text:
\section{Introduction}

\begin{comment}
*****************************************************************************
{\bf Question.} {\it Do we need to start with general discussion and
review of results and results from other authors? Where do we put
outline of paper?}
****************************************************************************
\end{comment}

 The question of coexistence in models of several predators feeding on one prey have been considered in many works. One question is to find parameter criteria for coexistence. A complicated question is to find out the form of the coexistence. Mathematically it means to examine the structure of the attractor, which can be periodic or of different chaotic types. In this work we introduce a construction of a positively invariant set, where it is possible to examine the attractor by estimating properties for a  Poincar\'{e} map. We also find out when it is possible or not to find the invariant set.

 We consider the system
 \begin{equation}\label{a1}
 \dot{x_1}={\phi}_1(s) x_1, \quad  \dot{x_2} = {\phi}_2(s)x_2,  \quad\quad
 \dot{s}=H(x_1,x_2,s).
 \end{equation}
 The function  $H = H(x_1,x_2,s)$  has the form
 $H=h(s)-{\psi}_1(s)x_1-{\psi}_2(s)x_2 .$ \\
 \vskip0mm
We assume the following conditions:
 \vspace{1mm}

 \noindent
 $A_1 :\quad$ All functions belong to the class
 $\, C^2 [ 0,\infty ) ,\,$
 and the variables $x_1, x_2, s$ are in the octant
  $\, R_3^+ \colon \;
 x_1 \geq 0 , x_2 \geq 0, s \geq 0 ,\,$ which is an invariant set.
 \vskip0.5mm

 \noindent
 $A_2 : \quad   {\psi}_i(0)=0, \quad {\psi}_i'(s)>0\,

 $ for  $s>0$.
 \vskip0.5mm

 \noindent
 Here and further we will suppose, that  $i$  takes values from the set $\{1,\,2\}. $
 \vskip0.5mm

\noindent $A_3 : \quad   {\phi}_i'(s)>0\,
$ for  $s>0,\quad$ and there exists
 ${\lambda}_i > 0$ such that  ${\phi}_i({\lambda}_i)=0. \quad$
\vskip0.5mm

\noindent $A_4 : \quad  h(0) = h(1) = 0 , \quad  h'(0) > 0 \;$  and
 $\, h''(s) < 0 \;$ for $ s>0. $
\vskip0.5mm

\noindent $A_5 : \quad   {\psi}_1 (s) < {\psi}_2 (s) \, $ for
$s>0$. \vskip0.5mm

\noindent $A_6 : \quad $ There exists  $\tau > 0\,$ such that
 $\, {\phi}_1(\tau) = {\phi}_2(\tau)  $
and
  ${\phi}_2(s)> \phi_1 (s) \; \Leftrightarrow \; s > \tau . $
\vskip0.5mm

 \noindent
 $A_7 : \quad  0  <  \tau  <  {\lambda}_2 <  {\lambda}_1  <  1 .  $
 \\

\begin{comment}
***************************************************************************
{\bf Question.}
{\it Do we need to explain more about these conditions and where they
are needed, of biological or math reasons?}
************************************************************
\end{comment}

\vskip0mm

 The vector field of system (\ref{a1}) we will denote by $\,{\cal F}. $
\vskip1mm

\begin{comment}
***************************************************************
  These and analogous systems with different assumptions on the rigth hand sides were considered by many authors
  (\, for example, in [2--5, 8--18, 22--23]\,
  \cite{ButlerWalt,ButlerHsuWalt,Cheng,Cushing,HelOwaidyElLeihty,candy,
  GeHarmis,Huang1,Huang2,Hsu2,Hsu3,Hsu4,Hsu5,Keener,Koch,smith1,smith2}
  both from mathematical and application view.
  ****************************************************************
  \end{comment}

    Systems with the following special choice of
  functions

 \begin{equation}\label{a2}
 h(s)=\gamma s(K-s),\qquad {\psi}_i(s)={\alpha}_i\frac{s}{s+a_i},\qquad
 {\phi}_i(s)=m_i{\psi}_i(s)-d_i,
 \end{equation}
 where all introduced parameters are positive, have been examined extensively.
 The general behaviour of such systems has been studied in
 \cite{Hsu4,Hsu3} and parameter conditions for different behaviour are given in
 \cite{Hsu5}. The possibility for coexistence connected with bifurcations were examined in \cite{smith1,ButlerWalt,Keener}. Many works have considered the situation when function $h$ is linear and thus condition $A_4$ is violated.
 More general systems are considered in \cite{smiththieme,alebra}.

 Such systems can have chaotic regimes. In particular, in
 \cite{osipov3,osipov4,osipov5} was given a bifurcation diagram with a chain of period doubling bifurcations for
  system (\ref{a1}) with (\ref{a2}), where
 \begin{equation}\label{a3}
 h(s)=s(1-s),\qquad {\phi}_i(s)=\frac{s-{\lambda}_i}{s+a_i},\qquad
 {\psi}_i(s)=\frac{s}{s+a_i}.
 \end{equation}
 The system with functions (\ref{a2}) were transformed into this system
 in \cite{Keener}. In addition in \cite{osipov3,osipov4,osipov5}  was assumed $m_i=1$ for these new parameters after the transform.
  A  one-dimensional discrete model was built with the same chain
 of bifurcations as  for the real Poincar\'{e} map.
 It was also shown that along this bifurcation path there is the possibility that
  the Poincar\'{e} map
 cannot be properly defined and there can appear a so called "spiral-like chaos".
 Here we modify the bifurcation path to correspond to our technics of constructing the invariant set.
 \smallskip

 In this work we consider a broad class of systems of the type
 (\ref{a1}),
 including the system with the right hand sides of form
 (\ref{a2}) and with  (\ref{a3})
 as the main example .
 We formulate sufficient conditions for correct definition of
 Poincar\'{e} map and, as a corollary, for absence of "spiral-like chaos".

 We note that it is well known that such systems are not directly applicable in biology without modifications, for example, because in the model some populations can go unacceptable low and still survive. Also in recent time most models include more complicated dependences on the variables. Usually the equations for predators are not fully independent on the other predator and functions $\psi$ and $\phi$ can include such dependence. Anyhow all these modifications often essentially use the technics worked out for our systems, why the study of system (\ref{a1}) is still motivated.

The outline of the paper is the following. After this introduction we give a short overview of local behaviour of the system. In Section 2 we consider the two dimensional behaviour in the  $(x_i, s)$-coordinate planes. Section~3 is the main section where we introduce comparison systems and the concept of a tangency curve we use for constructing the positively invariant set.  The boundary of the set will mainly be formed by parts of trajectories of a glued system. Finally in Section 4 we give some numerical results for cases, when the construction is possible and when not possible containing  more complicated chaos.

\subsection{Equilibria}

 From conditions  $A_1-A_7$
 follows, that the system has four equilibria:

\noindent
 $1^{\circ}. \quad {\bf O}\,(0,0,0), $  which is saddle with two-dimensional stable manifold $\,s=0\,$   and one-dimensional unstable: $ x_1 = x_2 = 0, \; s<1. $

\noindent $2^{\circ}. \quad {\bf O_1}\,(0,0,1), $
 which is a saddle
 with one-dimensional stable manifold
 $\, x_1 = x_2 =
0\,$
and a two dimensional unstable one.

\begin{comment}
*************************************
 which we will denote by
 $\,W_1^u. $
 \end{comment}

 \noindent
 $3^{\circ}.\quad$ Two points in the coordinate planes:

 $\; {\bf P_1}\,(x_1^0, 0, \lambda_1)\,$ и
 $\; {\bf P_2}\,(0, x_2^0, \lambda_2), $
 with index 1 in these coordinate planes.

 \smallskip
 From conditions $A_3$ and $A_7$ follows that there are never any equilibria
 in the interior of the positive octant.

 The type of the equilibria are immediately deduced from the form
 of the Jacobian matrix.
 At the equilibrium  $ {\bf O^*}\,(x_1^*, x_2^*, s^*)\,$
 the Jacobian matrix has the form
 \begin{equation}
  J^* \; =\; J\,({\bf O^*} )\quad  = \quad
  \left(
 \begin{array}{ccc}
 \phi_1 ( s^* ) & 0 &  \phi_1' ( s^* ) x_1^* \\
           0  &  \phi_2 ( s^* ) &   \phi_2' ( s^* ) x_2^* \\
   -\psi_1 ( s^* )  &  - \psi_2 ( s^* ) &   h'(s^*) -
 \psi_1' ( s^* ) x_1^* - \psi_2' ( s^* ) x_2^*
  \end{array} \right) \;.
 \end{equation}

Observing that the sign of the real parts of the eigenvalues are
determined by the sign of $\phi_i (s^ *)$
and $   h'(s^*) -
 \psi_1' ( s^* ) x_1^* - \psi_2' ( s^* ) x_2^*$
we can find the type of the equilibria of ${\bf P_1}$  and ${\bf P_2}$.
${\bf P_1}$ is a saddle with two dimensional stable manifold
in the coordinate plane, if
$ h'(\lambda_1) -\psi_1' ( \lambda_1 ) x_1^0 <0  $, and a source, if $ h'(\lambda_1) -
 \psi_1' ( \lambda_1 ) x_1^0 >0  $.
 ${\bf P_2}$ is stable, if
$ h'(\lambda_2) -\psi_2' ( \lambda_2 ) x_2^0 <0  $, and a saddle with one dimensional stable manifold, if $ h'(\lambda_2) -
 \psi_2' ( \lambda_2 ) x_2^0 >0  $.

  \section{Limit cycles in the coordinate planes}
\vskip1mm

The coordinate planes of system (1) are invariant two dimensional systems
and in this section we describe some known behaviour of these systems.

\noindent
Here we use a version of
 Zhang Zhi Fen
 theorem \cite{Zeng,ZhangZhiFen,ZhangZhiFen2}:
\vskip1mm

{\bf Theorem 1.}\quad {\em Consider the system
$$ \dot{x} = - \varphi ( y ) -  F ( x ) , \quad
 \dot{y} = g ( x )  . $$
Assume:

\noindent 1)\quad $g(x)\;$
satisfies the local Lipschitz condition,
  $xg(x)>0,\;x\neq 0,\quad
 G(+\infty)=G(-\infty)=+\infty,$  где   $G(x)=\int^x_0 g(x) dx;$

\noindent 2)\quad  $F'(x)$ is continuous,  $F'(x)/g(x)$ is non-decreasing on intervals
      $( - \infty , 0 )$ and $( - \infty , 0 )$,
  and is non-constant in any neighbourhood of
       $x=0. $

\noindent 3)\quad $\varphi (y)\;$
satisfies the local Lipschitz condition,
  $ y \varphi (y) > 0,\; y \neq 0, \qquad  \varphi (y) \,$
 is non-decreasing, $\quad
 \varphi (-\infty)=-\infty , \quad \varphi (+\infty)= +\infty \,;
 \quad \varphi (y)\,$
  has left and right derivatives at the point
 $x=0,$
  which are non-zero in the case
 $F'(0)=0. $

 Then the system does not have more than on limit cycle
 and, if it exists, it is stable.
 }\\

In  \cite{Sunhong}
was shown, that the problem of limit cycles in two dimensional systems
of type "predator-prey" often is solved by applying the
 Zhang Zhi Fen theorem.

