1$ & $b_2 $ & $b_3$ &nr & $a_1$ & $ a_2 $ & $a_3$ & $a_1$ & $a_2$ & $a_3$  & $K_{11}$ & $K_{22}$ & $K_{33}$  \\
		\hline
		c$\parallel$z$_g$ & (-12:372) & 90 & 0 & 85 & 0 & 0 &1 &  30 &  45 & -45 & 25 & 45 &-40 & $0.198$ & $0.185$ & $0.128$ \\
		a$\parallel$z$_g$ & (-12:372) & 90 & 0 & 0 & 90 & 0 &2 & -30 &  45 &  45 &-25 & 45 & 50 &   &   &  \\
		&           &    &   &   &    &   &3 &  30 &  45 & 135 & 25 & 45 & 140&   &   &  \\
		\cline{1-7} \cline{15-17}
		\multicolumn{7}{|c|}{(b) T=18K} & 4 & -30 &  45 & -135  & -25 & 45 & -130 & \multicolumn{3}{c|}{T=18K}\\
		\cline{1-7} \cline{15-17}
		& $c_1$ & $c_2 $ & $c_3$ &$b_1$ & $b_2 $ & $b_3$ & 5 & 30 & 135 &  45 &  25 & 135 & 50 &$K_{11}$ & $K_{22}$ & $K_{33}$ \\
		\cline{1-7} \cline{15-17}
		c$\parallel$z$_g$ & (-12:372) & 90 & 0 & 80 & 0 & 0 & 6 & -30& 135 & -45 & -25 & 135 & -40 & $1.14$ & $1.05$ & $0.67$ \\
		a$\parallel$z$_g$ & (-12:372) & 90 & 0 & 0 & 90 & 0 & 7 & 30 & 135 &-135 & -25 & 135 & 140   &   &   & \\
		&           &    &   &   &    &   & 8 & -30& 135 & 135 &  25 & 135 & -130  &   &   & \\
	\end{tabular}
	\end{ruledtabular}
\end{table*}

\subsection{Spin-lattice relaxation results

Spin-lattice relaxation $T_1$was measured with inversion-recovery pulse sequence at magnetic fields along [001] and [100] directions (Fig.~\ref{relax}). The magnetization recovery was exponential throughout all the measurements:
\begin{equation}
    M(\tau)=M_0(1-A\exp(-\tau/T_1)),
\end{equation}
where $M(\tau)$ is the magnetization at delay $\tau$ after inversion, $M_0$ is the equilibrium magnetization, and $A~\le$~2 is a constant depending on the accuracy of the inversion.

\begin{figure}[!ht]
		\includegraphics[width=0.5\textwidth]{Fig8.png}
		\caption{\label{relax} Temperature dependence of $^{31}$P spin-lattice relaxation rate in directions [100] (red dots) and [001] (blue dots). The inset shows that relaxation rate 1/T$_1$ is proportional to T$^7$ below T$_N$.}
\end{figure}

The relaxation rate at T $>$ 60 K is almost constant which is typical for a paramagnetic material, where the relaxation is caused by the fluctuation of the magnetic moments. Before the phase transition at T$_N$, a sharp spike occurs in the relaxation speed which is connected to the rapid slowing of the fluctuations. Below T$_N$, relaxation speed decreases sharply proportional to T$^7$. In case of $c~\parallel~B$, the relaxation rate seems to have a discontinuity in close vicinity of T$_N$. Here we note, that 1/T$_1$ $\propto$ T$^7$ was also observed for SrTCPO~\cite{Islam2018}.

In paramagnetic temperature region we can use the Moriya's theory of relaxation \cite{Moriya}, where:
\begin{equation}
	\frac{1}{T_1}=\frac{\gamma ^2_N \sqrt{2\pi} S(S+1)}{3\omega_E z'} H^2_{hf},
\end{equation}

Here $\gamma_N$ is the nuclear gyromagnetic ratio, $ S $ is the nuclear spin, $H_{hf}$ is the hyperfine field as in Eq.~\ref{C-J}, $z'=2$ is the number of nearest Cu$^{2+}$ neighbors for the nucleus and
$\omega_E=(|J| k_B/ \hbar) \sqrt{2 z S(S+1)/3}$ is the Heisenberg exchange frequency (in units rad$^{-1}$), where $z$~=~2  is the number of Cu$^{2+}$ ions as nearest neighbors to $^{31}$P, $S$~=~1/2 is the electronic spin, and $J$ is the exchange interaction

With the hyperfine field value of $H_{hf}$~=~7.650 kOe/$\mu_B$ and the relaxation rate for the paramagnetic region 1/T$_1$ = 1410 s$^{-1}$ we get an estimate for the exchange interaction inside the square cupola $J/k_B$~=~35~K with an exchange frequency of $\omega_E$~=~4.5$\cdot10^{12}$~rad/s. This value is in coherence with previous results of $J$~=~3.0~meV~=~34.8~K~\cite{Kimura2016magneto}.

\subsection{Local magnetic structure in the ordered state

The resonance frequencies by rotation of the single crystal around the [001] and [100] at T~=~6~K are given in Fig.~\ref{rot_6K}. The results are in coherence with the Knight shift temperature dependence (FIG.~\ref{Knight}). Once the magnetic field is turned around the $c$ axis, one can see that when $a\parallel$~B, there are four different magnetic field projections in the AFM region as given in FIG.~\ref{Knight}(a). When the crystal is oriented $c\parallel$~B, there are two different local field projections to the external field direction as given in FIG.~\ref{Knight}(b). Rotating the sample around $c$ and $a$ gives eight different rotation patterns for eight phosphorus ions in the unit cell. Each rotation pattern can be described by the equation:
\begin{equation} \label{lahendus}
F=K+L\cos(\alpha-\alpha_1)+M\cos(2(\alpha-\alpha_2)),
\end{equation}
where the constant term $K$ is the Larmor frequency plus average chemical shift; the second term describes the angle dependence of the local field projection to the external field direction. The third term describes the angle dependence of the resonance frequency due to turning of
the chemical shift tensor.

The rotation patterns around the [001] axis show two sets of lines (blue and red). The phase shift within the set is 90 degrees. The red lines are shifted from $b\parallel$~B by +16~degrees, while the blue lines are shifted -16~degrees. We can assign the blue lines to the phosphorus ions in ``up'' cupola and the red lines to the ions in ``down'' cupola. The rotation patterns of the crystal around the [100] (FIG.~\ref{rot_6K}(b), Table~\ref{tab:6K}b) are not so well resolved. Here, the approximation of the frequencies by Eq.~\ref{lahendus}  is not particularly good. A possible reason might be that the magnetic structure in 4.7~T magnetic field at $c\parallel$~B direction is not yet well settled at temperature 6~K. We found above (see FIG.~\ref{Tn}) that the ordering temperature in the direction $c\parallel$~B was T$_N$~=~8.8~K, while in case of $b\parallel$~B we had T$_N$~=~9.5~K.

