text:
\section{Introduction}

For  a bounded domain $\Omega \subset \R^N$ ($N \geq 2$) and a function
$h \in L^p(\Omega)$ for some
$p > \frac{N}{2}$ we consider the problem
\begin{equation}
\label{EE1}
\begin{array}{c}
- L u = H(x,u,\nabla u)+ h(x), \quad
u \in H^1_0(\Omega) \cap L^{\infty}(\Omega),
\end{array}
\end{equation}
where  $L$ is a general  elliptic second order linear operator  and  $H: \Omega \times \R \times \R^N \to \R $ is a Carath\'eodory function which satisfy the assumptions:
\vspace{2mm}
\begin{itemize}
\item[(L)] There exists  a family of functions $(a^{ij})_{1\leq i,j\leq N}$ with $a^{ij}\in L^{\infty}(\Omega)\cap W^{1,\infty}_{loc}(\Omega)$
  such that
$$
Lu=\sum_{i,j} \frac{\partial}{\partial x_j} \left(a^{ij}(x)\frac{\partial u}{\partial x_i}\right)
$$
and, there exists $\eta>0$ such that, for  a.e.  $x \in \Omega$  and all $ \xi \in \R^N$,
$$
\sum_{i,j}a^{i,j}(x)\xi_i\xi_j\geq \eta |\xi|^2.
$$
\item[(H1)] There exists a continuous function $C_1 : \R^+ \to \R^+$  and a function $ b_1 \in L^p(\Omega)$  such that, for  a.e.  $x \in \Omega,$  all $ u \in \R$ and all $ \xi \in \R^N,$
$$ |H(x,u,\xi)| \leq C_1(|u|)(|\xi|^2 + b_1(x)).$$
\item[(H2)] There exists a function $b_2 \in L_{loc}^N(\Omega)$ and a continuous function $C_2 : \R^+ \times \R^+ \to \R$ such that, for a.e. $ x \in \Omega,$  all $ u_1, u_2 \in \R$  with $ u_1 \geq u_2$ and all $ \xi_1, \xi_2 \in \R^N,$
$$H(x,u_1,\xi_1) - H(x,u_2,\xi_2) \leq C_2(|u_1|,|u_2|) (|\xi_1| + |\xi_2| + b_2(x)) |\xi_1 - \xi_2|.$$
\end{itemize}
As we shall see in the proof of Corollary~\ref{corolario},   a sufficient condition for (H2)
is that
for a.e. $x\in \Omega$,
 $H(x,\cdot,\cdot)\in {\mathcal C}^1(\R\times\R^{N})$  with
\begin{equation} \label{H3-1}
\frac{\partial H}{\partial u}(x,u,\xi)\leq 0, \ \mbox{a.e. } x\in \Omega, \ \forall  u\in \mathbb R, \ \forall \xi \in \R^N,
\end{equation}
and that there exists  a function $b_3\in L^N_{loc}(\Omega)$ and a continuous nondecreasing function $C:\mathbb R^+\times \mathbb R^+\to \mathbb R^+$ satisfying
\begin{equation} \label{H3-2}
\left|\frac{\partial H}{\partial \xi}(x,u,\xi)\right| \leq C(|u|)(|\xi|+b_3(x)), \ \mbox{a.e. } x\in \Omega, \ \forall  u\in \mathbb R, \ \forall \xi \in \R^N.
\end{equation}
Uniqueness of solution for problem \eqref{EE1} (with $Lu=\Delta u$) has been first studied in the work
\cite{BaMu} and after improved in \cite{BaBlGeKo} by requiring weaker regularity
conditions on the data.   The reader can also see  additional uniqueness results in \cite{B-P} for subcritical nonlinear term $H$  (with respect to $\xi$), i.e, when its growth is less than a power $|\xi|^q$ with $q<2$, and in the work \cite{AS} for the case that $H$ has a singularity at $u=0$.

Specifically,  in \cite{BaBlGeKo} the uniqueness of solution for every $h$ is proved  when it is assumed condition \eqref{H3-2} and the following strengthening of \eqref{H3-1}:
$$
\frac{\partial H}{\partial u}(x,u,\xi)\leq-d_0< 0, \ \mbox{a.e. } x\in \Omega, \ \forall  u\in \mathbb R, \ \forall \xi \in \R^N.
$$
However, in the case that it is only assumed the general hypothesis \eqref{H3-1} (together with \eqref{H3-2}), the authors require to the function $h$ to be sufficiently small in an appropriate sense. Furthermore, adapting the arguments of \cite{BaBlGeKo}, the case where \eqref{H3-1}-\eqref{H3-2} hold and $h$ has sign can also be covered.
Nevertheless,  the treatment of the general case \eqref{H3-1}-\eqref{H3-2} with no assumptions on $h$ seems out of reach with the approach of  \cite{BaBlGeKo,BaMu}.

The special case of (\ref{EE1})  given by
\begin{equation}\label{SC}
- \Delta u = d(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega) \cap L^{\infty}(\Omega)
\end{equation}
 is studied in  \cite{ArDeJeTa} by an alternative approach. Indeed, if $d, h \in L^p(\Omega)$ for some $ p > \frac{N}{2}, \mu \in L^{\infty}(\Omega)$, then it is proved that
 (\ref{SC}) has at most one  solution as soon as $d \leq 0$. Actually this condition is also necessary since  \cite[Theorem 1.3]{ArDeJeTa}  proves that  (\ref{SC}) may have two solutions if $d\gneqq 0$. See also, in that direction, Theorem 2  in \cite{JeSi} or Theorem 1,(iv)  in \cite{Si}.

 We also mention that a general condition which guarantees the existence of one solution to (\ref{SC}) is derived in \cite{ArDeJeTa}. This condition always hold when $d <0$ but also widely when $d \leq 0$. For example, we have existence of one solution whenever $\mu$ and $h$ have opposite  sign.
\medbreak

 The aim of this paper is to show that the approach of \cite{ArDeJeTa} can be
 generalized to treat, under the assumptions (L)-(H1)-(H2), equation (\ref{EE1})  and
 thus to cover additional situations where the approach of \cite{BaBlGeKo,BaMu} is
 not applicable.  As a counterpart of our approach we need to assume that the
 boundary of $\Omega$ is sufficiently smooth, namely that
 $\Omega$ satisfies the following condition (A) of \cite[p.6]{LU68}.

\begin{definition}
Let $\Omega \subset \R^N $ be an open set.  We say that  $\Omega$ satisfies condition (A)   provided   there exist
$r_0, \theta_0>0$ such that  if $x\in \partial\Omega$ and
$ 0<r<r_0$, then
$$
         \mbox{meas\,} \Omega_r \leq (1-\theta_0)  \mbox{meas\,}  B_r(x),
$$
for every component $\Omega_r $ of $\Omega\cap B_r(x)$, where $B_r(x)$ denotes the ball of radius $r$ centered at the point $x$.
\end{definition}

 For the reader convenience, we shall prove in the Appendix (see Lemma \ref{3.1}), that condition (A) holds true if $\partial \Omega$ is  Lipschitz.\medbreak

The main result of this paper is the following theorem.

\begin{thm}\label{main}
Assume that (L)-(H1)-(H2) hold and that  $\Omega$ satisfies condition (A). Then (\ref{EE1}) has at most one solution.
\end{thm}

The proof of Theorem \ref{main} is divided into two main steps. First we show that any solution of (\ref{EE1}) belongs to ${\mathcal C}^{0,\alpha}(\overline{\Omega}) \cap W^{1,N}_{loc}(\Omega)$ for some $\alpha \in (0,1)$. This result is obtained combining classical regularity arguments from \cite{Gi,LU68} which allow to conclude that it belongs to  ${\mathcal C}^{0,\alpha}(\overline{\Omega}) \cap W^{1,q}_{loc}(\Omega)$ for some $\alpha \in(0,1)$ and some  $q >2$. Here the fact that our solutions are bounded seems essential. Then a bootstrap argument  of \cite{BeFr, Fr} (see also \cite{DoGi}) comes into play. The key ingredient of this bootstrap is an interpolation result due to Miranda \cite {Mi} which says that any element of ${\mathcal C}^{0,\alpha}(\overline{\Omega}) \cap W^{2,\frac{q}{2}}_{loc}(\Omega)$ belongs to $W^{1,t}_{loc}(\Omega)$ for a $t >q$. Having obtained the announced required regularity the second step consists in
 establishing a comparison principle. Roughly speaking, we adapt an argument from \cite{BeMeMuPo}, based in turn on an original idea from \cite{BoMa} to show  in Lemma~\ref{UUniqueness} that if $u_1, u_2 \in H^1_0(\Omega) \cap W^{1,N}_{loc}(\Omega) \cap {\mathcal C}(\overline{\Omega})$
are respectively a lower solution and an upper solution of (\ref{EE1}), then $u_1 \leq u_2$ in $\Omega $. The uniqueness then follows from this comparison principle.
\medbreak

As we already mentioned  Theorem \ref{main} is sharp for equation (\ref{SC}). More globally the condition (H2), which in essence express the fact that $u \to H(x,u,\xi)$ is a non decreasing function and $\xi\to H(x,u,\xi)$ is locally Lipschitz, appears to us as an  almost necessary condition to guarantee the uniqueness.
\vspace{2mm}

Throughout the rest of the note we assume that $N \geq 3$.  The easier case $N=2$ is left to the reader.

