text:
\section{Introduction}\label{par:introduction}
The emission of $\beta$-radiation from an ensemble of oriented nuclei can exhibit a high degree of asymmetry.
This was first observed by Wu \textit{et al.}, with a low temperature spin-oriented sample of \ce{^{60}Co} nuclei proving that the weak force does not conserve parity\cite{Wu1957}.
Due to the magnitude of the observed asymmetry compared to other types of anisotropically emitted radiation, this effect is a promising probe for several nuclear effects\cite{PostmaStone1986}.
In particular, it can be used as a very sensitive means of detecting nuclear magnetic resonance (NMR) signals, which can be up to ten orders of magnitude more sensitive when compared to conventional NMR on stable isotopes\cite{Gottberg2014} as it allows one to measure signals from as few as 10$^7$ nuclei.

The $\beta$-asymmetry that is observed in $\beta$-decay asymmetry detected NMR ($\beta$-NMR) experiments, scales linearly with the nuclear polarisation\cite{PostmaStone1986}, i.e. the amount of first order nuclear orientation within an ensemble.
Therefore, the larger the polarisation is, the better the signal to noise ratio (SNR) is.
The high level of polarisation of the ensemble of nuclei is one of the reasons for the high sensitivity of the technique, the other being the detection by $\beta$-radiation.

The Larmor precession frequency of the nucleus and the spin-lattice relaxation time are directly affected by the electromagnetic (em) environment it experiences.
Therefore, the implanted nuclei can be used as probes of these local environments in the host material by measuring the resonance (Larmor) frequencies and relaxation times in $\beta$-NMR experiments.
To do so, nuclei that have a non-negligible beta-decay asymmetry parameter, that can be spin-polarised and have a short lifetime are required. Examples of such nuclei are \ce{^{8,11}Li}\cite{Neugart2008}, \ce{^{31}Mg}\cite{Neyens2005MeasurementState}, \ce{^{26,27,28}Na}\cite{Harding2020MagneticBiology, Kowalska2017}.
Other experimental requirements are: a stable and homogeneous magnetic field (either externally applied or internal to the sample), a radio-frequency (rf) source, a set of beta-detectors and the sample to be studied.

Radioactive ion beam (RIB) facilities, of either the in-flight or ISOL-type\cite{Blumenfeld2013}, provide many nuclei that are suitable for $\beta$-NMR.
Our experiment is located at ISOLDE, which falls into the ISOL-type category\cite{Borge2016, Borge2017}.
This facility uses a 1.4~GeV proton beam as a light projectile impinging on heavy target materials, containing e.g. uranium or lead\cite{Gottberg2016}.
The diverse mixture of simultaneously produced isotopes is selectively ionised and consecutively accelerated, mass-separated, and electrostatically guided to different experimental setups\cite{Catherall2017}.

The resulting low-energy ion beam does not exhibit any nuclear polarisation.
Laser optical pumping, the method used at our polarisation beamline at ISOLDE \cite{Kowalska2017, Gins2019}, is a very efficient method to produce a sample of highly oriented short lived isotopes\cite{Kowalska2017}.
This is however dependent on an available closed excitation-deexcitation loop which is generally available for alkali and alkaline-earth metals. Moreover, when multiple-frequency pumping is used other elements (e.g Argon)\cite{Gins2019} can be efficiently polarized using this technique as well.

Using an accelerating/decelerating electrode the ion beam is tuned into resonance with the laser light to allow for the optical pumping process to happen, next (in the case of alkali metals) the beam passes through a charge exchange cell which neutralises the beam.
A space of 2~m is left for the atoms to interact with the laser light, after which the beam goes through a transition magnetic field which allows the spins to adiabatically rotate into the direction of the main magnetic field (B$_{0}$)\cite{Gins2019,Kowalska2017}.
Next the beam is implanted into the sample material from where the $\beta$-radiation is emitted and observed by a set of detectors located with and against the direction of B$_{0}$. After each ion bunch, the $\beta$-count asymmetry between the two detectors is recorded.
To record a resonance spectrum the frequency of the applied rf-field is modified at each bunch.
To extract from the measured Larmor frequency either the nuclear g-factor or the magnetic field felt by the nuclei, one usually performs a reference measurement.
A reference measurement can be performed by implanting another isotope of the same element in the same sample, yielding then a ratio of g-factors.
Alternatively, the isotope of interest can be implanted in another sample, yielding then a ratio of the magnetic fields felt by the isotope (and thus sensitivity to e.g. a chemical shift or a Knight shift).

$\beta$-NMR measurements have been applied in nuclear structure studies and in material science studies on solid-state samples compatible with the high vacuum environment present at RIB facilities\cite{kowalska2021}.
In nuclear structure studies, they can be used to determine magnetic dipole and electric quadrupole moments of short-lived nuclei \cite{Neyens2005MeasurementState,Arnold1987,Geithner1999MeasurementNucleus11Be,Keim2000}.
In material science, they serve as a sensitive local probe of the internal and interface em-fields\cite{MacFarlane2015}.

Recently, there has been increased interest in extending the scope of applications of the technique to (bio-)chemical studies, which typically make use of liquid samples in which small chemical shifts of the NMR signal are measured\cite{Gottberg2014,Jansco2017}.
This goal poses several design and engineering challenges: first, the need to combine the liquid environment with high vacuum and second, the requirement of a part-per-million (ppm) homogeneous and stable magnetic field.
Additionally, several practical aspects that improve the operation and throughput of the setup are also important to consider.
Such as minimising the footprint of the $\beta$-detectors and the time spent on changing liquid samples.

Here, we report on the developments that have led to the high-accuracy liquid-sample $\beta$-NMR experiments using our experimental setup at ISOLDE\cite{Gins2019,Kowalska2017}.
The upgrades described below have enabled us to determine with unprecedented accuracy the nuclear magnetic dipole moment of the short-lived \ce{^{26}Na} isotope\cite{Harding2020MagneticBiology}.
\section{Methods}

\input{Sections/01_01-Locking}
\input{Sections/01_02-Shimming}
\input{Sections/01_03-Beta_Detectors}
\input{Sections/01_04-Sample_Handling}
\input{Sections/01_05-Experimental_Chamber}
\subsection{Field locking}\label{par:Locking}
B$_{0}$ (1.2~T) was supplied by a Bruker (Billerica MA) BE25 electromagnet corresponding to a \ce{^1}{H} resonance frequency around 52~MHz.
This is generally considered low-field for modern day NMR spectrometers\cite{Blmich2019,Minkler2020}.
Due to the crowded environment of the ISOLDE experimental hall, which contains lots of devices that generate (fluctuating) stray fields, fluctuations of B$_{0}$ are to be expected.
However, a stable B$_{0}$ is essential for $\beta$-NMR experiments, especially those performed in liquid samples, where chemical shifts of a few ppm are often measured\cite{InorgChemEncycl2011}.
These shifts can easily become unidentifiable by peak broadening due to poor magnetic field homogeneity and/or stability.
Therefore a magnetic field stability and homogeneity on the level of a few ppm or less is required.
Systematic B$_{0}$ measurements showed that besides rapid fluctuations of low amplitude a significant drift could be observed.

In order to reduce these field changes and to stabilize the magnetic field, a feedback system was implemented.
As part of this system the magnetic field was measured using the pulsed NMR method on \ce{^{1}H} inside \ce{H_{2}O} enclosed in a 3~mm (outer) diameter vacuum-tight vial.
The applied pulse length was tuned to cause a $\pi/4$ rotation of the magnetization vector.
The free induction decay (FID) of \ce{^{1}H} nuclei in water was measured using a transmitter/receiver coil tightly wound around the outside of the vial.
This signal was acquired by a PS2204a PicoScope (Pico Technology, Cambridgeshire, UK).
A LabVIEW (National Instruments, Austin TX) \cite{Elliott2007NationalMeasurement} program was used to compute a zero-filled Fast Fourier Transform (FFT) of the acquired signal to obtain the \ce{^{1}H} Larmor frequency, which is proportional to the magnitude of the magnetic field.
This frequency was in turn compared to the set point using the LabVIEW built-in PID control function.
The output of the PID function was used to determine the number of steps required by a stepper-motor driving a 10~k$\Omega$ variable resistor, connected in parallel to the magnet.
The variable resistor was in series with two 1~k$\Omega$ resistors, to avoid short-circuiting the power supply.
When coupled to the magnet's power supply (providing 38~A) the stepper-motor afforded an adjustment range of B$_{0}$ of 350~ppm.

The \ce{^{1}H} frequency measurement was repeated every 200 ms.
A faster repetition rate was not feasible due to the long spin lattice relaxation times ($T_{1}$) of \ce{^{1}H} in water, and the subdued signal strength of the FID in a low magnetic field.

\subsection{Absolute-field measurement}\label{par:absolute-field}
The measured \ce{^{1}H} frequency also allowed the determination of the absolute value of the external magnetic field $B_0$ at the position of the \ce{^{1}H} magnetometer, according to the following equation:

\begin{equation}
    B_0 = \frac{\nu_L h I}{\mu (1-\sigma)}
    \label{Eqn:extmagfield}
\end{equation}

\noindent Here, $\nu_L$ is the measured Larmor frequency, $h$ Planck's constant, $I$ the proton spin, $\sigma$=25.71(3)~ppm is the absolute shielding of \ce{^{1}H} in water at 300~K\cite{Garbacz2012,Makulski2018}, $\mu$ is the magnetic moment of the proton 2.79284734462(82) $\mu_N$ \cite{Schneider2017}.
To include the effect of the magnetic susceptibility of the probe, see Eq. (2) in ref. \cite{Harding2020MagneticBiology}.

