Wildlife enthusiasts who want a deeply immersive and enchanting experience with variety.
This 11-day Classic Camp and deluxe camping safari has been designed to take its time so you can explore Botswana's scenic northern areas from forests, floodplain, wetland and grasslands with a variety of activities, from walks, day and night wildlife-viewing on land and water, and the "Flight of Angels air transfer. Stay three-nights in each region to give you a deeper understanding of the movements and life of the local wildlife like elephants, lions, leopard, and water buffalos.
After arrival in Maun, you will be met by your guide or our representative and fly by light aircraft over the shimmering water-world of the Okavango Delta which represents life at its most fertile.
Lush Jacana Camp is situated in a permanently flooded region of the private Jao Concession of the Okavango Delta. A true water camp, it represents the essence of the Delta, with year-round mokoro safaris as well as island bush walks and, water levels permitting, motorboat cruises. In fact, when the flood levels are at their peak we are able to motorboat from the airstrip to the camp, a truly surreal arrival! On one of our full days, we will also enjoy game drives around the productive 'Jao Flats' region to the north of camp.
Jacana Camp is set in one of the wetland areas most densely populated with sitatunga and red lechwe. Wildlife concentrations depend on the water flow and volume, thus changing from season to season, but all the large animals can be found in the area including elephant, lion, leopard and buffalo. Pel's Fishing-Owl, Lesser Jacana, Western Banded Snake-Eagle and Coppery-tailed Coucal are just some of the birding highlights.
Over time, the Khwai area has metamorphosed into a wide range of exciting wildlife habitats – some of the most varied to be found in the entire Okavango Delta: a blend of forests, floodplain, wetland and grasslands. The narrow Khwai Channel is home to large mammals such as hippo and crocodile with buffalo and red lechwe often seen grazing along the fringe. The beautiful gallery riverine woodland found along the river provides further sanctuary to birds, primates and leopard. Elusive roan antelope often come to the river to drink. Activities focus around day and night game drives, nature walks and seasonal mokoro excursions.
Away from the river there is a wonderful mix of acacia and leadwood trees of varying sizes that abuts into mopane woodland. The latter, together with the permanent presence of water, attracts large numbers of elephant to the area. Larger predators include lion, wild dog and spotted hyaena, while birdlife found here is just as varied thanks to the colourful palette of habitats.
After a light breakfast, we fly north-east to the private Linyanti Concession. After a short game drive we arrive at our private Discoverer camp, which is elegantly set up under African ebony and knobthorn trees overlooking panoramic vistas of the Linyanti Swamps.
After a short morning drive and breakfast, we depart by light aircraft to the northern Chobe region of Chobe National Park. This area is famous for its vast herds of elephants in the dry season and other unique species such as the elusive puku and Chobe bushbuck that move to the river in the hottest hours of the day. Enjoy a light lunch on the boat cruise in a catamaran-style shaded boat.
We leave Botswana and fly to Livingstone International Airport, arriving at Toka Leya Camp in the late afternoon. On leaving Botswana, we fly over the Kazangula border, a point where the four countries of Botswana, Zambia, Zimbabwe and Namibia meet.
The grand finale is a guided tour of the Victoria Falls, one of the Seven Natural Wonders of the World. At 1708 metres wide, it is the largest curtain of water in the world and drops more than 100 metres into the sheer Zambezi Gorge.


text:
\section{Introduction}\label{sec:intro}
The Pound-Drever-Hall (PDH) locking technique  \cite{drever_laser_1983} is a popular method to stabilize the frequency of a laser to a stable optical resonator. It has been used to achieve lasers with sub-Hertz linewidth \cite{kessler_sub-40-mhz-linewidth_2012,schmid_simple_2019} and is applied in a wide range of fields, such as gravitational wave detection \cite{willke_stabilized_2010}, atomic physics \cite{hond_medium-finesse_2017,legaie_sub-kilohertz_2018} and metrology, \cite{grinin_two-photon_2020} just to name a few. The PDH method can also be used in the opposite way to stabilize the length of an optical resonator to a stable single-frequency laser with equally numerous applications \cite{wulfmeyer_2-m_2000,chen_injection-seeded_2022,zhang_seeded_2020,ricciardi_sub-kilohertz_2015}.

Despite its widespread and long-standing application, this technique is continuously refined and adapted to specific applications \cite{cygan_active_2011,gatti_wide-bandwidth_2015,izumi_self_nodate,zeng_stabilizing_2021,wang_artificial_2019}. The dynamic range of the standard PDH technique is limited by the additional zero crossings of the error signal at off-resonant frequencies. This typically limits the dynamic range (or capture range) of the lock to a fraction of the free spectral range (FSR) of the resonator given by
\begin{equation}
    \Delta f = \frac{c}{2L},
\end{equation}
where $c$ is the speed of light in the resonator and $L$ is the length of the (linear) resonator. The PDH error signal has a zero crossing right in the middle between two adjacent resonator modes at frequency detuning $\nu = \Delta f/2$ from the resonator mode. This zero crossing represents a stable lock point, where laser and resonator are stabilized in a totally off-resonant state. Such undesired stable operating points are also called Trojan operating points \cite{homer_odyssey_nodate, yen-ting_wang_practical_2013}. Since the modulation frequency is typically much smaller than the FSR of the resonator, a large disturbance (causing large laser frequency or resonator length variations) may lead to an erroneous stabilization on the Trojan operating point. When this occurs, the correct lock point must be restored either manually or via an automated process, which requires dedicated electronics and can take up to several ms \cite{schutte_experimental_2016,haze_note_2013,guo_automatic_2022}.

In this paper, we demonstrate a simple way to avoid off-resonant Trojan operating points in a PDH error signal, by modulating the seed laser at $\nu_{M} = \Delta f/2$, i.e. at half the FSR of the resonator. In doing so, the off-resonant lock point between two resonances is made unstable, resulting in an ``infinite'' capture range so that re-locking always occurs on a resonance independently of the size of the perturbation. Our scheme is particularly well suited for injection-seeding lasers or optical parametric oscillators.

The paper is organized as follows: In section \ref{sec:Theory} we present the theory of the PDH error signal, highlighting the peculiarities related to the use of $\nu_{M}=\Delta f/2$. We also emphasize the parameter range in which the locking scheme works best and we link our scheme to recent ideas which extend the linear range of the PDH error signal\cite{evans_lock_2002,li_broadening_2021,miyoki_expansion_2010}. In section \ref{sec:Experimental_Results} we present an implementation of our scheme in an injection-seeded thin-disk laser (TDL).

\section{PDH scheme without Trojan operating points}\label{sec:Theory}

\subsection{Analytical expression for the classic PDH error signal}
In general, a resonator, where the losses mainly occur at the end-mirrors, can be simplified to a two-mirror resonator, where the mirrors have power reflectivities $R_1$ and $R_2$. Without loss of generality, possible intra-resonator gain can be included in $R_2$ so that $R_2 > 1$ is possible.
For such a general resonator we define its finesse \cite{pollnau_spectral_2020} as
\begin{equation}
    \mathcal{F} = \frac{2\pi}{-\textnormal{ln}\left(R_{1}R_{2}\right)}.
\end{equation}
$\mathcal{F}$ is a measure of the sharpness of the resonances and can be approximated as the ratio
\begin{equation}
    \mathcal{F}\approx \frac{\Delta f}{\delta f},
\end{equation}
where $\delta f$ is the FWHM linewidth of the resonances. In this study $\nu$ denotes the relative detuning between the seed laser frequency and the nearest resonance frequency of the resonator $\textnormal{TEM}_{00}$ modes.

Depending on $\nu$, part of the phase modulated seed light is reflected from the resonator. Its electric field amplitude and phase relative to the input light is given by the complex reflection coefficient \cite{siegman_lasers_1986}
\begin{equation}\label{eq:F(nu)}
    F(\nu )=\sqrt{R_{1}}-\frac{(1-R_{1})\sqrt{R_{2}}\exp{\left[2i(\pi \frac{\nu}{\Delta f}+\phi)\right]}}{1-\sqrt{R_{1}R_{2}}\exp{\left[2i(\pi \frac{\nu}{\Delta f}+\phi)\right]}},
\end{equation}
where $\phi$ is an additional phase shift which the light might acquire over one resonator round trip (e.g. by propagating through a gain medium). For simplicity, in the following we set $\phi=0$.

From this reflection coefficient, the well known PDH error signal is obtained as \cite{black_introduction_2001}
\begin{eqnarray}\label{eq:e(nu)}
    \epsilon(\nu,\nu_{M})=&&-2\sqrt{P_{c}P{s}}\ \textnormal{Im}\left[F(\nu )F^{*}(\nu + \nu_{M})\right. \nonumber\\&&\left. -F^{*}(\nu )F(\nu - \nu_{M})\right],
\end{eqnarray}
where $\nu_{M}$ is the modulation frequency, $P_{c}$ and $P_{s}$ are the power in the carrier and the sidebands of the seed laser respectively, Im[...] takes the imaginary part and * denotes complex conjugation. Note that this is the error signal only for the case of demodulation at $\nu_{M}$ and phase delay $\Delta \varphi = 0$ (see Subsec.\ref{subsec:demod_phase}).

