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Healthy Sugar-Free Cookies: No-Bake Chocolate Oat Cookies

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Despite even the best-intentioned plans to stay on the straight and narrow when it comes to your health, sometimes those sugar-filled treats still have a way of sneaking into your day. We wanted to come up with a dessert that we could indulge in without having to feel badly about it and without sacrificing the work we’ve already put in, so we came up with these cookies. Not unlike our first batch of no-bake chocolate oat cookies, these oat cookies are amazingly easy and delicious—but they’re way better for us because they have no added sugar! Using natural peanut butter (we couldn’t resist throwing that in there), coconut oil and honey, we’re able to get great flavor without giving ourselves a cavity—hurray for healthier dessert!

Sugar-Free Chocolate Oat Cookies

Yield: 3 dozen

Ingredients

3 cups quick-cooking oats

3/4 cup honey

2/3 cup natural peanut butter, optional

1/2 cup coconut oil

1/3 cup unsweetened cocoa powder

1 1/2 teaspoon vanilla extract

1/4 teaspoon salt

Directions

Line 2 baking sheets with parchment paper.

In a medium saucepan over medium-high heat, combine honey, peanut butter and coconut oil, stirring until everything blends together smoothly.

Stir in oats, cocoa powder, vanilla and salt and mix until everything is fully incorporated and coated.

Use a spoon or small ice cream scoop to drop cookies down onto parchment-lined baking sheets, then place in freezer for at least 15 minutes to set.

Store in an airtight container either in the fridge or freezer (depending on how you like them) and enjoy!

Recipe adapted from 12 Tomatoes

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text:
Immigration Enforcement Priorities Have Been Abandoned—and That's Bad News for Everyone
Posted by Walter Ewing | Mar 12, 2018 | Border Enforcement, Detention, Enforcement, Interior Enforcement, State and Local
In order to effectively fight crime, law-enforcement officers must gain the trust of the communities they intend to serve. Trust encourages victims of crime, as well as potential witnesses, to come forward and help solve cases and prosecute criminals.
However, according to our latest analysis, the Trump administration has abandoned this approach by not prioritizing immigration cases and offenses based on the level of their severity. Prioritization simply means that law-enforcement officers initially focus on getting dangerous people off the street (like murderers), before turning their attention to people who are not a threat (such as workers without criminal records who overstayed a visa in order to get a job).
More precisely, the administration has expanded the list of "enforcement priorities" to the point that there aren't any priorities in practice. At present, nearly any non-citizen who has ever been convicted or charged with a criminal offense is a priority. It doesn't matter whether the conviction or charge was for bank robbery or entering the United States without inspection.
The administration immediately outlined their shifting immigration enforcement priorities in a January 2017 executive order. The Department of Homeland Security (DHS) subsequently issued a memorandum implementing the executive order, mandating that all DHS personnel "shall faithfully execute the immigration laws of the United States against all removable [individuals]."
This approach to immigration enforcement represents a major departure from the policies in place during the Obama administration.
For instance, the "Morton memo"—a June 2010 memo from then-Immigration and Customs Enforcement (ICE) Director John Morton—created three priority levels: 1) threats to national security or public safety (which included just about any immigrant with a criminal conviction of any kind); 2) undocumented immigrants who recently crossed the border; and 3) immigrants who didn't heed a previous order of removal, or who re-entered the country after being deported.
Though the system was far from perfect, the Morton memo was a concrete attempt to inject some rationality into what would otherwise be an utterly chaotic immigration-enforcement system.
Morton subsequently issued two more memos in June 2011 that offered guidance on the exercise of discretion. The primary memo stated that any deportable immigrant encountered by immigration authorities should be assessed on the basis of length of time in the United States, presence in the country since a very young age, education, military service, social ties to the United States, and age. In addition, this memo emphasized that "particular care" be taken with cases involving veterans, long-time legal permanent residents, children and elderly individuals, victims of domestic violence or trafficking, and people with serious health conditions.
In the absence of such prioritization, finite law-enforcement resources are wasted on the apprehension and removal of people who represent no danger to public safety.
Just as importantly, immigration enforcement without priorities needlessly tears apart U.S. families, communities, and workplaces. To attempt to remove all undocumented immigrants from our country's social fabric, without prioritizing those who pose a danger, needlessly harms millions of other people, immigrant and native-born alike.
FILED UNDER: Customs and Border Protection, Department of Homeland Security, featured, Immigration and Customs Enforcement
PreviousWhen Detention Is a Death Sentence
NextFewer International Students Are Choosing to Study in the United States
Walter Ewing
Walter A. Ewing, Ph.D., is an Editor and Writer at the American Immigration Council. Walter has authored numerous reports for the Council, including The Criminalization of Immigration in the United States (co-written in 2015 with Daniel Martínez and Rubén Rumbaut), which received considerable press attention. He has also published articles in the Journal on Migration and Human Security, Society, the Georgetown Journal of Law and Public Policy, and the Stanford Law and Policy Review, as well as a chapter in Debates on U.S. Immigration, published by SAGE in 2012. Walter holds a Ph.D. in Anthropology from the City University of New York (CUNY).

