text:
\section{Introduction}
It is well-known that, when a symmetry is used to determine a
first integral for a differential equation, the symmetry provides
an integrating factor for the equation and remains as a~sym\-met\-ry
of the first integral.
For first-order ordinary differential
equations the direct determination of the integrating factor is
known \cite{blumankumei} and algorithms for finding integrating factors for equations
of higher order have been developed. In 1999 Cheb-Terrab and
Roche \cite{chebroche} presented a syste\-ma\-tic algorithm for the
construction of integrating factors for second-order ordinary
differential equations and claimed that their algorithm gave
integrating factors for equations which did not possess Lie point
symmetries. In 2002 Leach and Bouquet \cite{leachbouquet} showed
that for all equations except one of which Cheb-Terrab and Roche \cite{chebroche}
had found integrating factors had symmetries which were not
necessarily point symmetries but generalised or nonlocal. In
the same year, 2002, Abraham-Shrauner \cite{abraham} also wrote a paper to
demonstrate the reduction of order of nonlinear ordinary
differential equations by a combination of first integrals and Lie
group symmetries. The latter and former motivated us hereby to
investigate the underlying
properties of autonomous integrating factors and the associated
integrals treated as equations and as functions.\  Observations
are made and inferred in general for any $n$th-order ordinary
differential equation of maximal symmetry. These will also be
extended to include other types of equations in a separate contribution.

Program {\tt LIE} \cite{head} is used to compute the symmetries
for the different cases considered. The knowledge of the
symmetries of first integrals of the equation does give rise to
some interesting properties of the equation itself. For example,
the Ermakov--Pinney equation \cite{ermakov, pinney} which in its
simplest form is
\begin{gather}
w'' + \frac {K} {w ^ 3} = 0, \label{1.1}
\end{gather}
where $K$ is a constant.  In theoretical discussions the sign of
the constant $K $ is immaterial and in fact it is often rescaled
to unity.

The general form of (\ref {1.1}), {\it videlicet}
\begin{gather*}
\ddot {\rho} +\omega ^ 2 (t)\rho = \frac {1} {\rho ^ 3}
\end{gather*}
occurs in the study of the time-dependent linear oscillator,  be
it the classical or the quantal problem, as the differential
equation which determines the time-dependent rescaling of the
space variable and the definition of `new time'. Some of the
references for this are \cite{lewis67, lewis68}.

Another origin of (\ref {1.1}) --- of particular interest in this
work --- is as an integral of the third-order equation of maximal
symmetry which in its elemental form is $y'''= 0$.

\section{Equations of maximal symmetry}

\begin{definition} We define a first integral $I$ for an
equation of maximal symmetry, $E=y^{(n)}=0$, as
$I=f\big(y,y',y',\ldots ,y^{(n-1)}\big)$, where
\begin{gather*}
\left.\frac{{\mbox{\rm d}}I}{{\mbox{\rm d}}x}\right|_{E=0}=0 \quad \iff \quad
\left.\frac{{\mbox{\rm d}}f}{{\mbox{\rm d}}x}\right|_{E=0}=0.
\end{gather*} This means that, if $g\big(x,y,y',y'',\ldots ,y^{(n-1)}\big)$ is an
integrating factor, then
\begin{gather*}
\left.\frac{{\mbox{\rm d}}I}{{\mbox{\rm d}}x}\right|_{E=0}=\left.g
E\left(x,y,y',\ldots ,y^{(n)}\right)\right|_{E=0}=0.
\end{gather*}
\end{definition}

We start by considering the well-known third-order ordinary differential equation
of maximal symmetry
\begin{gather}
y'''=0\label{1}
\end{gather}
 which has seven Lie point
symmetries. These are
\begin{gather}
G_{1} = \partial_{y},\qquad
G_{2} = x \partial_{y}, \qquad
G_{3} = x^{2} \partial_{y}, \qquad
G_{4} = y\partial_{y},\nonumber\\
G_{5} = \partial_{x},\qquad
G_{6}= x\partial_{x} + y\partial_{y},\qquad
G_{7} = x^2 \partial_{x} + 2xy\partial_{y}.\label{3aa}
\end{gather}
The algebra is $\{A_{1}\oplus_{s} sl(2,{\mathbb R})\}\oplus_s
3A_{1}$. The autonomous integrating factors for \eqref{1} are
$y''$ and~$y$. We list the symmetries and algebra when each of
the integrals is treated as an equation and as a function.

When we multiply $y'''=0$ by the integrating factor $y''$,
we obtain $y'' y'''=0$. Integration of this expression
gives $\mbox{$\frac{1}{2}$} \left({y''}\right){}^{2}=k$,
where $k$ is a constant of integration. This gives rise to three cases which we list as follows:
\begin{gather*}\arraycolsep=0em
\begin{array}{lll}
\multicolumn{1}{c}{y''=0} & &\multicolumn{1}{c}{y'' = k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},\vspace{1mm}\\
G_2 = x\partial_{y}, && G_2 = x\partial_{y},\vspace{1mm}\\
G_3 = y \partial_{y}, && G_3 =\left(\dfrac{1}{2} x^2 k - y\right)\partial_{y},\vspace{1mm}\\
G_4 = \partial_{x},& & G_{4} = \partial_{x} + 2xk\partial_{y},\vspace{1mm}\\
G_5 = x\partial_{ x}, && G_5 = x \partial_{x} + x^2 k \partial_{y},\vspace{1mm}\\
G_6 = x^2\partial_{x}+ x y \partial_{y}, &\qquad\qquad\qquad & G_6 = x^2 \partial_{x} +
\left(xy+\dfrac{1}{2} x^3 k\right)\partial_{y},\vspace{1mm}\\
G_7 = y\partial_{x},&& G_7 = \left(y-\dfrac{3}{2} x^2 k\right) \partial_{x} - x^3 k^2 \partial_{y}, \vspace{1mm}\\
G_8 = xy \partial_{x}+ y^2\partial_{y},& &G_8 = \left(x y -
\dfrac{1}{2} x^3 k\right) \partial_{x} + \left(y^2 - \dfrac{1}{4} x^4
k^2\right)\partial_{y},
\end{array}
\end{gather*}
and, when $y'' = k$ is treated as a function, we have
\begin{gather*}
G_{1} = \partial_{y},\qquad
G_{2} = x \partial_{y},\qquad
G_{3} = \partial_{x},\qquad
G_{4} = x\partial_{x}+2y\partial_{y}.
\end{gather*}

\begin{remark}
When $y'' = k$ is treated as an equation, we have
two cases, that is, $y''=0$ and $y''=k$ for which the algebra is
$sl(3,{\mathbb R}): 2A_{1} \oplus_{s} \{sl(2,{\mathbb R})\oplus A_{1}\}\oplus 2
A_{1}$ \cite{mubarakzyanov631, mubarakzyanov632, mubarakzyanov633}.
If $y''=k$ is treated as a function, the algebra is
$A_{4,9}^{1}: A_{2} \oplus_{s} 2 A_{1}$ \cite{mubarakzyanov631, mubarakzyanov632, mubarakzyanov633, paterasharpwinternitz}.
\end{remark}

If $y$ is used an the integrating factor, we obtain $y y''' = 0$.
Integration of this equation gives $y y'' - \frac{1}{2} {y'}{}^2 = k$ which can
be written as $\big(y^{1/2}\big)'' = {k}/{\big(y^{1/2}\big)^{3}}$ and is the
simplest form of the Ermakov--Pinney equation \cite{ermakov, pinney}.
As before we write down the point symmetries corresponding to the
three cases of the differential equation $u'' = k/u^{3}$, where $u
= y^{1/2}$. Program {\tt LIE}~\cite{head} gives the following:
\begin{gather*}\arraycolsep=0em
\begin{array}{lllll}
\multicolumn{1}{c}{u''=0}  &&\multicolumn{1}{c}{u'' = k/u^3} &&\multicolumn{1}{c}{u'' = k/u^3}\vspace{1mm}\\
G_1 = \partial_{u}, && G_1 = \partial_{x},&& G_{1} = \partial_{x},\vspace{1mm}\\
G_2 = x\partial_{u}, && G_2 = 2x\partial_{x}+u\partial_{u},&& G_2 = 2x\partial_{x}+u\partial_{u},\vspace{1mm}\\
G_3 = u \partial_{u}, && G_3 =x^{2}\partial_{x}+xu\partial_{u},&&G_3 =x^{2}\partial_{x}+xu\partial_{u},\vspace{1mm}\\
G_4 = \partial_{x},&&  &&\vspace{1mm}\\
G_5 = x\partial_{ x}, &&&&\vspace{1mm}\\
G_6 = x^2\partial_{x}+ x u \partial_{u}, &\qquad\qquad &&\qquad\qquad&\vspace{1mm}\\
G_7 = u\partial_{x},&& && \\
G_8 = xu \partial_{x}+ u^2\partial_{u}.&&&&
\end{array}
\end{gather*}
The transformation of $y y'' - \frac{1}{2} {y'}{}^2 = k$ to $u'' = k/u^{3}$
does not make a difference in terms of the symmetries as we just
have a point transformation in this case. The other obvious
integrating factors for \eqref{1} are $1$, $x$ and $\frac{1}{2} x^{2}$ which give
\begin{gather*}\arraycolsep=0em
\begin{array}{rcl}
1\cdot y'''= 0 &\quad\longrightarrow\quad & I_3 = y'',\vspace{1mm}\\
x\cdot y'''= 0 &\quad\longrightarrow\quad & I_2 = xy''-y',\vspace{1mm}\\
\dfrac{1}{2} x ^ 2\cdot  y'''= 0 &\quad\longrightarrow\quad & I_1 = \dfrac{1}{2} x ^ 2y''-xy'+y.
\end{array}
\end{gather*}
(Note that the numbering of the fundamental first integrals
follows the convention given in Flessas {\it et al} \cite{Flessas94, Flessas97}.)
\begin{itemize}
\itemsep=0pt
\item
 The
integration of equation \eqref{1}, which is a feature of the
calculation of the symmetries of all linear ordinary differential
equations of maximal symmetry \cite{mahomed90}, by means of
an~integrating factor gives a variety of results depending upon the
integrating factor used.
\item The characteristic feature of the
Ermakov--Pinney equation is that it possesses the three-element
algebra of Lie point symmetries, $sl(2,{\mathbb R})$, which in itself is
characteristic of all scalar ordinary differential equations of
maximal symmetry.
\end{itemize}

The fourth-order ordinary differential equation $y^{\mbox{\scriptsize iv}}=0$ has
autonomous integrating factors~$y'$ and $y'''$. If we use $y'$ as an integrating factor in
the original equation and integrate, we obtain
\begin{gather}
y'y'''-\frac{1}{2}(y''){}^2=k.\label{9a}
\end{gather}
Equation \eqref{9a} is a generalised Kummer--Schwartz equation
for $k=0$ and for $k\neq 0$ a variation on the Ermakov--Pinney
equation as it can be written in the form
\begin{gather*}
\left((y')^{1/2}\right)''=\left(k\Big/\left((y')^{3/2}\right)\right).\nonumber
\end{gather*}
The three cases for
the integral in \eqref{9a} treated as an equation and as a function
give the following results:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y'y'''-\dfrac{1}{2}({y''})^2=0}  &\qquad&
\multicolumn{1}{c}{y'y'''-\dfrac{1}{2}(y'')^2=k} &\qquad&
\multicolumn{1}{c}{y'y'''-\dfrac{1}{2}(y'')^2=k}\vspace{1mm}\\
G_1 = \partial_{x}, && G_1 = \partial_{x},&& G_{1} = \partial_{x},\vspace{1mm}\\
G_2 = x\partial_{x}, && G_2 = \partial_{y},&& G_{2} =  \partial_{y},\vspace{1mm}\\
G_3 = y \partial_{y}, && G_3 =x\partial_{x}+2y\partial_{y},&&G_{3} = x\partial_{x}+2y\partial_{y},\vspace{1mm}\\
G_4 = \partial_{y}.&& &&
\end{array}
\end{gather*}