In particular, this theorem is possible to use for the system

$$\dot{s} = h(s) -\psi (s) x,\quad \dot{x}=\phi(s) x. \eqno(*)$$

In this case the system is transformed to the form

$$ \dot{s} = F(s) -  x  , \quad
 \dot{x} = \varphi ( s )x  . $$

 where $F(s)=h(s)/\psi(s), \quad \varphi(s)=\phi(s)/\psi(s).$

We formulate the corresponding theorem in
 \cite{Sunhong},
 applied to the two dimensional restrictions of system (\ref{a1})
 to the coordinate planes.
 In the proof the system is transformed to a Lienard system used in Theorem 1.

{\bf Theorem 2.}\quad {\em Consider the system
$$ \dot{s} =  F ( s ) -x , \quad
 \dot{x} = \varphi ( s )x  , $$
 where $F(s)=h(s)/\psi(s), \quad \varphi(s)=\phi(s)/\psi(s).$

Suppose:

\noindent 1)\quad All functions are continuous and differentiable on
 $(0,\infty).$

\noindent 2)\quad  There exists  $\lambda  >0$ such that $\varphi(\lambda )=0$ and
$(s-\lambda )\varphi(\lambda ) >0, s\neq \lambda.$

\noindent 3)\quad $F'(s)/\varphi(s)$
is non-increasing on the intervals
  $(0,\lambda)$ and
$(\lambda,1)$.

Then the system has no more than one limit cycle which is always stable.
 }

\bigskip
We now consider the standard version of the two-dimensional system
corresponding to the functions in (\ref{a3}):
$$\dot{x}=\frac{s-\lambda}{s+a} x,\quad \dot{s}= s(1-s-\frac{x}{s+a}).$$

By scaling time it is transformed to the system
$$\dot{x}=(s-\lambda) x,\quad \dot{s}= s((1-s)(s+a)- x).$$

In the first quadrant the system has an equilibrium
$$P((1-\lambda)(\lambda +a),\, \lambda),$$
which is an asymptotically stable node or focus for
$\lambda \geq \frac{1-a}{2}$
and repelling node or focus for
 $$\lambda <\frac{1-a}{2}.$$
Using Theorem 2 this condition implies there will be a unique limit cycle in the plane.

\smallskip

Our main interest is in the case, where there are two limit cycles in
both coordinate planes. This requires
$ h'(\lambda_i) -
 \psi_2' ( \lambda_i ) x_i^0 >0  $ in the general case
 and $\lambda_i <\frac{1-a_i}{2}$ in our special case.

 \begin{comment}
 *******************************************''
DO WE USE THIS??

In future we will suppose this last condition to be satisfied
and moreover that
  $$a\leq \lambda.$$
As we assume this for $a=a_i$ and $\lambda =\lambda_i$ and the system (3)
in the coordinate planes $x=0$ and $y=0$ has this form there is always
one cycle in each plan, attracting inside the plane.
Our construction of the positive invariant set uses this behaviour.

****************************************************************
\end{comment}

\section{The Poincar\'{e} map}

While the behaviour of the two-dimensional systems in the coordinate
plane is well known, the behaviour outside the coordinate planes can be very
complicated in the case both predators survive and we can find behaviour not yet well understood.

It is clear from assumptions that all interesting behaviour will be
in the region where $s<1$.

In the system when the functions are chosen as in (\ref{a2}) and (\ref{a3}),
if $a_1>a_2$ in \cite{kustarov} is shown that the predator $x_1$ goes extinct if

$$\gamma > 1 +\frac{a_1}{\lambda_1} \left( \lambda_1 -\lambda_2\right)
+ \frac{\lambda_2}{a_1} \left( a_1 -a_2\right), \,\,
\gamma =\frac{\lambda_2 a_1}{\lambda_1 a_2} $$

\noindent or equivalently if

$$\lambda_1 > \frac{a_1\lambda_2 (a_2+1)}{a_1a_2 +\lambda_2 (a_1-a_2) +a_2}  $$

and the predator $x_2$ goes extinct in the case $\lambda_1<\lambda_2$.
Thus in this case we will concentrate on the case when these inequalities are not satisfied.

\begin{comment}
*********************************************************************
{\bf Question}. {\it Should we here or better somewhere else give some short
review about what is known and what not. And also history of development
from other works, ours and before?  For example, for which parameters it
is known the system has no inner solutions and what then happens, and
first detection of inner solution and our further developments.}
******************************************************************************
\end{comment}

 \subsection{Decomposition. Simple change of variables}

In order to construct a positively invariant set and understand something
about the behaviour inside this set we use comparison systems with simpler
two-dimensional behaviour.

\begin{comment}
*************************************************************************
{\bf Question}.  {\it Where should we tell and prove nothing interesting
appears outside the pos inv set?}

*****************************************************''
\end{comment}

In order to find the comparison systems we consider a transform of
the original system into new variables:
  $  \  m= x_1 + x_2 ,
 \quad \xi = x_1 / m  . $
 In the new variables system (\ref{a1}) obtains the form:
\begin{equation}\label{5}
\dot{m}= p ( s,\,\xi ) \,m,   \quad\quad \dot{\xi} = \sigma ( s ) \,
\xi ( 1 - \xi ),   \quad\quad \dot{s}= h(s)- q (s, \,\xi )\,m,
\end{equation}
 where
\begin{equation}\label{b2}
 p ( s,\, \xi ) = {\phi}_1(s) \xi + {\phi}_2(s)( 1 - \xi ),   \quad\quad
 \sigma ( s ) = {\phi}_1(s)  - {\phi}_2(s) ,   \quad\quad
 q (s,\, \xi ) = {\psi}_1(s) \xi + {\psi}_2(s)(1 - \xi ).
\end{equation}

 In the transformed system we can use
the knowledge about the two-dimensional system where the variable
$\xi$ is constant. The systems, where $\xi=0$ and $\xi=1$ and where the
three dimensional system has behaviour related to the two dimensional
systems in the coordinate planes $x_1=0$ and $x_2=0$ correspondingly,
turn out to be important as comparison systems.

\subsection{Comparison systems}

This subsection contains the main results obtained by using the
comparison systems mentioned in previous subsection.
From these it is easy to construct a positive invariant set.

We will need some notations:
 $$H = H(x,s) = h(s)-{\psi}_1(s)x_1 - {\psi}_2(s)x_2,\qquad
 H_i=H_i(x,s)=h(s)-m{\psi}_i(s),$$

 \begin{equation}
 \omega(s) = {\psi}_1(s){\phi}_2(s) - {\psi}_2(s){\phi}_1(s) ,\qquad
 l=l(x,s)=h(s)({\phi}_2(s)-{\phi}_1(s)) - \omega(s)m .
 \end{equation}

 We define the following surfaces:
 \begin{equation}
 {\cal L} = \{ (x,s) \in R_3^+ \mid \; l(x,s)=0 \}\, ,  \qquad
 {\cal S}_i = \{ (x,s) \in R_3^+ \mid \; H_i(x,s)=0 \}.
 \end{equation}

 In the future we will use these notations both for the functions
    $\; l(m,s), H_i(m,s)\;$   and for the corresponding
    curves in the two-dimensional space
 $\,m,s. $
 \vskip1mm

  We consider two comparison systems
  obtained for $\xi=1$ and $\xi=0$ and the corresponding vector
  fields
 ${\cal F}_i$:
 \begin{equation}\label{asr}
 \dot{x_1}={\phi}_i(s) x_1, \quad  \dot{x_2} = {\phi}_i(s)x_2,  \quad\quad
 \dot{s} = H_i ( x_1, x_2, s ).
 \end{equation}

  We notice that the planes, where $\xi$
 (and thus the proportion between the variables $x_1$ and $x_2$) is constant is invariant under these systems.

 These systems have integral surfaces generated by solutions in one plane.
 An integral surface is determined by an initial condition
 $m = m_0,\; s=s_0$. It contains this line and is usually a "spiral" surface,
 but  a tube if the intial condition is on the limit cycle and the line
 if the initial condition is the equilibrium. This surface can be considered as having an outer surface with normal vector pointing away from the line of
 equilibrium points.
  We denote representants for the integral surfaces by
${\cal{M}}_1$ and ${\cal{M}}_2$  correspondingly.

We  define the fields of  {\em outer normal vectors}
 $\overline{\bf n}_1$   and   $\overline{\bf n}_2$:
 \begin{equation}
 \overline{\bf n}_i =
 \overline{\bf n}_i\,( x_1, x_2, s ) =
 \,\left(\,-H_i(x_1, x_2, s),\,-H_i(x_1, x_2, s),\,  m\,\phi_i (s)\,\right).
 \end{equation}

 The vectors are orthogonal to solution curves of the comparison
 systems and to the line $m = m_0,\; s=s_0.$
 Thus the vector fields
  $\overline{\bf n}_i$ degenerate at the equilibrium points
 ${\cal F}_i $ and they are continuous and ortogonal
 to integral surfaces of systems  $(\ref{asr}_i), $
 passing through line $m = m_0,\; s=s_0.$

 \vskip1mm

In order to find out in which direction the solutions of the
original three dimensional system with vector field ${\cal F}$ crosses
the integral surfaces ${\cal{M}}_1$ and ${\cal{M}}_2$,
we consider the scalar product:
 \begin{eqnarray}\label{11}
 <\,\overline{\bf n}_1,\,{\cal F}\,> \; = &\; x_2\,[ h(\phi_1 -\phi_2)
 + m\,(\psi_1 \phi_2 - \phi_1 \psi_2)\,]\,= -l(m,s)\,x_2, \\ \label{12}
 <\,\overline{\bf n}_2,\,{\cal F}\,> \; = &\; x_1\,[ h(\phi_2 -\phi_1)
 + m\,(\psi_2 \phi_1 - \phi_2 \psi_1)\,]\,= l(m,s)\,x_1.\\
 \nonumber
 \end{eqnarray}

We note that these products are zero on the surface $\cal L$.

For this surface to have a nice form we introduce
 a new assumption\\

 $B_1 :\quad$ $\omega (s)\neq 0$ for $s>0.$\\

From $A_3,\, A_5,\, A_6$ and $A_7$ follows that
$\omega (s)>\phi_1(s) (\psi_2(s)-\psi_1(s))>0$ for $s>\lambda_1$
 and thus from $A_1$ and the assumption follows that  $\omega (s)>0$
for $s>0.$

From this assumption also follows that, in region
 $s>0$, the surface
$\cal L$ can be defined explicitly:
\begin{eqnarray}
m=m^*(s)= h(s)\,\frac{\phi_2(s)-\phi_1(s)}{\omega(s)}.
 \end{eqnarray}

The surface is defined only for
$ \tau\leq s\leq 1$.

From sign analysis of expressions
 \ref{11} and \ref{12}, we get the following result:

\smallskip

{\bf Lemma 1.}  {\it
The trajectories of system
 ($\ref{a1}$) intersect, in the region $m>m^*(s)$, transversally integral surfaces of
 ${\cal M}_1$ from its inner side to the outer and the integral surfaces
  ${\cal M}_2$ from the outer side  to the inner side.

The intersection occurs in opposite order in the region $m<m^*(s)$.