\section{Uniqueness results}
\label{Sectionuniqueness-0}

First we show that, when condition (A) holds, any solution of (\ref{EE1}) belongs to ${\mathcal C}^{0, \alpha}(\overline{\Omega})\cap W^{1,q}_{loc}(\Omega)$
for some $\alpha \in (0,1)$ and  $q >2$. This follows directly from the following two classical regularity results.

\begin{prop}
\label{Lem1}
Assume that  $\Omega$ satisfies the regularity condition (A) and that condition  (L) holds. Let $u$ be a solution of
$$
-L u + a(x,u, \nabla u) =0, \quad u \in H^1_0(\Omega) \cap L^{\infty}(\Omega).
$$
If there exists a constant $\mu >0$ and a function $b_1 \in L^p(\Omega)$ with $p > \frac{N}{2}$ such that
$$
|a(x,u,\xi)| \leq \mu  \left[ |\xi|^2 +b_1(x) \right], \mbox{ a.e. } x\in\Omega, \ \forall u\in \mathbb R, \ \forall \xi \in \mathbb R^N,
$$
then $u\in {\mathcal C}^{0,\alpha}(\overline \Omega)$ for some $\alpha   \in (0,1)$.
\end{prop}

\begin{proof}
This result is a special case of \cite[Theorem IX-2.2 p.441]{LU68}.
\end{proof}

\begin{prop}
\label{Lem2}
Assume that $L$ satisfies condition (L).
Let $u$ be a solution of
$$
- L u + a(x,u, \nabla u) =0, \quad u \in H^1_0(\Omega) \cap L^{\infty}(\Omega).
$$
If there exists a $\mu >0$ and a function $b_1 \in L^s(\Omega)$ for some $s >1$ such that
$$
|a(x,u,\xi)| \leq \mu  \left[ |\xi|^2 + b_1(x)\right], \mbox{ a.e. } x\in\Omega, \ \forall u\in \mathbb R, \ \forall \xi \in \mathbb R^N,
$$
then there exists an exponent $q >2$ such that $u\in W^{1,q}_{loc}( \Omega)$.
\end{prop}

\begin{proof}
This result is a special case of \cite[Proposition 2.1, p.145]{Gi}.
\end{proof}
\vspace{1mm}

Clearly Propositions \ref{Lem1} and \ref{Lem2} apply to the solutions of (\ref{EE1}).
\vspace{3mm}

The information that an arbitrary solution of (\ref{EE1}) belongs to  ${\mathcal C}^{0, \alpha}(\overline{\Omega})\cap W^{1,q}_{loc}(\Omega)$ for some $\alpha \in (0,1)$ and  $q >2$ is the starting point of a bootstrap argument which relies on the following interpolation result due to C. Miranda \cite{Mi}.

\begin{prop}\label{Lem3}
Let $ \omega \subset \R^N$ be a bounded domain   satisfying the cone property. Assume that $0 \leq \alpha <1$, $p \geq 1$ and let
$$t = \frac{p(2- \alpha) - \alpha}{1 - \alpha}.$$
Then any element of ${\mathcal C}^{0, \alpha}(\omega) \cap W^{2,p}(\omega)$ belongs to $W^{1,t}(\omega).$
\end{prop}

\begin{proof} This result is \cite[Teorema IV]{Mi}.
\end{proof}

Gathering Propositions \ref{Lem1}, \ref{Lem2} and \ref{Lem3} we obtain

\begin{lem}\label{regu}
Assume that conditions (L) and (H1)  hold and that $\Omega$  satisfies condition (A). Then any solution of (\ref{EE1}) belongs to
${\mathcal C}^{0,\alpha}(\overline{\Omega}) \cap W^{1,N}_{loc}(\Omega)$ for some $\alpha \in (0,1)$.
\end{lem}

\begin{proof}
Let $u$ be an arbitrary solution of (\ref{EE1}). As $u$ is bounded, we are in position to apply Propositions \ref{Lem1} and \ref{Lem2} with $\mu=\max_{[-\|u\|_{\infty}, \|u\|_{\infty}]}C_1(|u|)$. Then Propositions \ref{Lem1} and \ref{Lem2} implies that $ u \in {\mathcal C}^{0, \alpha}(\overline{\Omega})\cap W^{1,q}_{loc}(\Omega)$ for some $\alpha \in (0,1)$ and  $q >2$. If $q\geq N$ then the proof is done, while if $q<N$ we follow a bootstrap argument of \cite{BeFr, Fr}, see also \cite{DoGi}.  Since $u \in W^{1,q}_{loc}(\Omega)$,  the function $u$ is a weak solution of
\begin{equation}\label{t1}
 - L u = \xi(x) ,
\end{equation}
with $\xi(x) =   H(x,u,\nabla u)  + h(x) \in L^{\frac{q}{2}}_{loc}(\Omega)$,   by $(H1)$.
By a standard $L^p$-regularity argument, see for
example  \cite[Theorem~3.8]{Tr87}, we deduce that $u \in W^{2,\frac{q}{2}}_{loc}(\Omega)$.
Now using Proposition \ref{Lem3} which is valid on any regular domain
$\omega \subset \Omega$ it follows that
$$u \in   W^{1,t_1}_{loc}(\Omega)  \quad \mbox{where} \quad t_1 =  \frac{\frac{q}{2} (2- \alpha) - \alpha}{1 - \alpha} >q .$$ If $t_1 \geq N$ we are again done. Otherwise from (\ref{t1}) and    the cited classical regularity argument, $u \in W^{2, \frac{t_1}{2}}_{loc}(\Omega)$. Denoting
\begin{equation}\label{t2}
t_n = \frac{\frac{t_{n-1}}{2} (2- \alpha) - \alpha}{1 - \alpha} > t_{n -1} > q > 2
\end{equation}
by a bootstrap argument we get $u \in W^{2, \frac{t_n}{2}}_{loc}(\Omega)$ for all $n \in \N$ as long as $t_{n-1} < N$. We now claim that the  increasing
sequence $\{t_n\}$  exceeds the value  $N$. Indeed, arguing by contradiction, if $t_n<N$ for every $n\in\mathbb N$, then the limit
$l$ of $\{ t_n\}$ has to be
$l=2$.
This  contradicts   that $t_n >q >2$. At this point the proof of the lemma is completed.
\end{proof}

The motivation to  observe that any solution of (\ref{EE1}) has an additional regularity appears in the next comparison principle in $H^1(\Omega)\cap W^{1,N}_{loc}(\Omega)\cap {\mathcal C}(\overline\Omega)$. Recall that $u_1$ is a {\it lower solution of \eqref{EE1}} if $u_1^+\in H^1_0(\Omega)$ and, for all $\varphi\in H^1_0(\Omega)\cap L^{\infty}(\Omega)$ with $\varphi\geq0$ a.e. $x\in \Omega$, we have
$$
 \sum_{i,j=1}^N \int_{\Omega} a^{ij} \frac{\partial u_1}{\partial x_i} \frac{\partial \varphi}{\partial x_j}  \leq \int_{\Omega} H(x,u_1,\nabla u_1)\,\varphi + \int_{\Omega} h\,\varphi.
$$
In the same way, $u_2$ is an {\it upper solution of \eqref{EE1}} if $u_2^-\in H^1_0(\Omega)$ and, for all $\varphi\in H^1_0(\Omega)\cap L^{\infty}(\Omega)$ with $\varphi\geq0$ a.e. $x\in \Omega$, we have
$$
\sum_{i,j=1}^N \int_{\Omega} a^{ij} \frac{\partial u_2}{\partial x_i} \frac{\partial \varphi}{\partial x_j}  \geq \int_{\Omega} H(x,u_2,\nabla u_2)\,\varphi + \int_{\Omega} h\,\varphi.
$$

\begin{lem}\label{UUniqueness}
Assume that the hypotheses (L) and (H2) hold. Then if  $u_1, u_2\in H^1(\Omega)\cap W^{1,N}_{loc}(\Omega)\cap {\mathcal C}(\overline\Omega)$ are respectively  a lower solution and an upper solution of \eqref{EE1}, then $u_1\leq u_2$ in $\Omega$.
\end{lem}

\begin{proof}
Here we adapt an argument from \cite{BeMeMuPo}, based in turn on an original idea from \cite{BoMa}.
Consider the function $v=u_1-u_2$, which satisfies
\begin{equation}
\label{2}
\begin{array}{cl}
-L v \leq H(x,u_1,\nabla u_1)-H(x,u_2,\nabla u_2), &\mbox{in }\Omega,
\\
v\leq 0, &\mbox{on } \partial\Omega,
\\
v\in H^1(\Omega)\cap W^{1,N}_{loc}(\Omega) \cap {\mathcal C}(\overline\Omega).&
\end{array}
\end{equation}
\medbreak