The use of $y'''$ as an integrating factor gives $y'''=k$. If $k=0$, then we just have seven point symmetries
as those of equation \eqref{1}.
The two remaining cases give
\begin{gather*}\arraycolsep=0em
\begin{array}{lcl}
\multicolumn{1}{c}{y'''=k}  &\qquad &\multicolumn{1}{c}{y'''=k}\vspace{1mm}\\
G_1 = \partial_{x}, && G_1 = \partial_{x}, \vspace{1mm}\\
G_2 = x\partial_{y}, && G_2 = \partial_{y},\vspace{1mm}\\
G_3 = \dfrac{1}{2}x^{2}\partial_{y}, && G_3 =x\partial_{y},\vspace{1mm}\\
G_4 = \partial_{y},&&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5=x\partial_{x}+\dfrac{1}{2}{x^{3}}k\partial_{y}&&G_{5}=x\partial_{x}+3y\partial_{y},\vspace{1mm}\\
G_{6}=\left(y-\dfrac{1}{6}x^{3}k\right)\partial_{y},&&\vspace{1mm}\\
G_{7}=x^{2}\partial_{x}+\left(2xy+\dfrac{1}{6}{x^{4}}k\right)\partial_{y}. &&
\end{array}
\end{gather*}

Consider the fifth-order equation of maximal symmetry given by
\begin{gather}
y^{\mbox{\scriptsize v}}=0\label{2}
\end{gather}
with autonomous integrating factors $y$, $ y''$ and $y^{\mbox{\scriptsize iv}}$.
If we multiply \eqref{2} by the first integrating factor and integrate, we obtain the integral
\begin{gather}
yy^{\mbox{\scriptsize iv}}-y' y'''+\frac{1}{2}( y'')^{2}=k.\label{3}
\end{gather}
We consider the three cases for \eqref{3} treated as an equation with $k=0$, $k\neq 0$ and as a function.
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{yy^{\mbox{\scriptsize iv}}-y' y'''+\dfrac{1}{2}(y'')^{2}=0}
&\qquad & \multicolumn{1}{c}{yy^{\mbox{\scriptsize iv}}-y' y'''+\dfrac{1}{2}(y'')^{2}=k}
&\qquad &\multicolumn{1}{c}{yy^{\mbox{\scriptsize iv}}-y' y'''+\dfrac{1}{2} (y'')^{2}=k}\vspace{1mm}\\
G_1 = \partial_{x}, && G_1 = \partial_{x},&& G_{1} = \partial_{x},\vspace{1mm}\\
G_2 = x\partial_{x}, && G_2 = x\partial_{x}+2y\partial_{y},&& G_{2} = x\partial_{x}+2y\partial_{y},\vspace{1mm}\\
G_3 = y\partial_{y},&&G_3 = x^{2}\partial_{x}+4xy\partial_{y},&&G_3 = x^{2}\partial_{x}+4xy\partial_{y},\vspace{1mm}\\
G_4 = x^{2}\partial_{x}+4xy\partial_{y}. &&&&
\end{array}\hspace{-10mm}
\end{gather*}
\begin{remark}
For easier closure of the algebra in the first case $x\partial{x}$ can be written as $x\partial_{x}+2y\partial_{y}$.
\end{remark}

\begin{itemize}
\itemsep=0pt
\item
 We also observe that there is no difference when the
integral is treated as a function and as an equation. It is
important to note that, if $y$ is an integrating factor of
$y^{(n)}=0$, then the integral obtained using this integrating
factor always has the $sl(2,{\mathbb R})$ subalgebra.
\item We further
observe that for the peculiar value of the constant, that is, $k=0$, there is the
splitting of the self-similarity symmetry into two homogeneity
symmetries.
\end{itemize}

The integrating factor $y''$ with \eqref{2} gives the
following results
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y''y^{\mbox{\scriptsize iv}}-\dfrac{1}{2}  (y''')^{2}=0}
&\qquad & \multicolumn{1}{c}{y''y^{\mbox{\scriptsize iv}}-\dfrac{1}{2}  (y''')^{2}=k}
&\qquad &
\multicolumn{1}{c}{y''y^{\mbox{\scriptsize iv}}-\dfrac{1}{2} (y''')^{2}=k}\vspace{1mm}\\
G_1 = \partial_{x}, && G_1 = \partial_{x},&& G_{1} = \partial_{x},\vspace{1mm}\\
G_2 = x\partial_{x}, && G_2 = \partial_{y},&& G_{2} = \partial_{y},\vspace{1mm}\\
G_3 = \partial_{y}, && G_3 =x\partial_{y},&&G_{3} =x \partial_{y},\vspace{1mm}\\
G_4 = x\partial_{y},&&G_4=x\partial_{x}+3y \partial_{y},&&G_4=x\partial_{x}+3y \partial_{y},\vspace{1mm}\\
G_5=y\partial_{y}.&&&&
\end{array}
\end{gather*}
If we use $y^{\mbox{\scriptsize iv}}$ as the integrating factor of \eqref{2} and integrate, we obtain
\begin{gather*}
y^{\mbox{\scriptsize iv}}=k.
\end{gather*}
We delineate the three cases below:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y^{\mbox{\scriptsize iv}}=0}  &\qquad &
\multicolumn{1}{c}{y^{\mbox{\scriptsize iv}}=k} &\qquad &
\multicolumn{1}{c}{y^{\mbox{\scriptsize iv}}=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y}&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = x\partial_{y}, && G_2 = x\partial_{y}&& G_{2} = x \partial_{y},\vspace{1mm}\\
G_3 = x^{2} \partial_{y}, && G_3 =\dfrac{1}{2} x^2 \partial_{y}&&G_{3} =x^{2}\partial_{y},\vspace{1mm}\\
G_4 = x^{3} \partial_{y}, &&  G_{4} = \dfrac{1}{6}x^{3}\partial_{y}&&G_{4}= x^{3}\partial_{y},\vspace{1mm}\\
G_5 = y\partial_{ y}, &&G_5 =  \partial_{x}&&G_{5}=\partial_{x},\vspace{1mm}\\
G_6 = \partial_{x}, &&G_6 =6x\partial_{x} + x^{4}k\partial_{y}&&G_{6}=x\partial_{x}+4y\partial_{y},\vspace{1mm}\\
G_7 = x\partial_{x},&& G_7 = \big(24y-x^{3}k\big) \partial_{y},&& \vspace{1mm}\\
G_8 = x^{2}\partial_{x}+ 3xy\partial_{y},&&G_8 = 24 x^2 \partial_{x} + \big(72xy+x^{5}k\big)\partial_{y}.&&
\end{array}
\end{gather*}
The differential equation
\begin{gather}
y^{\mbox{\scriptsize vi}}=0\label{4}
\end{gather}
has integrating factors $y'$, $y'''$ and $y^{\mbox{\scriptsize v}}$. If we use $y'$ as the integrating factor, we obtain
\begin{gather*}
y'y^{\mbox{\scriptsize v}}-y''y^{\mbox{\scriptsize iv}}+\frac{1}{2}( y''')^{2}=
\end{gather*}
which leads to the cases below.
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y'y^{\mbox{\scriptsize v}}-y''y^{\mbox{\scriptsize iv}}+
\dfrac{1}{2} (y''')^{2}=0}  &\qquad &
\multicolumn{1}{c}{y'y^{\mbox{\scriptsize v}}-y''y^{\mbox{\scriptsize iv}}+\dfrac{1}{2} (y''')^{2}=k}
 &\qquad &
\multicolumn{1}{c}{y'y^{\mbox{\scriptsize v}}-y''y^{\mbox{\scriptsize iv}}+\dfrac{1}{2}(y''')^{2}=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = y\partial_{y}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = \partial_{x}, && G_3 =x \partial_{x}+3y\partial_{y},&&G_{3} =x\partial_{x}+3y\partial_{y},\vspace{1mm}\\
G_4 = x \partial_{x}.&& &&
\end{array}\hspace{-10mm}
\end{gather*}

The use of $y'''$ as the integrating factor for \eqref{4} leads to
\begin{gather*}
y'''y^{\mbox{\scriptsize v}}-\frac{1}{2}\big( y^{\mbox{\scriptsize iv}}\big)^2=k.
\end{gather*}

The three cases give the following results:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y'''y^{\mbox{\scriptsize v}}-\dfrac{1}{2} \big(y^{\mbox{\scriptsize iv}}\big)^2=0}  &\qquad&
\multicolumn{1}{c}{y'''y^{\mbox{\scriptsize v}}-\dfrac{1}{2} \big(y^{\mbox{\scriptsize iv}}\big)^2=k} &\qquad &
\multicolumn{1}{c}{y'''y^{\mbox{\scriptsize v}}-\dfrac{1}{2} \big(y^{\mbox{\scriptsize iv}}\big)^2=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = \partial_{x}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3=x\partial_{y}, &&G_3=x\partial_{y}, &&G_3=x\partial_{y},\vspace{1mm}\\
G_4=x^{2}\partial_{y},&&G_4=x^{2}\partial_{y}, &&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5 = y\partial_{y}, &&G_5 = x\partial_{x}+ 4y\partial_{y}, &&G_5 = x\partial_{x}+ 4y\partial_{y},\vspace{1mm}\\
G_6 =x \partial_{x}.&&&&
\end{array}
\end{gather*}
If we use $y^{\mbox{\scriptsize v}}$ as an integrating factor, we obtain
\begin{gather*}
y^{\mbox{\scriptsize v}}=k.
\end{gather*}
We also have the three cases as mentioned above to obtain
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y^{\mbox{\scriptsize v}}=0}  &\qquad &
\multicolumn{1}{c}{y^{\mbox{\scriptsize v}}=k} &\qquad &
\multicolumn{1}{c}{y^{\mbox{\scriptsize v}}=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = y\partial_{y}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = \partial_{x}, &&G_3 = x\partial_{y}, &&G_3 = x\partial_{y},\vspace{1mm}\\
G_4=x\partial_{y},&&G_4=x^{2}\partial_{y},&&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5=x^{2}\partial_{y},&&G_5=x^{3}\partial_{y},&&G_5=x^{3}\partial_{y},\vspace{1mm}\\
G_6=x^{3}\partial_{y},&&G_6=x^{4}\partial_{y},&&G_6=x^{4}\partial_{y},\vspace{1mm}\\
G_7=x^{4}\partial_{y},&&G_7=x\partial_{x}+\dfrac{1}{24}kx^{5}\partial_{y},&&G_7=x\partial_{x}+5y\partial_{y},\vspace{1mm}\\
G_8=x\partial_{x},&&G_8=\left(y-\dfrac{1}{120}kx^{5}\right)\partial_{y},&&\vspace{1mm}\\
G_9=x^{2}\partial_{x}+4xy\partial_{y},&&G_9=x^{2}\partial_{x}+\left(4xy+\dfrac{1}{120}kx^{6}\right)\partial_{y}.&&
\end{array}
\end{gather*}