Despite of that, one can clearly see the rotation patterns with two different amplitudes as expected for two different local field projections along the $b$ axis. The assignment of the resonances to ``up''  and ``down'' cupola is not unique. For example, we cannot distinguish the cases, where all the local field directions of one cupola have positive projection to the $c$ axis and the moments of the other cupola have negative projection, from the case, where the ions of one cupola have two positive and two negative projections and the field on ions of the other cupola have, respectively, two negative and two positive projections to the $c$ axis. The assignment in FIG.~\ref{rot_6K}(b) corresponds to the local field configuration as given below in FIG.~\ref{str:6K}.

\begin{figure}[!]
		\includegraphics[width=0.45\textwidth]{Fig9.pdf}
	\caption{\label{rot_6K}Rotation patterns of $^{31}$P NMR frequencies of BaTCPO single crystal at temperature T~=~6~K rotating 	around [001] (a) and [100] (b). The lines are approximations with Eq.~\ref{lahendus} using data in Table~\ref{tab:6K}.

	The main directions of a crystal $a\parallel$B, $b\parallel$B, and $c\parallel$B, $b\parallel$B are noted in the respective $x$ axes. The blue symbols are assigned to the sites in ``up'' cupola, the red symbols to the sites in ``down'' cupola.}
\end{figure}

\begin{table}[!]
	\caption{\label{tab:6K}The fitting parameters $K$, $L$, $M$, $\alpha_1$, and $\alpha_2$ of the rotation patterns according to Eq.~\ref{lahendus}
The upper table corresponds to the rotation of the crystal around the $c$ axis (as shown on FIG.~\ref{rot_6K}(a)), lower table corresponds to rotation  around the $a$ axis (FIG.~\ref{rot_6K}(b)) at temperature T~=~6~K.}

	\begin{ruledtabular}
		\begin{tabular}{c  c c c c c}
			nr & $K$ & $L$ &$\alpha_1$ & $M$ & $\alpha_2$ \\ [0.5ex]
			\hline
			1 & 81.59 & 0.56 & 347 & 0.075 & 155\\
			2 & 81.59 & 0.56 & 20 & 0.075 & 25\\
			3 & 81.58 & 0.56 & 80 & 0.075 & 50\\
			4 & 81.59 & 0.56 & 110 & 0.075 & 125\\
			5 & 81.59 & 0.55 & 170 & 0.075 & 155\\
			6 & 81.595 & 0.56 & 198 & 0.065 & 30\\
			7 & 81.59 & 0.575 & 258 & 0.078 & 50\\
			8 & 81.60 & 0.56 & 288 & 0.065 & 130\\
		\end{tabular}
		\begin{tabular}{c  c c c c c}
			nr & $K$ & $L$ &$\alpha_1$ & $M$ & $\alpha_2$ \\ [0.5ex]
			\hline
			1 & 81.47 & 0.62 & 294 & 0.17 & 87\\
			2 & 81.47 & 0.62 & 246 & 0.17 & 97\\
			3 & 81.45 & 0.29 & 212 & 0.17 & 72\\
			4 & 81.44 & 0.29 & 148 & 0.17 & 115\\
			5 & 81.47 & 0.62 & 114 & 0.17 & 84\\
			6 & 81.47 & 0.62 & 66 & 0.17 & 95\\
			7 & 81.45 & 0.29 & 32 & 0.17& 69\\
			8 & 81.45 & 0.29& 328 & 0.17 & 111\\% [0.5ex]
		\end{tabular}
	\end{ruledtabular}
\end{table}

\begin{figure}[!]
		\includegraphics[width=0.4\textwidth]{Fig10.png}
		\caption{ \label{axes}Scheme of local field direction on a phosphorus ion in BaTCPO crystal. B$_\text{int}$ is the local field,
		B$_a$, B$_b$, and B$_c$ are the projections of B$_\text{int}$ to the crystal $a$, $b$, and $c$ axis, respectively. B$_1$, B$_2$, and B$_3$ are the projections of B$_\text{int}$ to the $bc$, $ac$, and $bc$ planes, respectively. The latter amplitudes can be found from the rotation pattern parameters given in Table~\ref{tab:6K}. }
\end{figure}

The analysis of the data given in Table~\ref{tab:6K} can be carried out using the scheme of the local field direction as given in FIG.~\ref{axes}. Three cosine amplitudes $L$ in Table~\ref{tab:6K} correspond to the local field projections B$_1$, B$_2$, and B$_3$ in FIG.~\ref{axes}.
Using the gyromagnetic ratio of $^{31}$P $\gamma/2\pi$~=~17.237~MHz/T, we find B$_1$~=~36~mT, B$_2$~=~32.5~mT, and B$_3$~=~16.8~mT. The angles $\alpha$~=~$\pm$~16, $\beta$~=~$\pm$~66, and $\gamma$~=~$\pm$~32 degrees. It is not difficult to calculate the projections B$_a$~=~8.9~mT, B$_b$~=~31.2~mT,  and B$_c$~=~14.6~mT, as well as the module of the internal field B$_\text{int}$~=~35.6~mT.

As noted above, unique assignment of the resonances to certain phosphorus in the unit cell is not possible. One possible local field configuration is given in FIG.~\ref{str:6K}.

\begin{figure}[!]
	\includegraphics[width=0.4\textwidth]{Fig11.png}
	\caption{\label{str:6K}Possible configuration of induced static magnetic fields at phosphorus ions in BaTCPO unit cell. Red arrows represent the directions and size of the static magnetic fields, plus and minus sign mean the field direction to the front or to the back of the figure plane. Blue squares are Cu$^{2+}$ ions and the purple tetrahedrons show P ions.}
\end{figure}

The internal field at phosphorus ions consists of two components:
\begin{equation} \label{Bint}
B_\text{int}=B_\text{hf}+B_\text{dip},
\end{equation}
where $B_\text{hf}$ is transferred hyperfine field, and $B_\text{dip}$ is the dipolar field from the magnetic moments of Cu$^{2+}$ ions. In the following we assume that $B_\text{hf}$  is very well cancelled in AF ordered state, and the local magnetic field at phosphorus is due to dipolar field  of Cu$^{2+}$ ions.

We did calculate the dipolar field at each phosphorus ion of the unit cell assuming the \textit{two} magnetic structures proposed in Refs.~\cite{Kimura2016magneto,Babkevich2017}. In the calculation we did sum the dipolar field from every Cu$^{2+}$ inside a sphere of 50~\AA  \ around given phosphorus. At that we took into account that the unit cell of magnetic structure is doubled along $c$ direction, \textit{i. e.} the magnetic moments of every other layer along the $c$ axis were reversed. As a result, we obtain the following dipolar field projections along the $a$, $b$, and $c$ axis
\begin{align*}
	\text{a) }&B_a=37.5~\text{mT; }B_b=90.1~\text{mT; }B_c=11.2~\text{mT, }\\
	&B_\text{int}=97.7~\text{mT;}
\end{align*}
	for the structure noted $\varGamma_3(1)$, and
\begin{align*}
	\text{b) }&B_a=42.2~\text{mT; }B_b=36.0~\text{ mT; }B_c=0.75~\text{ mT, }\\
	&B_\text{int}=55.5~\text{ mT;}
\end{align*}
 for the structure noted $\varGamma_3(2)$.