For every $c\in\mathbb R$, let us consider the set
$\Omega_c=\{x\in \Omega \, :\, |v(x)|=c\}$ and
$$
J=\{c\in \mathbb R  \, :\, \mbox{meas\,}\Omega_c>0\}.
$$
As $|\Omega|$ is finite, $J$ is at most countable and, since for all $c\in \mathbb R$, $\nabla v =0$ a.e. on $\Omega_c$,  we also have
\begin{equation}
				\label{mes}
\nabla v=0 \mbox{ a.e. in } \bigcup_{c\in J} \Omega_c.
\end{equation}
Define
$
Z= \Omega \setminus \bigcup_{c\in J} \Omega_c
$ and, for all $k\geq 0$, choose
$ \varphi=(v-k)^+ \in H_0^1(\Omega )\cap L^\infty (\Omega)$
 as test function in \eqref{2},
to
 deduce by condition (L) tha
$$
\eta \,\|\nabla  (v-k)^+\|^2_{L^2(\Omega)}  \leq
\int_{\Omega}(H(x,u_1,\nabla u_1)-H(x,u_2,\nabla u_2))\, (v-k)^+ \, dx.
$$
Let $A_k=\{ x\in\Omega \ : \ v(x)\geq k\}$.  By \eqref{mes}, (H2) and $\|u_1\|_{\infty}\leq R$, $\|u_2\|_{\infty}\leq R$ for some $R>0$ we obtain a constant $M>0$ such that
\arraycolsep1.5pt
$$
\begin{array}{rcl}
\displaystyle
\eta \,\|\nabla  (v-k)^+\|^2_{L^2(\Omega)}
&\leq&
\displaystyle
\int_{A_k}(H(x,u_1,\nabla u_1)-H(x,u_2,\nabla u_2))\,  (v-k)^+ \, dx
\\
&\leq&
\displaystyle
M \int_{A_k \cap Z}  (|\nabla u_1|+|\nabla u_2|+b_2)\, | \nabla v |\,  (v-k)^+ \, dx
\\[3mm]
&=&
\displaystyle
M \int_{A_k \cap Z}  (|\nabla u_1|+|\nabla u_2|+b_2)\, | \nabla  (v-k)^+|\,  (v-k)^+ \, dx.
\end{array}
$$
Since  $v \in {\mathcal C}(\overline{\Omega})$ and $v\leq 0$ on $\partial\Omega$,  we have that $(v-k)^+$ has a compact support in $\Omega$, for all  $k >0$,  and hence
$(|\nabla u_1|+|\nabla u_2|+b(x))\in L^N(A_k \cap Z)$. This implies that
\begin{equation}
\label{3bb}
\begin{array}{rcl}
\eta \,\|\nabla  (v-k)^+\|^2_{L^2(\Omega)}
&\leq&
\displaystyle
M \||\nabla u_1|+|\nabla u_2|+b\|_{L^N(A_k \cap Z)}\|\nabla  (v-k)^+\|_{L^2(\Omega)} \| (v-k)^+\|_{L^{2^*}(\Omega)}
\\[2mm]
&\leq&
\displaystyle
\mathcal{S}^{-1}_NM \left\||\nabla u_1|+|\nabla u_2|+b\right\|_{L^N(A_k \cap Z)}\|\nabla (v-k)^+\|^2_{L^2(\Omega)},
\end{array}
\end{equation}
\arraycolsep5pt
where   $2^* =2N/(N-2)$ and $ \mathcal{S}_N$ denotes the Sobolev constant.
\medbreak

We want to prove that $v\leq0$. Indeed, assume by contradiction that $v^+\not\equiv 0$ and consider the non-increasing function  $F$  defined on ${]0, \| v^+\|_\infty]}$ by
$$
F(k)= \mathcal{S}^{-1}_NM \||\nabla u_1|+|\nabla u_2|+b\|_{L^N(A_k \cap Z)}, \ \ \forall \,  0<k<\| v^+\|_\infty
$$
and $F(\| v^+\|_\infty)=0$. By definition of $Z$ we have that $F$ is continuous and we can choose $0<k_0<\| v^+\|_\infty$ such that
$F(k_0) < \eta$. By \eqref{3bb},
$\eta \,\|\nabla  (v-k_0)^+\|^2_{L^2(\Omega)}\leq F(k_0) \|\nabla   (v-k_0)^+\|^2_{L^2(\Omega)}$, which implies that $\|\nabla  (v-k_0)^+\|_{L^2(\Omega)}=0$, i.e.
$v\leq k_0< \| v^+\|_\infty$, a contradiction proving that necessarily $v^+=0$ and hence $u_1\leq u_2$. This concludes the proof.
\end{proof}

\begin{proof}[Proof of Theorem \ref{main}]
Let $u_1$ and $u_2$ be two solutions of (\ref{EE1}). By Lemma \ref{regu} we know that $u_1$ and $u_2$ belong to ${\mathcal C}(\overline{\Omega}) \cap W^{1,N}_{loc}(\Omega)$. Thus it follows from Lemma \ref{UUniqueness} that $u_1 = u_2$.
\end{proof}

\begin{remark}
In the proof of Theorem \ref{main} the requirement that $\Omega$ satisfies condition (A) is used to show that any solution of (\ref{EE1}) belongs to
${\mathcal C}(\overline{\Omega})$. In turn this  property is used only in Lemma \ref{UUniqueness} to guarantee that for any solution $u$ of (\ref{EE1}) the set
$A_k=\{ x \in \Omega : u(x) \geq k\}$ is compact for any $k >0$. It is an open question if the conclusion of Theorem \ref{main} holds true without assumption (A).
\end{remark}

As a corollary of  Lemma~\ref{UUniqueness} and  Theorem \ref{main} we obtain  the following result which, under the condition (A),
improves
the results in  \cite{BaBlGeKo,BaMu} concerning (\ref{EE1}).

\begin{cor} \label{corolario}
Assume that $\Omega$ satisfies condition (A) and that condition (L) holds. Let
$H:\Omega\times\mathbb R\times \mathbb R^N \to \mathbb R$
be  a Carath\'eodory function satisfying (H1) and such that,
for a.e. $x\in \Omega$,
 $H(x,\cdot,\cdot)\in {\mathcal C}^1(\R^{N+1})$ with
$$
\frac{\partial H}{\partial u}(x,u,\xi)\leq 0, \ \mbox{a.e. } x\in \Omega, \ \forall  u\in \mathbb R, \ \forall \xi \in \R^N.
$$
Assume moreover there exists  a function $b_3\in L^N_{loc}(\Omega)$ and a continuous nondecreasing function $C:\mathbb R^+\times \mathbb R^+\to \mathbb R^+$ such that
$$
\left|\frac{\partial H}{\partial \xi}(x,u,\xi)\right| \leq C(|u|)(|\xi|+ b_3(x)), \ \mbox{a.e. } x\in \Omega, \ \forall  u\in \mathbb R, \ \forall \xi \in \R^N.
$$
If $u_1, u_2\in H^1(\Omega)\cap W^{1,N}_{loc}(\Omega)\cap {\mathcal C}(\overline\Omega)$ are respectively  a lower solution and an upper solution of \eqref{EE1}, then $u_1\leq u_2$ in $\Omega$. In particular,  (\ref{EE1}) has at most one  solution.
\end{cor}

\begin{proof}
We just have to prove that (H2) holds.
Let  $x\in \Omega$,  $u_1$, $u_2\in \mathbb R$ with $u_1\geq u_2$ and $\xi_1$, $\xi_2\in \mathbb R^N$. Define the function $F(t)=H(x,tu_1+(1-t)u_2,t\xi_1+(1-t)\xi_2)$, for every $t\in [0,1]$. Observe that $F\in {\mathcal C}^1(\mathbb R)$. Moreover we have
$$
\arraycolsep1.5pt
\begin{array}{rcl}
H(x,u_1,\xi_1)&-&H(x,u_2,\xi_2)  = F(1)-F(0)
\\
&=&
\displaystyle
\int_0^1 \frac{d}{dt}F(t)\,dt
\\
&=&
\displaystyle
\int_0^1 \frac{\partial H}{\partial u}(x,tu_1+(1-t)u_2,t\xi_1+(1-t)\xi_2)\,dt \, (u_1-u_2)
\\
&&
\displaystyle
+
\int_0^1 \frac{\partial H}{\partial \xi}(x,tu_1+(1-t)u_2,t\xi_1+(1-t)\xi_2) \cdot (\xi_1-\xi_2)\,dt
\\
&\leq&
\displaystyle
\int_0^1 \left|\frac{\partial H}{\partial \xi}(x,tu_1+(1-t)u_2,t\xi_1+(1-t)\xi_2)\right|\,dt\,\, |\xi_1-\xi_2|
\\
&\leq&
\displaystyle
\int_0^1 C_0(|tu_1+(1-t)u_2|)\, \left[|t\xi_1+(1-t)\xi_2|+ b_3(x)  \right]\,dt\,\, |\xi_1-\xi_2|
\\
&\leq& C_0(|u_1|+|u_2|)\, \left[|\xi_1|+|\xi_2|+ b_3(x)  \right]\,|\xi_1-\xi_2|.
\end{array}
$$
\arraycolsep5pt
This proves that (H2) is valid and we can apply  Lemma~\ref{UUniqueness} and  Theorem \ref{main} to conclude.\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
La communauté de communes du Mâconnais Charolais est une ancienne communauté de communes française, située dans le département de Saône-et-Loire et la région Bourgogne-Franche-Comté.

Composition

Compétences

Historique
 Le 1er janvier 2013, elle est rejointe par la commune de Pierreclos.
 Le , avec la mise en place du nouveau schéma départemental de coopération intercommunale, la communauté de communes fusionne avec la communauté de communes de Matour et sa région, pour former la communauté de communes Saint-Cyr Mère Boitier entre Charolais et Mâconnais.