For the differential equation
$
y^{\mbox{\scriptsize vii}}=0
$
we have the integrating factors $y$, $y''$, $y^{\mbox{\scriptsize  iv}}$
and $y^{\mbox{\scriptsize vi}}$. The integrals corresponding to these integrating factors respectively are
\begin{gather}\arraycolsep=0em
\begin{array}{l}
yy^{\mbox{\scriptsize vi}}-y'y^{\mbox{\scriptsize v}}+y''y^{\mbox{\scriptsize iv}}-\dfrac{1}{2}(y''')^2=k,\vspace{1mm}\\
y''y^{\mbox{\scriptsize vi}}-y'''y^{v}+\dfrac{1}{2}\big(y^{\mbox{\scriptsize iv}}\big)^2=k,\vspace{1mm}\\
y^{\mbox{\scriptsize iv}}y^{\mbox{\scriptsize vi}}-\dfrac{1}{2}\big(y^{\mbox{\scriptsize v}}\big)^{2}=k,\vspace{1mm}\\
y^{\mbox{\scriptsize vi}}=k.
\end{array}
\end{gather}
If $y$ is used as the integrating factor, we have
the integral $yy^{\mbox{\scriptsize vi}}-y'y^{\mbox{\scriptsize v}}+y''y^{\mbox{\scriptsize iv}}-\frac{1}{2}
(y''')^2=k$
which is treated as an equation for $k=0$, $k\neq 0$ and as a function. This gives the following results:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
G_1 = \partial_{x}, &\qquad & G_1 = \partial_{x},&\qquad& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = x\partial_{x}, && G_2 = x\partial_{x}+3y\partial_{y},&& G_2 = x\partial_{x}+3y\partial_{y},\vspace{1mm}\\
G_3 = y\partial_{y}, &&G_3 = x^{2}\partial_{x}+6xy\partial_{y}, &&G_3 = x^{2}\partial_{x}+6xy\partial_{y},\vspace{1mm}\\
G_4=x^{2}\partial_{x}+6xy\partial_{y}.&&&&
\end{array}
\end{gather*}
The integral corresponding to the integrating factor $y''$ leads to the following cases:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y''y^{\mbox{\scriptsize vi}}-y'''y^{\mbox{\scriptsize v}}+\dfrac{1}{2}
\big(y^{\mbox{\scriptsize iv}}\big)^2=0}  &\ \quad &
\multicolumn{1}{c}{y''y^{\mbox{\scriptsize vi}}-y'''y^{\mbox{\scriptsize v}}+\dfrac{1}{2}
\big(y^{\mbox{\scriptsize iv}}\big)^2=k}
&\ \quad
&\multicolumn{1}{c}{y''y^{\mbox{\scriptsize vi}}-y'''y^{\mbox{\scriptsize v}}+\dfrac{1}{2}
\big(y^{\mbox{\scriptsize iv}}\big)^2= k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = \partial_{x}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = x\partial_{y}, &&G_3 = x\partial_{y}, &&G_3 = x\partial_{y},\vspace{1mm}\\
G_4=x\partial_{x},&&G_4=x\partial_{x}+4y\partial_{y},&&G_4=x\partial_{x}+4y\partial_{y},\vspace{1mm}\\
G_5=y\partial_{y}.&&&&
\end{array}
\end{gather*}
For the integrating factor $y^{\mbox{\scriptsize iv}}$ we have the cases:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y^{\mbox{\scriptsize iv}}y^{\mbox{\scriptsize vi}}
-\dfrac{1}{2}\big(y^{\mbox{\scriptsize v}}\big)^{2}=0}
 &\qquad &
\multicolumn{1}{c}{y^{\mbox{\scriptsize iv}}y^{\mbox{\scriptsize vi}}
-\dfrac{1}{2}\big(y^{\mbox{\scriptsize v}}\big)^{2}=k} &\qquad &
\multicolumn{1}{c}{y^{\mbox{\scriptsize iv}}y^{\mbox{\scriptsize vi}}
-\dfrac{1}{2}\big(y^{\mbox{\scriptsize v}}\big)^{2}=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = \partial_{x}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = y\partial_{y}, &&G_3 = x\partial_{y}, &&G_3 = x\partial_{y},\vspace{1mm}\\
G_4 = x\partial_{y},&&G_4=x^{2}\partial_{y},&&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5=x^{2}\partial_{y},&&G_5=x^{3}\partial_{y},&&G_5=x^{3}\partial_{y},\vspace{1mm}\\
G_6=x^{3}\partial_{y},&&G_6=x\partial_{x}+5y\partial_{y},&&G_6=x\partial_{x}+5y\partial_{y},\vspace{1mm}\\
G_7=x\partial_{x}.&&&&
\end{array}
\end{gather*}

The last of the four integrating factors $y^{\mbox{\scriptsize vi}}$
 leads to $y^{\mbox{\scriptsize vi}}=k$. We have for the three cases the following results:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y^{\mbox{\scriptsize vi}}=0}  &\qquad &\multicolumn{1}{c}{y^{\mbox{\scriptsize vi}}=k}
&\qquad &\multicolumn{1}{c}{y^{\mbox{\scriptsize vi}}=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = \partial_{x}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = y\partial_{y}, &&G_3 = x\partial_{y}, &&G_3 = x\partial_{y},\vspace{1mm}\\
G_4=x\partial_{y},&&G_4=\dfrac{1}{2}x^{2}\partial_{y},&&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5=x^{2}\partial_{y},&&G_5=\dfrac{1}{6}x^{3}\partial_{y},&&G_5=x^{3}\partial_{y},\vspace{1mm}\\
G_6=x^{3}\partial_{y},&&G_6=\dfrac{1}{24}x^{4}\partial_{y},&&G_6=x^{4}\partial_{y},\vspace{1mm}\\
G_7=x^{4}\partial_{y},&&G_7=\dfrac{1}{120}x^{5}\partial_{y},&&G_7=x^{5}\partial_{y},\vspace{1mm}\\
G_8=x^{5}\partial_{y},&&G_8=x\partial_{x}+\dfrac{1}{120}kx^6\partial_{y},&&G_8=x\partial_{x}+6y\partial_{y},\vspace{1mm}\\
G_9=x\partial_{x},&&G_9=\left(y-\dfrac{1}{720}kx^6\right)\partial_{y},&&\vspace{1mm}\\
G_{10}=x^{2}+5xy\partial_{y},&&G_{10}=x^{2}\partial_{x}+\left(5xy+\dfrac{1}{3600}k5x^{7}\right)\partial_{y}.&&
\end{array}
\end{gather*}

The differential equation
\begin{gather}
y^{\mbox{\scriptsize viii}}=0\label{6}
\end{gather}
has integrating factors $y'$, $y'''$, $y^{\mbox{\scriptsize v}}$ and $y^{\mbox{\scriptsize vii}}$.
If we use $y'$ in \eqref{6} and integrate the resulting equation, we obtain the integral
\begin{gather}
y'y^{\mbox{\scriptsize vii}}-y''y^{\mbox{\scriptsize vi}}+y'''y^{\mbox{\scriptsize v}}-
\frac{1}{2}\big(y^{\mbox{\scriptsize iv}}\big)^2=k.\label{7}
\end{gather}

The three cases of the integral in \eqref{7}
being treated as an equation with $k=0$ and $k\neq 0$  and as a function are given
respectively below:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
G_1 = \partial_{y} &\qquad & G_1 = \partial_{y}&\qquad & G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = y\partial_{y}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = \partial_{x}, &&G_3 = x\partial_{x}+4y\partial_{y}, &&G_3 = x\partial_{x}+4y\partial_{y},\vspace{1mm}\\
G_4=x\partial_{x}.&&&&
\end{array}
\end{gather*}

If $y'''$ is used as an integrating factor, we obtain
\begin{gather*}
y'''y^{\mbox{\scriptsize vii}}-y^{\mbox{\scriptsize iv}}y^{\mbox{\scriptsize vi}}
+\frac{1}{2}\big(y^{\mbox{\scriptsize v}}\big)^2=
\end{gather*}
with the following respective cases:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
G_1 = \partial_{y}, &\qquad& G_1 = \partial_{y},&\qquad& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = y\partial_{y}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = \partial_{x}, &&G_3 = x\partial_{y}, &&G_3 = x\partial_{y},\vspace{1mm}\\
G_4=x\partial_{y},&&G_4=x^{2}\partial_{y},&&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5=x^{2}\partial_{y}.&&&&
\end{array}
\end{gather*}

The use of $y^{\mbox{\scriptsize v}}$ as an integrating factor gives
\begin{gather}
y^{v}y^{\mbox{\scriptsize vii}}-\frac{1}{2}\big(y^{\mbox{\scriptsize vi}}\big){}^2=k.\label{9}
\end{gather}
Equation \eqref{9} is of the Ermakov--Pinney type. The three cases can be delineated as follows:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y^{\mbox{\scriptsize v}}y^{\mbox{\scriptsize vii}}
-\frac{1}{2}\big(y^{\mbox{\scriptsize vi}}\big)^2=0}  &\qquad
&\multicolumn{1}{c}{y^{\mbox{\scriptsize v}}y^{\mbox{\scriptsize vii}}
-\frac{1}{2}\big(y^{\mbox{\scriptsize vi}}\big)^2=k} &\qquad
&\multicolumn{1}{c}{y^{\mbox{\scriptsize v}}y^{\mbox{\scriptsize vii}}
-\frac{1}{2}\big(y^{\mbox{\scriptsize vi}}\big)^2=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = y\partial_{y}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = \partial_{x}, &&G_3 = x\partial_{y}, &&G_3 = x\partial_{y},\vspace{1mm}\\
G_4=x\partial_{y},&&G_4=x^{2}\partial_{y},&&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5=x^{2}\partial_{y},&&G_5=x^{3}\partial_{y},&&G_5=x^{3}\partial_{y},\vspace{1mm}\\
G_6=x^{3}\partial_{y},&&G_6=x^{4}\partial_{y},&&G_6=x^{4}\partial_{y},\vspace{1mm}\\
G_7=x^{4}\partial_{y},&&G_7=x\partial_{x}+6y\partial_{y},&&G_7=x\partial_{x}+6y\partial_{y},\vspace{1mm}\\
G_8=x\partial_{x}.&&&&
\end{array}
\end{gather*}

If $y^{\mbox{\scriptsize vii}}$ is used as an integrating factor in \eqref{6},
we obtain $y^{\mbox{\scriptsize vii}}=k$ with the following symmetries for each of the three cases:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\multicolumn{1}{c}{y^{\mbox{\scriptsize vii}}=0}  &\qquad&
\multicolumn{1}{c}{y^{\mbox{\scriptsize vii}}=k} &\qquad &
\multicolumn{1}{c}{y^{\mbox{\scriptsize vii}}=k}\vspace{1mm}\\
G_1 = \partial_{y}, && G_1 = \partial_{y},&& G_{1} = \partial_{y},\vspace{1mm}\\
G_2 = y\partial_{y}, && G_2 = \partial_{x},&& G_{2} =  \partial_{x},\vspace{1mm}\\
G_3 = \partial_{x}, &&G_3 = x\partial_{y}, &&G_3 = x\partial_{y},\vspace{1mm}\\
G_4=x\partial_{y},&&G_4=\dfrac{1}{2}x^{2}\partial_{y},&&G_4=x^{2}\partial_{y},\vspace{1mm}\\
G_5=x^{2}\partial_{y},&&G_5=\dfrac{1}{6}x^{3}\partial_{y},&&G_5=x^{3}\partial_{y},\vspace{1mm}\\
G_6=x^{3}\partial_{y},&&G_6=\dfrac{1}{24} x^{4}\partial_{y},&&G_6=x^{4}\partial_{y},\vspace{1mm}\\
G_7=x^{4}\partial_{y},&&G_7=\dfrac{1}{120} x^{5} \partial_{y},&&G_7=x^{5}\partial_{y},\vspace{1mm}\\
G_8=x^{5}\partial_{y},&&G_8=\dfrac{1}{720}x^{6}\partial_{y},&&G_8=x^6\partial_{y},\vspace{1mm}\\
G_9=x^{6}\partial_{y},&&G_9=x\partial_{x}+\dfrac{1}{720}kx^{7}\partial_{y},&&G_{9}=x\partial_{x}+7y\partial_{y},\vspace{1mm}\\
G_{10}=x\partial_{x},&&G_{10}=\left(y-\dfrac{1}{5040}kx^{7}\right)\partial_{y},&&\vspace{1mm}\\
G_{11}=x^{2}\partial_{x}+6xy\partial_{y},&&G_{11}=x^{2}\partial_{x}+
\left(6xy+\dfrac{x^{8}}{5040}k\right)\partial_{y}.&&
\end{array}
\end{gather*}