 In comparison, our experiments above give the values:
\begin{align*}
&B_a=8.9~\text{mT; }B_b=31.2~\text{mT; }B_c=14.6~\text{mT; } \\
&B_\text{int}=35.6~\text{mT.}
\end{align*}
\begin{figure}[!]
		\includegraphics[width=0.375\textwidth]{Fig12.png}
		\caption{ \label{dipolar}Calculated dipolar field direction at phosphorus ions of the BaTCPO unit cell (a): assuming  structure of Cu$^{2+}$  magnetic moments $\varGamma_3(1)$ (given in Ref.~\cite{Kimura2016magneto} ), and (b): assuming the structure $\varGamma_3(2)$. The red arrows represent the dipole fields. The length of the arrows corresponds to the relative value of dipolar field in both cases and that in FIG.~\ref{str:6K}. Blue arrows represent directions of the Cu$^{2+}$ magnetic moments and their sizes in the two cases.}
\end{figure}

Calculated dipolar field directions at the phosphorus ions are given in FIG.~\ref{dipolar}.

Comparison of the experimental field pattern to the calculated dipolar fields gives remarkable similarity to the case calculated for $\varGamma_3(1)$ structure - the calculated dipolar field directions are close to the experimental values in FIG.~\ref{str:6K}, although the calculated B$_c$ value is relatively small and the calculated local field is 2.7 times larger than the experimental value. Three times larger value of the calculated dipolar field compared to the experimentally determined local field was reported earlier for dipolar field at Ba site in antiferromagnetic YBa$_2$Cu$_3$O$_{6.05}$ Ref.~\cite{Lombardi1996}. The authors ascribed this controversy to the possible effect of delocalization of the copper $d$~-~electron. Dipolar field calculated for $\varGamma_3(2)$ structure is quite different. It is almost confined to the $ab$ plane, with nearly equal B$_a$ and B$_b$ components. Therefore, we can conclude that the NMR data are better consistent with the magnetic structure $\varGamma_3(1)$.\\

\section{Conclusion}
We performed $^{31}$P NMR of the antiferromagnetic square cupola compound \BTCP/ in  the applied magnetic field B = 4.7~T and provided an in-depth overview of the local magnetic environment around the Cu$^{2+}$ cupolas. From the $^{31}$P NMR frequency dependence of the single crystal orientation we successfully determined the principal values of the $^{31}$P magnetic shift tensor and the orientation of eight magnetic tensors in the unit-cell at room temperature and at temperature T~=~6~K. The Knight shift temperature dependence in comparison of that of the bulk magnetic susceptibility enabled to determine the hyperfine field on $^{31}$P nuclei \textit{H}$_{\text{hf}}$~=~7.65(5) kOe/$\mu_B$ for $a\parallel B$ and \textit{H}$_{\text{hf}}$~=~7.40(5) kOe/$\mu_B$ for $c\parallel B$. The temperature dependence of $^{31}$P spin-lattice relaxation resulted in an approximation for the exchange interaction constant between Cu$^{2+}$ ions $J~= ~35K$. $^{31}$P NMR frequency dependence on the single crystal orientation in the antiferromagnetic state gave a clear picture of local magnetic fields at  $^{31}$P ions. The static magnetic field at every phosphorus was determined as $B_\text{int}~=~35.6$~mT. Experimental configuration of the local field was compared to the calculated dipolar field for several magnetic arrangement of the copper magnetic moments. We found that the magnetic structure $\varGamma_3(1)$ determined by the previous neutron diffraction studies~\cite{Kimura2016magneto,Babkevich2017} is most consistent with the NMR data.

\section*{Acknowledgemnts}
This research was supported by the Estonian Science Council Grants IUT23-7 and PRG4, the European Regional Development Fund Grant TK134, JSPS KAKENHI Grant Numbers JP17H01143, JP19H05823 and JP19H01847, and by the MEXT Leading Initiative for Excellent Young Researchers (LEADER).

redpajama_set_name: RedPajamaArXiv


text:
What A Friend We Have In Jesus Tin Whistle Sheet Music
Leaning on the Everlasting Arms Tin Whistle Sheet Music
A Christian Hymn for the tin whistle.
Back To Hymns And Christmas Songs For Tin Whistle
Faith Of Our Fathers Tin Whistle Notes
This is my interpretation of this song based on the Irish version as sang by Frank Patterson. I had a look at a rake of pieces of sheet music for this song and none of them came even close to the way I remember it being sang, so I decided to make up my one version the way I was thought it at school years ago. Included are the letter notes for flute / recorder.
Learn How To Play Faith Of Our Father's On Tin Whistle
Skye Chords And Lyrics By Runrig
These are the guitar chords in the key of A and the same one's that are used by Runrig.
Barbara Allen Tin Whistle Sheet Music
There are many versions of this folk song around. This is the version that's sang by Joan Baez. The song is a traditional British ballad. The music is in the key of D. Joan Baez plays it in the key of B Major.
I Hear Thunder Sheet Music And Tin Whistle Notes
This is a children's nursery song. The notes used are the very same as Frere Jacques.
Children's Tin Whistle Sheet Music
Five Little Ducks Tin Whistle Sheet Music
Along with the sheet music I have included the basic letter notes for the recorder / flute.
Children's Tin Whistle Songs
Bandiera Rossa Tin Whistle Sheet Music
This is Paul Anderson's own arrangement for Bandiera Rossa which he's playing in the youtube video on his low D whistle.
Gabriel's Oboe Tin Whistle Sheet Music
The first piece of music is in the key of D and goes fairly high, up to the high B in fact. The second is in a slightly lower key but all the G notes are sharp, which means if your playing this on a tin whistle you'll have to half block the G notes.
Einigkeit und Recht und Freiheit Sheet Music
Einigkeit und Recht und Freiheit Tin Whistle Sheet Music Notes for the German National Anthem.
Irish folk song lyrics, chords and a whole lot more

