text:
\section*{Introduction}

Recent designs of lens correctors for the large telescopes provide the field of
view of sub-arcsecond image quality up to $3^\circ$ in a Cassegrain system
(Hodapp et al., 2003), in a three-mirror Mersenn--Schmidt system (Paul, 1935;
Willstrop, 1984; Angel et al., 2000; Seppala, 2002), and in a prime focus of
hyperbolic mirror (Terebizh, 2004). In the two former cases, a telescope is
quite compact, while the surfaces of mirrors and lenses are complicated. In the
latter case, it is possible to achieve the above field even at all spherical
lenses, but the telescope length is about focal length of its primary mirror.

The Gregory system (both classic, with a paraboloidal primary, and aplanatic,
with ellipsoidal surfaces of the mirrors) has an attractive feature: its exit
pupil is not imaginary, as it takes place for the Cassegrain system, but real.
Usually, the Gregorian exit pupil is situated not far from the primary focus.
Such a position allows us to place a correcting optical element directly in the
exit pupil, providing efficient correction of aberrations of a two-mirror
system without auxiliary optics.

At first glance, the superposition of wide light beams near the primary focus
prevents to imposing a lens corrector in the Gregory system (see Fig.~1).
However, as shown below, it is possible to avoid additional obscuration, if we
make a hole at the center of the front lens of the corrector and shift the rear
its part to the primary mirror. As a result, we obtain a wide-field
catadioptric system that combines compactness with simple shape of the optical
surfaces\footnote{Strictly speaking, since both mirrors are optimized along
with the lens corrector, we deal not with a corrector to the pre-designed
aplanatic Gregory telescope, but with a new catadioptric system.}. The system
provides the sub-arcsecond field of view ${\sim2^\circ.5}$ in diameter even at
all-spherical corrector. It is worth noting that the spherical corrector for
the Gregory system repeats the lens corrector that was proposed earlier for a
single hyperbolic mirror (Terebizh,~2004). Subsequent aspherization of some
lens surfaces allows to achieve the field about $3^\circ$ in diameter.

In present paper, we discuss the Gregorian corrector with an example of a 6.5-m
telescope with the focal ratio $\phi \equiv F/D \simeq 1.9$. The effective
focal length of the telescope, $F \simeq 12.4$~m, allows to fit resolutions of
the optics and actual light detectors. The corrector consists of five lenses
made of the same, virtually any material. At use fused silica and simple
coating as a $MgF_2$ single layer, the telescope light transmission reaches
70\%. The detector window has some optical power, the field is slightly curved,
that is quite allowable, taking into account its linear size: approximately
0.5~m.

\begin{figure}[t]
   \centering
   \includegraphics[width=\textwidth]{fig_01c.eps}
   \caption*{Optical layout of the 6.5-m telescope with the spherical basic
   corrector. Ordering of the surfaces corresponds to the Table~2.}
\end{figure}

\section*{Basic system of the 6.5-m  telescope}

In a basic configuration of the telescope (Figs.~1,~2), the primary and
secondary mirrors are pure ellipsoids, while the lens surfaces are spherical.
General performance of the telescope for a case, when the field of view is
$2^\circ.3$ in diameter, is given in the Table~1; the parameters of its optical
layout are specified in the Table~2. At the description of the optical layout
we have introduced, for convenience, a fictitious surface No.~5, located close
to the paraxial primary focus.

Figures~3 and~4 show image quality provided by the basic system, optimized for
the field of view $2^\circ.3$. The circle diameter that contains 80\% of a
stellar image energy (designed, as usually, by $D_{80}$), varies within the
waveband $0.35-0.90\,\mu$m from $\sim0''.25$ at the center of the field up to
$\sim0''.50$ at its edge. The linear coefficient of central obscuration $\eta =
0.51$, so the effective aperture diameter of the system is 5.6~m. The fraction
of vignetted rays enlarges from the center of field to its edge less than on
2\%.

\begin{center}
 \small{
\begin{tabular}{|l|c|c|c|}
\multicolumn{4}{l}{\textit{Table~1. Basic system of the 6.5-m telescope}}\\
\hline
    & \multicolumn{3}{|c|}{}\\
    & \multicolumn{3}{|c|}{Waveband, $\mu$m} \\
 \multicolumn{1}{|c|}{Parameter} & \multicolumn{3}{|c|}{}\\
 \cline{2-4}
    &&&\\
    & 0.35 -- 0.45 & 0.54 -- 0.66 & 0.70 -- 0.90 \\
    &&&\\
\hline
 Field of view  & \multicolumn{3}{|c|}{}\\
 \qquad Angular  & \multicolumn{3}{|c|}{$2^\circ.3$} \\
 \qquad Linear   & \multicolumn{3}{|c|}{498 mm} \\
\hline
 Effective focal length, mm &12370.7 &12368.9 &12367.8 \\
\hline
 Relative focal length & \multicolumn{3}{|c|}{1.903} \\
\hline
 Length of the system  & \multicolumn{3}{|c|}{8797.3 mm} \\
\hline
 Scale, $\mu$m/arcsec  &59.97 &59.97 &59.96 \\
\hline
 Relative vignetting    & \multicolumn{3}{|c|}{} \\
 at the edge of field   & \multicolumn{3}{|c|}{1.7\,\%} \\
\hline
 Variation of the RMS
   &$5.9-14.7\,\mu$m &$5.0-8.0\,\mu$m &$5.4-11.0\,\mu$m \\
 image radius over field
   &$0''.10-0''.25$ &$0''.08-0''.13$ &$0''.09-0''.18$ \\
\hline
 Variation of $D_{80}$ from the
   &$15.8-31.6\,\mu$m &$14.4-22.1\,\mu$m &$16.8-29.7\,\mu$m\\
 center to the edge of field
   &$0''.26-0''.52$ &$0''.24-0''.37$ &$0''.28-0''.50$\\
\hline
 Transmission with the           &&&\\
 single layer of $MgF_2$         &$0.70$ &$0.71$ &$0.70$\\
\hline
 Maximum distortion  & 0.27\,\% & 0.28\,\% & 0.29\,\%\\
\hline
 The lens surfaces & \multicolumn{3}{|c|}{All spheres} \\
\hline
\end{tabular}
 }
\end{center}

\bigskip

The relative focal length of the primary mirror, $\phi_1 \equiv F_1/D_1$, is
about 0.92, for the secondary mirror we have $\phi_2 = 0.56$. Let us remind,
for comparison, relative focal lengths of three mirrors of the Large Synoptic
Survey Telescope (LSST) according to Seppala~(2002): $1.057$, $0.914$ and
$0.774$; the light diameters are $8.40$~m, $3.37$~m and $5.44$~m, respectively.
These mirrors are aspherics of the 6th--10th orders, the secondary mirror is
convex. The primary mirrors of the Large Binocular Telescope (LBT) of diameter
8.4~m have $\phi_1 = 1.14$ (Hill, 1996; Salinari, 1996).

\begin{figure}[t]
   \centering
   \includegraphics[width=0.90\textwidth]{fig_02c.eps}
   \caption*{Optical layout of the basic corrector. Numbers of lenses\\
    correspond to the Table~2, the detector window is marked by `W'.}
\end{figure}

\bigskip

According to the above data, we expect no specific problems at manufacturing of
monolithic primary for the proposed here system, but the secondary mirror seems
to be dangerously fast. However, we have to take into account that both mirrors
are the concave pure ellipsoids, which can be controlled during manufacturing
with the aid of the well-known and reliable methods. The other aspect of the
problem under discussion concerns the customary nowadays practice of including
the secondary mirrors to the active optics systems (e.g., on the LBT). These
mirrors properly change their shape under action of actuators, and have very
complicated form at each moment of time. For this reason, the initial form of a
secondary mirror in active system is not obliged to follow the exact design.
Further, it is known that making of fast mirrors becomes strongly simpler at
use of the mosaic technology (see, e.g., Mountain and Gillett,~1998;
Wilson,~1999). Let us notice, at last, that the f/number of a secondary depends
upon a set of general characteristics of a telescope, and, in case of need, one
can initially choose the characteristics in such a way that $\phi_2$ gets the
desirable range. All said above allows to hope, that manufacturing of a
secondary mirror for the proposed system is within modern technological
abilities.

\begin{center}
 \small{
\begin{tabular}{|c|c|c|c|c|c|c|}
 \multicolumn{7}{l}{\textit{Table 2. Parameters of the basic 6.5-m
  telescope, optimized for the field $2^\circ.3$}}\\
\hline
 Number  &         &Curvature &Thickness &      &Light    &Conic \\
 of the  &Comments &radius    &(mm)      &Glass &diameter &constant \\
 surface &         &(mm)      &          &      &(mm)     & \\
\hline
 1  &Screen &$\infty$   &0 &--- &3315.00 & 0\\
 2  &Vertex of &&&&&\\
    & secondary &$\infty$ &8355.89 &---  & 0  &0\\
 3  &Aperture &&&&&\\
    &diaphragm  &$\infty$   &441.42     &---  &6500.00  & 0\\
 4  &Primary &$-11993.55$ &$-5995.78$ &Mirror &6500.00 &$-0.866870$\\
 5  &Primary focus &$\infty$ &$-2801.53$ &--- &338.43 &0\\
 6  &Secondary &$3728.74$ &$2941.53$ &Mirror &3314.54 &$-0.194002$\\
 7$^{1)}$   &L1       &$3034.14$   &$100.00$  &FS$^{3)}$
       &1500.00 & 0\\
 8$^{2)}$  &         &$3835.23$   &$1601.82$ &---   &1466.74 & 0\\
 9    &L2       &$2587.74$   &$50.00$   &FS &758.08 & 0\\
 10   &         &$541.32$    &$42.41$   &---   &697.64 & 0\\
 11   &L3       &$736.49$    &$59.65$   &FS    &698.08 & 0\\
 12   &         &$1268.16$   &$481.986^{4)}$ &---  &693.44 & 0\\
 13   &L4       &$1532.40$   &$110.00$  &FS    &655.58 & 0\\
 14   &         &$-3638.17$  &$37.74$   &---   &644.04 & 0\\
 15   &L5       &$747.81$    &$105.00$  &FS    &601.65 & 0\\
 16   &         &$800.48$    &$78.00$   &---   &553.91 & 0\\
 17   &Window   &$-1452.45$  &$37.71$   &FS    &553.05 & 0\\
 18   &         &$-727.49$   &$10.00$   &---   &551.45 & 0\\
 19   &Detector &$2322.90$   &          &      &498.01 & 0\\
\hline
\end{tabular}
 }
\end{center}
 $^{1)}$  {\small The hole of 427.7~mm in diameter}.\\
 $^{2)}$ {\small The hole of 542.3~mm in diameter}.\\
 $^{3)}$ {\small $FS$~-- fused silica}.\\
 $^{4)}$ {\small The visual waveband is meant. The distances
 for the blue and red wavebands are 482.011~mm and 481.936~mm,
 respectively}.