The modulation frequency $\nu_{M}$ can be expressed in terms of the FSR as $\nu_{M} = \xi \Delta f$, where $0 < \xi \leq 1$ so that the PDH error signal can be re-written as
\begin{eqnarray}\label{eq:e(nu)_xi}
    \epsilon(\nu,\xi)=&&-2\sqrt{P_{c}P{s}}\ \textnormal{Im}\left[F(\nu )F^{*}(\nu + \xi \Delta f)\right. \nonumber\\&&\left. -F^{*}(\nu )F(\nu - \xi \Delta f)\right].
\end{eqnarray}
Inserting Eq.~\eqref{eq:F(nu)} into Eq.~\eqref{eq:e(nu)_xi} we find
\begin{eqnarray}\label{eq:e(nu)_general}
    \epsilon(\nu,\xi) =&&4\sqrt{P_{c}P_{s}} \frac{\sin\left(\xi \pi\right)}{G_{1}(\nu)}\left[\frac{G_{2}(\nu,\xi)}{G_{1}(\nu + \xi \Delta f)}\right. \nonumber\\&&-\left.\frac{G_{2}(\nu,-\xi)}{G_{1}(\nu - \xi \Delta f)}\right],
\end{eqnarray}
with
\begin{equation}
    G_{1}(\nu) = 1+\gamma^2-2\gamma\cos\left(\frac{2\pi\nu}{\Delta f}\right)
\end{equation}
and
\begin{eqnarray}
    G_{2}(\nu,\xi) =&& (\gamma^2 R_{1}-R_{2})\cos\left(\xi\pi\right)\nonumber\\&&+\left[\gamma-\gamma^3+\gamma(R_{2}-R_{1})\right]\cos\left(\frac{2\pi\nu}{\Delta f}+\xi\pi\right),
\end{eqnarray}
where
\begin{equation}
    \gamma = \sqrt{R_{1}R_{2}}.
\end{equation}
Instead of using the parameter $\gamma$, these equations can also be expressed in terms of the finesse by performing the substitution
\begin{equation}
    \gamma = \exp\left(-\frac{\pi}{\mathcal{F}}\right).
\end{equation}
Figure~\ref{fig:BasicPDH} shows an example of an error signal for $\xi=0.2$ and $\mathcal{F} = 40$ ($R_{1}=0.6$ and $R_{2}=1.42$). The capture range of the error signal is indicated as gray shaded area. The black full arrows indicate the direction of the feedback loop correction moving the system to the correct lock point ($\textnormal{TEM}_{00}$ resonance), whereas the open arrows indicate the region where the feedback loop steers the system erroneously towards the Trojan operating point. In the next subsection we present a method to avoid this stable but unwanted lock point.
\begin{figure}
\includegraphics[width=0.95\linewidth]{Basic_PDH_2.pdf}
\caption{\textbf{Top:} Simulation of a typical open-loop PDH error signal obtained by scanning the resonator length. The shaded area indicates the capture range of the feedback loop, i.e. the detuning region between resonator mode and seed laser frequencies that can be corrected. The arrows indicate the direction of the correction of the feedback loop. In this example the laser was modulated at $\nu_{M} = 0.2 \Delta f$ so that the red and blue sideband (RSB and BSB, respectively) lie at $\pm 0.2\Delta f$ from the carrier frequency. \textbf{Bottom:} Corresponding simulated intra-resonator intensity.}
\label{fig:BasicPDH}
\end{figure}
\subsection{Modulating at half the free spectral range}
If we modulate the seed laser at half the FSR of the resonator, i.e. $\nu_{M} = \Delta f/2$ or $\xi = 1/2$, Eq.~\eqref{eq:e(nu)_general} simplifies to
\begin{equation}\label{eq:e(nu,xi=0.5)}
    \epsilon(\nu,\frac{1}{2}) = 8\sqrt{P_{c}P_{s}}\frac{\left[\gamma^3-\gamma(1+R_{2}-R_{1})\right]\sin\left(\frac{2\pi\nu}{\Delta f}\right)}{1+\gamma^4-2\gamma^2\cos\left(\frac{4\pi\nu}{\Delta f}\right)}.
\end{equation}
In this case the blue and the red sidebands from neighboring resonances overlap and the error signal is free from Trojan operating points, as stressed by the shaded area spanning the whole region between two resonances in Fig.~\ref{fig:OurPDH}.

Since $0 < \gamma < 1$, we find
\begin{equation}
\epsilon(\nu,\frac{1}{2}) \begin{cases}
      \leq 0 & \text{for } \nu \in [-\Delta f/2,0]\\
      > 0 & \text{for } \nu \in (0,\Delta f/2]
      \end{cases}
\end{equation}
as the denominator in Eq.~\eqref{eq:e(nu,xi=0.5)} is a positive quantity. This guarantees that the only stable lock points coincide with the resonator resonances. The feedback loop will thus always re-lock on the nearest resonance independently of the size of the perturbation.
\begin{figure}
\centering
\includegraphics[width=0.95\linewidth]{OurPDH.pdf}
\caption{Similar to Fig. \ref{fig:BasicPDH} but for $\nu_{M} = \Delta f /2$. The shaded gray area covers the whole free spectral range, so that the capture range of the feedback loop is effectively "infinite". In this case the red and blue sidebands overlap at the detuning $\Delta f /2$.}
\label{fig:OurPDH}
\end{figure}

\subsection{Tolerable mismatch in the case \texorpdfstring{$\nu_{M}\neq\Delta f/2$}{Text}}
 For the practical realization of this locking scheme, it is key to understand the sensitivity of the error signal to a mismatch $\nu_{M} \neq \Delta f/2$. The maximal mismatch allowed to still achieve correct locking over the whole range is reached when the error signal has a saddle point at $\nu = \Delta f/2$ so that the sign of the error signal still only flips at $\nu = \Delta f/2$ (see Fig.~\ref{fig:OurPDH_Mismatch}).
\begin{figure}
    \includegraphics[width=0.95\linewidth]{OurPDH_Mismatch.pdf}
    \caption{\textbf{Top:} Similar to Fig.~\ref{fig:OurPDH} but in this simulation the seed laser was modulated with $\nu_{M} = \xi_{+}$ so that the error signal has a saddle point at $\Delta f/2$. In this simulation we use $\mathcal{F}=19$ ($\gamma=0.848$) and $\nu_{M} = 0.526 \Delta f$, as obtained from Eq.~\eqref{eq:xi_zeros}. The shaded gray area still covers the whole free spectral range so that the capture range of the feedback loop is still "infinite". \textbf{Bottom:} Corresponding simulated intra-resonator intensity. The red and blue sidebands no longer perfectly overlap at $0.5 \Delta f$, but the error signal is still usable.}
    \label{fig:OurPDH_Mismatch}
\end{figure}
To find the modulation frequency for which the saddle point appears in the error signal, we calculate the derivative of the error signal at $\nu=\Delta f/2$:
\begin{widetext}
\begin{equation}\label{eq:e(nu)_deriv}
    \frac{\partial \epsilon(\nu,\xi)}{\partial \nu}\bigg|_{\nu=\frac{\Delta f}{2}} = 16\sqrt{P_{c}P_{s}}\gamma\pi\frac{2\left[(\gamma^2 R_{1}-R_{2})\cos(2\xi\pi)-\gamma+\gamma^3\right]+\gamma_{0}}{\left(1+\gamma\right)^2\left( 1+\gamma^2+2\gamma \cos(2\xi \pi)\right)^2}\sin(\xi\pi)^2,
\end{equation}
\end{widetext}
where $\gamma_{0} = 1-\gamma^4-2\gamma (R_{2}-R_{1})+(\gamma^2-1)(R_{1}+R_{2})$. The non-trivial zeros of Eq.~\eqref{eq:e(nu)_deriv} are
\begin{equation}\label{eq:xi_zeros}
    \xi_{\pm} = \frac{1}{2}\pm\frac{1}{2\pi}\arccos{\frac{\gamma_{0}-2\gamma(1-\gamma^2)}{2(\gamma^2R_{1}-R_{2})}},
\end{equation}
which correspond to the minimal and maximal values that $\xi$ can take in order to avoid additional zero crossing in the PDH error signal. The allowed mismatch for a general resonator is illustrated in Fig.~\ref{fig:Mismatch}. The figure shows the two solutions obtained in Eq.~\eqref{eq:xi_zeros} versus the gain factor $\gamma$. The gray shaded area between the two curves indicates the allowed region of modulation frequencies in terms of $\xi$, where $\xi = 0.5$ means modulation at exactly half the FSR. Clearly, higher values of $\mathcal{F}$ (or $\gamma$) reduce the tolerance for a mismatch between $\nu_{M}$ and $\Delta f/2$. For this reason our scheme is particularly suited for injection seeding of laser resonators with not too high finesse. In red is indicated a typical value of $\mathcal{F} \approx 19$ (or $\gamma \approx 0.85$, with $R_{1}=0.5$ and $R_{2}=1.44$) which we used in our experimental verification (see Sec.~\ref{sec:Experimental_Results}). In this case we could tolerate $\nu_{M} \in [0.475 \Delta f,0.525 \Delta f]$, i.e. a mismatch between $\nu_{M}$ and $\Delta f$ of about $\pm 5$\,\%. This requirement is easy to satisfy either by mechanical design or by using a frequency-tunable modulator.
\begin{figure}
\includegraphics[width=0.95\linewidth]{Mismatch_3.pdf}
\caption{$\xi_{-}$ and $\xi_{+}$ versus $\gamma$ (see Eq.~\eqref{eq:xi_zeros}). The gray shaded area $(\xi_{-}<\xi<\xi_{+})$ indicates the allowed window of modulation frequencies in terms of $\Delta f$ yielding an "infinite" capture range (without Trojan operating points). The red line illustrates an example where $\mathcal{F}=19$ (see Sec.~\ref{sec:Experimental_Results}), allowing for $\nu_{M} \in [0.475\Delta f,0.525 \Delta f]$.}
\label{fig:Mismatch}
\end{figure}