The trajectories of the systems
 (\ref{a1}) and (\ref{asr}$_i$)
are tangent to each other on the surface $m=m^*(s)$,
in the projection to the $(m,s)$-space. }

{\it Proof}. The type of intersection with integral surfaces follows from that the fact, that the first scalar product is positive and the second
negative in $m>m^*(s)$. The scalar products are zero for $m=m^*(s)$, from which
follows the tangency. Thus the lemma is proved.

\smallskip

The systems
 (\ref{asr}$_i$) are projected to the  $(m,s)$-plane in a natural way:

 \begin{eqnarray}\label{14}
\dot{m}=  \phi_1(s) m,\quad & \dot{s} = h(s)-\psi_1(s) m; \\
\label{15}
\dot{m}=   \phi_2(s) m,\quad & \dot{s} = h(s)-\psi_2(s) m. \\
 \nonumber
 \end{eqnarray}

This defintion will give us one of the main technical
concepts of this work.

\smallskip

{\bf Definition 1}.
The projection of the surface
 $x+y=m^*(s)$ into the  $(m,s)$-plane forms a
curve $m=m^*(s)$, we will call {\sf tangency curve.}

\smallskip

We also need the following definition.

\smallskip

{\bf Defintion 2}.
The projections $S_1$ and $S_2$ of the isoclines of the comparison systems,
defined by the equalities
$m=h(s)/\psi_1(s)$ \ and  \  $m=h(s)/\psi_2(s)$
we will call  {\sf first and second main
isoclines}
correspondingly.

\smallskip

The following lemma gives us information about the position of
the tangency curve and the main isoclines.

\smallskip

{\bf Lemma 2}.
 {\it The main isoclines do not intersect in the positive quadrant of the
 $(m,s)$-space. Thereby the
 first main isocline $S_1$ will be outside
 the second $S_2$ relative to $s$-axis.

The tangency curve intersects the main isoclines at equilibrium
points of systems
 (\ref{14}-\ref{15})
and is outside the first main isocline, if
 $s>\lambda_1,$  between the main isoclines, if
 $\lambda_2<s<\lambda_1,$ and inside the second, if
$s<\lambda_2.$  }

\smallskip

{\it Proof}. The position of the main isoclines follows from $A_5$. The inequality $m^*(s) > \frac{\displaystyle h(s)}{\displaystyle\psi_i(s)}$ is equivalent
to
$\phi_2(s) (\psi_i(s)-\psi_1(s))>\phi_1(s) (\psi_i(s)-\psi_2(s)) $ because $\omega (s)>0$.
But then from $A_5$ follows equivalence with $\phi_i(s)>0$,
 which follows from
 $s>\lambda_i$ using  $A_3$. Analogously
 $m^*(s)< \frac{\displaystyle h(s)}{\displaystyle\psi_i(s)}$
follows from $s<\lambda_i$. These inequalities give the geometric conclusion of the lemma.

 \subsection{The standard system}
 We examine more carefully the expressions for the tangency curve in the case where we use  (\ref{a2})
 and (\ref{a3}) in the right hand sides.

 We calculate:

 \begin{equation}\label{16}\phi_2(s)-\phi_1(s) =\frac{\kappa_0
(s-\tau)}{(s+a_1)(s+a_2)},\quad \mbox{where} \quad
 \kappa_0 =a_1+\lambda_1 -(a_2+\lambda_2), \
 \tau=\frac{(\gamma-1)\lambda_1a_2}{\kappa_0}.
 \end{equation}

Moreover,

 \begin{equation}\label{17}
\omega(s)=-\frac{s-\lambda_1}{s+a_1}\cdot\frac{s}{s+a_2}+
\frac{s-\lambda_2}{s+a_2}\cdot\frac{s}{s+a_1}
=\frac{s(\lambda_1-\lambda_2)}{(s+a_1)(s+a_2)}.
 \end{equation}

\noindent
and the formula for the tangency curve becomes a quadratic expression:

 \begin{equation}\label{18}
m^*(s)=\frac{h(s)\kappa_0(s-\tau)}{s(\lambda_1-\lambda_2)}
 = (1-s)(s-\tau)\kappa, \quad \mbox{where} \quad \kappa =
 \frac{\kappa_0}{\lambda_1-\lambda_2}.
 \end{equation}

We notice that parameters giving the same tangency curve satisfy the equation

\begin{equation}
a_i=\lambda_i (\kappa -1) -\tau\kappa
\label{equ}
\end{equation}

\begin{comment}
***********************************************************************
{\bf Figure here!!!!}

{\bf Question} {\it cannot this just be part of previous
subsection.}
\end{comment}

 \subsection{Construction of the boundaries
 of the Poincar\'{e} annulus}

   Using the lemmas we construct an annular region where trajectories
  cross  the boundaries strictly in the inside direction. We use the region
  to define a Poincar\'{e} map to discretize the flow inside the
  annulur region. This region we will call
 {\sf Poincar\'{e} annulus.}

  We will build it in the
  $(m,s)$-plane. Its preimage in the
   $(m,s,\xi)$-space is a positively invariant
   region possible containing a non-wandering set
   with complicated structure.
   Also this 2-dimensional region we call Poincar\'{e} annulus.

We define  two continuous systems by gluing together
 two parts:

1) System ${\cal P}^i$ is defined by the vector field, which
coincides with the first comparison system (\ref{14}) outside
the tangency curve
 $\cal L$ (that's in region $m>m^*(s))$ and with the second
 system  (\ref{15}) inside. We will call this system
the {\sf inner} system.

2) System ${\cal P}^e$ is defined opposite:
the vector field coincides with the second comparison system (\ref{15})
outside the tangency curve $\cal L$ and with the first
system (\ref{14}) inside.
 We will call this system
the {\sf outer} system.

The orbits of the systems are correctly defined
and continuous
 everywhere except
on the segment  $[O_2,O_1]$ of the tangency curve.
This follows from the fact that the comparison vector fields
are collinear and non-degenerate on the curve
 $\cal L,$ and intersect this curve transversally.

 \begin{comment}
 **************************
 {\bf Question}. {\it This I do not fully understand, better formulations
 needed here.}
 ***********************
 \end{comment}

The segment  $[O_2,O_1]$ we denote by
 $\cal A$.

\begin{comment}
 and we observe that it always
 consists of points ?????
 for the orbits of
 the system.

 {\bf Question.} {\it I do not remember how is tochka vozvrata
 defined and how in English }
 \end{comment}

For the outer system the segment $\cal A$ is repelling
(orbits with initial conditions not on   $\cal A$ never
come on  $\cal A$), and for the inner system this segment is
attracting. The outer  system has one stable limit cycle and the inner system
has two limit cycles of which the outer is stable and the inner unstable.

\begin{comment}
************************************************************
defining ????? regimes:
up from $O_2$ to $O_1$ from the inner side of the segment
and down from  $O_1$ to  $O_2$ from the outer side.

{\bf Question.}
{\it Do not remember what is skolyashchie regimes in English}
\end{comment}

\paragraph{Construction of outer boundary.}
We look at the separatix of the unstable manifold of the equilibrium point
 $O_1$ of the outer system ${\cal P}^e$ and we denote its first
 intersection with the tangency curve $\cal L$, after passing line $s=\lambda_1$,
 by  $L_1$. It is clear that the intersection is below the
 segment $\cal A$. The next intersection of the orbit
 with the tangency curve we denote by   $L_2.$
 Thereby we have found a positively invariant set for the system. The boundary of
 it is given by the part of the separatrix and of $\cal L$ from $O_1$ to $L_2$ and   we will  take it as one boundary of the Poincar\'{e} annulus.

 \begin{comment}
 {\bf Question.}  {\it The concept "Bendixson sack" is not usual in English,
 and "Levinson compact" is for sure called something else.}

{\bf Figure here!!!!}
\end{comment}

\paragraph{Construction of inner boundary.}
  The outer boundary of the Poincar\'{e} annulus was constructed
  without problems. But the construction of the inner boundary
  is more problematic.
  We explain why.
  We choose an arbitrary point  $M$ on the curve $\cal L$ as the initial point
  for on orbit of the inner system ${\cal P}^i$.
  We will suppose that the initial point coincides with the
  upper point on $\cal L$ of an orbit of ($\ref{15}$) tending to the limit cycle
   from the
  inner side.
   There are two possibilities.
    Either the orbit of the point $M$ does not intersect with
     the segment  $\cal A$ or it intersects the segment.

\smallskip

     In the case of non-intersection the orbit tends to a limit cycle
     of system ${\cal P}^i$, which we will take
     as inner boundary of the Poincar\'{e} annulus.

  In this case, the Poincar\'{e} map for the full system
 (\ref{a1}) is defined in the following way:

In the $(m,s,\xi)$-space (or correspondingly in the
$(x,y,s)$-space) we consider the plane
 $S_{\varepsilon}: \, s=\varepsilon,$ where
$\varepsilon$
is chosen such that the intersection of the plane
with the Poincar\'{e} annulus consists of two rectangles
in the $(m,s,\xi)$-space. On $S_{\varepsilon}$ the  Poincar\'{e} map is defined as usually as the next
 intersection with $S_{\varepsilon}$.

In this case we will say that the Poincar\'{e} map is correctly defined.

\begin{comment}
Thereby we will assume $\varepsilon
\leq\l_2.$
\end{comment}

\begin{comment}
{\bf Question.}
{\it Should we write that we define the map on one of these rectangles?
Should there possible be own paragraph for explaining Poincar\'{e} map? }
\end{comment}

\smallskip

In the case, when the closure of the orbit has common points
with the special segment, we will speak about non-correct boundary
for the Poincar\'{e} annulus.

If the Poincar\'{e} map is correctly defined for some parameter values in the
standard system given by functions (\ref{a2}) and (\ref{a3}) and we increase $\lambda_2$ and
let $a_2$ satisfy the equality $(\ref{equ})$, it remains correctly defined.
This holds, because if we take the limit cycle for the inner boundary with
original parameters and consider the trajectory containing the outer part
of this cycle (outside tangency curve, where trajectories for new system coincide
with original) for the new $\lambda_2$ and $a_2$ then from Lemma 1 follows  that the trajectory for the new system inside tangency curve will be outside the limit
cycle.

Some concrete numerical results for the boundary are given in next section.

\begin{comment}
\begin{figure}[th!]

{\centerline{
\epsfxsize=110mm
\epsfbox{figure1poi2.eps}}}
\begin{picture}(0,0)(0,0)

\end{picture}
\caption{Illustration of tangency curve, main isoclines and construction
of boundary for outer system}
\label{poi2}
\end{figure}
\end{comment}

\begin{figure}[h!]
\begin{center}
\caption{Illustration of tangency curve, main isoclines and construction
of boundary for outer system}
\includegraphics[height=7.5cm,width=15cm]{figure1poi22b.png}\\
\label{poi2}
\end{center}
\end{figure}

\section{Numerical results}

All results here are given for the standard system given by functions (\ref{a2})  and
(\ref{a3}).