Présidence

Voir aussi
Communauté de communes Saint-Cyr Mère Boitier entre Charolais et Mâconnais
Intercommunalités de Saône-et-Loire

Sources
Le SPLAF (Site sur la Population et les Limites Administratives de la France)
La base ASPIC

Maconnais Charolais

redpajama_set_name: RedPajamaWikipedia


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text:
Zen and the Art of Microaggressions
Filed under: Guest Comment — Tags: AC/DC, Dukes of Hazzard, Lenny Bruce, Lovin — Bob Patterson @ 12:35 pm
[Trigger Warning: The following column may contain words, phrases, and/or topics that readers may find unsettling and upsetting. If not; then the columnist isn't doing his job correctly and must apologize.]
If the latest example of Berkeley Liberal thinking, which is called "micro aggression" is retroactively applied to Lenny Bruce's most famous quotes, he wouldn't be considered just a criminal but he would be regarded as an equal of the Nuremberg War Crimes Trial defendants. When the President of the United States recently used the n-bomb, he did not issue a trigger warning and consequently the Republicans became incensed. Their righteous indignation over the use of that word came perilously close to apoplexy.
It seems as if some political commentators do not want a lively discussion about various contentious topics but would rather have a verbal equivalent of the de facto Christmas truce that occurred at Christmas in 1914. Is neutralizing debate a liberal or conservative tactic? Is it an example of microaggression to even ask that question? If so who would approve such behavior other than Lenny Bruce and others from the Golden Age of Sick humor?
If Lenny Bruce were still alive today could he get away with asking this question: "Are the members of the United State Supreme Court acting like drama queens with their coy moves to postpone the announcement of their decisions for the most contentious cases from this year?"
If the conservatively owned mainstream media is satisfied with the Justices shenanigans, who outside the Berkeley city limits will object?
The mainstream media was spared the trouble of taking an in-depth look at the Berkeley Balcony tragedy that occurred early on June 16 because on June 17 a mass shooting occurred and the new media immediately switch the country's focus of attention to the mass murder story.
The gun manufacturing industry was spared another round of the gun control debate when the news commentators immediately directed the nation's attention to the Confederate flag issue. The power of political activism was underlined by the fact that several national merchandise chains quickly announced they were suspending the sale of Confederate flags.
Meanwhile, in Berkeley, while the elite of the journalism industry were in town to cover the aftermath of the balcony tragedy, a report by the Berkeley Police Review Commission was released. It immediately was criticized by local citizens for not accurately describing the police conduct on the evening of December 6, 2014 which had sparked the investigation.
It was asserted by some zealous observers to be a "cover-up" or what the kids would call "a white wash job." Is that a subtle way of saying that only honkies try to lie their way out of a nasty predicament?
KCBS news radio reported on Tuesday of this week that in the aftermath of the six student deaths in the balcony tragedy, no police investigation regarding possible criminal conduct was being conducted. The lawyers and the inevitable lawsuits would be the method for providing justice for the deaths.
On Thursday, the Alameda County District Attorney, Nancy O'Malley, announced that her office would be conducting a criminal investigation, which might produce manslaughter indictments.
Meanwhile, teachers were realizing that they had to provide students with "Trigger warnings," if their lectures contained any words, phrases, or topic which might cause emotional distress to the students in the audience.
If these criteria for conduct by teachers were retroactively applied to some of the "teach-ins" spawned by the Vietnam War, wouldn't many of the teachers have lost their jobs?
The item at the center of the microagressions storm was a Washington Post article written by UCLA law professor Eugene Volokh. It should be available via a quick Google News search.
The mainstream media seems to prefer focusing on soap opera news that prominently features sexual hanky-panky. The saga of the prison employee whose sex life caused extensive speculation on the cable news networks was getting more media attention in the USA than was any detailed analysis of the events in the Middle East. It even spilled over onto the network morning show interview of her husband. By Wednesday of this week Getty & Armstrong were asserting that the prison guard had been unfaithful to her husband with a number in triple digits needed for accuracy.
The fans of the Oakland Warriors had to wait forty years for their team to win the championship. The team owners can't wait for a chance to get a better deal from a different city to move and thereby increase the value of their team.
The new Bay Bridge seems to be a textbook example of the old political wisdom: Build in haste, repent at leisure.
The World's Laziest Journalist has predicted that the Justices would rule that it was unconstitutional and realize that our batting average number will be seriously affected by the inaccurate prediction.
This weekend the response of the paid commentators who work for mass media owned by wealthy conservative moguls should provide a very high level of entertainment because they might provide opinions that should require a strong trigger warning.
Will the media issue calls for patriots to calmly accept the ruling or will they try to stir up rancor and discontent? The weekend TV shows called "gab fests" may be highly charged and contentious and should be very entertaining this weekend.
Note: Next week's column will be posted on Thursday due to the long holiday weekend.
In his autobiography, "How to talk dirty and influence people," Lenny Bruce provided (on page 21) the essence of the cable news addict's philosophy: "I loved this because I wasn't as afraid of being killed in battle as I was of being bored."
Now the disk jockey will play the Lovin' Spoonful's "Did you ever have to make up your mind?," Waylon Jennings theme from the Dukes of Hazzard," and AC/DC's "Jailbreak." We have to go do a Google map search to find out where Thunder Road is. Have a "good ole boy never meanin' no harm" type week.

redpajama_set_name: RedPajamaCommonCrawl


text:
From The Photographer: Arete in East Africa
|In From the Photographer, Arete Stories
Arete is the expert storytelling agency for NGOs, UN bodies and foundations, and has been working across East Africa for more than twenty years. Our talented photographers, journalists and videographers support Arete by gathering content for emergency appeals and documenting the life-saving impact of UN agencies and NGO's; telling the stories that make a difference.
After four successive seasons without rain, communities across East Africa are facing the worst food crisis in 40 years.
'One person is likely to die of hunger every 36 seconds between now and the end of the year in drought-stricken East Africa as the worst-hit areas hurtle towards famine'.
The World Food Programme estimates that there are 89 million people who are acutely food insecure, and 16 million children and pregnant or lactating mothers are now malnourished.
The situation is being exacerbated by the conflict in Ukraine, which has shocked the global supply chain. According to WFP – the world's largest humanitarian agency focused on hunger and food security – 11% of the world's grain was provided by Ukraine before the war. Crucially, 40% of the wheat that provided staples for WFP's emergency food relief programmes came from Ukraine.
With no sign of relief for the people of East Africa, Arete has maintained a presence on the ground, collaborating with bodies like WFP and the Food and Agriculture Organisation of the United Nations (FAO), who continue to work tirelessly to provide vital aid. Using our consultants' experience and knowledge of the region, it is Arete's mission to keep the crisis in the public eye, to ensure that as many people as possible get the help they desperately need.
In our 'From the Photographer' series, we showcase the important work of our consultants and give them a chance to share their thoughts and experiences around their powerful imagery.
This edition of 'From The Photographer' is dedicated to our work in East Africa:
Abdulkadir – Videographer
"I have been a video journalist since 2008. I've worked for different international and national TV and other organizations. For the last 5 years I've been working for Arete as a freelance videographer covering humanitarian stories in Somalia
In Somalia there is severe drought caused by four consecutive years of no rain so I am now witnessing people suffer with hunger and sickness. Last April, I was capturing footage in an IDP camp and witnessed a little boy dying of disease".
A post shared by Arete Stories (@aretestories)
Abdulkadir produced the video above in collaboration with actor Dominic West and the World Food Programme for their emergency appeal.
Brian – Photographer
Redempter poses for a photograph with her son at their home in Kenya. The United Nations World Food Programme (WFP) provides social protection measures to vulnerable families through cash transfers in partnership with Kenya's national and local governments.
Brian / WFP / Arete
"I am a photographer based in Kenya with over 5 years of experience documenting stories of impact and change. I specialise in documentary, editorial, and commercial photography.
I started in written journalism but wanted another way to tell stories, so I taught myself photography to complement my writing. Then over time, I completely switched to storytelling through images. I have worked in Kenya, Uganda, Tanzania, South Sudan, Rwanda, Burundi and Zanzibar."
Kamene and her daughter Zipporah harvest pigeon peas at their farm in Kenya.
"It is common in this region to experience drought and floods due to the extremes of the wet and dry seasons. I have worked during floods caused by heavy rains. I was covering Western Kenya, and the heavy rainfall caused rivers to break banks and flood the areas around. This caused the displacement of people from their homes, disease and massive disruption.
So many people lost their lives and families and had to go through a system of identifying their loved ones and reunification in cases where their loved ones were found in other parts of the region. The floods caused massive disruption and it took months to rebuild communities."
Polina poses for a photograph in her wheelchair in Kenya.
Moustapha – Photographer
"I am a photographer and trilingual translator and have been a photographer for four years. I have worked with local and international humanitarian organizations that work in in Somalia and have worked more recently with Arete."
Abdi eats a meal with his siblings in Somalia. FAO increases access to food, water and basic necessities and protects livelihoods for severely drought-affected communities in Somalia.
Moustapha / FAO / Arete
"Working in Somalia during the last few years of drought, I have encountered many situations that shook my heart and challenged my faith in humanity".
Jama, a farmer, holds tomatoes and corn at his farm in Somalia.
Moustapha / Arete / FAO
"In early 2021, while on a photography assignment covering the impact of the drought in one of the IDPs on the outskirts of Mogadishu, I met a pregnant mother with 4 children and as usual I started taking photos of her and her children and all of a sudden, she burst into tears. I stopped taking photos, put the camera aside and asked her why she was crying, she said to me:
'It has never crossed my mind to come to an IDP camp because back before the drought happened, we were wealthy people, we had many livestock, we had a farm, and we were prosperous. Our livestock have perished in this drought and the farm has been badly affected.
We have been displaced from Bakool. On our way here, my eldest son died on the road due to thirst and hunger. When we came to the IDP, the suffering and the living conditions here made me want to return to where we have come from'
To me, the story of this mother gave me more of an idea of the severity of the drought in Somalia than all the news I have read on the internet."
A group of children smile and pose for a photograph in Somalia.
Isak – Photographer
Isak is a Somali photographer based in Somaliland and has worked with Arete for the last 7 years.
Farmer Mohamed and his family, settled far from home while following their livestock to pasture in Somaliland. FAO supports agropastoralists in Somaliland to strengthen their resilience through increased income from improved fodder value chains and provision of information for action.
Isak / FAO / Arete
A boy holds a lamb in Somaliland.
Mohamoud, an FAO beneficiary, poses for a photograph in Somaliland.
Ismail – Photographer
Ismail is a photographer based in Somalia. Having worked for Reuters and other major news organisations over the past two decades, Ismail has extensive experience in Somalia and across East Africa.
A farmer stands next to the remains of a dead cow on his farm in a drought-stricken area of Somalia. FAO helps to build the capacity of smallholder farmers across the entire value chain, focusing on production, post-harvest loss reduction and market linkages to improve food security and nutrition at the household level through collective action, aggregation, and the strengthening of cooperatives.
Ismail / FAO / Arete
(From left to right): Abdiasis Mohamed Siyaad Dahabshil, Amal Bank Manager; Farhana Carte, Chairwoman of Hiiraan Women Association; Ali Osman Husein, Deputy Chairman of Social Affairs of Beletweyne; and Nadar Tabah Maalin, Mayor of Beletweyne, admire produce from a stall at the agri-business trade fair for farmer cooperatives in Somalia.
A boy plays in Somalia.
East Africa is a complex and sometimes difficult region in which to operate. But the experience, expertise and resilience of our talented consultants mean that Arete can continue to work quickly and effectively, reacting to the current crisis as it rapidly evolves, and ensuring that the voices of the millions on the brink of famine are heard and that their stories told to the world.
Our award-winning journalists, photographers and content providers are eager to help you make a difference.
Contact us to find out how we can tailor our expertise to meet your needs.