\subsection{Dependence of the locking scheme on resonator finesse}
Our PDH locking scheme with $\nu_{M}\approx\Delta f/2$ is best suited for locking a low-finesse resonator to a seed laser. Indeed, Fig.~\ref{fig:OurPDH_CloseZero} illustrates how the error signal approaches zero between the carrier and the sideband for increasing $\mathcal{F}$. If the electronic noise on the error signal is too large, the error signal can have random zero crossings which would lead to Trojan operating points and jeopardize the whole idea of the half FSR locking. For example, a (conservative) noise level of 10\,\%, as indicated by the dashed horizontal line in Fig.~\ref{fig:OurPDH_CloseZero}, requires the finesse of the seeded resonator to be $\mathcal{F} \lesssim 55$ (or $\gamma \lesssim 0.95$).
\begin{figure}
\includegraphics[width=0.95\linewidth]{OurPDH_CloseToZero_2.pdf}
\caption{Simulated PDH error signal of Eq.~\eqref{eq:e(nu,xi=0.5)} for various values of resonator finesse $\mathcal{F}$ (gain factors $\gamma$). The horizontal dashed line indicates the 10\,\% level of the error signal. The error signals are normalized to have the same maximum.}
\label{fig:OurPDH_CloseZero}
\end{figure}
\subsection{Dependence of the locking scheme on the demodulation phase shift}\label{subsec:demod_phase}
Strikingly, our scheme is rather insensitive to variations of the phase shift $\Delta \varphi$ used in the demodulation (see Sec.~\ref{sec:Experimental_Results}). While the amplitude of the error signal decreases for $\Delta \varphi \neq 0$, the overall shape stays the same as shown in Fig.~\ref{fig:OurPDH_phase}. This propertiy simplifies the practical implementation and optimization of the PDH loop parameters.
\begin{figure}
\includegraphics[width=0.95\linewidth]{OurPDH_Phase.pdf}
\caption{Simulated PDH error signal with $\nu_{M} = \Delta f/2$ for various phase shifts $\Delta \phi$ in the demodulation process. The error signal is zero when demodulated in quadrature ($\Delta \phi = \pi/2$). Note that in this simulation the error signals are not all obtained with Eq.~\eqref{eq:e(nu,xi=0.5)} but have to be calculated separately for different values of $\Delta \varphi$.}
\label{fig:OurPDH_phase}
\end{figure}
\subsection{Comparison to schemes with a large linear locking range}
Recently, a PDH scheme has been proposed in which the conventional error signal is divided by the transmitted power $T(\nu,\nu_{M})$ from the resonator \cite{evans_lock_2002,li_broadening_2021} to obtain a new error signal
\begin{equation}\label{eq:linearizePDH}
    \tilde{\epsilon}(\nu,\nu_{M}) = \frac{\epsilon(\nu,\nu_{M})}{T(\nu,\nu_{M})}
\end{equation}
with an increased linear dynamic range. Our scheme can be combined with this approach, resulting in an error signal as shown in Fig.~\ref{fig:linearPDH}. The modified error signal merges the advantage of both schemes: an "infinite" (over the whole FSR) capture-range and a more linear behavior. The new error signal is more noisy between the resonance and the sidebands since $T(\nu,\nu_{M})$ (i.e. the denominator of Eq. \eqref{eq:linearizePDH}) is small in this region. However, for this large detuning the noise should not excessively disturb the proper working of the feedback loop, especially for low-finesse resonators. Moreover, non-linear filtering \cite{li_broadening_2021} may be employed to reduce this noise.
\begin{figure}
\includegraphics[width=0.85\linewidth]{OurPDH_ErrorSig_largeLin_full.pdf}
\caption{\textbf{Top:} Similar to Fig.~\ref{fig:OurPDH} but the simulated error signal contains (Gaussian) noise. \textbf{Middle:} Error signal $\tilde{\epsilon}(\nu)$ obtained with Eq.~\eqref{eq:linearizePDH}. \textbf{Bottom: } Corresponding simulated intra-resonator intensity.}
\label{fig:linearPDH}
\end{figure}

\section{Experimental verification}
\label{sec:Experimental_Results}
We tested the PDH lock at $\nu_{M}=\Delta f/2$ for an injection seeded pulsed thin-disk laser (TDL) at 1030 nm. While details on the TDL will be published elsewhere, its simplified scheme is sketched in Fig.~\ref{fig:Sketch_Osci}. A single-frequency laser with linewidth < 30 kHz (Toptica DL Pro) at 1030~nm wavelength was used to seed the TDL resonator. Resonant incoupling of the seed was achieved by stabilizing the length of the TDL resonator via the PDH method to the seed frequency. The TDL resonator length was adjusted by having one end-mirror mounted on a piezo-electric actuator (piezo). The resonator length was $L = 1.85$~m corresponding to a FSR of $\Delta f = c/2L= 81$~MHz. Phase modulating the seed laser at $\nu_{M}=\Delta f /2=40.5$~MHz thus allowed us to obtain the PDH error signal free from Trojan operating points as shown in Fig.~\ref{fig:OurPDH_Measured}. The phase modulation was achieved by current modulating the seed laser with the output from one channel of a function generator (Tektronix AFG1062). The second channel was set to the same frequency and used as a reference to demodulate the signal from the fast photodiode (PD) measuring the light reflected from the TDL resonator. The relative phase $\Delta \varphi$ between both channels could be adjusted on the function generator.

We first tested the robustness of our PDH locking scheme operating the TDL below lasing threshold in CW-mode. The finesse of the TDL resonator was $\mathcal{F} \approx 19$, and its length was locked to the seed while the TDL crystal was pumped at 350~W and water impingement-cooled from the back side. Figure~\ref{fig:longterm_lock} shows the intra-resonator intensity (red), the closed loop PDH error signal (black) and the feedback voltage signal to the piezo (blue) over more than 15 hours. During this time 5 relocks occurred (marked by arrows in the figure) when the high-voltage amplifier of the PID control unit ran into its limit. No false re-locking was observed.
\begin{figure}
    \includegraphics[width=0.95\linewidth]{OpticalSketch_simplified.pdf}
    \caption{Sketch of the injection seeded thin-disk laser. Electronic connections are shown in black. The seed laser is current modulated at $\nu_{M}$. The PDH feedback loop, containing a mixer, a pre-amplifier and a low-pass filter (LP), outputs the error signal, which is converted into a feedback signal in the PID controller. The feedback signal is applied to a piezoelectric actuator stabilizing the length of the thin-disk laser resonator. PBS: polarizing beam splitter, HV: high voltage, $\lambda /4$: quarter-wave plate, PD: photodiode, $\Delta \varphi$: phase shifter, HR: high-reflectivity mirror.}
    \label{fig:Sketch_Osci}
\end{figure}
\begin{figure}
    \includegraphics[width=0.95\linewidth]{OurPDH_Measured.pdf}
    \caption{\textbf{Top: } Open-loop error signal of our PDH lock modulated at $\nu_{M} = \Delta f/2$ measured with a fast photodiode ("fast PD" in Fig.~\ref{fig:Sketch_Osci}). The trace was obtained by scanning the length of the seeded thin-disk laser resonator while the seed laser was modulated at $\nu_{M}=40.5$~MHz. \textbf{Bottom:} Corresponding intra-resonator intensity measured with the photodiode ("PD intra" in Fig.~\ref{fig:Sketch_Osci}) monitoring the leakage light behind an end-mirror of the resonator.}
    \label{fig:OurPDH_Measured}
\end{figure}
\begin{figure}
    \includegraphics[width=0.95\linewidth]{Lock_Longterm_4.pdf}
    \caption{Measurement of the long-term stability of the PDH locked injection-seeded thin-disk laser resonator operated below lasing threshold. Closed-loop error signal, intra-resonator power and high-voltage (feedback) signal applied to the piezo element controlling the resonator length, are plotted versus time. Over the course of 15 h five relocks marked by the arrows occurred, when the PID servo-box reached its maximal output voltage. Relocking does not affect the intra-resonator power stability, demonstrating no false locking. The saw-tooth like oscillations in the feedback signal are due to temperature variations in the ambient air.}
    \label{fig:longterm_lock}
\end{figure}
\begin{figure}
    \includegraphics[width=0.95\linewidth]{Relock_disk_2.pdf}
    \caption{Measured closed-loop error signal, intra-resonator power and high-voltage (feedback) signal applied to the piezo element controlling the resonator length, versus time after pulse extraction. In this case pulses of 10~mJ energy where extracted at a pump power of 350 W. The traces are obtained from an average over 100 pulses.}
    \label{fig:relock_disk}
\end{figure}

We then tested the transient behavior of our PDH lock by seeding the TDL in CW and pulsing it with a repetition rate of 100~Hz to introduce a large disturbance in the laser dynamics. As expected, a laser pulse strongly perturbs the PDH error signal and, for a short time ($<1$~\textmu s), also saturates the fast PD. However, the saturation is beneficial since it limits the sensitivity of the feedback loop to the pulse, because the constant (saturated) signal from the PD is mixed with the reference and low-pass filtered down to zero during this time. Hence, the error signal is zero while the PD is saturated, which prevents the feedback loop from correcting the TDL resonator length by an excessive amount, essentially leaving the resonator freely drifting until the PD recovers.

