text:
\section{Introduction} \label{sec-Intro}
The nonlinear Ermakov-Pinney (EP) equation has long been known to have profound connections with the linear equations of identical operatorial form without the inverse cubic nonlinearity and because of this it has been seen as an example of `nonlinearity from linearity' \cite{KD}. A historical overview has been written by Leach and Andriopoulos \cite{LA} and the fundamental importance of the EP equation for parametric oscillators, both classical and quantum-mechanical, with their vast application reaches, is well established in the literature.

Already in 1880, Ermakov introduced the following pair of equations \cite{E80}
\begin{eqnarray}\label{i-1}
 \left\{ \begin{array}{ll}
 \ddot{y}+\omega^2(t)y=0~,\\
\ddot{x}+\omega^2(t)x- \kappa x^{-3}=0~,
\end{array} \right.
\end{eqnarray}
for which the linear equation is endowed with the so-called Ermakov dynamic invariant
\begin{equation}\label{i-2}
I_{0-\kappa}(x,y,\dot{x},\dot{y})=\kappa\left(\frac{y}{x}\right)^2+(x\dot{y}-y\dot{x})^2~.
 \end{equation}
We label here this invariant by the tuning parameters of the nonlinear term of the two equations. When $\kappa=0$ one gets $I_{00}=W^2$, where $W$ is the Wronskian of two solutions of the linear equation. Thus, Ermakov's invariant can be considered as a generalization of the Wronskian. Modern research on this invariant started in the 1960s when Lewis rediscovered it and also provided applications in quantum-mechanics \cite{lewis67}.
In particular, Ray and Reid \cite{rr} and also Sarlet \cite{s} introduced the following generalized Ermakov systems
\begin{eqnarray}\label{i-es}
 \left\{ \begin{array}{ll}
 \ddot{y}+\omega^2(t)y-\frac{1}{y^3}\frac{f(x/y)}{x/y}=0~,\\
\ddot{x}+\omega^2(t)x -\frac{1}{x^3}\frac{g(y/x)}{y/x}=0~,
\end{array} \right.
\end{eqnarray}
and their associated invariants
\begin{equation}\label{i-inv-fg}
I_{-f-g}=2\int^{x/y}f(\eta)d\eta+2\int^{y/x}g(\eta)d\eta +(x\dot{y}-y\dot{x})^2~.
 \end{equation}
When $f=0$ and $g=\kappa (y/x)$ the invariant $I_{0-\kappa}$ is recovered.
 Recent works on the connections of the Ermakov systems with the nonlinear superposition principle belong to Cari\~nena and collaborators \cite{c1,c2} where the reader can find more references.
 The importance of Ermakov equations stems from the fact that they can be used to model the propagation of laser beams in nonlinear optics \cite{gon}, magneto-gas dynamics \cite{rs}, the mean field dynamics of pancake-shaped Bose-Einstein condensates \cite{herring}, and cosmology \cite{ro,hl} and the same is expected from Ermakov systems.

 \medskip

 In this paper, we determine the general solution of an Ermakov equation with an Abel-integrable nonlinear dissipation $g_\lambda(u)$ and constant `frequency' function $\omega^2(\zeta)=\lambda^2$:

 \begin{equation}\label{ab-h}
 u_{\zeta \zeta}+g_\lambda(u)u_\zeta+\lambda^2u +b u^{-3}=0~.
 \end{equation}
We get the solution using the corresponding integrable Abel equation and also we give a theorem for obtaining the general solution if a particular solution is known. In the latter case, the phase of the solution is of the Milne type \cite{Milne} and the Ermakov invariant for a pair of {\em nonlinear dissipative} Ermakov equations of the type \eqref{ab-h} with different nonlinearity parameters $b$ and $c$ is used in the derivation.
 We emphasize that Ermakov equations with nonlinear dissipation have never been considered before. For the general case of Ermakov equations with a linear dissipative term one has to resort on numerical methods because there are no Lie symmetries and reductions to simpler forms are useful only in particular cases \cite{haas-10}.

\medskip

 The paper is structured as follows. We first discuss briefly the basic properties of the simplest nondissipative Ermakov equation corresponding to the constant `frequency' case.
 We next discuss the special EP equation with dissipation determined by Chiellini's integrability condition for the corresponding Abel equation of the first kind \cite{prev}. Its general solution is obtain through a method that makes usage of the Ermakov invariant of a pair of such dissipative Ermakov equations. Finally, the method is also applied to Chiellini-dissipative Ermakov equations with higher order Ermakov nonlinearities for which we also provide the general solutions.
 The paper ends up with some conclusions and three appendices in which several related mathematical issues are included for self-consistency reasons.

\section{The simplest EP (SEP) equation}\label{S2}

\subsection{Solution of SEP}\label{ssep}

As is well known, if we have two linear independent solutions $u_1$, and $u_2$ to
\begin{equation}\label{a9}
u_{\zeta\zeta} +h(\zeta)u=0,
\end{equation}
then a particular solution of the corresponding EP equation
\begin{equation}\label{a10}
v_{\zeta\zeta}+h(\zeta)v+cv^{-3}=0
\end{equation}
is given by \cite{P}
\begin{equation}\label{a11}
v(\zeta)=\sqrt{u_1^2-\frac{cu_2^2}{W^2}}~,
\end{equation}
where $W$ is the Wronskian of the two linearly independent solutions, while the general solution can be written $v_g(\zeta)=(\alpha_1 u_1^2+\alpha_2 u_2^2+2\alpha_3 u_1u_2)^{1/2}$, with the three constants constrained by the condition $\alpha_1\alpha_2-\alpha_3^2=c$.

\medskip

Let's take the simplest case, i.e., $h(\zeta)=\lambda^2$, a constant.
\begin{equation}\label{a12}
u_{\zeta\zeta} +\lambda^2 u=0~.
\end{equation}

We call the EP equation for this case as SEP
\begin{equation}\label{a13}
v_{\zeta\zeta}+\lambda^2v+cv^{-3}=0~,
\end{equation}
which we also write in the form
\begin{equation}\label{a13bis}
v_{\zeta\zeta}+h_\lambda(v)=0, \qquad h_\lambda(v)=\lambda^2v+cv^{-3}~.
\end{equation}
From (\ref{a11}), its solution can be written in the form
\begin{eqnarray}\label{a14}
 \left\{ \begin{array}{ll}
\tilde{v}_{-}(\zeta)=\sqrt{1+\Big(1-\frac{c}{\lambda^2}\Big)\,{\rm sinh}^2\lambda\zeta} ~, &  \lambda^2<0~,\\
\tilde{v}_{0}(\zeta)=\sqrt{1-c\zeta^2}~, & \lambda^2=0~,\\
\tilde{v}_{+}(\zeta)=\sqrt{1-\Big(1+\frac{c}{\lambda^2}\Big)\sin^2\lambda\zeta}~, & \lambda^2>0~.
\end{array} \right.
\end{eqnarray}
The case $\lambda^2>0$ corresponds to the simple harmonic oscillator.

\medskip

\subsection{SEP equation with Chiellini dissipation}\label{S4}

We build now the Ermakov-Pinney equation with Chiellini-type dissipation as an equation of the following format
 \begin{equation}\label{v-heq}
 v_{\zeta \zeta}+g_\lambda(v)v_{\zeta}+h_\lambda(v)=0~,
 \end{equation}
where $h_\lambda(v)$ is as given in (\ref{a13bis}).  The dissipation term $g_\lambda(v)$ is obtained from $h_\lambda(v)$ using Chiellini's integrability condition \cite{prev}
\begin{equation}\label{Chiell}
\frac{d}{dv}\left(\frac{h(v)}{g(v)}\right)=kg(v),\qquad \qquad k, \, {\rm a\,\, real\,\, constant}
\end{equation}
for Abel's equation of the first kind $dy/dv=h_\lambda(v)y^3+g_\lambda(v)y^2$ corresponding to (\ref{v-heq}). From (\ref{Chiell}) one easily gets
\begin{equation}\label{a19}
g_\lambda(v)=\frac{\lambda^2v^2+cv^{-2}}{\sqrt{k \lambda^2 v^4+c_1 v^2-kc}}~.
\end{equation}
Before proceeding further, we want to mention that one can not get rid of the Chiellini dissipation term $g_{\lambda}(v)$ because this term corresponds to the quadratic nonlinearity of the Abel's equation
\begin{equation}\label{Abel2}
\frac{dy}{dv}=g_\lambda(v)y^2+h_\lambda(v)y^3,
\end{equation}
see Appendix A.

The inverse of the Abel solution, $\frac{1}{\eta}=\frac{g_\lambda(v)}{h_\lambda(v)}|_{k=-2}$, see \cite{prev}, is obtained from
\begin{equation}\label{a20}
\frac{1}{\eta}=\frac{v}{\sqrt{-2 \lambda^2 v^4+c_1 v^2+2c}}~,
\end{equation}
which gives
\begin{equation}\label{a21}
\zeta-\zeta_0=\int \frac{vdv}{\sqrt{-2\lambda^2v^4+c_1v^2+2c}}~.
\end{equation}
Depending on the sign of $\lambda^2 $ we have the following cases which give the {\it general solution} of \eqref{v-heq}

\begin{eqnarray}\label{rs10}
 \left\{ \begin{array}{ll}
v_{-}(\zeta)=\sqrt{\frac{-c_1 \mp \sqrt {16 \tilde{\lambda}^2 c-c_1^2}\sinh\big (2 \sqrt {2} \tilde{\lambda} (\zeta-\zeta_0) \big )}{4  \tilde{\lambda}^2}}~, &  \lambda^2=-\tilde{\lambda}^2<0\\
v_0(\zeta)=\sqrt{c_1(\zeta-\zeta_0)^2-\frac{2c}{c_1}}~, & \lambda^2=0~,\\
v_{+}(\zeta)=\sqrt{\frac{c_1 \pm \sqrt {16 \lambda^2 c+c_1^2}\sin\big (2 \sqrt {2} \lambda (\zeta-\zeta_0) \big )}{4  \lambda^2}}~, & \lambda^2>0.

\end{array} \right.
\end{eqnarray}

It is worth noting that if we take $c=0$, the reduced equation
 \begin{equation}\label{v-hred}
 v_{\zeta \zeta}+g_\lambda(v)v_{\zeta}+\lambda^2v=0
 \end{equation}
 has the harmonic solutions $v_{1r}=\frac{\sqrt{c_1}}{\sqrt{2}\lambda}\sin \sqrt{2}\lambda \zeta$ and $v_{2r}=\frac{\sqrt{c_1}}{\sqrt{2}\lambda}\cos \sqrt{2}\lambda \zeta$ as if the nonlinear dissipation is not acting at all and the equation \eqref{v-hred} is linear. Thus, one can also construct solutions of \eqref{v-heq} in the standard Pinney form. The only feature is that the amplitudes of the harmonic modes are inverse proportional to the frequency.