To determine the magnetic field in the center of the magnet, where the sample is located, the field difference between the magnetometer and the sample positions has to be taken into account.
We have done so by measuring the field with the \ce{^{1}H} magnetometer at both locations, and the relative difference amounted to 20(3)~ppm.
The biggest source of uncertainty in the determination of the absolute magnetic field at the location of the sample was due to the uncertainty in the probe's position.
\subsection{Magnetic field shimming}
To address the 2$^{nd}$ order spatial fluctuations, or inhomogeneities, of the magnetic field in the center of the magnet, two shimming coils were designed.
They were installed concentric and in contact with the magnet poles.
For the design of the coils, the patent of G{\"u}nthard \emph{et al.} was used \cite{Gunthard1960}, which states that a pair of shimming coils placed directly against the poles of a magnet with a mean radius (A) of 0.43 times the distance between the poles (G) can effectively correct for 2$^{nd}$ order inhomogeneities, without introducing any inhomogeneities of the 4$^{th}$ order.
G{\"u}nthard \emph{et al.}\cite{Gunthard1960} also describe that the required current (I) can be calculated with:

\begin{equation}\label{eq:ShimCur}
    I = \frac{2 B_2 A^3}{N \mu_0 1.36}
\end{equation}

\noindent where $\mu_0$ is the magnetic permeability of air, N the number of coil windings and $B_2$ the second order inhomogeneous contribution to the field.
For ease of use and precision, the coils were manufactured as a double-layered printed circuit board (PCB). Figure \ref{fig:ShimCoil} shows a picture of one of the shimming coils.

\begin{figure}
    \centering
    \includegraphics[height=\columnwidth]{Shim.jpg}
    \caption{Detailed picture of a double layered printed circuit board shim coil.}
    \label{fig:ShimCoil}
\end{figure}
\subsection{\(\beta\)-detectors}
As can be seen in the exploded view of the experimental chamber in Figure \ref{fig:ExplodedChamber}, a pair of double-layer plastic scintillator detectors were placed close to both magnet poles, i.e. along and opposite to the direction of spin polarisation.
Within the detectors, both 2-mm scintillator layers (Eljen Technology EJ-212) were insulated against light travelling between them with a 23.62~$\mu$m layer of aluminum.
Silicon Photon Multipliers (SiPMs) (onsemi MICROFJ-60035) were coupled to the scintillators, and the signal was amplified by on-board operational amplifiers.
This kept the detector system small, power efficient, and very resistant to external electronic noise sources.
Because of the use of SiPMs, the detectors were not affected by the 1.2T magnetic field, thus eliminating the need for light guides.

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{Fig01_Chamber.pdf}
    \caption{Exploded view of the experimental measurement chamber. The following parts are shown: (a) PCB shimming coil, (b) $\beta$-detectors, (c) \ce{^{1}H} magnetometer, (d) sample ladder, (e) $\beta$-windows, (f) rf-excitation coil, (g) collimator, (h) front viewport, (i) bottom plate with viewport, and feedthroughs, and two empty flanges for expansion purposes (j,k). See text for further details.}
    \label{fig:ExplodedChamber}
\end{figure}
\subsection{Sample exchange system}
To reduce the time spent on changing liquid samples, a sample ladder shown in Figure \ref{fig:SampleLadder} was developed.
The entire ladder fits within the 30~mm internal diameter of the rf excitation coil.
Individual sample holders, made of 8~mm diameter mica sheets (i) or reference crystals (ii), are mounted on 3D printed Polylactic acid (PLA) structures, (iii) connected to two ceramic rods (iv), which are fixed to a vacuum flange (v).
This flange, in combination with a linear translation stage (vi) and tilt adjust (vii), allows for coarse and fine adjustments of the sample position in all 3 dimensions.

To align the sample a theodolite is used to look through the end of the beamline at the back of the sample ladder.
The centre of the mica is indicated by a contrasting dot made at the back of the PLA structures.
This dot is used to position the sample in the centre of the pole axis and the vertical axis by changing the position of the linear stage and tilt adjust.
To centre the sample in the beam axis a similar dot on the lowest sample holder is observed through a viewport on the bottom-plate of the experimental chamber (Figure \ref{fig:ExplodedChamber} (i)) as the tilt adjust is changed.
After the tilt adjust has been correctly set only the position of the linear stage had to be moved to change between the different sample positions.

The sample exchange system allows to measure up to five samples in rapid succession, reducing the time spent changing samples (more than an hour per sample) during the measurement time by a factor of five.

\begin{figure}
    \centering
    \includegraphics[height=1.2\linewidth]{Fig02_SampleLadder.pdf}
    \caption{Sample exchange ladder that allows for the rapid exchange of samples. Shown are (i) the mica sheet sample holder, (ii) reference crystals, (iii) PLA mounting structures, (iv) ceramic rods, (v) vacuum flange, (vi) the linear translation stage and (vii) tilt adjust.}
    \label{fig:SampleLadder}
\end{figure}
\subsection{Experimental vacuum chamber}
The experimental vacuum chamber, shown in Figure \ref{fig:ExplodedChamber}, was designed and CNC-machined to tightly fit in-between the magnet poles, and to maximize the available space inside it.
On each side of the vacuum chamber, a plate housing a Printed Circuit Board (PCB) shimming coil on one side (a), and a $\beta$-detector on the other (b), is mounted on the outside of the chamber.
Concentric with the magnet, 200~$\mu$m thick aluminum sheets act as "$\beta$-windows" (e).
They form the boundary between the vacuum inside the chamber and the atmospheric pressure outside, while still allowing the $\beta$-particles to pass through to the detectors with as little absorption as possible.
Inside, the vacuum chamber (100x40x200 mm) accommodates a 30~mm inner-diameter rf-excitation coil (f), the \ce{^{1}H} magnetometer (c), and movable sample ladder (d), with a NaF reference crystal and mica sample holders.
At the front of the chamber, there is an in-vacuum pocket that can be used to mount a collimator (g) or a differential pumping cone.
The upper part of the front side houses a large viewport for sample observation (h).
The bottom of the chamber is closed off with a bottom plate equipped with a viewport for sample alignment purposes (i) and two vacuum feedthroughs with SMA connectors for rf connections.
In the back, two additional flanges (j,k) are available for future setup expansions, e.g. sample manipulation and temperature control.
\section{Results}
In this part, we present the results achieved thanks to the upgrades described in the previous section.

The implemented locking system has allowed us to effectively stabilize the magnetic field down to the ppm level.
As shown in Figure \ref{fig:FieldLock}, the fluctuations of the magnetic field were substantial when the locking system was turned off.

When powered without the locking system, the magnet exhibited significant field instability while the power supply and magnet coils reached a temperature equilibrium.
This can take up to 10~hours.
The field change observed during this period has been as high as 300 ppm.
Following this initial instability the field shows an oscillation with a period of roughly 5~hrs and an amplitude of 17~ppm, which correlates with periodic changes in the ISOLDE cooling water temperature.
By comparison, with the locking system enabled (see the insert of Figure \ref{fig:FieldLock}), the field deviates around a set point by approximately $\pm$ 0.6~ppm.
The disturbances in the otherwise smooth lines are caused by manual interventions in the direct vicinity of the magnet during which the regulation system was turned off.
Upon restarting the system it cycles through most of its range before finding back the locked frequency.
This is the cause of the large spikes at the end of the intervention.

 \begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{Fig03_Regulation.pdf}
    \caption{The change of the magnetic field compared to a reference value over time with the locking system off (blue) and on (orange). The insert shows a zoom of the regulated data. The spikes in the data are due to interventions on the experimental chamber requiring the regulation to be temporarily turned off. Once turned back on, the system cycles through most of its range before regaining the locked frequency. The initial drift of the unregulated data is due to slow equilibration of the magnet and power supply. The subsequent oscillations are caused by fluctuations in the cooling water and ambient temperature.}
    \label{fig:FieldLock}
\end{figure}

The shimming coils improve the homogeneity of $B_0$ within the sample volume to the single digit ppm level in every direction as shown in Figure \ref{fig:ShimCompare2}. With the shimming coils turned off, $B_0$ follows a parabola deviating by over 20~ppm from the center to 9~mm outwards on either side along the pole-axis.
With the shimming coils turned on, the deviation is reduced to only 4~ppm over the same distance.

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{Fig04_ShimCompare.pdf}
    \caption{Spatial deviation of the magnetic field when going away from the magnet's center towards its poles. Red symbols: shimming coils turned off; Blue symbols: shimming coils on; Orange line shows the median field across the sample site and the shade area indicates a 1~ppm difference from this line.}
    \label{fig:ShimCompare}
\end{figure}

Because the sample is oriented with a 45 degrees angle to the horizontal plane (Figure \ref{fig:SampleLadder}) the sample volume extends 3~mm from the magnet center in the vertical and beam axis directions, and 4mm in the magnet-pole axis. Figure \ref{fig:ShimCompare2} shows the final shimmed magnetic field ($B_0$) along all three axes around the centre of the magnet.
This is the highest achieved homogeneity across the three combined dimensions, as trying to optimize the homogeneity in one axis further, decreases it in the others dimensions.
Between the magnet poles and the vertical axis $B_0$ follows a flat parabola with the center approximately in the magnet's middle, resulting in a maximum deviation from the median field along these axes at the sample site of 0.8 and 0.2~ppm respectively.
However, along the beam axis $B_0$ follows almost a straight line, resulting in a maximum deviation from the median field of 2.1~ppm.

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{Fig05_ShimCompare2.pdf}
    \caption{Final shimming results for the magnetic field along all three axes, relative to the magnetic field in the centre of the magnet (taken as 0 ppm). Blue symbols:  field deviation along the central pole-to-pole axis, orange symbols: deviation along the vertical axis, green symbols: deviation in the horizontal (beam) direction. The shaded blue area indicates the sample space in the pole-to-pole direction, and the shaded red area the sample space in the other two directions.}
    \label{fig:ShimCompare2}
\end{figure}

This field stability has allowed us to determine the magnetic moment of an unstable nucleus with two orders of magnitude higher accuracy than possible before.
Until recently\cite{Harding2020MagneticBiology, Mihara2019}, studies of the magnetic moment of exotic nuclei through $\beta$-NMR have relied on solid-state hosts as implantation sites \cite{Yordanov2007,Rogers1986, Connor1962, Matsuta1995}.
In the case of sodium, magnetic moment studies were performed using a NaF crystal, with cubic lattice structure, which retained the nuclear spin-polarisation for up to 40~s \cite{Kowalska2017, Keim2000}.
Resonances were achieved with a full width at half maximum (FWHM) in the order of $10^{-4}$ of the resonance frequency \cite{Keim2000}.
However, with liquid-state hosts, it is possible to obtain resonances with a FWHM down to two orders of magnitude smaller, whilst retaining the nuclear polarisation long enough to observe it through $\beta$-NMR.
The narrowing of the resonance lines is due to fast molecular tumbling within the liquid sample, effectively averaging out the anisotropic contributions found in solid-state NMR spectra.
Figure \ref{fig:SolidVsLiquid} shows a comparison the resonance width of \ce{^{26}Na} in a solid state host (NaF; blue), versus a liquid state host (BMIM-HCOO; green).
The insert in Figure \ref{fig:SolidVsLiquid}, is a zoomed in part of the spectra in order to show the resonance from the liquid host.