We choose $a_1=\lambda_1=0.1, \, a_2=0.0075,\,\lambda_2=0.01$ and calculate
$\tau\approx 0.00137, \, \kappa \approx 2.028$.
In this case the stable limit cycle of the inner system is intersecting
the tangency curve at about $s=0.85$ and the unstable cycle at $0.384$.
If we increase $\lambda_2$ to 0.02 and calculate $a_2$ from formula
(\ref{equ}), the stable limit cycle of the inner system is intersecting
the tangency curve at about $s=0.905$ and the unstable cycle at $s=0.2703$.
If we increase further $\lambda_2$ to 0.05 and calculate $a_2$ from formula
(\ref{equ}), the stable limit cycle of the inner system is intersecting
the tangency curve at about $s=0.95$ and the unstable cycle at $s=0.1595$.
A bifurcation diagram showing how attractor for Poincar\'{e} map changes with
$\lambda_2$ is given in Figure \ref{gunfig}.

\begin{comment}
\begin{figure}[th!]

{\centerline{
\epsfxsize=110mm
\epsfbox{biffos.eps}}}
\begin{picture}(0,0)(0,0)

\end{picture}
\caption{Bifurcation diagram when $a_1=\lambda_1=0.1$ and $\lambda_2=\nu \, 0.01$ and
$a_2$ is chosen so that we stay on tangency curve determined by
$a_2=0.0075,\, \lambda_2=0.01$. Horisontal axis represents the parameter $\nu$ and
vertical represents the variable $\xi$. The Poincar\'{e} map is defined on the
outer rectangle of the Poincar\'{e} annulus on level $s=0.1$}
\label{gunfig}
\end{figure}
\end{comment}

\begin{figure}[h!]
\begin{center}
\caption{Bifurcation diagram when $a_1=\lambda_1=0.1$ and $\lambda_2=\nu \, 0.01$ and
$a_2$ is chosen so that we stay on tangency curve determined by
$a_2=0.0075,\, \lambda_2=0.01$. Horisontal axis represents the parameter $\nu$ and
vertical represents the variable $\xi$. The Poincar\'{e} map is defined on the
outer rectangle of the Poincar\'{e} annulus on level $s=0.1$}
\includegraphics[height=7.5cm,width=15cm]{biffos.png}\\
\label{gunfig}
\end{center}
\end{figure}

In the case when the Poincar\'{e} map is correctly defined, very often there is a strong
contraction in the $m$-direction and in \cite{osipov3} is shown by numerical experiments and theoretical estimating arguments that the one dimensional model map
given by

$$ f(v)= \beta + v -\frac{k_1+k_2 e^ v}{1+v} u$$

\noindent where  $\beta ,\, u$ and $k_i$ are constants and $v=\ln (x_2/x_1)$
gives a good approximation.

In the case when the Poincar\'{e} map is not defined correctly we can find
interesting "spiral-like" chaos for parameter values
$a_1=0.5,\, \lambda_2=0.2,\, a_2=0.002$  and $0.33\leq \lambda_1\leq 0.42$
and $a_1=0.2,\, \lambda_2=0.2,\, a_2=0.01$  and $0.4\leq \lambda_1\leq 0.5$.
We observe that in this case the equilibrium in $x_1 s$-plane is stable
inside the coordinate plane and there is no periodic solution.
Examples of more  complicated chaos are also easy to find when there
are limit cycles in both coordinate planes, for example, if
$a_1=\lambda_1 =0.25,\, \lambda_2=0.163,\, a_2=0.06$.

\section{Conclusion}
We have introduced the concept of tangency curve as an important tool for constructing a positively invariant set, where we can define a
Poincar\'{e} map for examining the structure of attractors of system (\ref{a1}).
For the special case, where functions are given by (\ref{a2}) and (\ref{a3}),
we have given a concrete numerical example of a bifurcation diagram for this Poincar\'{e} map.
Except general conditions on the system, we have introduced a geometric condition for the existence of our invariant set. Our conditions are sufficient for the existence of the invariant set, but not necessary. For example, the bifurcation path in \cite{osipov4} does not satisfy the geometric condition for all parameters, but it is possible to find a good invariant set, where to define a Poincar\'{e} map.
In general, in case of functions (\ref{a2}) and (\ref{a3}), there is a lower limit for parameter $\lambda_2$ when our conditions are not more satisfied. We also give numerical examples of more complicated "spiral-like" case where no similar invariant set of the type we constructed is possible to find.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


A variety of the most ancient and precious cotton in the world.
West Indian Sea Island cotton, known as "gossypium barbadense" or "black seed", is one of the most ancient and precious cotton types in the world, discovered in the early eighteenth century in the British West Indies. Its production, equal to just 0.006% of the world's long-staple cotton, is now concentrated mainly in Barbados, Antigua and Jamaica, areas that constitute a real paradise climate. About 110 million bales of cotton are produced each year, globally, of which 2 million are extra-long staple cotton. The annual production of Sea Island Cotton is just 130 bales.
The Albini Group has secured an important partnership with ECCI Cotton (an association formed by small local farmers and supported by the Ministry of Agriculture of the island) for the exclusivity of 100% of Sea Island cotton grown in Barbados, which corresponds to an annual production of just over 70 bales.
Sea Island Cotton of Barbados is distinguished from all other species of cotton thanks to its unique characteristics: the considerable staple length of the fibre, arriving at 36/37 mm, the high strength, equal to 40 gr/tex and the good percentage of uniformity (86%). Besides the length, the fibre is exceptionally fine, proved by the micronaire, between 3.1 and 3.4, together with a significant brightness (a degree of reflectance of 73).
The cultivation of Sea Island follows a particular process. The seeds are carefully selected to ensure the highest quality and sowing is done mechanically in an extremely regular way. Irrigation takes place mainly naturally, through the heavy rains.
The organization responsible WISICA (West Indian Sea Island Cotton Association) inspects every kilo of cotton produced locally and issues the Certificate of Authenticity for yarns marked SEA ISLAND guaranteeing the purity of this precious raw material.
Fabrics obtained from Sea Island cotton are silky to touch, full-bodied, homogeneous, with an ability to revive and improve with each wash.


