text:
\section{Introduction}
Black holes are famously objects where the spatial paths of light are drastically bent by the curvature of space-time. While light itself cannot escape the central mass at the event horizon, at further distances light may orbit the black hole. In the generic case of a non-rotating and electrically neutral black hole [ie. a Schwarzschild black hole \cite{Schwarzschild1916}] the event horizon is located at radial coordinate $R_s=\frac{2GM}{c^2}$, while photons may follow unstable circular orbits at $\frac{3}{2} R_s$, which is the so-called photon-sphere or last photon orbit. Any photon orbiting below this distance will plunge into the black hole, while light that remains further away will spiral out towards infinity.

However, depending on the photon's proximity to the last photon orbit it may complete several orbits before spiralling into the event horizon or out towards infinity \cite{Luminet1979,Stuckey1993}. As we approach the limit where the photons graze the exact critical orbital radius the photon will orbit an infinite number of times. Inversely, from the perspective of an observer at infinity this implies that light from any point (from the event horizon to the background) may orbit the black hole an arbitrary number of times. For each of these paths the light will reach the observer slightly closer to the edge of the black hole's shadow \cite{Perlick2010}. Therefore, the observer will see the entire surface of the event horizon and the entire universe repeating infinitely near the edges of the black hole. This infinite mapping has been extensively studied with the deflection angle diverging logarithmically in the strong field limit (see \cite{Darwin1959,Luminet1979,Bozza2002,Perlick2010,Munoz2014,Gralla2019}).

However, we present a methodology, which differs from previous research by reformulating the trajectory of light in terms of a second order differential equation and quantifying its linear stability. In \S \ \ref{SimOrb} we investigate how small deviations away from the optical edge of a black hole behave with a ray-tracing algorithm. We supplement with an analytical derivation in \S \ \ref{LinSta}. In both the numerical and analytical case we will show that small perturbations grow exponentially. Inversely, each additional orbit will be mapped to an exponentially thinner ring, with each subsequent image a factor $e^{2 \pi}$ thinner. Ultimately, this paper investigates a well known problem from a new analytical perspective suggesting not only the deflection angle but the entire trajectories of light near the photon-sphere are prescribed by two duelling exponential functions.

Crucially, this approach is generalizable to any spherically symmetric black hole or even the equatorial plane of a spinning black hole. In \S \ \ref{GenKerr}, the exponentials dependence on the spin is derived and illustrated. Here it is proved for the first time that the spatial frequency of prograde and retrograde images will respectively increase and decrease from the Schwarzschild case.

\begin{figure*}[t!]
\begin{center}
\includegraphics[width=0.98\linewidth]{fig2_2.png}
\caption{Simulated rays of light satisfying Eq. \ref{eq:endu} with $\delta_0 < 0$ (left) and $\delta_0 > 0$ (right) with coloring indicating magnitude of $\delta_0$. The black hole is shaded in grey with the last photon orbit indicated with a dotted grey line. Each successive light-trajectory plotted is a factor of 2 closer to the photon capture radius with the resulting deflection angle increasing just below 40 degrees. Thus, the logarithmic scaling towards the photon capture radius maps to a linear evolution in $\phi$. }
\label{raysoflight}
\end{center}
\end{figure*}

\newpage

\section{Analytical Setup}
The Schwarzschild metric has the form in units with the speed of light, $c=1$:

\begin{equation}
    ds^2 = \Big( 1-\frac{R_s}{r} \Big) dt^2 - \Big( 1-\frac{R_s}{r} \Big)^{-1} dr^2 - r^2 d\theta^2 - r^2 \sin^2(\theta) d\phi^2
\end{equation}

Without loss of generality we can set the orbital plane of the light $\theta=\frac{\pi}{2}$. Introducing the 2 conserved quantities, angular momentum and energy, we can for a mass-less particle reduce the equation for the trajectory of light to (\cite{Musiri2019,Stuckey1993}):

\begin{equation}
    \Big( \frac{dr}{d\phi} \Big)^2 = -\Big( 1-\frac{R_s}{r} \Big) r^2 + \frac{r^4}{b^2}
    \label{metric}
\end{equation}

Here $b$ is the constant ratio of a photon's angular momentum to energy. Rewriting the differential with $\phi$ is only applicable if there is an angular evolution, so Eq. \ref{metric} does not apply in the limiting and trivial case of light moving radially towards or away from a black hole. Using the substitution $u = R_s/r$ and differentiating both sides with $\frac{d}{d\phi}$ yields the simple second order equation:
\begin{equation}
    \frac{d^2u}{d\phi^2} = \frac{3}{2} u^2 - u
    \label{eq:endu}
\end{equation}

We can immediately reproduce the stationary orbit of the photon sphere for the Schwarzschild black hole by setting $\frac{d^2u_{eq}}{d\phi^2} = 0$: $r_{eq} = \frac{R_s}{u_{eq}} = \frac{3}{2} R_s$. Note, the trivial equilibrium solution for $u=0$ (ie. at infinite distances from the black hole) will not be discussed further.

\section{Simulated Orbits}
\label{SimOrb}

Given the differential equation (eq. \ref{eq:endu}) relating distance to the angular deflection we can numerically integrate Eq. \ref{eq:endu} using quartic Runga-Kutta (see Fig. \ref{raysoflight}). In this approach we are propagating the light from an observer to the black hole or the background universe. This yields the same light-path as the opposite direction, because the solutions of Eq. \ref{metric} are independent of the direction of the light. Integrating Eq. \ref{eq:endu} requires 2 initial conditions: In Cartesian coordinates we center the black hole at the origin, set the initial direction of light to be $\hat{v}_0 = (-1, 0)$ and the initial position $\vec{r_0} = (d_0, b_0+\delta_0)$. Here $b_0$ (the critical impact parameter) is the distance within which photons are captured and outside which photons are deflected. Here $d_0$ can be arbitrarily large given $b_0$ at that distance which in the $\lim_{d_0 \to \infty} b_0 = \frac{\sqrt{27}}{2} R_s$ becomes the photon capture radius commonly found in literature \cite{Schutz2009}. $\delta_0$ is our initial perturbation which we use to avoid the ambiguity of defining the closest approach for light rays that spiral within the photon sphere.
Importantly, $\delta_0$ is interpretable as how far the observer is looking away from rim of the optical black hole.

The path for light with varying $\delta_0$ can be seen in Fig. \ref{raysoflight}. Positive and negative perturbations will respectively spiral out to infinity or plunge into the event horizon as expected. As $\delta_0$ becomes smaller the deflection angle increases. Note, $\phi$ increases linearly when moving logarithmically closer to the photon capture radius.

\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{both-delta3.png}
\caption{Angle of rotation for simulated light-rays as a function of deviations from the equilibrium (in dimensionless units with $\delta_0 = l/R_s$) with $\phi=0$ representing unbent light-rays. For both small positive and negative perturbations a clear exponential relation to $\phi$ is visible. }
\label{Deviations}
\end{center}
\end{figure}

In Fig. \ref{Deviations} the results can be seen for positive (where the angle $\phi$ is the unwrapped deflection angle) and negative perturbations (with the angle $\phi$ being defined as the angle orbited around the black hole at the time when photons cross the event horizon). For large perturbations ($|\delta_0|>10^{-2}$)
the relationship between angle and distance is not simply exponential. However in the small perturbation regime ($|\delta_0| < 10^{-2}$) a tight exponential relationship is visible. To determine the exponent in the exponential regime, we can fit, $\phi = s \ln(\delta_0) + c$, and with slope: $s = -1.0000 \pm 0.0001 $.
Inverting this expression for $\delta_0$ implies that to achieve another orbit requires being a factor of $f = e^{-2 \pi s} = 535.60 \pm 0.45$ closer to the optical edge of the black hole.

\begin{figure*}[t!]
\begin{center}
\includegraphics[width=\linewidth]{phasespace3.PNG}
\caption{ Entire (left) and zoomed-in (right) phase-space portrait for light trajectories obeying Eq. \ref{eq:endu} with the arrows' coloring indicating the magnitude of change (brighter hues implies longer vectors). $u = 1$ is the event-horizon, $u=0$ represents infinity and $u=\frac{2}{3}$ is at the photon sphere.
If $u=\frac{2}{3}$ and $\frac{d u}{d \phi}=0$ the photons are on circular orbit, so this represents a fixed point. Notable, this is not a stable fixed point as deviations will in general grow. The stable and unstable manifolds are drawn which in the enlarged version are approximately linear. The stable manifold evidently represents a separatrix between the initial conditions of trajectories which will cross the event horizon or be ejected to infinity. Thus, the stable manifold is equivalent to the optical rim of the black hole. }
\label{phasespace}
\end{center}
\end{figure*}

\section{Linear Stability}
\label{LinSta}

To interpret these numerical results we will utilise linear stability analysis by adding small perturbations, $u \rightarrow u_{eq} + \delta$ to the equilibrium solution of Eq. \ref{eq:endu}.

\begin{equation}
    \frac{d^2(u_{eq}+\delta)}{d\phi^2} = \frac{3}{2} (u_{eq}+\delta)^2 - (u_{eq}+\delta)
    \label{eq:perturb1}
\end{equation}

Linearlizing the equation around $u_{eq} = \frac{2}{3}$ one gets:

\begin{equation}
    \frac{d^2\delta}{d\phi^2} = \delta + \frac{3}{2} \delta^2 \approx \delta
    \label{eq:perturb}
\end{equation}

Which has the solution:

\begin{equation}
\delta = \delta_1 e^{\phi} + \delta_{-1} e^{-\phi}
\label{eq:perturbsol_sch}
\end{equation}

Evidently the first term grows in magnitude while the latter decreases, with the constants $\delta_1$ and $\delta_{-1}$ determining in which regime each term dominates. The constants are set by the initial conditions of the trajectory, which will be discussed further in \S \ 4.2. Note the dual exponential form is to be expected as the equilibrium solution is a saddle point.

\subsection{Intuition through manifolds}
An alternate perspective on these exponential solutions is in the phase-space of Eq. \ref{eq:endu}. This is shown in Fig. \ref{phasespace} where for every initial condition ($u,\frac{du}{d\phi}$) a vector is plotted indicating the angular change in both variables (ie. $\frac{d u}{d \phi},\frac{d^2 u}{d \phi^2}$). The trajectories terminating at $u=1$ (ie. $r=R_s$) are the rays of light reaching the event horizon, while infinity is at $u=0$. Most trajectories will cross the photon-sphere with radial velocities, but if $\frac{d u}{d \phi}=0$ on the photon-sphere then the photon will stay in its circular orbit indefinitely. Thus, orbits on the photon-sphere represent a fixed point in the phase-space.