It is also possible to construct a different form of the general solution for a SEP with Chiellini dissipation in terms of a particular solution as follows. We first get a particular solution from (\ref{rs10}) by fixing $\zeta_0=0$ and $c_1=\gamma$

\begin{eqnarray}\label{r1022}
 \left\{ \begin{array}{ll}
v_{\gamma -}(\zeta)=\sqrt{\frac{-\gamma \mp \sqrt {16 \tilde{\lambda}^2 c-\gamma ^2}\sinh\big (2 \sqrt {2} \tilde{\lambda} \zeta \big )}{4  \tilde{\lambda}^2}}~, &  \lambda^2=-\tilde{\lambda}^2<0\\
v_{\gamma 0}(\zeta)=\sqrt{\gamma \zeta^2-\frac{2c}{\gamma }}~, & \lambda^2=0~,\\
v_{\gamma +}(\zeta)=\sqrt{\frac{\gamma  \pm \sqrt {16 \lambda^2 c+\gamma ^2}\sin\big (2 \sqrt {2} \lambda \zeta \big )}{4  \lambda^2}}~, & \lambda^2>0.

\end{array} \right.
\end{eqnarray}

Then, the solution of the equation
\begin{equation}\label{gen-Erm}
 u_{\zeta \zeta}+g_\lambda(u)u_\zeta+\lambda^2 u +b u^{-3}=0~,
 \end{equation}
 with $g_\lambda$ as given in (\ref{a19}) is provided by the following theorem.

\medskip

{\bf Theorem}.
For the Ermakov equation (\ref{gen-Erm}),
with $v_\gamma(\zeta)$ the particular solution as given in (\ref{r1022}), and $g_\lambda(v)$ given by (\ref{a19}), the general solution $u(\zeta)$ is obtained by

\begin{eqnarray}\label{a24bis}
 \left\{ \begin{array}{ll}
u_{-}(\zeta)=\sqrt{\frac{-I_{bc} \mp \sqrt {-I_{bc}^{2}+4bc}\,{\rm sinh}\big (2 \sqrt {c} (\Theta-\Theta_0) \big )}{2c}}v_{\gamma -}(\zeta)~,  &  \lambda^2=-\tilde{\lambda}^2<0\\
u_{0}(\zeta)=\sqrt{I_{bc}(\Theta-\Theta_0)^2-\frac{b}{I_{bc}}}v_{\gamma 0}(\zeta)~,  &  \lambda^2=0\\
u_{+}(\zeta)=\sqrt{\frac{I_{bc} \pm \sqrt {I_{bc}^{2}+4bc}\,{\rm sin}\big (2 \sqrt {c} (\Theta-\Theta_0) \big )}{2c}}v_{\gamma +}(\zeta)~,  &  \lambda^2>0\\
\end{array} \right.
\end{eqnarray}

where the phase $\Theta=\int \frac 1{v_{\gamma}^{2}}d \zeta$ is of the Milne type \cite{Milne}, and $I_{bc}$ is the following quantity
\begin{equation}\label{a25}
I_{bc}=-b \Big (\frac v u \Big)^2-c \Big (\frac u v \Big)^2+(u_{\zeta} v- u v_{\zeta})^2,
\end{equation}
which is the Ermakov invariant for an Ermakov pair of equations of type \eqref{gen-Erm} of nonlinear parameters $b$ and $c$, respectively.

\medskip

A version of this theorem for the non-dissipative case can be found in a paper by Qin and Davidson \cite{qin}.

\medskip

{\it Proof:}\\

First, we construct the (invariant) quantity $I_{bc}$, using (\ref{a25}).

Then, using $\Theta=\int \frac 1{v_{\gamma}^{2}}d \zeta$, and $\theta =\frac u v$ in (\ref{a25}) we obtain the following separable equation
\begin{equation}\label{a26}
\frac{\theta d \theta}{\sqrt{b+ I_{bc} \theta^2+c \theta ^4}}=d \Theta~.
\end{equation}

(\ref{a26}) has the same format as (\ref{a21}) with $c=-2\lambda^2$, $I_{bc}=c_1$, $b=2c$.

But from $\theta=\frac{u}{v}$, one gets $u=\theta v$ which leads to (\ref{a24bis}).

\medskip

Two more lemmas on $I_{bc}$ are given in the Appendix B, whereas the factorization of the dissipative Ermakov equations on which we focus here can be found in Appendix C.

\subsection{Abel-dissipative SEP equations with $2m-1$ negative power nonlinearity }\label{S6}

In this subsection, we show that the method of obtaining the general solution of the previous section can be also applied to equations with higher order Ermakov nonlinearties and associated Abel dissipation.

Reid has shown in \cite{reid} that the general solution to
\begin{equation}\label{r5}
v_{\zeta \zeta}+h(\zeta)v=q_m(\zeta)v^{-(2m-1)}
 \end{equation}
is
\begin{equation}\label{r4}
v(\zeta) = \left(u_1^m+\frac{\tilde{c}}{(m-1)W^2}u_2^m\right)^{\frac{1}{m}}
 \end{equation}
provided that $u_1$ and $u_2$ are two independent solutions of (\ref{a9}), and
\begin{equation}\label{r6}
q_m(\zeta) =\tilde{c}(u_1u_2)^{m-2}~.
 \end{equation}
Notice that (\ref{r4}) is a direct generalization of (\ref{a11}).
We are interested in a general solution to
\begin{equation}\label{r7}
u_{\zeta \zeta}+g_\lambda(u) u_{\zeta}+h(\zeta)u=q_m(\zeta)u^{1-2m},
 \end{equation}
via the machinery of invariants.

First, let us choose $h(\zeta)=+\lambda^2, 0, -\lambda^2$, then (\ref{r5}) has solutions
\begin{eqnarray}\label{r10}
 \left\{ \begin{array}{ll}
 v_{-}(\zeta)=\big(a^me^{m \lambda \zeta}+\tilde{c}_mb^me^{-m\lambda \zeta}\big)^{\frac{1}{m}}~, &  h(\zeta)=-\lambda^2\\
 v_0(\zeta)=(1+\frac{\tilde{c}}{m-1}\zeta^m)^{\frac{1}{m}}~, & h(\zeta)=0~,\\
v_{+}(\zeta)=\big(a^m\cos {m \lambda \zeta}+\tilde{c}_mb^m \sin{m\lambda \zeta}\big)^{\frac{1}{m}}~, & h(\zeta)=\lambda^2,

\end{array} \right.
\end{eqnarray}

where

\begin{equation}\label{r11}
 \tilde{c}_m=\frac{\tilde{c}}{4\lambda^2(ab)^m(m-1)}~.
 \end{equation}
 For simplification, let us write (\ref{r10}) as

\begin{eqnarray}\label{r12}
 \left\{ \begin{array}{ll}
 v_{-}(\zeta)=\big(Ae^{m \lambda \zeta}+Be^{-m\lambda \zeta}\big)^{\frac{1}{m}}~ \\
 v_0(\zeta)=(1+B_0\zeta^m)^{\frac{1}{m}}\\
v_{+}(\zeta)=\big(A\cos {m \lambda \zeta}+B \sin{m\lambda \zeta}\big)^{\frac{1}{m}}~,

\end{array} \right.
\end{eqnarray}
where $A=a^m$, $B=\frac{\tilde{c}}{4 \lambda^2 a^m (m-1)}$, $B_0=\frac{\tilde{c}}{m-1}$ and by integrating
 $\Theta_{\mp}=\int \frac{1}{{v_{\mp}}^2}d\zeta$ and $\Theta_{0}=\int \frac{1}{{v_{0}}^2}d\zeta$ leads to
\begin{eqnarray}\label{r13}
 \left\{ \begin{array}{ll}
\Theta_{-}(\zeta)=\frac{Ae^{2m \lambda \zeta}+B}{2 \lambda B \big(Ae^{m \lambda \zeta}+Be^{-m\lambda \zeta}\big)^{\frac{2}{m}}}{}_2F_1\Big(1,\frac{m-1}{m};\frac{m+1}{m};-\frac{A}{B}e^{2 m \lambda \zeta}\Big)\\
\Theta_0(\zeta)=\zeta\, {}_2F_1\Big(\frac{1}{m},\frac{2}{m};\frac{m+1}{m};-B_0\zeta^m\Big) \\
\Theta_{+}(\zeta)=-\frac{\sin^{\frac{2}{m}}\big(m \lambda \zeta +\arctan\frac{A}{B}\big)\cos \big(m \lambda \zeta +\arctan\frac{A}{B}\big)}{m \lambda \big(A\cos {m \lambda \zeta}+B \sin{m\lambda \zeta}\big)^{\frac{2}{m}}}{}_2F_1\Big(\frac1 2, \frac 1 2+\frac 1 m ; \frac 3 2;\cos^2\big(m \lambda \zeta +\arctan\frac{A}{B}\big)\Big)~.

\end{array} \right.
\end{eqnarray}

Finally, the solution to (\ref{r7}) is $u=v\theta$, with $\theta$ obtained by integrating (\ref{a26}).

Using the same $\lambda = \frac 1 2 $, together with $a=b=\tilde{c}=c_1=1$, then the solution is the following
\begin{eqnarray}\label{r14}
 \left\{ \begin{array}{ll}
u_{-}(\zeta,m)=\big(e^{\frac {m \zeta}{2}}+\frac{1}{m-1}e^{-\frac {m  \zeta}{2}}\big)^{\frac{1}{m}}\big(-1\mp \sqrt{3}\sinh(\sqrt{2}\Theta_{-})\big)^{\frac{1}{2}}~, & h(\zeta)=-\lambda^2~,\\
u_{0}(\zeta,m)=\big(1+\frac{1}{m-1}\zeta^m\big)^{\frac{1}{m}}\big(\Theta_0^2-1\big)^{\frac{1}{2}}~, & h(\zeta)=0\\
u_{+}(\zeta,m)=\big(\cos{ \frac {m \zeta} 2}+\frac{1}{m-1}\sin {\frac {m \zeta}{ 2}}\big)^{\frac{1}{m}}\big(1\pm \sqrt{5}\sin(\sqrt{2}\Theta_{+})\big)^{\frac{1}{2}}~, & h(\zeta)=\lambda^2~,
\end{array} \right.
\end{eqnarray}

where
\begin{eqnarray}\label{r15}
 \left\{ \begin{array}{ll}
\Theta_{-}(\zeta)=\frac{(m-1)e^{m \zeta}+1}{\Big(e^{\frac {m\zeta}{2}}+\frac{e^{-\frac {m \zeta}{2}}}{m-1}\Big)^{\frac{2}{m}}}\, {}_2F_1\Big(1,\frac{m-1}{m};\frac{m+1}{m};-\left(\sqrt{m-1}e^{\frac{m \zeta}{2}}\right)^2\Big) \\
\Theta_0(\zeta)=\zeta\, {}_2F_1\Big(\frac{1}{m},\frac{2}{m};\frac{m+1}{m};-\frac{1}{m-1}\zeta^m\Big) \\
\Theta_{+}(\zeta)=\frac{2 \sin^{\frac{2}{m}}\big(\frac {m  \zeta}{2} +\arctan{(m-1)}\big)\cos \big(\frac{m\zeta}{2} +\arctan{(m-1)}\big) }{ m \big(\cos \frac {m \zeta} 2 +\frac{1}{m-1} \sin \frac {m \zeta}2 \big)^{\frac{2}{m}}} {}_2F_1\Big(\frac1 2, \frac 1 2+\frac 1 m ; \frac 3 2;\cos^2\big(\frac{m\zeta}{2} +\arctan(m-1)\big)\Big)~.
\end{array} \right.
\end{eqnarray}