Figure~\ref{fig:relock_disk} shows the intra-resonator power (red), the closed loop error signal (black), and the applied feedback voltage to the piezo (blue) during and just after a pulse extraction from our TDL. No false re-locking was observed also in this pulsed operating mode. The 20~ns long laser pulse (coupled out at $t=0$) disturbs the error signal for a short time. The fast saturation of the diode signal limits the excursion of the error signal so that the error signal stabilizes already after 40~\textmu s and the TDL resonator is again locked on resonance with the seed. Such a short stabilization time could in principle allow our system to deliver injection seeded pulses at 10-20~kHz repetition rate.

\section{Discussion and Conclusion}\label{sec:Conclusion}
We proposed a modified PDH locking scheme, where the error signal is free from Trojan operating points, by phase modulating the seed laser at half the FSR of the seeded resonator. In this way the dynamic range of the PDH lock is broadened to "infinity" (the full FSR), ensuring correct re-locking to a resonator $\textnormal{TEM}_{00}$ mode even after large perturbations.

We applied this technique to seed a thin-disk laser at 1030~nm from which we obtained single-frequency pulses of 20 ns length and 35 mJ pulse energy. The disk-laser was tested for >15~hours and no false locking was observed.

Our method requires good alignment and mode-matching of the seed to the resonator since higher-order transverse modes distort the PDH error signal and can lead to Trojan operating points. However, operating seeded laser resonators in $\textnormal{TEM}_{00}$ is not problematic thanks to aperture effects (e.g. soft aperture of the gain medium) and since typical seed lasers already run in $\textnormal{TEM}_{00}$. The reduction of the finesse due to the aperture effects is advantageous in our approach since a high finesse would lead to a PDH error signal very close to zero for detunings between the carrier and the sidebands, which, in the presence of excessive noise might trap the feedback loop and behave like a Trojan operating point.

Our locking scheme is particularly useful in situations where single-frequency operation of a master-slave system is required under rough conditions or over an extended period of time. For example, high-power/energy injection-seeded laser systems subject to large fluctuations and drifts of the running conditions would benefit from such a robust locking mechanism. Compared to widely used ramp-fire techniques \cite{lemmerz_frequency_2017,dai_development_2018,cao_theoretical_2020}, our method avoids the disadvantage of scanning the position of the end-mirror to obtain the resonance condition. Better stability and higher repetition rates might thus be feasible. Recently high-frequency RF-drivers, EOMs and photodiodes with bandwidths >~50~GHz have become available so that our technique can be applied to resonators shorter than 1~cm. This extends the range of applications of our technique to, for example, injection-seeded OPOs.

\begin{acknowledgments}
We acknowledge the support of the following grants:
The European Research Council (ERC) through CoG. \#725039; the Swiss National Science Foundation through the projects SNF 200021\_165854 and SNF 200020\_197052; the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Initiative EXC 1098 PRISMA (194673446), Excellence Strategy EXC PRISMA+ (390831469) and DFG/ANR Project LASIMUS (DFG Grant Agreement 407008443); the French National Research Agency with project ANR-18-CE92-0030-02;

\end{acknowledgments}
\section*{Author Declarations}
\subsection*{Conflict of Interest}
The authors have no conflicts to disclose.
\subsection*{Author Contributions}
\noindent
\textbf{Manuel Zeyen:} Conceptualization (equal), Data curation (lead), Formal analysis (lead), Investigation (lead), Methodology (equal), Project administration (equal), Visualization (lead), Writing – original draft (lead).
\textbf{Lukas Affolter:} Data curation (equal), Investigation (supporting).
\textbf{Marwan Abdou Ahmed:} Resources (supporting).
\textbf{Thomas Graf:} Resources (supporting).
\textbf{Oguzhan Kara:} Investigation (equal).
\textbf{Klaus Kirch:} Conceptualization (supporting), Funding acquisition (equal), Project administration (supporting), Resources (equal).
\textbf{Miroslaw Marszalek:} Data curation (equal), Visualization (supporting), Writing – review \& editing (lead).
\textbf{François Nez:} Conceptualization (equal), Funding acquisition (equal).
\textbf{Ahmed Ouf:} Validation (equal), Writing – review \& editing (supporting).
\textbf{Randolf Pohl:} Funding acquisition (equal), Resources  (equal).
\textbf{Siddharth Rajamohanan:} Validation (equal).
\textbf{Pauline Yzombard:} Writing – review \ editing (supporting).
\textbf{Aldo Antognini:} Conceptualization (equal), Funding acquisition (lead), Methodology (equal), Project administration (lead), Supervision (equal).
\textbf{Karsten Schuhmann:} Conceptualization (lead), Formal analysis (supporting), Investigation (supporting), Methodology (equal), Project administration (supporting), Supervision (lead), Writing – review \& editing (supporting).

\section*{Data Availability Statement}

The data that support the findings of this study are available
from the corresponding author upon reasonable request.

redpajama_set_name: RedPajamaArXiv


text:
Q: Finding the analytic function of $z$, given the real part
Problem. The real part of an analytic function $f(z)$ is given by $3x^2y-y^3$. Find the imaginary part. Find the analytic function of
$z$.

Attempt. I begin by applying the Cauchy-Riemann Equations. As $f(z)$ is given to be analytic, we may conclude that:
$$\frac{\partial u}{\partial x}  = \frac{\partial v}{\partial y}\;\;\;\;\;\;\frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}$$
Where $u(x,y)$ and $v(x,y)$ are the real and imaginary parts of $f(z)$, respectively ($x,y\in\mathbb{R}$). Hence,
$$\frac{\partial v}{\partial y} = 6xy \;\;\;\;\;\;\; -\frac{\partial v}{\partial x} = 3x^2-3y^2$$
Integrating these, we obtain:
$$f(z) = \int 6xy\;dy = 3xy^2 + C(x)\;\;\;\;\;\; f(z) = \int -(3x^2-3y^2)\;dx = 3xy^2-x^3 + C(y)$$
Then, the imaginary part of $f(z)$ is given by the sum of the two integrals, $6xy^2 - x^3$, hence:
$$f(z) = 3x^2y-y^3 + i(6xy^2-x^3)$$.

Unfortunately, I seem to have erred somewhere. Where have I gone wrong? Is this a valid approach?

A: It is $v(x,y)=3xy^2+C(x)$. We know that $v_x(x,y)=3y^2-3x^2$ so $C'(x)==-3x^2$ Hence $C(x)=-x^3+A$ where A is a complex constant. Now$f(z)=u(x,y)+iv(x,y)$

A: $u(x,y) = 3x^2y-y^3
$
$u_x = v_y =6xy
$
$ u_y=-v_x = 3x^2-3y^2$
$  dv = \frac{\partial v}{\partial x}dx + \frac{\partial v}{\partial y}dy$
$  dv = -\frac{\partial u}{\partial y}dx +\frac{\partial u}{\partial x}dy$
$v = (-3x^2+3y^2)dx +6xydy$
this is an exact differential  equation( check it)
so $v = \int_{y=constant}3y^2-3x^2dx + \int_{x=0}6xydy$ \
$v=3y^2x-x^3 +c_1
$
$f(x,y)= u(x,y)+v(x,y)=3x^2y-y^3 +i(3xy^2-x^3-c_1)
$

redpajama_set_name: RedPajamaStackExchange


Sea anemones are found in the order Actiniaria, while tube anemones (also known as tube dwelling anemones) belong to the order Ceriantharia. Both anemone types belong to the subclass Anthozoa are are thus comparatively closely related to stony corals.
A Tube anemone is equipped with a tube into which it can withdraw, and it creates this tube by secreting mucus and organelle threads. Tube anemones spend their lives buried down in soft sediment, where they catch food using their outer tentacles. Once the food is caught, the anemone uses its smaller inner tentacles to devour it. Two examples of fairly well-known tube anemones are the Burrowing Anemone (Ceriantheopsis austroafricanus) and the Lesser Cyliner Anemone (Cerianthus lloydii).
A majority of sea anemones have an adhesive foot and live attached to a surface, but some species are pelagic and drift around in the ocean. The pelagic sea anemones have a gas chamber that cause them to float upside down in the water.
Sea anemones often have large polyps and this feature makes them very beautiful and sought after by aquarists. Most species are 2-3 centimeters in size, but there are sea anemones that never grow bigger than 4 millimeters. Some of the largest known sea anemones are truly striking, reaching a size of nearly 2 meters. Of course, keeping such huge anemones in captivity is beyond the scope of most hobby aquarists.
You do not need a sea anemone to successfully keep clown fish in captivity. In an environment without predators, the clown fish does not depend on the anemone for protection. Keeping an anemone alive is much more intricate than keeping a clown fish, so please refrain from getting a live anemone unless you have the required know-how and are willing to adjust your aquarium to suit the needs of a sea anemone. Your clown fish will do just as well without an anemone or with an artificial anemone. Clown fish will even reproduce without an anemone in captivity.