redpajama_set_name: RedPajamaCommonCrawl


text:
Arnold Schwarzenegger compares US Capitol mob to Nazis
This Sunday, Jan. 10, 2021, image from a video released by Schwarzenegger shows former Republican California Gov. Arnold Schwarzenegger delivering a public message. Schwarzenegger compared the mob that stormed the U.S. Capitol to the Nazis and called President Donald Trump a failed leader who "will go down in history as the worst president ever." (Frank Fastner/Arnold Schwarzenegger via AP)
Former California Gov. Arnold Schwarzenegger compared the mob that stormed the U.S. Capitol to the Nazis and called President Donald Trump a failed leader who "will go down in history as the worst president ever."
The Republican said in a video he released on social media on Sunday that"Wednesday was the Night of Broken Glass right here in the United States." In 1938, Nazis in Germany and Austria vandalized Jewish homes, schools and businesses during an attack that became known as Kristallnacht or "the Night of Broken Glass."
"The broken glass was in the windows of the United States Capitol. But the mob did not just shatter the windows of the Capitol, they shattered the ideas we took for granted," he said. "They trampled the very principles on which our country was founded."
Schwarzenegger, who was born in Austria, compared the Proud Boys — a far-right American extremist group — to the Nazis. Some Proud Boys leaders were arrested in the nation's capital, before and after Wednesday's riots.
"President Trump sought to overturn the results of the election — and of a fair election," Schwarzenegger said in the video. "He sought a coup by misleading people with lies."
Schwarzenegger called Trump a failed leader and said he took solace that Trump's presidency was coming to an end and "would soon be as irrelevant as an old tweet."
He called for national unity and vowed his support for President-elect Joe Biden after mobs loyal to Trump broke into the U.S. Capitol, causing a temporary suspension of the electoral count. Members of Congress later returned and certified the results.
Five people died, including a Capitol police officer. Scores of rioters have been arrested and many more are being sought after the brazen attack.
"And to those who think they can overturn the United States Constitution, know this: You will never win," Schwarzenegger said.
During the video, which runs for more than seven and a half minutes, Schwarzenegger likened American democracy to the sword he brandished in his early role as "Conan the Barbarian," which he said only grows stronger when it is tempered.
Schwarzenegger, best known for his movie role as the Terminator, was elected as California's governor in 2003 during a special recall election. He was later elected to a full term.
"I believe, as shaken as we are about the events of recent days, we will come out stronger because we now understand what can be lost," he said, adding that those behind Wednesday's riots — and those that fomented them — will be held accountable.
KANNAPOLIS, N.C. (AP) — Dorothy Schmidt Cole, recognized last year as the oldest living U.S. Marine, has died at age 107.
Beth Kluttz, Cole's only child, confirmed Friday that her mother died of a heart attack at Kluttz's home in Kannapolis, North Carolina, on Jan. 7.
by Brian Hutton Jr. / Jan 18, 2021
While we have seen only a trace of snow in the Triangle so far this winter, the North Carolina mountains continue to get a steady stream of snow and customers to the ski resorts.
One of the few things you can do and naturally social distance is hit the slopes to ski or snowboard.
On this Martin Luther King Jr. Day, the nation takes a pause, with many Americans using the holiday as a day of service. A kindergartener in Indianapolis, Indiana, is already well ahead in making a difference.
Five-year-old Amor Coleman is a little girl with big ideas. In her kindergarten classroom, she noticed the books rarely include characters that look like her. So, she decided to fix that and started collecting books for Black History Month for friends at school.


text:
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April 12, 2021 • 5m
Hard on the issues, easy on the people
Wade Arnold
@wadearnold
I will judge my success at Moov based on the experiences of my employees. Not how many people we hire, how much money we raise, or how many dollars we move through our platform. Of course, these things are essential. But the milestones related to these areas of the business don't matter if my people don't feel challenged, accepted, safe, respected, inspired, and like they are doing the best work of their lives. For me, that's the end goal—to make Moov the best place anyone has ever worked.
With that in mind, I want to share some thoughts about leadership. And I can't talk about leadership without talking about trust. Trust is one of the most crucial aspects of a startup. Heck, it might even be the most important. The speed at which the team can run—make decisions, collaborate, ship features, execute plans—is entirely predicated on how much trust everyone has with each other.
At Moov, we seek a positive exchange of trust. We strive to give first, treat others with respect, and are hard on the issues but easy on the people.
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Let me be clear. This thinking does not come from the traditional best sellers on management. And you know which ones I mean. I could give you my own 48 Laws why these "leaders" got it wrong. These books' pages read like how-to guides on how to be a prick, destroy creativity, and stifle innovation. They may have worked at some point in history, but not today.
Compare those books to the leadership wisdom of John Doerr, Clayton Christensen, or Eric Schmidt. The difference is polarizing. Why? To understand, let's look at what Brené Brown calls power over versus power with.
Leaders who work from a position of power over believe that power is finite and use fear to protect and hoard power. They believe that being right is more important than getting it right.
Leaders who work from a position of power with believe that power becomes infinite and expands when shared with others. They believe that getting it right is more important than being right.
Power over environments allows people to become replaceable cogs in the assembly line. If you can justify a machine over the wage worker, you do. This mindset assumes that the wage worker creates no value outside the task they were assigned to complete. However, in the new economy, creativity is what wins and keeps companies thriving.
Think of the creation of Gmail. Regardless if Paul Buchheit created it in Google's 20 percent time or not (it's the legendary policy of allowing engineers to divvy off part of their work hours for personal projects), it doesn't matter. What does matter is this: In that environment, workers are responsible for any aspect of the value creation—not just a single task. Anything those smart creatives needed to do to make the system better was more important than any singular task.
On an assembly line, we drive costs out of defined product offerings at a specific price. It's a mindset of scarcity. In a creative culture, and specifically at Moov, we take a different approach—a mindset of abundance. We believe there is always more to accomplish and more value to create. Because of this, we empower everyone here to embrace their epiphanies and act on them.
When you bring on new teammates, trust them to do what you hired them to do, then get out of the way. It's magical. They go, and they go fast. Not because I told them to, but because the culture and our environment encourage them to do so.
When you get the environment right, everyone can do remarkable things. And getting the environment right means that people have a deep sense of trust and cooperation. But this only happens when leaders—when I—put everything on the line to protect my people.
As Simon Sinek said in Why Good Leaders Make You Feel Safe, "Great leaders would never sacrifice the people to save the numbers. They would sooner sacrifice the numbers to save the people."
Leaders who prioritize the wellbeing of their employees end up with a more loyal workforce. If you inspire and support your people, they will do whatever it takes to see your company's vision become a reality. Why? Because they know their leader would do the same for them.
Of course, there are challenges along the way, and it's not all rainbows and unicorns. But something that moves us forward is the principle of disagree and commit. Once we have a decision, everybody commits to it, and we work together to execute. This simple framework allows for healthy tension throughout our various teams but keeps everyone aligned on what needs to be delivered.
So, back to that hard on the issues, easy on the people statement. For me, that's my foundation, connecting all of these aspects of leadership. I want nothing more than to create a blame-free but problem-aware environment. Being tough on the process and easy on people allows us to stay focused on resolving the issues at hand while maintaining relationships and respect for each other.
Together we agree on how we work and how we respond to problems. And we're uncompromising in establishing these process norms. We follow the agreed process and work together to improve it. The pace of change in technology is inevitably forcing all companies, especially startups, to focus energy battling the marketplace and not wasting it on internal politics. And if you can't do that, then it's time to find another gig somewhere else.
At Moov, we set standards that are fair but non-negotiable. We treat people with respect. We support and develop everyone towards personal and organizational goals. And when we do all of that, when we put people first, communicate openly and honestly while giving and demanding our best from each other, we outpace our goals and move on to the next one.
Why I joined Moov—Jared Jones
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Tom and his sweetheart Angela have a date. Tom loves Angela very much and he cannot stop kissing her again and again. However, there are many persons around them and it makes a problem for them to kiss. Help Tom turns this moment to a romantic date. Help Tom to kiss Angela when nobodies are watching them. And be careful, Tom has three chances, if he failed, he cannot continue to kiss his beloved Angela. Play the game and help lovers not be caught by other animals. Have fun!
Angela: a Cat That Swims!