Note that for the case $m=2$ which is the standard EP case the solution simplifies to

\begin{eqnarray}\label{r16}
 \left\{ \begin{array}{ll}
u_{-}(\zeta,2)
\sqrt{\left(e^\zeta+e^{-\zeta}\right)\Big(-1\mp \sqrt 3 \sinh \big(\sqrt 2 \arctan e^{\zeta}\big)\Big)}~ \\
u_0(\zeta,2)=\sqrt{(\zeta^2+1)(\arctan^2 \zeta -1)}~\\
u_{+}(\zeta,2)
\sqrt{(\cos\zeta+\sin \zeta ) \Big(1\pm \sqrt 5 \sin \big( \rm arctanh \frac{\cos\zeta-\sin \zeta}{\sqrt 2}\big)\Big)}~.
\end{array} \right.
\end{eqnarray}

Plots of the $u$ solutions for different values of $m$ and all the other parameters set to the value of unity are given in Figs.~(\ref{fig-e1})-(\ref{fig-e5}). Solutions $u_-$ are real, while $u_+$ are periodically pure real and pure imaginary. As for the solution $u_0$ displayed for the case $m=2$ in Fig.~(\ref{fig-e0}), it is pure imaginary on a symmetric interval around the origin and real in the rest. Notice also the diminishing of the amplitudes with increased order of the negative-power nonlinearity. But the most interesting feature of the `dissipative' solutions is that they may have larger amplitudes than the nondissipative ones on some time intervals. This reveals the presence of gain effects. Indeed, from the plots of the function $g(\zeta)$ in Figs.~(\ref{fig-e6})-(\ref{fig-e8}), one can infer that this function is not always dissipative but it also has gain intervals.

\medskip

\section{Conclusion}\label{S-Concl}

A class of dissipative Ermakov-Pinney equations, either with standard $m=2$ or higher-order $m>2$ nonlinearities, and with nonlinear dissipation of the Abel-Chiellini-integrable type has been introduced. The general solutions are obtained directly by the Abel equation route and also using the dynamic invariant of Ermakov pairs of equations of this type and the particular solution of one member of the pair, both in the standard case and in the case of any odd Ermakov nonlinearity. The technique based on Abel's equation we used here is unique to the constant frequency systems and cannot be directly generalized to the case of time-dependent oscillators. This is due to the fact that the Chiellini integrability condition which plays a central role in obtaining the results do not apply to the cases when there exist an explicit dependence on the independent variable. Another remarkable aspect is that the Chiellini nonlinear dissipative function is in fact a dissipation-gain function which could have interesting applications in the propagation of pulses.

\newpage

{\bf Appendix A: The Abel equation}\\

The importance of Abel's equation in its canonical forms stems from the fact that its integrability cases lead to closed form solutions to nonlinear ODEs of the form
\begin{equation}\label{n1p}
u_{\zeta \zeta}+f_2(u) u_{\zeta}  +f_3(u)+f_1(u) u^2_{\zeta}+f_0(u) u^3_{\zeta}=0~.
\end{equation}

This can be expressed by the following Lemma.

\begin{quote}
{\bf Lemma 1}: Solutions to a general second order ODE of type (\ref{n1p}) may be obtained via the solutions to Abel's equation (\ref{Abel}), and vice versa using the following relationship
\begin{equation}\label{n10}
\frac{du}{d\zeta}=\eta(u(\zeta))~.
\end{equation}
\end{quote}

{\bf Proof}: To show the equivalence, one just need the simple chain rule
\begin{equation}\label{eq1}
\frac{d^2u}{d\zeta^2}=\frac{d \eta}{d u}\frac{du}{d\zeta}=\eta \frac{d \eta}{d u}
\end{equation}
which turns (\ref{n1p}) into the second order Abel equation in canonical form
\begin{equation}\label{eq2}
\frac{d \eta}{du}\eta+f_2(u)\eta+f_3(u)+f_1(u)\eta^2+f_0(u)\eta^3=0.
\end{equation}
Moreover, via transformation of the dependent variable
\begin{equation}\label{eq3}
\eta(u)=\frac{1}{y(u)}
\end{equation}
(\ref{eq2}) becomes
\begin{equation}\label{Abel}
\frac{dy}{du}=f_0(u)+f_1(u)y+f_2(u)y^2+f_3(u)y^3
\end{equation}
and letting $\hat{y} =y e^{\int {f_1(u)du}}$, one gets
\begin{equation}\label{n2p}
\frac{d \hat{y}}{du}=f_0(u) e^{- \int{f_1(u) du}}+f_2(u) e^{\int {f_1(u)du}}\hat{y}^2+f_3(u)e^{2\int {f_1(u)du}}\hat{y}^3,
\end{equation}
which is an Abel equation without the linear term.

\bigskip

{\bf Appendix B: Two lemmas for $I_{bc}$}\\

Here we formulate two lemmas related to $I_{bc}$.

\bigskip

{\it Lemma 1: The invariant $I_{bc}$ is related to the factoring functions of the Ermakov equations of the corresponding system.}\\

Let $\Phi_1$, and $\Psi_1$ be the first factoring functions of two nonlinear Ermakov ODEs as in the previous appendix. Then, according to (\ref{a6bis}),
$u=c_u e^{\int \Phi_1 d \zeta}$, and
$v=c_v e^{\int \Psi_1 d \zeta}$. Then, using (\ref{a25}) we have
\begin{equation}\label{a28}
I_{bc}=\theta^2 v^4 (\Phi_1-\Psi_1)^2-m \cosh \Big( \int (\Phi_1-\Psi_1) d \zeta \Big)~,
\end{equation}
where $m=2\Big ( b \frac{c_v^2}{c_u^2}+c \frac{c_u^2}{c_v^2} \Big)$.

\medskip

{\it Lemma 2: $I_{bc}=c_1$. }\\

If one writes (\ref{a25}) as
\begin{equation}\label{a29}
I_{bc}=-b \frac 1{\theta^2}-c \theta^2+\Big(\frac{d\theta}{d \Theta}\Big)^2,
\end{equation}
using chain rule and (\ref{a26}) and by substituting $\Theta=\int \frac {1}{v^2} d \zeta$ leads to $I_{bc} \equiv c_1$.\\

\bigskip

  {\bf Appendix C: Factorization of dissipative Ermakov ODEs}\\

The Ermakov ODEs with nonlinear dissipation-like coefficients, i.e.,

\begin{equation}\label{a1}
u_{\zeta\zeta} +g(u) u_{\zeta}  +h(u)=0~, \qquad h(u)\equiv  h_\lambda(u)=\lambda^2u+q_m(\zeta)u^{-(2m-1)}
\end{equation}
can be factored in the form

\begin{equation}\label{a2}
\left(\frac{d}{d\zeta}-\Phi_2(u)\right)\left(\frac{d}{d\zeta}-\Phi_1(u)\right)u=0~.
\end{equation}
This gives

\begin{equation}\label{a3}
u_{\zeta\zeta}-\frac{d}{d\zeta}\left(\Phi_1(u)u\right)-\Phi_2u_{\zeta}+\Phi_1\Phi_2u=0~.
\end{equation}
Furthermore, employing the grouping of terms used by Rosu and Cornejo-P\'erez \cite{rcp1, rcp2, rcp3}, one gets

\begin{equation}\label{a3a}
u_{\zeta\zeta}-\left(\Phi_1+\Phi_2\right)u_\zeta+\left(\Phi_1\Phi_2\right)u=0~.
\end{equation}

\medskip

Then, we have
\begin{eqnarray}
 \left\{ \begin{array}{ll}
g(u)=& -(\Phi_1+\Phi_2+\frac{d\Phi_1}{du}u)\\
h(u)=& (\Phi_1\Phi_2)u~,
\end{array} \right.
\end{eqnarray}

 \medskip

 From (\ref{a2}), we also have
\begin{equation}\label{a5}
u_{\zeta}=\Phi_1 u
\end{equation}
which leads to
\begin{equation}\label{a6bis}
u=c_1\, e^{\int^{\zeta} \Phi_1(u(x))dx}~.
\end{equation}
This is identical to a well-known result in the case of linear equations, especially in supersymmetric quantum mechanics, where it gives the ground state wavefunction in terms of the superpotential.
Since $\Phi_1=\frac{v_\zeta}{v}$ and $\Phi_1\Phi_2=\frac{h}{v}$, and additionally we know that $v_\zeta=\eta=\frac h g$, then we get
$$\Phi_1=\frac{\eta}{v}=\frac{\sqrt{-2 \lambda^2v^4+c_1 v^2+2 c}}{v^2},$$

$$\Phi_2=g=\frac{\lambda^2v^2+cv^{-2}}{\sqrt{-2 \lambda^2 v^4+c_1 v^2+2c}}~,$$
which is exactly the dissipative term for which the equation is integrable.

\begin{figure} [x]
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{fig1new.eps}
  \caption{(Color online). The dissipative solution $u_-(\zeta)$ (blue) and the non-dissipative solution $v_-(\zeta)$ (red) for the case $m=2$. All the parameters are set to unity in all of the plots.}

  \label{fig-e1}
 \end{figure}

\begin{figure}  [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{fig2new.eps}
  \caption{(Color online).  The modulus square of the same solutions for the case $m=3$ with the same code of colors.}
  \label{fig-e2}
 \end{figure}

\begin{figure}  [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{fig3new.eps}
  \caption{(Color online) The dissipative $u_+(\zeta)$ solution and the non-dissipative $v_+(\zeta)$ solution for the case $m=2$ and the same color code.}
  \label{fig-e3}
 \end{figure}

\begin{figure}  [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{fig4new.eps}
  \caption{(Color online) The modulus square of $u_+(\zeta)$ and $v_+(\zeta)$ solutions for the case $m=3$ and the same color code.}
  \label{fig-e4}
 \end{figure}

\begin{figure} [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{fig5new.eps}
  \caption{(Color online) The modulus square of $u_+(\zeta)$ and $v_+(\zeta)$ solutions for the case $m=4$ and the same color code.}
  \label{fig-e5}
 \end{figure}

\begin{figure}  [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{new-zero.eps}
  \caption{(Color online).  The dissipative solution $u_{0}(\zeta)$ (blue) and the non-dissipative solution $v_{0}(\zeta)$ (red) for the case $m=2$.}
  \label{fig-e0}
 \end{figure}

\begin{figure} [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{g2.eps}
  \caption{(Color online) Chiellini dissipation function $g(\zeta)$ for $v_-$ and $\lambda^2=-\frac{1}{4}$.}
  \label{fig-e6}
 \end{figure}

\begin{figure} [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{g1.eps}
  \caption{(Color online) Chiellini dissipation function $g(\zeta)$ for $v_+$ and $\lambda^2=\frac{1}{4}$.}
  \label{fig-e7}
 \end{figure}

\begin{figure} [!ht
   \centering
    \includegraphics[width= 10.15 cm, height=11 cm]{g3.eps}
  \caption{(Color online) Chiellini dissipation function $g(\zeta)$ for $v_0$ and $\lambda^2=0$.}
  \label{fig-e8}
 \end{figure}