text:
aoginvest.com
AOG is created
Oil trading
Mining, Samax Gold
Downstream, service stations
IPO Samax Gold
Upstream, Addax Petroleum
Rice trading, Ascot
Downstream, West Africa expansion
(10 years)
Sale of Samax Gold
Mining, Axmin
Downstream, East Africa
Downstream, LPG
Downstream, lubricants
Trading, Tradex
Downstream, the "Oryx" brand
Downstream expansion
Leader in oil trading
Downstream consolidation
IPO Addax Petroleum
Creation Addax Bioenergy
Sale of Addax Petroleum
Upstream, Oryx Petroleum
Creation AOG Real Estate
Downstream, Lubricants in West Africa
IPO Oryx Petroleum
Birth of Oryx Energies
Addax Bioenergy certifications
(25 years) AOG repositioning and rebranding
Real Estate, 1st property sale
Oryx Petroleum, 1st production and sales
Addax Bioenergy, 1st production
Real Estate, 1st investments in Spain
Addax Bioenergy transfer
Consolidation Oryx Petroleum
An entrepreneurial spirit, the ability to recognise opportunities and take calculated risks, without compromising its values. We will continue to evolve as an established, but never establishment, firm, with always a twist of the unexpected.
1987	AOG is created
The Addax and Oryx Group (AOG) is founded in December 1987 by Jean Claude Gandur and 3 associates, with an expertise in international trade and Africa. The Group begins in oil trading in West Africa.
1987	Oil trading
The Addax and Oryx Group (AOG) starts out in oil trading in West Africa in December 1987.
1987 Mining, Samax Gold
AOG demonstrates from the start its ability to diversify its investments and take calculated risks, entering Africa's mining sector with an investment in gold exploration company, Samax Gold.
1989 Bunkering
As part of its strategy to take products to end users, AOG launches Addax Bunkering Services in 1989, in order to supply ships and offshore platforms with the fuels, lubricants and associated services they need. Addax Bunkering Services will become a key player in the African bunkering market.
1989	Downstream
AOG is quick to understand the importance of access to energy for Africa's social and economic development. In 1989, it acquires Esso's petroleum depot in Senegal as a first step towards supplying consumers and industry directly with the products they need.
1989	Downstream, service stations
AOG acquires a majority stake in oil company Phoenix, in Nigeria, in 1989. It is the Group's first investment in service stations in Africa. Through the years, its network of service stations will expand and consolidate, before investments grow again from 2013.
1996	IPO Samax Gold
Samax Gold, formed in 1987, is developing well and is listed on the Toronto stock exchange in 1996.
1994	Upstream, Addax Petroleum
With the creation of its upstream exploration and production company, Addax Petroleum, AOG becomes an integrated oil company, active in exploration-production, trading and the storage and distribution of oil products in sub-Saharan Africa. Addax Petroleum begins with the development of marginal oil fields in Nigeria, before expanding its operations in Africa and the Middle-East.
1997	Rice trading, Ascot
Leveraging its expertise in international trade, AOG creates Ascot Commodities in 1997, a company active in rice trading and that mainly imports into sub-Saharan Africa. 10 years later, Ascot will be among the top 10 international companies in the sector. Ascot ceases its activities in 2010, as AOG refocuses on the energy sector.
1997	Downstream, West Africa expansion
In 1997, AOG expands its downstream activities in West Africa, as it pursues its strategy of supporting development in the region. It begins the construction of an oil and gas terminal in Benin, with the objective of extending access to energy along the West African coast, including landlocked countries like Burkina Faso, Mali and Niger. The investment is hailed as the largest private investment in West Africa for a number of years. The terminal is inaugurated in 1999.
1997	(10 years)
After 10 years, thanks to a dynamic investment strategy and an exceptional ability to recognise opportunities, AOG has already become an integrated oil company, active in oil exploration-production, trading, and the storage and distribution of oil products in sub-Saharan Africa. Its entrepreneurial spirit has also led the Group to diversify into related sectors, like mining or rice trading, which require expertise in trading and/or Africa.
1998	Sale of Samax Gold
AOG sells Samax Gold to Ashanti Goldfields in 1998. Founded in 1987 and listed on the Toronto stock exchange in 1996, Samax has successfully developed gold exploration projects in Tanzania, Ghana, Senegal and the Republic of Congo.
1998	Mining, Axmin
Leveraging its success with Samax Gold, sold the same year, AOG continues its interest in the African mining sector as it invests in Axmin, active in gold exploration in Africa. Axmin successfully develops projects in Burkina Faso, Mali, Senegal, Tanzania and the Central African Republic. It is listed on the Toronto Stock Exchange in 2001. AOG will gradually withdraw from the company, as it refocuses on the energy sector.
1999	Downstream, East Africa
AOG invests for the first time in East Africa, when it acquires AGIP's assets in Tanzania, including 75 service stations, a lubricants blending plant and 50% of TIPER, a former refinery that it will convert into oil storage. Like in West Africa, the Group aims to contribute to development in the region by facilitating access to energy, including for landlocked countries in the Great Lakes region and Zambia.
1999	Downstream, LPG
AOG enters the LPG (Liquefied Petroleum Gas) market in 1999, when it inaugurates its oil and gas terminal in Benin (started in 1997) and opens an LPG terminal in Tanzania the following year. The strategy is clear: to promote LPG as a healthier, safer and more ecological energy alternative to firewood, charcoal and kerosene. LPG develops strongly from 2001, thanks in particular to the « Oryx MiniGas » concept, launched in Benin, which offers a small LPG cylinder, together with cooking accessories, at an affordable price for low-income families. The concept is a great success and will be deployed to other countries in the region.
1999	Downstream, lubricants
Through its acquisition of AGIP Tanzania, AOG is able to enter the lubricants market thanks to the existing blending plant. The blends are designed in Geneva, adapted to Africa's harsh conditions, and produced close to the market for consumers and industry. AOG opens a second blending plant in 2011 in Togo to serve West Africa.
1999	Trading, Tradex
In order to expand its oil supply to non-producing countries, AOG takes a 30% stake in oil trading and export company, Tradex, in Cameroon, with the aim of supplying countries in the CEMAC region (Economic and Monetary Community of Central Africa).
2002	Downstream, the "Oryx" brand
From 2002, AOG uses the "Oryx" brand for all its downstream activities (storage and distribution). It launches the same year its range of "Oryx" lubricants in West Africa.
2003	Downstream expansion
AOG makes significant investments in its downstream activities between 2003 and 2005. It launches fuel and lubricants distribution activities in Mauritania (acquisition of Exxon-Mobil assets), develops its network of service stations in Senegal and Côte d'Ivoire, launches LPG operations in Burkina Faso and Côte d'Ivoire (acquisition of Shell assets), and opens a strategic storage terminal in Sierra Leone, becoming a key player on the west coast of Africa.
2004	Leader in oil trading
In 2004, AOG's trading arm, under the "Addax" brand, is the leading independent oil trader in Africa. This includes the export of production from AOG's upstream company, Addax Petroleum, towards refineries in West Africa, Europe, North America and Asia. It exports oil from Nigeria, Cameroon, Gabon and Côte d'Ivoire, and imports oil to respond to the needs of non-producing African nations. Its trading arm has also established a presence in Asia and the Caspian region.
2005	Downstream consolidation
AOG decides to consolidate its downstream activities in 2005, after several years of strong development. It reduces its service station network in Tanzania and stops its distribution activities in Mauritania. At the same time, it confirms the successful strategic shift towards the development of LPG on the continent. LPG activities are underway in Benin, Burkina Faso, Côte d'Ivoire and Tanzania. The Group will pursue this strategy over the coming years to become one of the key players in LPG in sub-Saharan Africa.
2006	IPO Addax Petroleum
Addax Petroleum, AOG's oil exploration and production company, is listed on the Toronto Stock Exchange in 2006, with an average annual production of 90,000 barrels/day.
After 20 years, AOG is considered a major player in the energy market, with a presence in 15 countries and 900 employees. The Group has grown through acquisitions, partnerships and direct investments. Thanks to oil trading and downstream activities, it supplies and distributes fuels, lubricants and LPG across sub-Saharan Africa. It is also a leader in niche markets like bunkering and rice trading. AOG has successfully developed oil exploration and production operations in Africa and the Middle East. Its success confirms the model of continuous investment and diversification, based on a strong entrepreneurial dynamic and a capacity to take calculated risks.
2008	Creation Addax Bioenergy
Leveraging its experience in fuels and Africa, AOG creates Addax Bioenergy in 2008 with the ambition to develop a sustainable model for bioenergy and green electricity from sugarcane in Sierra Leone. Partnerships with international development agencies, strict social and environmental rules, lengthy prior evaluations and dialogue with local communities. The approach includes other contributions to local communities through a Farmer Development Program, together with innovative solutions that provide landowners with recognised land rights for the first time.
2009	Sale of Addax Petroleum
AOG sells its upstream company, Addax Petroleum, to Chinese conglomerate Sinopec in 2009. It is the largest Chinese acquisition of a foreign oil company at the time (US$7.24 billion). Created in 1994, Addax Petroleum developed oil fields in Africa and the Middle East, and had reached average annual production of over 140,000 barrels/day at the time of the sale.
2010 Upstream, Oryx Petroleum
AOG decides to further pursue opportunities in the upstream industry with the creation of Oryx Petroleum, which rapidly acquires promising exploration licenses in the Kurdistan Region of Iraq.
2010 Creation AOG Real Estate
Following the sale of Addax Petroleum, AOG diversifies further, expanding this time into real estate. AOG Real Estate makes direct (with specialised partners) and indirect investments in commercial real estate in Europe and North America, rapidly demonstrating the same ability to successfully recognise opportunities and take calculated risks. It makes its first direct investments in London in 2010, followed by others in London, Malta, Paris and Madrid (from 2016).
2011	Downstream, Lubricants in West Africa
With a continued focus on delivering energy products directly to consumers and industry in Africa, AOG invests in a second, ultra-modern lubricants blending factory, this time in Togo, to serve the needs of West Africa. Its initial factory in Tanzania, acquired in 1999, continues to supply East Africa.
2013	IPO Oryx Petroleum
Oryx Petroleum, AOG's upstream oil exploration and production company, created in 2010, is listed on the Toronto Stock Exchange in 2013.
2013	Birth of Oryx Energies
Oryx Energies is born of the merger of AOG's trading and downstream activities in 2013. Oryx Energies is an integrated platform that masters the value chain from the acquisition of products on the open market (trading) to their storage and distribution to end users in sub-Saharan Africa. It is the consecration of the strategy of complementarity pursued for many years. Significant investments are planned and executed over the following 5 years, with the objective of reinforcing its position as one of the most important private players in the energy sector in the region (new terminal in Las Palmas, more service stations, more LPG cylinders and storage facilities, and its first-ever panafrican advertising campaign).
2013	Addax Bioenergy certifications
In 2013, Addax Bioenergy receives certifications that confirm the sustainable model that it has sought to apply. It receives the first African certification by the Roundtable for Sustainable Biomaterials (RSB). It then becomes the first operation in Sierra Leone to be registered as a Clean Development Mechanism (CDM) project of the United Nations Framework Convention on Climate Change (UNFCCC), and the first sugarcane-based power generation facility for ethanol production to be registered as a CDM in Africa.
2013	(25 years) AOG repositioning and rebranding
As it reaches its 25th year, AOG proceeds with an extensive repositioning and rebranding in order to better reflect the significant diversification of its investments over the years. It becomes simply AOG, reflecting its Addax and Oryx heritage, while recognising that it has evolved into a diversified investment group, active in the energy, real estate and capital investment sectors. It is also the opportunity to articulate the culture and values that have always been at the heart of its success: Alert, Principled, Adaptable.
2013	Real Estate, 1st property sale
Created in 2010, AOG Real Estate completes its first major property redevelopments (with its partners) in London and Paris, in 2013, and sells the Paris renovation (the ex-Panhard factory) to a French real estate firm. It will continue an active management of its real estate portfolio.
2014	Oryx Petroleum, 1st production and sales
Oryx Petroleum, AOG's upstream oil exploration and production company created in 2010, begins production and makes its first crude oil sales in the Kurdistan Region of Iraq.
2014	Addax Bioenergy, 1st production
Addax Bioenergy begins the production of sustainable biofuels and green electricity from sugarcane in Sierra Leone. The first sales take place in 2015.
2016	Real Estate, 1st investments in Spain
AOG Real Estate makes its first investments in Spain in 2016, with 2 construction projects in Madrid. It takes advantage of the high real estate prices in London to sell three of its properties at record capitalisation rates, in anticipation of the potential currency effects of the UK referendum on its membership of the European Union. It also has direct investments in Geneva, London, Madrid, Malta and Paris, as well as holdings in US real estate funds.
2016	Addax Bioenergy transfer
AOG transfers majority ownership of Addax Bioenergy, its sustainable bioenergy and green electricity production company in Sierra Leone, to a group of investors led by Sunbird Bioenergy Africa, in order to ensure its future success. Created in 2008, activities had been suspended in 2015, after seven years of investment, due to the significant impact of a number of unforeseeable events, including the Ebola outbreak in 2014.
2016	Consolidation Oryx Petroleum
Following the fall in oil prices in 2014, Oryx Petroleum strengthens its financial position with funding from a new shareholder, Zeg Oil and Gas. It restructures, continues production in the Kurdistan Region of Iraq and develops its license area offshore Senegal and Guinea Bissau.
AOG has come a long way in 30 years to become a diversified private investment group. It has kept its commitment to energy in Africa, while diversifying its investments towards commercial real estate in Europe and North America, and other capital investments. Whatever the sector, AOG is recognised for its entrepreneurial spirit, its ability to recognise opportunities and take calculated risks, without compromising its values. It will certainly continue to evolve as an established, but never establishment, firm, with always a twist of the unexpected.

redpajama_set_name: RedPajamaCommonCrawl


OTS's Yachad Program for Jewish Identity brought the beauty of Rosh Hashana, Yom Kippur, Sukkot and Simchat Torah to more than 145,000 Israelis this year through their annual "Holidays are for Everyone" initiative, designed to ensure that Jewish traditions are accessible and meaningful for all Jews.
Yachad's traditional "Shofar BaPark – Shofar in the Park" project has partnered with the Tzohar organization for the third consecutive year, in order to bring the excitement to even greater numbers of people. The result: more than 45,000 participants flocked to the program, which was held in 250 parks, public spaces and community centers across Israel.
The Rosh Hashana events were followed by "Yom Kippur for Everyone" – also run in partnership with Tzohar this year. Composed of abridged prayers, singing, reflections and group discussion, the free services drew 50,000 secular, alienated or unaffiliated Israelis to 350 community centers and public parks from Eilat in Israel's south to Katzrin in the Golan Heights.
Ortal's mother, Tzippy, explained: "I grew up in a traditional home, but I gave up on religion years ago. Recently, I've been feeling bad that my children are completely unaware of their heritage… it's just not an important part of their lives. We all discussed it and we thought we'd give the Yachad event a try. And honestly, until today I didn't even realize how much I missed that sense of connection," she said.
One of the greatest sights in Israel begins immediately at the conclusion of Yom Kippur, when people across the country begin constructing their sukkah. The Yachad coordinators harnessed the momentum by bringing their communities together for the building of big, bright and welcoming communal sukkot.
"Hakafot Shniyot is a great communal event in every sense of the phrase, with representatives of every stream, gender, age and ethnicity," notes Givat Massuah Yachad coordinator, Racheli Semo. "We made sure that the Torah could be held by everyone who wanted – to show all the participants that the Torah belongs to them too. When we offered the scrolls, specifically, to secular people who had not spent the previous day in synagogue, the pride and happiness were clearly etched on their faces," she says.
"This time of year is bursting with festivals, fasts and intermediary holidays and thus holds the potential to inspire thousands of secular Israeli Jews who are searching for meaning," explains Yachad's Educational Director, Yigal Klein. "Beyond our flagship Rosh Hashana and Yom Kippur programs, our coordinators reached approximately 50,000 Israelis through selichot tours and activities surrounding Sukkot and Simchat Torah — all run through Yachad's ongoing partnership with the Israeli community centers," he relates.