\section{Relationship between fundamental integrals\\ and integrals obtained from integrating factors}
Consider the example of the third-order ordinary differential equation
$
y'''=0
$
with the three fundamental integrals together with the appropriate
associated point symmetries from the subalgebra $sl(2,{\mathbb R})$:
\begin{gather*}\arraycolsep=0em
\begin{array}{lcl}
G_7 = x^{2}\partial_{x}+2xy\partial_{y},&\qquad& I_1 = \dfrac{1}{2} x^{2} y''-xy' +y,\vspace{1mm}\\
G_6 = x\partial_{x}+y\partial_{y}, && I_2 = xy''-y',\vspace{1mm}\\
G_5 = \partial_{x}, && I_3=y''.\vspace{1mm}
\end{array}
\end{gather*}
The numbering of the symmetries follows that of the listing of Lie point
symmetries in (\ref{3aa}) and the ordering of the integrals is in terms of their solution symmetries.
Then the autonomous integral associated with the integrating factor $y$ comes from the combination
\begin{gather*}
J=I_{1}I_{3}-\frac{1}{2} I_{2}^{2} =yy''-\frac{1}{2} {y'}{}^{2}.
\end{gather*}
\begin{proposition}
All the integrals obtained using $y$ as an integrating factor
always have the $sl(2,{\mathbb R})$ subalgebra whereas the fundamental
integrals only have one of the $sl(2,{\mathbb R})$ elements.
\end{proposition}
\begin{proof}
To prove the first proposition we consider the $sl(2,{\mathbb R})$
subalgebra $\Lambda_{1}=\partial_{x}$, $\Lambda_{2}=x\partial_{x}+y\partial_{y}$ and
$\Lambda_{3}= x^{2}\partial_{x}+2xy\partial_{y}$ and the fundamental integrals
$I_{1}$, $I_{2}$ and $I_{3}$ respectively. Then we have the
following:
\begin{gather*}\arraycolsep=0em
\begin{array}{lclcl}
\Lambda_{1}I_{1} = I_{2}, &\qquad& \Lambda_{2}I_{1}= I_{1},&\qquad& \Lambda_{3}I_{1}= 0,\vspace{1mm}\\
\Lambda_{1}I_{2}= I_{3}, && \Lambda_{2}I_{2}= 0,&& \Lambda_{3}I_{2}= -2I_{1},\vspace{1mm}\\
\Lambda_{1}I_{3}= 0, && \Lambda_{2}I_{3}= -I_{3},&&\Lambda_{3}I_{3}= -2I_{2}.
\end{array}
\end{gather*}

We also observe that $\Lambda_{i}J =0$ for $i=1,2,3$. In fact it is easy
to show that $\Lambda_{i}J =\epsilon_{ijk}I_{j}I_{k}$. This is shown below as follows:
\begin{gather*}
\Lambda_{1}J = I_{2}I_{3}-I_{2}I_{3}=0,\\
\Lambda_{2}J = I_{1}I_{3}-I_{1}I_{3}=0,\\
\Lambda_{3}J = -2I_{2}I_{1}+2I_{1}I_{2}=0.\tag*{\qed}
\end{gather*}\renewcommand{\qed}{}
\end{proof}
In general we have
\begin{gather}
I_{ni}=\sum_{j=0}^{n-i-1}\frac{(-1)^{j}x^{(n-j-i-1)}}{(n-j-i-1)!}y^{(n-j-1)}, \qquad i=0,1,\ldots,n-1,
\end{gather}
so that for $n=3$, $I_{30}=I_{1}$, $I_{31}=I_{2}$ and $I_{32}=I_{3}$.
The symmetries $\Lambda_{1}, \Lambda_{2}$ and $\Lambda_{3}$ operating on the fundamental integrals then yield
in general
\begin{gather*}
\Lambda_{1}I_{ni} = I_{n,i+1},\\
\Lambda_{2}I_{ni}= (1-i)I_{ni},\\
\Lambda_{3}I_{ni}= -(n+i-3)(n-i)I_{n,i-1},\\
I_{nn}=0.
\end{gather*}
If we take for example $\Lambda_{3}I_{3i}= -i(3-i)I_{3,i-1}$ with $n=3$ and $i=0,1,2$, we obtain
\begin{gather*}
\Lambda_{3}I_{30}=0,\\
\Lambda_{3}I_{31}=-2I_{30},\\
\Lambda_{3}I_{32}=-2I_{31},
\end{gather*}
where as above $I_{30}=I_{1}$, $I_{31}=I_{2}$ and $I_{32}=I_{3}$.

\begin{proposition}[\cite{moyoleach}]
If we take the equation of maximal symmetry $y^{(n)}=0$, the
$sl(2,{\mathbb R})$ subalgebra maps back to itself and is preserved.
\end{proposition}

\begin{proposition}
For the fifth-order equation $y^{\mbox{\rm \scriptsize v}}=0$
 the autonomous integral emanating from the integrating factor $y$
  can be obtained from $J=I_{0}I_{4}-I_{1}I_{3}+\frac{1}{2} I_{2}^{2}$, where
\begin{gather*}
I_{0}= \frac{1}{24}x^{4}y^{\mbox{\rm \scriptsize iv}}-\frac{1}{6}x^{3}y'''+
\frac{1}{2} x^{2} y''-xy' +y,\\
I_{1}= \frac{1}{6}x^{3}y^{\mbox{\rm \scriptsize iv}}-\frac{1}{2} x^{2} y'''+xy'' -y',\\
I_{2}= \frac{1}{2} x^{2}y^{\mbox{\rm \scriptsize iv}}- x y'''+y'',\\
I_{3}= x y^{\mbox{\rm \scriptsize iv}}- y''',\\
I_{4}=y^{\mbox{\rm \scriptsize iv}}.
\end{gather*}
\end{proposition}

\begin{proposition}
The fourth-order equation also has an autonomous integral $J$
 defined as $J=I_{1}I_{3}-\frac{1}{2} I_{2}^{2}$, where
\begin{gather*}
I_{1}= \frac{1}{2} x^{2}y'''- x y''+y',\\ I_{2}= x y'''- y'',\\
I_{3}=y'''.
\end{gather*}
\end{proposition}

\begin{proposition}
It can be shown that the differential equation $y^{\mbox{\rm \scriptsize vi}}=0$
also has the autonomous integral $J$ which is defined as
$J=I_{0}I_{6}-I_{1}I_{5}+I_{2}I_{4}-\frac{1}{2} I_{3}^{2}$ with the $I_{i}$ $(i=0,6)$ being redefined appropriately.
\end{proposition}

\section{Conclusion}
If $y^{(n)}=f\big(x,y,y',\ldots ,y^{n-1}\big)$ is an $n$th-order ordinary
differential equation and $g\big(x,y,y',\ldots ,$ $y^{n-1)}\big)$
$=k$ is an integral, the integral obtained by multiplying the
equation by the integrating factor and integrating once possesses
certain symmetries when treated as a function, an equation for
the general constant and a configurational invariant (k=0). It is
important to note that, if $y$ is an integrating factor of
$y^{(n)}=0$, then the integral obtained using this integrating
factor always has the $sl(2,{\mathbb R})$ subalgebra whereas the
fundamental integrals only have one of the $sl(2,{\mathbb R})$ elements. We
further observe that for the peculiar value of the constant,
$k=0$, there is the splitting of the self-similarity symmetry
into two homogeneity symmetries. The third-order ordinary
differential equation is actually special and leads to the
Ermakov--Pinney type equation. The fourth-order ordinary
differential equation $y^{\mbox{\scriptsize iv}}=0$ has $y'$ as one of its
autonomous integrating factors which leads together with the the
original equation upon integration to the generalised
Kummer--Schwartz equation. An extension to other types of
equations will be completed in a separate contribution. The
question of what Lie point symmetries of an ordinary differential
equation are also shared by all its first integrals will form the
basis for the next contribution.

\subsection*{Acknowledgments}
SM thanks the National Research Foundation of South Africa and the Durban Institute of Technology for their support.
PGLL thanks the University of KwaZulu-Natal for its continuing support.

redpajama_set_name: RedPajamaArXiv


text:
Brookes Bell working on mitigating battery fire risks at sea
Brookes Bell is heavily involved in an industry-wide effort to manage the risk of lithium-ion battery fires by providing practical guidance to shipowners and managers, particularly car carriers, ro-ro and ro-pax operators. Whilst the volumes of electrical vehicles moved by sea has increased significantly, IMO safety regulations have not kept pace. Many shipping companies are now implementing changes to their safety systems and operational practices which necessarily go well beyond the minimum standards.
Although electrical vehicles are not inherently dangerous, when they do catch fire, the time and response requirements are very different to other fire types. A combination of improved detection systems, vessel design and crew training can help reduce the risk of a runaway fire occurring which is impossible to extinguish.
Adrian Scales, a Chartered Master Mariner and Brookes Bell's Director of Nautical, has been leading Brookes Bell's efforts in this field for the past 24 months. He says:
"My eyes were opened to the scale of the problem following discussions at one of the weekly NW Outport meetings of the Honourable Company of Master Mariners (HCMM). An experienced Second Officer who was working on a cross-Channel ferry raised the topic. Given my background on ferries, it piqued my interest and enabled me to reflect with my own concerns about how vulnerable the people who work on these ships are when it comes to fires on the vehicle decks. The situation was then cemented as a serious problem when I attended as SCR on a ro-pax fire in Greece during early 2022. This event at which lives were lost as the vessel and her cargo were consumed by fire. Around 30% of all passenger vehicles currently carried on cross-Channel ferries are fully electric or hybrid vehicles."
Lithium-ion fires have some extremely challenging characteristics. They create a self -sustaining reaction (thermal runaway) which is very difficult to stop. The battery cell temperature can rise incredibly fast, within milliseconds, and the energy stored is released very suddenly. They are very hot and can reach 1,200 degrees centigrade. They generate significant quantities of toxic and hazardous gases, present electrocution as well as explosion risks.
But dealing with these types of fire at sea brings in even more challenges. On land, large volumes of water are typically used to douse the fire. But on car carriers and ro-pax vessels with large, spacious longitudinal decks, the stability of the vessel is at risk with this approach. Access to the vehicles on a car carrier is typically restricted with little headroom. Expecting crew to deploy fire blankets is not necessarily the answer given that when a car deck is full, it will take 5 –10 minutes to reach a specific car. Fire blankets themselves can weigh between 25kg and 40kg and the crew deployed will be wearing a full fire suit and breathing apparatus, which take another five minutes to put on. Another option might be carbon dioxide douses, but these degrade over time and are in limited supply.
According to Adrian Scales, much of the current fire safety equipment on board may no longer be fit for purpose. Brookes Bell is working with fire responders, authorities and other industry experts to highlight the anticipated and likely problems that will be faced.
The good news is that the industry is already in the process of developing methodologies to deal specifically with the risks of battery fires on board different vessel types.
The main purpose of current discussions is to try an implement is a simple three step process for ships crews as follows:
DETECT as quickly as possible (heat, smoke and gas detectors and ideally CCTV/IR);
CONTAIN as swiftly as possible (drenchers, CO2, Hi-Fog, boundary cooling etc);
PROTECT/EVALUATE review options and perhaps seek clarification and guidance as to the next steps (boundary cooling, fire teams, SCBA approach etc) from Fire Fighting Experts.
Brookes Bell is one of a number of contributors to the Vehicle Carriage Safety Forum (VCSF) which includes a large number of shipowners committed to investing in equipment, retraining crew and learning from each other for Ro-Ro vessels. Thereafter we are also active members of the Cargo Incident Notification System (CINS), a container shipping line initiative which is working in parallel to VCSF is also looking to consolidate the industry's approach. Brookes Bell is also working with the UK Chamber of Shipping and UK Authorities as part on an initiative to ensure sufficient planning and response is in place to deal with an incident on a vessel off the UK coast or in a UK port.
"We know how the ships work," says Adrian Scales. "We are able to work with other experts to evaluate solutions and develop simple response systems which can hopefully be implemented by any crew."
Brookes Bell is able to call on a multi-disciplinary team of 23 Master Mariners who are based variously in the UK, USA and Asia, and work closely with our inhouse fire experts, scientists and engineers. The specialist lithium battery team led by Adrian Scales includes Danny Millett and Karley Smith from the Master Mariner Team and fire specialists Karwei So and Yvonne Tung from the Scientists Team.
The company investigates, troubleshoots and advises on a broad range of marine and energy matters and enjoys a reputation for being the 'go-to' firm for casualty investigation, forensic analysis, technical dispute resolution and expert witness work. Working across the UK, Europe, Asia Pacific and the Americas Brookes Bell has a global presence. Alongside our investigative and expert witness services, Brookes Bell has a state-of-the-art laboratory, The Lab, providing the marine, energy, industrial and manufacturing industries with access to world-class forensic analysis and investigative services.
Find out more about Brookes Bell's Master Mariner services today
For more maritime and energy industry news and developments, explore the Brookes Bell News and Knowledge Hub…