How do you know if your website is working for you? If your business has a website then you need Google Analytics. Google Analytics will allow you to monitor your websites performance over time which you should do on a regular basis to ensure what you are doing is working. If not, you are likely to be wasting your time and effort.
This shows you how many times your website has been accessed. A session means visits and doesn't refer to how many individual people have visited your website.
The difference between a session and a unique visitor or new user is how many times that individual goes to your website.
When it comes to your website traffic, you will want both new visitors and returning visitors.
It means exactly what it says, a new visitor is classed as a person visiting your website for the first time and if they return to your website at a later date then they will be classed as a returning visitor.
New visitors are likely to only be researching so generally won't be ready to speak to someone. However, returning visitors are more likely to get in contact with you, so if your numbers don't match up you might be doing something wrong.
This will tell you where your traffic is coming from. These channels are Organic Search, Direct, Referral and Social.
Where your traffic comes from will vary depending on the company. For example, well-known companies will generally have 50% plus traffic coming directly to their site as people don't need to search for them.
It is important you know where your traffic is coming from so you know where to focus your efforts.
The bounce rate means how many people have entered your website and left it from the same page.
Ideally, you would want this number to be low (under 50%) but it obviously depends on what marketing strategies you are using. If the bounce rate is high on your homepage then there is likely something wrong with it.
The average session duration means how long the average visitor stays on your website for.
Of course, longer is better. Ideally, your avg. session duration will be between 1-3 minutes. If your website has a very low avg. session duration then it probably means you don't have enough information.


text:
Q: How to add a line under a button? I have a button like below with a line underneath. This is achieved by using text-decoration-line: underline. My problem with this is the line is only as long as the text in the button (All).
How can I get it to be the same length as the button while the button's corner remains a bit rounded as it is?
[Edit]: My apology, I've forgot to add that I use btn class from bootstrap. One of the answers is what I what I want to achieve but with btn class from bootstrap. Again, my apology.

A: use pseudo-elements
Like this

button {
  position: relative;
}
button::before {
  content: "";
  position: absolute;
  top: 150%;
  left: 0;
  width: 100%;
  height: 0.6rem;
  background-color: rgb(61, 61, 61);
}
<button>HelloWorld</button>

A: border-bottom: 2px solid black;
you can set border bottom below the button, also you can adjust paddings and stuff to make your line look good.
In case of rounded ones, border-radius is the option possible
Another way is to add < hr / > tag

A: Thanks for the helps but I've fixed this by wrapping the button in an element and have the underline works for the parent of the button instead of the button. This means the underline is for the parent's element not the button itself which allows the underline to have the same width as the button.

A: For this to work you need to increase the left and right padding of the text element. When the text element plus its padding-left and padding-right have exactly the same width as the button itself, it will look like you want to have it.
For you to achieve this you have to remove the button padding first, otherwise you'll just get double padding and the border would never go all the way out to the sides. You can overwrite Bootstrap in your own stylesheet, for example like this:
.btn {
  padding-left: 0;
  padding-right: 0;
}

.btn a {
  padding-left: 2.2rem;
  padding-right: 2.2rem;
}


text:
Baptist Life
Latest Florida Panthers News
CHICAGO (AP) — Joel Quenneville barking out instructions from behind the bench. A young team with a couple budding stars showing signs of improvement. It was a familiar scene, with quite a twist. The Florida Panthers got Quenneville a win in his return to Chicago, using a hat trick by Frank Vatrano to beat...
ST. PAUL, Minn (AP) — Doink. Doink. Winner. Noel Acciari scored with 5.6 seconds left in the third period and the Florida Panthers rallied to win their fifth straight game, beating the Minnesota Wild 5-4 on Monday night. Despite his stick being held by Ryan Suter, Acciari was able to tip in a shot from the...
CHICAGO (AP) — In some Chicago circles, certainly every one that includes a hockey rink, it's just "Q." Only one letter is necessary for a man so revered there is a Twitter account for his mustache with more than 40,000 followers. Q returns Tuesday night. Joel Quenneville leads the Florida...
Panthers beat Red Wings 4-1 for season-high 4-game streak
DETROIT (AP) — The Florida Panthers were thrilled to have banged-up goaltender Sergei Bobrovsky back on the ice. He was pretty happy about it, too. Bobrovsky made 27 saves, helping Florida beat the Detroit Red Wings 4-1 on Saturday night to win four straight for the first time this season. "Great to...
Panthers down another goalie, injured Driedger to miss weeks
SUNRISE, Fla. (AP) — Florida goalie Chris Driedger will miss several weeks with what's believed to be a groin injury, the latest health issue at that position for the Panthers. The Panthers announced the diagnosis Saturday, calling it a lower-body injury. Driedger was hurt midway through the first...
Boyle scores winner, Panthers hold off Kings 4-3
SUNRISE, Fla. (AP) — Sam Montembeault came off the bench to help the Florida Panthers hang on for a win. Brian Boyle scored the eventual winning goal and the Panthers held off a late surge to beat the Los Angeles Kings 4-3 on Thursday night to win their third straight game. Montembeault made 23 saves for...
Vegas Golden Knights fire Gallant, name DeBoer new coach
Gerard Gallant was abruptly fired by the Vegas Golden Knights on Wednesday less than two years after leading them to the Stanley Cup Final in their first season of existence and winning NHL coach of the year honors along the way. Peter DeBoer, fired last month by the San Jose Sharks, takes over immediately and...
Huberdeau sets franchise points mark, Panthers over Leafs
SUNRISE, Fla. (AP) — Jonathan Huberdeau is looking ahead after becoming the career points leader for the Florida Panthers. Huberdeau had a goal and an assist, surpassing Olli Jokinen for the points lead with 420, and the Panthers beat the Toronto Maple Leafs 8-4 on Sunday night. "It's cool....
Acciari, Bobrovsky lift Panthers over Canucks 5-2
SUNRISE, Fla. (AP) — Noel Acciari just keeps getting the puck in the net during the best scoring streak of his career. Acciari did it again Thursday night with two more goals and Sergei Bobrovsky made 30 saves in his first start in three games to lift the Florida Panthers over the Vancouver Canucks 5-2....
Hall lifts Coyotes over Panthers 5-2 for 4th straight win
SUNRISE, Fla. (AP) — When the Arizona Coyotes hit the road, they feel right at home. Taylor Hall scored the go-ahead goal late in the second period and the Coyotes won their fourth straight game, 5-2 over the Florida Panthers on Tuesday night. Arizona is 14-6-3 on the road and will play three of the next...
More Stories from Kentucky Today
With family looking on, Hagans puts on a show as Cats sweep Bulldogs
PHOTO GALLERY: Cats hold off Georgia for 14th win
Bill dealing with Kentucky hemp industry first to pass House