What better way to celebrate Easter than with the candy-colors of springtime? Think you're too old for an Easter basket? Think again! Order a lush basket of Easter flowers from TOLEDO FLORIST & GIFTS for yourself or any bunny who needs a little pick-me-up! Whether your style is bright and cheery gerbera dasies, or powdery pastel lilies, this Toledo florist has you covered!
Say "thanks" with a beautiful Thanksgiving cornucopia. For your Thanksgiving Day flowers, think TOLEDO FLORIST & GIFTS for the best in autumn beauty. Who could resist the golden browns, rustic reds and cheerful oranges? Whether you're hosting a Thanksgiving day feast, or simply getting together with close family, flowers are always welcome around the table. Have extended family who cannot make it in for the holiday? Say you are thankful for them by sending Thanksgiving flowers to their home. Just give TOLEDO FLORIST & GIFTS a call and we'll take care of the rest.
Sometimes the best way to show your boss just how much you appreciate their fine leadership is by sending flowers. With a National Boss Day gift of flowers from TOLEDO FLORIST & GIFTS, your boss will know exactly how you feel. Everyone wants a raise. Raise your boss's spirits this Boss Day with one of the many colorful flower arrangements from TOLEDO FLORIST & GIFTS in Toledo, OR.
Sweetest Day gift baskets from TOLEDO FLORIST & GIFTS in Toledo are the perfect gift for this tasty holiday. Not only are they filled with your favorite sweet snacks, but they can be customized to be even more sweet for your special someone. Have a candy gift basket made for your friend who loves to snack. For chocolate lovers, you could send a candy bar gift basket or a gourmet chocolate gift basket, it just depends on your Sweetie's taste. Just give TOLEDO FLORIST & GIFTS a call and we'll help you find the perfect treat for your Sweet.
Tis the Season! Time to pull out the lights and put up the tree! At TOLEDO FLORIST & GIFTS, we specialize in all-things Christmas! With the trendiest Christmas accessories and ornaments, you are sure to find exactly what you need for your holiday decor at TOLEDO FLORIST & GIFTS in Toledo. Whether you're planning for a Christmas party or just decorating your home for the holiday, we've got you covered. From traditional, to playful and fun, you will find the Christmas decorations you need at TOLEDO FLORIST & GIFTS.
Nothing says "I Love You" more clearly than sending roses on Valentines Day. Whether it's a first date, first anniversary or the fiftieth, TOLEDO FLORIST & GIFTS can help you find the perfect gift for your sweetheart on this Day of Love. Don't forget to show your friends and family some love too with a special delivery from TOLEDO FLORIST & GIFTS. Browse our Valentines Day flowers online or call us for custom creation. No matter where you need to send roses, TOLEDO FLORIST & GIFTS in Toledo can help!


text:
What's Growing On?
Be a Garden Volunteer
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We Have Critters!
While we miss having the students in the garden, the quiet has allowed the critters to take over the gardens! We have baby birds, insects and even a lizard! We have put nest boxes in some of our gardens and the birds have moved in.
House wrens are about 4-1/2"-5-1/4" or 11-13 cm. They are small, very busy birds with a thin bill. The female lays 6-7 eggs that are white with reddish brown spots. The female incubates the eggs for about 12-15 days. The young leave the nest after 12-18 days. The female usually lays two clutches a year.
They feed mostly on all kinds of insects. Caterpillars provide the most nutritious food for the babies. The wrens are mostly cavity nesters. The male begins building several nests and the female picks one nest which she finishes. The nest has a foundation of twigs, with a soft cup of plant fibers, grass, weeds, hair and feathers.
Do we have an alligator living in the Theuerkauf Garden? No! We have a Southern Alligator Lizard (Elgaria multicarnita)! We've seen this little critter living in the plant matter. Alligator Lizards are native to the Pacific Coast of North America. They live in all kinds of habitats such as grasslands, chaparral, forests and even our urban gardens.
These reptiles have some interesting ways to defend themselves. They can pack quite a bit with their strong jaws. They can poop on you which has been described "as smelling like a dead fish that's been left out in the sun for several days". They can even detach their tails, which wiggle so the lizards can scurry away!
The females lay two clutches of eggs, usually in May and June. The eggs hatch during late Summer and early Fall. The Mama Lizard will stay with her eggs to guard them until they hatch.
These lizards can live from 10-15 years. They eat things like small arthropods, slugs, other lizards and even bird eggs. We're very happy to have this lizard living in our garden.
Stefani Brandt
P.O. Box 4121, Los Altos, CA 94024
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text:
Consumers in Colorado High on Marijuana Edibles
By Sean Kelley April 20, 2015
Fizzy drinks, chocolate truffles, ice cream—these aren't your parents' pot brownies. In Colorado, where marijuana was legalized in 2012, the edibles market is bubbling up. In fact, one company recently installed equipment to fill up to 1,000 bottles per hour of THC-infused sodas.
While edibles are often seen as pot consumption for beginners, the stakes are high: Edibles made up 45% of the recreational market in 2014—the first year of recreational pot sales. They also made up the bulk of controversy. Emergency rooms are seeing more admissions from overconsumption of marijuana edibles. The treats may have even played a role in two suicides and a murder, and the state has already had to pass new legislation.
The nascent pot edible industry has also come under attack for marketing products to children. And for quality control: In a report released earlier this year, the state concluded that serving sizes were confusing—a single cookie, for example, could contain up to 10 servings of THC, the active ingredient in marijuana.
Despite the problems, edibles are immensely popular: 5 million marijuana edibles—including brownies—were sold in 2014.
Self-described pot-trepreneur Anthony Franciosi, founder of Ant's Organic, says new legislation and new testing are helping standardize the food products. Manufacturers must now clearly mark a dose on a product. For example, if a chocolate bar has multiple servings, the bar could have lines on it indicating each 10mg dose—a standard set by the state. (The state of Washington has the same standard; Oregon still hasn't legalized edibles for recreational use due to the complexity of regulating edibles.) An individual package may not contain more than 10 doses.
"Edibles are a great way to enjoy cannabis without drawbacks like odor and smoking in general," Franciosi says. "You just have to treat them with respect."
Because unlike smoking marijuana, THC, the active ingredient in marijuana, takes longer—up to 2 hours—to reach the blood stream, Franciosi says.
New marijuana users are more likely to try edibles first, Franciosi adds, and that's where the problems start. (Just ask The New York Times columnist Maureen Dowd.)
For manufacturers the consistency problem starts with the raw cannabis. High-quality weed may contain 20% THC or higher, leading to edibles that had more kick than advertised. A 2014 Denver Post study found THC levels all over the place.
"They've gotten very strict at this point," Franciosi says. "The people who are finding the most success are the manufacturers who have the most consistent quality and consistent potency."
Under the new state law, which went into effect in February, manufacturers are now restricting that potency. Dosages must clearly be labeled and individual edible packages cannot contain more than 100mg of THC. Some edible makers are making products with 90 mg or less to limit risks.
Still, testing edibles isn't an exact science, according to a March 2015 study, which found advertised THC levels inconsistent with the THC levels in the actual edible.
That's why Franciosi recommends beginners start low and go slow. Whether you're trying ice cream, soda, or truffles (advice we can get behind, regardless), "Just eat one."