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text:
Q: pots API [object object ] in react native I had a problem sending data to the server.
when I try to submit data via postman successfully with the response below
and if I activate
'Content-Type': 'application / json'
i have a problem that is
JSON Parse error: Unrecognized token '<'
{
    "status": 200,
    "message": "success login",
    "id_kurir": "3",
    "username": "tester",
}

When I try with code, I get an error that is [object object]
this my code :
constructor(props) {
    super(props);
    this.state = {
      Uname : '',
      Upass : ''
    }
  }

  login= ()=>{
    const {Uname,Upass} = this.state;
    fetch('https://example.com/login', {
      method: 'POST',
      // headers: {
      //   'Accept' : 'application/json',
      //   'Content-Type': 'application/json'
      //},
              body: JSON.stringify({
              username: Uname,
              password: Upass
            })
      })
      .then((response) => response.json())
      .then((responseJson) => {
          alert(responseJson);
          console.log(JSON.stringify(responseJson));
        }).catch((error)=>{
          console.log(error);
        })
      Keyboard.dismiss();
  }

           <Form style={styles.mainForm}>
              <Item style={styles.formItems}>
                <Input placeholder="Username" style={styles.Input} onChangeText={Uname => this.setState({Uname})}/>
              </Item>
              <Item style={styles.formItems}>
              <Input style={styles.Input} secureTextEntry={true} onChangeText={(Upass) => this.setState({Upass})}/>
              </Item>

              <View style={styles.Button}>
                {/* <Button block style={styles.mainBtn} onPress={() => this.props.navigation.navigate('home')}> */}
                <Button block info style={styles.mainBtn} onPress={this.login}>
                  <Text style={styles.btnText}>Submit</Text>
                </Button>
              </View>
            </Form>

where is the fault?

A: The server probably a 404 or 500 error. Instead of response.json() use response.text() you will get the html in text.
I assume Your server is not taking JSON formatted body
Try using below code.
Option 1:
fetch('https://example.com/login', {
    method: 'POST',
    body: JSON.stringify({
        username: Uname,
        password: Upass
    })
}).then(response => response.text()).then((text) => {
  if (Platform.OS === 'android') {
    text = text.replace(/\r?\n/g, '').replace(/[\u0080-\uFFFF]/g, '');
    // If android, remove unwanted chars.
  }
  return text;
}).then(response => JSON.parse(response));

Option 2:
fetch('https://example.com/login', {
    method: 'POST',
    body: JSON.stringify({
        username: Uname,
        password: Upass
    })
}).then((response) => response.text()).then((responseJson) => {
    alert(JSON.stringify(responseJson));
    console.log(JSON.stringify(responseJson));
}).catch((error) => {
    alert(JSON.stringify(error));
    console.log(error);
})

redpajama_set_name: RedPajamaStackExchange


Description: It is no surprise that Tom utilizes air brushing skills to paint this canvas. His day job involves being a motorcycle and automobile painter. When he accumulates enough money to travel, he often goes to South America and carves and paints. This particular piece shows a South American country in which the military is taking over. The view is from the passenger portion of the inside of a truck. In the rear view mirror you can see a helmeted soldier standing at the driver's side of the vehicle. Out of the front windshield you can see a black-gloved hand snatching away a baby. There is also a man standing who is completely engulfed in flames while a soldier walks away with his back to him. It appears that this man's protest is being completely ignored by the military establishment. In addition, there is a sign leaning up against the red pick-up truck (occupied by several villagers) which states Total Control in Spanish.


Italian eyewear brand Persol has decided to commemorate their celebrated past with their latest Vintage Celebration Collection.
After the success of last year, the journey into Persol's archive continues. Four new colours from 1960 have been re-discovered, and their vintage flavours will enrich Persol collection.
The journey started in 2013, bringing 4 historical havanas back to life… to continue this year rediscovering other 4 colors which made the spirit of the 60s.
The three main frame models for the collection include the Terra Di Siena 1969, Tabacco Virginia 1961, and Caffe 1968. Each model features six different optical and sun styles, all of which share similar brown colorways – reflected by their respective names. It's really great seeing a brand like Persol remaining true to their identity and what made them so popular to begin with. True classics will never die, a sentiment Persol illustrates time and time again.


text:
Tribunal finds taxpayer not entitled to input tax credits for the purchase of scrap gold
Posted on February 23, 2017 by chrissievers
In Eastwin Trade Pty Ltd and Commissioner of Taxation [2017] AATA 140 the Tribunal found that the taxpayer did not discharge its onus of showing that it was entitled to input tax credits for the purchase of "scrap gold" from suppliers. The taxpayer held tax invoices that were said to record the transactions, but the primary issue before the Tribunal was whether the asserted purchases of gold were real transactions and if so, what was purchased and from who – the Tribunal observing that reality was not sufficiently established by the invoices themselves or by the taxpayer's accounting records.
The purchases and sales of gold by the taxpayer were said to operate as follows:
the seller would contact the taxpayer about a delivery of gold in "dore" (taxable) form and the taxpayer would contact potential buyers
the taxpayer would take delivery of the gold and would lock in the price when buyers came to pick up the gold
the taxpayer would remit payment to the supplier and would receive a purchase invoice from the supplier a few days later
the gold was delivered to the taxpayer at night, in car parks
The taxpayer relied on tax invoices dated 13 January 2014 to 25 September 2014 purportedly evidencing expenditure of $143.3m on the purchase of about three tonnes of gold dore and invoices dated 8 January 2014 to 26 September 2014 purportedly evidencing total sales of $143.9m of a similar quantity of gold dore.
The principle matters relied on by the Commissioner in the objection decision were as follows:
inconsistent supply information – during interviews with the taxpayer in July and August 2014 the taxpayer had identified one entity as its only supplier (first supplier), but only provided information about another supplier (second supplier) after being told that the initial supplier had been incorporated in April 2014.
incorrect or cancelled ABN – the ABN on invoices from the second supplier was that of an apparently unrelated entity, and that had been cancelled on 28 April 2014. The ABN of the first supplier was cancelled in September 2014 with effect from 1 April 2014.
no GST registration – neither of the suppliers were registered for GST
unrelated payments/absence of consideration – all payments contended to have been made by the taxpayer were to a bank account of a company with no demonstrable connection with either supplier
uncorroborated supply – the taxpayer could not provide any contact details for whether supplier – that inability, the "car park" mode of delivery for three tonnes of gold, and the payments to an unrelated recipient, led to an absence of satisfaction that any of the suppliers had in fact supplied the invoiced items to the taxpayer.
no basis to treat documents as a tax invoice – in the absence of satisfaction that a "creditable supply" had in fact occurred there was no basis to exercise the discretion conferred by s 29-70(1B) of the GST Act.
The Tribunal observed that there was objective evidence that the taxpayer had sold gold dore and that this fact was at least consistent with the taxpayer also having purchased gold dore. However, this in itself was not relevantly probative of dore purchases. The Commissioner also made the following contentions:
the taxpayer's sales invoicing practices, with their precise statement of gold content, and absence of complaint from customers, indicated an actual gold content knowledge that could only have been possessed by someone who had created the dore bars from bullion;
there were practicable means, and a significant commercial incentive, for a person to engage in a practice of purchasing gold bullion and smelting it into dore;
the taxpayer's dore bars had a physical appearance consistent with such an operation having been carried out; and
the taxpayer's various transaction records tended to establish the likelihood that it had possession of the gold for long enough to have undertaken such a smelting process.
The Tribunal observed that the Commissioner's hypothesis about the commercial motivation to purchase bullion – in a disguised transaction – and then convert it to dore, involved two main assumptions. The first assumption was that the dore is saleable at a GST inclusive price less than 110% of the "spot price" for fine gold. The second assumption was that the disguised transaction involved a bullion purchase being dishonestly presented as a taxable supply, and either the GST component of the sale not reported (by the vendor), or made the subject of a false claim for input tax credits (by the purchaser). Once that assumption was made, the Commissioner's submissions explained how the smelting of bullion, and its subsequent sale as a taxable supply, could provide a significant commercial benefit to the seller.
The Tribunal noted that the Commissioner's contention was a hypothesis and there was no direct evidence that the taxpayer carried out any bullion conversion activities and the Tribunal accepted that the taxpayer was right to emphasise the absence of evidence tending to establish its participation in the purchase, and subsequent "conversion", of bullion. Nevertheless, the Tribunal found that the critical matter that the taxpayer had to establish was what it did in fact acquire.
The Tribunal concluded (at [92]) (after a detailed analysis of the oral and documentary evidence) that they taxpayer had failed to establish the identity and reality of any "supplier" entity. Given this finding, the Tribunal concluded as follows:
My view is that meaningful conclusions about the detailed "registration", "enterprise" and "consideration" contentions could not be reached where the evidence merely points to the fact of some kind of acquisition, but is devoid of any credible details about the identity and reality of the "supplier" and that entity's circumstances and activities.
The central issue in this case was whether the taxpayer actually made creditable acquisitions of gold dore – i.e., whether the transactions were real. The approach of the Tribunal to this issue was outlined at [24]:
Eastwin's submissions accepted that the evidentiary onus imposed on it by TAA 53 s 14ZZK required it to establish, on the balance of probabilities, that its asserted purchases and sales of gold dore were real transactions. That reality is not sufficiently established either by the invoices themselves:- see Bayconnection Property Developments Pty Ltd and Commissioner of Taxation [2013] AATA 40; (2013) 90 ATR 488 at [86] and RV Investments (Aust) Pty Ltd as Trustee for the RV Unit Trust and Commissioner of Taxation [2014] AATA 158; (2014) 94 ATR 670 at [72]; or by a taxpayer's accounting records:- Richard Walter Pty Ltd v Commissioner of Taxation (1996) 67 FCR 243 at 247 per Lockhart J. Nevertheless, invoices may provide part of the evidence establishing the reality of the underlying transaction, and Eastwin relied on them. This involved Eastwin in grappling with two main factual questions – (i) who was its supplier, and (ii) what was delivered to it.
In this case, the taxpayer actually did sell gold dore. A clear inference is that it must have also purchased gold. The difficulty for the taxpayer was that it could not positively show who it bought the gold from and what it actually bought – in particular whether it bought the gold in dore form (taxable) or as bullion (non-taxable).
← Federal Court finds UberX drivers supply "taxi travel" to customers
UK Upper Tax Tribunal hands down two decisions on VAT and tripartite agreements →

redpajama_set_name: RedPajamaCommonCrawl


Seat plan for admission test published. Student can see exam schedule and search seat plan from here.
Application fee for each unit taka 475/-.
Chittagong University admission test admit card has been published. Applicants can download admit card and Seat Plan to use User ID and password.
Admission test will be held in two shift of each unit. First shift admission test will be started from 09:45am and 2nd shift from 02:15pm. Seet the schedule and the shift is devided by roll number range.
See the details exam schedule from below.
Chittagong University admission test seat plan (2018-2019) given below as an attached file after publishing.


text:
Q: How can I get transaction fee through Coinbase API? How to get a transaction fee before sending transaction through coinbase API?
Or how to set a transaction fee for a transaction through coinbase API?