The set of initial conditions which converge towards the photon sphere (which is called the stable manifold) is indicated with a blue line. Photons on this trajectory will asymptotically approach the photon sphere. Conversely, the unstable manifold (ie. the set of initial conditions which reach the fixed point for $\phi \to - \infty$) is plotted in red. The symmetry between stable and unstable manifolds seen in the phase-space is due to the Schwarzschild metric and therefore Eq. \ref{eq:perturbsol} being independent of the direction of time.

As seen in Fig. \ref{phasespace} (left) for the stable and unstable manifolds $\frac{\partial u}{\partial \phi}$ is in general not linear in $u$, but when we are close to the fixed point ($\delta^2 < |\delta|$, see Eq. \ref{eq:perturb}), the relationship becomes approximately linear. Importantly, there are two sets of eigenvectors around the photon sphere. The first with an eigenvalue of $-1$ (the exponentially approaching term) and the unstable manifold with an eigenvalue of $+1$ (the exponentially diverging term). Thus, the phase space clearly follows the intuition of Eq. \ref{eq:perturbsol_sch}.

The different signs of the eigenvalues proves that the fixed point is a saddle-point. A saddle-point is inherently unstable as a perturbation from the photon sphere will generically result in an exponential divergence. Evidently, the positive eigenvalue implies that a trajectory will diverge exponentially from the bound orbit with a factor $e^{\pi n} = e^{\gamma n}$ for each half orbit n. Here the Lyapunov exponent, $\gamma$ [defined in \cite{Johnson2020}] characterizes the instability of the bound orbit relative to a half-orbit n. Thus, for the Schwarschild case for the photon sphere, $\gamma=\pi$.

Lastly, notice the eigenvalues around the fixed point in $u$ are also the eigenvalues for $r$ as $\frac{\partial u}{\partial \phi} = u \Rightarrow \frac{\partial r}{\partial \phi} = -r$. Therefore, the $\pm 1$ eigenvalues in ($u,\frac{\partial u}{\partial \phi}$) corresponds to the eigenvalues $\mp 1$ in ($r,\frac{\partial r}{\partial \phi}$).

\subsection{A tail of two exponentials}
Given Eq. \ref{eq:perturbsol_sch} we find the linearlized solutions:

\begin{equation}
u = u_{eq} + \delta_1 e^{\phi} + \delta_{-1} e^{-\phi}
\label{7}
\end{equation}

\begin{equation}
\frac{du}{d \phi } = \delta_1 e^{\phi} - \delta_{-1} e^{-\phi}
\label{8}
\end{equation}
When investigating the trajectory of light close to the black hole both exponential terms are needed to cross the equilibrium distance (see Eq. \ref{7}) or for $\frac{d u}{d \phi }$ to change sign (as seen in Eq. \ref{8}). The importance of both exponential terms is also illustrated in Fig. \ref{Distance}, where the light approaches the photon sphere exponentially (with each rotation bringing it a factor $e^{2 \pi}$ closer) until at a crossover-angle of $\phi_c \approx 6 \pi$. After this the divergent $e^{\phi}$ dominates and the light is ejected towards infinity. If $\delta_{1}$ had the opposite sign then $\frac{du}{d\phi}$ would remain negative so the crossover-angle would be on the last photon orbit, after which the light would diverge exponentially from the photon-sphere towards the black hole. Curiously, this implies the angle swept by the ray around the black hole prior to the photon sphere is similar to the angle swept by the ray from the photon-sphere to the event horizon.

Notably, the light-ray on the trajectory exactly on the rim of the black hole's shadow (ie. $\delta_0=0$) is the solution which is exponentially approaching the photon-sphere indefinitely as it neither diverges towards the black hole or the background universe. It follow that the convergent exponential and in extension $\delta_{-1}$ must be independent of $\delta_{0}$. Instead $\delta_{-1}$ is set by the approximate distance where the linearised expression holds ($\delta_{-1} \approx 1$). Any deviations from the critical impact parameter, $\delta_0 \neq 0$, will grow exponentially, which implies $\delta_1$ (the divergent exponential) is set by $\delta_0$. Thus, the order of magnitude estimates neatly follow the fitted lines in Fig. \ref{Distance}.

\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{both-sol.png}
\caption{ The radial distance between a light-ray (with $\delta_0 = 10^{-15}$) and the last photon orbit as a function of deflection angle [in blue]. The predicted analytical combination of an exponentially declining ($e^{-\phi}$) and exponentially growing ($e^{\phi}$) term is indicated with a yellow dashed line. Evidently, each term dominates at different angles of $\phi$, with fitted lines suggesting $\delta_1 \approx 10^{-16}$ and $\delta_{-1} \approx 1$. For $u-u_{eq} \approx 1$, the linearised solution no longer holds. }
\label{Distance}
\end{center}
\end{figure}

While the derivation is only applicable in the linearized regime the implications reach beyond the immediate surroundings of the photon-sphere, as the total deflection of light may be dominated by the angular rotation, while the photons are in the linearized regime. When investigating the total deflection angle or angle of rotation for light (as seen \S \ 3) we are solving the trajectories for light moving away from $u_{eq}$, where the divergent exponential must dominate. Each additional orbit of light will be mapped a factor $f = e^{2 \pi}$ nearer the rim of the black hole's shadow, because decreasing $\delta_0$ by a factor $e^{2\pi}$ delays the exponentially growing term exactly one orbit. Furthermore, it should be noted that the predicted analytical value, $f = e^{2 \pi} \approx 535.49$, is remarkably close to the numerically fitted relationship seen in \S \ \ref{SimOrb}.

\begin{figure*}
\includegraphics[width=0.99\linewidth]{KerrFixedPoint-3.png}
\caption{Phase-space portrait for light trajectories obeying Eq. \ref{eqn:kerr} with a=0.5 (left: prograde and right: retrograde) with the arrows' coloring indicating the magnitude of change (brighter hues imply longer vectors). The stable and unstable manifolds are drawn which behave approximately linear with a flatter and steeper slope than Fig. \ref{phasespace} for respectively the prograde and retrograde orbits. Note the substitution $u=\frac{1}{r}$ does not remove the critical impact parameter unlike the Schwarzschild case. Therefore the figure remains in $r$ not $u$ like Fig. \ref{phasespace}. }
\label{fig:Kerr-phaseportrait}
\end{figure*}

Additionally, for deflected light it is noteworthy that the closest approach to the photon-sphere will only decrease by a factor of $e^{\pi}$ for each additional orbit, because the cross-over angle is set by the intersection of the two exponential terms. Similarly, for light crossing the photon-sphere the angle swept from the event horizon to the photon-sphere is similar to the angle swept from the photon-sphere to the observer, as the cross-over angle is still defined by the intersection.   \vspace{15mm}

\section{Generalization to Kerr Metric}
\label{GenKerr}
It should be emphasised, that the Schwarzschild metric is the limiting case of a non-spinning black hole. Without this requirement one gets the so-called Kerr metric (Here written in Boyer–Lindquist coordinates with $\Sigma=r^2+a^2 cos(\theta)$ and $\Delta = r^2 - R_s r + a^2$):

\begin{align*}
ds^2 &= \Big( 1-\frac{R_s r}{\Sigma} \Big) dt^2 + \frac{2 a R_s r}{\Sigma} sin(\theta)^2 dt d\phi \\
    &- \frac{(r^2+a^2)^2 - \Delta a^2 sin(\theta)^2}{\Sigma} sin(\theta)^2 d\phi^2 - \frac{\Sigma}{\Delta} dr^2 - \Sigma d\theta^2
\end{align*}

Here $0 \leq a \leq 1$ is the angular momentum factor, so naturally the Kerr metric reduces to the Schwarzschild metric for $a=0$. For orbits in the equatorial plane (where a 2-dimensional analysis is still an exhaustive description) we set $\theta=\frac{\pi}{2}$. Further deliberation on non-equatorial orbits may be found through elliptic integrals as expressed in \cite{Gralla2020}. Introducing the 2 conserved quantities, angular momentum and energy, the trajectory of photons reduces to (\cite{Cramer1997}):

\begin{equation}
    \Big( \frac{dr}{d\phi} \Big)^2 = \frac{( r^2 - R_s r + a^2)^2 \left[ 1 + \frac{R_s}{r^3} (b-a)^2 - \frac{1}{r^2} (b^2 - a^2)  \right] } {\left[ \frac{R_s a}{r} + (1-\frac{R_s}{r})b \right]^2}
\end{equation}

With $b$ once more being the constant ratio of a photon's angular momentum to energy. Differentiating both sides with $\frac{d}{d\phi}$ yields a second order differential equation.

\begin{align*}
    \frac{d^2r}{d\phi^2} &=  \frac{(2r-R_s)(r^2 - R_s r + a^2) \left(1 + \frac{R_s(b-a)^2}{r^3} - \frac{b^2 - a^2}{r^2} \right)}{\left[ \frac{a R_s}{r} + (1-\frac{R_s}{r})b \right]^2} \\
    &+ \frac{\frac{a R_s-b R_s}{r^2}(r^2 - R_s r + a^2)^2 \left(1 + \frac{R_s(b-a)^2}{r^3} - \frac{b^2 - a^2}{r^2} \right)}{\left[ \frac{a R_s}{r} + (1-\frac{R_s}{r})b \right]^3} \\
    &+ \frac{(r^2 - R_s r + a^2)^2 \left(1 + \frac{3 R_s(b-a)^2}{r^4} - \frac{2(b^2-a^2)}{r^3} \right)}{2 \left[ \frac{a R_s}{r} + (1-\frac{R_s}{r})b \right]^2} \numberthis \label{eqn:kerr}
\end{align*}

The phase portrait for Eq. \ref{eqn:kerr} for $a=0.5$ is illustrated in Fig. \ref{fig:Kerr-phaseportrait}. As before, the fixed point is set by the roots of $\frac{dr^2}{d\phi^2}$, which will depend on $a$. In contrast to the Schwarzschild parameterization, Eq. \ref{eqn:kerr} depends on $b$, so the critical impact parameter of prograde and retrograde orbits must be evaluated at any $a$ (for clarification see \cite{Cramer1997}).