\bigskip

\begin{figure}[t]
   \centering
   \includegraphics[width=0.75\textwidth]{fig_03c.eps}
   \caption*{Spot diagrams of the 6.5-m telescope with spherical
    basic corrector\\ for the field angles $0;\, 0^\circ.3;\, 0^\circ.6;\,
    0^\circ.9$ and $1^\circ.15$ (the rows). The columns correspond to
    the wavebands $0.35-0.45\,\mu$m, $0.54-0.66\,\mu$m and
    $0.70-0.90\,\mu$m, respectively. The box width is $1''$ ($60\,\mu$m).}
\end{figure}

\begin{figure}[t]
   \centering
   \includegraphics[width=0.75\textwidth]{fig_04c.eps}
   \caption*{Basic telescope: Integral energy distribution along radius
   in a star image for the waveband $0.54-0.66\,\mu$m and the field
   angles $0;\, 0^\circ.3;\, 0^\circ.6;\, 0^\circ.9$ and $1^\circ.15$.
   The similar distribution in the diffraction-limited image and the
   $80\%$-level are also shown.}
\end{figure}

\begin{figure}[t]
   \centering
   \includegraphics[width=0.75\textwidth]{fig_05c.eps}
   \caption*{Spot diagrams of the 6.5-m telescope with spherical
    corrector for the\\ field angles $0;\, 0^\circ.3;\, 0^\circ.6;\,
    0^\circ.9$ and $1^\circ.2$ (the rows). The columns correspond to the wavebands
    $0.35-0.45\,\mu$m, $0.54-0.66\,\mu$m and $0.70-0.90\,\mu$m, respectively.
    The box width is $1''$ ($60\,\mu$m).}
\end{figure}

\begin{figure}[t]
   \centering
   \includegraphics[width=0.75\textwidth]{fig_06c.eps}
   \caption*{Spot diagrams of the 6.5-m telescope with aspheric
    corrector for the\\ field angles $0;\, 0^\circ.5;\, 0^\circ.75;\,
    1^\circ.0$, $1^\circ.25$ and $1^\circ.50$. The columns correspond to the
    wavebands $0.35-0.45\,\mu$m, $0.54-0.66\,\mu$m and $0.70-0.90\,\mu$m,
    respectively.
    The box width is $1''$ ($60\,\mu$m).}
\end{figure}

\bigskip

The aperture diameter and general characteristics of the telescope were mainly
determined by condition, that the diameter of the front corrector lens L1 (see
Fig.~2) is no more than 1.5~m (the front lens of the LSST corrector is 1.34~m).
A central cone-shaped hole should be made in L1 for passage of light beam
reflected by the primary mirror. It is possible to manage without the hole,
supposing double passage of light through the lens L1, but the image quality in
a correspondingly optimized system is not so high.

Note that lens sizes are close to those in the prime focus corrector to a
single hyperbolic mirror of 4~m in diameter (Terebizh,~2004). Thus, application
of a Gregory corrector allows to essentially increase the telescope aperture~--
in this case from 4.0~m up to 6.5~m,~-- while the system length has decreased
from 10.8~m down to 8.8~m.

The focal surface of about 0.5~m in diameter is a convex sphere of curvature
radius about 2.3~m. The corresponding sag at the field edge is 13.4~mm.
Relatively small field curvature does not prevent to placing a set of matrix
detectors, which own sizes are less than $\sim25$~mm.

There are a few ways to control focusing at change of the spectral range; we
choose, as an illustration, variation of the distance between the third and
forth lenses. Namely, according to the Table~2, one should shift the rear part
of the corrector only by $+25\,\mu$m and $-50\,\mu$m to turn from the visible
range to the blue and red wavebands, respectively.

Under the pixels size ${\sim 15\,\mu}$m, which is typical for the modern CCD's,
one pixel corresponds to $0''.25$. Thus, about $1-2$ pixels cover a star image
of $D_{80}$ in diameter, and we may consider as feasible the matching of
resolution of the optical system with that of the detector and the atmosphere
image quality.

The telescope light transmission has been estimated, assuming the simple
coatings~-- the single  $\lambda/4$ layer of $MgF_2$. Of course, the modern
multi-layer coatings will ensure best transmission of light.

It is important to note, that the corrector is close to an afocal system, so
the optical power of the telescope is determined mainly by its mirrors.
Evidently, just that feature allows to avoid chromatism and, as a consequence,
to attain the large field of view. This general principle is true also for
other catadioptric systems.

\section*{Extending the field of view}

The all-spherical corrector provides the field up to about $2^\circ.5$. Fig.~5
depicts, as an example, the spot diagrams for the field $2^\circ.4$ in
diameter. Comparison with the Fig.~3 shows that the image quality has worsened
only a little. Further extension of the field meets difficulties caused, first
of all, by accepted here restriction of the sizes of the corrector front lens.

As is well known, there is a quite simple, from a designer's point of view, way
to attain the more wide field of an optical system: the aspherization of the
all or some surfaces. Certainly, this way complicates technical realization of
the system. In particular, the tolerances becomes much more hard, so both the
fabrication and use of the telescope is laborious. Ultimately, these factors
have an essential effect on the cost of the telescope. Nevertheless, many large
telescopes that are now in progress include polynomial aspherics up to 10th
order. In our case, aspherization of some surfaces of the lens corrector,
namely, adding the terms of 4th, 6th and 8th orders, provides the sub-arcsecond
field of view about $3^\circ$ in diameter (Fig.~6).

Even the wider field of view is attainable by applying the polynomial aspherics
not only on the lenses, but also onto the (concave) mirrors of the system. We
shall not consider here this opportunity, as now the main task is to give the
general description of the lens corrector for a quasi-Gregory telescope.

\section*{Concluding remarks}

Let us estimate the \textit{throughput}\footnote{\textit{\'Etendue} (Fr.)} $E$
of the proposed telescope and, for comparison, that of the LSST and a 4-m
one-mirror telescope. The frequently used now parameter $E$ is defined as
product of the telescope effective area by the solid angle, corresponding to
its field of view. Table~3 gives approximate values of $E$ for the two field
sizes. All systems under consideration include the lens field correctors.
Obviously, to continue discussion it is necessary to take into account also a
number of concomitant factors, as that: a reality of manufacturing of the
optical surfaces of required form, the tolerances on temporal stability of the
whole set of parameters, the operation cost of a telescope etc.

\begin{center}
 \small{
\begin{tabular}{|l|c|c|}
\multicolumn{3}{l}{\textit{Table 3. Throughput of some telescopes
 $(m^2\,deg^2)$}}\\
\hline
  & \multicolumn{2}{|c|}{}\\
  \multicolumn{1}{|c|}{} & \multicolumn{2}{|c|}{Field of view} \\
  \multicolumn{1}{|c|}{Telescope} & \multicolumn{2}{|c|}{}\\
  \cline{2-3}
  & $2^\circ.3$ & $3^\circ.0$ \\
\hline
One-mirror 4.0-m telescope        &&\\
with a prime-focus corrector      & 46    & 78  \\
Two-mirror 6.5-m Gregory with     &&\\
the corrector at the exit pupil   & 102   & 170 \\
Three-mirror 8.4-m LSST with      &&\\
the three-lens corrector          &  --   & 264 \\
\hline
\end{tabular}
 }
\end{center}

\bigskip

It is worth mentioning, that the two-mirror telescope alone, taken as a part of
the considered here catadioptric system, provides the image of an axial
point-like object of $0''.15$ in diameter, but a quarter of degree off-axis
image is already $6''$ in diameter. Nearly the same characteristics has the
aplanatic version of a Gregory telescope without lens corrector.

In the Introduction, we have touched on the attractive features of the Gregory
telescope: reality of its exit pupil and concave form of the secondary mirror.
Let us remind also, that it is much easier in the Gregory system to design an
efficient baffles than in the Cassegrain system (Terebizh,~2001).

Naturally, the described above 6.5-m telescope is only one of examples; our
main purpose was to attract attention to possibility of versatile use of the
central and periphery zones of the front lens of the corrector placed in the
exit pupil of a two-mirror Gregory telescope. Proceeding from the basic
configuration, it is possible to design systems with account of the particular
conditions and auxiliary optics (e.g., filters and the atmospheric dispersion
corrector). The scaling of the system to smaller diameters does not meet
problems, but scaling to larger diameters causes increasing of the corrector
front lens.

\bigskip

The author is grateful to V.V.~Biryukov for useful discussions.

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text:
Q: Python running significantly faster than C++? Something seems wrong here I've been using Python to do some quick prototyping before translating it to C++ and found that the Python code in some cases seems to run significantly faster than the C++ code!
Consider this simple loop written in both Python and C++:

python:
import numpy as np
import datetime

N = 16777216
f_s = 8000.0
t_s = 1/f_s

y = np.empty(N)

start = datetime.datetime.now()

for n in range(0,N):
    y[n] = np.sin(2*np.pi*1000*n*t_s) + 0.5*np.sin(2*np.pi*2000*n*t_s + 3*np.pi/4)

stop = datetime.datetime.now()
duration = stop - start

print("duration ", duration.microseconds, " microseconds")

Output:

duration  842000  microseconds

C++:
#include <chrono>
#include <cmath>
#include <iostream>
#include <vector>

int main() {
    int N = 16777216;
    int f_s = 8000;
    double t_s = 1.0 / f_s;

    std::vector<double> x(N);

    auto start = std::chrono::high_resolution_clock::now();

    for (int n = 0; n < N; ++n)
    {
            x[n] = std::sin(2 * M_PI * 1000 * n * t_s) + 0.5 * std::sin(2 * M_PI * 2000 * n * t_s + 3 * M_PI / 4);
    }

    auto stop = std::chrono::high_resolution_clock::now();
    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(stop - start);

    std::cout << "duration " << duration.count() << " microseconds." << std::endl;
}

Output:

duration 1993000 microseconds.

The Python code does seem to take a significant amount of time to startup, while the C++ code runs instantly. (Maybe the Python interpreter is doing some optimization at startup that takes a long time?) But even with that fact aside, once the Python code is running, the loop itself runs significantly faster in Python.
This thoroughly surprised me but I can't seem to figure out how Python is running this loop so fast. I even tried compiling the C++ code at different optimization levels to see if somehow the compiler was just doing a bad job of optimizing. The C++ example above was compiled with g++ -O3 to improve optimization. When that didn't cut it I even tried g++ -Ofast which improved runtime to 1205000 microseconds, but it was STILL significantly slower than the Python loop!
I've tried Googling around but I can't find any real explanation... How could this be happening? How can I get better performance from my C++ loop?? I would expect I could get at LEAST as fast as the Python loop if not faster.