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{Fig06_SolidLiquidCompare.pdf}
    \caption{A comparison between the resonance width of \ce{^{26}Na} in a solid state host (NaF; blue), and a liquid state host (BMIM-HCOO; green). The deviation from the centre of each peak is given on the x-axis. The insert shows the resonance in the liquid host.}
    \label{fig:SolidVsLiquid}
\end{figure}
\section{Discussion}
In this article, we have presented in detail the technical solutions that allow to perform $\beta$-NMR studies in liquid samples with high absolute accuracy.

One of the key innovations we introduced is the magnetic field locking and measurement system that maintains the stability of the magnetic field down to the ppm level over hours and which allows us to determine the absolute value of the field with ppm accuracy.
Another improvement is the PCB-shimming coils, which improve the magnetic-field homogeneity to 1-5~ppm within the volume of the sample.
Furthermore, the use of state-of-the-art SiPMs has allowed us to obtain a very compact $\beta$-detection system opening up the space to observe the behavior of liquid samples in real time.
Finally, a special sample handling system shortened the time spent on changing samples by a factor of 5.
With the combination of these features, frequencies of $\beta$-NMR resonances in different hosts have been measured with unprecedented accuracy, paving the way for new applications of the technique.
At the same time, further improvements are possible, and these and some general characteristics are covered in the following sections.

\subsection{Locking system}
The present field locking system reads out the magnetic field every 200~ms, and adjusts the current at least once per second.
This measurement rate is 5 times faster than the previously used commercial Metrolab PT2025 magnetometer (Geneva, CH).
In addition, the probe is smaller and is fully vacuum compatible.
However, the rate at which the current in the electromagnet can be adjusted is the limiting step in the feedback loop.
Specifically, the control and adjustment of the stepper-motor-driven variable resistor takes longer than the measurement time of the \ce{^{1}H} NMR magnetometer.
Decreasing the time it takes to adjust the current can improve the field control further by making use of every measured \ce{^{1}H} frequency, thus reducing the time interval between consecutive field adjustments.

The \ce{^{1}H} magnetometer's other strength comes from the fact that it is based on the \ce{^{1}H} NMR frequency in water.
The absolute NMR shielding for \ce{^{1}H} in water has been calculated much more accurately than in other liquid or solid hosts, thus leading to a more accurate magnetic field readout at the NMR probe's position.
The determination of the absolute magnetic field can be done concurrently with $\beta$-NMR measurements.
Relative measurements via the resonance frequency of a reference $\beta$-NMR nucleus in a known host, which is both time-consuming and less accurate, are therefore unnecessary.

Furthermore, our \ce{^{1}H} magnetometer uses pulsed NMR, which eliminates the need to modulate the static magnetic field (as is done in the PT2025 probe).
Thanks to this, the magnetometer does not disturb the magnetic field experienced by the probe nuclei at the sample location.
Additionally the diameter of the magnetometer's rf coil is much smaller than the continuous-wave $\beta$-NMR excitation coil and the applied frequencies are far apart, excluding cross-talk between the two rf coils.

At the same time, because the $\beta$-NMR coil is relatively large, the \ce{^{1}H} probe is positioned 25~mm away from the sample location, where the field is different and less homogeneous than at the sample's location in the magnet's center.
Though this does not affect the locking capabilities of the system, it leads to a field offset that needs to be measured and corrected for, in order to accurately determine the magnetic field at the sample position.
As the field's gradient increases, so does the uncertainty of this correction.
Even a small change of the probe's position can then result in a slightly different measured field.
At present, this uncertainty is the largest contribution to the total uncertainty in the value of the magnetic field at the sample's position.
Higher accuracy in the determination of the magnetic field at the sample position can be reached, e.g. by measuring the magnetic field very close to, or even at, the exact position of the sample.
For example, in conventional NMR spectrometers, this is done by measuring the resonance frequency of \ce{^{2}H} present in heavy water (\ce{D_{2}O}) mixed into the solvent.
In $\beta$-NMR, protons in the solvent molecules can be used for the same purpose if an excitation and pickup coil is used to acquire a conventional \ce{^{1}H} NMR signal from the sample itself.

\subsection{Shimming coils}
The main achievement of the shimming coils was to reach 1~ppm homogeneity over a distance of several millimeters.
Because the coils are made as PCB boards, they are very robust compared to wire wound coils.
They are also cheap and easy to manufacture reproducibly.
The optimal current setting can easily be calculated using Eq. \ref{eq:ShimCur}, requiring only minor fine tuning afterward.

A consequence of this design, which is dependent on the distance between the poles of the electromagnet, is that the corrections of the field in the axial and radial directions are coupled.
This means a compromise must be found between the field homogeneity in different directions.
Thus, a small gradient arising from the tail of the transitional field used to adiabatically rotate the atomic spin and consecutively decouple the nuclear and electron spin of the incoming beam of probe isotopes \cite{Kowalska2017}, can not be corrected by this system.

The magnetic field homogeneity could be further improved by analysing the field map, and by designing additional coils to correct for remaining field inhomogeneities.
This would however quickly become very complicated, as one would need to take into account not only the field at the sample site, but also along the beam path, to make sure that field adjustments made by any additional shimming coils do not negatively affect the aforementioned transitional field.
The extra space required for additional shimming coils will also be a limiting factor.

\subsection{Sample handling system}
Because the sample handling system reduces the time spent on exchanging samples 5 fold, it significantly increases the number of samples that can be tested during an experimental campaign.
It also allows for the fine adjustment of each sample's position, resulting in reproducible sample alignment.
When used in combination with the upstream collimator at the front of the experimental chamber, the sample handling system allows to have the polarised beam implanted solely in the well-aligned sample.
This prevents background $\beta$-counts that could arise from parts of the beam being implanted in materials other than the sample.

During previous experiments, a NaF crystal was mounted at the bottom of the ladder, for reference and inspection purposes.
The mica substrate used to hold the liquid samples is compatible with biological samples, easy to clean, and allows to create a thin, sub-millimeter layer of the liquid hosts (corresponding to 5-20~$\mu$L of liquid), which also makes it possible to use solvents only available in very small quantities.
As with all other parts situated between, or close to the magnet poles, the sample handling system is made of non-magnetic material, and thus does not disturb the static magnetic or the rf fields.

The sample handling system is actuated manually.
A clear improvement from the operational standpoint would be the automation of sample positioning.
In addition, it does not yet include sample temperature measurements and control.
These will be implemented in future developments of the system.
Due to the lack of an efficient vacuum-liquid barrier and the sample orientation at 45° to the vertical, the sample handling system is only suitable for relatively viscous vacuum-resistant solvents.
Low viscous solvents would simply flow off of the sample holder and non-vacuum-resistant solvent will evaporate and/or freeze due to the low pressure.

Ideally, for biochemical studies, one would want to perform measurements in water, as this is what is routinely done in conventional NMR studies.
To achieve this goal, new technical approaches will be necessary to combine the no/low-vacuum environment required by water (because of its high vapour pressure), with the high-vacuum environment of RIB facilities.
Solutions that warrant investigation for that specific purpose are differential pumping setups, allowing poor vacuum around the sample, combined with better vacuum along the path of the beam of unstable nuclei, or the encapsulation of samples to protect the high vapor pressure solvents from evaporation in the vacuum.
Both of these approaches present their own hurdles.
In the case of a high final pressure in a differential pumping setup, the gas present right before the sample will significantly scatter the incoming beam due to beam-gas interactions, which will significantly decrease the $\beta$-NMR SNR.
In the case of encapsulation, the window material must be able to withstand the pressure gradient, but also transmit most of the beam without affecting its spin polarisation.
Interactions between the beam and the window heavily depend on the material used for the window, its thickness, and the energy of the beam.
For low energy beams such as in our setup (up to 50~keV), the window should be less than 100~nm thick, even possibly only 50~nm thick, which makes it very brittle.
For high energy beams used at in-flight facilities, the window can be thicker.
This allowed Mihara \textit{et al.} \cite{Mihara2019}, to perform a $\beta$-NMR measurement of \ce{^{17}{N}} in water.

\subsection{Beta detectors}
The current beta-detection system is a significant improvement compared to previous systems, which also relied on two pairs of thin plastic scintillators, however these were coupled to conventional PMs.
Since conventional PMs are very sensitive to magnetic fields, they needed to be covered in Mu-metal and kept almost 1~m away from the center of the magnet, necessitating the use of light guides.
The whole system took up lot of space, making any manipulation impractical, and mostly preventing visual inspection of the implantation site.
It was also very heavy, and thus cumbersome to assemble and to get ready for operation.
The present system is lighter and more compact, with $\beta$-detectors (scintillator and SiPMs) located inside the magnet, but still outside of the NMR chamber.
In the future it should be possible to craft a set of detectors to be placed closer to the sample in vacuum.
These could be made significantly smaller if the covered solid angle is kept constant.
Besides this, one can consider designs with more complex geometries, so as to take full advantage of the beta decay angular distribution and the effect of the magnetic field on beta-particle trajectories.

\subsection{Experimental chamber}
Our experimental chamber design was to a large degree determined by the vacuum regime (no need for vacuum better than $10^{-6}$~mbar), the magnet to be used, and by respecting previously made design decisions.
It allows to accommodate all necessary elements: $\beta$-NMR excitation coil, \ce{^{1}H} magnetometer, samples, detectors and shimming coils.
Additionally, it has 2 viewports, combined with the viewport at the end of the beamline, allowing to check the alignment, circular polarisation, and power of the laser beam, to define the position of each sample holder after sample change and finally to observe the behaviour of the liquid sample on the substrate.
The chamber is made of heat treated (T6) 6082 aluminium alloy and has standard-sized flanges compatible with the UHV standard CF (using elastomer instead of copper gaskets), which makes the installation and alignment easier.

The rf-excitation coil was designed to not obstructed the incoming beam, allow for the maximum solid angle of $\beta$-radiation through the "$\beta$-windows, and the best homogeneity of the applied rf-field perpendicular to B$_{0}$ over the sample volume given these two boundary conditions.