redpajama_set_name: RedPajamaCommonCrawl


Whereas the Master, Wardens and other free men of the Mystery or Art of the Tylers and Bricklayers of the City of London and the suburbs of the same (hereinafter referred to as the Tylers' and Bricklayers' Company) were incorporated by a Royal Charter of Incorporation granted by Her Majesty Queen Elizabeth on the 3rd day of August in the year 1568 and in the tenth year of Her said Majesty's Reign in which Charter among other rights and privileges it was granted that the said Tylers' and Bricklayers' Company should be persons able and capable in law to acquire possess and receive in fee and perpetuity lands tenements rents reversions and other possession to the value of Fifty Pounds per annum beyond reprises from any person or persons whatsoever willing to give devise sell or assign the same to them to have and to hold to them and their successors for ever in aid of the support of poor men and women brothers and sisters of the said company the statute concerning not putting lands or tenements to mortmain or any other statute act ordinance provision or restriction thing or matter thereof to the contrary made or provided to be made notwithstanding.
AND WHEREAS as the result of a Judgement in an action of Quo Warranto brought against the Corporation of the City of London given in the Court of King's Bench in the Trinity Term in the 35th year of the Reign of His Majesty King Charles the Second the said Tylers' and Bricklayers' Company surrendered to His said Majesty all and singular the powers franchises liberties privileges and authorities whatsoever and howsoever granted or used or exercised by the Company by virtue of any right title or interest in them placed by any Charters Letters Patent Custom or Prescription.
AND WHEREAS the said Tylers' and Bricklayers' Company was afterwards reincorporated by a Royal Charter of Incorporation granted by His Majesty King James the Second on the 18th day of February in the year 1685 and in the first year of his said Majesty's Reign in which Charter among other rights and privileges it was granted that the said Tylers' and Bricklayers' Company might have purchase receive and possess to them and their successors for ever manors messuages lands tenements possessions and hereditaments so that the same did not in the whole exceed the clear annual value of Three Hundred Pounds of lawful money of England the statute of not putting lands and tenements in mortmain or any other statute act ordinance or provision heretofore made or any other thing cause or matter to the contrary thereof notwithstanding and that they and their successors might forever have hold and enjoy all goods chattels lands tenements possessions and hereditaments which they then had and possessed or of which any persons were or should be seised to their use.
AND WHEREAS it has been represented to Us by the humble petition of the said Tylers' and Bricklayers' Company that by virtue of the said Charters divers lands tenements and hereditaments have been purchased and received whereof certain have been sold and other lands tenements and hereditaments have been purchased with the moneys thereof accruing but that doubts have arisen whether the said Company acting inder the powers of the said Charters conferred upon them of selling of otherwise disposing of any of the said lands tenements and hereditaments were and are entitled to apply the proceeds of sale thereof in the purchase or acquisition of other lands tenements and hereditaments and if so what if any is the limit to be imposed upon them.
AND WHEREAS the said Petitioners by their said petition further showed and submitted that it would be for the benefit and advantage of the Petitioners that the proceeds of sale of any of the lands tenements and hereditaments held by them under the powers aforesaid should if deemed desirable be applicable in the purchase or acquisition or on the security of other lands tenements and hereditaments or interests therein. And further that either the capital of the Petitioners or any surplus income which may from time to time become available for investment or re-investment should if deemed desirable be applicable in the purchase or acquisition of lands and hereditaments tenements rents or reversions or otherwise in or upon any real security freehold or leasehold And further that having regard to the amount of the present rents and profits arising from the lands and hereditaments now held by the Petitioners both on their own account and as Trustees for certain Charities which they administer and to the progressive increase in the value thereof and of such rents and profits and to the present favourable opportunity for further investment in lands and hereditaments or upon the security thereof it is desirable that the Petitioners should be given and granted licence and power to purchase accept and hold in mortmain in perpetuity messuages lands tenements or hereditaments in addition to those now belonging to them of a yearly value not exceeding Thirty Thousand Pounds in the whole.
AND WHEREAS the Petitioners by their said petition humble prayed that having regard to the circumstances therein set out We would be graciously pleased to grant to the Petitioners a Supplemental Charter for the purposes aforesaid subject to such terms and conditions (if any) as to Us might seem fit which we are minded to do.
NOW KNOW YE that We being satisfied that it is to the interest of the said Master and Wardens of the Mystery of Art of the Tylers and Bricklayers of London that the powers conferred by the said Charter of Her late Majesty Queen Elizabeth and by the said Charter of His Majesty King James the Second hereinbefore recited should be extended in manner herein after mentioned of Our Special Grace certain knowledge and mere motion DO by these presents for Us Our Heirs and Successors will grant and declare (notwithstanding anything in the said Charter or Letters Patent in Mortmain to the contrary) that the powers of the said Master and Wardens of the Mystery or Art of the Tylers and Bricklayers of London to hold land may be extended and that they may be for ever able and capable in the law (without any further licence in mortmain) to take purchase accept hold and enjoy to them and their successors messuages lands tenements or hereditaments in addition to those now belonging to them the clear yearly value of which shall not exceed in the whole £30,000 such value being computed as at the time of the acquisition or purchase of the same and from time to time to grant demise alienate or otherwise dispose of the same or any part thereof and further in the event of any of the lands messuages tenements or hereditaments now vested in them as aforesaid or which may be purchased or acquired by them hereafter under the powers hereby conferred upon them being at any time sold or disposed thereof may be applied by the said Petitioners in the purchase of other lands messuages tenements or hereditaments to be held by the said Petitioners in the purchase of other lands messuages tenements or hereditaments to be held by the said Petitioners and their successors in mortmain in perpetuity.
AND WE do remit any forfeiture which may have been incurred by the said Master and Wardens of the Mystery or Art of the Tylers and Bricklayers of London in the acquisition of lands and hereditaments since the Charter of Her late Majesty Queen Elizabeth bearing date the 3rd day of August in the 10th year of Her Late Majesty's Reign.
AND WE do for Ourself Our Heirs and Successors give and grant Our Licence to any person or persons and any Body Politic or Corporate to assure in perpetuity or otherwise or to demise to or for the benefit of or to purchase from the said Master and Wardens of the Mystery or Art of Tylers and Bricklayers of London and lands tenements or hereditaments whatsoever situate in Great Britain or Northern Ireland within the limits of value aforesaid hereby nevertheless declaring that it shall not be incumbant upon such person or persons or Body to enquire as to the value of the property which may at any time or times be or have been acquired or held by the said Master and Wardens of the Mystery or Art of Tylers and Bricklayers of London.
AND WE do will ordain and declare that these presents shall be considered Supplemental to the said Charter of Her Majesty Queen Elizabeth and shall be construed therewith as one instrument.
AND WE do for Ourself Our Heirs and Successors grant and declare that this Our Charter or the enrolment thereof shall be in all things valid and effectual in law according to the true intent and meaning thereof and shall be taken construed and adjudged in the most favourable and beneficial sense for the best advantage of the said Master and Wardens of the Mystery or Art of Tylers and Bricklayers of London as well in Our Courts of Record as elsewhere by all Judges Justices Officers Ministers and other Subjects whatsoever of Us Our Heirs and successors and non-recital mis-recital or other omission defect or thing to the contrary notwithstanding.
These Letters to be made Patent.
WITNESS Ourself at Westminster the Twenty-first day of March in the second year of Our Reign.
BY WARRANT under the King's Sign Manual.


text:
The headquarters of the European Draughts Confederation are located at Paul Keres Chess House in Tallinn, Vene street 29. The headquarters were opened with a festive ceremony on April 23rd, 2009.
European Draughts Confederation Headquarter in Tallinn
The cover from the plaque with the EDC logo on the façade of Tallinn House of Chess, which has become a centre for mind sports for Tallinn and Estonia, was removed by Estonian Minister of Culture Laine Jänes, the mayor of Tallinn Edgar Savisaar, the Secretary-General of the Estonian Olympic Committee Toomas Tõnise and head of Tallinn Youth and Sports Department Rein Ilves.
This location – Vene street 29 – is mentioned for the first time in Tallinn´s documents already in 1362, but there is no information about the building. The building itself is first mentioned in a document that dates back to the year 1405.
European Draughts Federation Headquarter in Tallinn
More detailed information about the architecture of the building gives a testament from the year 1727. The building has had owners from different nationalities, including French and Scottish. During the renovation in 1968, the building was changed into a chess school.
There were rooms for classes, board and trainers and a separate room for library. New renovation started in 1973; in 1975 it was decided to be named Paul Keres Chess House that was opened on the 21st of November.
Chess House bought a library with 3000 books from Dombrovski, who was a collector of chess literature. Later, Paul Keres´s library with 2000 books was added to the collection. The museum room of Paul Keres was opened in 2004.
Paul Keres
Paul Keres (January 7, 1916 – June 5, 1975), was an Estonian chess grandmaster, who Keres narrowly missed a chance at a World Chess Championship match on five occasions.
He won the 1938 AVRO tournament, which led to negotiations for a World Championship match against Alexander Alekhine, but the match never took place due to World War II.
Then after the war he was runner-up in the Candidates' Tournament on four consecutive occasions. Due to these and other strong results, many commentators consider Keres to be the strongest player never to become World Chess Champion. He was nicknamed "The Crown Prince of Chess".


Bodiam Castle is a 14th-century moated castle near Robertsbridge in East Sussex, England. It was built in 1385 by Sir Edward Dalyngrigge, a former knight of Edward III, with the permission of Richard II, ostensibly to defend the area against French invasion during the Hundred Years War. Of quadrangular plan, Bodiam Castle has no keep, having its various chambers built around the outer defensive walls and inner courts.
Its corners and entrance are marked by towers, and topped by crenellations. Its structure, details and situation in an artificial watery landscape indicate that display was an important aspect of the design of the castle as well as defence. It was the home of the Dalyngrigge family and the centre of the manor of Bodiam. Possession of Bodiam Castle passed through several generations of Dalyngrigges, until their line became extinct, when the castle passed by marriage to the Lewknor family. During the Wars of the Roses, Sir Thomas Lewknor supported the House of Lancaster, and when Richard III of the House of York became king in 1483, a force was despatched to besiege Bodiam Castle. It is unrecorded whether the siege went ahead, but it is thought that Bodiam was surrendered without much resistance. The castle was confiscated, but returned to the Lewknors when Henry VII of the House of Lancaster became king in 1485. Descendants of the Lewknors owned the castle until at least the 16th century.