I am running Python 3.7.2
The C++ example was compiled using g++.exe (MinGW.org GCC-6.3.0-1) 6.3.0 with the -O3 compiler switch to improve optimization.
I also tried compiling the C++ code in a linux environment with g++ (GCC) 4.8.5 20150623 (Red Hat 4.8.5-36) with similar results.

A: You are not using the microseconds component of timedelta correctly. It only gives you the sub-second microseconds portion of the time measurement, not the total elapsed microseconds. This code highlights your mistake
from datetime import datetime, timedelta

start = datetime(2019, 1, 1, 12, 0, 0, 0 )
end   = datetime(2019, 1, 1, 12, 0, 1, microsecond=500000 )
diff = end - start

print('Total duration=',diff)
print('Total seconds=', diff.total_seconds())
print('microseconds=', diff.microseconds)

# output
Total duration= 0:00:01.500000
Total seconds= 1.5
microseconds= 500000

Use total_seconds and multiply by 1e6, or just change your tests to report the results in seconds.
Note C++ should win this easily. Your loop has a fixed number of iterations that are known at compile time, and none of the calculations depend on each other. A good optimizing C++ compiler should chunkify, or partially unroll, that loop and use SSE instructions to perform small sets of computations in parallel.

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text:
Endeavour is a British television detective drama series created by Russell Lewis and co-produced by Mammoth Screen and Masterpiece in association with ITV Studios. It is a prequel to the long-running Inspector Morse series and was first broadcast on ITV in the United Kingdom on 2 January 2012 and on PBS in the United States on 1 July 2012, as part of the Masterpiece Mystery! anthology. Eight series have been broadcast, with the latest completed on 26 September 2021. Series 9 is scheduled to air on 26 February 2023 and shall be the final series.

An Endeavour episode may comprise some of the following cast members: Shaun Evans (DC/DS Endeavour Morse), Roger Allam (DCI Fred Thursday), James Bradshaw (Dr Max DeBryn), Anton Lesser (CS Reginald Bright), Sean Rigby (PC/DS Jim Strange), Jack Laskey (DS Peter Jakes), Caroline O'Neill (Win Thursday), Jack Bannon (Sam Thursday), Sara Vickers (Joan Thursday), Abigail Thaw (Dorothea Frazil), Dakota Blue Richards (WPC Shirley Trewlove), Lewis Peek (DC George Fancy), Simon Harrison (DI Ronnie Box) and Richard Riddell (DS Alan Jago).

On 23 May 2022, ITV and Mammoth Screen announced that Endeavour would end after nine series, bringing the total number of episodes to 36, including the pilot episode.

Series overview

Episodes

Pilot (2012)

Series 1 (2013)

Series 2 (2014)

Series 3 (2016)

Series 4 (2017)

Series 5 (2018)

Series 6 (2019)

Series 7 (2020)
Series 7 took place in 1970, with Russell Lewis writing the episodes. In the US, Series 7 aired Sundays August 9–23, 2020 (9:00 pm) on PBS as Masterpiece Theater.

Series 8 (2021)
Series 8 was broadcast from 12 September 2021 and took place in 1971, with Russell Lewis writing and Shaun Evans, Ian Aryeh and Kate Saxon directing the episodes.

Series 9 (2023)

Series 9 is scheduled to air on 26 February 2023, with the final three episodes set in 1972. It will be the final series to air, by agreement of PBS Masterpiece, ITV and the cast. This was posted to the Endeavour Twitter account on 23 May 2022. Russell Lewis will write the final three episodes. Shaun Evans, Nirpal Bhogal and Kate Saxon will direct the final three episodes. The story comes to its logical end in Series 9, in telling how Inspector Morse developed into the character of the Morse series, across 72 hours of television episodes in ten years. Filming was underway in Oxford on 22 May 2022. The announcement of the final season was made a week or so before Season 8 began airing in the US on 19 June 2022.

Notes

References

External links

Lists of British crime television series episodes
Lists of British drama television series episodes
Inspector Morse
ITV-related lists

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• Orders office supplies to support human resources operations and various special events.
• May perform new hire orientations.


Description: London, Educational Supply Association Holborn Series 1875-77 according to Bodleian Library Engravings in the text. . 166x104mm blindstamped cloth (edges & spine faded/tips sl.rubbed) 208pp. Prize inscription dated 1880 to front free endpaper,endpapers foxed/browned rest of book entirely clean and tight. Each story preceded with a short list of words broken down into syllables and the readings include words marked with an asterisk which are to be found in the vocabulary at the end of the book, and the sections are followed by dictation and home exercises in grammar.


Our instructors here are Silverstone are all highly skilled drivers. Many of them compete in various world class competitions and they all have a passion for racing.
The Silverstone instructors will help you get the most out the your driving experience by giving you hints and tips and coaching you on how to handle the car, the track and those tricky corners.
Click on the instructor below to find out more about their driving history and experience.


Our Dentist, Brandi Yates, DMD, aims to provide patients with a safe, comfortable,and relaxing environment that supports and encourages the continuance of regular oral health care. We offer general dentistry and cosmetic dentistry services to be your comprehensive family dentist. Call our dental office and schedule a visit today and find out how we can help make you smile!
Whitening allows teeth that have darkened over time due to coffee, wine, smoking, or age to return to a whiter and younger look. Our office offers Opalescence GO that is pre-filled professional whitening trays only available through your dentist. You can get a more customized whitening treatment with our custom made take-home trays. This second option fits more closely to your teeth and allows you to purchase bleach refill tubes at our office as needed. We also provide in-office whitening for faster results.
A bridge is a porcelain or zirconia appliance that is used to replace a missing tooth. It is an alternative treatment option to that of an implant. When a tooth is missing, a crown can be placed on the tooth in front of and behind the missing tooth, and a fake tooth (or pontic) is connected between the two crowns. This type of tooth replacement is fixed into place with cement and cannot be removed by the patient. The custom bridge provides a great cosmetic option to replace a missing tooth.
Implants provide the latest technology in replacing teeth. Whether replacing only one tooth or multiple teeth, implants are a great option for the long-term results. An implant is made from titanium and surgically placed into the bone. It functions similar to the root by supporting the tooth. After the implant is completely stable in the bone, the abutment (a small connector) and custom crown are placed. The dental implant provides a strong and durable way to restore chewing function.
A crown (or what many call a cap) is a full covering of a tooth to strengthen and protect a fractured or weakened tooth. When a tooth has a large filling that needs to be changed, many times if an even larger filling is placed it can weaken the tooth. It's at this point that your dentist may recommend a crown. Typically made of porcelain or zirconia, a crown matches your tooth in color and is custom made to fit your tooth.
If it has been awhile since your last dental check-up or if you have swollen, red, and tender gums you may be a candidate for SRP. Scaling and Root Planing, also known as a deep cleaning, is a non-surgical therapy done to treat gum disease. This procedure is performed to remove plaque and tartar (hardened plaque) that has accumulated under the gum line. The build-up causes tissue inflammation and bone loss and ultimately leads to loosening of teeth and tooth loss. Early intervention is also important due the link between oral health and some chronic diseases such as heart disease and diabetes. Deep cleanings may take a series of appointments depending on the severity. After the procedure, it is recommended that you are monitored and cleaned on a more frequent basis. To help you heal, your dentist and dental hygienist may recommend a prescription strength rinse or gel.
Bruxism occurs when you grind your teeth or clench your jaw. You may suffer from this if you experience headaches, jaw pain, sensitivity, and broken/worn teeth. Bite splints or occlusal guards can be used as a treatment for bruxism. The appliance is custom made by your dentist to be worn on your upper or lower arch. Bite splints prevent your teeth from touching and can relieve pressure on your jaw joints.
Regular dental visits every six months is essential to your oral health. These routine visits sometimes can help you save time and money by catching small problems before they turn into extensive treatment. Routine cleanings prevent the bacteria from building up that can lead to gum disease and tooth decay. At your visit, your dentist can also take x-rays to identify any hidden problems that need to be addressed.


Quality, design, craftmanship and high-tech are the ingrediencies in our advisory and production. The knowledge about design and quality set a high standard for the production. Here we combine craftmanship traditions with new ways of production, CAD/CAM design programs and CNC-controlled workstations.
We value design and quality. Therefor we work closely with architects, lighting designer and engineers.


text:
\section{Introduction}

We say that a positive integer is square-free if it is not divisible by the square of any prime. It was first shown by Estermann \cite{estermann} in 1931 that every sufficiently large positive integer $n$ can be written as the sum of a prime and a square-free number. In particular, he proved that the number $T(n)$ of such representations satisfies the asymptotic formula
\begin{equation} \label{estermannformula}
T(n) \sim \frac{c n}{\log n} \prod_{ p | n} \bigg( 1+\frac{1}{p^2-p-1} \bigg),
\end{equation}
where
\begin{equation} \label{artin}
c=\prod_p \bigg( 1 - \frac{1}{p(p-1)} \bigg) = 0.3739558\ldots
\end{equation}
is a product over all prime numbers which is known as Artin's constant (see Wrench's computation \cite{wrench} for more details). In 1935, Page \cite{page} improved Estermann's result by giving a bound for the order of the error term in (\ref{estermannformula}), using estimates for the error in the prime number theorem for arithmetic progressions. Mirsky \cite{mirsky} extended these results in 1949 to count representations of an integer as the sum of a prime and a $k$-free number, that is, a number which is not divisible by the $k$-th power of any prime. More recently, in 2005, Languasco \cite{languasco} treated the possibility of Siegel zeroes (see Davenport \cite{davenport} for some discussion on this) with more caution so as to provide better bounds on the error.

The objective of the present paper is to prove the following theorem which completes the result of Estermann.

\begin{thm} \label{main1}
Every integer greater than two is the sum of a prime and a square-free number.
\end{thm}

We prove this theorem by working in the same manner as Estermann, though we employ explicit estimates on the error term for the prime number theorem in arithmetic progressions. Specifically, if we let
$$\theta(x;q,a) = \sum_{\substack{p \leq x \\ p \equiv a (\text{mod } q)}} \log p$$
where the sum is over primes $p$, we require estimates of the form
\begin{equation} \label{error}
\bigg| \theta(x;q,a) - \frac{x}{\varphi(q)} \bigg| < \frac{\epsilon x}{\varphi(q)}
\end{equation}
where $\epsilon>0$ is sufficiently small and $x$ and $q$ are suitably ranged. Good estimates of this type are available due to Ramar\'{e} and Rumely \cite{ramarerumely}, but are only provided for finitely many values of $q$. It turns out, however, that this is sufficient, as the Brun--Titchmarsh theorem is enough for the remaining cases.