\begin{equation}
    b_{retrograde} = - 3 R_s \cos \left(\frac{\arccos(a)}{3} \right) - a
    \label{eq_bret}
\end{equation}
\begin{equation}
    b_{prograde} = 3 R_s \cos \left(\frac{\arccos(a)}{3} \right) - a
    \label{eq_bpro}
\end{equation}

Retrograde and prograde orbits are obtained by evaluating the critical impact parameter with Eq. \ref{eq_bret} and \ref{eq_bpro}. For any given spin we may then determine the fixed points, $r_{eq}$ such that $\frac{\partial r^2}{\partial  \phi^2}$=0. One root, $\Delta=0$, representing the event horizon with the remaining real root describing the photon circle (see Fig. \ref{fig:s}). Linearizing generically yields:

\begin{figure}[t!]
\begin{center}
\includegraphics[width=0.99\linewidth]{s.png}
\caption{Radii of photon circle, $r_{eq}$ (top), and linear coefficient of Taylor-expansion, $s$ (bottom). Retrograde orbits (in dotted blue) and prograde orbits (in dashed red).  The location of the photon circle is in agreement with \cite{Bardeen1972}, while the generic result $s>0$ for $0 \leq a < 1$, implies that the fixed point will always be a saddle point with eigenvalues $\pm \sqrt{s}$ and therefore unstable. Notable at $a=1$ the two real fixed points of prograde motion bifurcate}
\label{fig:s}
\end{center}
\end{figure}

\begin{equation*}
    \frac{dr^2}{d\phi^2} =  s \cdot (r - r_{eq}) + O( (r-r_{eq})^2 )
\end{equation*}

Importantly, we once more we get a family of two exponentials and for the first time derive the exponential unwinding for the strong field limit of light:

\begin{equation}
r = r_{eq} + \delta_1 e^{\sqrt{s} \phi} + \delta_{-1} e^{- \sqrt{s} \phi}
\label{eq:perturbsol}
\end{equation}

For any spin, $a$, the exponential coefficient, $s$ is shown in Fig. \ref{fig:s}. Evidently the fixed point is still a saddle point and therefore unstable. Here, the exponential divergent term corresponds to Lyapunov exponent of $\gamma = \pi \sqrt{s}$ as trajectories will diverge from the photon sphere with a factor of $e^{\pi \sqrt{s}}$ over a half orbit. Notable, the exponential coefficient $s$ results in a even faster divergence of the logarithmic angle for retrograde orbits. For $\lim_{a \rightarrow 1}(s_{retrograde})=\frac{27}{16}$, so another orbit would require being a factor of $f = e^{2 \pi \sqrt{\frac{27}{16}}} \approx 3500$ closer to the optical edge of the black hole. Conversely, for prograde orbits the exponential function unwinds evermore slowly for larger spins.
For a black hole spinning with $a=0.99$ (as potentially observed \cite{McClintock2006}), where $s=0.012$, only a factor $f = e^{2 \pi \sqrt{0.012}} \approx 2$ is required. Here, each repeated image would merely be a factor of 2 closer to the optical edge of the black hole. In the limit of an extreme Kerr field, $\lim_{a \rightarrow 1}(s_{prograde}) = 0$, the eigenvectors collapse and the fixed point becomes a degenerate node. Thus, an extremely rotating Kerr black hole has no exponential trajectories for the prograde motion.

Thus, when viewing the equatorial plane of a spinning black hole both prograde and retrograde reflections display the exponential repetition, but prograde copies of a source will repeat rapidly compared to the retrograde copies. This asymmetry has potentially far-reaching applications to observables as any observational signature is limited by the brightness of subsequent images decreasing sharply (see \cite{Johnson2020}). Therefore, the rapid spatial repetition of prograde images will provide the first observational signatures of the exponential repetition within detection capabilities.

Lastly, the mathematical generality of two real eigenvalues existing for all $a$ should not go unstated. Regardless of the spin of the black hole, there will always exist a family of a convergent and divergent exponential. These exponentials prescribe the entire trajectories of light near the photon orbits. Their prescription implies that any source object in the plane be repeated in an exponentially thinner series of copies, with the scale of repetitions set by the spin of the black hole. \newline

\section{Conclusion}
\label{Conclusion}
This work introduces a family of two distinct exponential solutions which together provide a succinct description of the \emph{entire} orbital trajectories of light near a Schwarzschild black hole. Thereby we provide analytical insight into the solutions previously developed (see \cite{Darwin1959,Luminet1979,Bozza2002,Perlick2010,Munoz2014,Gralla2019}).

Our formalism provides a few important interpretations. Firstly, it states that the deflection angle of background light will diverge logarithmically when the trajectory approaches the last photon orbit. Equivalently, from the perspective of a distant observer looking at the optical edge of the black hole (the photon capture radius) the entire background will be mapped to exponentially thinner rings. Secondly, the event horizon of the black hole itself will be mapped repeatedly in exponentially thinner rings just inside the photon capture radius. Therefore, any object accretting onto the black hole may be observed repeatedly nearer and nearer the optical edge. Thirdly, this edge of the black hole is the location of both the stable and unstable manifold.

The proof presented here is immediately generalizable to any spherically symmetric space-time (such as a Reissner-Nordstrøm black hole). Such metrics can similarly be written as a second order differential equation in $r$ with steady state and perturbed solutions. Further work may investigate these exponentials, which will in general be characterised by a constant, $s \neq 1$, to be multiplied on $\phi$ in the exponents of Eq. \ref{eq:perturbsol}.

Importantly, as seen in \S \ \ref{GenKerr}, our methodology may even be applied to non-spherically symmetric black holes, such as the spinning black holes of the Kerr Metric. With increasing spin, the exponential coefficient, $s$, of prograde trajectories decreases while retrograde conversely increase. Thus, proving that the side of the black hole which rotates towards the observer repeatedly mirrors the universe in wide bands. In the limit of an extremely rotating Kerr Hole, the $s_{retrograde}=\frac{27}{16}$ and $s_{prograde}=0$. Thus, there is no logarithmic divergence for prograde reflections when $a=1$, but given any spin $a<1$, there exists an exponential family prescribing the trajectories.

Philosophically, there is a mathematical beauty within the dual exponentials of Eq. \ref{7} and Eq. \ref{eq:perturbsol}. The exponentials prescribes, that an observer at infinity will see the entire black hole's event horizon and anything accreting onto the black hole mapped infinitely when looking closer towards the photon capture radius of the black hole. Just beyond the photon capture radius, the exponentials dictate, that the observer will also see the entire universe mirrored in exponentially smaller slivers until the quantum limit. A divergence which certainly merits further reflection. \newline

The author would like to thank Mogens Høgh Jensen, Martin Pessah, Charles Steinhardt and Nikki Arendse for useful deliberations and insightful feedback. The Cosmic Dawn Center (DAWN) is funded by the Danish National Research Foundation under grant No. 140.

\newpage
\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


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text:
Q: Why foreach enters into if only on first loop? If I loop through foreach loop only on first time it enters into if and gets variable values, so each next time it still have old values. why?
If I print_r($i) and kill it responds:
A0A0A0A0A0A0A0A0A0A0A0A0A0A0TXTTXT16
Real amount is end of it(16). So that means it loops 16 times through loop but into if enters only on first loop of if $type changes. So $type doesn't get new value each time it runs through loop.
Code I have:
    $recordTypes = array('CnameRecord', 'ARecord', 'MxRecord', 'TxtRecord');
    foreach ($recordTypes as $type) {
        $modelName = $type::model()->tableName();
        $record = $type::model()->findAllbySql("SELECT * FROM $modelName WHERE vhost_id LIKE $id");
        if ($record) {
            foreach ($record as $key=>$rec) {
                if ($type == 'ARecord'){
                    $type = 'A' + $i;
                    $hostname = $rec['sub_vhost_name'];
                    $points_to = $rec['points_to'];
                    $ttl = $rec['ttl'];
                } else if ($type == 'CnameRecord') {
                    $type = 'CNAME';
                    $hostname = $rec['hostname'];
                    $points_to = $rec['points_to'];
                    $ttl = $rec['ttl'];
                } else if ($type == 'MxRecord') {
                    $type = 'MX';
                    $priority = $rec['priority'] . '    ';
                    $points_to = $rec['points_to'];
                    $ttl = $rec['ttl'];
                    $hostname = $rec['host'];
                } else if ($type == 'TxtRecord') {
                    $type = 'TXT';
                    $hostname = $rec['hostname'];
                    $points_to = '"' . $rec['txt_value'] . '"   ';
                    $ttl = $rec['ttl'];
                }
                $i++;
                print_r($type);
                $custom_content = $hostname . ' ' . $ttl . '    ' . 'IN' . '    ' . $type . '   ' . $priority . $points_to . "\n";
            }
        }
    }
print_r($i);die;

A: you are using:
foreach ($recordTypes as $type) { ...

And inside the foreach you're modifying the "type" var, so in the next loops through $record, you'll fail any if statement.
Change the $type var (inside if statements) to another var name and try again.

redpajama_set_name: RedPajamaStackExchange


For the upcoming school year, the LM Hershey Campus will offer half day, full day and flex kindergarten options. The flex option allows students to start as half-day students and then transition to full-day based on the individual student's development. The full-day kindergarten program matches the regular school day of 8:15 a.m.-3:05 p.m. The half-day option also starts at 8:15 a.m., but dismisses at 11:50 a.m.


SAN DIEGO—The Ken Blanchard Companies®, a global leader in workplace learning and leadership development, recently announced Sheldon Harris, former President of Cold Stone Creamery, as the newest member of its Board of Directors.
Boutique entertainment and lifestyle public relations agency welcomes new client.
Oakbio reveals ongoing n-Butanol and biofuels program in public announcement of their grant award for "Conversion of industrial CO2 emissions into biofuels and chemicals"
5 years ago, 3380 views, By Wizard World, Inc.
iDealshare VideoGo updated to support merging and converting F4F, F4M, F4V, FLV, WebM, OGV to MP4, AVI, WMV, MOV, FLV, MKV, VOB, and etc.
5 years ago, 2754 views, By Foreword Literary, Inc.
Texas Swim Academy (www.texasswimacademy.com) is excited to announce that the U.S. Small Business Administration (SBA) has awarded Texas Swim Academy owners, Kathleen and Bruce McMordie with the 2014 Entrepreneurial Success Award.
After the great success and appreciation that Premia India Runway week earned in 2 days…. came with a surprise on the finale.
The new #1 auto industry educational event is teaming up with the Carolinas Independent Automobile Dealers Association to offer members an unprecedented FREE 12 month membership into the Unfair Advantage Automotive Mastermind Group.
5 years ago, 2252 views, By LostNMissing Inc.
Paul Sinclair Review - What To Sell On Amazon To Make Big Money?
Port of Spain, Trinidad, April 20, 2014. The GES and ORBIT Solutions Caribbean Conference on Strategic Human Resource Management 2014 will focus on assisting HR practitioners with the latest research and thought on the issues surrounding the use of.