Just wrapped shooting the film Win For Life last night. It was a looong week, but a really good one. Some really funny stuff, and some pretty cool stunts, all of which I got to do (except the driving, apparently you need some sort of special training to fake run another car off the road...), there should be some cool footage to add to the reel pretty soon...now back to getting stage ready.


text:
ICMG
Executive Bureau
Honoured with the ORDER of MERIT of the ICMG
ICMG Charter
Mediterranean Confederations
PREVENTION OF THE MANIPULATION OF COMPETITIONS
The seminar of Albanian NOC "The role and importance of the athletes' commission"
IOC President reaffirms commitment to fight against corruption
Τhe Olympic Committee of Bosnia, EYOF Sarajevo & East Sarajevo won Peace and Sport award!
The Albanian NOC organised a seminar entitled "The role and importance of the athletes' commission" with athletes and students of the Sports University of Tirana.
The seminar focused on creating the structures needed to create a platform for the athletes' voice and the reformation of the NOC's Athletes' Commission. In November, the NOC organised technical courses for weightlifting and canoe-kayak coaches, supported by Olympic Solidarity and the respective IFs, and in cooperation with the national federations.
The two courses were led by IF experts, and attended by 20 participants for weightlifting and 18 for canoe-kayak.
Greece, Montenegro and Italy reached the Men's Water Polo World League Super Final
The 50th anniversary year of the European Olympic Committees
Modern Pentathlon athletes visit the Olympic Museum of Egupt
The exhibition "Legends of Sports" in Sports Museum of Madrid
Meeting of the Athletes' Commission of the Moroccan National Olympic Committee
IOC President highlights increased role of sport and solidarity in his New Year's video message
The anniversary video for the 70 years of the Mediterranean Games
Majlinda Kelmendi proclaimed ambassador of 'Let's colour the country' campaign
The Turkish Olympic Committee launched the "TOC Academy"
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text:
Gaussian Package
=================

Inference
---------

Use this module to do inference in Gaussian Bayesian Belief Networks.

.. automodule:: pybbn.gaussian.inference
    :members:
    :undoc-members:
    :show-inheritance:
    :special-members: __init__

redpajama_set_name: RedPajamaGithub


1. Read all directions before using.
2. Shake vigorously before use.
3. Protect surrounding area from overspray.
4. Point spray tip away from face.
5. Hold bottle 8-10 inches away from surface.
6. PAPER, PHOTOS, CARDBOARD & FOIL: Spray a thin, light coat to one surface. Join materials and continue to apply pressure periodically making sure to secure corners. Allow to dry 1-3 minutes.
9. IMPORTANT – CLEAN AFTER EACH USE: To prevent clogging, remove and rinse nozzle/straw. Pump warm tap water through sprayer until all adhesive is cleared out. Then dry, replace in the bottle, secure cap. *Maximum strength may not be reached for 1-5 hours. Styrofoam may require an overnight cure.


Connor Mackenzie Bloom, booked by Washington State Patrol for vehicular homicide.
Lucille Jennifer Brueggemann, booked by Whatcom County Sheriff's Office for a drug court violation.
Riley P. Crane, booked by Lynden Police Department for driving under the influence.
Lance Richard Dawson, booked by Whatcom County Sheriff's Office for third-degree malicious mischief.
Harold Lynn Garner, booked by Department of Corrections for a swift and certain warrant.
James Patrick Kelly, booked by Bellingham Police Department for second-degree burglary and third-degree theft.
Mathew Wayne Kirkey, booked by Whatcom County Sheriff's Office for second-degree burglary.
Daniel Patrick Meador, booked by Department of Corrections on a department detainer.
Rashid Jehangir Mistry, booked by Everson Police Department for theft of a motor vehicle.
Bobby Michael South, booked by Whatcom County Sheriff's Office and Bellingham Police Department for failure to appear on both first-degree criminal impersonation and third-degree theft.
Tyne A. Stormo, booked by Washington State Patrol for driving under the influence.
Sarah Margaret Sturgeon, booked by Bellingham Police Department for third-degree theft and shoplifting.


text:
Q: LibUsbDotNet doesn't open device I use latest LibUsbDotNet nuget package in Visual Studio 2017 on Win 10. For my full speed USB device with 2 interrupt endpoints and 1 bulk IN endpoint I installed WinUSB driver using zadiq 2.4 utility.
LibUsbDotNet can see my device when UsbDevice.AllDevices is called.
However, it can't open my device using:
UsbDeviceFinder MyUsbFinder = new UsbDeviceFinder(VID, PID);
UsbDevice MyUsbDevice = UsbDevice.OpenUsbDevice(MyUsbFinder);

MyUsbDevice is null, no exception thrown.
I also tried to install different drivers (libusbk and libusb-win32), with no success.
Some time ago I coded an C++ app to communicate with my USB device using libusb library - and it works since then without any issue.
Is there anyone who can confirm that libusbdotnet is working product? I welcome any advice how to find what is wrong. Thanks.

A: This is a bug in UsbDeviceFinder, where int.MaxValue is used instead of null to ignore a value. This makes UsbDeviceFinder unusable and all examples that use it don't work.
The workaround is to use

MyUsbDevice = context.Find(device => device.ProductId == ProductId && device.VendorId == VendorId);

instead of

MyUsbDevice = context.Find(MyUsbFinder);

A: First find your vendor id & product id by using device manager, input device , details then Hardware ID.
Next, You need to download LibUsbDotNet_Setup.2.2.8.exe and run setup. During setup you should enable filter and choose your input device per your vendor id. Then your code will find the device afterwards

redpajama_set_name: RedPajamaStackExchange


Jennifer Lawrence covered a wide range of topics during her visit with Howard Stern. As we reported earlier, the Hunger Games alum stopped by the radio icon's SiriusXM show in order to promote her latest flick, Red Sparrow.
The sexiest Howard Stern show regulars include several hot women who stop by Stern's studios and inspire almost instantaneous fantasies among Stern's regular l.
Mix - Howard Stern 2003 E! Show. Benjy Apologizes To Chuck Zito Howard Stern Show - Duration. Howard Stern Girls Get 13,645 views.
The Howard Stern Show is an American talk radio show hosted by Howard Stern. He had a naked woman on the show for the first time and attempted to make another.
Russian woman, 27, dies in. Howard Stern photographs bikini-clad wife Beth for a. The 6ft5in shock jock has been hosting some variation of The Howard Stern Show.
Tonight, Howard Stern appears in a place many people thought they'd never see him National primetime broadcast television. The legendary shock jock begins.
Stern Show  Verified account. a staffer named Chris told Howard the 68-year-old has a few demands in the studio. "He's a diva.".


WIMBROW, Patricia Gail, of Fowlerville, passed away Saturday, November 10, 2018. She was a wife, mother, grandmother, great‐grandmother, and friend who opened her heart and home to everyone with a hug and a smile. She saw beauty in everything and expressed this through drawing, painting, and photography. Pat has joined her husband, Ron Sr., sister, Norene, brother, "Buzz", and son, Ronnie Jr. in heaven. Her gentle and kind nature will be sadly missed, yet lovingly remembered by her children: Gayle, Carol, Rosie (Chris), Jesse (Amy), Morgan, and Dallas (Connie), siblings: Betty (Bob), Charlene, Jack (Kyle), and Jan, grandchildren: Jordan (Erin), Clayton, Robert (Danielle), Cody, Dylan (Cabrina), Carson, Caleb (Allison), Paige, Tatum, Danielle, Calypso, Remington, and Emmerson, 8 great‐grandchildren, and numerous nieces, nephews and friends. A celebration of Pat's life will be held at 2:00 PM Saturday, November 24, 2018 at the Conway Township Hall, 8015 North Fowlerville Road, Fowlerville, Michigan 48836.


This is the first installment in the series of videos showing the work we've done on the first minute of Durian.
This is a glimpse into our process... this first sequence will evolve greatly over time.
Uploaded on Oct. 27th, 2009.


Churning out twice the energy it consumes, the company aims to ease the strain on the state's aging electric grid.
Diamond Wipes International has invested heavily in its solar project since 2011 -- dropping $1.6 million for its new 3,360-panel installation on its Chino, Calif., facility last year. So far, this investment seems to be paying off.
"The solar system is cranking away," says Tom Hill, vice president of marketing and sales at Diamond Wipes. "As a matter of fact, we're generating about double our burn rate at this time of year, so we are contributing to the overall good of the state."
By feeding this power back into the grid, Diamond Wipes is racking up huge savings in energy costs while also reducing the strain on the system to help prevent more of the region's frequent, costly outages.
"You can probably imagine how disastrous it would be for small and midsize manufacturers like ours, often running the machines and lines 24 hours a day for five to six straight days at a time to accommodate the growth and service customers better, to experience even just a few minutes of blackout," says Diamond Wipes CEO, Even Yen.
"Fortunately for us, the local energy grid we are connected to has been reliable since we relocated into the area a few years back. But it is definitely a concern for me as various infrastructures, not just electricity, continue to age," she explains.
The solar installation working on the grid with distributed generation helps relieve many of these concerns for companies across the system, providing a high-tech solution to an aging infrastructure.
For companies thinking about the future of energy, this is a critical point.
"To think that one day not too far from now we can no longer take electricity for granted, there's a sense of slow but sure impending disaster," says Yen. "This is a big challenge that no one company can overcome by itself. I like to think that we are doing our part by investing into our solar energy system right here and now."


Oxford University Press is pleased to offer complimentary desk and examination copies to qualified instructors. In order for your request to be processed, please browse our catalog for the desired text and follow the link to request an examination copy. Allow approximately 3-4 weeks for regular delivery.
Rush requests cannot be processed through this form. If you need a book in less than 3-4 weeks, email Higher Education Sales at higher.education@oup.com. Please include course name/number, expected enrollment, and the date you need the book.
For additional assistance when considering titles for adoption, please contact your sales representative at 800-280-0280.
Students: posing as instructors is both a violation of your school's honor code and criminal fraud. Students found impersonating instructors will be turned over to the authorities at their institutions for appropriate action.


Michael Conforto homered and drove in three runs, and the Mets scored five times in the fourth inning off Julio Teheran before holding out to beat the Atlanta Braves 7-5 on Monday night.
On the day the Mets placed ace Noah Syndergaard on the 10-day DL with a partial tear of his right lat muscle, Robert Gsellman (1-2) almost blew an early 6-1 lead. Gsellman allowed five runs in five-plus innings.
Five Mets relievers combined for four scoreless innings. Jeurys Familia pitched the ninth for his second save.
Conforto led off the game with his seventh homer and added a two-run single in New York's five-run fourth inning off Teheran (2-2). With New York's lead down to 6-5, Jose Reyes added a homer off Ian Krol in the eighth. Atlanta's Ender Inciarte hit his fifth homer to lead off the first.
Syndergaard was placed on the 10-day disabled list after an MRI revealed a partial tear of his right lat muscle. The Mets say there is no timetable for his return. Syndergaard left his start Sunday against Washington in pain. He grimaced after throwing a pitch and grabbed his side under his right arm.