Different magnet configurations, however, come with significantly different constraints.
For example, for a solenoidal magnet, the chamber design will not easily give access to a viewport for sample observation. The design of a sample ladder would also not be a trivial task.

\section{Conclusion
The upgrades described in the present manuscript open new avenues for $\beta$-NMR studies.
They have already allowed for the determination of the magnetic moment of the short lived nucleus \ce{^{26}Na} with ppm precision \cite{Harding2020MagneticBiology}.
This achievement, together with accurate hyperfine structure measurements \cite{Stroke2000}, should allow for the study of the distribution of nuclear magnetism through the hyperfine anomaly (the effect of the non-point like size of the nucleus on the hyperfine structure\cite{Persson2013}).
The distribution of nuclear magnetisation can in turn shed light on open questions in nuclear structure physics, in particular about the distribution of neutrons inside the nucleus \cite{Hagen2016,Thiel2019}.

Another application that these upgrades will be essential for, is the study of interactions between metal ions and biomolecules with $\beta$-NMR \cite{Crichton2019BioInorgChem,Crichton2020PractBioInorgChem}.
One example of such interactions is the interaction between DNA G-Quadruplexes and sodium or potassium ions \cite{Carvalho2020,Wu2003,WONG2005,wong2009}.
Presently, we are exploring the most suitable potassium probes for G-quadruplexes studies \cite{Karg2020proposal}, as well as isotopes of several other elements relevant to protein folding \cite{Jansco2017}.
Together with our previous $^{26}$Na measurement \cite{Harding2020MagneticBiology} this will be of direct use in our current investigations into this topic.
\section{Acknowledgements}
This work was supported by the European Research Council (Starting Grant 640465),
the UK Science and Technology Facilities Council (ST/P004423/1),
EU project ENSAR2 (654002),
the Ministry of Education of the Czech Republic (LM2018104),
the Wolfgang Gentner Programme of the German Federal Ministry of Education and Research (05E15CHA),
and by the Swiss Government Excellence Scholarships for Foreign Scholars program.
\section{The Elsevier article class}

\paragraph{Installation} If the document class \emph{elsarticle} is not available on your computer, you can download and install the system package \emph{texlive-publishers} (Linux) or install the \LaTeX\ package \emph{elsarticle} using the package manager of your \TeX\ installation, which is typically \TeX\ Live or Mik\TeX.

\paragraph{Usage} Once the package is properly installed, you can use the document class \emph{elsarticle} to create a manuscript. Please make sure that your manuscript follows the guidelines in the Guide for Authors of the relevant journal. It is not necessary to typeset your manuscript in exactly the same way as an article, unless you are submitting to a camera-ready copy (CRC) journal.

\paragraph{Functionality} The Elsevier article class is based on the standard article class and supports almost all of the functionality of that class. In addition, it features commands and options to format the
\begin{itemize}
\item document style
\item baselineskip
\item front matter
\item keywords and MSC codes
\item theorems, definitions and proofs
\item lables of enumerations
\item citation style and labeling.
\end{itemize}

\section{Front matter}

The author names and affiliations could be formatted in two ways:
\begin{enumerate}[(1)]
\item Group the authors per affiliation.
\item Use footnotes to indicate the affiliations.
\end{enumerate}
See the front matter of this document for examples. You are recommended to conform your choice to the journal you are submitting to.

\section{Bibliography styles}

There are various bibliography styles available. You can select the style of your choice in the preamble of this document. These styles are Elsevier styles based on standard styles like Harvard and Vancouver. Please use Bib\TeX\ to generate your bibliography and include DOIs whenever available.

Here are two sample references: \cite{Feynman1963118,Dirac1953888}.