redpajama_set_name: RedPajamaCommonCrawl


text:
CONSTITUTIONAL AND LEGAL ISSUES RELATING TO ZAKAT ON COMPANIES
In this article, "company" means a limited company.
In my articles written since 2013, I have posed the question supported by my arguments, as to whether a company is liable to pay zakat since, in law, it has a separate legal entity from the shareholders and it is not a natural person capable of believing or disbelieving in the articles of faith (rukun iman) and, therefore is neither a Muslim or a non-Muslim and zakat is a religious obligation on individual Muslims. (The articles are available on my websites.)
In this article, I am focusing mainly on the constitutional and legal issues arising therefrom.
We should begin from List II (State List) of the Ninth Schedule of the Federal Constitution (State List).
"Zakat, Fitrah and Baitulmal or similar Islamic religious revenue;"
We must bear in mind that List II is a legislative list, meaning that matters stated therein are within the jurisdiction of the State Legislative Assembly (SLA) to make laws. Hence, SLA had made provisions regarding payment of zakat. An example is section 86 of the Administration of the Religion of Islam (State of Selangor) Enactment 2003 (Enactment 1 of 2003):
" Section 86. Power to collect and distribute zakat and fitrah
Majlis is empowered to collect and distribute zakat and fitrah due from every Muslim person in the State of Selangor in accordance with Hukum Syarak on behalf of His Royal Highness the Sultan."
Note the words "….empowered to collect ….zakat… due from every Muslim person…." The National Language version uses the words "orang Islam" for the words "Muslim person". There is no definition of "person". However, section 2 defines "Muslim" as follows:
"Muslim" means—
(a) a person who professes the religion of Islam;
(b) a person either or both of whose parents were at the time of the person's birth, a Muslim;
(c) a person whose upbringing was conducted on the basis that he was a Muslim;
(d) a person who is commonly reputed to be a Muslim;
(e) a person who has converted to the religion of Islam in accordance with section 108; or
(f) a person who is shown to have stated, in circumstances in which he was bound by law to state the truth, that he was a Muslim, whether the statement be oral or written;"
Note that in all the subsections, the description attached to the word "person" could only mean that the word "person" refers to a natural person. It cannot be anything else because:
1. Only a natural person can be a Muslim or a non-Muslim, a believer or a non-believer;
2. Zakat, one of the Five Pillars of Islam, is an obligation on Muslims (who must necessary be natural persons);
3. Islamic law, the subject matter of the enactment legislated pursuant to List II (State List), Ninth Schedule of the Federal Constitution, is only applicable to Muslims (who must necessary be natural persons).
Pausing here, the Majlis is empowered to collect zakat from Muslims, who must necessarily be natural persons. I submit that the drafters of the enactment understood the position or did not even think of providing for collection of zakat from companies, because zakat is not an obligation on companies as no company is a Muslim, or, for that matter, a non-Muslim.
Section 21 of Syariah Criminal Offences (Selangor) Enactment 1995 (Enactment No. 9 of 1995) makes it an offence for non-payment of zakat and fitrah:
"Any person who is liable to pay zakat or fitrah but –
(a) refuses or willfully fails to pay such zakat or fitrah; or
(b) refuses or willfully fails to pay such zakat or fitrah through an amil appointed, or any other party authorized, by the Majlis to collect zakat or fitrah,"
Section 37 of the same enactment also makes it an offence for any person who collects zakat without authority.
I submit that these provisions too are only applicable to natural persons who are Muslims for the reasons I have given in discussing section 86 of the Enactment 1 of 2003 above.
In addition:
1. Companies is a federal matter and state law cannot impose zakat obligation on them.
2. A company is not "a person professing the religion of Islam" referred to in the State List.
3. A company is not a Muslim by definition in section 2 of the said enactment and the enactment is not applicable to non-Muslims.
Do not think that there is a lacuna in the law. The law is correct when it legislated that the word Muslim refers only to a natural person. What appears to be one mistake after another only arises when the word is wrongly applied to companies.
Now, let us look at fatwa. I shall only refer to the State of Selangor. The Fatwa Committee of Selangor had issued a fatwa on obligation of companies to pay zakat. In this article, I am not arguing whether it is correct or not. I am merely pointing out that even if it is gazetted, it has no legal effect on companies because:
1. A fatwa of the committee is only binding on individual Muslims. Section 49
(1) provides:
"(1) Upon its publication in the Gazette, a fatwa shall be binding on every Muslim in the State of Selangor as a dictate of his religion and it shall be his religious duty to abide by and uphold the fatwa, unless he is permitted by Hukum Syarak to depart from the fatwa in matters of personal observance."
2. The enactment is made pursuant to the State List which confers jurisdiction to SLA in respect of the "creation and punishment of offences by persons professing the religion of Islam…." A company is not a person "professing the religion of Islam."
3. Section 21 of Enactment No. 9 of 1995 is only applicable to individual Muslims.
4. Syariah Court only has jurisdiction over Muslims.
I repeat that it is not a lacuna in the law. It is the wrong extension of the religious obligation of individual Muslims to legal entities created by human beings that makes the law appears to be wrong.
Now, let us look at section 6A (Tax Rebate) of the Income Tax Act 1967 (ITA 1967). That section was added by act A380 and operative from year of assessment 1977 (I stand corrected if there was a similar earlier provision). That section 6A allows rebate (including for zakat – subsection (3)) to be given to "individual resident".
"individual" is defined in section 2 as follows: '"individual" means a natural person;" In other words, that section only allows tax rebate for zakat to be given to natural persons and not to companies.
I submit that the drafters of section 6A of the ITA 1967 too knew what they were doing. They drafted the law to give tax rebate to natural persons who pay tax because only natural persons can be Muslims and are obliged to pay zakat.
We will now look at subsection (11A) of section 44 of the ITA 1967.
Section 44 is a section applicable to taxpayers, individual and companies, in calculating their total income. Frankly, I do not understand what that section says. However, as we are not calculating the total income of a taxpayer, it does not matter. For our purpose, it is enough to say that in calculating the total income of a taxpayer, individual as well as companies, zakat perniagaan may be deducted.
So, it is argued that the law recognizes that companies do pay zakat periagaan. Therefore, companies are obliged to pay zakat.
I accept that that the law recognizes that companies do pay zakat periagaan as deduction for it is given in calculating the total income of a company. However, that does not mean that, under Shariah, they are obliged to pay zakat. The income tax authority is not the authority to determine whether companies are obliged to pay zakat.
When companies show that they pay zakat perniagaan and ask for deduction similar to that given to individuals, what more in the light of the "fatwa" of the Majlis Fatwa Kebangsaan, certainly the tax authority will accept their representation and urge the government to move the Parliament to provide for it.
These confusions had arisen as a result the imposition of zakat on companies arising from lack of appreciation of the concept of separate legal entity. If you go further, for example, into the issues arising from companies whose shares are owned by Muslims and non-Muslims, haul, what type and whose zakat the companies are obliged to pay and the method of calculating the zakat, we get even more confused. Companies too are equally confused, leading to different practices.
I think, we should retreat to the starting point: zakat is for natural persons who are Muslims. Collect from them whatever zakat from whatever source they are required to pay under Shariah. Tax is for companies. Collect from them whatever tax they are required to pay under the law.


Probably the most important work of historical geography ever written is The Sacred Bridge, by Anson F. Rainey and R. Steven Notley. At $100, you may need convincing that it's worth the sacrifice. I look at it this way: take the number of years left in your life and divide $100 by that. It is worth a few bucks a year to have such an extensive reference tool at arm's length. Leen Ritmeyer has posted a brief review of the book on his blog. If you don't need the original languages, you can cut the price in half by purchasing Carta's New Century Handbook and Atlas of the Bible.
If you'd like a free classic to offset the expensive purchase, you can download the entire work of George Adam Smith's Historical Geography of the Holy Land (pdf). This is the 4th edition (of 26!), but as far as I know, the content is largely the same. I am not sure if residents outside the US have access.
Not sure about $100 for the Sacred Bridge (I'll ask my library to get it); but a free PDF download of Smith is a wonderful deal.
Sadly the Historical Geography of the Holy Land is NOT available here. Any chance someone who has a pdf copy might do the rest of us the service of uploading it to Archive.org?


Farmers' Markets – They're opening up around the Greenbelt which means you can grab your favourite meats, breads, veggies, and beer for your BBQ this long weekend.
Brewery Discovery Routes – We did the planning for you! Visit one (or more) of the breweries listed in our itineraries that will help you discover Ontario's craft brewery scene. Pint in hand, sit back, relax, and take it easy.
Greenbelt Route – Love biking? So do we! Developed by the Waterfront Regeneration Trust these biking trails will take you through natural features, cultural attractions, and local amenities, making it easy to explore the Greenbelt.
Greenbelt Walks – It's unbelievable how much variety the Greenbelt holds, from marshes and wetlands, to forests and ravines, to meadows, rivers, fields, and more. Check out our Greenbelt Walks to find a hike near you and discover the Greenbelt.
Greenbelt Explore – These itineraries will help you experience the beauty and diversity of Ontario's protected Greenbelt. The recommended itineraries can be customized to match any interests and deliver something for everyone.


Advocacy representation in the ECD sector.
4 Member Meetings/ Networking Opportunities a year.
Periodicals and newsletters including up-to-date information on current events and policies within the early childhood development sector as well as resources, articles and publications.
Professional Development Courses and Workshop Access – Gr R training, Teaching the Little Ones, 5 Love Languages, relational and interactive management training at a minimal fee.
Access to wholesale prices and retail discounts to educational equipment.
Preschools 4 Africa Affiliated Schools is an advocacy initiative for the Early Childhood Development Sector and is an umbrella body for all Preschools, Day Cares and Early Childhood Development Centres regardless of the programme they follow.


Well, the weather gods smiled on us this month as veterans from all across the Tampa Bay area converged on the south Skyway rest area for a day of fishing with the Tampa Bay Chapter of Heroes on the Water. Too bad the fish gods didn't go along with the deal. Our first trip in some time that the wind didn't blow, and the fish were nowhere to be found.
Volunteers getting the kayaks ready for our vets.
I like to think that these trips aren't all about the fishing. Once upon a time (for me, anyway) it wasn't a successful trip unless I caught something worth bragging about. But I've learned that there is something more to them. Bonding with a friend or son, letting go of the day's burdens and enjoying what the day has given you, just being on the water and relaxing - these are things our trips supply. I was told by one of the vets joining us for the first time that he just wanted to fish, and that's what he did. He was first out and one of the last ones back, hot and tired, but with a big smile on his face. Just the way we like it.
When kayak fishing, always carry a paddle with you. No matter what.
Thanks to all our volunteers and to John Bishop and Greg Becker for the extra photos. And a big thanks to Mark Robichaux for cooking another fine meal.