FREE pair of tickets to the London Homebuilding & Renovating Show this September for EVERY reader - worth £36!
I am a big homebody type person, as much as I do love to explore and enjoy days out, and our home really is our castle, however humble. I have loved interior design for as long as I can remember and seek inspiration from magazines, Instagram and also home related shows - I just can't get enough of decor! That's why I am really excited to share this special offer with you... as all To Become Mum Readers can claim a pair of free tickets to attend the London Homebuilding & Renovating Show (21 - 23 September 2018, ExCeL, London) - worth £36!
Across three packed days, visitors to the show can speak to over 500 exhibitors and access free advice sessions, seminars and masterclasses on essential topics which can tackle any problem, from implementing the latest intelligent security systems to funding a remodelling project.
And thanks to the team and this little blog of mine, YOU could be going with your DIY mad hubby or interiors buff buddy for free.
I've included all you need to know about the show below, and you can also follow this link for more details. Just keep scrolling for my exclusive free ticket link to claim. And be sure to tell your friends too, there's really no catch - just free tickets to the show for everyone who stops by this post!
According to the UK Land Registry, most of all the publicly owned land available for new homes will be registered by 2020 to boost housing development. To help equip and upskill consumers intent on taking matters into their own hands when it comes to creating their dream home, The London Homebuilding & Renovating Show is returning to ExCeL between 21 - 23 September. The event, which will be sponsored this year for the first time by Checkatrade, a directory of recommended and trusted tradesmen, will provide practical help and advice to those who want to progress with their property ventures.
The show, which will also be sponsored by Nethouseprices, a platform that provides free access to the latest house prices for England and Wales, will offer self-builders and renovators the chance to discover innovative products from over 360 specialist brands that will be exhibiting. Visitors will also have access to over 45 free seminars and masterclasses, and 750 plus advice sessions on a wide range of sectors including architecture; kitchens; bathrooms; ventilation; lighting; doors and windows etc.
The event will be filled with free advice on any issues a self builder or renovator has, and will host a multitude of resources for every project all under one roof. In addition, real case studies who have gone through the building process will be available to talk to on site, so visitors can discuss similar challenges they're facing.
Consumers can hold 15-minute discussions with celebrity TV property experts on the Saturday of the event. Charlie Luxton, sustainable architectural designer and presenter of Channel 4's 'Best Laid Plans', will be talking about eco living, new architectural ideas and homes of the future. Julia Kendell, interior design expert for BBC's 'DIY SOS The Build' and ITV's '60 Minute Makeover', will be assisting visitors who are looking to transform their houses through stylish and resourceful interior designs.
Attendees who would like to discuss their building plans with an array of property experts will benefit from the Ask the Expert area inside the Advice Centre, sponsored by Internorm, Europe's leading window brand. This area will welcome visitors to hold free consultations with eight residential property specialists via interactive sessions. The experts include Michael Holmes (director of content and product development for Homebuilding & Renovating magazine); Jason Orme (editorial director of Homebuilding & Renovating magazine); Bob Branscombe (chartered surveyor and builder); Chris Reeves (legal expert and a chartered builder and lawyer); Mariana Pedroso (interior design expert and architect); Allan Corfield (self-build expert); Sally Tagg (planning expert); Mark Stevenson (managing director at Potton & Kingspan Timber Solutions Ltd).
In the Advice Centre, show-goers can also explore the Ask the Builder area and meet members of the Federation of Master Builders. In addition, the Ask the Architect area will be welcoming over 15 experienced architects from the Royal Institute of British Architects (RIBA) to assist consumers in achieving their dream home, maximising their budget and developing solutions to improve their quality of life.
Sally Tagg will be on hand at the Planning Clinic to answer visitors' questions on how to obtain planning permission. Sally's years of experiences will ensure that the latest tactics to success are shared with the consumers so that they can avoid common mistakes and pitfalls.
There will also be live presentations in the Tricks of the Trade section hosted by experienced tradespeople who'll be laying bare up-to-date information on how to save money on everyday DIY jobs undertaken around the house.
The mobile app will provide visitors with a personalised experience, guiding them through their day. This will include information on all the features at the exhibition so that consumers won't miss a thing. In addition, an interactive timetable will be displaying the times and locations of all seminars and masterclasses, as well as alerting the user on any exclusive offers from exhibitors.
To claim your free pair of tickets, courtesy of To Become Mum, visit this specific link: -www.homebuildingshow.co.uk/tobecomemum.
Terms & Conditions: Please note that tickets must be redeemed before on 3pm on 20th September 2018. Additional T&Cs apply: www.homebuildingshow.co.uk/terms.


The two-year Master's degree program in leadership in tourism & hospitality was developed together with the tourism industry and offers the managers of tomorrow an optimal management training for a national or international career in tourism.
All this is part of the challenging tasks a manager faces. Of course, they must also have business expertise. The Master's degree in Leadership in Tourism & Hospitality focuses on the areas of leadership, entrepreneurship, international tourism management, tourist networks and design thinking, so as to properly prepare our students for their future successful career in tourism.
We support students in building up a professional network with notable personalities in the tourism industry, for example by giving them access to our "Executive club".
Sign up for our newsletter "All About Studying at FHWien"


Wonderful Chantilly 3 Piece Lounge Seating Group By Wildon Home ?
Easy Ukee 3 Piece Conversation Set By Ophelia & Co.
Just for you! Eris Indoor/Outdoor Loveseat Cushion top design By Brayden Studio. Eris Indoor/Outdoor Loveseat Cushion very well made, sleek and simple. Complete your living room furniture with a modern Eris Indoor/Outdoor Loveseat Cushion. Its elegent sturdy, attractivce and it looks expensive and a best value for the money. Eris Indoor/Outdoor Loveseat Cushion is one of the most homy, cozy, beautiful look and exotic Eris Indoor/Outdoor Loveseat Cushion especially for the price and made of fantastic products. Great quality, easy to assemble, delivery on time and in perfect condition. Eris Indoor/Outdoor Loveseat Cushion is good merchandise at fair prices and wonderful free shipping. Guarantee damaged claim by offering to send parts or to keep the item at a discounted price. Great buy would definitely recommend. Shop with our low-price guarantee and find great deals on ##ptitle# and more!. Reading the reviews helped you purchase.
There are not that many people that also have a bar set up at home. For many, it might seem like something unnatural or otherwise suitable as a living space but if done right it can genuinely include personally towards the inside of an condo or home. The very first thing that needs to be on the grocery list is some an adjustable club feces. They'll prove their really worth when having someone more than or web hosting a little celebration. Bar stool simply provides a special contact that transforms the room. Having adjustable bar stools does bring in some advantages. The first major in addition is they consider very little space on the floor. They are made to be small but comfy enough. Talking about comfort and ease, barstools are not that bad. Even if they're little, they still provide decent assistance. A number of them even have a little bit of back again support along with a gentle cushioned surface. For adjustments, most of them possess a adjustable peak. The most important aspect that makes a club feces so easy to acknowledge is always that they swivel. A great feces is designed in a way that it's hard to lower and comfy enough. The good news is that there's an abundance when it comes to design variety. There are many greatly adjustable barstools to choose from but we'd to choose just 10. Only 10 of them were deemed purchase deserving because of their build quality, style and general utility. Here's what we put together for the listing of the recommendations for the top ten greatest flexible bar stools in 2018.
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When the Chesterfield may be the graceful gentleman amongst couches, the Cabriole may be the grandes dame. Noted for its uncovered wood and stylish legs, reminiscent of the Louis XV time period, the cabriole also has a unique silhouette. It was additionally a popular shape within the work of furniture maker Thomas Chippendale. Typically, the rear is 1 constant item with out cushions and it has a stylish bending line. This particular cabriole version includes gems within the tufts for additional glamour. It's a couch design that can be as simple or opulent as you wish. Upholstered having a luxurious material like velvet produces a much different style sensation than if it had been padded in a more moderate, textural natural. The main aura of style stems from its general shape and lithe thighs meaning it will always lend a processed air to a room.
This is actually the next couch on our checklist. It's additional comfy and incredibly well suited for little rooms or attic living. It is padded in rayon fabric, potential customers inset control keys that provide a stylish diamond-tufted design. It is made from durable supplies and the legs are constructed with durable wooden to add to its durability. The loveseat has an java discolored wood thighs and no-tagging foot caps. It offers a comfortable froth cushioning and rayon fabric furniture that makes it extremely magnificent. It features a longue spot that provides an exceptional space for resting.
This set includes a one left equip sofa set, two armless sofa models and something part couch set. This gives enough room to accommodate your family and friends. The material is 100Percent polyester for sufficient comfort and durability. The advantage of this couch established may be the matching and mixing of seats within the available space within the room for a ideal shape. And also allows for fitted even just in little rooms. It takes just mild putting together.Additionally, it functions drive cushions for maximum comfort. You might want to try this set. It works well.
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Carolina Light Grey Fabric Sofa Couch is well known because of its stunning comfort and impressive style. It has a modular design that enables for many agreement choices to meet your requirements.The set functions gentle material and forces soft cushions to bring about the desired comfort. More to the point, its of a good size to accommodate you along with the family of friends. Depending on the space and your desired shape, you are able to mix and match the I chairs to produce a remarkable form. Its recommended for all those with little areas and needs a sofa.
With almost 100 5-star reviews, this reclining loveseat is recommended because of its comfort and ease, durability, appearance and easy set up. Along with gentle, but supportive soft cushions, it features a gliding system, so that you can put your ft up and rock (though, not simultaneously.) Padded with ultra-durable glued leather, this lying loveseat will resist holes, rips and stainswhich is a good thing, since it also includes a storage area system (where you can hide your treats, of course) and a two-mug owner. Whether youre settling set for a Netflix excessive or viewing football together with your crew, this lying loveseat offers the comfort and durability with out breaking the bank.
Copyright © Eris Indoor/Outdoor Loveseat Cushion By Brayden Studio in Patio Conversation Sets All right reserved.