It should be noted that the best known asymptotic result in this area is that of Chen \cite{chen}, who proved that every sufficiently large even number is the sum of a prime and another number which is the product of at most two primes. Chen's result is, at present, the closest one seems to be able to get towards a proof of the Goldbach conjecture, which famously asserts that every even integer greater than two can be written as the sum of two primes. It would be interesting to see if one could modify the explicit proof of this paper to consider, instead of square-free numbers, numbers which are products of at most $m$ primes (where $m$ is fixed).

\section{The Proof}

\subsection{The Setup}

Let $n\geq10^{10}$ be a positive integer. We will prove Theorem 1 for this range before resorting to direct computation for the remaining cases. As convention would have it, we let $\mu: \mathbb{N} \rightarrow \{-1,0,1\}$ denote the M\"obius function, where $\mu(n)$ is zero if $n$ is not square-free; otherwise $\mu(n)=(-1)^{\omega(n)}$ where $\omega(n)$ denotes the number of distinct prime factors of $n$. As such, we have that $\mu(1)=1$. For a positive integer $n$, it can be shown that the sum
$$\mu_2 (n) = \sum_{a^2 | n} \mu(a)$$
is equal to $1$ if $n$ is square-free and zero otherwise. Thus, it follows that the expression
$$T(n):=\sum_{p \leq n} \mu_2(n-p)$$
counts the number of ways that $n$ may be expressed as the sum of a prime and a square-free number. We will employ logarithmic weights so as to use the known prime number estimates with more ease, and so we define
$$R(n) := \sum_{p \leq n} \mu_2(n-p) \log p.$$
We note that $n$ is the sum of a prime and a square-free number if and only if $R(n) >0$. As such, the majority of this paper is dedicated to finding a lower bound for $R(n)$. The expression for $R(n)$ can be rearranged so as to involve weighted sums over the prime numbers in arithmetic progressions:
\begin{eqnarray*}
R(n) & = & \sum_{p \leq n} \log p \sum_{a^2 | (n-p)} \mu(a) \\
& = & \sum_{a \leq n^{1/2}} \mu(a) \sum_{\substack{p \leq n \\ a^2 | (n-p)}} \log p \\
& = & \sum_{a \leq n^{1/2}} \mu(a) \theta(n; a^2, n).
\end{eqnarray*}
We will split the range of this sum into three parts, for we shall use a different technique to bound each of them. Note first that if $(a,n)>1$, then we have trivially that $\theta(n;a^2,n) \leq \log n$. Thus, we may write
\begin{equation} \label{bigdaddy}
R(n) > \Sigma_1 + \Sigma_2 + \Sigma_3 -n^{1/2} \log n
\end{equation}
where
\begin{eqnarray*}
\Sigma_1 & = & \sum_{\substack{a \leq 13 \\ (a,n)=1}} \mu(a) \theta(n; a^2, n), \\
\Sigma_2 & = & \sum_{\substack{13 < a \leq n^A \\ (a,n)=1}} \mu(a) \theta(n; a^2, n), \\
\Sigma_3 & = & \sum_{\substack{n^A < a \leq n^{1/2} \\ (a,n)=1}} \mu(a) \theta(n; a^2, n),
\end{eqnarray*}
and $A \in (0,1/2)$ is to be chosen later to optimise our result. We will use the estimates of Ramar\'{e} and Rumely \cite{ramarerumely} to bound $\Sigma_1$; this is the reason for the specific range of $a$ in this sum. We will then use the Brun--Titchmarsh theorem to bound $\Sigma_2$. Finally, $\Sigma_3$ will be bounded using trivial estimates.

\subsection{Arithmetic estimates}

We first consider the sum
$$\Sigma_1 = \sum_{ \substack{a \leq 13 \\ (a,n)=1}} \mu(a) \theta(n; a^2, n).$$
Theorem 1 of Ramar\'{e} and Rumely \cite{ramarerumely} provides estimates of the form
\begin{equation}
\bigg| \theta(n;a^2,n) - \frac{n}{\varphi(a^2)} \bigg| < \frac{\epsilon_a n}{\varphi(a^2)}.
\end{equation}
In particular, by looking through the square moduli in Table 1 of their paper, we have values of $\epsilon_a$ for all $1 \leq a \leq 13$ which are valid for all $n\geq 10^{10}$. We therefore have trivially that
\begin{eqnarray} \label{big1}
\Sigma_1 & > & n \sum_{ \substack{a \leq 13 \\ (a,n)=1}} \bigg( \frac{\mu(a)}{\varphi(a^2)} - \epsilon_a \frac{\mu^2(a)}{\varphi(a^2)} \bigg) \nonumber \\
& > &  n \bigg( \sum_{(a,n)=1} \frac{\mu(a)}{\varphi(a^2)} - \sum_{\substack{a>13 \\ (a,n)=1}} \frac{\mu(a)}{\varphi(a^2)}- \sum_{a \leq 13} \frac{ \epsilon_a \mu^2(a)}{\varphi(a^2)} \bigg).
\end{eqnarray}
We wish to estimate the three sums in the above parentheses. We denote the leftmost sum by $S_{n}$, and note that we can bound it below by Artin's constant (\ref{artin}) \textit{viz.}
\begin{eqnarray*}
S_{n} := \sum_{(a,n)=1} \frac{\mu(a)}{\varphi(a^2)} & = & \prod_{p \nmid n} \bigg(1- \frac{1}{\varphi(p^2)} \bigg) \\
& = & \prod_{p \nmid n} \bigg(1- \frac{1}{p(p-1)} \bigg)\\
& \geq & \prod_{p} \bigg(1 - \frac{1}{p(p-1)}\bigg) = c.
\end{eqnarray*}
Wrench \cite{wrench} has computed this constant to high accuracy; it will suffice for the purpose of Theorem \ref{main1} to note that $S_n \geq c>0.373$.

We will, for the moment, neglect the middle sum in (\ref{big1}), for it shall be considered jointly with a term in the estimation of $\Sigma_2$. Thus, in our estimation of $\Sigma_1$, it remains to manually compute the upper bound for the rightmost sum. This is a straightforward task which is done in reference to Table 1 of Ramare and Rumely's paper \cite{ramarerumely}. We get that
$$ \sum_{a \leq 13} \frac{\epsilon_a \mu^2(a)}{\varphi(a^2)} < 0.005.$$

We now bring $\Sigma_2$ into the fray; the explicit Brun--Titchmarsh theorem (see Montgomery and Vaughan \cite{montgomeryvaughan}) provides the bound
$$\theta(n; a^2,n) < 2 \bigg(\frac{\log n}{\log(n/a^2)} \bigg) \frac{n}{\varphi(a^2)}.$$
Clearly, in the range $13 < a \leq n^{A}$ we may bound
$$\frac{\log n}{\log(n/a^2)} \leq \frac{1}{1-2A}$$
and so we have the estimate that
$$\theta(n; a^2,n) = \frac{n}{\varphi(a^2)} + \epsilon \bigg(\frac{1+2A}{1-2A} \bigg)\frac{n}{\varphi(a^2)}$$
where $|\epsilon| < 1$. We may then bound $\Sigma_2$ from below by
$$\Sigma_2 > n \sum_{\substack{13 < a \leq n^A \\ (a,n) = 1}} \frac{\mu(a)}{\varphi(a^2)} - n \bigg(\frac{1+2A}{1-2A}\bigg) \sum_{\substack{13 < a \leq n^A \\ (a,n)=1}} \frac{ \mu^2(a)}{\varphi(a^2)}.  $$
We can then add this to our estimate for $\Sigma_1$ to get
\begin{eqnarray} \label{sigma1and2}
\Sigma_1 + \Sigma_2 & > & n \bigg( S_{n} - 0.005 - \sum_{\substack{a> n^A \\ (a,n)=1}} \frac{\mu(a)}{\varphi(a^2)} - \bigg(\frac{1+2A}{1-2A}\bigg) \sum_{\substack{13 < a \leq n^A \\ (a,n)=1}} \frac{ \mu^2(a)}{\varphi(a^2)} \bigg) \nonumber \\
& > & n \bigg(S_n -0.005 - \bigg(\frac{1+2 A}{1- 2 A} \bigg) \sum_{a > 13} \frac{\mu^2 (a)}{\varphi(a^2)}\bigg).
\end{eqnarray}
We can estimate the sum in the above inequality by writing it as follows:
\begin{eqnarray*}
\sum_{a > 13} \frac{\mu^2 (a)}{\varphi(a^2)} =\sum_{a=1}^{\infty} \frac{\mu^2(a)}{\varphi(a^2)} - \sum_{a\leq 13} \frac{\mu^2(a)}{\varphi(a^2)}.
\end{eqnarray*}
The infinite sum is less than 1.95 (see Ramar\'{e} \cite{ramare} for example), and the finite sum can be computed by hand to see that the sum in (\ref{sigma1and2}) is bounded above by 0.086. Thus
\begin{equation} \label{sigma12}
\Sigma_1 + \Sigma_2 > n \bigg(S_n - 0.005 - \bigg(\frac{1+2A}{1-2A}\bigg)(0.086)\bigg).
\end{equation}

For $\Sigma_3$, we have trivially that
\begin{eqnarray} \label{sigma3bound}
|\Sigma_3| & < & \sum_{n^{A} < a \leq n^{1/2}} \theta(n;a^2,n) \nonumber  \\
& < & \sum_{n^{A} < a \leq n^{1/2}} \bigg(1+\frac{n}{a^2} \bigg) \log n \nonumber \\
& < & n^{1/2} \log n + n \log n \sum_{n^{A} < a \leq n^{1/2}} \frac{1}{a^2} \nonumber \\
& < & n^{1/2} \log n + n^{1-2A} \log n + n \log n \int_{n^{A}}^{n^{1/2}} t^{-2} dt \nonumber \\
& = & n^{1-2A} \log n + n^{1-A} \log n.
\end{eqnarray}

\subsection{A Lower Bound for $R(n)$}

We can now provide an explicit lower bound for
$$R(n) \geq \Sigma_1 + \Sigma_2 + \Sigma_3 -n^{1/2} \log n.$$
We combine our explicit estimates (\ref{sigma12}) and (\ref{sigma3bound}) and divide through by $n$ to get that
\begin{eqnarray*}
\frac{R(n)}{n} & > & S_{n}- 0.005-\bigg(\frac{1+2A}{1-2A}\bigg)(0.086) \\
& - &n^{-1/2} \log n - n^{-2A} \log n - n^{-A} \log n.
\end{eqnarray*}
For sufficiently small $A$ and large $n$, the right hand side will be positive. For any $n$, we have $S_n > 0.373$; it is a simple matter to choose $A=1/4$ and verify that the right hand side is positive for all $n \geq 10^{10}$. That is, Theorem \ref{main1} is true for all integers $n \geq 10^{10}$.