There are so many different styles of web counters to choose from at AmazingCounters.com that we have to break it down to 20 categories. Browse each of the categories to find the style that is the ideal match for your website. Below are the free web counters in the LCD category. Click the links at the bottom of the page to browse other categories of free hit counters.
Instantly Create a Free Web Counter!


Buying and managing the right properties!
We will have four table topic speakers talking about the key steps to help us avoid the most common pitfalls and explain the logic behind building a residential rental business meant to last. There will be four speakers speaking about four distinct steps. During the meeting we will rotate from one speaker to the next.


text:
EN .
FR .
Med Culture is a Technical Assistance Unit funded by the European Union for the promotion of culture as vector of Human, Social and Economic Development in South Mediterranean countries.
READ MORE ABOUT EU COOPERATION
Med Culture
Themes, Activities and Tools
Training of Trainers
National Focus Groups
Thematic Studies
Funding Culture
Key Conventions
Culture Express_RSS feed
EU Cooperation
OVERCOMING BARRIERS FOR GREATER CULTURAL MOBILITY
In order to showcase their work, make a name for themselves abroad or continue learning, artists from Southern Mediterranean countries are faced with many obstacles, the first of which involves obtaining a visa.
In 2016, Palestinian visual artist Majdal Nateel was selected for residency in Greece. A graduate of the School of Fine Arts at the University of Al Aqsa, and now based in Gaza, this artist was certain to approach the project with earnestness and sincerity. The residence, offered by the Roberto Cimetta Fund, is financed by a European fund and aims to "promote culture and mobility as essential elements in the European Union's external relations." However, in the end Nateel's visa was not granted.
The first step towards artists' mobility is obtaining a visa, the invaluable key for travellers, and this often requires immense patience. It is a long process and may very well end in a refusal. Especially since, given the security context of recent years, visa regulations have hindered the initiatives put in place to bridge the gap between countries from the North and South.
As a resident of the Gaza Strip, Majdal Nateel must first obtain a letter of invitation from a recognised cultural institution or gallery in the country she wishes to visit. This invitation is for the embassy of the inviting country, which is located in Jerusalem. Before she can go to the meeting, she must first obtain permission from the Israeli authorities to cross the border between Gaza and Israel, which can take up to forty days. "If I'm lucky", says Madjal, "and I finally get the visa, I have to make a similar request in Jordan in order to cross the border and board a plane."
The other option is to pass through the Rafah border post to Egypt, but this too requires patience. "The last time I took this passage was in 2013 for a flight to Cairo, Rome. Once permission is granted to leave the Gaza Strip, you have to cross the border post which is only open for a few days a year for security reasons."
LONG AND UNCERTAIN PROCEDURES
An obstacle course that Ghassan el Haj knows well. This graduate in Political Science works for the Fekra Arts Institute in Gaza. During a programme coordinated by MedCulture, he was authorised to cross the Erez Crossing on the same day as his scheduled flight to Casablanca where the workshop was to take place. "The Israeli authorities called me at 9 am to tell me that my request was accepted. Impossible to reach Amman airport on time. But thanks to the organisers I was able to change my flight to the following day and finally make it to Morocco," he explains.
According to him, besides the long wait following every request, the most frustrating part is the absence of objective criteria for granting a visa, "including from the Jordanian side. No-one knows why their requests are rejected. Sometimes it works, sometimes it doesn't," he sighs.
In Libya, since the start of 2017, all 18-45 year-old nationals must be accompanied to be granted permission to leave the country. This is supposed to prevent young Libyans from joining the ranks of the Islamic State organisation. And to make things even more complicated for Libyan artists, most diplomatic missions have been closed in their country. They must therefore travel to Tunis to go through the necessary procedures, experiencing the long queues at the Ras Jedir border crossing, for a total journey of 750 kilometres between the Tunisian capital and Tripoli.
It is impossible to paint a unique picture of the difficulties faced by artists from Southern Mediterranean countries. For Omar Abi Azar, a member of the Lebanese theater company Zoukak, mobility is no longer a problem: "We have been around for ten years, and most of our members have a Schengen visa. But for Syrian artists that's another issue." Projects were often abandoned due to lack of time for filing visa applications.
Omar Abi Azar gives a bitter account of the current situation in the Arab cultural world as it faces this dilemma: "Financial and even intellectual dependence makes Western stages vital to artists in the Arab world. Many organisations in Europe have worked, and are still working, on the mobility issue, but this does not prevent the post-colonial condescension which governs the relationship and which translates into the need for a visa."
Whether they want to take part in a workshop, showcase their work or expand their market, artists from the Southern Mediterranean region undergo long, costly and unpredictable procedures, without necessarily having access to the required information to learn about administrative demands. According to the Visa Restrictions Index[i] of 2015-2017, the free movement situation is particularly critical for nationals of countries at war (Palestine, Sudan, Eritrea, Yemen, Libya, Somalia, Syria, Pakistan, Iraq and Afghanistan), as well as for nationals of countries experiencing political and economic difficulties, who are struggling to be admitted into foreign countries.
Paradoxically, according to Marie Le Sourd, secretary-general of the network On the Move and an expert in artistic and cultural mobility issues, regional exchanges seem to be even more complicated. "It's sometimes easier for artists in Southern Mediterranean countries to go to Berlin than to Tunis. Exchanges within the region are also hampered by administrative issues, visas and internal transport costs[ii]," she explains. "In fact, there is often an absence of opportunities for exchanges at a regional level for artists, such as Moroccans, with their Jordanian or Lebanese counterparts."
Since 2015 Morocco has required every Syrian or Libyan national entering Moroccan territory to obtain a visa. In 2016, Turkey also reinstated the visa requirement for Syrian nationals. The play Alors que je t'attendais (While I Waited for You), written by Syrian playwright Mohammad Al Attar and directed by Omar Abusaada, brings together comedians from across the region. The troop, which had been rehearsing in Turkey, had to look for another country to meet in. They also had to negotiate, and not without difficulty, for residence permits for the artists from Jordan, Egypt, Lebanon and Syria.
CREATIVE DIFFICULTIES
Faced with this enduring and renewed challenge, artists sometimes take a different stance and feed their work with these obstacles. This is the case with Palestinian artist and photographer Emily Jacir, who punctuates her creations with the theme of mobility. In her series Sexy Semite, produced between 2000 and 2002, she placed small ads to invite Israelis to marry Palestinians and thus give them the possibility to travel. In her work Where We Come From, she uses the power of her US passport to break through boundaries, and convey messages from exiled Palestinians to the occupied territories.
Similarly, Palestinian photographer and videographer Khaled Jarrar, who has repeatedly been prevented from travelling abroad to present his work, calls into question the situation at country borders, in particular through his project At the Checkpoint. If mobility is constrained, creation and imagination are, after all, two of the ways in which these barriers can be overcome.
[i] https://henleyglobal.com/files/download/hvri/HP_Visa_Restrictions_Index_170301.pdf
[ii] http://on-the-move.org/about/ourownnews/article/15173/artists-mobility-and-visas-a-step-forward/
Arab documentaries riding the crest of the...
When we talk about documentaries from the Maghreb and the Middle East (MENA), we often come up with the conclusion that documentary films are struggling to find their place in the Arab...
Cultural Thought and Practice in Morocco
The itinerant workshop Thought and Practice (Pensée et Pratique P&P), on the initiative of the René Seydoux Foundation, was held from the 22nd to the 24th January 2015 in Casablanca...
Make way for Egypt's Independent...
Source: IETM - International network for contemporary performing arts The art practitioners, art aficionados, cultural journalists and – above all – the regular audience members of Egypt...
© MedCulture 2015
This website has been produced with the assistance of the European Union. The contents of this website are the sole responsibility of the Med Culture Technical Assistance Unit and can in no way be taken to reflect the views of the European Union.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: wait for Plymouth Boot Screen to quit After installing Nvidia Driver to Centos , the boot screen pop out this error
wait for Plymouth Boot Screen to quit. It remains there forever. Alt-F3/F2/F4/F5 still works for me but i need the Gui Interfaces. How should i do it.

A: The reason i getting this error is due to my NVIDIA Quadro K2200 Graphic card.
My monitor had only VGA display, displaying it with onboard VGA, it prompt the error.  when i changed it to a Monitor with a DVI. It succeed boot into the OS. So, what i think the problem that is causing the problem is the signaling issue.
The NVIDIA card cannot change the digital signaling to  analog signal.


Dolomite has been used as a minor source of magnesium, but today most magnesium is produced from other sources. Calcined dolomite is also used as a catalyst for destruction of tar in the gasification of biomass at high temperature. Dolomite is relatively soft and can easily be crushed to soft powder.


It's important that small business owners and the self-employed have access to affordable, quality coverage. That's exactly what this bill does.
PHOENIX – An Arizona state senator promises that a health bill legislators are working on will help small business owners and the self-employed afford quality coverage.
Republican Sen. Kate Brophy McGee said the proposed association health plans would give those two groups the same kind of access to insurance as large companies.
"Take a one-man (or) a one-woman shop. Combine them in a 50,000-member pool … then it takes on the shape of big company buying insurance," Brophy McGee, of Phoenix, told KTAR News 92.3 FM on Wednesday.
Brophy McGee, on the job since 2011, chairs the Health and Human Services Committee. She previously served as a representative from 2011 to 2016.
The Phoenix Chamber of Commerce, Arizona Technology Council and the Arizona Association of Realtors think Senate Bill 1085 is a good idea because it reduced costs and expanded coverage.
Brophy McGee said they were misrepresenting the bill.
The bill was, "a huge tool in the toolbox," Brophy McGee said.