text:
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Part of my xml file is below.
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        <para>Etiam at ligula et tellus ullamcorper ultrices.</para>
    </levelledPara>
</description>

XSL code:
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
    xmlns:xs="http://www.w3.org/2001/XMLSchema"
    exclude-result-prefixes="xs"
    version="2.0">
    <xsl:output method="html"></xsl:output>

    <xsl:template match="/">

         ...

                ...

<xsl:apply-templates select="//levelledPara" mode="toc"/>

                ...

        ...

<xsl:template match="levelledPara" mode="toc">

    <xsl:value-of select="title"/>
    <xsl:if test="levelledPara">

        <xsl:apply-templates select="levelledPara" mode="toc"/>

        </xsl:if>

</xsl:template>

Desired output:

Heading [1]

Heading [1.1]

Heading [1.2]

Heading [1.3]

Heading [1.4]

Heading [1.4.1]

Heading [1.4.2]

Heading [1.4.3]

Heading [1.4.3.1]

Heading [1.4.3.1.1]

Heading [1.4.3.1.2]

Heading [1.4.3.2]

Heading [1.4.3.3]

Heading [1.4.3.4]

Heading [1.4.4]

Heading [1.4.5]

Heading [1.5]

Heading [1.6]

Heading [2]

Heading [3]

Actual output:

Heading [1]

Heading [1.1]

Heading [1.2]

Heading [1.3]

Heading [1.4]

Heading [1.4.1]

Heading [1.4.2]

Heading [1.4.3]

Heading [1.4.3.1]

Heading [1.4.3.1.1]

Heading [1.4.3.1.2]

Heading [1.4.3.2]

Heading [1.4.3.3]

Heading [1.4.3.4]

Heading [1.4.4]

Heading [1.4.5]

Heading [1.5]

Heading [1.6]

Heading [1.1]

Heading [1.2]

Heading [1.3]

Heading [1.4]

Heading [1.4.1]

Heading [1.4.2]

Heading [1.4.3]

Heading [1.4.3.1]

Heading [1.4.3.1.1]

Heading [1.4.3.1.2]

Heading [1.4.3.2]

Heading [1.4.3.3]

Heading [1.4.3.4]

Heading [1.4.4]

Heading [1.4.5]

Heading [1.4.1]

Heading [1.4.2]

Heading [1.4.3]

Heading [1.4.3.1]

Heading [1.4.3.1.1]

Heading [1.4.3.1.2]

Heading [1.4.3.2]

Heading [1.4.3.3]

Heading [1.4.3.4]

Heading [1.4.3.1]

Heading [1.4.3.1.1]

Heading [1.4.3.1.2]

Heading [1.4.3.1.1]

Heading [1.4.3.1.2]

Heading [1.4.3.2]

Heading [1.4.3.3]

Heading [1.4.3.4]

Heading [1.4.4]

Heading [1.4.5]

Heading [1.5]

Heading [1.6]

Heading [2]

Heading [3]

It seems that the template is applied over and over for the whole nested content. I can't figure out what may be the problem here.

A: It looks as if you should only select

<xsl:apply-templates select="/description/levelledPara" mode="toc"/>

for the first processing step, then your other template takes care of the recursive processing of nested elements.

redpajama_set_name: RedPajamaStackExchange


For three years, Serbia was not eligible for funding from the Global Fund, which resulted in the closure of harm reduction programs around the country. The movie, prepared by NGO Re Generation, gives a glimpse of the desperate situation faced by injecting drug users in Serbia, and also explores the consequences of the closure of needle exchange programs in Belgrade, whilst trying to assess the current situation in the country!
Serbia is at the crossroads of a number of heroin trafficking routes. It has a significant population of injecting drug users – 20,000 according to the official estimates. Thanks to grants from the Global Fund to Fight AIDS, Tuberculosis and Malaria, several harm reduction services were introduced during the first decade of this century. Approximately two thousand people enrolled in opiate substitution programs, and four needle exchange programs provided sterile equipment to injecting drug users. The prevalence of HIV among drug users was low, though access to harm reduction services was far from adequate – the best indicator of risk being the high prevalence of Hepatitis C infections.
The last grant from the Global Fund ended in June 2014. The Government made no commitment to continue funding the programs, and there are no other international donors available to step in and cover the harm reduction funding gap. This resulted in closing of all needle and syringe projects except one, which is operated by Association Prevent in Novi Sad. Three years later, the Government has changed but the programs are still out of focus when it comes to national funding!
What it means for Serbia at this point, and what it will mean for the future of the needle and syringe programs in the country is yet unknown. To find out more, watch the movie "Without Shift" produced by NGO Re Generation with support of Drug Reporter, exploring the opinions of different stakeholders on the topic.
Nova stranka first to sign "Declaration on Sustainable National Response to HIV"