A: The Coinbase "fee" is the difference between the buy and the sell rate. At the moment It works out to about 1.8%. This is the overall fee, with the miner fees included.
You can query the difference between https://api.coinbase.com/v2/prices/BTC-USD/buy and https://api.coinbase.com/v2/prices/BTC-USD/sell


Mechanical engineering is considered as being the most diverse out of all the engineering disciplines, as it's used in a range of different industries. A mechanical engineer is responsible for designing and constructing various components that are important in industries such as manufacturing and construction.
This field of engineering also plays an extremely important part in how some everyday domestic items work – things that you probably didn't know were products of engineering.
As a leading manufacturer of an extensive range of spring products, including compression springs, we know exactly how important engineering is – especially mechanical engineering. Our springs are used in a large amount of different domestic products, which would all cease to exist without engineering.
Could you imagine a world where engineering didn't exist? A lot of the things that you come across every day simply wouldn't work. In fact, most of the things wouldn't have even been invented without mechanical engineering.
Below we highlighted its importance by imagining a day in the life without engineering – from getting up in the morning, throughout the day, to going to bed in the evening.
The first thing you probably do when you wake up in the morning is reach for your light switch so that you can actually see what you're doing. Unfortunately, in a world where mechanical engineering doesn't exist – neither does your light switch! Oops! Your light switch contains a spring which just wouldn't have been developed yet. In fact, without your electricity meter – you're going to be permanently in the dark for the foreseeable future.
Now you're going to have to attempt to get ready in the dark – at least you can have a shower right? Nope. Without the existence of engineering, your house wouldn't have the pleasure of a shower – because you wouldn't have any water valves providing water anywhere in your house.
You've given up by now, and just want to get to work on time, but your day is about to get a lot worse. You normally cycle to work, as your work is a fair few miles away, and you like to keep healthy. Unfortunately, your super helpful fold up bicycle is nowhere to be found. This is because it requires components that don't even exist in a world where mechanical engineering has disappeared. Not only that, all your door locks have disappeared – so there is no way that you can leave your house unattended today.
You've realised that without an electricity meter, you're not going to be making any cooked meals today. You've eaten the last of the snacks in your house, when you suddenly get a good idea – have a barbeque! It only takes a few minutes to realise that your barbeque is also a victim of a day without engineering, as it can't be made without machinery that has been designed by; you guessed it, a mechanical engineer.
You've had a really rubbish day, in which you haven't been able to get anything done because nothing seems to be working anymore. All you feel like doing is sinking down into your comfy bed and falling asleep – hopefully tomorrow will be better! Unfortunately, your bed which was nice and firm last night, no longer contains the mattress springs that are needed to support you. Without this springs, you might as well be sleeping on the floor. These springs are extremely important for getting a good night's sleep!
As you can see, there are a lot of things we use every single day, that rely heavily on the field of engineering. We wouldn't be able to get anything done, as we helpfully highlighted above.
Here at Airedale Springs, we are extremely proud to be part of the engineering sector; it's a fascinating field that is continuously growing.
All our products are of a high standard, and can be used in a number of different industries. If you have any questions, please contact us by giving us a call on 01535 643456 and a member of our friendly staff will be happy to help you out.


We always have a fully experienced Trail Rider with our group to help explain and guide our newer riders through any new experiences.
Each of our scheduled rides and events throughout the year are fully explained in advance with detailed Trail Ratings, Descriptions, Parking information, Estimated Time Range and suggested supplies and have been ridden prior by one of experienced Trail Leaders.
At Parker Trail Riders we believe in preserving the trails we ride and have a high level of Trail Etiquette we follow both for the safety of our members and the pristine Colorado trails we use.
Our first Ride will be at Dawson's Butte on April 7th! Click here for the flyer.
11mayAll DayTrail Ride "Splish Splash"
This trail ride will include at least one water crossing. An impromptu clinic on water crossing will be included with this ride!
Trail Ride "Summer Fun Ride"
16junAll DayTrail Ride "Summer Fun Ride"
This will be an intermediate level ride.
27julAll DayTrail Ride "Under Stars"
25augAll DayTrail Ride "Harvest Ride"
Trail Ride "Fall Color Ride"
14sepAll DayTrail Ride "Fall Color Ride"
See the fall colors and enjoy a fun trail ride!


text:
The Hellenistic World
The manufacture and material of ancient coinage
Using Coins as Sources
Online publication date: December 2015
3 - The manufacture and material of ancient coinage
from Appendices (by Andrew Meadows)
Peter Thonemann, University of Oxford
DOI: https://doi.org/10.1017/CBO9781316091784.015
Ancient coinage was hand made, in two senses. First, the actual process of striking the coins was carried out by hand. A coin was produced by placing a blank piece of metal on a die set within an anvil, or similar anchoring device. This is known to numismatists as the 'obverse die', or sometimes the 'anvil die'. A second die on the end of a punch (the 'reverse die') was then placed on top of the blank and hit forcefully with a hammer, probably several times. The result was a flat, roundish piece of metal with, usually, designs or 'types' on both sides (Fig. 10.1).
The second hand-crafted element of coin production was the engraving of the designs that appeared on ancient coins. Unlike modern coin dies, which are all mechanically copied from a single master engraving, each ancient die was individually engraved and thus different from every other. These two elements of hand production create an interesting mixture of results. On the one hand, there is an individuality of design of dies, which allows us to trace the products of an ancient mint in a way that is impossible for modern coins. It also allows us to count the number of dies used to produce a particualr coinage, and thus to quantify it. On the other hand, manual striking, although not nearly so fast as modern machine production, allows for the production of thousands of identical or closely similar objects within a very short space of time. Coins, in this sense, are one of the very rare examples from the pre-modern world of mass production.
The substance of ancient coinage was also profoundly different from that of today's coins. In origin, coinage was a monetary instrument of intrinsic value. The earliest coins, produced in Asia Minor from the mid-seventh to mid-sixth century BC were made of carefully controlled amounts of electrum, the alloy of gold and silver. Subsequently, most probably under the influence of the prevailing monetary tradition of the Near East, coinage came largely to be produced in high-quality silver (from the latter part of the sixth century BC through to the first century AD), with gold being produced when circumstances of supply or demand particularly prompted it.
Peter Thonemann


So far, we have preached the entire book of Habakkuk, but in a single sermon. This was inspired by the unbelievable murder of the sons who are members of our congregation. The young man was on his way to church on a Sunday morning, waiting in his car on a cold Alaska morning, when suddenly a crazed man on a murder spree that morning stumbled upon him, took out his gun, and killed him for his car. At such questions, one can only ask "Why?"


The path to self-improvement, self-awareness, or whatever you want to call it is rocky, winding, convoluted, strewn with obstructions (I suspect of our own making), and littered with shiny objects designed to distract us, and keep us from reaching truth. I don't know why it is this way. I just think it is.
For truth is where improvement lies. And of course you all know by now what I think of truth. It like 'fact' is merely a perception. So is truth that personal a thing? Truth or the perception of truth is so personal that it can only be my truth, and not necessarily your truth?
I am seventy-one and no closer to wisdom than the day I was born. Is truth wisdom? Or does wisdom lead us to truth? I think of these things every time I learn something new about myself.
Recently I discovered that under the guise of love I have been judgmental. Judging the actions of those I love, but not realizing it was judging, rather thinking it was love mixed with ennui and fear?
I mentally objected that my nearest and dearest were judging me. There is no question that they love me. And they think their concern is in my best interest.
When you sit in judgement of anyone, you place yourself above them.
You may think you are loving them, but when you judge, that is not love. It is judgement.
To truly love you must not judge but must accept. Right or wrong you accept.
Your love provides a safe place. You are the rock.
We are all human. We make the worst decisions at times. And at those times those who love us never stop.
The most difficult thing is to realize that no matter how old you are there are always lessons to learn. And even more humiliating is the realization that so many others recognize the Truth long before you.
I will never again judge those as right or wrong, those whom I love.
Sometimes we know the truth but for whatever reason choose not to see it, or believe it, because we want it to be something else. The he and she of it can change.
If there is a snake in your life are you willing to look at the truth, as painful as it can be? We glorify truth, but the reality is that truth can be painful. It can hurt to the core. There is nothing easy about truth. Sometimes we can live with what we want to believe but sometimes choosing to not see the truth can be dangerous. Be safe my friends. Be safe.
Run don't walk. It is better to face the truth and be safe. Some of life's snakes do not bite fatally at first. Just nips of discomfort unsettling your mind and soul, confusing you and putting you in constant angst.
The moral of the story is clear but as one who has built in rose colored glasses it took a long time and a few snakes whose bites I survived before I was ready to deal with reality. I rather suspect that a few unfortunate situations we get ourselves into, we in fact had a pretty good inkling would turn into the snake.
Do we hate the snake? No, we just accept its character and nature. You cannot hate it for its nature, we just have to be smart enough to part company ASAP and say NO. Enough is enough is enough.
Amy at http://souldipper.wordpress.com/2012/03/28/occupy-blogosphere-thursday-march-29-2012/#comment-8507 has a brilliant post today including an amazing use of egg shells that I would never have thought of.
Amy of course had a brilliant answer as will most of you and it was not until I was completing my comment to her that I realized Regina's question was for me, unsettling. When I first saw the presentation my heart thrilled to the potential of it all and then the strangest feeling settled over me.
Yup. That feeling was fear. It scares me to think I could do something, achieve something, without fear. Yes Regina, the very thought is freeing. Or it should be. If I let go of my fear?
I'm thinking that before I can leap to fearlessness I am going to require some guidance on getting there. Does anyone else understand the fear of fearlessness or am I just not grasping the whole idea? Am I afraid of being fearless? The answer has to be 'yes'.
Logically I understand that those who excel have set aside any fear preventing success. Would I like to overcome fear. I sure would. It just all seems a little too scary.
Any and all advice is sincerely welcome. There must be a way around this road block.
I can see overcoming fear of some tangible thing or at least trying to overcome it but my fears in some things are actually a security. Or perhaps an excuse.
Raw bundles of energy learning to assimilate into life give all in laughter, running and the work of the day which may include miles of trucks on knees, bionicals that soar to mighty heights and giggling with delight when this little piggy goes to market find restful recharging in the afternoon nap.
The simplicity of giving it your all should be a more obvious lesson to those of us who transitioned from toddler to adult. How did we miss it? At least for most of the grown up persuasion it seems daily toils are an effort and concentration seems to be on getting through it. We utter words, axioms, as though verbalizing acknowledges the wisdom but feel forbidden to actually do it full time. Stop and smell the roses. Love what you do.
The back end of that last one is do what you love and is something I could never quite figure out. For one thing not everyone could say what they love and so wander through live gritting their teeth doing something they think they do not love.
I probably could not have named one thing I loved to do in my youth. Sure, I was a nurse to the core of me and loved it. It was my calling. But as a high schooler I worked every weekend and holiday and whether it was a laundry or grocery store or factory I loved it all. For me I guess the pleasure was in the doing.
What if….we woke up tomorrow and decide to love everything we do? Love that alarm and morning stretch, love that shower and first sip of coffee, love the action of getting dressed, love that drive or walk, love that work?
There are all kinds of songs that say be glad for what we are given. You know it may not change the world but I bet it will change us and who knows energy may abound.
Some have a dream and belief and will reach it but for most of us ordinary folk the true pleasure of life is all around us in the most mundane things. And yes when we earn our rest at day's end it will be one of regeneration although I believe the whole world could use the benefits of an afternoon nap. After all some of the most brilliant people in the world grabbed a little midday shut eye, probably because in their waking hours they gave it their all.
Where is Spatial Visualization When You Need It?
Thinking in pictures. Conceptualizing. Imagination with application. Good taste. Classic lines. Feng Shui. Positive Energy flow.
Heck, I am throwing ideas/things out there like partially cooked spaghetti against a wall, hoping something sticks.
Genes genes the musical fruit, the more you eat the more you …oops that's beans not genes. In my search for perfection or even comfortable mediocrity I am forced to accept the gifts I have naught, as in 'missed the train on that one'.
I am presented with a lovely living, creative, work space in my son and DIL's home and I am bereft, befuddled, beyond the ability to organize. You see, I have no talent. None. In fact my good taste gene is so deficient I do not even have the skill to copy another.
Now maybe you can help. Please visualize. The room is rectangular and while actually measuring would be rather mundane I can describe it as a nice chip shot length, say 9 yards by a comfortable putt of 5 yards.
I have 'things' to place in the room and no idea where to begin because the flow of energy through the current design is nothing more than the bump and grind of error.
By days end there will be some sense of order, of comfort and no doubt a good degree of exhaustion, because thinking in areas where you were never meant to be is taxing on a soul who was I am sure destined to have all and sundry ready to do her bidding. Reality bites. Truly.
I have been thinking about contentment and wondering where the spice of life jumped off my mind rack.
It's funny that it would be on my mind and that thinking about it would be such a challenge and it is. The very thought today is niggling and wriggling and just out of grasp of making sense. And then the clouds of confusion parted as I read my blogs of wisdom and mirth and more wisdom.
Whaaat? It may not be a good thing? In fifteen words she once again rocked my world. You see at this juncture in my life I thought the goal was contentment. Immediately I scolded myself for stupidity, for short sightedness, for allowing a fall into the abyss of paths lost.
I know better than that but somehow I lost sight of the fact that contentment like happiness cannot ever be the goal. It is the product of our work of our actions. It is a reward. We must do we must not just be.
Well Susan, that changes everything in my life. Everything. So now I am off to do, to achieve, to live, to accomplish.
And may all of you do wonderful things today also!