\section*{References}

redpajama_set_name: RedPajamaArXiv


text:
Ranking the DC Comics Movies
by Brian Gill
Listeners of the show and people who know me in real life know about my Completionism, a life altering condition that forces me to be all in or all out on pretty much everything in my life. I like lists, I like rankings, but in order for my brain to work properly (or very NOT properly as the case may be), I feel like I have to have as much knowledge as I can possibly have about said subjects. As such, when I set out to put together a ranking, I feel like I HAVE to do a deep dive into the particular franchise or universe I'm writing about in the interest of fairness. Sometimes, that's no problem. I love the Marvel movies and have no problem watching any or all of them any time. The DC movies are, ahem, a different animal.
I want to put this out there right up front: I love Batman. He's my favorite superhero, hands down. Moreover, growing up, outside of Spider-Man, all of the comic book characters I cared about were DC, not Marvel. I desperately WANT the DC universe of films to be as good if not better than the Marvel universe just because of my longtime interest in the characters. I would be lying, however, if I said that was anywhere close to the truth. The DC brand has been dragged through the movie mud repeatedly and dredging through this collection of films was a chore at times, a punishment at others. This is an incredibly top heavy list, followed by a host of films that, in my book, range from "not good" to "very bad" to "oh sweet Death, please come and take me quickly." I tried to stay positive but, dear readers, this was a difficult task. Here now, I present to you my official ranking of all the DC comic and graphic novel film adaptations from worst to first.
(NOTE: I didn't have time/interest/brain power to see Steel, Supergirl, or the Swamp Thing movies. I am okay with these exclusions.)
21. Batman & Robin (1997) Rotten Tomatoes: 11%, Worldwide Gross: $238M
After having watched all of these illustrious movies over the last couple weeks, I think it would be more than fair to put Catwoman or even Green Lantern at the bottom of this list. They're probably actually worse movies. But Batman & Robin physically hurts me. There's not one frame, one line of dialogue, one subplot that works for even 30 seconds and that just should not be possible in a Batman movie. From the Bat Nipples on the Bat Suit on down, this movie is a travesty. I think watching it again actually took years off my life.
20. Catwoman (2004) Rotten Tomatoes: 9%, Worldwide Gross: $82M
True story: I had never had the pleasure of seeing Catwoman until I started this project. Lucky me. Who would've guessed that a movie directed by someone who goes by simply Pitof would be bad. This is a special kind of bad, though. Catwoman has an atrocious script and features probably the worst performance that an Oscar winner has ever given. Seriously, it's a wonder that Halle Berry's golden statue wasn't reposesseded after this mess. My favorite scene was when Catwoman, imbued with special powers from some cat she saved, uses her abilities to play a game of sexualized one-on-one basketball with Benjamin Bratt while a host of elementary school kids look on in awe.
19. Green Lantern (2011) Rotten Tomatoes: 26%, Worldwide Gross: $219M
I hadn't seen Green Lantern since I attended a midnight premiere in 2011. (Side note: I'd like to punch 2011 me in the face.) What an absolute trainwreck. To be fair, Reynolds himself isn't TERRIBLE as Green Lantern but he's also not good and he certainly doesn't do anything to bring up the material. Also, Green Lantern gets special credit for attacking my eyes with some of the worst special effects I have ever seen in my entire life.
18. Superman IV: The Quest for Peace (1984) Rotten Tomatoes: 12%, Worldwide Gross: $36.7M
Wooo boy, this one is a peach. Preachy and outdated even when it premiered, The Quest for Peace basically finished the job that Superman III started and killed off the character for 20+ years. Made on a shoe string budget and featuring a clearly uninterested cast, the highlight of this movie is when Superman uses a net to ferry all of the world's nuclear weapons into the sun. Seems logical.
17. Jonah Hex (2010) Rotten Tomatoes: 12%, Worldwide Gross: $10.9M
With a cast that includes Josh Brolin, John Malkovich, and Michael Fassbender based off of a fairly beloved graphic novel, you would think that Jonah Hex would be at least passable. And you would be wrong. Even the studio knew they had a dud in their hands, opening it against Toy Story 3 and essentially pulled it from theaters after two weeks. In truth, I don't think Jonah Hex is QUITE as legendarily bad as the buzz surrounding it would have me believe but that certainly doesn't mean it's anything less than "very, very bad."
16. Superman III (1983) Rotten Tomatoes: 26%, Worldwide Gross: $59M
I have a (VERY) small soft spot for Superman III because at least it attempted to do something a little different by bringing in Richard Pryor. But oh sweet goodness, what a TERRIBLE plot! I know it was 1983 and our understanding of computers and satellites was minimal but sheesh, the stuff that Pryor's character is able to do with access to one satellite is so absurd that it becomes unwatchable. And while Superman splitting into two separate beings is a fun twist, the battle before and after said split is awful.
15. The Losers (2010) Rotten Tomatoes: 49%, Worldwide Gross: $29M
The Losers so badly wants to be fun and yet it fails to come through on that effort time and time again. A decent cast (including Idris Elba and Chris Evans just before his break out as Captain America) is overshadowed by a cumbersome, uninteresting plot and a painfully bad performance by Jason Patric as the lead villain. The bad taste Patric leaves behind is really the only thing I remembered from The Losers before my rewatch and I thought he couldn't possibly be as bad as my memory would have me believe. But no, he's incredibly bad and he takes what could be a B- sort of movie and plunges it downward.
14. Batman Forever (1995) Rotten Tomatoes: 41%, Worldwide Gross: $336M
There are parts of Batman Forever that work in some capacity or another. Kilmer isn't a bad Batman, really, and some of the action set pieces hold up fairly well. But it is just so far over the top in almost every scene that after 20 minutes or so you start to feel like Jim Carrey is in your house and he's just SCREAMING in your ear. To me, the whole thing boils down to horrendous direction, which makes the decision to give Joel Schumacher a shot at Batman & Robin even more frustrating.
13. Man of Steel (2013) Rotten Tomatoes: 56%, Worldwide Gross: $688M
This is undoubtedly the most frustrating film on this list. I didn't care for Man of Steelupon first viewing and had soured on it even further over the last three years. When I sat down to rewatch it, I was struck by how good the stronger moments (the father-son element, some of the early action sequences, a slightly different take on the Superman origin story, etc.) really are…and how those moments are completely swallowed up by bad camera work, stilted dialogue, and a vision of Superman (and the universe he exists in) that thoroughly flies in the face of what Superman is all about. In the hands of a better director, I think Man of Steel could be a very fine film; instead, it's mostly a mess.
12. Batman Returns (1992) Rotten Tomatoes: 80%, Worldwide Gross: $266M
Batman Returns gets worse with every viewing. Ten years ago I would've probably had this one somewhere around the top five. Five years ago, it would drop a bit but would still find a place in the top ten. Now, I think it only sits this high because of how much I dislike the films beneath it. On the plus side, Keaton is fine and DeVito is creepily great. On the downside, Pfeiffer's Catwoman is excruciating from beginning to end and Burton lets almost every scene drag on and on, like he forgot the camera was rolling. In hindsight, we were probably past the Burton experience in 1992, it just took 15 years to realize it. Regardless, time has not been kind to Batman Returns.
11. Constantine (2005) Rotten Tomatoes: 46%, Worldwide Gross: $230M
Okay, I like Constantine. It's a bit of a guilty pleasure for me. Back off, we all have our weak spots! I would never say this is a "good" movie but I kind of dig Keanu's zoned out take on the character and I've always found the concept interesting. Moreover, Peter Stromare's portrayal of the devil in the final act is, I think, fantastic and bumps the movie as a whole up a grade or two for me.
10. Watchmen (2009) Rotten Tomatoes: 65%, Worldwide Gross: $185M
I will say this for Zack Snyder's epic adaptation: it tries hard. I think as a whole, Watchmen rides the "is it good or bad?" fence in nearly every scene but there are moments of greatness (mostly involving Rorschach) and moreover, the graphic novel it's based on is probably unfilmable if we're being honest. I mostly despise Snyder's sensibilities but it is ironic that it is Watchmen, on the surface his least accessible film, that brings out his best work (minus the music cues, most of which are awful). It's a VERY flawed film but at least it's one that received an honest effort.
9. Batman The Movie (1965) Rotten Tomatoes: 80%, Worldwide Gross: $3M
Campy, cheeky, and somewhat stupid, the original Batman movie is still a whirlwind of fun. Most people of my generation grew up with the Batman TV series playing some role in our lives and I probably watched the movie a hundred times in my younger years. I can't say that the movie has held up over the last 50 years save for one element: It's still extremely fun to watch. Adam West for president.
8. Superman II (1981) Rotten Tomatoes: 89%, Worldwide Gross: $108M
I'm not entirely sure which versions of Superman II I've seen and which I haven't. Production issues resulted in Richard Donner being replaced at the helm and a final cut that was different from the original concept. Regardless, Reeve's Superman saves this movie for me. Lois Lane, somewhat annoying in Superman, becomes INCREDIBLY annoying in Superman II and the fight between Superman and Zod looks pretty terrible 30+ years later. But Reeve really hits his peak here and carries the film to greater heights than maybe it deserves.
7. Superman Returns (2006) Rotten Tomatoes: 76%, Worldwide Gross: $391M
I will stand by Superman Returns as a quality comic book movie and I think it is the Superman movie that comes the closest to capturing the spirit of its hero while also delivering a somewhat interesting plot. I think it's much more re-watchable than any of the other Superman films. It has two big problems, however. For one, at times it falls into a pattern of over-romanticizing the hero and his values to the point of become hokey. But more important, Bryan Singer and company missed on casting almost entirely. Brandon Routh isn't a bad actor by any means but he doesn't jump out at you as Superman. Kate Bosworth is overmatched by her role and seems out of place. And Kevin Spacey is just plain bad as Lex Luthor, which is weird because it seems like he'd pull this off quite well. I think if you made this movie with different actors but kept everything else the same, it's a better product overall.
6. Superman (1978) Rotten Tomatoes: 93%, Worldwide Gross: $300M
This is one of those times when I'm forced to weigh the difference in personal opinion and objective criticism. I actually don't care for this movie much. I think it's boring and for the most part, it just doesn't speak to me in tone or content. But, I can recognize that it's a well-made movie featuring a quality actor in a prestige role and accept that while it's not my cup of tea, it deserves a prominent place on this list.
5. V for Vendetta (2005) Rotten Tomatoes: 73%, Worldwide Gross: $132M
I had V quite a bit lower on my list when I first sat down to put this thing together. But after my re-watch, I came away much more impressed with the movie than I'd ever been before. It's actually better in 2016, I think, than it was in 2005 and that's quite an achievement. I'm a sucker for dystopian glimpses into the future but I gotta be honest, this one doesn't seem too farfetched given the insanity of the Donald Trump phenomenon. V is well acted (the last truly good Portman performance?) and the writing mixes "playful" and "deathly serious" in an interesting way that keeps the plot moving at a solid pace.
4. The Dark Knight Rises (2012) Rotten Tomatoes: 87%, Worldwide Gross: $1.08B
I love The Dark Knight Rises. That's not an extremely popular opinion but I'll defend it to my dying day. To me, the big issues with the film are Bane's mask (fixed on the blu-ray) and the over-packed plot. That could've been fixed by splitting the movie into two parts but then people would've accused Nolan and WB of money grubbing so it's kind of a lose-lose. Obviously I think it's the weakest of the Nolan Batman films but it's still a darn good movie and one that wraps up a tremendous trilogy quite well, I think.
3. Batman (1989) Rotten Tomatoes: 72%, Worldwide Gross: $411M
I debated moving this one up a slot based on my personal attachment to it. Seeing Batman in the theater at age six was a formative experience for me. I love Keaton's Batman, I love Nicholson's Joker, and I think it's an example of what Burton is capable of when his crazy creativity is harnessed appropriately. You could release Batman tomorrow and it would look almost just as good now as it did in 1989. It holds up extremely well in my book (minus the weird musical cues; late 80's pop/hip-hop should be eradicated from our society). "Have you ever danced with the devil in the pale moonlight?" is an AWESOME quote. Plus, Batman gets extra credit for being THE standard of what a superhero movie should look like for a solid 15 years.
2. Batman Begins (2005) Rotten Tomatoes: 85%, Worldwide Gross: $374M
I remember only being vaguely interested in Batman Begins back in 2005 and now that seems ridiculously foolish. Nolan's vision for the Batman reboot is so fantastic and his choice for the Caped Crusader was superb. Mock the voice all you like, but Christian Bale played both sides of the Batman-Wayne coin tremendously well. I'm not sure there's ever been a better origin story in the comic book movie universe and Batman Begins sets the table brilliantly for what was to come.
1. The Dark Knight (2008) Rotten Tomatoes: 94%, Worldwide Gross: $1.04B
This should come as no surprise as really there's no other sensible option to sit at the top of this list. The Dark Knight is the greatest superhero movie of all-time and in my book, it's not particularly close. From a technical standpoint, it is a master class in filmmaking: shot selection, sound editing, production design…they're all perfect. PERFECT. Add in a very strong narrative, an outstanding cast, and an iconic, untouchable performance and you've got an incredible film, regardless of comic book affiliation. I don't think there will be a better superhero movie in my lifetime and I'm completely okay with that.

redpajama_set_name: RedPajamaCommonCrawl


Camp & Associates Land Surveying, Inc. was founded in LaGrange, Georgia, in 1968 by Hugh Camp as J. Hugh Camp & Associates. For over four decades, Camp & Associates has met the land surveying and planning needs for thousands of residents and businesses in and around Troup County. With over 40,000 plats readily available at their office, they are equipped to handle any surveying project and deliver the most accurate and precisely detailed maps and documents necessary to meet your needs and legal requirements.
Leading the experienced staff is Georgia Registered Land Surveyor, P. C. "Clint" Flynn, Company VP with 32 years experience in all aspects of Land Surveying. Clint attended Southern Polytechnic State University and most recently owned and operated P.C. Flynn Land Surveying Co. in Greenville, Georgia for 20 years before joining the firm of Camp & Associates in 2016. He brings a solid reputation as being professional, ethical and thorough.
With a forty year tradition of quality service and a reputation for excellence, Camp & Associates is a full service company that handles the gamut of surveying needs-from commercial and residential development to governmental and cadastral surveying.


text:
Q: How can I turn off VisualStudio including all .cs files? VisualStudio is adding all .cs files it finds under the project folder to the project (it used to not do this - this may be due to being a .Net 5.0 app). How can I turn this functionality off?
The problem I have is running the debugger for a .Net 5.0 process in a docker container, it copies the files to a subfolder (under backtest) and I think is running that set of files. But as it's under the main project folder, those files then get added to the project.