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I wish I could get credit for doing a postdoctoral fellowship in child psychology; emphasis on the pre- and early adolescent stage. I'm about to complete some of the best training I've had for a long time! Two of my grandchildren are finishing up the semester of school they spent here with us at the Westover Center. They have been up close and personal with us probably for the first time in their entire lives. Only for a couple of fairly short stints have they lived near us, and outside of an awesome 10 day vacation we all took together a couple of years ago, we really haven't been able to spend all that much one on one time with these grandchildren. So we seized the opportunity, knowing that God had just put a big one right in our laps; a blessing, I mean. But blessings are like freedom—we all want them, but both require a great deal of responsibility!
We did not hesitate to step up to the plate when we could see that my son and daughter-in-law would have to maneuver some major hurdles for a few months in order to transfer residency from Georgia to Wisconsin. And we surely didn't know exactly what to expect, though we weren't too nervous, since we're already veterans, having four grown children and growing grandchildren. Additionally, we see a lot of kids in our practice, so how hard could this be?? Well, the kids are preparing to leave next weekend and I'm on the reflecting end of the past five month whirlwind. As I write, I'm thinking about the lessons learned.
Now that you get the idea about Kody, I want to let you know that I also learned about humility (not that this is the first time I've been humbled by the children in my family). I was more than gently reminded that you should never get a big head about yourself, as kids are extremely adept at leveling that playing field with little effort exerted. I had little to say when the band teacher called to tell me that my burgeoning tuba player had not brought in his lesson materials for weeks and it was intimated that it was because I was teaching my grandson! That band teacher probably thought, "Who does that crazy doctor think she is, anyway?" Remember that we're still relatively new to this area and since we have no younger children, I have had little interaction with the faculty of the local schools.
Oh, yeah, that's just Kody; I told you we had two kids, right? Well, let's see….Saundra, his older sister, who brought her flute along to join the band. Well, she told the band instructor that her flute was in the shop and she couldn't play for at least the first two weeks of the semester! Lord, love a duck, as my mother used to say. Come to find out, Georgia schools are way behind good ol' Iowa in music education and my granddaughter was intimidated. Well, Grandma does play the flute, so a few lessons at home (along with getting the flute 'out of the shop' and participating at school) and that girl was off and runnin'. She's so proud of her 'mad skills' as she calls it!
Saundra found out that she has a family trait that she thinks came from me; a sharp tongue and the gift of sarcasm. Oh, that girl eats it up! Although the sarcasm can still roll, I have worked very hard at keeping it relatively innocuous these days—you know, just for fun and nobody gets hurt. Saundra is working on that now herself. When she has a great line for her brother, she is holding back (mostly); and when a cutting remark slips out (sometimes too good to pass up!), she and Grandpa have a signal called 'back up the bus.' She apologizes, makes the beeping sound of the bus backing up and even includes the whooshing of the brakes and opening the door (see, she's learning about the fun side of sarcasm)!
Saundra seems to love the professional end of the practice. She's always ready to assist with paperwork, filing, etc. I'm hoping the exposure to our private practice might influence her just a little bit! Kody became an expert pooper scooper during the past few months. I can't begin to guess the number of plastic grocery bags of dog doo my grandson scooped from our yard. It was all happily deposited there by Dudley, Holly, and Recon—two Great Danes and a German Shepherd—think about it! Kody decided that the cold Iowa winters are at least good for one thing; frozen non-stinky dog poop!
Grandpa and I have tried to keep up with it all; the kids came with their dog, Recon, so he now walks three dogs in the morning. We are also on a good dog food plan with the local feed store where you buy 12 bags of dog food and get the 13th free; and they load it up for you and everything! And yep, we've already used up one card and received our freebie bag—and we're talking' 50 lb. bags of dog food, which explains the above 'poop issue'. Grandpa is a good citizen and picks up after them; the whole town is grateful, I'm sure! We have had to find donators of plastic bags to support our cause.
The bottom line is that we are exhausted! I don't know how we raised the four we had! We found ourselves falling asleep in front of the TV before bedtime many a night like old fuddy-duddies! My practice has a high percentage of children, as well, so we would leave our office work to spend evenings with our grandkids. The kids adjusted themselves to our hectic schedule and chose to wait to eat with us in the evenings, sometimes quite close to their bedtimes. They seemed to love to have that evening meal together so we could hear about their adventures that day. I'll miss all the laughter around the table when they go home, that's for sure.
I'll also miss our home church time together. We went through a couple of video series with the kids which provided special times of sharing their individual spiritual walks with us. They were interested, asked good questions, and brought thoughtful comments to our discussion. I am so thankful that we opted to have church as a family for these few months we had together.
Churchill also aptly stated this: "We make a living by what we get, but we make a life by what we give." It has been a sacred privilege and gift of precious time that my husband and I have had the opportunity to spend the past five months with Kody and Saundra. I trust it has made a positive investment in their lives, as it has in ours. At the very least, I'm sure they went away with some crazy Grandma and Grandpa stories to share with their own kids some day!


text:
$750,000 settlement reached with DC attorney general in case involving funds used in 2017 Trump inauguration
By Kara Scannell, CNN
Updated 11:47 AM EDT, Tue May 3, 2022
Report says Trump hid over $70 million in losses at key hotel
The Trump Organization and the Presidential Inaugural Committee will pay a total of $750,000 to settle with the Washington, DC, attorney general's office over allegations they misspent money raised for former President Donald Trump's inauguration.
The Trump Organization will pay $400,000 and the PIC will pay $350,000, according to a person familiar with the settlement. As part of the deal, the money will be directed to two DC nonprofits, DC Action and Mikva Challenge DC, the DC attorney general's office said.
In announcing the settlement, DC Attorney General Karl Racine said, "After he was elected, one of the first actions Donald Trump took was illegally using his own inauguration to enrich his family. We refused to let that corruption stand. With our lawsuit, we are now clawing back money that Trump's own inaugural committee misused."
In a statement released by the Trump Organization, the former President said the settlement reflects "absolutely no admission of liability or guilt."
"As crime rates are soaring in our Nation's Capital, it is necessary that the Attorney General focus on those issues rather than a further leg of the greatest Witch-Hunt in political history," Trump said. "This was yet another example of weaponizing Law Enforcement against the Republican Party and, in particular, the former President of the United States. So bad for our Country!"
Lee Blalack, an attorney for the inaugural committee, said the committee is confident it would prevail at trial but settled to avoid "significant costs" of litigation. He said the committee's insurer, which is funding the settlement, would have paid twice as much to go to trial.
According to a settlement agreement filed with the court, it acknowledges that the defendants dispute the allegations and are settling "to avoid the cost, burden, and risks of further litigation" and that neither defendant is admitting any "wrongdoing, unlawful conduct, or liability."
Racine sued in 2020 accusing the 2017 Presidential Inaugural Committee of coordinating with the former President's family to "grossly overpay" for event space for inauguration events in January 2017 at the Trump International Hotel in DC. The inaugural committee wasted approximately $1 million of charitable funds in overpayment for the use of event space at the Trump Hotel in violation of District law, according to the lawsuit. They also alleged the committee paid nearly $50,000 to cover an outstanding debt for a block of rooms reserved by the Trump Organization at the Loews Madison hotel.
The Trump Organization has agreed to sell the Washington, DC, hotel to CGI Merchant Group, a Miami-based investment firm. CGI is partnering with Hilton Worldwide Holdings to operate the hotel under the Waldorf Astoria name. The deal is supposed to close soon.
CLARIFICATION: This story's headline has been updated to reflect that the Trump Organization is only paying part of the settlement. The story also has been updated to include additional developments.