Winner chosen at random will be announced at 10:00PM, Sunday.
Each comment will be the next line in the story!
1) Read the comments below – specifically the most recent comment.
** I will open the story with the first comment which will be the first few lines from chapter 1 of Night of the Living Dead Christian, by Matt Mikalatos.
2) Add your ONE SENTENCE comment as your version of what the next line in the story should be. *Please continue the story from the previous comment only.
3) Share a link to this contest/post on your Facebook or Twitter (use buttons below).
Note: I will remove any comments I see as inappropriate.
Have fun. Ready …. Set … WRITE!
I kept pinching myself to make sure that I was awake. It seemed like one of those dreams that was actually real.
On any other night I could have brushed it off as no big deal, but there was just something about this night that was not quite right.
You might think it was Halloween, but it wasn't, it was July 17th.
people were walking around the neighbourhood in monster-like costumes/masks.
CHAPTER 1: WHO ARE THE PEOPLE IN YOUR NEIGHBORHOOD?
Monsters don't exist. I had been telling myself that for nearly a week. But it was the sort of night you could almost believe in them. …….


text:
Finally, a Study Shows that This Emotion IS a Symptom of Postpartum Depression
Family Self-Care
Is Anger a Symptom of Postpartum Depression?
July 4, 2018 by Kate Schweitzer First Published: June 28, 2018
It might come as a surprise to no one that anger can be related to postpartum mood problems in women, and yet that very emotion is not once included in the widely used Edinburgh Postnatal Depression Scale screening tool. (You know, the sheet your ob-gyn likely had you fill out at your six-week postpartum appointment, that included prompts like "I have blamed myself unnecessarily when things went wrong" or "I have been anxious or worried for no good reason.")
However, a new study from the University of British Columbia shows that anger is, in fact, a significant feature in postpartum mood disturbances, and researchers recommend that women be screened for it, in addition to depression and anxiety, specifically.
"Many mothers have expressed feeling let down by others in terms of support from partners, family members, and health-care providers as well."
"There's some evidence that indicates that being both angry and depressed worsens the intensity and length of depression," PhD candidate Christine Ou, who authored the study that was published in Birth, said in a university interview. "That can have many negative effects on the mother, child, and family, and on the relationship between parents."
The data analysis — which examined postpartum depression literature over a 25-year time period — also found that feelings of powerlessness, a mismatch between reality and expectations of motherhood, and unmet expectations of support contributed to anger in the context of postpartum depression.
"Mothers may feel that they have not met their own expectations and that also others may judge them because, for example, they're formula-feeding instead of breastfeeding," Ou said. "Many mothers have also expressed feeling let down by others in terms of support from partners, family members, and health-care providers as well."
1 Mom Perfectly Describes the Fine Line Between Anxiety and Postpartum Depression
Because postpartum anger hasn't been closely examined up until now (according to Ou, the reason is because in some cultures, it's not seen as "acceptable"), the results can't determine which comes first — depression or anger. To that end, Ou and her coauthor Wendy Hall believe this analysis serves as a vital starting point.
"We know that children who are exposed to parental anger or depression are at a greater risk of developing emotional problems," Hall said. "It's important for healthcare providers to examine maternal anger in the postnatal period in order to understand and manage that risk."
Image Source: Unsplash / Christian Fregnan
Family Self-CarePostpartum DepressionParenting News
Mom Gently Reminds the World That Maternity Leave Isn't a Vacation in Any Way, Shape, or Form
by Murphy Moroney 6 hours ago
Hospital Sign Shaming New Parents For Being on Their Phones Is Not What the Doctor Ordered
Today in Very Important News: Build-A-Bear Is Releasing a Baby Yoda Plush
We're Counting the Days to March After Seeing This Relatable Trailer For FX's New Parenting Show
by Alessia Santoro 5 days ago