redpajama_set_name: RedPajamaStackExchange


text:
How did salutary neglect affect the colonies?
Greg Palms asked, updated on November 30th, 2021; Topic: salutary neglect
Indeed, salutary neglect enabled the American colonies to prosper by trading with non-British entities, and then to spend that wealth on British-made goods, while at the same time providing Britain with raw materials for manufacture.27 mai 2011
Quite so, why was salutary neglect created?
Salutary neglect, policy of the British government from the early to mid-18th century regarding its North American colonies under which trade regulations for the colonies were laxly enforced and imperial supervision of internal colonial affairs was loose as long as the colonies remained loyal to the British government ...25 juin 2019
Whence, how did salutary neglect affect the colonies quizlet? Effects of Salutary Neglect: colonists grow accustomed to the habit of self-government fostered by the Crown's indifference. assemblies grew stronger between 1700 and 1750. weild much power in colonial affairs, about on par witht the amount weilded by royal governors.
Forbye, why was the salutary neglect important?
It was a system of loose imperial control over the colonies and a lax enforcement of trade laws. The Navigation Acts made it impossible for colonists to trade with nations other than England. ... The result of the period of salutary neglect was that the colonists learned to govern themselves and manage their own economies.
What happened when salutary neglect ended?
French and Indian War and the End of Salutary Neglect 1754-1775. As a result of debts accrued during to the French and Indian War, England gradually ended their policy of salutary neglect toward the colonies, eventually leading to the American Revolution.
17 Related Questions Answered
Why would the colonists resist the end of salutary neglect?
The French and Indian War led to the end of salutary neglect because the colonists were getting into trouble with neighboring colonizations. ... The colonists resisted this because they were used to smuggling and doing other things that they were able to get away with that now they cannot.
Why did Britain allow the colonists to not obey all of the British laws?
The British government demanded that the colonists pay higher and higher taxes. ... They wanted the right to vote about their own taxes, like the people living in Britain. But no colonists were permitted to serve in the British Parliament. So they protested that they were being taxed without being represented.20 juin 2013
Why did the British use salutary neglect?
Salutary neglect was an unofficial British policy of non-enforcement of trade regulations on their American colonies during the 17th and 18th centuries. The purpose was to maximize economic output amongst the colonists while maintain some form of control.21 févr. 2019
How did the policy of salutary neglect benefit England?
It regulated trade between England and its colonies and its purpose was to ensure that only England benefited from Colonial trade. How did the policy of salutary neglect benefit england and the colonies? -It saved money and both sides made money when the ship business developed.
What was the significance of the policy of salutary neglect quizlet?
Salutary Neglect is the British policy of letting the colonies ignore most of the British Laws. This policy changed when Britain was broke after the French and Indian war and needed the Colonies to start paying taxes and following their laws.
What was the period of salutary neglect quizlet?
Salutary neglect is an American history term that refers to an unofficial and long-term 17th & 18th-century British policy of avoiding strict enforcement of parliamentary laws meant to keep American colonies obedient to England.
What was the significance of Ashanti and Dahomey?
What was the significance of Ashanti and Dahomey? These African states became powerful through the slave trade. On the rice plantations of South Carolina and Georgia, the birthrate of slaves was high.
How did the colonists respond to the end of salutary neglect?
The policy and era of Salutary Neglect lasted from the 1690's to the 1760's and benefited the colonists boosting their profits from trade. The British reversed their policy of Salutary Neglect to raise taxes in the colonies to pay for the massive war debt incurred during the French and Indian Wars.
What is an example of salutary neglect?
Currency Act, 1751: Act passed by British Parliament that affected the colonies by adjusting the currency. The point of this attack was to raise revenue for Great Britain. It was a clear example of how Salutary Neglect was coming to an end with the French and Indian War.
How did Pontiac's rebellion lead to the proclamation of 1763?
In response to Pontiac's Rebellion, a revolt of Native Americans led by Pontiac, an Ottawa chief, King George III declared all lands west of the Appalachian Divide off-limits to colonial settlers. This royal proclamation, issued on October 7, 1763, closed down colonial expansion westward beyond Appalachia.9 sept. 2019
Why were the colonists angry about the proclamation of 1763?
The Royal Proclamation of 1763 was very unpopular with the colonists. ... This angered the colonists. They felt the Proclamation was a plot to keep them under the strict control of England and that the British only wanted them east of the mountains so they could keep an eye on them.
How did Britain's neglect of the colonists gradually lead to independence?
How did Britain's "salutary neglect" of the colonies gradually lead to their de facto independence? ... The policy made it so the colonies were tied to Britain in terms of trade and the way they were governed. England's failure to enforce the laws in the colonies left people there with a feeling of more independence.
Who did America trade with after the revolution?
American merchants maintained trade with Mediterranean countries, and opened trade with China in the 1780s. Mediterranean trade, however, was hampered by pirate attacks; and American ships no longer had the protection of the British Navy.
What did the British do to the colonists?
The British further angered American colonists with the Quartering Act, which required the colonies to provide barracks and supplies to British troops. Stamp Act. Parliament's first direct tax on the American colonies, this act, like those passed in 1764, was enacted to raise money for Britain.
How were the colonists rights violated?
In 1765 Parliament passed the Quartering Act that said the colonists needed to find or pay for lodging for British soldiers stationed in America. ... They protested, saying that these taxes violated their rights as British citizens. The colonists started to resist by boycotting, or not buying, British goods.
How did Britain punish the colonists?
The Coercive Acts of 1774, known as the Intolerable Acts in the American colonies, were a series of four laws passed by the British Parliament to punish the colony of Massachusetts Bay for the Boston Tea Party. The Boston Port Act was the first of the Coercive Acts. ...
How did the colonies practiced self government during salutary neglect?
Salutary neglect was a large contributing factor that led to the American Revolutionary War. Since the imperial authority did not assert the power that it had, the colonists were left to govern themselves. These essentially sovereign colonies soon became accustomed to the idea of self-control.
When did the Sugar Act begin and end? 17
Where did the New England colonies come from? 15
What are the 4 main economic activities of the New England colonies? 16
What was in the New England colonies? 24
How many British colonies were there in the world? 16
What are the current British colonies? 14
How do I pay my target bill online? 20
What is the opposite of concatenation? 20
What wood is strongest? 20
Can you play Zoo Tycoon? 20
How do you remove plastic molly bolts from drywall? 20


text:
Q: how to transfer query string to controller's action in unit test? i have an Mvc controller which looks like:
public class PaymentController : Controller
{
    public ActionResult ApiReturn()
    {
        var notify_id = Request.QueryString["notify_id"];
        return null;
    }
}

how do i transfer the query string "notify_id" when i do unit test for this ApiReturn, my unit test for this action is like below:
[TestClass]
public class PaymentControllerUnitTest
{
    [TestMethod]
    public void TestApiReturn()
    {
        var paymentController = new PaymentController();
        paymentController.ApiReturn();
    }
}


text:
Home/News/USA News/Russian air show, not the invasion of Ukraine, shown in the photo
Russian air show, not the invasion of Ukraine, shown in the photo
remon2022-02-26
The claim: Image shows Russian plane shot down by Ukraine
An old photo of a plane seemingly falling from the sky has resurfaced on social media amid Russia's invasion of Ukraine.
"BREAKING!! Ukrainian military allegedly shot down Russian fighter jets," read the caption of a Feb. 24 Facebook photo, which shows a plane leaving a trail of smoke and flames.
Since Russia's announcement early February 24 of a military operation in Ukraine, similar versions of the claim have racked up hundreds of interactions on Facebook and Instagram, according to CrowdTangle, a social media analytics tool. .
"Ukrainian army says it shot down six fighter jets and a helicopter belonging to Russia," it read. a tweet from February 24 with the picture.
Many blogs and websites recently posted the same image and description.
Follow us on Facebook! Like our page to get updates throughout the day on our latest debunkings
But the photo was taken years ago, as reported by independent fact-checking organisations. It has nothing to do with Russia's invasion of Ukraine.
USA TODAY has reached out to social media users who shared the photo for comment.
The picture is from 2015
The image in the post was taken on August 22, 2015, during an air show celebrating Russian National Flag Day, according to the photo's caption on Shutterstock.
The description says the photo shows a flight group called "Falcons of Russia" demonstrating a Sukhoi Su-27, a Russian fighter jet that was first introduced in 1985.
Other photos of air shows held around this time at Zhukovsky International Airport near Moscow are featured on Getty Images, Aviation International News and Shutterstock.
The International Aviation and Space Salon, Russia's largest air show held every two years, took place in late August 2015, according to the Moscow Times. Footage from the event shows aircraft maneuvers similar to the one depicted in the image.
USA TODAY and other fact-checking organizations have debunked footage purporting to show the Russian invasion of Ukraine. Some social media users have falsely claimed that a May 2020 video of a Moscow flyover showed Russian planes flying over Kiev, the Ukrainian capital.
Fact check: The photo shows an airstrike in the Gaza Strip, not a Russian invasion of Ukraine
Our opinion: False
Based on our research, we rate the claim that an image shows a Russian plane shot down by Ukraine as FALSE. The photo was taken in August 2015 during an air show in Russia.
Our fact-checking sources:
Reuters, Feb 24, Fact Check – Photo of plane falling from sky is from 2015 air show
Shutterstock, August 22, 2015, Photo
Britannica, November 28, 2017, Sukhoi Su-27
Getty Images, August 21, 2015 The Russian Navy's Sukhoi Su-30SM jet fighter performs its demonstration flight at the MAKS-2015 airshow near Zhukovsky
Aviation International News, August 25, 2015, MAKS Moscow Airshow opens in Zhukovsky
Shutterstock, August 22, 2015, Photos
The Moscow Times, August 27, 2015, MAKS 2015 Airshow Best Deals and Announcements
The Moscow Times YouTube, August 26, 2015 Russian Air Force struts at MAKS 2015 Airshow
USA TODAY, February 24, fact check: Viral video shows January post on TikTok, not Russian invasion of Ukraine
USA TODAY, February 24, Fact Check: Video Shows Russian Military Flying Over Moscow in 2020, Not Ukraine in 2022
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Lauren Boebert appalled Americans only own 46% of guns in the world
LGBTQ+ History Month 2023: 20 Quiz Questions and Answers
Powerball numbers for Wednesday night's $653 million jackpot draw
California's snowpack is now the thickest in decades


GLENMONT — Applebee's Flapjack fundraiser for The Helderberg Christian School in Berne will be held 8-10 a.m. Feb. 16 at Applebee's, 291 Route 9W, Glenmont. Tickets are $7. Advance tickets available through school office, 518-499-5416.


text:
Cresciuta a Charleston (Carolina del Sud), ha iniziato come modella nella sede di Miami della Elite Model Management per proseguire, nella sua carriera nello spettacolo, come attrice. Al suo primo provino per una parte in S1m0ne con Al Pacino, la Scott fu rifiutata ma quell'audizione le permise di recitare in A.I. - Intelligenza Artificiale nel ruolo di Gigolo Jane. Da allora l'attrice è apparsa in serie televisive come Dark Angel nel ruolo di Asha Barlowe e in Birds of Prey nel ruolo di Helena Kyle/Cacciatrice e in film come A testa alta, S.W.A.T. - Squadra speciale anticrimine, Tresspassing (inedito in Italia) e Trappola in fondo al mare.

Era stata scelta per interpretare l'episodio pilota della sit-com Joey con Matt Le Blanc, ma è stata sostituita da Andrea Anders.

Nel film 12 Round è la fidanzata del detective Danny Fisher (John Cena), Molly Porter.

L'attrice è dislessica.