The 21ft deck of my vintage lorry provides ample space to create an arrangement for your Loved One. Each display is unique to you and can reflect your Loved One's profession, their hobby or anything else close to their heart.
Themes can be created to depict the whole spectrum of occupations from a Scaffolder to a Teacher. Some have already been used and some are still on the drawing board for people who are pre-planning their funeral.
Lorry Drivers can have a Theme related to a vehicle they drove or the cargo they often carried and these can range from a simple Flat Bed through to a Triple Decked Livestock Container.
Tradesmen, such as Builders or Plumbers can have their tools, which I can provide, positioned between the Floral Tributes.
If your Loved One's interests or hobby was one of the key things in their life, then a wide range of options exist as I have built many Themes including a Mobile Disco for a part-time Disc Jockey and a two levelled Dolls House approximately 1/6 scale.
Sports Fans can have a suitable environment created behind their main Floral Tribute, Football Shirt or Rugby Ball in front of Posts. Musicians can have a replica Keyboard or Guitar. Motorists can have the rear of a 1950's touring saloon with a hamper on the boot. A Flag associated with your Loved One's homeland can be hung on the head-board.
If young Grandchildren are providing a 'Pillow' then this can be part of a bedstead, including a bed-side light and an alarm clock, if the concept of Grandad going to sleep is an image that makes the concept of death any easier.
The ability exists to secure items on the top of the coffin, including a standard spray or an individual item such as a hat or cuddly toy. A mini Theme could be created on top of the coffin or for Naval Personnel the coffin itself could be transformed into a Battleship or a Submarine.
Any type of coffin can be accommodated of any shape or size and two coffins can be carried side by side allowing people who have died together to be carried together.
You may have your own ideas of what you would like so please don't be afraid to make any suggestion, as it never ceases to amaze me what can be possible with the help from the Support Members of my team. I will be delighted to explore your ideas and build the support structures provided that this is possible within the timescales.
Of course, you don't have to have any theme at all.
Following your decision to use me, your Funeral Director confirms the arrangements. I then speak to the Florist to establish the type and number of Floral Tributes.
Next, I create a drawing of the potential design options and e-mail or fax these to you. Once you confirm you are happy with the design, I build the Support Structures required.
I will take digital pictures of the final display and forward these to you.
The quality of the display is obviously dependant on the skill and imagination of your florist.
I carry a transparent fly sheet which can protect the coffin during inclement weather however, this has only been used once since 2002.
Standard Prices are quoted for carrying the coffin and flowers, the creation of Themes from wooden models or complex Floral Tribute arrangements involve an additional premium.
Please click on the pictures below to see a slide show of any theme that is of particular interest.


Your face when your like wow that wasn't the best intro ….
August is nearly done – thank goodness? Why 'thank goodness' you ask – well because the release weeks at times left much to be desired. September 2014 is definitely promising with a number of new releases. After examining a whole list via amazon.com, here are my 10 most Anticipated albums for September 2014!
I haven't exactly 'hearted' Maroon 5 as much as once did – Overexposed was my least favorite album – but who can resist Adam Levine's vocals seriously? "Maps" is no "This Love," but let's keep our fingers crossed V is truly special.
The Christian rap thing isn't necessarily my lane (being honest), but I am a fan of Lecrae by all means.
Usually, this guy prefers powerhouse vocals, but Jhené Aiko definitely provides an interesting antithetical approach. Her coolness works, or at least it did on Sail Out EP.
It's Barbra Streisand – there really is nothing else to say. The legendary vocalist has a fantastic voice STILL at 72 years old.
Tony Bennett and Lady Gaga really recorded an album? Amazing. Judging by the track list, it's definitely in Tony Bennett's lane, but who wouldn't want to record with a legend? Plus, after ARTPOP was more lukewarmly received, Gaga likely needs to plan her next career/album move.
The Wilco front man is releasing this highly anticipated solo album. Jeff Tweedy is one of the most versatile musicians of the times, and Sukierae should prove to be exceptional.
My girl Jennifer Hudson is back with her long-awaited third album, JHUD. "Walk It Out" definitely satisfied me, even if it was more gimmicky than Hudson's past work, but it wasn't exactly a radio staple. Hopefully, Hudson really tries to promote this album. R&B has been suffering for sales.
It's a shame more people aren't on the Lenny Kravitz bandwagon – he's a truly awesome musician. Regardless is no one else indulges, this guy will be there to buy.
Weezer's last album Hurley wasn't my favorite, but that doesn't dissuade me from being excited about a new album from the aging hipsters.
Previous Post Nicki Minaj's "Anaconda" Video Is A Raunch-Fest!


Overview The Abortion Study Group was formed by the Family Relations Committee to discuss the Yearly Meeting's position on abortion issues. It met monthly for two years, and wrote position papers supporting the pro-life and pro-choice points of view. Records include minutes, reports, correspondence, and miscellaneous papers.
Scope and Contents Records include: Clerk's correspondence, 1981-1985.