It so remains to prove this result for all integers in the range $3 \leq n <10^{10}$. If $n$ is even, we have the numerical verification by Oliviera e Silva, Herzog and Pardi \cite{silva} that all even integers up to $4 \cdot 10^{18}$ can be written as the sum of two primes. Thus, every even integer greater than two may be written as the sum of a prime and a square-free number.

Thus, we need to check that every odd integer $3 \leq n \leq 10^{10}$ can be written as the sum of a prime and a square-free number. For each $n$, we subtract a prime number $p$ and check that the result is squarefree. This is a straightforward computation; we ran this on \textsc{Mathematica} and it took just under 3 days on a 2.6GHz laptop. The computation was eased somewhat by subtracting primes which were close in size to $n$.

\subsection*{Acknowledgements}

The author wishes to thank Dr Timothy Trudgian for many helpful conversations regarding the present paper.

\clearpage

\bibliographystyle{plain}


The last build for 1.8.9 that I can find is here.
Do note that this will be massively outdated. We're currently working on support for 1.10.
Closing this topic now as it's 3 weeks old and seems to have been resolved.


My question it's about the beta bios update that Asrock launch on december 15th to let OC on non-K Skylake cpu's.
Recently on january 27th thet have launch an oficcial bios update that correct a bug on Skylake cpu's.
There is the option to OC non-K Skylake cpu's on this last stable bios of Z170's motherboards?.
Has Asrock implement the OC non-K skylake cpu's on all the stable bios launched after december 15th or the only bios that with this capablility is the december 15th beta bios?.
Thanks, peroni for the confirmation.
One more question for you, because i see you have simimilar configuration than me (i5, SSD 950 Pro).
The OC of the BLK, will affect the PCI-e lines of the SSD?. I suposed not.
Bus speeds (PCIe lanes etc) are not affected by the BCLK no. This is why BCLK overclocking is possible on Skylake where it was not, at least anywhere near as much, on Haswell and going back to Sandybridge.
at least on the Z170M Pro4S, SKYOC does not work really good with the beta bios, nor the 2.40.
you can set a vid offset to a non k cpu which will only work if you leave bclk @ auto.
when you increase bclk you are able to set any voltage you want but it will not affect the vid, so you are very limited to the oc by the default vid..Yes, you can leave offset @auto -> 1.05v, or +400 -> 1.05v.
i already mailed to the support weeks ago but no answer.
I am having exactly the same problem with my Z170M Pro4S, on both L2.23 and L2.40, firstly there is no voltage control, only voltage offset options, secondly, if I change my BCLK to anything, the voltage will always be stick at auto (1.088v).
Should I refund this board and go for a Gigabyte or Asus which have similar price?
I just spent a few hours figuring out that I could only increase voltage offset effectively if I leave BCLK at 100. wish I would have saved my time and read your posts. I'll add to the inquiries to ASrock of this and hopefully that can fix it for us, but with all the intel trying to close the door on the non-k oc, maybe Its safer to just get a different board that allows Vcore adjustments. any suggestions?
First, Sky OC is officially dead, if you haven't noticed all the UEFI updates flooding in for Z170 boards.
This is a news item at PC enthusiast websites, so you can find stories about it all over the Internet.
If you like Sky OC, don't drink the poison UEFI update. The poison is actually microcode 0x76. The rest is any UEFI options related to Sky OC. The latter are worthless anyway, once you have the former.
Given this development, there of course will NOT be any fixes for bugs related to Sky OC.
But doesn't anyone remember the limitations that were part of Sky OC? There used to be a list of them posted on ASRock's website, which is probably gone now for obvious reasons.
Regarding the VID and offset voltage UEFI setting, that behavior may be normal for a non-K processor. That is, the ability to override the VID with an offset. For a non-K processor at stock clock, what is the use of that?
Sky OC worked, but it was far from perfect. All the limitations that did NOT exist in the golden days of over clocking (before Sandy Bridge) that have been added since then were not washed away by Sky OC.
Sky OC tried to use a difference in Skylake processors that exists for the first time since Sandy Bridge. That is, the CPU BCLK is not shared with the PCIe lanes, DMI3 lanes, etc. So the CPU BCLK can be changed without affecting (and crashing) the other things that depend on a stable clock value.
To bad it is not that simple. Other changes along the way since Sandy Bridge, and some new to Skylake, have weird side affects when the CPU BCLK is changed. Like the integrated graphics no longer working, C States no longer functional, and... was it no CPU temperature or no VCore reading, I think the former. For me personally, some of those shortcomings made Sky OC much less attractive.
Another thing, VID and VCore are not the same thing. With Adaptive voltage, the actual VCore can be lower and higher than the VID.
Actually, I want someone to tell me what voltage option(s) are available besides Manual, with Skylake processors.
For example, what is the Auto setting equivalent to?
Is Adaptive still an option with Skylake?
We think we know these things, but do we?


Masterfully high-fired in Encinitas, CA this White Speckle terra cotta planter from Norden is how I'm planning to add some more deserty / costal greenery to my home this season. Norden's ceramics like this one are designed for repurposing and reusing and are a solid go-to for both indoor and outdoor use. Get set below.
Joanne Petit-Frère takes sculpture into new realms with her incredibly complex hair designs, which call upon influences as diverse as maths, nature, engineering, chemistry, garment construction, Old World architecture and Africa and the Americas. Her work was recently at the centre of a media controversy after the architectural braided crown she created for Solange was airbrushed out of the Evening Standard magazine's cover story. The publication apologised after the singer posted the image on social media and referenced her own song, Don't Touch My Hair.


There is lack of data about the correlation between hemostatic markers and the clinical and biological risk factors (RFs) for venous thromboembolism (VTE) in medical inpatients without suspicion of acute VTE.
To evaluate the coagulation activation status in patients with current known RFs for VTE, the authors measured 2 markers of hypercoagulability, thrombin antithrombin (TAT) complexes and D-dimers, at day 1 in 165 patients hospitalized in internal medicine wards without suspected acute VTE. All known RFs for VTE were systematically assessed at admission and classified in a chronological way as permanent or transient.
Surprisingly, TAT values followed a multimodal distribution. D-dimers showed a normal distribution after a logarithmic transformation (P = .34, Shapiro—Wilk test). Interestingly, a significant progression in D-dimer levels was found according to the chronological classification of RFs. D-dimer variations on multivariate analysis (not applicable for TAT because of the multimodal distribution) correlated independently with a recent inability to walk and an increase in C reactive protein level more than 10 mg/L.
(a) this study is the first to describe the variations of hypercoagulability markers according to a systematic screening of RFs for VTE in inpatients without suspicion of acute VTE, (b) TAT appeared as a less relevant marker of hypercoagulability than D-dimers in internal medicine inpatients, (d) the chronological classification of RFs identified clearly groups at risk for the prethrombotic state, and (d) an increased hypercoagulability state was demonstrated in patients with an association between a recent immobility and increased inflammatory markers.


The American Lighthouse Council (ALC) is a preservation practitioners' organization, and does not answer the general public's lighthouse history, heritage and tourism questions. Those matters are handled admirably by other lighthouse organizations and sites, and the ALC purposely avoids duplicating their efforts.
To contact the ALC, please send an email to either Mike Vogel at (bufkeeper@gmail.com) or Jeff Gales (jeff@uslhs.org). For those seeking expertise or comments from the lighthouse community, we may post a blog query or refer your query to one of our committees of experts.


text:
Puerta de Hierro puede referirse a:
 Puertas de Hierro, un desfiladero en el río Danubio.
 Puerta de Hierro (Madrid), puerta monumental situada al noroeste de Madrid.
 Nudo de Puerta de Hierro, zona de la M-30 situada en torno al monumento.
 Ciudad Puerta de Hierro, barrio residencial cercano al monumento.
 Real Club Puerta de Hierro, club social y complejo deportivo cercano al monumento.
 Hospital Universitario Puerta de Hierro Majadahonda, inicialmente situado en Ciudad Puerta de Hierro y posteriormente trasladado a Majadahonda.
 Instituto de Investigación Biomédica Puerta de Hierro Majadahonda, órgano gestor de la investigación biomédica que se realiza en el Hospital Universitario Puerta de Hierro Majadahonda.
 Puerta de Hierro (Guadalajara), una colonia en la ciudad mexicana de Zapopan.
 Torre Aura Puerta de Hierro, edificio de ese distrito.
 Torre Centro Médico Puerta de Hierro, edificio de ese distrito.
 Puerta de Hierro, localidad argentina en el partido de San Miguel (provincia de Buenos Aires).
 Puerta de Hierro, el exilio de Perón (2012), película argentina.


text:
//Identity Theft
Episodes of identity fraud soar to record levels in latest study conducted by Cifas
Cifas, the UK's leading fraud prevention service, has released new figures showing that identity fraud has continued to rise at unprecedented levels during the first six months of 2017. A record 89,000 identity frauds were recorded, which is up 5% from last year. Representing...
Equifax Survey: "Almost one third of Brits risk ID theft by sharing too much information online"
An online survey conducted by YouGov in conjunction with Equifax reveals a significant portion of social media users risk identity theft by giving fraudsters easy access to personal information. The survey finds that almost one third (30%) of British adults with a social media...
80% of shoppers demand transparency from online retailers after data breach incident
Online shoppers want retailers to be transparent and honest if they've suffered a security breach. That's according to a new UK consumer survey commissioned by NTT Security, the global information security and risk management company. The research results, announced...
"Customers 'turning away' from breached organisations" reports Thales e-Security
Huge fines have been imposed on some organisations following a data breach, but what's the long-term impact of such an event? A study conducted by Thales e-Security has shown that the majority of people would reduce or eliminate their use of an organisation's products or...
The Inherent Dangers of Seduction
The swift pace of life today coupled with the overriding requirement in the business world to remain in constant contact might open us up to being targeted by those who would steal our identities, money or other highly valued possessions. Phillip Wood outlines why, on occasion,...
'Not With My Name' campaign targets growing threat of identity crime in the UK
Millions of people in the UK are failing to take basic steps like redirecting post or updating firewalls in order to protect their identities from criminals, a new survey has shown. Indeed, the survey results have been published just as the City of London Police and partner...
Cifas Fraudscape study shows 27% rise in identity fraud during first quarter of 2015
New data shows that identity fraud was the dominant fraud threat in the first quarter of 2015. 34,151 confirmed instances of identity fraud have been recorded by Cifas, the UK's Fraud Prevention Service, representing a 27% increase from the same period of the previous year...
CIFAS: "Protective Registration Service now available seven days a week"
CIFAS – the UK's fraud prevention organisation – has announced that a fraud prevention service designed to protect individuals from identity fraud will now operate at weekends as well as during the normal Monday-Friday working week. The CIFAS Protective Registration...