Filmografia

Cinema
 A.I. - Intelligenza Artificiale (Artificial Intelligence: A.I.), regia di Steven Spielberg (2001)
 S.W.A.T. - Squadra speciale anticrimine (S.W.A.T.), regia di Clark Johnson (2003)
 A testa alta (Walking Tall), regia di Kevin Bray (2004)
 Trespassing, regia di James Merendino (2004)
 Lost, regia di Darren Lemke (2004)
 Trappola in fondo al mare (Into the Blue), regia di John Stockwell (2005)
 Just Friends - Solo amici (Just Friends), regia di Roger Kumble (2005)
 Puff, Puff, Pass, regia di Mekhi Phifer (2006)
 The Kingdom, regia di Peter Berg (2007)
 Strange Wilderness, regia di Fred Wolf (2008)
 12 Round (12 Rounds), regia di Renny Harlin (2009)
 Incubo biondo (One Small Indiscretion), regia di Lauro David Chartrand-DelValle (2017)
 Secret Obsession, regia di Peter Sullivan (2019)

Televisione
 Criminal Mastermind , regia di Troy Miller (2001)
 Dark Angel - serie TV (2001-2002)
 Birds of Prey - serie TV (2002-2003)
 Deceit , regia di Matthew Cole Weiss (2006)
 Jericho - serie TV (2006-2008)
Christmas Mail (2010) - film TV
 Il marchio dell'inganno (Unstable), regia di Michael Feifer (2012) - film TV
 I segreti non riposano in pace (Summoned), regia di Peter Sullivan (2013) - film TV
 Una babysitter pericolosa (The Nightmare Nanny), regia di Michael Feifer (2013) - film TV
 Unreal - serie TV (2015)
 Uno sconosciuto in casa (A Stranger with My Kids), regia di Chad Krowchuk – film TV (2017)
A Tale of Two Coreys, regia di Steven Huffaker – film TV (2018)
 The Flash- serie TV, cameo (2019)

Videogiochi
 The Last of Us - voce (2013)
 The Last of Us Part II - voce (2020)

Doppiatrici italiane
Nelle versioni in italiano delle opere in cui ha recitato, Ashley Scott è stata doppiata da:
Laura Lenghi in Birds of Prey, Una babysitter pericolosa
Barbara De Bortoli in Dark Angel, Unreal
Alessandra Korompay in I segreti non riposano in pace
Cinzia De Carolis in Trappola in fondo al mare
Rachele Paolelli in Incubo biondo
Chiara Colizzi in A testa alta
Ilaria Latini in Jericho
Elda Olivieri in Secret Obsession

Da doppiatrice è sostituita da:
 Lucy Matera in The Last of Us, The Last of Us Part II

Altri progetti

Collegamenti esterni

Attori televisivi statunitensi
Irlando-americani

redpajama_set_name: RedPajamaWikipedia


In this podcast, we are chatting all about travel systems Bella Baby expert Sharon Cummins. We discuss what you need to look out for when deciding on 'the one' and the do's and don'ts of finding the right travel system for you, your family and your lifestyle. This is a really useful 'how to' for new parents. We talk through the mechanics of a travel system – what is it? What is included typically? The all-important lifestyle consultation; why it is essential to assess your lifestyle to find the right travel system to best suit your needs and to fit in with where you live and how you explore your world. Lead-times and your guide when to place your order. Why is a carrycot so important for your baby's health and development? What about future-proofing your travel system to double up your pushchair? Making life easier, with deposits and payment plans. Sharon's one top tip when you pick up your travel system to master your travel systems mechanics! For more useful parenting podcasts click here and don't forget to subscribe. We would be honored if you took a moment to rate and review Nine Months On! We greatly appreciate you joining us and we hope you have enjoyed this podcast! Thank you so much for your support.


text:
Watch of the Week: Breitling's Super AVI Watches Are Inspired by WWII-Era Warplanes
Breitling Super AVI CollectionCourtesy Image
by Michael Charboneau
Pilot watches are among the most interesting breeds of watch because of their storied history. One of the first-ever wristwatches was designed in 1904 for a famous Brazilian pilot who was tired of fumbling around with a pocket watch mid-flight. While Breitling's pilot watch experience doesn't reach quite that far back, the brand is known for its exceptional pilot watches, and its latest collection draws on that heritage—pulling inspiration from actual airplanes. The new Super AVI Collection includes five timepieces based on the renowned "Co-Pilot" AVI pilot watch released in 1953, and the watches are a tribute to four iconic World War II-era fighter aircraft: the North American P-51 Mustang, Vought F4U Corsair, Curtiss P-40 Warhawk, and de Havilland Mosquito.
"This collection embodies that sense of nostalgia for the early days of aviation when pilots relied on their watches as onboard tools," Breitling CEO Georges Kern said in a press release. "But you don't have to be a pilot or vintage-aircraft buff to appreciate the exceptional craftsmanship and rugged design."
TAG Heuer's Night Diver Shines Above and Below the Tide
The starting point for all five of the new watches is the original Ref. 765 AVI pilot's watch, released in 1953. After its debut, it quickly became a popular choice among aviators, and it earned the nickname "Co-Pilot" for its reliability and ease of use. (Breitling launched a re-issue of that timepiece last year.)
To design the Super AVI watches, Breitling took design hallmarks of the Co-Pilot—like large Arabic numerals and triple sub-dials—and refined them with aesthetic details pulled from the four WWII-era aircraft. All the models feature large 46mm cases and, like any good tool watch, they're built for ease of use: The oversized crown and knurled bezel makes them easy to grip and manipulate. They're also built with a GMT complication for tracking two time zones at once (the red-tipped hand tracks a second time zone using the indices on the inner ring of the bezel). Whether you fly your own plane or prefer a window seat on a commercial jet, that's always a helpful feature to have close at hand.
The Best Apple Watch Bands for Every Style and Budget
Aesthetically, the Super AVI watches are as diverse as the planes they honor. The Super AVI P-51 Mustang, for example, comes in two versions. One features a stainless-steel case with a black dial and brown leather strap, and the other features a red gold case with an "anthracite" dial and black leather strap. The Super AVI Tribute to Vought F4U Corsair replicates that plane's eye-catching blue color scheme with its own deep blue dial, while the Super AVI Curtiss Warhawk features an olive drab dial, white sub-dials, and red accents that evoke the aircraft's fearsome "shark mouth" nose art.
No matter which you choose, you'll get a capable pilot's watch—and a little piece of history on your wrist, too.
[Starting at $7,750; breitling.com]
Watch of the Week: G-Shock's MT-G Series Gets a Colorful Upgrade
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21 Best Body Lotions for Men
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20 Best Face Serums for Men
Watch of the Week: Shinola's New Diver Boasts Punchy Colors
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Quince Knocked it Out of the Park With the Mongolian Cashmere Crewneck Sweater
Keep Your Hands Safe This Winter With the Smartwool Cozy Grip Gloves
Class Up The Office With These Florsheim Castellano Wingtip Oxfords


So who was that first winner on PokerStars mobile?
So you're at home, playing a tournament on PokerStars and the internet goes down. Who knows what caused it, apart from one of those illogical and irrational assumptions anyone would make in a time of such crisis - bad weather, a piece of furniture blocking the signal, or an IP address conflict that not even switching everything off and switching everything on again can shift. And all the while you're being blinded away.
In the old days this was a problem. But not anymore. The advent of mobile technology means you can download the PokerStars client on your smart phone or tablet, and always have a Plan B. So go ahead, kick your Wi-Fi router and shout a bit when the signal drops. Just be sure to grab your phone as you do so.
For many PokerStars players playing on our mobile site is now a matter of routine. But it wasn't long ago that the technology was brand new. So thinking logically that means there was a day when it was first launched and first played on. There was a first hand played on mobile, a first pot won, then then a first tournament.
That's how David "dmf81" Forsyth played a small part in PokerStars history.
"I don't remember much about the win," said Forsyth. "But it's fun to think that I was the first winner of an MTT using the mobile app. It's also surprising too given I'm normally behind the times as far as tech is concerned!"
It might not seem like an enormous achievement, but it was a first; one that represents one of the milestones PokerStars is celebrating this month to mark our 100 millionth player. Who cares that it wasn't a weekend major, or a COOP event?
"The win itself sounds lame, but we all have to build a poker bankroll from somewhere!"
Forsyth, 34, downloaded the PokerStars app on his phone after seeing an advert on his way home one day. He took part in a PokerStars promotion that was running at the time for UK players, whereby the winner of a monthly league would win a full package to a UKIPT event.
"Entry was £1.10 with a couple of hundred entrants and the win was for £50 or so," explained Forsyth. "I think I finished second in the league that month and won a $109 tournament ticket on top of my winnings from the MTTs."
Not bad while using a screen the size of, well, a smart phone.
Since then Forsyth, who usually plays $25 no-limit games on PokerStars, keeps his phone handy for those dreary bus rides home, or to simply unwind after a busy day. At the very least it's a way to make a commute profitable, or to make a few dollars while waiting for the lights to change.
Like a lot of players Forsyth got interested in poker after watching Late Night Poker, and then started playing freerolls online (again, like others, taking a freeroll win as a sign of great things to come).
"I was doing a lot of dumb things like misreading boards e.g. bet/calling huge river jams with top set when the obvious straight or flush came in because I thought I still had the nuts."
But freerolls had another use, helping him grasp the rules and subtleties of the game without risking his own money. Then, armed with a small bankroll he began grinding micro-tournaments.
"I was doing okay but wanted to get better."
Reading articles and websites he began having some success, steps that ultimately lead to the games he plays now.
"The most important thing I learned early on is that poker is a continuous learning process and to never assume that you're a good player."
It's the kind of discipline that has helped him become the poker player he is, which, as we're saluting today, is one able to win anywhere, including on the move.
If you want to join him you can download the PokerStars app here.


text:
Cercle Brugge Koninklijke Sportvereniging este un club de fotbal din Bruges, Belgia, care evoluează în Prima Ligă. Echipa susține meciurile de acasă pe Stadionul Jan Breydel, ce are o capacitate de 29.945 de locuri.