Nathaniel Rosa is a London based photographer known for creating a strong visual style of imagery for advertising and commercial clients.
Into the depths of the forests at the eastern most edge of our country we took four brand ambassadors from the very 'London' running apparel brand Soar to Escape the country for this motion piece.
Luxury cycling clothing brand Le Col, whose - incidentally - products I really believe in, asked me to create a set of 'bold' images to launch Sir Bradley Wiggins' new winter range. After some faffing on foot it quickly became apparent that we should hire a tuc tuc and chase light round Oxford Circus for an hour - like kids.
A Levi's apparel style film. Tom and I both had a laugh creating this; we both knew we wanted to explore Thetford forest and create a visual synergy between fashion and nature. We actually went into it with the licensed song in mind, and built the direction of shooting around the feeling of defiance the track gave us.
A motion ident created for innovative aerodynamic sport brand Rule 28 to use across their networks and distributors for the Black Friday promotion. Low budget love!
In the south of Spain on a winter's evening model and upcoming cycling talent Ollie Jones and I shot some lookbook frames for Le Col clothing brand. A mini lookbook for the current seasons' range.
With a commissioned runner as talent, roaming guerrilla-style and permit-less around London with Soar Running's new winter tights and lightweight running top, we created a bunch of standout images for then soon to be released garments.
A subject that needs as much attention and openness as possible. A cycling team and client VELO partnered with Prostate Cancer UK to help try to spread the word about the effects, symptoms and diagnoses of this disease throughout the elite cycling scene. There was a fairly large instagram ad purchase for this motion piece and I hope the project went some small way to helping.
Chilled out and spec; Tom and I just do our thing. Creating still frames earlier in the day then with the sun lowering we journeyed to a road that had captivated us previously with its 'American-feeling' wide open sense of space and filmed what can only be described as a character study.
Tuscan escape with cycling brand Huez to create a strong garment range lookbook. Vibes, food, locations, logistics, hard work.


Last month the Vicar and I spent some Nectar points on a garden swing. Sitting on it is incredibly relaxing but we had to make some rules about usage by children as we anticipated that over-vigorous swinging might ensue.
A lovely way to celebrate one of my babies being in double figures now.


We study how the choice of the regularization parameter affects the quality of the reconstruction of the dielectric permittivity for an inhomogeneous medium, with data consisting of boundary observations of the electric field. Our method is based on the minimization of a Tikhonov functional and uses a finite element method for computations of the electric field. We conclude that the choice of the regularization parameter does not affect the quality of the reconstruction significantly in the studied cases, and can even be removed with results not significantly different from those with regularization.


text:
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What is Intel known for?
Intel is known for making computer processors and other semiconductor chips. The company was founded in 1968 and has since become one of the largest chipmakers in the world. Intel processors are used in most PCs and laptops, and the company also makes chips for servers, workstations, and other devices.
What is Intel company overview?
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, in the Silicon Valley. It is the world's second largest and second highest valued semiconductor chip manufacturer based on revenue after being overtaken by Samsung, and is the inventor of the x86 series of microprocessors, the processors found in most personal computers (PCs). Intel supplies processors for computer system manufacturers such as Apple, Lenovo, HP, and Dell. Intel also manufactures motherboard chipsets, network interface controllers and integrated circuits, flash memory, graphics chips, embedded processors and other devices related to communications and computing.Founded in 1968 by Gordon Moore and Robert Noyce, Intel was employee number 12 at the time of its founding. Arthur Rock (investor and venture capitalist) helped them find investors, while Max Palevsky was on the board from an early stage. Moore and Noyce had left Fairchild Semiconductor to found Intel. Rock was not an employee, but he was an investor and was chairman of the board.Intel was incorporated in California in 1969.Initial public offering on the Nasdaq Stock Market in 1971 under the ticker symbol INTC. The company went public at $24 per share, and raised $6.8 million. Intel was the first company to develop the microprocessor, which was invented by Ted Hoff in 1971. The microprocessor would eventually make possible the personal computer (PC).In 1979, Intel launched the 8086 16-bit microprocessor. The 8086 gave rise to the x86 architecture, which eventually became ubiquitous in PC compatible systems.In 1988, Intel introduced the 386 32-bit microprocessor, which extended the 8086's instruction set and added a paging feature that allowed the processor to access more than 1 megabyte (MB) of memory.In 1993, Intel introduced the Pentium line of processors, which included several groundbreaking technologies, such as the ability to execute multiple instructions at the same time (a technology known as superscalar design) and the use of advanced branch prediction.In 1995, Intel released the Pentium Pro, which was the first processor to use the now-commonplace technique of caching the most frequently used instructions in a processor's on-chip memory (known as a cache).In 1997, Intel released the Pentium II, which was the first processor to use the Socket 7 interface.In 1999, Intel released the Pentium III, which was the first processor to use the now-commonplace technique of integrating the processor's cache into the same chip as the processor itself (known as a cache-on-chip or Co-processor).In 2000, Intel released the Pentium 4, which was the first processor to use the now-commonplace technique of executing instructions in parallel using multiple processing cores (known as hyper-threading).In 2008, Intel released the Core line of processors, which marked a significant change in the company's processor design philosophy. Prior to the release of the Core processors, Intel's processors were designed to be the fastest and most powerful processors available. The Core processors, on the other hand, were designed to be more energy-efficient and to provide a better balance between performance and power consumption.In 2010, Intel released the Sandy Bridge microarchitecture, which represented a significant improvement in processor performance and power efficiency.In 2012, Intel released the Ivy Bridge microarchitecture, which further improved on the performance and power efficiency of the Sandy Bridge microarchitecture.In 2013, Intel released the Haswell microarchitecture, which represented the biggest improvement in processor performance and power efficiency in over a decade.In 2014, Intel released the Broadwell microarchitecture, which improved on the performance and power efficiency of the Haswell microarchitecture.In 2015, Intel released the Sky
What are major contributions of Intel?
Intel's major contributions are in the area of microprocessor technology. Intel is the inventor of the x86 series of microprocessors, the processors found in most personal computers. Intel also manufactures motherboard chipsets, network interface controllers and integrated circuits, flash memory, graphics chips, embedded processors and other devices related to communications and computing.
What is Intel's strategic advantage?
Intel has a number of strategic advantages that have allowed the company to become the world's largest semiconductor manufacturer. Firstly, Intel has a very strong brand and is the market leader in microprocessors. This gives the company a significant competitive advantage as customers are more likely to choose Intel over its rivals. Secondly, Intel has a very efficient manufacturing process and is able to produce chips at a lower cost than its competitors. This allows the company to sell its chips at a lower price, making them more attractive to customers. Finally, Intel has a strong research and development team which allows the company to continually innovate and bring new products to market. This has helped the company to maintain its position as the market leader in microprocessors.