text:
import React from "react";
import { createRenderer } from "react-test-renderer/shallow";
import { findAllWithType } from "../src";

const OtherComponent = () =>
;

const YetAnotherComponent = () =>
;

const TestWithTypes = () => (

    <OtherComponent test={1} />
    <OtherComponent test={2} />
    <OtherComponent test={3} />
    <YetAnotherComponent test={1} />
    <YetAnotherComponent test={2} />
    <YetAnotherComponent test={3} />

);

describe("`findAllWithType`", () => {
  let renderer;
  let tree;

  beforeEach(() => {
    renderer = createRenderer();
    tree = renderer.render(<TestWithTypes />);
  });

  it("should find three `OtherComponent` components", () => {
    const found = findAllWithType(tree, OtherComponent);

    expect(found.length).toBe(3);
  });

  it("should find three `YetAnotherComponent` components", () => {
    const found = findAllWithType(tree, YetAnotherComponent);

    expect(found.length).toBe(3);
  });

  it("should find four `div` components", () => {
    const found = findAllWithType(tree, "div");

    expect(found.length).toBe(4);
  });

  it("should find no `button` components", () => {
    const found = findAllWithType(tree, "button");

    expect(found.length).toBe(0);
  });
});

redpajama_set_name: RedPajamaGithub


text:
Tag Archives: Workers' rights
by nonnie9999 | March 28, 2011 · 12:00 am
Cheeseheadstrong
From TALKING POINTS MEMO:
Yet another shoe has dropped in the battle over Wisconsin Gov. Scott Walker's (R) anti-public employee union law — with state Republican leaders now apparently defying or attempting to circumvent a court order that temporarily blocked implementation of the law.
The judge's order "restrain[ed] and enjoin[ed] the further implementation" of the law, including the prevention of Secretary of State Doug LaFollette (D) from publishing the act in the Wisconsin State Journal, which acts as the state's official newspaper for the purpose of giving the public official notice of new laws — the final step for the law to take effect. That decision is now going through an appeals process, which remains up in the air.
But now, state Republicans have had the bill published through a different office — the Legislative Reference Bureau, which handles drafting and research for the legislature — according to the LRB's statutory requirement to publish legislation within ten days of enactment.Interestingly, the LRB itself says that this publication does not constitute action that would put the law into effect. But the state's Republican leaders disagree. Senate Majority Scott Fitzgerald (R) says the LRB publication constitutes official publication and the insists the law will take effect Saturday.
Filed under Democrats, humor, movies, parody, politics, Republicans, Senate, snark, Wordpress Political Blogs
Tagged as collective bargaining, Doug LaFollette, governor, Legislative Reference Bureau, LRB, Peter Barca, recalls, Scott Fitzgerald, Scott Walker, Secretary of State, unions, Wisconsin, Wisconsin Legislative Council, Wisconsin State Journal, Workers' rights
The Pain in Maine's Due Plainly to His Reign
Yesterday, the Raisin reported on Governor Paul LePage of Maine ordering the Department of Labor to remove a mural that celebrates the history of labor in the state. There's going to be an awful lot of blank wall space, so I thought we'd try to help and suggest a replacement. I did a little digging, and i found out about something called the Maine Heritage Policy Center. From WLBZ (Bangor):
Tarren Bragdon has risen to a position of influence as CEO of the Maine Heritage Policy Center, and was the leader of Gov. Paul LePage's transition team. He goes In the Arena with Pat Callaghan to talk about the efforts to shrink the state budget and reform government.
The Maine Heritage Policy Center says Gov. LePage's proposed budget doesn't make enough cuts. The center believes Maine should cut 4,000 state jobs. Bragdon talks about that, as well as collective bargaining rights for state employees, and Gov. LePage's decision to create private advisory groups to counsel him on business matters– which will not be subject to Maine's open meeting laws.
Why is that important? Well, this is from Dirigo Blue:
Trevor Bragdon has stepped down as the State Director of AFP Maine, and will be replaced by long-time Republican legislator Carol Weston.
AFP Maine is a chapter of Americans for Prosperity, an AstroTurf front group founded by David Koch, a major funder of libertarian groups across the country. Trevor Bragdon is the brother of Tarren Bragdon, the Executive Director of the conservative Maine Heritage Policy Center (MHPC), and one of the co-chairs of Gov. Paul LePage's transition team. MHPC has ties to the Heritage Foundation in D.C., which also receives money from the Charles G. Koch Charitable Foundation.
Anyone else think it's quite a coincidence that the Koch brothers' names keep popping up when anyone is discussing the new Republican governors who are trying to pull the rug out from anything that's good for the middle class and the poor? With that in mind, I've come up with a picture that I think will look just great on the walls of the Maine Department of Fellating Corporate Bigwigs Labor.
Filed under humor, New Hampshire, parody, politics, Republicans, snark, Wordpress Political Blogs
Tagged as 2010 election, AFP, Americans for Prosperity, Budget, Business, Charles G. Koch Charitable Foundation, Charles Koch, collective bargaining, conservatives, corporations, David Koch, Dirigo Blue, governor, Heritage Foundation, Koch Brothers, Koch Industries, Labor, Labor Department, Libertarian, Maine, Maine Heritage Policy Center, middle class, Missouri, Ohio, Open Meetings Law, Paul LePage, poor, right-to-work, Scott Walker, Tarren Bragdon, Tea party, Tom Winsor, Trevor Bragdon, unions, wages, Wisconsin, Workers' rights
Maine Event
From the Sun Journal:
AUGUSTA — Gov. Paul LePage has ordered the removal of a 36-foot mural depicting Maine's labor history from the lobby of the Department of Labor.
Worker advocates described the move as a "mean-spirited" provocation amid the administration's high-tension standoff with unions.
Filed under humor, parody, politics, Republicans, snark, television, Wordpress Political Blogs
Tagged as AFL-CIO, art, Budget, Business, César Chávez, disasters, Frances Perkins, Franklin Roosevelt, governor, History, jobs, Judy Taylor, Labor, Labor Department, Laura Boyett, Maine, Maine People's Alliance, Paul LePage, progressives, right-to-work, teachers, Triangle Shirtwaist Factory, unions, worker safety, Workers' rights
by nonnie9999 | February 20, 2011 · 12:15 am
From the Atlantic:
One is a bald, blue-eyed former hospital executive brand new to public office. Another is a career politician who leads statewide motorcycle tours to boost tourism. And the other is a former congressman and FOX News host who called a cop who gave him a traffic ticket last month an "idiot."
All three are newly elected Republican governors facing massive political upheaval over their slash-and-burn approach to state spending and rejection of billions of federal dollars for high-speed rail projects.
Call them the "Three Scrooges": Rick Scott of Florida, Scott Walker of Wisconsin, and John Kasich of Ohio. Walker and Kasich replaced Democrats, and Scott replaced a Republican-turned-independent.
Original movie poster
Oops, I forgot one…
Filed under Barack Obama, Congress, Democrats, Florida, Fox News, humor, Jeb Bush, John Boehner, movies, parody, politics, Republicans, snark, Wordpress Political Blogs
Tagged as 2012 election, Budget, Chris Christie, civil service, collective bargaining, economy, governor, health care, high-speed rail, John Kasich, Labor, law enforcement, Madison, middle class, Minnesota, New Jersey, Ohio, pensions, police, poor, protests, Rick Scott, schools, Scott Walker, seniors, Tea party, teachers, Tim Pawlenty, Twitter, unions, Wisconsin, Workers' rights
Walker vs. Walk-Out
From msnbc:
MADISON, Wis. — Gov. Scott Walker on Friday ruled out a compromise proposed by a key union to retain collective bargaining rights in exchange for public workers accepting benefit cuts.
At a press conference, Walker said he could not consider the offer by the largest state workers union because it only covered some public employees and came late in the process.
Walker and other Republicans have been trying to pass a controversial bill that would end a half-century of collective bargaining for most public workers in Wisconsin.
Filed under Barack Obama, Constitution, Democrats, humor, movies, parody, politics, Republicans, Senate, snark, Texas, Wordpress Political Blogs
Tagged as Assembly, Bob Ziegelbauer, boycott, Budget, collective bargaining, conservatives, deficit, Egypt, governor, health care, Health Insurance, Hosni Mubarak, Illinois, Independents, Jon Erpenbach, Madison, Mark Miller, Milwaukee, pensions, Peter Barca, Scott Fitzgerald, Scott Walker, Tea party, teachers, Tim Cullen, unions, Wisconsin, Workers' rights
Talk Like an Egyptian…Tyrant
From The Washington Post (Editorial):
In Egypt, workers are having a revolutionary February. In the United States, by contrast, February is shaping up as the cruelest month workers have known in decades.
The coup de grace that toppled Hosni Mubarak came after tens of thousands of Egyptian workers went on strike beginning last Tuesday.
But even as workers were helping topple the regime in Cairo, one state government in particular was moving to topple workers' organizations here in the United States. Last Friday, Scott Walker, Wisconsin's new Republican governor, proposed taking away most collective bargaining rights of public employees.
Filed under California, Democrats, humor, movies, parody, politics, Republicans, snark, Wordpress Political Blogs
Tagged as Andrew Cuomo, Cairo, collective bargaining, Corporate greed, corporations, economy, Egypt, governor, health care, Health Insurance, Hosni Mubarak, Jerry Brown, Middle East, National Guard, New York, pensions, profits, revolution, Scott Walker, teachers, unions, wages, Wisconsin, Workers' rights
In Order to Form a More Perfect Union…or Not
From The Washington Post:
As business and labor gird for battle over legislation that would make it easier for workers to organize, the debate could be transformed by a "third way" proposed by three companies that like to project a progressive image: Costco, Starbucks and Whole Foods.
Like other businesses, the three companies are opposed to two of the Employee Free Choice Act's components — a provision that would allow workers to form a union if a majority sign pro-union cards, without having to hold a secret-ballot election, and one that would impose binding arbitration when employers and unions fail to reach a contract after 120 days.
But the companies' chief executive officers say they also recognize that just opposing the legislation, commonly called "card check," is not enough because of the widespread perception in Democrat-dominated Washington that there is not a level playing field between labor and business. So the CEOs have come up with ideas they hope will form the basis of new legislation.
Original DVD cover.
Filed under Congress, Corporate greed, Democrats, humor, Mark Pryor, movies, parody, politics, snark, Tom Harkin, Wordpress Political Blogs
Tagged as AFL-CIO, arbitration, Arkansas, Bill Samuel, Blanche Lincoln, Burger King, Business, card check, CEOs, Chamber of Commerce, Costco, EFCA, Employee Free Choice Act, Employee Free Choice Group, filibuster, George Miller, Home Depot, Howard Schultz, James Sinegal, John Mackey, Labor, Mark Warner, National Right to Work Committee, Starbucks, Teamsters, unions, Wal-Mart, Warren Buffett, Whole Foods, Workers' rights