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Home Bundesliga Three Clubs That Could Surprise in the Bundesliga This Season
Three Clubs That Could Surprise in the Bundesliga This Season
Andrew Thompson
Bayern Munich's consummate 2-0 win against Borussia Dortmund in the German Super Cup signifies the coming of yet another exciting Bundesliga campaign. It's difficult to look past the Bavarian giants to win yet another title, but beyond that the league looks set for a surprise or two.
Last season we saw the reemergence of Dortmund under Thomas Tuchel, the dark horse run of Mainz under Martin Schmidt, Ingolstadt's impressive mid-table finish and the relegation of a German footballing institution in VfB Stuttgart. What unexpected happenings does the Bundesliga have in store for us this time around? Here are three clubs that could surprise us in the coming season:
They may divide opinion in the German footballing community, but RB Leipzig could be primed to take the Bundesliga by storm. Finishing top of the 2.Bundesliga last season, club head Oliver Mintzlaff and sporting director Ralf Rangnick have set a target to become an established club challenging for Europe within five years. The board has also put the construction of a new 55,000-seat stadium on the docket, further proof of their desire to push forward.
Their business in the transfer market this summer only serves as evidence that they are ready to act on the promise of moving forward. Austrian headmaster Ralph Hasenhuttl, the man responsible for Ingolstadt's impressive showing last season, was brought in after Rangnick moved upstairs. The initial step of having a manager with Bundesliga experience was the right call.
If their move for Hasenhuttl was no doubt a positive, it's Leipzig's transfer business that has made many stand up and take notice. Guinean international Naby Keita, one of the standout performers in the Austrian Bundesliga with Red Bull Salzburg, was purchased for €15million. But it's the business that saw highly-touted German youngster Timo Werner, coming to the club from relegated Stuttgart for €10million, that was just as impressive.
With those additions, Die Roten Bullen will now boast one of the most potent attacking sides in Germany. The likes of Emil Forsberg, Marcel Sabitzer and Davie Selke were already performing admirably for the club, meaning additional reinforcements in midfield and up-front could not only turn a head or two, but it could fire them to mid-table in the club's first ever season in the German top flight.
Potential XI: Gulacsi; Halstenberg, Orban, Nukan, Klostermann; Ilsanker, Keita; Sabitzer, Forsberg, Werner; Selke
Their third-placed finish last season was certainly seen as a massive success, beating out Borussia Monchengladbach and Schalke for the coveted final automatic Champions League place. Already blessed with a myriad of talented footballers, some have tipped the North Rhine-Westphalia club for even bigger things in the season to come.
Manager Roger Schmidt is looked upon favorably as one of the most tactically astute managers in the Bundesliga, and this is the basis for any further success the BayArena side could garner this campaign. He's already brought German wunderkind Julian Brandt through the ranks and made him into a crucial attacking asset down the left-hand side. Another highly-touted German, Jonathan Tah, had a brilliant season last year and is well on his way to becoming one of the most formidable center backs in Germany while still only being just 20 years old.
Schmidt also brought the best out of former Manchester United and Real Madrid wantaway Javier Hernandez, who proved his detractors wrong after a brilliant campaign that saw him bag 17 goals, falling behind only Robert Lewandowski, Pierre-Emerick Aubameyang and Thomas Muller in the goal charts. Already blessed with an excellent XI to challenge both domestically and in Europe, Leverkusen still made some key additions in the transfer market to strengthen the first team.
The deal for Danny Da Costa, the 22-year-old right back from Ingolstadt, is one of the best pieces of business of the entire summer – Leverkusen potentially found their right back for the next six years. With Stefan Kiessling injured and aging, German international forward Kevin Volland was brought in from Hoffenheim, giving him the perfect platform to finally make good on his promise and fire his way up the national team depth chart. The third big piece of business, signing up Austrian international Julian Baumgartlinger, gave Leverkusen arguably the most underrated holding midfielder in the Bundesliga over the last few years.
With added strength in depth, a potential XI that rivals even that of Dortmund, and a tactically brilliant manager, Leverkusen are looking capable of quite the shock this season – beating Dortmund to second place.
Potential XI: Leno; Wendell, Toprak, Tah, Jedvaj; Baumgartlinger, Aranguiz; Calhanoglu; Brandt, Bellarabi, Hernandez
One of the most storied and passionately supported sides in the country, Hamburger SV are coming off poor showings in recent seasons, finishing 16th, 16th, and 10th in the last three campaigns. Though the 2015/16 installment was an improvement in the standings, it is still deemed insufficient for a club with the history that Hamburg has.
Only finding the back of the net 40 times in 34 outings last season, not only did Hamburg fail to score at a consistent enough clip, but they genuinely lacked the requisite creativity beyond the reborn Lewis Holtby. It is this issue that manager Bruno Labbadia has targeted this summer, and the business done by the club that could see them in much better straights this time around.
To address the concerns in the creativity department, Hamburg brought in the highly-rated Filip Kostic from Stuttgart. Though relegated, Kostic was their most influential attacking player (apart from Daniel Didavi), and a move to remain in the Bundesliga is absolutely deserved. Die Rothosen also brought in Croatian youngster Alen Halilovic from Barcelona. Though the move is effectively a two-year loan given the low fee buy-back clause Barca put into the deal, Halilovic has long been tipped to have a bright future, and his creative abilities from central areas will reduce the pressure that rested on Holtby's shoulders last season.
Additional moves were made for young strikers Bobby Wood (from Union Berlin) and Luca Waldschmidt (from Eintracht Frankfurt). Despite the club having decent center forward options in Pierre-Michel Lasogga and Michael Gregoritsch, the pacey options off the bench provided by the young and hungry newcomers can help Labbadia expand on his tactical options.
Though a magical run into Champions League would be the pipe dream to end all pipe dreams, and not at all unattainable, Hamburg is certainly capable of shocking the Bundesliga with a very unexpected finish in the Europa League places. They'll have to beat out the likes of Wolfsburg, Mainz, and Schalke to do it, but we've seen stranger events unfold in the past.
Potential XI: Adler; Ostrzolek, Djourou, Cleber, Sakai; Holtby, Ekdal; Halilovic; Kostic, Muller, Lasogga
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An American, but a lover of the beautiful game, Andrew Thompson has been active in the sport for 25 years as a player, a coach and now a freelance writer. He's a diehard Arsenal supporter, but also has a special place in his heart for Borussia Dortmund and the German Bundesliga. You can find other work of his at Outside of the Boot, A Bergkamp Wonderland, and he is a podcast regular with The Football Hipsters Podcast.


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NLRB Extends Comment Period on Joint-Employer Proposal
Wednesday, October 31, 2018 8:59 AM - stover@abc.org - ABC News, Regulations, GA - Employment -
On Oct. 30, the National Labor Relations Board announced an extension of the comment period on its proposed rule that would set a new standard for determining joint-employer liability under the National Labor Relations Act. The deadline for submitting comments has been extended from Nov. 13 to Dec. 13, 2018.
According to the Sept. 13 NLRB press release, the proposal aims to foster predictability, consistency and stability in the determination of joint-employer status, and therefore clarifies the standard in a way that promotes meaningful collective bargaining and advances the purposes of the NLRB.
Under the proposal, an employer may be found to be a joint employer only if it possesses and exercises substantial, direct and immediate control over the essential terms and conditions of employment and has done so in a manner that is not limited and routine. The "essential terms and conditions of employment" that establish a joint-employer relationship include the ability to hire, fire, discipline, supervise and direct employees of a second employer, according to an analysis published by ABC's General Counsel, Littler Mendelson P.C.
The analysis also discusses the significance of understanding an employer's joint-employer status, saying it can affect bargaining with a union representing jointly employed workers, joint and several liability for unfair labor practices committed by the other employer and labor picketing.
ABC plans to submit comments to the NLRB. The public may submit comments on the proposed rule here.
On Aug. 27, 2015, the Obama NLRB issued a decision in Browning-Ferris Industries, which uprooted more than 30 years of precedent and greatly expanded joint-employer liability under the NLRA. The decision imposed unnecessary barriers to and burdens on contractor and subcontractor relationships throughout the construction industry.
In December 2017, however, the Trump NLRB attempted to reverse BFI in the Hy-Brand case. Unfortunately, in February 2018, the board vacated the Hy-Brand decision for procedural reasons. Thus, BFI is once again the NLRB standard.
ABC has been a vocal opponent of the expanded definition of joint employer, and has supported legal and legislative efforts to restore the standard that was in place for more than 30 years.
« New Video: ABC Student Chapters Help Construction Management Majors Learn and Grow
ABC Announces New Director of Workforce Development »
August Construction Unemployment Rates Down in 49 States Year Over Year
March Construction Unemployment Rates Down Year-over-year in 37 States


Here you can discover the best Allergy, Sinus & Asthma Medicine in Amazon Best Sellers, and find the top 100 most popular Amazon Allergy, Sinus & Asthma Medicine.
Investors may have jettisoned the stock because they anticipated the 2007 slump in patent expirations and its inevitable impact on earnings.
As Ilina perfectly summed it up, this kind of travel 'makes the snow family larger and the world smaller' and you end up growing so much richer from the inside.
She didn't think it was likely he would want to do surgery, though.
Well, but may I say, that Douglas Dare's 'Whelm', in my opinion, is one of the best if not best of all this year.
Kind of messy but makes it easier to use every morning.
The necessity for due inhibition must be impressed upon young people in whom the instinct is strong, easily aroused and precociously developed.
In the meantime, I would ring every doctor in your area to make an appointment, and also leave your number should there be any cancellations in which you will be able to be seen earlier.
So what causes these sensations and what can you do about it?
This is smaller, less bulky, lighter & very organized.
The black DVD-format case, with its graphic white print, just begs you to pick it up and take a closer look.
I stopped using it a try and regain the hair a really beautiful flawless finish regardless of how long it lasted.
I waited too long once with my daughter, took her to the ER for blood in her urine and it was strep, needing IV antibiotics and an overnight stay in the hospital.


Technology | Kopf Logistics Group Now hiring Independent freight agents. Call Jeanie - 574-349-5600 today!
At Kopf, we know you have many options to choose from to haul your freight or load your trucks. That's why Kopf champions investment in technology, whether to optimize the performance of our fleet, or to match your shipping needs with the capabilities and capacity of our contract carrier network. Our business office is professionally staffed with employees trained to utilize TMS technology to simplify shipping processes and allow Kopf to haul more loads. We also make use of a cloud-based disaster recovery system to minimize down time in our business office in the event of an accident or natural disaster.
Our transportation management technology will provide you with a simple, yet powerful way to manage your supply chain. Technology made to measure joins together transportation expertise, solid business practices and people to tap its full power. Exciting features like interface customization and customized reporting automate and analyze your logistics process, saving time and money.
For our shippers, deploying technology is a practical decision centered on our desire to provide an outstanding service experience in a complex marketplace. Hauling freight is our livelihood, and we value building customer relationships that stand the test of time. Our technology allows us to be responsive to your needs and enhances good business decisions time and again.
For our Independent Freight Agents, Kopf's technology helps simplify multi-faceted shipping processes and comply with regulations, so you can focus on developing new business opportunities and grow your sales revenue and commissions.
For our contract carriers, Kopf's technology is designed to give it the ability to quickly match its available freight to your equipment and help you produce more billable miles. We also help you keep reporting costs down, embracing the use of paperless technologies to gather required documents and speed up freight settlements to your bank account.


text:
package it.unibz.inf.ontop.spec.mapping.transformer;

import com.google.common.collect.ImmutableList;
import it.unibz.inf.ontop.spec.mapping.MappingAssertion;

/**
 * Renames variables,
 * so that two mapping source queries do not share a variable name
 */
public interface MappingVariableNameNormalizer {

    ImmutableList<MappingAssertion> normalize(ImmutableList<MappingAssertion> mapping);
}

redpajama_set_name: RedPajamaGithub


The Auckland lawyers at Quay Law | New Zealand.
We are a well established and successful law firm based in Remuera – Auckland, New Zealand.
The approachable and experienced team at Auckland law firm Quay Law enjoy working with a diverse range of successful companies and private clients.
Our focus is always on fostering a personable yet professional relationship that underpins the specialised legal services Quay Law provides to you, in the time frame you require.
Our services are of a high quality, yet are pragmatic and affordable.
Auckland lawyer Ian Mellett of Quay Law, holds a B Comm, LLB, H Dip Tax and is admitted to practice both in New Zealand and overseas.
He is friendly and courteous and focuses on building long-lasting relationships with his clients.
Ian is able to advise you on all aspects as set out in the firm's practice areas.
He is a past member of the Remuera Business Community Council and New Zealand Tax Council.
To contact our Auckland lawyers please call Quay Law on ph: +64 9 5232408.


Buy The Chronicles of Sherlock Holmes by Paul D. Free UK delivery on eligible orders. Okay, in a nutshell, here's the review of The Sherlock Chronicles–buy it. *FREE* shipping on qualifying offers. For fans of the show, this will be an absolute treasure to read. BBC Books's beautiful Sherlock Chronicles is the ultimate guide to our favourite crime drama. Sherlock: Chronicles [Steve Tribe] on Amazon.com. A visually stunning and comprehensive guide to the hit BBC series, Sherlock: Chronicles tells the full story of the show as you've never seen it before. Buy Sherlock: Chronicles by Steve Tribe by Steve Tribe from Waterstones.com today! Gilbert (ISBN: 9780709086871) from Amazon's Book Store.