A leading clothing manufacturing company in Kwa-Zulu Natal is looking for an experienced Time Study Analyst to develop work measurement procedures and conducts time‐and‐motion studies to promote efficient and economical utilization of personnel, equipment,and facilities. Allwear * Newcastle * Permanent * Full Time - Introduction - Duties & Responsibilities * Conduct observation and analysis of personnel and work procedures to determine time-and-motion requirements of job duties. * Analyze work study data and equipment specifications to establish time and production standards. * Apply mathematical analysis to determine validity and reliability of sampling and work study statistics. * Document and correct potential safety and ergonomic issues observed during the time study process. A leading clothing manufacturing company in Kwa-Zulu Natal is looking for an experienced Time Study Analyst to develop work measurement procedures and conducts time‐and‐motion studies to promote efficient and economical utilization of personnel, equipment,and facilities. Allwear * Newcastle * Permanent * Full Time - Introduction - Duties & Responsibilities * Conduct observation and analysis of personnel and work procedures to determine time-and-motion requirements of job duties. * Analyze work study data and equipment specifications to establish time and production standards. * Apply mathematical analysis to determine validity and reliability of sampling and work study statistics. * Document and correct potential safety and ergonomic issues observed during the time study process.
Life Green Group * RANDPARK AREA * Permanent * Full Time - Desired Experience & Qualification * ADVANCED UNDERSTANDING OF WORDPRESS TO BUILD AND IMPLEMENT CHANGES ON WEBSITE BACKEND. * ADVANCED DESIGN CAPABILITY IN ADOBE PHOTOSHOP, IN DESIGN AND ILLUSTRATOR TO DESIGN AND OR EDIT PRESENTATIONS, BROCHURES, BUSINESS PROFILES, LOGOS, STATIONERY, ETC. * BUSINESS CARD DESIGN AND SETTING UP THE QR CODES FOR NEW EMPLOYEES/NEW BUSINESS CARDS TO BE IMPORTED INTO THE DESIGN. * DEVELOP AND DESIGN * MONITOR AND ADAPT SEO REGULARLY * SOCIAL MEDIA - WEBSITE, FACEBOOK AND WRITING BLOGS. * MARKETING - MAGAZINE ADVERTISING, EDITORIALS, NEWSLETTERS, ETC. * COMPANY LOGO - BRANDING. * PHOTOSHOOTS. * GENERAL AD HOC MARKETING DUTIES. * SELF MOTIVATED. * TEAM PLAYER ABLE TO TAKE INSTRUCTIONS AND EXECUTE IDEAS. * FLEXIBLE * AVAILABLE ON WEEKENDS - ON REQUEST - Please note: If you have not been contacted within 2 weeks. unfortunately you have not been successful. Life Green Group * RANDPARK AREA * Permanent * Full Time - Desired Experience & Qualification * ADVANCED UNDERSTANDING OF WORDPRESS TO BUILD AND IMPLEMENT CHANGES ON WEBSITE BACKEND. * ADVANCED DESIGN CAPABILITY IN ADOBE PHOTOSHOP, IN DESIGN AND ILLUSTRATOR TO DESIGN AND OR EDIT PRESENTATIONS, BROCHURES, BUSINESS PROFILES, LOGOS, STATIONERY, ETC. * BUSINESS CARD DESIGN AND SETTING UP THE QR CODES FOR NEW EMPLOYEES/NEW BUSINESS CARDS TO BE IMPORTED INTO THE DESIGN. * DEVELOP AND DESIGN * MONITOR AND ADAPT SEO REGULARLY * SOCIAL MEDIA - WEBSITE, FACEBOOK AND WRITING BLOGS. * MARKETING - MAGAZINE ADVERTISING, EDITORIALS, NEWSLETTERS, ETC. * COMPANY LOGO - BRANDING. * PHOTOSHOOTS. * GENERAL AD HOC MARKETING DUTIES. * SELF MOTIVATED. * TEAM PLAYER ABLE TO TAKE INSTRUCTIONS AND EXECUTE IDEAS. * FLEXIBLE * AVAILABLE ON WEEKENDS - ON REQUEST - Please note: If you have not been contacted within 2 weeks. unfortunately you have not been successful.
This position is for a Drone Pilot Site inspector. * Prior experience with commercial Drone Piloting Mobax Group (Pty) Ltd. * Irene * Permanent * Full Time - Introduction - MOBAX'S core business is the supply of Professional Telecommunications Services and Products to the South African market. Duties & Responsibilities - You will be required to do reconnaissance of sites, masts and property using drone photography to do analysis and audits. This position is full-time and based in Centurion. Projects are coming in rapidly and hard work is required. However, the work is very rewarding and part of a growing company * Travel to the drone * Identify, document and video/photograph analysis via Drone operations with an SA Approved Commercial license. * Complete required forms as directed. Identify and collect documentation. * Will * Document and update databases * Coordinate and participate in customer meetings. This position is for a Drone Pilot Site inspector. * Prior experience with commercial Drone Piloting Mobax Group (Pty) Ltd. * Irene * Permanent * Full Time - Introduction - MOBAX'S core business is the supply of Professional Telecommunications Services and Products to the South African market. Duties & Responsibilities - You will be required to do reconnaissance of sites, masts and property using drone photography to do analysis and audits. This position is full-time and based in Centurion. Projects are coming in rapidly and hard work is required. However, the work is very rewarding and part of a growing company * Travel to the drone * Identify, document and video/photograph analysis via Drone operations with an SA Approved Commercial license. * Complete required forms as directed. Identify and collect documentation. * Will * Document and update databases * Coordinate and participate in customer meetings.
A limited number of Senior Lecturer/Lecturer/Junior Lecturer positions have recently become available in the Department in these fields. Temporary Junior Lecturer: Computer and Digital Systems / * An applicable Bachelor's degree (such as BEng) in Electrical and Electronic Engineering, as recognised by the Engineering Council of South Africa (ECSA), to qualify for registration as a Professional Engineer; * Registration as a Professional Engineer; Stellenbosch University * Stellenbosch * Fixed Term * Full Time - Introduction - Electrical and Electronic Engineering - Machine Learning and Data Engineering (Three-year term appointment) The Department of Electrical and Electronic Engineering at Stellenbosch University offers leading educational and research programmes in the fields of computer and control systems as well as machine learning and data engineering. A limited number of Senior Lecturer/Lecturer/Junior Lecturer positions have recently become available in the Department in these fields. Temporary Junior Lecturer: Computer and Digital Systems / * An applicable Bachelor's degree (such as BEng) in Electrical and Electronic Engineering, as recognised by the Engineering Council of South Africa (ECSA), to qualify for registration as a Professional Engineer; * Registration as a Professional Engineer; Stellenbosch University * Stellenbosch * Fixed Term * Full Time - Introduction - Electrical and Electronic Engineering - Machine Learning and Data Engineering (Three-year term appointment) The Department of Electrical and Electronic Engineering at Stellenbosch University offers leading educational and research programmes in the fields of computer and control systems as well as machine learning and data engineering.
To adhere to correct procedures as per the Service Desk Operational Manual and escalate as and when required. * Complete ad hoc tasks within the Service Desk environment as and when required. * Pretoria * Temporary * Full Time - Introduction - Qualified and Experienced Helpdesk Technicians are required for a 2 year contract. Duties & Responsibilities * Attending to incoming voice and email calls by listening attentively to the customer, determining customer needs and logging calls on Remedy accurately. * Efficient and effective logging and allocation of incoming / involved parties in ensuring all calls are attended to and closed. * Updating of user information on the Remedy system to ensure an up to date database. * Relating parent and child calls. * Ensure that all calls are logged within Remedy as per the required operational processes. To adhere to correct procedures as per the Service Desk Operational Manual and escalate as and when required. * Complete ad hoc tasks within the Service Desk environment as and when required. * Pretoria * Temporary * Full Time - Introduction - Qualified and Experienced Helpdesk Technicians are required for a 2 year contract. Duties & Responsibilities * Attending to incoming voice and email calls by listening attentively to the customer, determining customer needs and logging calls on Remedy accurately. * Efficient and effective logging and allocation of incoming / involved parties in ensuring all calls are attended to and closed. * Updating of user information on the Remedy system to ensure an up to date database. * Relating parent and child calls. * Ensure that all calls are logged within Remedy as per the required operational processes.
Consultant, Presales (Cape Town based) responsible for providing subject-matter expertise on the API Management and Identity and Access Management (IAM) product portfolio. * 5+ years' experience as Presales, solution architect or working with enterprise software products or services, specifically in the field of API's, API Security and IAM * Both direct and partner Presales activity experience will be seen as a benefit - DS Associates * Northern Suburbs * Permanent * Full Time - Introduction - and support sales opportunities. Duties & Responsibilities * Provide product advice and technical guidance to sales teams and key business partners. * Create and deliver innovative product demonstrations for prospects, customers and partners on-site and remotely. * Provide technical expertise and leadership to conduct trials, Proof of Concept (POCs), complex demos, etc. Consultant, Presales (Cape Town based) responsible for providing subject-matter expertise on the API Management and Identity and Access Management (IAM) product portfolio. * 5+ years' experience as Presales, solution architect or working with enterprise software products or services, specifically in the field of API's, API Security and IAM * Both direct and partner Presales activity experience will be seen as a benefit - DS Associates * Northern Suburbs * Permanent * Full Time - Introduction - and support sales opportunities. Duties & Responsibilities * Provide product advice and technical guidance to sales teams and key business partners. * Create and deliver innovative product demonstrations for prospects, customers and partners on-site and remotely. * Provide technical expertise and leadership to conduct trials, Proof of Concept (POCs), complex demos, etc.
Sales, Manager, Security, strategy, targets, process, client, client engagement, mentor, coach, people management, sales team, selling, leadership, ICT Security sales manager, ICT, Cyber security, solutions selling - A global technology and managed services provider, recognised for investing in talent, is now looking for an experienced Security Sales Manager in Johannesburg. Have you gained Sales experience in Security? The primary objective of the Sales Manager is to take responsibility for in order to assist in the achievement of sales targets through the allocation of territories and targets resulting in outstanding sales performance. This Sales Manager , but they are not a departmental or divisional manager. The Sales Manager achieves their sales targets through effective allocation of their team's territories and targets, and ensuring outstanding sales performance. Sales, Manager, Security, strategy, targets, process, client, client engagement, mentor, coach, people management, sales team, selling, leadership, ICT Security sales manager, ICT, Cyber security, solutions selling - A global technology and managed services provider, recognised for investing in talent, is now looking for an experienced Security Sales Manager in Johannesburg. Have you gained Sales experience in Security? The primary objective of the Sales Manager is to take responsibility for in order to assist in the achievement of sales targets through the allocation of territories and targets resulting in outstanding sales performance. This Sales Manager , but they are not a departmental or divisional manager. The Sales Manager achieves their sales targets through effective allocation of their team's territories and targets, and ensuring outstanding sales performance.
As the digital age continues to evolve and grow all around the globe, the IT industry is becoming a very popular career choice for those with the drive to succeed. The best part about the IT industry is the fact that it is incredibly diverse - there truly is a career path for everyone. Below, we take a look at everything you need to know about breaking into, and working in, the IT industry, along with what to expect from the different types of IT jobs and how to work your way to 'the top' of your professional game.
Obviously, the IT field is a specialised one, which means that a tertiary education focusing on IT in general is a must for all aspiring technical experts. An institution that focuses on both theory and practical elements of the IT world is your best bet as it will allow you to build on all of the essential skills necessary in order to ensure success within the industry once you have graduated and are ready to look for a job.
A web programmer is generally responsible for the optimal functioning of a company's website and computer programmes / software. The web programmer is incredibly tech-savvy and spends a lot of time writing coded instructions for programmes and the World Wide Web.
A database analyst will be responsible for designing databases for companies, ensuring that said databases operate effectively at all times. He or she designs the databases in line with the client's needs and instructions, and may be hired to maintain and update the database as necessary.
Nowadays, interactive content is an imperative part of any and every company's digital marketing strategy. As a result of this, there is currently a high demand for multimedia developers. These professionals utilise specialist development tools, programmes and software in an effort to create innovative and exciting interactive content.
Often considered an entry-level position for those interested in kick-starting their IT careers, an IT technician focuses on assisting clients with any questions, queries or problems that they may be having with the company's software applications or technical products. These technicians will often assist clients over the phone or by obtaining access to their computers remotely. Technical know-how and excellent communication skills are a must.
A software engineer spends his / her time designing and creating helpful software applications according to a client's needs and expectations.
When it comes to the administration of database management systems, the database administrator is considered the 'go to' guy and is responsible for planning, implementing, configuring and maintaining all database administration systems.
Generally, a network administrator will focus his / her time and energy on maintaining and optimising a company's LAN (Local Area Network).
A systems analyst is the trusted expert within an organisation who takes the time to research and recommend software, programmes and systems according to the company's needs and shortcomings (he or she will do this with the company's budget constraints in mind). As such, he or she will have a firm grasp on the IT industry in general, especially when it comes to specific products that are currently available on the market.
A webmaster knows all that there is to know about the process of administrating, maintaining, organising and implementing a website for a company.
Who is Best Suited to a Career in the IT Industry?
A continual search for knowledge: Seeing as though the IT industry is constantly changing, every IT professional needs to ensure that he / she is up to date with the latest happenings and developments. Knowing this, constant research and involvement in terms of industry events is extremely important.
Reliability: For most businesses, the IT portion of the organisation is the back-bone of all of the internal operations and is essential for ensuring optimal productivity at all times.
Flexibility: The IT needs of a company are rarely consistent, which means that every IT professional needs to be able to adapt to an ever-changing work environment. This also means that the ability to work inconsistent hours is often a must, and that the professional should ensure that he / she is always available should any crises occur.
Problem Solving: Oftentimes, the IT professional will need to work hand in hand with other professionals within the organisation in order to solve problems and innovate in terms of business success and improvement. As a result, problem solving skills are necessary and are sure to enhance one's potential for career growth and development.
Ultimately, the IT industry provides aspiring experts with a wide array of opportunities and varying career paths. However, regardless of which path you choose to follow, the underlying secret to success is always your drive to succeed, as well as your determination to keep up with the changes in the industry and use them to your advantage in an effort to enhance and further develop the company for which you are working.
Once you have decided that the IT industry is the best fit for you, and you have completed your degree, the time will come to start looking for a job. In order to streamline the process, and increase your chances of landing the perfect job, it is recommended that you make use of a reliable job portal such as PNet. Not only will you gain access to the most sought after jobs in the country, but you will also be able to familiarise yourself with the best companies to work for within the industry.
For more career advice ideal for hard-working young professionals, be sure to pay our blog a visit. To view the latest job listings from the South African IT industry, click here. Start with PNet - the top recruiters do.


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Home / Entertainment / Selena Gomez: social media is bad for young people
Selena Gomez: social media is bad for young people
The Wolves singer has been inching her way back into the public eye over the past few months, and returned to platforms like Instagram in January.
Gomez, who has more than 150 million Instagram followers, has also posted less on social media than many other celebs amid her struggles. "Do you think I should wear red on a red carpet", asked Deepika.
A performer with an extensive following on social media says that the platforms are risky. "It's selfish - I don't wanna say selfish because it feels rude - but it's unsafe for sure". I noticed with me, I got kind of depressed looking at these people who look lovely and awesome, and it would just get me down a lot.
"I think it's pretty impossible to make it safe at this point", Gomez said. "I'm grateful I have the platform".
"I also don't do a lot of pointless pictures. I like to be intentional with it". It just scares me. I'll see these young girls at meet and greets. I see these young girls ... It can be great in moments. I mean, you still can't tell me who the hell "Selena Gomez" is - but Gomez, as he calls her, "I really like".
In late 2018, Gomez revealed to Vogue Magazine that part of her therapy involved stepping away from her popular social platforms. "She's a remarkable person".
"Please stop reading into things so much and making something out of nothing". Back in March, the star revealed: "I'm now in the studio and it's going really good".
It is that time of the year again when we have our favourite stars glide down one of the most prestigious red carpets in the world.
The singer's appearance at Cannes comes just a week after she skipped out on the 2019 Met Gala. A study released in 2017 showed that there has been a dramatic rise in teen suicides since 2011 - a rise, the study suggested, that could be linked to social media use, cyberbullying, and the temptation most social media users have to portray their lives as "perfect" and "Insta-worthy".
Paul Pogba will leave Man Utd after fan abuse - Patrice Evra
Jeremy Kyle Show suspended after guest death
Watch the Super Mario Maker 2 Nintendo Direct here
Serena Williams' injuries growing into major worry


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Giant Oaks Gains a Victory
Not only is the Clark Handicap a notable Grade II thoroughbred racing event on the racing calendar but it is also a part of the history of the Churchill Downs Racecourse, as it was first run in 1875. This makes it one of the oldest horse racing events in the country. On Friday, 26 November 2010, the Louisville racecourse was once again well supported by loyal racing fans who came to watch the 2010 edition of the Clark Handicap unfold at Churchill Downs. And for trainer Chris Block, it was a moment that has been a year in the making.
The Clark Handicap has a purse amount of $500 000 and eleven competitors walked into the starting gates to participate in this year's event. When it came down to the final moments of the Clark Handicap, it was a face-off between just two horses, namely race favorite Successful Dan and Giant Oaks. Both four-year-old horses gave it their all as they headed towards the finish line, but Successful Dan was able to push his head out before Giant Oaks, leaving Block to think another victory had eluded them once again. But not even a second after the horse's finished the race, did the objection sign appear, leaving spectators, owners and jockeys confused and unsure of the race's outcome. Stewards objected to the victory, as there seems to have been a little scuffle as the field had turned into the homestretch. According to the stewards, Successful Dan bumped into Redding Colliery. A fact which jockey Rosie Napravnik confirmed, saying "He slammed me pretty hard. He knocked us completely off stride." Julien Leparoux, jockey for Successful Dan, defended his mount saying a sudden move from Demarcation caused Successful Dan to accidently veer into Redding Colliery's path, but this was not supported by the stewards.
This led to Giant Oaks being placed into first position, giving him his first victory for the year. In every event, Giant Oaks had come close to victory, but had not been able to push through, leaving his trainer to wonder if his beautiful colt would ever get a break. But now it has finally arrived for Giant Oaks, leaving Block to comment that, "This guy, we've worked so hard getting him where he's at today, this has to rank right up there."