The most significant proposal in decades to reform MARTA is sailing through the legislative process at the state Capitol and could be up for a vote in the House as early as next week.
So far, no serious objections to the proposal have been raised in public by MARTA or the three governments that control MARTA – Atlanta, and Fulton and DeKalb counties, though union has voiced opposition. The sponsor said the bill intends to help MARTA serve its current and future riders.
"I hope that the bill is received in the way it is intended – and that is to improve MARTA's financial conditions so that we can, hopefully, see some future expansion of the system," said Rep. Mike Jacobs (R-Brookhaven), who chairs the MARTA oversight committee.
House Bill 264 was approved Thursday by the House Transportation Committee. That sets it up for consideration by the full House after it is put on the calendar by the Rules Committee. The Rules Committee did not post the bill on the chamber's Feb. 19 calendar, and the committee is to meet that day to set the calendar for future votes.
HB 264 is unusually long – 22 pages – and each is needed to flesh out all the concepts outlined in the preamble of a bill that, if enacted, would take effect Jan. 1, 2014.
In between the beginning and the end, the 18 points address issues about MARTA's management that have been discussed since at least 1999. That's the year the Legislature created GRTA, and its very existence refocused attention on the oversight and management MARTA.
For example, GRTA has outsourced the operations of the Xpress bus service. That has long begged the question: If a state entity can outsource jobs, why can't MARTA outsource some jobs in order to cut costs?
The labor issue is significant for MARTA, which inherited a labor union when it was created from the remains of a prior bus system that served Atlanta. Legacy costs are as much a part of MARTA's struggles with its balance sheets as they are for many governments across the country.
In a report released last autumn, outsourcing was among the recommendations of the extensive KPMG performance evaluation of MARTA that was initiated by MARTA's board of directors. And it also raised the profile of federal laws that require MARTA to provide certain benefits to those jobs now covered by collective bargaining – even after those jobs are outsourced.
Former MARTA CEO Beverly Scott told the Legislature's MARTA oversight committee in October that "there has to be some change" in the legacy pension structure. About 3,000 of MARTA's 4,500 employees are members of Amalgamated Transit Union No. 732, according to the audit.
Jacobs said the original bill has been tweaked to accommodate the federal law. MARTA would lose some federal funding, if not all of it, if it were not compliant with the requirements of the federal Department of Labor.
The bill would have grievances heard by an arbitrator appointed by the governor who is a retired judge of superior court, court of appeals, or state supreme court.
Jacobs said the proposed law, if enacted, would be "strongly advisory" over the collective bargaining negotiations slated to occur later this year between MARTA and the union.
The bill requires the county delegations to represent various geographic regions. Two of Fulton's three representatives would be required to reside north of Atlanta's city limits and be appointed by mayors of the cities in north Fulton. One must reside in south Fulton, and be appointed by the mayors of the cities of south Fulton and the county's board of commissioners. Currently, all appointees are made by the county commission.
For DeKalb, the bill would move one appointment from the county commission to the mayors of cities located wholly in DeKalb — meaning Atlanta doesn't have a seat at that table. Currently, all four of the county's MARTA representatives are appointed by the county commission.


Click on the Descendant tree tab in the Report control form.
Print a drop-line chart of descendants of the selected person.
Enter the code (without the "P") of the person who will be at the root of the tree. If you do not know the person's code, click on the "Select person" button and select the person from the list.
The width of the lines used to connect people in the chart.
Set this option to include every generation from the root person. With this option off, you can enter the required number of generations in the box to the right. 0 generations would print the root person and his spouse only, 1 generations would print the root person and all his children, etc.
Include the surnames for children. Child surnames can generally be deduced from the surname of the father so you may want to turn this option off to save space.
Wrap any surnames onto the line below the person's firstnames. This can be used to save horizontal space.
Include person and family codes.
Include birth or christening dates.
Include death or burial dates.
Include places for any of the above date events.
Include user-defined fields for people and families.


JIANG Yu-jie,YAO Zhi-gang.Collaborative Empty Container Allocation between Liner Companies in Random Environment.Packaging Engineering,2019,40(5):162-168.
The work aims to study the impact of random factors on two empty container allocation modes in order to show the superiority of collaborative empty container allocation mode in random environment. Considering the randomness of empty container demand in a port and empty container shipping capacity limit, the minimum cost of empty container allocation in the decision period was taken as objective to set up the collaborative empty container allocation model between liner companies in random environment. Then, through an example, the influence of different port service level and capacity restriction level on empty container allocation decision was discussed, and the sensitivity of stochastic factors in the empty container allocation system was analyzed. When liner companies adopted the conservative-cost decision, the conservative-service decision, the risk-cost decision, and the risk-service decision, the total cost difference of two empty container allocation modes was respectively 9638, 22 862, 10 710, and 19 284 dollars. In summary, reducing the capacity restriction level can compress the total cost of empty container allocation, but increasing the port service level will add the total cost of empty container allocation, and the advantage of collaborative empty container allocation mode is more obvious when the port service level and the capacity restriction level are at a high level. Compared with the individual empty container allocation mode, the collaborative empty container allocation mode can weaken the influence of stochastic factor fluctuation in the empty container allocation system on the total cost of empty container allocation.


Inline Filling Systems has hundreds of world class customers from A to Z with very high standards of performance. We list some of those companies below as an example of the professional standards our equipment has to meet in order to sell to these companies. But our most important customers are small to medium sized companies just like Inline Filling Systems. They are the backbone of the economy, the bread and butter of our industry, and the future of our company. We look forward to supporting them as they grow and prosper.
Please note: The appearance of these companies who have purchased from us does not represent an express or implied endorsement of Inline Filling Systems by them.