redpajama_set_name: RedPajamaCommonCrawl


text:
package trait;

import java.util.LinkedList;
import java.util.List;

import org.bukkit.ChatColor;
import org.bukkit.entity.EntityType;
import org.bukkit.event.Event;
import org.bukkit.event.entity.EntityDamageEvent;

import de.tobiyas.racesandclasses.eventprocessing.eventresolvage.EventWrapper;
import de.tobiyas.racesandclasses.traitcontainer.interfaces.TraitResults;
import de.tobiyas.racesandclasses.traitcontainer.interfaces.annotations.configuration.TraitConfigurationField;
import de.tobiyas.racesandclasses.traitcontainer.interfaces.annotations.configuration.TraitConfigurationNeeded;
import de.tobiyas.racesandclasses.traitcontainer.interfaces.annotations.configuration.TraitEventsUsed;
import de.tobiyas.racesandclasses.traitcontainer.interfaces.annotations.configuration.TraitInfos;
import de.tobiyas.racesandclasses.traitcontainer.interfaces.markerinterfaces.Trait;
import de.tobiyas.racesandclasses.traitcontainer.traits.passive.AbstractPassiveTrait;
import de.tobiyas.racesandclasses.util.bukkit.versioning.compatibility.CompatibilityModifier;
import de.tobiyas.racesandclasses.util.traitutil.TraitConfiguration;
import de.tobiyas.racesandclasses.util.traitutil.TraitConfigurationFailedException;

public class DamageReduceTrait extends AbstractPassiveTrait{

	@TraitEventsUsed(registerdClasses = {EntityDamageEvent.class})
	@Override
	public void generalInit(){
	}

	@Override
	public String getName() {
		return "DamageReduceTrait";
	}

	@Override
	protected String getPrettyConfigIntern() {
		return "damage reduce: " + operation + " " + value;
	}

	@TraitConfigurationNeeded( fields = {
			@TraitConfigurationField(fieldName = "operation", classToExpect = String.class),
			@TraitConfigurationField(fieldName = "value", classToExpect = Double.class)
		})
	@Override
	public void setConfiguration(TraitConfiguration configMap) throws TraitConfigurationFailedException {
		super.setConfiguration(configMap);

		operation = (String) configMap.get("operation");
		value = (Double) configMap.get("value");
	}

	@Override
	public TraitResults trigger(EventWrapper eventWrapper) {   Event event = eventWrapper.getEvent();
		if(!(event instanceof EntityDamageEvent)) return TraitResults.False();
		EntityDamageEvent Eevent = (EntityDamageEvent) event;

		if(Eevent.getEntityType() != EntityType.PLAYER) return TraitResults.False();

		double oldValue = CompatibilityModifier.EntityDamage.safeGetDamage(Eevent);
		double newValue = getNewValue(eventWrapper.getPlayer(), oldValue, "value");

		CompatibilityModifier.EntityDamage.safeSetDamage(newValue, Eevent);
		return TraitResults.True();
	}

	public static List<String> getHelpForTrait(){
		List<String> helpList = new LinkedList<String>();
		helpList.add(ChatColor.YELLOW + "Your taken damage will be decreased or divided by an value.");
		return helpList;
	}

	@Override
	public boolean isBetterThan(Trait trait) {
		if(!(trait instanceof DamageReduceTrait)) return false;
		DamageReduceTrait otherTrait = (DamageReduceTrait) trait;

		return value >= otherTrait.value;
	}

	@TraitInfos(category="passive", traitName="DamageReduceTrait", visible=true)
	@Override
	public void importTrait() {
	}

	@Override
	public boolean canBeTriggered(EventWrapper wrapper) {
		Event event = wrapper.getEvent();
		if(!(event instanceof EntityDamageEvent)) return false;
		EntityDamageEvent Eevent = (EntityDamageEvent) event;

		if(Eevent.getEntityType() != EntityType.PLAYER) return false;

		return true;

	}
}

redpajama_set_name: RedPajamaGithub


Here is a list of helpful court documents which you may fill out and print from your personal computer. For more information regarding any of these documents please contact the court directly.
You are required to provide the total number of copies of a document or form for use by the court, the parties, and any other entity that is required to receive the form. See the upper-right hand corner of each form to determine the mandatory number of copies. It is recommended that when completing a form online, you print the number of copies you will need for filing with the court and serving on the parties. Otherwise, you will have to photocopy the proper number of copies before filing the form with the court. If you do not provide the court with the accurate number of copies, the court might reject the form for nonconformance under the authority of Michigan Court Rule 8.119(C). Unless specifically required by court rule or statute, the court is not responsible for making copies of forms for you.
This set of forms is used in claiming lawful possession to personal property possessed by another individual. The forms are filed in the district court when the personal property has a value of $25,000 or less. The forms are filed in the circuit court when the personal property has a value of more than $25,000.
This set of forms is used in small claims division of district court. The forms must be filed in the district court.
This set of forms is for use in garnishment to collect a money judgment. The forms must be filed in the circuit court if the judgment is from the circuit court or district court if the judgment is from the district court.
This set of forms is for use in landlord-tenant and land contract matters. The forms must be filed in the district court.
This set of forms is used to obtain, modify, or terminate a personal protection order. The forms must be filed in the family division of the circuit court.


Roads in New Zealand are different to the rest of the world.
For a safe and enjoyable driving experience while on vacation, make sure you're familiar with the important New Zealand road rules below.
Do not drink and drive. Driving under the influence of alcohol or drugs is a crime in New Zealand.
For more comprehensive information on New Zealand's road rules, read the full New Zealand Transport Authority Booklet for Overseas Drivers.


text:
SanDiegoVille Street Artist Profile - JT Estrela - Sandcastle Artist of Ocean Front Walk in Pacific Beach
By Ryan Lewis | SanDiegoVille Art Director and Contributor
Against a backdrop of rolling waves and San Diego sun on the peak mainline of the PB boardwalk, a low-key 'dude' in his 30s scratches away at a grand, nearly 1-ton sand-packed sculpture of an ornate conch shell. A ball cap, sunglasses, and dark tan are the uniform of a man spending full days on the outskirts of prime beach real estate, lugging carts filled with buckets of sand and seawater up from the surf and sculpting large and very temporary modern artworks.
JT Estrela was born in North Dakota, but mainly grew up near the atlantic beaches of Jacksonville, FL. Artistic endeavors were only musical – playing the violin as a child – until his mid-twenties when on a beach trip with friends furnished a creative spark. As beach days go, full of random acts of connecting with the beloved environment, JT began mounding up sand, crafting abstract miniature architecture from the generously-formable, special brand of earth. Besides his curious hands, only a butter knife (brought for snacks) was used for more intricate details.
JT doing his thing
In JT's humble reflection, his first attempts were "pieces of crap"(no doubt in unavoidable comparison to his more recent, very accurate depictions of everything from nature to comic strip characters), but a book of photos from his start-up days shows him working on castles that are indeed impressive, especially in their geometry, as he used no molds but simply hand-form and 'chisel'. He had yet to learn the nuances of the science he has now cultivated - small things, such as keeping water on hand to add for solidarity. JT says it was really just luck that his structure began to come together, as it was purely intuitive that first time. "All I did was just make a big pile like this [he quickly gets down on his knees near his station and, forearm-deep, begins mounding sand]. I guess I got lucky because it was moist enough and kinda held its shape." And, simultaneously, an act of presumably-fleeting amusement began to form itself into something significant as well. "Just because I thought it was so much fun."
After grad school, where JT received his masters degree in education (atop his bachelor's in mathematics), he jumped coasts to San Diego's Ocean Beach, where he stayed for a 5-year stretch, contributing his newfound hobby to the renown loose environment. He recounts how things really clicked:
"I was a block and half from the beach, so I would go to the beach a lot. Plus, I was single at the time, and when you're building sand castles, ladies would always come by and be like, 'hey, whatcha doin'?" All of a sudden, I'm the interesting guy, ya know? They came to talk to me! So, yea, it was fun, and motivational to realize it was making an impression."
And now, JT will mark his one-year anniversary of his workshop-display at Thomas Ave. and Ocean Boulevard in happening Pacific Beach. JT emphasizes "I have surely refined a lot of my techniques. It took me months [since being here] to figure out that I can just cover [the statues] up. I can just wrap 'em up and leave it there and then, I have a much better chance to have them appear for while."
JT struggled a bit at first, trying to make new pieces every day, and suffered in exhibit and donations since a large portion of the day was devoted to build-up, with recognizable art not forming until later in the afternoon. Leaving them unprotected when he left 'the office' also exposed the structures to become more fleeting than he could keep up with.
"Every night they would get wrecked. Every night, by somebody." An admirability surfaces as JT displays positivity and perseverance in his moderate expression of a discouraging blight in action; one that, paradoxically, contrasts the creativity and service he embodies. The late-night, malicious destruction of his sculptures is something JT has endured (and faithfully pressed on from) countless times over since stationing in PB, but he says it's only been about 4 times that vandals have made efforts against his art since learning to cover and protect them when he's gone. His pleasant, un-wavered confidence in and devotion to his fellow man is illustrated by his willingness to still at times leave his work un-veiled, such as when he has fully completed a piece or needs a few days off or out of town.
"The only thing that is gonna work, is neighborhood-watch style. Like, if ya see anybody touching this stuff that isn't me, just tell them to knock it off if you feel like it. But I would never want anyone to get into a fight."
Additional aspects that contribute to the charm of JT's dynamic exhibit, besides his candid manner, include a signboard for displaying messages to passerby while he's immersed in sculpting, and a photo album for showing his development and the scope of his work. Particularly attractive are JT's trademark donation receptacles, which have amounted to legitimate sand sculptures themselves, complete with hollow interior, hole atop for receiving money, and impressive hand-etched typography done with only eye-measurement (no straight-edge or ruler). Although donations are of definite value to his time and energy-costly endeavors, JT is cool in his refrain from making the monetary support feel obligatory.
And to help flourish his art, he engages the simultaneous challenges and inspirations inherent in competition. For the past 5 years, JT has varied from his typical solitary practice and began overseeing a team in the US Open Imperial Beach Sandcastle Competition. Though the Imperial Beach competition has been scrapped, he will engage fellow sculptors again this August (Labor Day weekend) in The Sandcastle Sculpting Challenge, an invite-only competition at the B Street Pier in Downtown San Diego.
While the rewards of granting receptive San Diego locals and visitors with a unique brand of art really encourages JT, he also recognizes the importance of maintaining the fairness, reciprocity, and sustainability inherent in gaining donations for his open art. Yet JT accepts a possible sobering reality that his fun-in-the-sun creating earth-art in flux may be insufficient for a desirable income. And he swaps hats dramatically, pending to trade his bathing suit for a business suit in his current studies to become an actuary. When prompted about the role sand art plays for him, he enigmatically muses, "I kinda like, ya know, made a fuckin' lemonade stand… Life handed me lemons, I made a lemonade stand." Though consciously providing levity and understatement of his artistic service, a childlike twinkle of pride shows through.
There's an inkling that a main reason behind this satisfaction is the ultimate location of his 'stand'. Regardless of adequate financial compensation, JT's contentedness with his place of business is full-on:
"Well not only is this my city, my home, and I love this place; the weather is fantastic, the sunshine… look at this place" as he pans around, smile glaring. "There are a lot of beautiful people passing by all the time. The people-watching is just fantastic out here; like, ya can't beat it. There's a lot of traffic and tourists that come through here. Tourists come to San Diego, and it's the tourists that are looking to have experiences, and, like, see some sandcastles!"
And JT shows clear excitement as he relays the reassuring interactions experiences each day, and even though portions of his audience who tip are small, he acknowledges that, just as with the vandalism, it's a reality whose remedy is likely beyond the scope of any practical methods he can take at this point:
"If you just sit here and listen to people as they walk by, every third person is like 'cool!', 'wow', or 'oh my God', 'look at that', 'that's so awesome' 'check it out!', 'wait, stop.. go back!' Ya know? They appreciate it. They don't always donate for it; in fact it's probably more like 5 to 1 (if that).. like 5 people taking a picture to every 1 donating. But if you're gonna do this in public, it's gonna be mainly free."
What airs very refreshing and virtuous about JT is his courageous acceptance of stark realities, renunciation of attachment to desired outcomes, and recognition of and immersion into his role for 'the now'. He is of full realization that he may have to eventually transition from his adult sandbox to a sobering position behind desk and calculator, and he seemingly does, to a degree, lament the prospective departure, yet it remains perfectly pleasing the way in which he continues to carry out his craft with tenacity, deft, and content.
Finally, to cater to our SanDiegoVille's foodie followers, JT mentioned his noteworthy local eats:
"People ask me 'where's a good place to get something to eat?' All the time, whenever someone asks me this, I always have to take the opportunity to mention that Joe's Crab Shack, as 'corporate' or 'chain' as they are, the managers there are super-freakin' cool, and they've given me storage to use in their garage for free. They let me store all my stuff: my wagon, my equipment. They let me store it there, just because they're cool. They could have easily said 'no', just to be done with it and not have to have any kind of pain in the ass, but they didn't. They're like, 'Yea, we got space. We can clear this out, and…' The management at Joe's is really down-to-earth; no 'corporate'-mentality. So props to Joe's for that."
"Papa Luna's is one of my favorite little places in PB. Empanadas! I like Papa Luna's. It's unique; like the only empanada joint around here, and they're always changing up their menu. It's gonna be about 9 dollars for three empanadas, which is the magic number; four is too many, two isn't quite enough. It's on Garnet, across from Play It Again Sports. What do I always get? The 'Sunny Goat'.. it has goat cheese, Italian sausage, and sun-dried tomatoes. Yea, I like Papa Luna's. I do. And it's not a hugely well-known place. I'm sure none of the tourists have ever heard of it, but it's a good little shop."
Be sure to check out JT's sand art at the end of Thomas Ave. on Ocean Front Walk, and feel free to reach out via email or in person for observational lessons in sand sculpting. For more information and photos, follow his San Diego Sand Castles Facebook page and visit JT's website at sandiegosand.com.