text:
TX: The Right Way to Protect Schools
Over the last few years, several incidents in which one or two men have undertaken violence at schools. They typically put on paramilitary garb and bring enough weaponry to terrorize the entire school. Many large school districts have metal detectors in high schools, but a metal detector is useless against someone who comes in with no intention of surrendering his weapon. Aside from militarizing the schools, protecting schoolchildren while they learn seems to be a difficult task. Doing so while maintaining a positive learning atmosphere seems especially daunting.
Well, a new method to combat the violence comes from the Burleson, Texas school district.
Commentary: Why Does Habeas Corpus Hate America?
The reality is, without habeas corpus, a lot of other rights lose their meaning.
But if you look at the actual Bill of Rights - the first ten amendments to that pesky Constitution - you'll see just how many remain.
Well, ok, Number One's gone.
If you're detained without trial, you lose your freedom of religion, speech, the press and assembly. And you can't petition the government for anything.
Number Two? While you're in prison, your right to keep and bear arms just may be infringed upon.
Even if you're in the NRA.
AL: Get the guns out of your homes
More school shootings, and the inevitable commentary on the evening news: "I didn't think this sort of thing could happen here."
The heartfelt, but naive belief that murderous rampages "don't happen here" begs the question: "Where do you think such things happen?"
FL: After fatal shooting, man comes to terms with self-defense
His voice shakes. He can't work, he says, can't concentrate. He's 260 pounds of tough guy, but tears fall as he relives the moment he killed a man.
It has been a week since police say Christopher Welker, 26, caught two robbery suspects outside his Hollywood, Fla., home, trying to steal the new chrome rims off his truck in the middle of the night. During a scuffle for one suspect's gun, Welker shot one dead and wounded the other.
FL: Kottkamp's record for GOP solid
"I just think the right to bear arms is a sacred constitutional right that we ought to protect. That's one of those bills where you're going to have to pick sides," said Kottkamp. "I've tried to support legislation that created an environment where businesses could flourish in the state but that's not what's at issue here. It's just a fundamental right to bear arms."
I'm sticking to my guns on this one
It is with great pride that I present the world's first bulletproof column on the subject of guns. That's right, I can say anything I want to say about guns without fear or risk of taking potshots from anyone on any side of this volatile issue.
Yeah, right.
I know I'm dreaming. I know that all I have to do is say the word "guns" and lots of people will start getting their hackles up.
MD: Guns R Us
Hear that? It's the deafening silence of politicians not talking about how the way to deal with gun violence is to deal with guns.
A Baltimore 8-year-old brought a loaded gun to school last week that his classmate accidentally fired about the same time an Amish school in Pennsylvania was being razed in memory of five girls shot to death there by an intruder the week before. Those events closely followed fatal school shootings in Colorado and Wisconsin and the arrest of a Missouri middle-schooler armed with an assault rifle.
MN: Dealing with school violence
Still, any credible discussion of school safety requires raising the question of how and why teenagers can get guns so easily.
And why does a tormented, suicidal adult, such as the one who shot 10 Amish school girls and killed five of them, have ready access to a semiautomatic pistol, a shotgun, 600 rounds of ammunition and a high-voltage stun gun?
PA: Controlling violence
Rendell challenged Swann to appear with him at a news conference to urge the Legislature to buck Second Amendment fanatics and endorse the plan. To his disgrace, Swann has refused to join the effort, a particularly shameful position for an African-American candidate to espouse, given the senseless slaughter that disproportionately threatens young blacks.
MS: Gun restrictions won't make schools safer
The recent tragic outbursts of gunfire in schools across the land are sure to result in loud calls for a "solution." This will cause the expenditure of vast sums of taxpayer dollars for research, studies and the formation of expert panels such as the one called for by President Bush.
Virtually all of these efforts will center around keeping guns out of our schools and, beyond providing salve to the psyches of those who hate and fear firearms, will accomplish nothing to make our children safer.
Anyone with a basic understanding of firearm safety and a little common sense could point out how to get more meaningful results quickly and at very little expense.
FL: School shootings debated, while gun control avoided
Bush's silence on guns symbolizes a broader trend. Children being shot or shot at in their schools used to elicit widespread talk about gun laws, but that hasn't been the prominent reaction since a rash of school shootings in 1999 that began with Columbine sparked debate.
Especially in the last six years, pro-gun groups have overpowered gun-control advocates on Capitol Hill and in many states.
"I think Americans are starting to be rational about this," said Rep. Cliff Stearns, an Ocala Republican who wrote a bill shielding gun manufacturers from "nuisance" lawsuits, which became law late last year.
WA: A spate of really bad ideas that can fit on a bumper sticker
You can hardly be surprised at Republican Rep. Frank Lasee's interest in this issue: One of those shootings took place in his state. There, on Oct. 1, a 15-year-old boy shot Weston Schools Principal John Klang to death. Still, Lasee's proposed solution has raised eyebrows.
As others debate solutions ranging from heightened security to increased vigilance against bullying, Lasee has cut through the namby and the pamby. He wants to pass legislation that would allow properly trained teachers and administrators to carry concealed handguns on school property.
Somalia: Islamists in bid to rid Somalia of illegal guns
Mogadishu - Somalia's Islamists plan to do what many believe to be impossible in a country synonymous with anarchy — take the guns away from one of the world's most heavily armed populations.
Abdullahi Maalim Ali, head of internal security for the Islamists who control the capital Mogadishu and most of south-central Somalia, said the Islamists will go door-to-door collecting weapons owned by ordinary Somalis and organisations.
MO: Scott Co. sheriff's records lacking
The auditors also wanted to know why Ferrell, according to gun inventories, removed 10 guns from the gun vault in his last week in office. Ferrell, in a reply to the auditors, said he only took five and that he gave auditors a letter from each gun owner acknowledging they received their property.
IL: Illinois Fraternal Order Of Police (ILFOP) Is Out TO DISARM CITIZENS
Don't be fooled. Anyone who says they want to ban one class of firearms really wants to ban all firearms. Yesterday we had the spectacle of ILFOP President Ted Street all kissy face with Paul Helmke, president of the Brady Campaign to Prevent Gun Violence, endorsing Tammy Duckworth for congress. You are known by the company you keep Mr. Street.
TX: City should be gun-shy about these toys
I asked my 6-year-old what he thought about making toy guns that look like the real thing illegal in Dallas. "It's good," he said, playing a game of Othello in his dinosaur underwear. Why, I asked. "Because people might get confused." Exactly.
CT: Carrying a Gun, Yes, but Disputing a Wild-West Image
The mayor of this unpretentious, blue-collar town -- a place few would consider an Eastern version of the Wild West -- pointed to the navy sock peeking above his sturdy oxford shoe and said he would never strap a handgun there, to his ankle. No, he said, the left pants pocket would provide him with a quicker draw. On a crisp early fall afternoon in his wood-paneled office in Town Hall, Mayor James R. Miron demonstrated his carrying preferences, though he also took pains to dispute the image of himself as a gun-toting sheriff. That image emerged last week when local newspapers quoted anonymous sources who claimed that Mr. Miron attended Town Council meetings with a firearm strapped to his ankle.
MA: As Congress caters to NRA, mayors battle illegal guns
This week, Boston is hosting the International Association of Chiefs of Police, the world�s oldest and largest nonprofit organization of police executives. While they are here, they will discuss the challenges facing law enforcement. This same shared purpose and sense of duty has brought 109 Democratic, Republican and independent mayors from 44 states together to form Mayors Against Illegal Guns (MAIG). Our mission is to fill the void left by the federal government�s dereliction of its commitment to public safety.
FL: Hollywood officer accused of pointing gun at family during road rage
A Hollywood police officer is under investigation by Plantation police, accused of pointing a gun at a family of seven in an off-duty road rage incident, police records show.
"I see him reach for the gun and I was like, `Oh no, not this,'" Calle said. "He just comes out, points the gun at my head and says, `Don't call the police because I'm a cop.'"
"Don't reach for nothing because I will shoot you right now," the man with the gun said, according to police reports. He trained his gun on all seven in the van -- finger on the trigger, Calle's family told police.
Most kid homicides happen outside school
Submitted by: Protector
The horrific school shootings in Colorado, Wisconsin and at an Amish schoolhouse in Pennsylvania -- which left six girls and a principal dead, all within a week -- have caused many to wonder just how safe our children are.
Truth is, young Americans die at the hands of other people at an alarming rate, greater than any other Western nation. Every day in 2003, an average of about 15 youth, ages 10 to 24, were victims of intentional and accidental killings, according to the most recent statistics available from the federal Centers for Disease Control.
Very few of them died in school shootings.
Note: Comparing 19-24 year olds with school children doesn't seem reasonable as that age group is into gangs and drugs which are dangerous.
IL: ISRA-PVF Calls Upon Gov. Blagojevich to Resign
In light of the growing funding scandal within his campaign organization, the ISRA-PVF is calling upon Gov. Blagojevich to withdraw his bid for reelection and step down as the state's chief executive.
Those who do not learn from the mistakes of history are doomed to repeat them. � George Santayana


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Juicy Jay's Blueberry Sampler is number one if you love blueberries. You get a good variety of different paper types and flavor densities. Juicy Jay's Blueberry Hemp Wraps will have the most flavor packed in its wraps. These delicious wraps are manufactured using pure hemp and come with two wraps per package. Juicy Jay's also has its King Size Blueberry papers that are triple dipped for full flavor these will roll up nicely in an 110mm rolling machine. Juicy also makes cones, and Juicy Jones Cones are easy to load if rolling isn't your specialty. Along with those scrumptious Juicy Jay's products, you get their Superfine Blueberry Hill papers that are also triple dipped but with a thinner paper, you get less flavor in your smokes and more on your lips.


text:
The Best Ways to Cook Lobster
By: Launie Sorrels
How Do I Reheat Leftover Boiled Lobster?
How to Boil 1.5 Pounds of Lobster
How to Boil Lobster at Home
How to Cook Live Lobster
How to Cook Lobster
Lobster is considered a favorite to seafood lovers, and it is simple to make. Lobster can be boiled, steamed or baked. Grilling is another possibility, but this type of cooking is reserved for hard-shelled lobsters. The hard-shelled lobster has more meat per pound than the soft-shelled, but the soft-shelled has a sweeter taste.
Boiled Lobster
Place the pot on the stove with enough water to cover the lobster. Bring the water to a fierce boil. Add 1 tbsp. of salt. Place the lobster into the water. For a store-bought lobster, boil it for 10 minutes plus 3 minutes per pound. For a soft-shelled lobster reduce the time by 3 minutes. Cook a live lobster in a similar way. Boil it for 2 minutes, then reduce the heat to simmer and cook the lobster for 15 minutes plus 5 minutes per 8 oz. over the first pound. For a soft-shelled lobster, reduce the time by 3 minutes.
There is an ongoing debate on how humane it is to cook a live lobster. According to the Lobster Institute lobsters, like insects, do not have a well enough developed nervous system to feel pain. If this is still a concern of yours, then you can put the lobster into the freezer for 5 to 10 minutes. The cold causes the lobster to sleep. When boiled, it does not wake up in time to realize what's happened.
Steamed Lobster
A lobster pot is recommended when steaming lobster, but it is not necessary; a steam pot can be used. Steaming is very similar to boiling but takes a little more time. Place the pot on the stove with enough water to cover the lobster. Bring the water to a fierce boil. Add 1/2 cup of salt. Place a store-bought lobster into the water and steam it for 14 minutes plus 3 minutes per pound. For a soft-shelled lobster, reduce the time by 3 minutes. For live lobster, steam it for 18 minutes plus 5 minutes per 8 ounces over the first 1 1/2 lbs. For a soft-shelled lobster, reduce the time by 3 minutes.
Baked Lobster
Preheat the oven to 425 degrees F. Bake the lobster for 3 to 4 minutes, flip, and cook for another 4 minutes. For soft-shelled lobster, reduce the time by 2 minutes. It is not recommended to cook a live lobster this way for obvious reasons.
Cooking and eating a lobster
How to Cook Lobster. Including boiling, steaming, grilling and serving.
Lobster: How to Cook Lobster, Nutritional Values, Facts
Lobsters with Laura
Cooking Maine lobster
Lobster Recipes
Launie Sorrels is a veteran who has worked as a chef and has more than two decades of martial arts training. His writing has developed from his experience as a quality assurance manager for Microsoft and IBM. Sorrels has a degree in computer science and is currently working on his journalism degree.


The planet lies in ruin. An inmate named Marcus Fenix – once left to die – is humanity's only hope versus the relentless Locust. Gears of War: Ultimate Edition for Windows 10 is loaded with new content including five campaign chapters not included in the Xbox 360 version. Windows 10 players will also receive the Deluxe Weapon Skin Pack and 11 bonus multiplayer characters.
Every aspect of the original Gears of War has been beautifully remastered and modernized, including lighting, environments, characters, and cinematic scenes. This is the first at its best!
Includes five additional, exhilarating campaign missions that follow Delta Squad as they battle their way to Timgad Station not included in the Xbox 360 original.
Go deeper into Gears fiction with five Gears of War comic books, which can be unlocked and read within the game.