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You can hire PHP, Wordpress, CakePHP, Magento, Joomla, iOS, Android Programmers, web designers and developers from a virtual environment to complete the expert job you need. Speak to Seraph InfoTech and you can use our professionals on your parole to complete any projects you may require assistance with. You get all of this advantage with none of the people managing or training responsibilities; we take care of all of that.
Skills and Expertise, together with High Quality Communication, to deliver Results to our clients that adhere to their Requirements on Excellence, Time and Cost.
Quality is at the forefront of everything we do. We take the lead in the professional development of innovative web solutions, using all of our experience and expertise to deliver the on time, to budget and with exceptional level of quality that our clients expect. Our quality assurance regime supports not only our internal practices but also the complete satisfaction of our clients.
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text:
Angelina Jolie and Brad Pitt agree to 'finalise' divorce – report
Posted On : April 3, 2018 Published By : WENN
Angelina Jolie and Brad Pitt have "respectfully agreed terms" to settle their divorce amicably within weeks.
According to editors at British newspaper The Sun, the Salt star, who originally filed for sole custody of the former couple's six children, has since decided to allow Brad to have access to them. And she has been in discussions with her ex concerning the logistics of childcare while they both work and travel.
The agreement is expected to be filed imminently after the pair received court approval to continue their negotiations in February.
"The terms of the divorce are now agreed," a source close to Angelina told the news outlet. "They are being finalised by both legal teams, but will be filed within weeks."
Angelina filed for divorce in September 2016, amid an accusation that the Fury actor was involved in a physical altercation on a plane with their son Maddox, 16.
After Brad was cleared of wrongdoing by the Los Angeles County Department of Child and Family Services (DCFS), he was later granted visitation rights to Maddox, Pax, 14, Zahara, 13, Shiloh, 11, and twins Vivienne and Knox, nine.
In a big turnaround, the pair are reportedly now on good terms, and determined to ensure that going forward they maintain a "respectful relationship" for the sake of the children.
"The key thing is that they agree to custody sharing, with Brad having access and working with Angelina on logistic issues about work and travel," the source continued. "There were rumours the divorce was being called off, but that's not the case."
The actress and filmmaker recently took a year off from work to focus on the needs of her young family.
"Everything was just stopped," she explained to People magazine in September. "I'm really sitting and talking with them because everything affects them. Every location, every type of project, I'm going to have to adjust it to however much they can handle."
Insane magic trick with ball
Daily Dose- April 3, 2018 (2)


You have a Bachelor's degree in Biomedical Sciences or a related discipline (as evaluated by the Board of Examiners) and a strong motivation to succeed.
An online knowledge test and an online interview may follow before you are admitted to the programme.
Biomedical scientists want to minimise the impact of diseases for humans and humankind. Smart, global visionaries are needed who want to solve health care issues in the lab and in the field.
Radboud University aims to educate the best biomedical scientists with not just a thorough understanding of the molecular, individual and population aspects of human health and disease, but also with unique areas of expertise. To do this we have constructed a Master's programme in Biomedical Sciences that gives students the opportunity to construct their own programme based on personal academic and professional interests. Students choose one of three specialisations belonging to one of the research institutes and combine that with one of three career profiles. The research institute will be your learning environment, and a mentor of the institute will help you design your programme.
The programme provides students with a solid base in research methodology, statistics and biostatistics, laboratory research and communication skills. Leading scientists in fields ranging from metabolism, membrane transport, neuromuscular disease and inflammation to screening efficacy, clinical interventions and evidence-based medicine are involved in the teaching programme as lecturers and tutors.
A majority of our graduates become researchers in government departments, research organisations, universities and medical or pharmaceutical companies. Graduates also opt for careers as communication advisors or scientific consultant/advisor with a background in biomedical science, an expertise that is much in demand.
Why study Biomedical Sciences at Radboud University?
Possibility of specialising in any aspect of biomedical sciences from molecule (2 specialisations) to man (1 specialisation) to population (3 specialisations).
You can design your own programme so you can make it truly fit your academic and professional interests. A tutor will help you set up the best possible programme.
The programme has a strong career-driven focus with embedding in a research institute as a starting professional, room for long internships and the possibility to choose between a career profile in research, communication or consultancy.
Health care issues and biomedical research are placed in context. In the programme links are made between research and patient care (from bench to bedside), and vice versa.
Biomedical Sciences at Radboud University has a great reputation and graduates are highly valued by research institutes and health-care organisations all over the world.
Each of the three research institutes has its own mentors that are responsible for maintaining the quality of the programme as well as for coaching students in their specialist area. This system provides intensive career consultancy – an extremely valuable feature which is often lacking in other educational programmes in this field.
Thanks to the flexibility of designing a personal programme, graduates of the Radboud University's Master's programme in Biomedical Sciences will have developed a truly unique expertise in the field of biomedical science. You can broaden your view from molecule to man to population, or go in-depth into just one of these areas. Either way, you will have gained a new and refreshing perspective. And the intensive internships will guarantee you are prepared to enter the work force so that you can quickly start to play a vital role in improving human health.
There are various scholarships available for studying at Radboud University Nijmegen. Please check which scholarship is applicable in your case.
Orange Tulip Scholarship: Open to students from Brazil, Mexico, Indonesia and China - offers a tuition fee waiver of 6,750 euros and exemption from visa and health insurance costs.
Fulbright-Radboud Scholarships: Open to excellent American students - the grant will be paid in 12 monthly instalments of 1,050 euros, international travel and the cost of the residence permit will be covered.
Erasmus Mundus ERANET: Open for Russian candidates - applicants may be undergraduate exchange students, Master's students, doctorate and post-doctorate candidates, as well as academic and administrative staff.
Sino-Dutch Bilateral Exchange Scholarship: Open to students from China - the Dutch contribution to the scholarship consist of monthly allowance 1,000 euros, international travel costs 1,400 euros, tuition/research fee 1,906 euros, it also covers the cost of visa, insurance and other.
DIKTI-Neso Scholarships: Aimed at lecturers at higher education instituations in Indonesia who wish to pursue a PhD or Master's at a university in the Netherlands. A DIKTI scholarship includes allowances for living expenses, insurance, travel costs, tuition fees and more.
Dutch Student Finance: EU/EEA students and Swiss students under 30 years of age are eligible if they are working at least 56 hours per month in the Netherlands, or have been living in the Netherlands for five years or more. Dutch student finance consists of four components: a basic grant, a supplementary grant (depending on the parental income), a student travel product, and a loan.


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Home/News/Precision Drilling announces combination with Trinidad Drilling
Precision Drilling announces combination with Trinidad Drilling
Precision Drilling has announced that it has entered into an arrangement agreement with Trinidad Drilling pursuant to which Precision has agreed to acquire all of the issued and outstanding common shares of Trinidad on the basis of 0.445 common shares of Precision for each outstanding Trinidad Share pursuant to a plan of arrangement.
The aggregate transaction value is approximately $1,028 million, including the assumption of approximately $477 million in Trinidad net debt. Upon completion of the transaction, existing holders of Trinidad Shares will collectively own approximately 29% of Precision.
"This transaction creates exceptional value for both Trinidad and Precision shareholders," Kevin Neveu, President and Chief Executive Officer of Precision, said. "The combination provides a truly unique opportunity to combine two highly focused drilling contractors that are pursuing similar growth initiatives and competitive strategies and importantly, operating similar Tier 1 assets."
"From a strategic perspective, Trinidad is a perfect fit with Precision. We can realize immediate synergies, estimated to be over $30 million, through fixed cost reductions, operational efficiencies and reduced public company costs," Mr Neveu continued. "Over the long term, the additional scale will further strengthen Precision's operating leverage and positions the company to service our customers' continued transition to high-performance drilling services with high-spec AC rigs. Additionally, this combination allows us to better differentiate our service offering through our combined industry-leading drilling technology initiatives and a larger operating platform. The incremental free cash flow generated through this combination will ensure Precision meets or exceeds our long-term debt reduction targets and improves our financial flexibility to pursue growth opportunities in the United States and in international markets."
The Precision Board has unanimously approved the transaction and determined that the transaction and the entry into of the arrangement agreement are in the best interests of Precision. The Precision board has voted to recommend that holders of Precision shares vote in favor of the ordinary resolution approving issuance of Precision shares pursuant to the transaction. RBC Capital Markets, financial advisor to Precision, delivered a fairness opinion to the Precision board to the effect that, the consideration to be paid under the transaction is fair, from a financial point of view, to Precision.
Similarly, the Trinidad board has unanimously approved the transaction and determined that the transaction and the entry into of the arrangement agreement are in the best interests of Trinidad and its shareholders. The Trinidad board has resolved to recommend that holders of Trinidad securities vote in favor of the special resolution approving the transaction. TD Securities, financial advisor to Trinidad, delivered a verbal fairness opinion to the Trinidad board to the effect that, the consideration to be paid under the transaction is fair, from a financial point of view, to holders of Trinidad shares.
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Przyczyny wyłączenia sportu paraolimpijskiego z polskiego środowiska sportowego w opinii paraolimpijczyków / Exclusion of Paralympic Sport from the Sporting Community in Poland and its Causes according to Paralympic Athletes
Joanna Sobiecka
Advances in Rehabilitation > 2011 > 25 > 1 > 29-39
Introduction: The aim of this paper is to present the views of paralympic competitors on the causes of the alienation of Polish paralympic sport from the sporting community of healthy persons between 1972 and 2006.
Material and methods: This survey, prepared by means of diagnostic questionnaire method, was addressed to 435 competitors with locomotion or vision impaired, permanently residing in Poland and who participated in the Summer and Winter Paralympics between 1972 and 2006. Three groups of the surveyed subjects were created: Group One - 135 persons (1972-1988), Two - 94 (1992-1998), Three - 206 (2000-2006).
Results: The analysis of the data allows to say that the main causes of the separation of paralympic sport from the sporting community of healthy persons were attributed, first of all, to lack of information and promotion in the mass media. They also saw the difference in the way they were treated in comparison with able-bodied competitors and lack of appreciation by the healthy people who were supposed to work for the development of sport. According to the subjects, there was no integration among able-bodied athletes and disabled competitors themselves in Polish sport, which made it impossible for the paralympians to take part in common training sessions, training camps, and sporting events. The organisational structure in Poland has led to the isolation of the sport for disabled persons because it involved a closed circle of athletes associated with sports clubs, where only disabled persons trained. It should be mentioned that those causes were brought about by government and non-governmental institutions, the sporting community itself and social attitudes towards the sports practised by the disabled.
Conclusions: Despite the socio-economic transformation underway in Poland, the athletes had to cope with some recurring problems in the consecutive years of the paralympic games, which did not allow them to benefit from the changes that should have brought them closer to able-bodied athletes. Following the opinions voiced by the surveyed subjects, the government and non-governmental institutions have taken significant steps to eliminate the causes of the exclusion of Polish paralympic athletes from the sporting community. However, no such activities have been undertaken to eliminate the causes existing in the sporting community itself and in social attitudes.
DOI 10.2478/rehab-2013-0003
Zakład Sportu Niepełnosprawnych, Wydział Rehabilitacji Ruchowej Akademia Wychowania Fizycznego w Krakowie
Sport paraolimpijski Środowisko sportowe Wyłączenie sportu
Paralympic sport Spoting community Separation of sport
Publication languages: English
Data set: PSJD
De Gruyter Open
1. Mason F. Creating Image and Gaining Control: The Development of the Cooperation Agreements Between the International Olympic Committee and the International Paralympic Committee. In: Wamsley KB. Barney RK. Martyn SG (eds.). The Global Nexus Engaged: Past. Present. Future Interdisciplinary Olympic Studies. London: ON: ICOS: 2002. pp.113-122.
RELATION NAME
3. DePauw KP. Gavron S.T (eds.). Challenges and Controversies in Disability Sport. In: Disability Sport. Human Kinetics: 2005. second edition, pp. 241-255.