We get asked this question about Mentawai Surf Trip in the TPW office quite a bit and we thought who better to give you the answer than Toasty, The Perfect Waves resident surf guide at the Aloita Resort & Spa in the Mentawai.
So over to you mate, can you give us the low down on your boards and what you would suggest as the perfect travelling quiver and would you suggest travelling with two boards?
My boards are custom shaped by Mitchel Beck – Itchy Shapes. His a local lad and a mate of mine from where I grew up surfing at Long Reef Beach on Sydney's northern beaches and knows what I need from a shaper and surfers point of view to get the best board for particular waves under my smelly feet.
Perfect two board quiver: realistically you should bring 3 boards to the ments.
Bring your favourite short board for the easy fun days under 5ft. Then bring a board 2 inches longer than your short board for the medium days with a good strong glass job.
Lastly, if you can get your hands on a board anything around the 7ft mark depending on your height and weight with a bit more foam in it to get you over the line on the bigger days and it also makes paddling into these big beasts a lot easier!
I personally travel with my 3 favourite boards on quick two week trips . 2 short boards and one big boy, I'd take more but the airlines peg you down to 30kgs baggage allowance, so once your clothes go in for board padding in the board bag, you're just about on the limit.
Join Toasty at the Aloita Resort on some of these beauties and enjoy an ice cold beer with him afterwards!
My favourite board is my old sunburnt brown 5'8 itchy shapes pin tail. I haven't changed the wax in 4 years; she's been around the globe a fair few times, has nice deep foot wells in the deck and has never let me down. It's not so much about how a board looks and fancy paint jobs, it's all about how it performs under your feet!
Toasty in the Ments in ALL PICTURES.


Credit card (Eurocard, Master Card, Visa): please indicate the number of your credit card and its validity on the booking Fax or per phone.
Of course if you arrive before your Bungalow is ready, you can already start to enjoy the other service of our Camping. If you arrive after 6 pm, we kindly ask you to give us notice in advance (phone 0039 O473 667242).
The travel insurance is valid form the moment of booking to the date of arrival.
How do I take the insurance?
IMPORTANT: please indicate in your booking confirmation or in the confirmation form if you want to take out the insurance.
receipt of an unexpectet judical summons.
* In the event of sickness/accident please have a detailed medical certificate made out by the treating doctor.
before the policy is taken out (in the case of trip cancellation) or before the start of the trip (in the case of trip interruption) (except for check up examinations).
The contractual basis are the EUROPÄISCHE travel insurance conditions (Hotel Industry) 2012 (ERV-RVB Hotel Industry 2015) Any discrepancies or differences created in the translation are not binding and have no legal effect for compliance or enforcement purposes.
- between 45 days before arrival the price for 1 overnight.
- between 30 days before arrival 20% total price for the booked period.
- between 15 days before arrival 40% total price for the booked period.
- between 7 days before arrival 60% total price for the booked period.
- between 1 days before arrival or no show 70% total price for the booked period.
Do you have to leave early? If due to the short notice we cannot let the apartment/suite to other guests, we have to invoice the total amount of the booked period. We therefore suggest you take out a further insurance for early departures.


Today's favourite colours are crimson, vermilion and scarlet red. According to Wikipedia, scarlet is closer to red than vermilion that has a slightly more orange flavour. Crimson has a tiny bit of blue mixed in. These are my three top reds at the moment. Bright, cool pink gets the fourth place!


text:
Former East German secret police captain says NSA spying 'a dream come true'
A former agent of the Stasi, the much-feared East German communist secret police, has said that the recently revealed NSA spying program would have been his agency's "dream come true" because it has collected "so much information, on so many people." Wolfgang Schmidt, 78, said in an interview with McClatchy newspapers that it is "the height of naivete" to think that the information will never be used against U.S. citizens. (more…)
Thursday, Jun 27th, 2013 at 10:40 pm


Ms. Ladha says the MBA has filled a gap in her knowledge, giving her skills in strategic thinking.
This story is the 14th in a series that features students and graduates who are using their business degrees in non-traditional fields.
Shereen Ladha was working in an advertising and marketing agency in Toronto a couple of years ago while balancing a blossoming side career producing and dancing in Bollywood-inspired videos that she posts on YouTube.
Justin Bieber's song Sorry had rocketed to No. 1 on the charts at the time, and Ms. Ladha had an idea to infuse some of her Indian culture into a remix of the song and make a dance video of it. So she booked a studio and a crew of dancers, but then a deadline came up at work, demanding her attention. She had to scramble to get the work done, then rush to the studio an hour away and roll the cameras.
"That was definitely a point for me where I was wondering if I could actually do this," the 30-year-old Toronto-based dancer, choreographer and instructor says.
The video not only got finished but it was also picked up by media outlets around the world, including BuzzFeed, Huffington Post and CTV News. The viral video now has almost one million views and it's not even the most-viewed video on her dancewithSL YouTube channel.
This sort of balancing act has become business as usual for Ms. Ladha. Through experience and education, she has figured out how to excel in both the artistic and corporate worlds.
The most recent addition to her education is an MBA from York University's Schulich School of Business in Toronto. The degree and her specialization in marketing and strategy have not only given her dance career a business foundation but it has also helped her land a new office job – she's now a senior strategist with McCann Canada in Toronto, a role she started in January.
While doing her undergrad in business at McGill University in Montreal, she kept her dance life and her school life separate, thinking people would find the mix unprofessional or confusing.
"Through my MBA, I decided that this was the thing that made me unique and it was proof I could bring a creative aspect to strategy and consulting – the thing I do now," she says.
"It started getting woven into my daily life and daily conversations I would have with people. All my social media accounts were public, so if they ever looked me up or were friends with me, they'd know about it. There was such a positive response."
Ms. Ladha was a participant on the TV program Canada's Got Talent in 2012 as part of a dance troupe while working as a market analyst at Nielsen Co. in Toronto. She began her MBA in 2013.
in 2012 as part of a dance troupe while working as a market analyst at Nielsen Co. in Toronto. She began her MBA in 2013.
She says there were two key classes she took while at Schulich that have been beneficial to her career: one on social media and another on customer experience design.
The first course taught her how to use social media to tell a "story" to an audience rather than just for person-to-person communication.
And without the design course she may not be where she is today, she says. One class focused on personal branding, and one of her assignments was to design her own website.
"If it hadn't been for that one class I wouldn't have ever reconciled the two worlds that exist for me: the world of business and strategy and consulting, and my world of dance. If I wasn't forced to sit there and see this blank website, see who I am [and] put it on a page … I don't think I'd be able to find the balance between the two."
Taking her MBA, she was able to apply learning to real-life situations and understand the theories better.
"I always knew I wanted to do a masters, and I think the MBA would always help me get that strategic thinking, and fill that gap I was missing to be able to be in a purely strategic role," she says.
Her art isn't limited solely to YouTube. She has appeared in Hollywood and Bollywood films, toured with Bollywood personalities, and has choreographed and performed in spectacles such as the 2015 Pan American Games opening ceremony in Toronto. Her latest venture is a cross-Canada dance tour, for which she has choreographed the routines and dances as well. She books the shows on weekends so she can tour and work at the same time.
The success of the Sorry remix, she says, has given her a more robust platform to have more people understand her as a person and artist.
"To hear news outlets all over the world talk about this video taking the world by storm and it bringing Bollywood to all these Canadian news outlets, it felt like I was accomplishing my mission – which was to showcase my art to the world, but also to teach people about my culture, which is what my art is rooted in," she says. "That's what I felt really good about."


text:
Q: how do I combine two or more variables in laravel Here is an example
Variable 1:
$encodedtoday = MemberProfile::whereDate('created_at', '=', $today )
->where('encoded_by', 'Mark')->count();