In the scope of forest surveys, several flights were performed over plots of land R&SD owned and located in the vicinity of Daugavpils, Eastern Latvia. Flights performed with Phantoms III and IV drones covered pieces of land of circa. 8 ha in area.


text:
Week of 3/27/17
Jeff Hoover photo by Timothy D. Easley
Props with one correction to Franklin Clark for Monday's piece in Central Kentucky News-Journal: Bestiality bills die in legislative session. It looks like Clark reached out to Kentucky Farm Bureau, Kentucky Houndsmen, two Republican legislators, plus ASPCA and HSUS. Amazingly, only the Houndsmen were unavailable for comment.
Jeff Hoover's spokesperson went on record saying the short 2017 session was reserved for "serious, economy-related bills" — does the House Speaker think sexual assault doesn't deserve to be taken as seriously as, say, protecting the rights of students to distribute political leaflets on school grounds? (Yeah, that one passed.) One correction though: Clark reports that first degree animal cruelty happens "when a person makes four-legged animals fight for pleasure or profit." That's a forgivable mistake, given that Kentucky's animal cruelty law outlawed countless forms of animal fighting for over 30 years. In the 2016 session, however, the General Assembly stripped the KRS of everything but dog-on-dog fighting.
The Nevada legislature waited until the final day to introduce a bill that would outlaw animal sexual assault in NV. If it passes, the measure would make bestiality a gross misdemeanor, unless the animal suffers serious injury, in which case the crime becomes a felony.
A man was arrested and charged in Arizona last week after he allegedly engaged in what one journalist terms "full on sexual intercourse" with a family's pet goat. Luckily, Arizona's bestiality law is not restricted to sexual assault upon dogs and cats. (The Kentucky General Assembly briefly considered a bill that would have made bestiality a crime, but only if it involved a cat or dog.)
And how about one more victory lap for the bestiality ban that went into effect last week in Ohio? Raping an animal in the Buckeye State can land you in jail for up to 90 days with a $750 fine and a second-degree misdemeanor conviction on your record. So in the eyes of Ohio's criminal code, bestiality is better than carrying a gun without a permit (a first degree misdemeanor), but worse than painting graffiti on a mass transit bus (a third degree misdemeanor). Also, the new law allows telecommunications companies unrestricted rights-of-way, a provision dozens of Ohio cities are now challenging in court.
ArizonabestialityGoatJeff HooverKentuckyKentucky Farm BureauKentucky HoundsmenNevadaOhio
« Week of 3/20/17
Week of 4/3/2017 »


This 15,000 word novella contains coarse language, angst driven young adults, and a lot of pent-up frustration.
Eighteen year old Jade may not have the perfect life, but it's good enough. A senior at high school, dating the popular, likeable - but possessive Connor, a loving - abet alcoholic brother and a blunt best friend Nina. She's angry, trying to rein in her temper, and learning not to lash out. It's become increasingly difficult since Reed walked back into her life.
It's been three long years since he left, since he left Jade and never looked back. It destroyed then fifteen year old Jade, and she hasn't been the same since.
As she battles with old resurfaced feelings for the man that left her shattered, her life is falling apart around her. It seems everyone is hiding a secret, devastating enough to destroy what little of Jade's spirit is left.
She only ever has enough love for three people at any one time, with Reed in the picture, does she have room for one more?
I really enjoyed Those Four Little Words, and devoured it within one sitting. I feel privileged to have had the opportunity to be the first person to read this angst driven, emotionally charged book in it's entirety.
Jade is genuine, her persona is realistic and true to life. I spent the first half of four letter words on edge, the tension is unbearable and you know something is coming. It was an emotional read, my only complaint is that I want more! Christina Channelle seemed to hint at there being another book... There had better be lady, I need to know!
A dreamer, Christina Channelle holds two degrees in health sciences but has always had a passion for writing. You will find her reading other young adult novels, or typing up a new story on her computer. She resides in Ontario, Canada.


text:
Joaquín José de Muro y Vidaurreta (Logronyo, 27 d'octubre de 1797 – Madrid, 1859) va ser un polític espanyol, marquès de Someruelos i ministre durant la minoria d'Isabel II d'Espanya.

Membre del Partit Moderat, va ser diputat per Logronyo i Soria en diverses legislatures entre 1834 i 1844 i president del congrés entre 22 de setembre de 1837 i 1 de gener de 1838 senador per Logronyo en 1837 (encara que no va ser admès per no tenir l'edat reglamentària), en 1840 i vitalici en 1845;
ministre de Governació entre el 16 de desembre de 1837 i el 6 de setembre de 1838 en el gabinet de Narciso Heredia y Begines de los Ríos i dues vegades alcalde de Madrid en 1844 i 1847. També fou director de la Real Sociedad Económica Matritense de Amigos del País.

Referències

Diputats riojans al Congrés dels Diputats
Alcaldes de Madrid
Polítics logronyesos
Ministres riojans del Govern d'Espanya
Senadors madrilenys al Senat espanyol
Ministres madrilenys del Govern d'Espanya
Diputats madrilenys al Congrés dels Diputats
Naixements del 1797
Morts el 1859

redpajama_set_name: RedPajamaWikipedia


text:
Trivia Playing!
Answers With Questions
Answers At Bottom of Page
Questions With Answers > 1950s > 1953
1950 Trivia 1951 Trivia 1952 Trivia 1953 Trivia 1954 Trivia 1955 Trivia 1956 Trivia 1957 Trivia 1958 Trivia 1959 Trivia
1950s Trivia Questions and Answers From The Year 1953
1953 trivia quiz questions about miscellaneous and random topics.
What Conference opens in Rangoon, Burma?
A: The Asian Socialist Conference .
The United States President, Harry S. Truman, announces that the United States has developed a what?
A: A hydrogen bomb.
Marshal Josip Broz Tito is chosen President of what country?
A: Yugoslavia.
Georg Dertinger, foreign minister of East Germany, is arrested for what?
A: Spying.
In the United States, 71.1% of all television sets are tuned into the I Love Lucy TV show to watch what happen?
A: To see Lucy give birth.
Dwight D. Eisenhower succeeds who as the 34th President of the United States?
A: Harry S. Truman.
What Arthur Miller drama opens on Broadway?
A: The Crucible.
What Walt Disney feature film premieres?
A: Peter Pan.
President Dwight D. Eisenhower refuses a clemency appeal for whom?
A: Ethel and Julius Rosenberg.
James Watson and Francis Crick of the University of Cambridge announce what?
A: Their discovery of the structure of the DNA molecule.
Greece, Turkey, and Yugoslavia sign what?
A: The Balkan Pact.
Joseph Stalin suffers a stroke which renders him unconscious until his what on March 5?
A: Death.
Nikita Khrushchev is selected as what?
A: First Secretary of the Soviet Communist Party.
An earthquake hits western Turkey, killing how many people?
A: 250.
The 25th Academy Awards ceremony is held and it is the first one to be what?
A: Broadcast on television.
Jonas Salk announces what?
A: His polio vaccine.
Who gets elected as the United Nations Secretary-General?
A: Dag Hammarskjöld.
Ian Fleming publishes his first what?
A: James Bond novel, Casino Royale in the United Kingdom.
Where did Mickey Mantle hit a 565 foot home?
A: At Griffith Stadium in Washington, D.C.
Mantle's home run is believed to be the what?
A: The longest home run in baseball history by many historians.
What happened in Jordan?
A: Hussein is crowned King.
Aldous Huxley first tries what?
A: The psychedelic hallucinogen mescaline.
An F5 tornado hits in the downtown section of what city in Texas, killing 114?
A: Waco, Texas.
At Rogers Dry Lake who becomes the first woman to break the sound barrier?
A: Jackie Cochran.
At the Nevada Test Site, the United States conducts its only what?
A: Nuclear artillery test: Upshot-Knothole Grable.
Sir Edmund Hillary and Tenzing Norgay become the first men to reach the summit of what mountain?
A: Mount Everest.
The first Chevrolet "what" is built at Flint, Michigan?
A: Corvette.
Fidel Castro and his brother lead a disastrous assault on what?
A: The Moncada Barracks.
The Korean War ends with the what?
A: Korean Armistice Agreement.
Soviet prime minister Georgi Malenkov announces that the Soviet Union has a what?
Four million workers go on strike in France to protest against what?
A: Austerity measures.
The second Kinsey Report, Sexual Behavior in the Human Female, is what?
A: Published in the US.
The CIA helps to overthrow the government of Mohammad Mosaddegh in Iran, and retain whom on the throne?
A: Shah Mohammad Reza Pahlavi.
U.S. Senator John Fitzgerald Kennedy marries whom?
A: Jacqueline Lee Bouvier at St. Mary's Church in Newport, Rhode Island.
The UNIVAC 1103 is the first commercial computer to use what kind of memory?
A: Random-access memory.
U.S. president Dwight D. Eisenhower appoints who as Chief Justice of the United States?
A: Earl Warren.
Who resigned as prime minister of Israel?
A: David Ben-Gurion.
What civil war begins?
A: The Laotian Civil War.
The Douglas D-558-2 Skyrocket, piloted by Scott Crossfield, becomes the first manned aircraft to do what?
A: Reach a speed of Mach 2.
Hugh Hefner publishes the first issue of what?
A: Playboy magazine in the United States.