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Jessica Cejnar / Thursday, July 11, 2019 @ 7:08 a.m. / Local Government
Yurok Tribe's New Police Chief Meets Del Norte Supervisors: O'Rourke Says Cross-Deputation Agreement Will Increase Department's Presence Off Reservation
Though his department is understaffed currently, the Yurok Tribe's new police chief envisions a time when his officers will serve residents both on and off the reservation.
The tribal police department has already provided backup to the Del Norte County Sheriff's Office, Chief Greg O'Rourke told county supervisors on Tuesday. The tribe's goal is to have 20 sworn officers on staff by 2025, he said.
"For up here in Del Norte County, our patrol staff would have a sergeant and five officers," O'Rourke said. "Our patrol schedule will allow for 18 hours of coverage, but we'd still have time where we'd have no coverage."
Chief Greg O'Rourke at his swearing-in ceremony earlier this year. Photo: Yurok Tribe.
O'Rourke the first recruit from the Yurok Tribe Public Safety Department to go through the police academy in 2000. He said he was in the same academy class as Del Norte County Sheriff Erik Apperson. O'Rourke's 19-year career in law enforcement includes six years' service with the Hoopa Tribal Police Department and 12 years' service with the Humboldt County Sheriff's Office.
When O'Rourke came back to the Yurok Tribe Public Safety Department as its chief in March there were only four sworn members on staff. O'Rourke said three people quit when he and his lieutenant, Jacob Morris, took the oath of office forcing them to rebuild the department.
"I think that may have been a blessing in disguise," O'Rourke said. "We have the opportunity now to lay down a solid foundation for a sustainable law enforcement program. But it takes time to build up a department, especially building a department that has a law enforcement culture that's going to be nurturing and supportive of new officers coming in."
Since March, O'Rourke's department has hired two new officers from the 123rd police academy. Two other new recruits started the current academy Monday, O'Rourke said. His department's also in the process of bringing on two lateral officers
O'Rourke said he's also working to bring on part-time staff to enforce the tribe's fishing codes on the Klamath River. As his department grows, O'Rourke said the tribe plans to hire a warden sergeant and two wardens that would not only enforce the tribe's fishing regulations but also respond to calls for water rescue and search and rescue services.
O'Rourke also noted that cross deputation agreements on both sides of the county line means that a cop will be able to respond to calls for service in the southern part of Del Norte in a timely manner. The tribe's police officers will also be able to back up sheriff's deputies in other parts of the county, he said.
"Even though we look to eliminate a reliance upon the sheriff's office to be able to offer comprehensive law enforcement to the reservation, it doesn't mean we're looking to separate from the sheriff's office," O'Rourke said. "Quite the opposite. We intend to integrate more with the sheriff's office both in Humboldt and in Del Norte County. That level of cooperation, the level of mutual training and that level of working together, boots on the ground, can offer the citizens in Del Norte County and Humboldt County more law enforcement services."
Brian Donahue became the first Yurok Tribal Police officer to be cross deputized with the Del Norte County Sheriff's Office in January 2018. Before he administered the oath of office to Donahue, Apperson called the occasion a cause for celebration, saying it represents more than two years of work between the county and the tribe.
Cross deputation with the Yurok Tribe was a topic Apperson brought up frequently when he ran for his first term as Del Norte County Sheriff in 2014.
On Tuesday, Del Norte County District 1 Supervisor Roger Gitlin asked O'Rourke how many calls for service he expects his officers to be able to respond to off the Yurok Reservation as the tribe's law enforcement footprint grows.
Though he didn't know what the volume for service calls would be as his department evolves, O'Rourke said the only time his officers would look to the sheriff's office for help would be for larger crimes in the Klamath area. But, he said, his officers would be able to keep the peace, identify witnesses and begin initial interviews while waiting for a sheriff's deputy.
"That type of preliminary investigation to major crimes goes a long way to help prevent further crime," O'Rourke said.
It's ultimately the tribe's goal to have its detectives work "hand-in-hand" with detectives from Humboldt and Del Norte counties, O'Rourke said.
Gitlin's colleague, District 3 Supervisor Chris Howard brought up the recent endangered species designation for spring-run chinook salmon on the Klamath and Trinity rivers.
The California Fish and Game Commission recommended the Klamath-Trinity spring-run chinook as a candidate for the California Endangered Species Act list in February. This afforded the salmon run the protections of an endangered species.
In April, however, state Fish and Game commissioners approved a shorter sport fishing season with a reduced bag and possession limit for the spring-run chinook despite its candidacy for protection. Recreational fishermen could start fishing for spring-run chinook on July 1.
Howard noted that the tribe, which supported the spring-run chinook's candidacy for the California ESA list, also has a substantial gill net fishery for spring-run salmon. He asked O'Rourke how he would go about enforcing the current designation.
"Is it a policy or a natural resource law that is created by the Tribal Council then you guys enforce, let's say, state law, which bans the take of spring-run chinook?" Howard asked.
O'Rourke said he hopes to hire part-time staff to enforce fishing regulations on the Klamath River.
"If a non-tribal member, for example a Hoopa Tribal member, who is native but not necessarily a Yurok Tribal member comes up and fishes, we have the option to be able to impose tribal code onto them or go a state route," O'Rourke said. "That's going to be up to the discretion of the officer."
If a non-tribal member who is a non-native is caught fishing for spring-run chinook, with the deputation agreement between the tribe and Del Norte County Yurok police officers will be able to enforce state regulations.
"One of the benefits of the deputation agreement is it allows boots on the ground options," O'Rourke said. "Options could either be applied to what's going to be the most effective at enforcing or stopping illegal behavior or options (could be) to provide a quicker path to resolve what the situation is."
Man With Several Warrants Found in Possession of Stolen ATV, Firearms at McKinleyville Gas Station, Deputies Say
CHP: Traffic Hazard at Highway 199 N Dn 12.20
OUTAGE: Power Outage in Blocksburg; 12 Customers Affected
HIGHWAYS: Route 199 One-way Traffic Operation


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China Bans Its National Football Players From Getting Tattoos
1 year ago David
Footballers who play for China's national team have been banned from getting tattoos – and advised to remove ones they have – under a new directive.
The country's sports administration body said recruiting new players with tattoos at national level and to youth squads was "strictly prohibited".
The administration said the move would help set a "good example for society".
Some national stars, including defender Zhang Linpeng, have previously been told to cover their tattoos.
China has been increasingly stepping up regulation since mid-2018 to stop tattoos being shown on screens. Some professional footballers have since been covering their arms with long sleeves to hide their body art.
In a statement, the country's General Administration of Sport (GAS) said national players with tattoos were "advised to have them removed".
"In special circumstances, the tattoos must be covered during training and competition, with the consent of the rest of the team," it said.
In Chinese culture a stigma has been attached to tattoos – in the past they were used to brand criminals and the tattoo still has links to organised crime groups in east Asia. Tattoos among ethnic groups were often seen as a mark of the uncivilised.
They are disapproved of by China's ruling Communist Party, but have become increasingly popular among young Chinese.
Earlier this year, China's broadcasting regulator announced that it was tightening rules on what it described as "unhealthy content".
Television and internet appearances by sports personalities and celebrities have been restricted in cases involving tattoos and men's ponytails – in some instances these have been blurred from screens.
Last December, a women's university football match in China had to be called off after players were told they were not allowed to have dyed hair.
The match organisers, the National Youth Campus Football League, said in a statement at the time: "Athletes at all stages shall not have tattoos, dye their hair, wear weird hairstyles, or wear any accessories, otherwise they will be ineligible for the competition."
Source*
davidmerrick@eunews24.com
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Symantec Corp. announced its acquisition of Appthority, a privately held company that offers comprehensive Mobile Application Security Analysis. This technology gives Symantec customers the critical ability to analyze mobile apps for both malicious capabilities and unsafe and unwanted behaviors, such as vulnerabilities, risk of sensitive data loss, and privacy-invasive actions.
The acquisition of Appthority demonstrates Symantec's continued commitment to securing modern (e.g. iOS, Android) endpoints and operating systems, as it brings innovation to its portfolio that addresses this vital security need. Last year, Symantec acquired Skycure, a leading Mobile Threat Defense (MTD) technology, that enabled the launch of Symantec Endpoint Protection Mobile (SEP Mobile).
Appthority's technology will be built into SEP Mobile, further enhancing Symantec's ability to protect the broadest spectrum of modern endpoints and operating systems. This extends Symantec's leadership in delivering the most comprehensive endpoint security solution available (recently named a leader by the Gartner Magic Quadrant for Endpoint Protection Platforms, Forrester Wave for Endpoint Security Suites, and AV-Test Institute Best Protection Awards).
With its Integrated Cyber Defense platform, Symantec now stands as the only company that offers solutions that can protect modern and traditional endpoints (Windows, MacOS, Linux, iOS, and Android) at the device, application, network, identity and cloud layers.
Symantec also announced its acquisition of Javelin Networks, furthering its commitment to endpoint innovation. Javelin Networks is a privately held company that offers advanced software to help enterprises defend against Active Directory-based attacks.