Variable 2:
$encodedtoday = MemberProfile::whereDate('created_at', '=', $today )
->where('encoded_by', 'Michael')->count();

Variable 3:
$encodedtoday = MemberProfile::whereDate('created_at', '=', $today )
->where('encoded_by', 'John')->count();

I know this can be done in array or something. Please show me

A: Try like this:
$encodedtoday = MemberProfile::whereDate('created_at', '=', $today )
->whereIn('encoded_by', ['Mark','Michael','John'])->count();

Hope this helps

A: You can create a array for encoded by names and then pass to whereIn condition as follow:
$encoded_by = ['Mark','Michael','John'];
$encodedtoday = MemberProfile::whereDate('created_at', '=', $today)
->whereIn('encoded_by', $encoded_by)->count();
return $encodedtoday;

A: You can define $encodedtoday = 0;
then keep adding count for all like this:
$encodedtoday += MemberProfile::whereDate('created_at', '=', $today )
->where('encoded_by', 'Mark')->count();

$encodedtoday += MemberProfile::whereDate('created_at', '=', $today )
->where('encoded_by', 'Michael')->count();

$encodedtoday += MemberProfile::whereDate('created_at', '=', $today )
->where('encoded_by', 'John')->count();

So here, $encodedtoday will have final count.


text:
Champions List
Boxing Home
Jimmy Kelly aiming to join Manchester's world champions
By Nathan Middleton & Liam Bradford
From the section Boxing
http://www.bbc.com/sport/boxing/35106561
Jimmy Kelly (centre) hopes to add his name to the current Manchester belt holders
For a city associated with football and its music scene, Manchester is going through an incredible period of success in the world of boxing.
At the moment there are four world champions from Greater Manchester in Tyson Fury, Scott Quigg, Anthony Crolla and Terry Flanagan.
That number could rise to five this weekend if Wythenshawe's Jimmy Kelly can beat Liam Smith to take the WBO light-middleweight title.
"They're all fantastic fighters and I would be proud to add my name to that list," said Kelly.
The 23-year-old beat Martin Fidel Rios in his last outing to take the WBO intercontinental title but is seen as the underdog against Liverpool's Smith at the Manchester Arena on Saturday.
Jimmy Kelly (centre) with Sale Sharks players Will Addison, Tommy Taylor, Danny Cipriani and Magnus Lund
"Everyone keeps saying 'was I surprised to get the fight?' But I wasn't surprised at at all and I'm going to take his title," he told BBC Radio Manchester.
"It doesn't matter if people have heard of me or not, I've been around for a long time I've just not been in the public eye.
"I'm a fantastic fighter, I'm world rated - I'm number seven in the world so it speaks for itself.
"I've just gone about my business. I'm not to bothered about slagging this person off or trying to get publicity, I've just let my fighting do my talking."
England's boxing capital?
After Ricky Hatton retired in 2009, Manchester struggled to find not only a new fighter to call their own but also big fights to get excited about.
The likes of Mike Tyson and Joe Calzaghe fought at the Manchester Arena in the past and Kelly's dad took him to watch his idols.
"Lets have it right, Ricky Hatton wasn't supposed to win that fight against Kostya Tszyu and neither was Joe Calzaghe when he faced Joe Lacy, and I'm just going to add my name to the underdog," he said.
Kelly is trained by former British and Inter-Continental middleweight champion Ensley Bingham at Moss Side boxing club, also known as Champs Camp, and is unbeaten in his 14 fights so far with seven knockouts.
He has been around boxing since the age of four and is a four-time national junior champion, so why does he think Manchester is thriving when it comes to boxing?
"There are a lot of tough housing estates around that build that inner toughness into kids," he stated.
"I'm from Wythenshawe which is a tough estate and I think you're just bred differently from estates like that.
"We've had something to channel our energy into like boxing and we've just put that mental toughness and grittiness into a sport, and we've just succeeded.
"Success breeds success, it started off with one boxer being a world champion and it's just gone on and on.
"I look at Tyson Fury, who I've known since I was a kid, and keep saying 'I used to train with him when I was young before he even had an amateur fight,' so if he can do it, I can do it."
The Mancunian against the Scouser
Liam Smith (left) and Jimmy Kelly show off their football support before their fight
As with the build-up to most fights, the digs began at the press conferences with Smith saying the fight was 'just wages for Christmas' for him, accusing Kelly of not having the ability to fight him.
Merseysider Smith, 27, who has three brothers that are all professional boxers, is trained in Manchester by Joe Gallagher - the man who has led Scott Quigg and Anthony Crolla to world titles.
"It's sort of like a footballer being a boxer," said Kelly. "A footballer wants to play for United, they want to play at Old Trafford and it's just the same with boxing.
"You go and watch a local fighter doing well who has come from similar background to yourself and you think 'what would it be like to have that sort of atmosphere and that sort of opportunity?'
"You see people before you do it and it just gives you the confidence and I'm massively confident I'm going to be world champion."
British Boxing Board of Control
Read more on British Boxing Board of Control
Boxing England
Read more on Boxing England
Boxing Scotland
Read more on Boxing Scotland
Boxing Ireland
Read more on Boxing Ireland
Boxing Wales
Read more on Boxing Wales
Chelsea discuss Mourinho future
Read more on Jose Mourinho: Chelsea board discuss manager's future
Henry joins BBC team for Euro 2016
Read more on Euro 2016: Thierry Henry joins BBC team in France
Murray retains Mauresmo as coach
From the section Tennis
Read more on Andy Murray: Scot retains Amelie Mauresmo as coach for 2016
How to get into boxing
Read more on Get Inspired: How to get into boxing


text:
Hisense Brings Roku TV Platform To The UK
Roku is planning an assault on Europe starting with the U.K. and it's teaming up with Hisense to do it.
Hisense is already a big partner of Roku's, one of a dozen or so manufacturers that sell televisions in the U.S. running the Roku TV operating system. Now, on its 50th anniversary, Hisense will launch the first Roku TVs in the U.K. before the end of the year.
Roku is one of the biggest TV platforms in the U.S. but its presence in Europe is minuscule. But at IFA 2019, Roku's chief executive officer Anthony Wood said the company is aiming to expand all over the continent, with the U.K. the first market in its sights.
Hisense didn't reveal much about the Roku TVs it's planning, other than to say they'll all be 4K models in a range of sizes up to 65-inches. The company plans to announce further details closer to launch.
"We are pleased to bring the Roku TV licensing program to Europe and look forward to the first Hisense Roku TVs in market this year," Wood said in a press briefing at IFA.
For those unfamiliar with Roku, the platform enables access to a number of popular subscription services including Netflix, Amazon Prime Video and YouTube. It also has its very own, ad supported streaming service, called the Roku Channel.
Roku faces some tough competition in Europe though as it's going up against rivals including Google's Android TV, Apple's tvOS, Samsung's Tizen, and LG's WebOS.
It will also face competition from Amazon, which said at IFA last week that it's expanding its own FireTV platform into Europe, starting with Austria, Germany and the U.K.
Still, Roku is hoping to win over many more TV makers besides Hisense. At IFA, CEO Wood made the prediction that "purpose built operating systems" such as Roku's will likely come out on top, just as they did on smartphones and PCs.
"While consumers love Roku TV's simplicity and advanced features, TV manufacturers benefit from the low cost of manufacturing, a variety of technology options, and support from Roku," Wood said. "The ability to quickly bring to market a leading smart TV experience that is regularly updated by Roku and is packed with entertainment gives TV manufacturers an edge in the competitive TV business."


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Sports betting regulation
Voters in Maryland, Louisiana and South Dakota back sports betting
4th November 2020 | By Robin Harrison
Sports betting is coming to Louisiana, Maryland and South Dakota, after voters backed measures on yesterday's (November 3) election ballot to regulate the vertical.
In Louisiana, legal wagering garnered support from voters in 55 of the state's 64 parishes, according to preliminary results. This was facilitated by Senate Bill 130, authored by Senator Cameron Henry.
The measure was strongly supported by Louisiana Wins, a coalition of sports betting supporters that led the charge for a yes vote.
"The people of Louisiana have spoken," Louisiana Wins' Ryan Berni said. "Louisiana was missing out on tax revenue from not having legal sports wagering, and now we will be able to raise revenue to support our state's many needs.
"Our Louisiana Wins coalition brought together industry, business groups, and community leaders to educate voters and approve this ballot measure that will help fund priorities here in Louisiana," he said. "We look forward to working with the Louisiana Legislature as they develop a framework for sports wagering in the 2021 legislative session so that we can deliver on the mandate from voters and quickly bring that tax revenue home to Louisiana."
During the campaign, a study commissioned by the state Department of Economic Development estimated that Louisiana was missing out on as much as $330m in taxable revenue, after previous attempts to regulate betting came to nothing.
This memorably saw retiring Senator Danny Martiny filibuster a fantasy sports tax bill in the 2019 legislative session, after its sponsors would not incorporate real-money wagering into their document.
As Louisiana only permits amendments to tax rates or new taxes to be debated in non-fiscal (even numbered) years, it was unable to set duties and fees for the industry, which must now be debated in the 2021 legislative session.
In Maryland, 66.2% of votes were cast in favour of legal wagering, with high ranking officials including Governor Larry Hogan having declared their support for betting in the state.
As with Louisiana, the issue now returns to the legislature, which will be required to develop a framework for betting. Senator Craig Zucker, who drafted the measure that was ultimately placed on the ballot, had initially set out a full model for sports betting regulation, though this was removed from the final bill.
Zucker's Senate Bill 4 proposed $2.5m license fee, plus an annual $250,000 renewal charge, and 20% gross revenue tax. Online operators would also be permitted to operate wagering on behalf of a master licensee, for a fee of at least $5,000.
This was later amended to allow betting at three racetracks, Pimlico Race Course, Laurel Park and Maryland State Fairgrounds, as well as in the Washington Football Team's FedEx Field.
In South Dakota, meanwhile, Amendment B, to legalize sports betting in the city of Deadwood, was approved by a 58.5% to 41.5% margin, according to the Associated Press.
This expands the range of legal gambling products in the state to add wagering to blackjack, craps, poker, roulette and slot machines, all of which are also only available in Deadwood, in the West of the state.
Again, no fees or duties have been set out for the vertical, though Amendment B stated that money raised through legal wagering would be used for the historic restoration and preservation of Deadwood.
For readers looking for more on the election, there will be a live discussion ahead of this year's Sports Betting USA Digital, led by Global Market Advisors' Brendan Bussman on November 5.
Joining Brendan for the session will be MGM Resorts' Ayesha Khanna Molino; FanDuel's Stacie Stern; John Pappas of Corridor Consulting and Brianne Doura-Schawohlf from EPIC Risk Management. Register now to book your place.
Photo by cottonbro from Pexels
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