text:
Alejandro Jimenez-Flores, Johana Moscoso, Mary Tremonte, Sharmyn Cruz Rivera + nibia pastrana santiago
Triangulating Distances (an ACRE group show)
Elastic Arts is proud to present Triangulating Distances, a group show in conjunction with ACRE's summer residency program. The exhibition features Alejandro Jimenez-Flores, Johana Moscoso, Mary Tremonte, Sharmyn Cruz Rivera + nibia pastrana santiago, curated by Jordan Martins. It runs from September 10th through November 13th, viewable during all of Elastic's events and by appointment.
Artists Cooperative Residency and Exhibitions (ACRE) was founded in 2010 as a summer artist-residency program seeking to create a fertile territory for artists to not only experiment freely with their practice but also to cross-pollinate among one another. The artists in Triangulating Distances illustrate the ACRE program's full gamut of creative practice, collaborative strategy, and geographical variety, with artists based in Chicago, Toronto, and Puerto Rico making work that is, at times, personal, political, ephemeral, formal, and practical. While the work here does not hover around a fixed theme, it invokes the complex network of exchange that its participants are engaged in, both in the context of the ACRE residency and outside of it.
Alejandro Jimenez-Flores arrives at his painted abstractions by circulating through physical and digital terrains, collecting various visual-semiotic fragments, and transcoding them onto his canvases. While his compositions are indebted to the more purely formalist traditions of modern painting, Jimenez-Flores constantly takes such painterly experimentation out of his studio to absorb fresh linguistic fragments. He states that "this process started as an impulse to slow down the persistent sign exchange happening around me and my personal involvement with it as a maker and consumer of signs."
Colombian-born/Chicago-based performance/dance artist Johana Moscoso reinterprets personal and cultural rituals, heightening the communicative potential of bodies in motion. For the opening of Triangulating Distances, Moscoso will present a work developed at ACRE entitled "Lohs see-Eh-teh coh-LOH-rehs," channeling memories of the Colombian island from where her mother's family comes. She remembers that her grandmother had a ritual to "cool her off on hot days in San Andrés. On her vanity she had a box that contained a cotton applicator in which she used to put powder over her body. As she touched her skin with the cotton ball, white smoke emerged from her skin like magic. It was a powder as thin and volatile as baby powder. Thinking of this ritual reminded me of the impeccable white sand of San Andrés. When the waves roll over the sand on the beach you can begin to see one of the seven colors."
Toronto-based Mary Tremonte uses various printmaking techniques to create large-scale and visually playful installations directed at political issues such as water rights, often as a member of the Justseeds Artists' Cooperative. Her installation of sculptural objects and silk-screened imagery "is a meditation on the simultaneous soft power and vulnerability of freshwater, looking to three of the Great Lakes as sites…. These freshwater reserves are arguably the greatest natural resources in North America, and are increasingly vulnerable to extraction by private corporations, such as Nestle and Coca-Cola, invasive species such as the zebra mussel, and pollution from industrial and fossil fuel extractive processes."
Chicago-based curator Sharmyn Cruz Rivera and dancer/choreographer nibia pastrana santiago have been collaborating since 2006, when they met as undergraduates at the University of Puerto Rico in San Juan, where pastrana santiago is now based. At ACRE, they developed a project called "WATERSHED," which they describe as "a collaborative practice using found objects, failed memories of archetypal Tropical and Americana imagery, and our bodies as conduit to negotiate the disparities of being Puerto Ricans in the Midwest." For this exhibition, they will be reapproaching this collaborative practice in an event on November 11th, transforming Elastic's space into a zone of mutated symbolism, improvised gestures, and participatory action. The sculptural "score" that their practice follows is on display for the full duration of the exhibition.
The eclectic modes of inquiry represented in this show reflect the plurality of practices at play in the contemporary art discourse, and the immediate synchronicities between the works are intriguing. Water is addressed as a passageway, as a body surrounding islands in two oceans, as a natural resource, as a sense memory poetically reinvoked through movement. Objects in Cruz Rivera's and pastrana santiago's "WATERSHED" operate as hypertextual talismans that allude both to specific cultural iconography and interpersonal experiences, echoing Jimenez-Flores's process of refracting found marks into abstraction. Moscoso and Tremonte present individual dance and print projects, respectively, in this exhibition, but through their ACRE residency, they also explored the space between their practices to question what can emerge at the intersection of bodily movement and political movement. If the climate at ACRE allows for the thinking and activity of individual artists to spill over into one another's territory, such cross-disciplinary promiscuity is on full display in Triangulating Distances.
Triangulating Distances is curated by Jordan Martins, visual arts programmer at Elastic.
Exhibition title: Triangulating Distances (an ACRE group show)
Artists: Alejandro Jimenez-Flores, Johana Moscoso (featured image), Mary Tremonte, Sharmyn Cruz Rivera + nibia pastrana santiago
September 10th–November 13th 2016
September 10th, 7-10pm
"WATERSHED" event with Sharmyn Cruz Rivera and nibia pastrana santiago: November 11th 8m
Artist Websites:
http://alejandrojflores.com/
http://justseeds.org/artist/marytremonte/
http://johanamoscoso.com/home.html
http://www.sharmyncruzrivera.com/bio
http://www.nibiapastrana.com/


text:
Is Bosnia safe? The lowdown on safety in Bosnia and Herzegovina
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When is the best time to visit Bosnia and Herzegovina?
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Hiking in Bosnia and Herzegovina: Everything You Need!
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Bosnian Cuisine: The Most Delicious Dishes to Try!
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How to Get from Sofia to Bucharest (3 Ways)
Romania and Bulgaria are two neighbouring nations with a shared history but also a fair amount of differences. The most notable being that the Romanian language hails from Latin, and so they write using the same alphabet that we do, while Bulgarians are Slavic and use the Cyrillic alphabet. But the two nations both came under the thumb of Communism in the 20th century and, today, are flourishing cities of brutalist architecture that hides a bustling art scene, a wonderful food scene, and a fascinating history. It's easy to get from Sofia to Bucharest, and[...]
3 Romania Itinerary Ideas (7, 10, and 14 Days)
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Visiting Romania for the First Time
Before you head to the land of endless rolling hills, dramatic mountain ranges, and medieval towns that is Romania, there are a few things that are important to know. You'll want to think about exactly how expensive travelling around Romania is, how safe the country is, the top places to visit in Romania, and even more besides. Here's everything you need to know before visiting Romania for the first time. How to get to Romania There is a surprising number of options to choose from when it comes to how to get to Romania. The most obvious is to take[...]
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Romania in the winter: is it worth it?
Romania is an enormous country, and much of its landscape is made up of mountains, hills, and valleys. Situated yourself in the centre of Transylvania and you'll find yourself on a perfectly flat valley plain that spreads out for miles, but on every side of you on the horizon is a jagged and harsh mountain range. Romania is like a fantasy world of dramatic and sublime rocky terrain, dense forests, and rolling green hills. All of this changes dramatically in the winter months. It gets freezing cold, snow falls heavy, and all the green hills are coated with a w[...]


I've tried to make the introduction flow, and make the points that follow more complete. I've added a section on Meditation, Actuality and Whole being, implying steps towards being a part of reality from identified in what we experience. Yet to present the physical references, movement and exercises.
If I can start with the Central Nervous System (CNS). You may be familiar with the idea that the brain creates, or at least is involved in creating, what we experience. Vision, for example, is processed in the brain from information received by the eyes and "projected", for us to experience.
But what about our self, having the experience?
We can wind this back to the start and question in the first place, whether the brain creates anything at all. Strictly speaking, the activity detected in the brain with MRI scans may only be "para-phenomena" – that they coincide with (or parallel) the "events" in our reality (that we observe) but do not necessarily cause them. Is there a basis or a creator to the self and what we experience, or are we just what is?
Let me put aside these issues, about what is created or not (i.e, fundamental and irreducible in themselves) and what the CNS does or does not do, to make this point : that there is no brain without a living whole being. We can consider then our whole being to be the basis of our reality, including the self.
It means our whole creates our reality and projects it through the CNS. Projection is the role that the CNS plays in the manifestation of our reality. The whole self or being is the definitive entity of reality. We, as projection, are a part of our whole being.
Normally, we think "I'm it" and "that's the world out there", that we are the "definitive entity" and the world we experience is reality. We function well enough in this familiar way. Yet, unless we keep ourselves busy, occupied (with something) or diverted (away from the rest, as in occupational and diversional therapy), there's also a sense of incompleteness or that there must be more. Certainly there's uncertainty, and plenty of occasions and reasons for anxiety or depression.
I do not wish to deny anything of our self and what we experience, nor draw us beyond boundaries best accepted, outside or within. But a part is simply invalid, apart from it's whole. We are displaced from our whole in being projected, and isolated from our whole as we identify, in our self and with what we experience, within projection.
Our reality is a part. All that can be of our reality, of "conscious experience and self witnessed", is projection. Till we learn to be a part of who encompasses and permeates our all, we remain isolated in our part, lost from our whole. All directions are in vain, as we grasp at our fleeting moments in avoidance of this, our truth.
Our whole being includes both the solid body and projection, is more than their sum, and is in and of reality. In our "actuality", the existence of our reality as projection, we can be in relation with our whole, as his or her part. And as a part of our whole being, we are also a part of reality.
Following is a practice, outlined with stepping stones towards our being in relation with our whole. Our notion and sense of reality is not reality. Like a yacht that must "tack" away from the wind of reality and can only zig zag towards it, we talk about and feel what reality "must be like" in an indirect way. In our projected actuality, however, we are aligned directly with our whole as a part. Then, as a projected part, we can refer to reality itself in our whole being and be affected in our relation with our whole.
In a word, the theory is projection.
1. Part theory – in our projected actuality we may be "in relation with" our whole. We are validated in this "being in relation with" as a part is by its whole.
Winching (see below in The 5 steps to establish – 4.) : because we are, as a part, limited.
2. Whole body method – we can refer to (core), contemplate (who must be there, who must be more than the sum of his/her parts including those parts projected and solid, who sums), commune with (Nothingness – absence in projection), and connect with (through projection) our whole.
As a part of reality, our whole being is in and of reality (we are in and of projection as a part of our whole being), and spirited (as are all other whole entities in reality) with the one essence of his/her whole being and the entirety of reality (All creation).
We can introduce our whole in prayer (love and compassion, forgiveness and support, to emulate and become, depend and surrender, feel and receive, we can refer to our whole who encompass and permeate all we experience, distance, presence and process), meditation/experiencing (who has the eyes and other sense organs and projects what we experience), posture/exercise (who has a body), work/play/living (who actually is, does and lives).
Physicality (to follow). References, body movement/exercise, relationship.
1. Actuality – there is our actuality, our existence in fact as projection.
2. Whole being – is in and of reality. He or she creates our reality and projects it through the Central Nervous System.
3. How we are shaped or structured in our actuality goes hand in hand with what happens – isolation from our whole to integration as a part, as we "place" our self and our reality in our shaped actuality, like positioning an engineering or architectural block to initiate some structural process (robots in "Transformers", temple booby traps in an "Indiana Jones'" adventures where the placement of a skull etc causes the whole temple to shift), to be affected by "being in relation with" our whole.
5. What it is all about – we become more a part, and our whole becomes more complete with integrating parts. Godly being of reality, spirited at core (unconditional love, God presence), encompassing our all (our self and our sense of others, near and far, and of all times and places we may sense being in or being in touch with) and our part.
Consider the world out there, your self having an experience, the witness behind, deeper being below, and the conscious above. These displaced aspects of our reality extend in different directions and in differing distances that imply space in a very direct and immediate way.
This space, including the shapes of our aspects, is actuality, our being projection and a part. Refer to from this, the actuality of our greater part, the whole self and whole being.
– CNS : level, domed and split brain; vertical spine; even nerve roots. Goes with a "complete" (with integrating parts) whole being in alignment with gravity, horizon and the zenith.
– Nothingness : the absence of the whole being and reality from our projected reality. Though as sense it is projected, Nothingness it is the whole being who encompasses and permeates our reality of conscious experience and self.
– Core : the reference for the whole being; of whom his or her solid body and organs, as well as projection are parts. Other end is the clue.
– Notion : The whole being who must be there, in and of reality. More than the sum of the parts. Alive as a part of reality, next to other whole beings. Who must be breathing, doing, alive, being of reality.
– focused : breath, one point, self, whole self, god, a sense, here and now, circle, mirror, light, candle light, movement, uprightness, a direction, numbers.
– mindful observance : allow for conscious experience and self (our reality) to settle as is, into their depth, in face of a transcendent witness.
the matter in fact of our existence as projected in space. Includes the witness and the layers of disassociation towards our subconscious, our outside and inside worlds, the existence of things and the presence of others (what and who we experience) within them (worlds or realms), the conscious, depths, "other side" and "other end". In the immediate instance we may recognise the world out front, our self back in, the witness behind, deeper being below and the conscious above. The various directions in which these aspects of our reality occur infer space that, together with the space they themselves occupy, is our projected actuality.
refer, contemplate, consider, commune, connect (Whole body method), for being in relation with our whole.