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Major measles outbreak strikes anti-vaxxer stronghold in Washington state
Brad Reed
A major measles outbreak has struck a county in Washington state where vaccination rates of children have been plummeting.
Local news station KATU reports that health officials in Clark County this week announced there have now been 22 confirmed cases of measles — including 19 cases in which the infected children were not vaccinated.
KATU says that publicly available health statistics show that vaccination rates have experienced a massive drop over the past thirteen years.
"More than 91.4 percent of all kindergartners had completed all their immunizations in the 2004-2005 school year," KATU reports. "That number fell to 76.5 percent in the 2017-2018 school year. For measles, the number of vaccinated kindergartners fell from 96.4 percent to 84.5 percent over that same time period."
Dr. Jason Hanley, the Emergency Department Medical Director at PeaceHealth Southwest Medical Center, said it's been "an interesting week" at his facility because measles is normally "a relatively rare disease."
PeaceHealth has also been advising children who have not been vaccinated for measles to not enter into its facility.
Breaking Banner
Tana Ganeva
On Monday, the Daily Beast reported that the new 007 -- the special agent in the James Bond series -- will be portrayed by the black actress Lashana Lynch.
The announcement set off predictably racist and sexist reactions.
Perhaps the most prominent right-winger to voice his displeasure was Ben Shapiro, who complained that it didn't make sense for Bond to be a woman because of the character's signature seduction moves.
"Bond is about the guns and the girls," Shapiro said, noting that a woman in a seductive role was not realistic.
REVEALED: The government just 'dramatically' expanded its investigation of Jeffrey Epstein
Cody Fenwick, AlterNet
Federal investigators have been able to "dramatically expand" their investigation into financier and sex offender Jeffrey Epstein as prosecutors bring sex trafficking charges against him, Assistant U.S. Attorney Alex Rossmiller said in court on Monday.
The government revealed the expansion of the case at the day's bail hearing. In searching the defendant's house, investigators found an old passport with Epstein picture and a fake name that listed Saudi Arabia as the location of his residence, the prosecutor said.
The judge was surprised at this revelation, NBC News reported, asking the attorney, "Say again?"
Rep. Will Hurd (R-TX) on Monday became the first Republican lawmaker to unequivocally condemn President Donald Trump's racist attacks against four Democratic lawmakers.
When asked by CNN's Christiane Amanpour about Trump's weekend tweets, in which he told Reps. Ilhan Omar (D-MN), Alexandria Ocasio-Cortez (D-NY), Ayanna Pressley (D-MA) and Rashida Tlaib (D-MI) to "go back" to their countries despite the fact that all four are American citizens, Hurd did not hold back on repudiating the president's statements.
"Those tweets are racist, and xenophobic," he said. "They're also inaccurate. The four women he's referring to are actually citizens of the United States."
MSNBC host says Trump just openly embraced racists: 'This actually feels different to me'


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email: jazz@triphazardjazz.co.uk
Hot jazz, cool music. Cool jazz, hot music.
A jazz band available for events around Essex, North & East London.
From 3 to 7 piece + singers
Types of Music
Jazz standards, swing, ballads, latin, blues and such. From cool to funky.From relaxed to hot.
Who's in the band
This will vary. A three piece may consist of sax, keyboard, bass; four piece add drums; five piece add trumpet or trombone; six piece add another sax.
Singers can be added to any size band.
The actual musicians will also vary. There is a pool of excellent musicians to be drawn from. Trip Hazard is no rehearsed band.
The guys/girls get together on the gig and play jazz. The unrehearsed nature gives the music an edge, an excitement, a frisson that can be lost in set bands.
What the band is not
It is not a 'function' band (although we obviously play at functions), the sort of band required to play a range of styles to suit the occasion - (Knees Up Muvver Brown, Irish Washer Woman, Gay Gordons, Hava Nagila, Okey-Cokey or whatever). We've been there and done that. We play jazz, and that's pretty much it (well you might get a Happy Birthday out of us).
We are also not loud.
Why the name Trip Hazard?
It basically came about by accident. The band started some years ago based on primarily a group of ex-professional/semi-pro musicians who still wanted to perform.
We played at many charity events - school fêtes, church bazaars, country shows etc. At one regular church event (regular as in every 2 years) a photographer from the local paper asked the name of the band. It didn't have one but a cable had been run from the church to the grave yard where we were set up (don't ask) and there was a sign, pointing in our direction saying, you've guessed it, 'Trip Hazard'. At last a positive story about Health & Safety.
There is no truth to the story that band acquired its name after a couple of people tried to dance to us. Dancing is allowed provided suitable waivers have been signed.
Some of the band have also played under the banner of the Woodford Wheezards performing, to great acclaim, at events during the annual Woodford festival.
How long is 32 bars? This depends on location, time required and so forth but £150 per musician would be a good guide.
So if you want a real jazz band for an event at home or in a hall or pub or restaurant or wherever, whether it be private, corporate or public, phone 070107 25267 or email for a quote giving timings, location and nature of the event.
A few sound bites
Some live, and decidedly unrehearsed, stuff from the Woodford Festival:
Take the 'A' Train Exactly Like You Indiana Satin Doll
Pennies From Heaven Just Friends This Can't be Love Wave
The tracks below were recorded live, on an mp3 player/recorder, with a bunch of the guys at a jam session:
This text will be replaced by the flash music player if you ebable Java Script.
ABP. 2011_1217


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Brazil: Imprisoned Socialist Ex-President Calls for Calm Following Bolsonaro Win
Former Brazilian Lula Da Silva urged supporters of his socialist Workers Party (PT) on Monday to stay calm and not rush to judgment about what President-elect Jair Bolsonaro's leadership will entail, according to reports.
Ben Kew
30 Oct 2018, 4:07 PM PDT
Bolsonaro Supporters Tell Brazilian Socialists: 'Go to Cuba'
Supporters of Brazil's president-elect Jair Bolsonaro mocked supporters of socialist rival Fernando Haddad on Sunday evening, urging them to move to Cuba if they prefer a leftist government.
Martel: Bolsonaro Won Brazil's Presidency by Not Interrupting the Left's Mistakes
"Jair Bolsonaro being president was a ridiculous proposition two years ago," wrote Igor Gielow in Brazil's Folha de Sao Paulo on Sunday about the president-elect.
Frances Martel
29 Oct 2018, 9:53 AM PDT
Conservative Jair Bolsonaro Elected President of Brazil
Brazilians elected Jair Bolsonaro of the right-wing Social Liberal Party (PSL) their new president Sunday, granting him a double-digit lead over socialist opponent Fernando Haddad.
Brazil's Bolsonaro Makes Final Anti-Corruption Push: 'Our Country Isn't a Criminal Gang'
Conservative firebrand Jair Bolsonaro has made his final pitch to voters ahead of Brazil's presidential election on Sunday, as he prepares to face off against socialist candidate Fernando Haddad in an election that has polarized Latin America's most populous country.
Brazil: Bolsonaro's Poll Lead Narrows on Weekend of Presidential Election
Datafolha, a prominent pollster in Brazil, published the last major Brazilian presidential election poll expected before this weekend on Thursday, finding a sizable, though diminished, lead for conservative Jair Bolsonaro over socialist candidate Fernando Haddad.
26 Oct 2018, 12:17 PM PDT
Brazil: Stabbing, Facebook Censorship Fail to Stop Conservative Jair Bolsonaro's Presidential Lead
Jair Bolsonaro, conservative candidate in Brazil's presidential race, is likely to achieve a historic victory Sunday despite an assassination attempt limiting his campaign schedule and reports of censorship on Facebook.
25 Oct 2018, 10:06 AM PDT
Report: Brazil's Presidential Frontrunner Bolsonaro Spooking Beijing with Anti-China Stance
Communist Party authorities fear the election of conservative firebrand Jair Bolsonaro in Brazil's presidential race this weekend following his remarks warning against Chinese investment, Reuters reported.
Brazilian Socialist Presidential Candidate: Allies 'Probably' Got Rich off Corruption
Brazilian presidential candidate Fernando Haddad of the socialist Workers' Party (PT) said in an interview Monday that that "probably, yes" there were political allies of his who illegally used campaign funds while in office, once again forced to discuss allegations of widespread corruption within the PT.
Brazil: Child Kills Father in Socialist Attack Ad Against Bolsonaro
Fernando Haddad, the socialist Workers' Party (PT) candidate for president of Brazil, published an attack ad on social media Wednesday implying that conservative rival Jair Bolsonaro's victory would result in accidental homicides by children becoming the norm in the country.
Brazil Presidential Poll: Conservative Bolsonaro Has 16-Point Lead over Socialist
A poll published by the Brazilian firm Datafolha on Thursday found conservative presidential candidate Jair Bolsonaro holding a 16-point lead over socialist rival Fernando Haddad, a margin wider than between any two presidential candidates in a run-off in that country since 2002.
Brazil: Socialist Presidential Hopeful Visits Prison for Campaign Marching Orders from Lula
Fernando Haddad, the socialist Workers' Party (PT) candidate for president in Brazil, made his first public act since securing a spot in this month's run-off election a visit to prison on Monday, where PT leader Luiz Inácio Lula da Silva is serving a 12-year prison sentence for corruption.
8 Oct 2018, 7:49 PM PDT
Brazil: Conservative Bolsonaro Wins Round 1 of Presidential Race, Heads to Run-off with Socialist
Conservative candidate Jair Bolsonaro won the first round of Brazil's presidential election Sunday, securing the top spot against socialist Fernando Haddad in a run-off race scheduled for October 28.
Brazil: Conservative Jair Bolsonaro Peaks in Polls Two Days from Presidential Election
Brazil's conservative presidential candidate Jair Bolsonaro reached 39 percent support in a poll released Thursday, a new high placing him 14 points ahead of the second place candidate just three days from the national election.
5 Oct 2018, 12:21 PM PDT
Brazil: Conservative Frontrunner Gaining Support from Socialist Voter Base
Brazil's conservative presidential frontrunner Jair Bolsonaro appears to be gaining support from voters typically considered loyal to the socialist Workers' Party (PT) and could now feasibly win enough votes to prevent a second round run-off, polls this week showed.
Brazil: Bolsonaro Gains 6 Points with Women After Claim He Threatened to Kill Ex-Wife
Brazilian conservative candidate Jair Bolsonaro gained six points among women voters in a poll released Tuesday, less than a week after he was accused of threatening to kill his ex-wife and after a weekend in which leftist feminist protests drew thousands to convene nationwide to reject his candidacy.
Brazil Elections: Poll Finds Modest Boost for Bolsonaro After Stabbing
A poll published by the Brazilian research firm Datafolha on Tuesday found that conservative presidential frontrunner Jair Bolsonaro expanded his lead by two points since being stabbed at a campaign rally last week.
11 Sep 2018, 6:57 PM PDT