Save £16.50 (including VAT) on individual prices with this Starter Pack!
6 vinyl roll-up boards with 50mm or 55mm squares. Ideal for clubs or schools. Letters and numbers used for algebraic notation are printed around the border. Overall dimensions approx. 51 x 51cm (20 x 20 inches).
Please specify board colour and size when ordering.


All donations are put to immediate use here in Northern Ireland. We work with people who are often forgotten by society and aim to improve their lives by addressing their alcohol or drug addiction.
You can make a secure donation online using everyclick.com. Click here to find out more and donate.
By paying a minimum of £10 a year, you can support the work of Addiction NI. You'll also be invited to the Addiction NI Annual General Meeting and other events we may hold. Membership is also open to organisations. Contact us below to find out more about becoming a member of Addiction NI.
Contact us via the form below or call 028 9072 5472 to find out more about making a regular donation to Addiction NI through your salary.
Addiction NI welcomes ideas for fundraising events. These can include running marathons, sponsored walks, gala events or any other event you can think of that would raise money for Addiction NI. To talk about your fundraising idea you can call our Fundraising Manager on 028 90725472 or fill in the form below.


text:
Being Nice
This morning on the ride to work I was thinking about the things I've always liked about the Christmas season. As a Christian, there is the celebration of the birth of Christ, which I LOVE, but there's something else. Ideally this time of year, people seem to try a little harder to be nice to each other. There's this "Well hey, I'll do that for you... it's Christmas!" thing going on. As if we are required to have an excuse to do something helpful or friendly to someone! Being nice at Christmas is even a big part of our holiday entertainment selections, such as the story about the Grinch and the one about Ebeneezer Scrooge. Of course, at Christmastime we have historical precedent for "being nice at Christmas" in people like Saint Nicholas (not Santa Claus... the canonized Saint) and Duke Wenceslas (yes, he was real, but no, technically he was not a king, no matter what the song says) who took the opportunity of the season to be very generous to others. But I doubt either of them would want acts of kindness to be limited to the last month of the year! If they were here today, doubtless they would tell us to extend our kindness and generosity every time the opportunity presented itself, whether in December or some other month.
But there's something about this "Christmas spirit" that's imperfect. The problem is that we so often do our kind and generous deeds because we want to be kind and generous people... or even worse, we do them because we feel like we have to. And in reality, good deeds that are done because we feel somehow compelled to do them, or because we want to feel warm fuzzy feelings inside... those good deeds just don't measure up for God. To us, those good deeds seem very altruistic, and certainly they do make a difference to others, but God sees them as dirty, nasty clothes that badly need washing (Isaiah 64:6). (And if you really want to know just how "polluted" those "garments" are, do a little research! Trust me, Isaiah was painting quite a negative picture there!)
But there is a way to do good deeds that is acceptable to God. The key is simply to let those good deeds flow to others, via ourselves, by inspiration from God. As though we were wires carrying power from God to the persons we are ministering to. And how do you know if you're doing something that way or some other way? Well, you certainly need to be in tune with the Holy Spirit, and you get that way through worship and prayer and Bible study; that's just Being A Christian 101. I suspect that while we are on this imperfect world with imperfect bodies and not-quite-totally-renewed minds, there will always be at least a small element of selfishness in doing something nice for someone to whom we owe nothing; after all, it does feel nice to do something kind and then be appreciated for it. But I think that the more in tune we are to the Holy Spirit, the less that matters to us and the more it matters that we are doing what is pleasing to God. And in a nutshell, that is what the Christian Life is all about: doing what is pleasing to God, no matter what happens as a result and no matter what the cost.
As we move out of the "oughts" (I look forward to telling kids in future years that "I remember the great Tulsa blizzard of ought-nine!" hehe) into the twenty-tens and -teens, here's an idea: let's seek to daily be more like Jesus. Let's seek to do only the Father's Will. But let's not do it because we know it's the right thing to do and make up our minds to do it; let's do it because we are so close to God and He has influenced our attitudes so much that it has become natural for us to do His will. Because His nature has become our nature. Not because we are trying to act like Him, but because we have in reality become a little more like Him!
Oral Roberts Memorial Service
ESV Study Bible On Sale
To Live or To Die
Charges Dropped


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Q: mixing text and citations in R markdown Is it possible to mix regular text and citations in R markdown documents so that they looked as follows: (Author 2018; Methods)
Currently, I've tried ([@Author2018]; *Methods*) which gives ((Author 2018); Methods), and [@Author2018; Methods] results in a knitting error.
Any thoughts would be greatly appreciated!

redpajama_set_name: RedPajamaStackExchange


Joe Biden has announced he will not run for president, saying he no longer has the time to mount a campaign, and then proceeded to give what sounded like his campaign speech. I wonder if he wrote this speech before deciding, figuring he could use most of it regardless of his decision.
Mr. Biden seemed to chide Mrs. Clinton for distancing herself from Mr. Obama lately, as she has done on trade, Syria, Arctic drilling and other issues. "Democrats should not only defend this record and protect this record, they should run on the record," he said.
While Biden declined to run in the primaries, it was clear he would like to have run if the situation were different, and he would like to be president. By criticizing Clinton and speaking like a candidate, Biden made it clear that if Clinton's campaign should implode, which remains quite possible, he is ready to serve. With multiple investigations in progress regarding Clinton's unethical behavior as Secretary of State, it is certainly a possibility that Democrats will wake up before the convention and realize how dangerous it could be running with her heading the ticket in the general election. If Sanders is unable to defeat her, it is easy to see the math play out where the Sanders delegates and the super delegates could outnumber committed Clinton delegates and create an open convention. If the news were bad enough, it is even conceivable that some of Clinton's delegates would rethink their support.
Unfortunately the Democrats should probably change their symbol to the ostrich instead of the donkey as, other than for Sanders (until recently an independent), they seem oblivious to the trouble the party is in nation-wide. They might also take a few lessons from Justin Trudeau, as John Nichols discussed in The Nation.
Seeing Biden continue to criticize Clinton today raises the question of whether he will continue to knock Clinton, hoping to increase the chances of her being forced from the race. Plus if he does prefer Sanders, would he ever openly support him over Clinton?
I don't think it is very likely Biden would openly endorse Sanders, but if he did it would be a move comparable to when Ted Kennedy endorsed Barack Obama. Both Ted Kennedy and Caroline Kennedy endorsed Obama in 2008, citing the same types of faults we continue to see in Hillary Clinton. Such a move from Biden, this time endorsing Sanders, would provide a tremendous boost to Sanders' campaign.
For now, the same media which has downplayed Sanders prospects from the start will promote the idea that Clinton is the inevitable winner. We must keep in mind that such media predictions have frequently been wrong in the past. While there is no doubt Clinton is the front runner, her nomination cannot be said to be inevitable months before a single vote has been cast. As I noted earlier in the week, the polls are not at all predictive in a nomination battle.This polling report from December 2007 described how Clinton had a huge lead over Obama. In December 2003, Howard Dean was pulling away in the polls. Eventual winner John Kerry was in sixth place with only 4 percent, even trailing Al Sharpton.
This race is far from over. While the media is dwelling on the Benghazi hearings this week, and this could have a bearing at how she is perceived, the real scandals which will harm Clinton in an election campaign are not based upon this Republican witch hunt, and are not going to go away. Bernie Sanders could pull an upset, like Obama in 2008 or Kerry in 2004, or the party might yet still call on Joe Biden.
Posted in Barack Obama, Bernie Sanders, Hillary Clinton, Joe Biden, John Kerry, Politics, Scandals. Tags: Barack Obama, Bernie Sanders, Hillary Clinton, Joe Biden, John Kerry, Scandals. RSS feed for comments on this post.. TrackBack URL.


Need help? Feel free to PM me In-Game (SantaDash), Discord (Lance I SantaDash#4303), or ask here!
Hey peoples how is everyone?
If you need additional help, feel free to ask me here on the Forums, on Discord, or In-Game.


Robo recall and a few other games which I have bought have gone missing.
They are not hidden in my library. I have tried updating all software and games are still not appearing.
further to this issue I have tried to search them in the games store and I need to purchase them again. This is NOT the first time this has happened and it is very annoying! anyone able to help asap?


Holocene marine microfossils from North Queensland. Approx 8000 years old. Presented on grid viewing slide with cover. 40 specimens per slide.
Photo is a representative image only. Species will vary from slide to slide.


This Alfa Romeo 147 2.0 Twin Spark was produced from 2001 to 2008. It's a front-wheel drive front-engined compact hatchback with a choice of 3-5 doors & 5 seats. With 148 hp, the naturally aspirated 2 Liter 16v Inline 4 gasoline engine accelerates this 147 2.0 Twin Spark to 62 mph in 9.3 seconds and on to a maximum speed of 129 mph. Having a curb weight of 2921 lbs, it achieves 26.4 mpg on average and can travel 418 miles before requiring a refill of its 15.9 gallon capacity fuel tank. It comes with a 5 speed manual gearbox. Luggage space is 9.9 cubic feet, but can be expanded to 36.4 cubic feet for larger loads.


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First: 'Tis the season for giving and sharing… and holiday shopping. Whether it's toys, clothes, books, or electronics, chances are that most of these items were manufactured in factories. Joshua Freeman walks us through the history of factories, and how they continue to shape our modern world.
Next: Do you ever find yourself flipping through photo albums and feeling nostalgic for old times? Well, according to Krystine Batcho, longing for the past can shape how we think about the present. And in some case, it can be beneficial.
Finally: In the era of fake news and sensationalist media, public trust in local and national news outlets is waning. But libraries are increasingly coming to the rescue and in the process are steadily reshaping the face of journalism.