Palmares
Jupiler League(3)
Divizia Secundă Belgiană
Campioni(4)
Vice-campioni(1)
Cupa Belgiei
Campioni(2)
Vice-campioni(4)
Supercupa Belgiei
Vice-campioni(2)

Cercle Brugge în Europa

Legături externe
 Official Website //
 Cercle Brugge at UEFA.COM
 Cercle Brugge at EUFO.DE
 Cercle Brugge at Weltfussball.de
 Cercle Brugge at Playerhistory.com
 Cercle Brugge at Transfermarkt.de
 Cercle Brugge at Football Squads.co.uk
 Cercle Brugge at National Football Teams.com
 Cercle Brugge at Football-Lineups.com
 Ultras Bryggja '05
 Cerclemuseum.be: Cercle Brugge Fan site with individual player data
 Cercle Brugge XtraTime Fanpage

Cluburi de fotbal Belgia


text:
Q: Probability distribution on trajectories of stochastic process. In Nelson's book "Radically Elementary Probability Theory", chapter 3, he defines a stochastic process over a finite probability space $\left<\Omega,pr\right>$ and indexed by a finite set $T$ as a function $\psi : T \rightarrow \mathbb{R}^{\Omega}$.  (Hence $\psi (t)(\omega) \in \mathbb{R}$ for any $t\in T$ and $\omega \in \Omega$.)  Then he goes on to define a trajectory of the stochastic process as $\psi(\cdot)(\omega)$ for any $\omega \in \Omega$.
Next he defines $\Lambda_{\psi}$ to be the set of trajectories of $\psi$, and he defines a probability distribution $pr_{\psi}$ by $$pr_{\psi}(\lambda) = Pr\left\{\psi(t) = \lambda(t) \: \forall t \in T\right\}$$
He claims that $\left<\Lambda_{\psi},pr_{\psi}\right>$ is then a finite probability space.
Question: The author is using some probabilistic shorthand in his definition of $pr_{\psi}$, which is totally opaque to me.  Can someone please spell out more explicitly what is the proper definition of $pr_{\psi}$?
Bonus points if you can illustrate with with an example--e.g. $\Omega = \{H,T\}$ as a model of a coin flip.

A: Earlier, the author defined for a subset $A\subset\Omega$,
$$Pr(A):=\sum_{\omega\in A}pr(\omega).$$
Very often in probability, if $X$ is a random variable defined on $\Omega$, we will use the abbreviation $\{X\in A\}$ for the set $\{\omega\in\Omega:X(\omega)\in A\}$. So the full definition of $pr_\psi$ is
$$pr_\psi(\lambda):=Pr\{\omega\in\Omega:\psi(t)(\omega)=\lambda(t)\text{ for all }t\in T\}=\sum_\omega pr(\omega)$$
where the sum is over all $\omega\in\Omega$ such that $\psi(t)(\omega)=\lambda(t)$ for all $t\in T$. To see that $(\Lambda_\psi,pr_\psi)$ is a finite probability space, notice that $\Lambda_\psi$ is simply the range of the function $\Omega\to\mathbb R^T:\omega\mapsto\psi(\cdot)(t)$ which must be finite since $\Omega$ is finite. Now if we sum over $\lambda\in\Lambda_{\psi}$, we find
$$\sum_{\lambda\in\Lambda_{\psi}}pr_\psi(\lambda)=\sum_{\lambda\in\Lambda_\psi}\sum_{\omega:\psi(\cdot)(\omega)=\lambda}pr(\omega)=1$$
since each $\omega\in\Omega$ appears in the double sum exactly once.
For an example, let's consider tossing a coin $3$ times. Our probability space is
$$\Omega:=\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\},\\
pr(\omega):=\frac18\text{ for all }\omega\in\Omega.$$
A random variable on this space could be the total number of heads, or $5$ if the first toss is a tail and $1$ otherwise, or the number of tails in the first two tosses minus the number of heads in the third toss, etc. A stochastic process with index set $T=\{1,2,3\}$, on the other hand, would be something like
$$\psi(t):=\{\text{the number of heads after the first $t$ throws}\}.$$
In this case, our space of trajectories is
$$\Lambda_\psi=\{(1,2,3),(1,2,2),(1,1,2),(1,1,1),(0,1,2),(0,1,0),(0,0,1),(0,0,0)\}$$
and our probability distribution is
$$pr_\psi(\lambda)=\frac18\text{ for all }\lambda\in\Lambda_\psi.$$
One can imagine, without too much difficulty, that if you chose a more complicated definition for $\psi$, we could have multiple values of $\omega$ yield the same trajectory, in which case we would get a different $pr_\psi$.
For what it's worth, I find this a rather strange way to teach probability and stochastic processes.


text:
import json

class DataBase(object):
    def __init__(self, json_location):
        f = open(json_location)
        self.database = json.load(f)
        f.close()

    def get_database(self):
        return self.database

    def get_card_name(self, card_id):
        l = []
        for v in self.database.values():
            l.extend(v)
        for item in l:
            if item['id'] == card_id:
                return item['name']
        return None

redpajama_set_name: RedPajamaGithub


Giulio Potenza (°1990) started the piano at the age of six and has since then established himself as a respected concert pianist, teaching and performing extensively across Europe.
Giulio Potenza has studied with professors Gabriele Baldocci, Pascal Rogè, Denize Gelenbe and Mikhail Kazakevich (Trinity Laban Conservatory, 2012-2015), and Bruno Canino (Milan, 2009-2010). He has attended piano and chamber music master classes and lessons held by eminent professors such as Andrzej Jasiński, Franco Scala, Martino Tirimo, Barry Snyder, Irina Chukovskaya, Martin Kasik, Andrei Gavrilov, Pascal Rogè, Christopher Richter, Irene Inzerillo, Riccardo Risaliti, Wihan Quartet, Magini Quartet. He holds Postgraduate and Artist Postgraduate Diplomas from the Trinity Laban Conservatory and a Bachelor in History from University of Palermo. He completed his undergraduate music studies at the conservatory of Trapani (Italy) under professor Walter Roccaro.
He has performed throughout the world including United States, Asia, Spain, France, U.K., Swiss, Norway, Switzerland, Malta, Belgium, Holland and invited to play at prestigious international festivals and venues including Martha Argerich's Lugano Project of Lugano 2015, the Bangkok Piano Festival, the Palermo Classica International Music Festival of Palermo, Festival dei Due Mondi of Spoleto, the Hammerklavier International Piano Series of Barcellona, the Bolzano Piano Festival, the Grieg in Bergen International Festival of Bergen, the Fringe Festival of Edinburgh, the Hammamett Piano Festival of Tunis, the Carnegie Hall of New York, Siam Ratchada Auditorium and Martin Hall of Bangkok, Filarmonica of Oviedo, St. Martin in the Fields, Steinway Hall, Conway Hall, St. John's Smith Square, Balckheat Hall of London, Bridgwater Hall of Manchester, Cauchi Hall of Malta, Kabuso Auditorium in Øystese, Bernanos Auditorium of Paris, Theater aan de Parade in Holand, Bellinzona Theater of Lugano, Baldini Hall of Rome, Auditorium St. Stafano of Florence, Stavanger Chatedral of Stavanger, Massimo Theater (ONU Hall) of Palermo.
Giulio also performed for major music societies such as the Concordia Foundation in London, Arcades Musiques of Le Buisson de Cadouin, Sociedad Filarmonica de Oviedo, Maggio della Musica of Naples, Vanesborg Music Society of Vanesborg, Edinburgh Society of Musicians of Edinbhurgh.
As a soloist, he has performed with the Florence Symphonietta Orchestra, directed by Piero Bellugi, the University of London Symphony Orchestra, directed by Daniel Capp and the North Beds Orchestra directed by Jan Kaznowski.
He has collaborated with many renowned artists such as Jose Menor, Daniel Rivera, Gabriele Baldocci, Nicolas Dupont, Stefano Farulli, Zoe Freedman, Philip Martin.
In 2014, as a result of his interest for four hands/two pianos composition, Giulio started a collaboration with the Norvegian pianist Oda Voltersvik (Volt&Potenza Duo). The Duo's debut CD "Χορεία", including a commissioned contemporary work by the Irish composer P. Martin, was been released in April 2016 under the Velut Luna label.
In 2017 he has released a cd including the piano and violin repertoire of Leoš Janáček for Da Vinci Classic label.
His recitals and recordings have been broadcast by BBC Radio 3, Rai Radio 3, Radio Musiq3, Radio Breda Klassiek, Radio Klara, the Swiss Classical Radio, Radio Vaticana, and Rai National Television.
Giulio has won prizes at several important piano competitions including the Hanna Brooke prize for piano, for his excellence in the concert career at the Trinity Laban Conservatory; 2nd prize at the Bradshaw & Buono International Piano Competition of New York (2016); 1st prize at the Seiler International piano competition (2002); 1st Prize at the Stratford and East Concerto Competition of London (2015) ; 3rd Prize at the Geertruidenberg Klassiek International Music Competition in Netherland (2018); "Highly Commended Award" at the Jacques Samuel Piano Competition of London (2012).
Giulio was also selected by London's Concordia Foundation as participant to the Young Artists Programme.
He is professor of piano at the Conservatory of Music "A. Scontrino" of Trapani and at the Windsor Piano Academy and regularly gives master classes in the UK and abroad. Furthermore, is the artistic director of the Windsor International Piano Competition and of the Windsor Piano Festival.


Size: For Cards & Bills.
1 Long slot for Banknotes (100mm tall; ~270mm long).
Wallet has one section for full size bank notes; 8 slots for credits cards, 2 inside pockets.
Other objects used for product shooting (watches, cards, buckles and other accessories) are not for sale.
Genuine Alligator Leather Wallet. All meticulously handcrafted in Italy by Italian artisan.
Main Material: Genuine Alligator leather.
Inner Material: Italian Calf Leather. Color: Black.


The Career Management Center (CMC) is working very hard to strengthen the bond between its alumni and the university. Alumni are crucial to the present and, most importantly, the future of IIT. IIT's success depends on a thriving, energetic, and engaged alumni base in order to advance the best interests of the university.
We are proud of our graduates and we know that many former students are doing very valuable things for our society and working in exciting places. Each of you should be very proud of your achievements! I hope that your IIT experience has a positive and lasting effect in your education and career goals for the future.


The full time, four semesters, two year MBA program was introduced in the academic year 2014. Under the guidance of the Director Dr. R Gopal, the program was incubated by Captain Shashikant Koppikar. He is a veteran of the aviation industry with a total experience of over 45 years. The program has been designed, keeping in mind employability across a wide spectrum of segments within the aviation industry, such as the Airlines, Airports, Airfreight, Corporate aviation and Airport planning. The accent is on finance, economics and management aspects specific to aviation.
Industry insiders and independent consultants alike are unanimous about the growth prospects of Indian aviation. Already the 9th largest in the world, it is expected to grow five times the present size by 2030, to become the 3rd largest. It is but natural that such explosive growth will require specialist aviation managers in large numbers. The recent policy pronouncements by the central and state governments are a clear pointer in the direction of growth.
At present there is a dearth of institutions in India, providing specialist higher education in the field of aviation management. Dr. D. Y. Patil School of Management's MBA program aims at filling up this gap to provide aspiring aviation managers a career opportunity, which at once will be both rewarding and satisfying.