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TV reviewTelevision
Cheer review – absolute proof that cheerleaders are gravity-defying gods
Forget everything you thought you knew about cheerleaders ... Cheer. Photograph: Courtesy of Netflix
This awe-inspiring Netflix show follows a cheerleading team as they try to flip, toss and pyramid their way to the top. Are the bruises and breakages worth it?
Lucy Mangan
@LucyMangan
Thu 9 Jan 2020 10.27 EST
Last modified on Thu 9 Jan 2020 11.05 EST
Simply watching Cheer, Netflix's documentary series about cheerleading champions from Navarro college in Texas is like being in the marines. Seeing the dedication, resilience and innate talent of the athletes, many of whom come from profoundly troubled backgrounds and have seized upon the sport and the specialised college course as an almost literal lifeline, will break you down. ("What," you will find yourself asking, "is there in my pathetic simulacrum of existence that can compare to this ennobling vision of humanity unspooling across six hour-long episodes before my sofa-spread, doughy form?" and no answer will come.)
But then it will build you back up. "Look what the human body is capable of!" you will start to think, as 40 students made entirely of muscle and sinew bend, flip, form pyramids, toss and catch each other midair – and generally disapply all known laws of physics. They are as gods, and if you cannot hope to emulate, you will surely wish to serve.
The members of the Navarro squad are competitive cheerleaders (distinct from football cheerleaders who dominate the public image of the activity), and its practitioners are somewhere between acrobats, dancers and weightlifters, while maintaining the stamina of long-distance runners. The series focuses, refreshingly, on the graft, not the glamour – which comes for a few fleeting minutes at the end of a year's training when state teams converge on the national championship in Daytona to compress all their work into one routine around 200 seconds long. And although it registers friendships and fallings-out, it does not make them into soapy storylines. It prefers, equally refreshingly, to dig deep into the many qualities that must combine to make a single performer, and then how they must coalesce into one team.
The multiple daily practices are relentless, the technical prowess required is daunting, and the singularity of vision amounts to monomania. Any illusions you ever had about cheerleading will shatter within minutes. Scales will fall from your eyes more quickly than a flyer from a shonky pyramid practice. Flyers are the smallest, lightest squad members – the most easily launched and caught in basket tosses, and the ones catapulted to the very top of any formation.
Each episode fills in, without sensationalism or sentimentality, the backstories of various squad members. The gravity-defying tumbler Lexi, for example, was a teenage runaway. Flyer and tumbler Morgan became near suicidal through childhood neglect by her parents. Now, she competes alongside the others, despite having only a fraction of their training. By the end of it she has surpassed even the highest expectations. And the stunter (one of the rocks on which formations are built) and tumbler La'Darius has endured parental neglect, sexual abuse at his carer's home and violence from his brothers who, horrified by his homosexuality but scared what it would mean for him, tried to "beat him into a man". He survived a suicide attempt and now moves with impossible strength, skill and grace throughout the routine that we watch come together over the 68 days they have before Daytona.
Astonishing … coach Monica Aldama in Cheer. Photograph: Courtesy of Netflix
Moulding, training, scolding, mothering and policing them all is their astonishing coach, Monica Aldama. She is loved, feared and respected by every student, as well she should be, and she smiles only when there is something to smile about. My days of even dreaming of being an elite athlete may be long behind me, but the goal of becoming even 1% of what Aldama is will never leave me. She is the first and last word in fairness, discipline and tenacity, and she knows each one of "my kids" to their very bones. For the first time in most of their lives, they have someone who demands the best of them and who will give the best of herself right back.
She holds them accountable for their actions – her rules about behaviour, social media, drug use and so on are ironclad – but her support is unwavering. She is a (self-described) conservative, churchgoing Texan, but in loco parentis to several gay teenagers (although only La'Darius describes himself as such on screen) and in an ongoing argument with her pastor about his attitudes. "I will debate you up one side and down the other if you talk about my boys," she said. "I won't be changed."
She has a more robust attitude than many mothers might to the injuries that befall her offspring, but she and her squad are in it to win it. If the price paid in hairline fractures, dislocated joints and deep tissue bruising seems too high to civilians – well, that's why we remain civilians, spread out doughily on our sofas while we watch others soar.


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Living and Working in Dublin's Fair City
By Alex Paisner . January 9, 2013
Global Experiences' Dublin Location Coordinator Dara give us her insight into living and working in the heart of Ireland: Storied Dublin.
Having lived and worked in Dublin as well as a range of other European cities I definitely think anyone who opts to come here on an internship is in for a treat! Dublin is rich in culture and history and its blend of the modern with the traditional make it an enticing and exciting place to be. Dublin has a wealth of tourist attractions (museums, art galleries etc.), is famous for its vibrant nightlife and from our cobbled streets and ancient castles to our bustling bars and restaurants there really is something for everyone.
Dublin is not only the youngest city in Europe (with 50% of the population under the age of 25!) but it is also one of the friendliest! This geniality extends to the workplace where friendships are often formed over the photocopier and indeed many people's social lives are connected to work. Mention to your workmates that you're interested in yoga/jogging/the cinema (or any other activity that takes your fancy) and chances are that before you can say "top of the morning to you" you'll have been whisked off to join a local club or group by a colleague with similar interests. In the past, our interns have joined football clubs, rugby teams and reading groups amongst other things.
A recurrent observation from our interns is that working life and social life in Ireland are much more intertwined than back home. While most big global companies are now also based in Ireland, the workplace tends to be smaller here which lends to a more intimate experience for employees. Many interns report of being introduced to a Dublin institution, i.e. the pub by their work colleagues and of work outings becoming a regular feature of their stay here. There is no better way to discuss the previous week's work or dissect the office gossip than over a pint of creamy Guinness in a cozy snug with your colleagues at the end of the working week ! In a similar vein, many of the friendships formed by interns are with their new workmates who are only too happy to act as local guide and host to their new chums!
Something else of note is that that the Irish work approach differs in that hierarchies are less prominent than in the US. You are just as likely to find the company director on tea-making duty as the office junior so interns should not be insulted if required to do menial tasks as these are often shared by all.
Interns are usually encouraged to work on their own initiative but this does not mean that you can't ask for help or advice. You may be given a project and left to your own devices but this is usually to encourage your independence and should not be interpreted as been left to work alone – your colleagues should be only too pleased to help if you ask them.
While a more informal and personal approach is undoubtedly a feature of the Irish workplace, this should not be mistaken for unprofessionalism. The Irish work environment, while certainly culturally different to that of the US, is an excellent place to gain experience in your chosen profession. Interns based here have been delighted with the skills they have acquired and the valuable experience attained during their stay on our Emerald Isle.