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What did fanpop use to be like?
go go power rangers!
salut PEDOS!
Okay people, who else is tired of the troll questions?
Can we all agree not to answer any of that perv questions?
Can toi make a LONG liste of foods people with braces can't eat?
Is it just me ou is there an increasing number of mean people on fanpop?
If a fork were made of or would it still be considered silverware?
Isn't Disney World just a people trap operated par a mouse?
Whats yur favori COOKIE???
What song best describes your life?
Knock Knock..Who's there?...Sonny...Sonny Who?
I like pizza yes I do I like pizza how about you?
Ok guys i need ur help:how do u say"'this is heaven'" in French and Spanish?
IT'S SUMMER!!!
type the last 3 letters of your name on Google images and post the picture that comes first.
Answer: Robin: Bin... ¬_¬
Type your name at google's images and post the first picture that comes
WHat will toi do if toi found a talking apple?
I hate my Life very so much!!!
Are toi economical with the truth?
Post the funniest picture ever this compition is only in one heure
These questions are starting to really get annoying...
Love/hate Eminem?
if toi Could change your username,Whatw ould toi change it to?
Do toi tell people about fanpop?
Believe it ou not i was going to die about an heure il y a
Why do we have to respect onions?
Who knows how to get to the hommage House on Sonny With a Chance?
What are u gonna do this summer???
salut WHAT THE?????
Are toi a fighter?
I lay my luv on u...
I'm heartbroken...please help.
what's your favourite season?
CAN toi WATCH ALL OF THIS IN ONE!?!?!?!?
...this...if creepy
Why would there be stinkbugs in the world? I mean honestly! What is their purpose? Do they do anything other than freak people out?
What is your favourite télévision programme?
LUV/hate Avril Lavigne
Love/Hate Chris Brown?
Let's all go get baked!
Love/hate Nicki Minaj?
Who should I do my project on?
Love/Hate Ke$ha
do u think also that he's hot?
if toi r a fan af def leppard what is your fav song par def leppard
What song makes toi jump up out of surprise when toi hear it?
Do toi like pop tarts?
Ever contacted Fanpop?
salut guys,im 'lloonny' but with new account
What's your favori kind of pizza?
Do toi like my icon?
What's your favori kind of chips?
Do toi like to draw?
So I was wondering.
Is there any way..
What do toi think of this song?
Is XxiggyrawkxX a boy ou s girl?
Guys why can't we all just ge along, why do we have to fight?
how can toi tell the difference between snapping Turtles and normal Turtles ?
Does it annoy toi when your parents go through your stuff?
Wanna chat with me?
THE POOR SHIFT BUTTON!
The celebreties in 10 years
am i getting this right??
im soooo boared send me a pic of the most boaring pic u can find....!!!?!?!?!?!
Do toi have a character? If so, Please tell me about them! ^^
Send me a freaky pic plz!?!?!?!?!?!?!?!?!?!?!?
Post a pic of something that means everything to you.
aléatoire picture time!
send me your fav pic in the world
what's toi favori soda
I know that you're probably tired of these kind of questions, but
send me a pic that discrbes toi
Where is Fegelein?
salut YOU!
OK! Wanna have a caption contest here?
Was Alexander the great gay ou not ?
If toi could have any animated character's super power which power do toi choose and who's power?
tell me what u think :D
What would toi do if you...
What's the scariest thing that's ever happened to you?
The most embarrasing thing happened to toi
Do toi think this montrer is stupid?
what is the first game toi ever played?
Person 1: Chuck Norris. Person 2: Where AAAAHHH!!!!! Person 1: Aha made toi look!!! Chuck Norris: *punches person 1* ..... *walks away*
What annoys toi the most these days?
did guys judge girls par their physical apperance?
What is your most favori song...ever?
Who likes...
A bit uncomfortable,but,please answer..
I need someones' opinion.
What are some good songs to listen to after toi break up?
Post the cheesiest line you've ever heard.
seriously NEED help!
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American Lutheran Church
Kingsbury Emergency Management
Record amount of felony drug arrests in Pennington County
by: KELOLAND News
Posted: Nov 14, 2019 / 12:09 PM CST / Updated: Nov 14, 2019 / 12:09 PM CST
PENNINGTON COUNTY, S.D. (KELO) — The Pennington Sheriff's Department says they've made a record amount of felony drug arrests this year.
In a tweet, they say that methamphetamine is to blame for much of the violence in the county.
Methamphetamine is to blame for much of the violence in our communities. Law enforcement is arresting in record numbers. Now we're seeing more resources go into prevention and treatment.
Call to report suspected drug activity. Turn to the Care Campus for treatment options. pic.twitter.com/961lI9RR02
— Pennington County SO (@PennCoSheriff) November 14, 2019
Showing the number of arrests they've made this year compared to 2018. They've arrested a over 1,300 felony drug arrests this year.
Flashback Friday: Winter exchange program in 1984
SIOUX FALLS, S.D. (KELO) -- With winter tightening it's icy grip on KELOLAND Friday, we go back to 1984 to see how one group of exchange students fared in a wintery wonderland.
In this week's Flashback Friday, see how the student's from Thomasville, Georgia, felt about the snow.
DES MOINES, Iowa (AP) - Authorities in Iowa had to round up more than 1,700 piglets after a semi-trailer overturned on a freeway just north of Des Moines.
The crash happened Thursday afternoon when the truck and trailer overturned on an ramp to Interstate 35. Iowa State Patrol troopers had to close the ramp at times as crews worked to capture and unload hundreds of pigs.
Bishop Dudley Hospitality House not turning anyone away during bitterly cold temps
by Brady Mallory / Jan 16, 2020
Going outside for a few minutes in this sub zero weather is uncomfortable. Now imagine living on the streets when it's this cold. That's the reality for many men and women in the area. The Bishop Dudley Hospitality House where staff is making room to help the homeless to get out of the elements.
On Thursday morning, you could find Hashim Gabon reading a book at the Bishop Dudley Hospitality House. He would love to turn the page on this dangerously cold weather.


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What a nice treat!
Ubisoft Is Giving Away Free In-Game Content Every Day This Week
Here's some good news for Ubisoft gamers as the company is giving away free in-game content for your favourite video games every day this week!
Credit: Ubisoft
The free content is part of Ubisoft's 'Happy Holidays' giveaway campaign and it kicked off yesterday (December 14th) with free DLC for Assassin's Creed: Valhalla.
Yesterday Ubisoft gave owners of Assassin's Creed: Valhalla the Seafarer Settlement Pack and the Legendary Bayek outfit (inspired by 2017's Assassin's Creed: Origins) for both the female and male versions of Eivor.
? 1 free gift per day!
? From December 14 to December 18.
? Today's gift: Assassin's Creed Valhalla Rewards pack.
? https://t.co/DlFzQzZKx1
— Ubisoft (@Ubisoft) December 14, 2020
Both DLC packs are available for all platforms on which Assassin's Creed: Valhalla is available but you'll only have 24 hours from the launch of the free content to claim it. The free content will go live at 1pm GMT/8am ET each day.
So hopefully by the time you read this article and if you're fast enough, you'll be able to claim the Seafarer Settlement Pack and the Legendary Bayek outfit, but if not you'll at least have something new to claim.
To claim all the free content from Ubisoft's Happy Holidays giveaway campaign you'll just have to register via Ubisoft Connect or Ubisoft.com.
If you don't own Assassin's Creed: Valhalla or any of the content given away with the associated games included in the giveaway, you can still claim the free content to be used at a later date as confirmed via the tweet below.
You can still claim the gift and you will be able to access when you have a copy of the game ?
Following the launch of Assassin's Creed: Valhalla sales were so good that launch was twice as successful as 2018's Assassin's Creed: Odyssey.
In our review of Assassin's Creed: Valhalla we said that the game is "definitely worthy of the Assassin's Creed name".
However "It doesn't quite improve on Odyssey in enough ways for me to say that it's better," You can read our review of Assassin's Creed: Valhalla here.
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Featured Image Credit: Ubisoft
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Hearing the news that you are being made redundant is never easy to absorb and much like when any relationship ends it is always better to hear the news in person.
But with the invention of the internet and mobile phones it is no longer the case that employers and employees work out of the same office space, or indeed the same town or city.
With an increasing number of employees working off-site it can sometimes be impossible for an employer to relate the news face-to-face.
It is not essential that an employee is made redundant face-to-face, but it is essential employers consult with members of staff in a fair way over any impending redundancies.
Due to an increase in flexible working and firms outsourcing their work off-site, it can sometimes be impractical for managers to be in close contact with their employees when redundancies occur. If you are based on the opposite side of the country to a number of your staff you may wish to delegate out the task of making them redundant to another member of your staff or senior management. You must make sure that any employees you are making redundant are armed with the same information as other employees that are being made redundant face-to-face.
If one member of staff is based far away it should be enough to contact them via the telephone and send them written confirmation of their redundancy, telling them the exact same information that you told the other members of the workforce in person.
If staff are absent due to illness when you are making redundancies you must make an effort to try and meet with the employee and if possible visit them at home, that is off course if they want this.
You must ensure that the redundancy process you have in place is fair and does not discriminate against those who are not in work. All employees should be told at roughly the same time where possible and each given a chance to speak with somebody about the process.
Making redundancies is never easy and you could find it tempting to try and avoid the issue or deal with it over the telephone or via email.
But if you work within close proximity of the people you are making redundant you should try your utmost to tell them face-to-face. Not only does telling your employees face-to-face show a sense of respect and camaraderie it also helps avoid any potential issues down the line concerning unfair dismissal.
If you cannot tell your employees face-to-face they may have questions that go unanswered and argue that the redundancy process was not explained clearly enough to them when you carried out the redundancy.
The way in which you make your employees redundant is important, it is not just enough to tell them that they have been made redundant you must also support them and go out of your way to tell them directly where possible. Things can be explained better in person and if there are any questions it is better to speak directly about them rather than decipher what the other is thinking over the telephone or email.
Hi I was made redundant on the 28/02/19 we were told when we got home from work after being there all day . They told us all not to bother coming back as the company was going into administration. We have had no consultation period or letters just out last pay slip and p45 . And a letter telling us a code for claiming our redundancy from the government. Should we have had a consultation period there were 23 staff .
We are on a 30 day consultation (from 5/3/19) period. After that our whole team of five face a 30 day notice period of redundancy. We have also been told not to let the 20 plus colleagues in a small office know the company has made this decision. We are aware that only 1.3 of the five jobs is safe and have been told we need to prove our worth over the 30 consultation period. Is this fair practice?
Good morning, I was told I was part of a redundancy pool and was safe but after they had already made the decision of who they were making redundant. Is this fair process?
You can calculate what you should be officially owed via the gov.uk link here. Much also depends whether there is an upper limit cap i.e (20 years' service) - you would have to speak to your employer directly regarding this matter.
My employer told me my job was at risk of redundancy via email. I work nights but was in later on in the day that we were emailed. I have still not had a face to face meeting. Is this a ok for them to have informed me via email?
Hi my husband has just received a letter from his company saying he is at high risk of redundancy. Along with this letter was a form to fill out for voluntary redundancy. My husband filled this in straight away and took it in to work but they have refused it. Can they do this?