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Vassar Student Association
All Positions & Committees
Certified Organizations
Activism/Social Justice
Games/Programming
Major/Career
Theatre/Film
Preliminary Organizations
Archives & Docs
Amnesty International (amnestyinternational.vsa@vassar.edu)
The Vassar chapter of Amnesty International is affiliated with the national human rights-based organization. Our group discusses and educates both ourselves and the wider Vassar community on issues of human rights throughout the world. We take actions such as letter-writing, fundraising, petition signing and lobbying in response to the issues we discuss.
Healing 2 Action (healingtoaction.vsa@vassar.edu)
Our goal is to unlearn the concepts of Healing and Action and instead allow ourselves to define these terms at an individual level, using our own experiences and needs. Healing and Action are inseparable, and we as an org work will help others determine what they look like for themselves. In doing so, we seek to dismantle the systems of white supremacy, carceral logics, racial capitalism and all other systems of oppression by challenging institutional power and reimagining co-existence.
LiNK (Liberty in North Korea) (link.vsa@vassar.edu)
LiNK at Vassar is a chapter of Liberty in North Korea, a nonprofit organization that works to help North Korean refugees resettle and raise awareness for North Korean human rights issues. LiNK at Vassar works to raise money to donate directly to LiNK and increase awareness on Vassar's campus. We meet weekly and host campus-wide and community events such as benefit concerts, open mics, and food deliveries.
Students for Justice in Palestine (sjp.vsa@vassar.edu, sjpvassar@gmail.com)
Students for Justice in Palestine at Vassar supports the Palestinian struggle against Israeli apartheid and settler colonialism. We believe that while the Palestinian people must be able to determine their own future, we have a duty to organize around calls for an international solidarity movement in opposition of Israeli state and settler violence. We meet on a weekly basis and hold a variety of events and actions throughout the year. Vassar SJP stands behind the Boycott, Divestment and Sanctions (BDS) movement's demands of the full decolonization of all Arab lands, the implementation of the right of return and the end to systemic and open Israeli racial discrimination. We reject all forms of discrimination and racism and are open to anyone interested in working towards a free Palestine.
Students for Sensible Drug Policy (ssdp.vsa@vassar.edu, ssdpvassar@gmail.com)
The Underground (underground.vsa@vassar.edu)
We are Vassar's Human trafficking awareness organization — we attempt to educate the Vassar and greater Poughkeepsie community about modern slavery. We put on lectures, screenings and events pertaining to human trafficking awareness. Our most attended event is the Red Sand Gala where students and community members pour red sand in the cracks of surrounding sidewalks to symbolize those who slip through the cracks of society into human trafficking.
Vassar Animal Rights Coalition (VARC) (animalrightscoalition.vsa@vassar.edu, varc@vassar.edu)
The Vassar Animal Rights Coalition (VARC) works to combat species-based violence and encourage people to reflect upon the societal paradigms that support the objectification of non-human animals. VARC addresses multiple layers of animal rights issues, including animal exploitation through the food, medical, and cosmetic industries, and the human rights issues associated with these industries. VARC works on a number of ongoing campaigns and activities; in the past, these activities have included film screenings, discussions, conferences, and direct work with rescued individuals.
Students for Equitable Environmental Decisions (SEED) (seed.vsa@vassar.edu)
Vassar's Students for Equitable Environmental Decisions (SEED) is an environmental group on campus that aims to further sustainability and environmental justice through activism, advocacy, and increased communication between students, faculty, and administration. We also work with CASC (The Climate Action and Sustainability Committee) in the administration to advocate for dramatic sustainability reform on campus at an administrative level. We believe climate justice is not an independent issue, and has strong ties to the fight against racism, classism, and imperialism. Join us in furthering the conversation on climate justice, carbon neutrality, Vassar fossil fuel divestment, and environmental sustainability at Vassar.
Vassar Greens (greens.vsa@vassar.edu)
Vassar Greens is committed to fighting for a livable planet through environmental and social justice. We promote a greener lifestyle by promoting zero-waste education and sustainable initiatives. We encourage translating personal sustainable habits to larger campus initiatives.
Vassar Organizing Israel Conversations Effectively (VOICE) (jstreetu.vsa@vassar.edu)
VOICE (Vassar Organizing Israel/Palestine Conversations Effectively) aims to engage the Vassar community in rigorous dialogue examining the harmful ways in which the western states perceive and oversimplify ethnic conflict, specifically in Israel/Palestine. We also aim to encourage progressive activism that prioritizes human rights, coexistence, and sustained justice for all peoples in the region, as well as all historically and currently marginalized identities around the world. We facilitate this through open community dialogue, centering those in the middle of the issues, comparative international analysis, and occasional educational programming. In doing so, we advocate against the white Christian hegemonic influence in our approach to understanding this conflict.
Vassar Prison Initiative (prisoninitiative.vsa@vassar.edu)
The Vassar Prison Initiative (VPI) is a non-hierarchical organization committed to raising awareness about issues related to the prison industrial complex. Our activities include an annual publication, film screenings, book drives, and engagement with local activism. In addition to these initiatives and general education efforts on campus and in our community, the VPI works in conjunction with the academic prison programs on campus and responds to pressing prison-related issues as they arise. It is our hope that through our programming, educational outreach, and activism, we can contribute to the fight for justice for incarcerated people and the de-carceration of America.
Vassar Voices for Planned Parenthood (actout.vsa@vassar.edu)
VVPP aims to facilitate a community organizing relationship between members of the Vassar community and PPMHV centered around reproductive justice. In order to accomplish this, we have six major functions:
-Get members of the Vassar community who say they stand with PP to commit to taking direct action.
-Act as a fundraising and advocacy source for PPMHV
-Pop the Vassar bubble; use our motivation to extend outreach in Poughkeepsie, Dutchess County, Marist and other schools in the area
-Gain institutional support in order to acquire reproductive health resources
-Support, unite and collaborate with other student organizations
-Organize on-campus and off-campus informational events about reproductive health and justice
Vassar Disability Coalition (VDC) (access.vsa@vassar.edu)
The VDC is a student organization dedicated to improving campus accessibility for students with disabilities (Access branch) and providing a space to discuss disability issues (Inclusion branch).


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Zenkoku Ippan Tokyo General Union (Tozen, 東ゼン) is as its name suggests, a union which does not restrict membership to those working in any one industry, trade or workplace.
The union traces its origins back to 1956; almost as long as the history of legalized organized labour in Japan.
Nearly all of Tokyo General Union's members are foreign nationals most working in Tokyo, Kanagawa, Saitama, Chiba, Gunma and Tochigi Prefectures. Tozen is one of only three or four general unions in the Tokyo area which has a large number of foreign workers.
Although the Tokyo General Union doesn't restrict membership, it is true to say that it has developed areas of concentration and specialization. Members generally are employed in the banking, foreign language teaching, and publishing industry.
The smallest branch has just three members; while the largest has over 30. The branches oversee the day-to-day affairs of the union at each workplace. Each chapter negotiates with the employers regarding annual salary working conditions. It is only when a chapter encounters trouble or needs special assistance that the staff of the Tokyo General Union central office step in.
Chapter unions are brought together in a number of ways. Firstly, the Executive Committee of Zenkoku Ippan Tokyo General Union has about twenty positions and members of many different chapters are well represented. Second, there are regular scheduled meetings for representatives of all chapters to come together. Newsletters, postal mailouts, e-mailings and Internet web pages are other ways in which information and experiences are shared. There are also plenty of social events organised by the union, where members of different branches can meet.
Tozen is a fighting union! That means that the union is willing to engage in industrial action in pursuit of its aims. In the case of dispute cases, the union wlll use any and all legal means at its disposal (such as engaging in strikes, rallies and leafletings, filing injunctions and dispute cases at the Labour Commission and Tokyo District Court), to achieve victory. This cannot be said of all unions in Japan, however.


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Q: Shared hosting - Subdomain without main domain I'm looking to host a site that will be accessed through a subdomain (mysite.mainsite.com) of another site (mainsite.com). I have set the main domain for my shared hosting account as mainsite.com and I'm about to set an A-record for mysite.mainsite.com to point to the IP of my server and add mysite.mainsite.com as a subdomain in cPanel.
The mainsite.com will however never be pointed to my server, so it somehow feels like I'm "cheating". My question is simply, should this work or am I missing something?

A: From the viewpoint of the DNS system, it is absolutely ok. A hostname can contain a "." without any problem.
This leads to the difference between domains and zones. If you have a host named a.b.example.com, which is registered by an a.b record in your zone example.com, you will have a b.example.com domain too, but only the a.b.example.com and example.com zones.
Of course, the glue records in your parent nameservers need to be set up accordingly.


Masculine fragrance Gentlemen Only by Givenchy from 2013 is a modern homage to the classics of the house—Givenchy Gentlemen from 1974. After the original, Gentlemen Only Intense was launched in early 2014 and in early 2015 we have a new edition called Gentlemen Only Casual Chic.
Gentlemen Only Casual Chic is a fresh woody and spicy fragrance. Seductive and elegant, it is designed for a relaxed, charming and witty man of style. Top notes include a refreshing tonic of cardamom, ginger and juniper. The comfortable heart contains woody notes of birch and cedar. Its seductive base includes sandalwood and ambroxan.