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President Trump 'cheats like hell' at golf, says LPGA star
During those outings, the article states, Pettersen noticed some of Trump's tendencies on the green. Why? Because it's what she would have done for any friend who obtained a new job or position, and winning the presidential election is "quite something" after all. (more...)
Wanderers Stadium pitch rated as poor
Andy Pycroft the referee forwarded a report to Cricket South Africa (CSA) which said, "The pitch prepared for the final Test was a poor one". Dean Elgar with an unbeaten 86 was the top-scorer in the match. The Test ended in India's favour, but will be remembered for posing serious questions for batsmen in the middle. The ICC stipulates that the "objective of a Test pitch shall be to allow all the individual skills of the game to be demonstrated by the players at various stages of the ... (more...)
Liverpool won't sign Coutinho replacement in January
After an 18-match unbeaten run in all competitions, the Reds have just tasted back-to-back defeats in the Premier League against Swansea and against West Brom in the FA Cup . A 2-0 defeat at relegation rivals Stoke in their most recent league game, on January 20, was a significant setback, and the FA Cup has provided little consolation since then, with a team showing eight changes held 1-1 at home by Championship strugglers Birmingham on Saturday. (more...)
Sterling Returns For Manchester City As Guardiola Names Strong Line-Up v Cardiff
Sane was injured during City's FA Cup win at Cardiff last weekend. City remain in contention for all four competitions, but Guardiola fears more of his players will suffer serious injury if officials don't act. Mass confusion, even without VAR! What a surprise. Are we saying Sane was in the line of the ball? However, there was no doubt after 37 minutes when Silva's inviting cross was headed down and in by the in-form Raheem Sterling . (more...)
Bulls, Pelicans Continuing Discussions On A Niko Mirotic Trade
The Pelicans have expressed a hesitancy for the Bulls to pick up the Mirotic option for 2018-'19 because they're uncertain if they'd want him and his $12.5 million salary for that season. He missed the first 23 games of the season after teammate Bobby Portis knocked him out on October 17 with a punch that left the young forward with a concussion and facial fractures. (more...)
Amir Khan throws water at Phil Lo Greco during heated press conference
Canadian Lo Greco riled Khan by bringing up the British fighter's personal life including his troubled relationship with his wife. Khan responded by splashing water towards Lo Greco at the Liverpool press conference, prompting security to intervene before Khan insisted he would take the bout as seriously as ever. (more...)
Arsenal agree deal with Barcelona for 18 year-old wonderkid
The 18-year-old completed his medical and agreed terms today. McGuane, 18, joined the Gunners at Under-6 level and broke into Arsene Wenger's first-team this season, making two appearances in the Europa League at the end of a year ago. (more...)
Kia Motors Teases SP Concept SUV - To Debut At Auto Expo 2018
Commenting on the company's plans, Kia Motors Corporation President Han-Woo Park said, "We aim to set a new standard in the Indian auto industry by providing consumers with world- class products and services, while engaging with and giving back to the local community". (more...)
West Ham keen on Schneiderlin loan deal
Schneiderlin has struggled to produce his best form since joining Everton from Manchester United last January after being brought in by Ronald Koeman. West Ham boss David Moyes is reportedly assessing Schneiderlin in his plans to add a defensive midfielder before Wednesday's January transfer deadline. (more...)
Real Madrid watching Mauro Icardi closely - Argentina's Jorge Sampaoli
Real Madrid now sit fourth in La Liga, 19 points off leaders Barcelona albeit with a game in hand. Mauro Icardi joined Inter Milan from Sampdoria in July 2013. "Icardi is being watched and is nearly tempted by Real Madrid". Icardi and his wife and agent Wanda Nara appear perfectly happy in Milan, and while they have periodically hinted at a departure, they've mostly talked up the club and their connection to it. (more...)
Arsenal Interested in Summer Move for Atletico Madrid's Yannick Carrasco
Simeone is open to the idea of selling Carrasco this winter and made the 24-year-old available in the January transfer window. Irrespective of the player's performances from now till the end of the season, Atletico are expected to demand a price more than £50 million in the summer. (more...)
Formula E reveals next generation auto
Formula E unveiled its second-generation race auto this week ahead of an official debut at the 2018 Geneva Motor Show on March 6. The first generation of all-electric FIA Formula E race cars didn't make a huge splash, but the second generation wants to remedy that. (more...)
Former Michigan governor to be named Michigan State interim president
Engler was elected Michigan's 46th governor in 1990 and served until 2003. A Detroit News investigation found that 14 staff members at MSU, including Simon, were notified of sexual abuse allegations involving Nassar over two decades. Reacting to several media reports that Engler will be named to the post , State House Speaker Tom Leonard, a DeWitt Republican, said in a statement that the former governor is the "right choice.". (more...)
Titans officially name defensive and offensive coordinators
The moves follow the news of offensive coordinator Matt LaFleur taking the same position with the Tennessee Titans . Vrabel spent Tuesday through Thursday at the Senior Bowl in Mobile, Alabama, with general manager Jon Robinson and several other key Titans front-office members interviewing candidates to fill his staff. (more...)
IOC Concerned About Integrity of Doping Sample Bottles Ahead of 2018 Olympics
WADA said in a statement it had been alerted by an accredited laboratory in Cologne that bottles manufactured by Swiss manufacturer Berlinger could be opened after being frozen. In the 2014 Sochi Olympics doping scandal detailed in a report by Canadian lawyer Richard McLaren, investigators discovered that Russian staff involved had developed a way of opening "tamper-proof" sample bottles undetected. (more...)
Pistons' Bradley obtainable for commerce
ESPN's Adrian Wojnarowski reported earlier the Pistons had made Bradley available, with Detroit's asking price "significant". Now, the Pistons are searching for a return on Bradley prior to the possibility of losing him without compensation in free agency, league sources said. (more...)
Roger Goodell 'Concerned' About Catch Rule, Promises Review Before Next Season
Details of the league's plan to tweak the rule are not yet clear. For everything that instant replay has done to help the game, it's made a mockery over this simple question: what is a catch? The meeting occurred shortly after the controversial ending to New England's Week 15 win at Pittsburgh on December 17. (more...)
Wentz reveals knee injury worse than originally thought
This has been in place of Pro Bowl quarterback Carson Wentz , who has been on the mend from a torn ACL and LCL since early December. The second-year quarterback, who grew up in North Dakota, was the face of the Eagles team he led to an 11-2 record at the time of his injury, which immediately prompted questions about how far they could go without their starter. (more...)
Former Padres, D-Backs GM Towers Dies At 56
He most recently worked as a Reds scout and special assistant to the general manager. Towers was diagnosed with anaplastic thyroid cancer in December 2016. The D-backs won the NL West in 2011 and with a 94-68 record lost to the Milwaukee Brewers in the NLDS. Astros manager A.J. Hinch held up a sign honoring Towers during baseball's "Stand Up to Cancer" moment at last year's World Series. (more...)
Man City make late £60m move for Mahrez
It is also claimed that Mahrez will attempt to "force the transfer", and that the Leicester board will resists any offers. Pep Guardiola's side have just broken their transfer record with a £57m move for Athletic Bilbao defender Aymeric Laporte. (more...)


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Powerviolence és un subgènere musical del hardcore punk extremadament dissonant i ràpid que està relacionat amb el thrashcore i el grindcore. En comparació amb el grindcore, que conté aspectes musicals del heavy metal, el powerviolence implica un increment de les qualitats més desafinades del hardcore punk. Com els seus predecessors, sol tenir una càrrega sociopolítica i iconoclasta.

Història
Siege és considerat el grup pioner del poweviolence juntament amb Infest. Com a gènere es va consolidar a principis dels anys 1990 amb bandes com Man Is the Bastard, Crossed Out, Neanderthal, No Comment, Capitalist Casualties i una sèrie de grups que es van inspirar en Hüsker Dü, SSD, Deep Wound, Neon Christ, Hirax, Impact Unit, Dirty Rotten Imbeciles, Negative FX i Corrosion of Conformity.

El segell discogràfic Slap a Ham Records del vocalista i baixista de Spazz, Chris Dodge, va impulsar el creixement del powerviolence, publicant discos influents de Neanderthal, No Comment, Crossed Out, Slight Slappers i Spazz. Fiesta Grande va ser el nom d'un festival anual de powerviolence celebrat al 924 Gilman Street entre 1993 i 2000. El segell 625 Thrashcore (fundat pel bateria de Spazz Max Ward) va iniciar un festival de temàtica similar el 2003, anomenat Super Sabado Gigante.

Estil
Tot i que el terme powerviolence incloïa inicialment una sèrie de bandes estilísticament diverses però que estilísticament compartien la velocitat, la intensitat, els breakdowns i els canvis de tempo constants. Les cançons de powerviolence solen ser breus, algunes de menys de vint segons. Grups com Man Is the Bastard, Plutocracy, Azucares i No Le$$ van estar influïts pel rock progressiu i el jazz fusió.

Alguns grups com Man Is the Bastard i Dystopia van abraçar l'anarcopunk i el crust punk, posant èmfasi en els drets dels animals i l'antimilitarisme. Grups com Despise You i Lack of Interest van escriure lletres sobre misantropia, drogues recreatives i conflictes socials. A més, grups com Spazz i Charles Bronson compten amb lletres en què es burlen del postureig dels aficionats al hardcore i el metal. Altres grups de powerviolence són The Locust, Dropdead, Black Army Jacket, Hellnation i Rorschach. Weekend Nachos, Nails, Magrudergrind, Early Ceremony, Hatred Surge, Mind Eraser i Full of Hell es consideren grups de poweviolence contemporanis.

D'altra banda, l'emoviolence és un subgènere que combina elements de powerviolence i screamo: veus cridades, ritmes explosius, ús extensiu de la retroalimentació de l'amplificador i petits elements de melodia. El terme «emoviolence» va ser creat de broma per la banda In/Humanity, i s'aplica a bandes com Orchid, Usurp Synapse, Jeromes Dream, i Pg. 99.

Referències

Gèneres del punk


FTSE 100 Forecast - Sell in May and Go Away !
In a week that ended with the FTSE falling over 100 points from high of 6137, we revisit the age old adage of selling in May and go away !
As my analysis will show the market is now primed for a serious correction after fulfilling a years target in less than 4 months !
The 6 months from 1st May to 31st Oct are usually the worst for the stock market, i.e. since 1965, returns for the FTSE All-Share index in the six summer months between April 30 and October 31 have averaged just 2.2%, whereas the period from 1st Nov to 30th April are usually the best, where returns have averaged 14.3% !
Looking at recent activity, clearly we have had the best !, with the FTSE rising from 5300 to a high of 6136, 836 points or 15.7% , right inline with the seasonal expectation !
Back on 31st December, I forecast a target high for the FTSE during 2006 of 6000, that has now been exceeded well before the year end and during the bullish stock market period. Now similarly I am anticipating a strong downswing that is likely to last some six months going into Late October 2006.
1. Resistance Line - At 6136, the FTSE is probably made its high for most of the year, and is now unlikely to break it until possibly the rally that takes place during the end of 2006, if at all !
2. Support - Key support lies along 5500, and is thus the natural target for any correction.
3. MACD - (Bottom indicator) - After breaking above the ascending triangle, during January, lead to a sharp rally in the FTSE, which has brought the FTSE to a very overbought state, and is screaming correction !, The most recent decline is creating a cross and thus a trigger for that correction to commence in the coming days, the target low for the correction would be to hit the lower support trend-line.
5. Uptrend Line - Similar to the key support area along the previous high at 5,500, the main uptrendline cuts in currently at 5480 support area for the FTSE.
6. Time - The recent moves from Bottom to top have been in the order of 5 to 5.5 months, and thus suggest the FTSE is overbought also in time terms, and implies a lengthier correction time wise, of at least 1 month and probably much longer, which would suggest an ABC pattern to the correction, to stretch the correction out somewhat.
Target - Based on the above analysis the FTSE is targeting between 5600 and 5480, with the major support in the region of 5,520 and thus the strongest targeting price.
Time - Seasonal analysis suggests a trend that will likely to the FTSE into a low in late Sept / Early October 06, and thus implying an ABC pattern, i.e. after an initial decline to form wave A, a B wave rally with a final C wave decline to possibly new low for the move.
Stop-Loss - Clearly the stop loss should be above the high of 6136, say 6150. As a break of the high would imply a resumption of the uptrend.


BCEOHRN Annual General Meeting 2015.
The meeting included viewing of the documentary EARTH ON FIRE that focuses on mega fires as they relate to our forests and ecosystem. Unique challenges now face forests around the world, and you will learn more about the delicate balance between fire, trees, and the climate. What this film lacks in frills, it makes up for in facts about fire and its important role in the global system.
May 15, 2014. Harbour Centre Campus of Simon Fraser University. Vancouver, BC.
BCEOHRN Executives presented their reports, we held an election for the Board of Directors positions, we presented and discussed new business and developed plans for 2014/2015.