redpajama_set_name: RedPajamaCommonCrawl


text:
Bandwidth Hawk: Another Detour for Rural Residents
July 2017 •
By Steven S. Ross |
Welcome to the world of white boxes (for the haves) and white spaces (for the have-nots).
What will historians make of a year in which major national carriers gobbled up content providers and, after years of fighting the FCC on net neutrality, decided they could simply redefine it instead? A year in which the White House took six months to add broadband to its list of infrastructure worthy of construction, but the FCC summoned a large group of legal, technical and political minds to a Broadband Deployment Advisory Committee (BDAC) to devise ways to streamline network deployment rules without bigly annoying existing large carriers?
A year in which equipment vendors came close to completing their transformations into software companies, leaving the manufacture of most fiber and copper electronics, even the most advanced models, to a few big players like Nokia and Huawei and to nearly anonymous factories? In which a few nimble, smaller players such as Calix and ADTRAN pushed intelligence to the network edge and even to users' premises while mighty Microsoft bragged about placing major bets on scraps of leftover TV "white spaces" spectrum to deliver – wait for it – wait longer –wait some more – 3 Mbps (well, maybe 10 Mbps in some places, Microsoft hopes) by 2022?
The contrast between companies such as ADTRAN, Calix, Cisco and Corning, which envision 10 Gbps fiber networks that instantly, and in most cases automatically, adjust to network traffic loads – and Microsoft, which has a goal of helping 2 million rural U.S. customers gain any kind of access through cranky, slow wireless, exposes the contrast between the broadband haves and the have-nots.
FOR THE HAVES
The Open Network Operating System (ONOS, onosproject.org) is an open-source operating system for running software-defined networks. About 50 partners have signed on. Calix offers what is, at least for the moment, a more mature operating system of its own, AXOS, with a particular focus on the network edge. Oversimplifying a bit, vendors and users can build their own modules to snap into ONOS or AXOS (or similar operating systems coming soon) and control a wide range of emerging generic "white box" network equipment. SDN becomes SDA – software-defined access.
The idea is to run these operating systems mainly on Linux x86 computers (cousins to our laptops) near customers. The approach is scalable – the more customers, the more x86 computers. It's faster and more secure than sending data back deep into the cloud. And it's more reliable because mistakes will affect few customers, if any. Corning and other fiber producers note that it works even better with higher fiber counts – which increases overall deployment cost by just a few percent.
FOR THE HAVE-NOTS
But what about areas with low population density? Fiber is still an option, given the right conditions (lots of poles with cheap access, short drops, not many trees or rocks in the ground), even down to four or five customers per route mile. The fiber can be supplemented with point-to-point wireless, which generally does not require tall towers and offers lots of bandwidth, but can be unreliable in bad weather.
For even lower densities, Microsoft proposes long-distance Wi-Fi using the white space "buffer" spectrum between old UHF TV channels. In the United States, white spaces are scattered around 600 to 700 MHz, varying by region. It really is Wi-Fi – the IEEE standard for this technology is 802.11af. A typical installation would be on a tower that serves customers up to 10 miles away and provides 3 Mbps.
Microsoft and others have been building a database for prospective deployers to find out where the channel scraps are. Its first U.S. deployment was a 2009 test in Claudville, Virginia, where Microsoft partnered with Dell and Spectrum Bridge. Working with existing and potential ISPs such as rural electric co-ops, it has proposed connecting 2 million by 2022 for $10 billion – $5,000 a premises for one rural resident out of every 20. How is that competitive, given the low revenue potential?
Has the United States really sunk that low?
Contact the Hawk at steve@bbcmag.com.


text:
\section{Introduction}\label{s1}

Let $\Omega$ be an open domain in ${\mathbb{R}}^n$ (bounded or unbounded) with compact boundary $\partial\Omega$. Throughout we assume that $\partial\Omega$ is an
$(n-1)$-dimensional (not necessarily connected) $C^{\infty}$-manifold. Let $\mathcal {A}$
be the differential expression
\begin{equation}\label{2.10}
\mathcal {A}=\sum_{0\le |\alpha|,|\beta|\le m}(-1)^\alpha D^\alpha
a_{\alpha, \beta}(x)D^\beta, \quad a_{\alpha, \beta}(\cdot)\in
C^{\infty}({\overline\Omega}),
\end{equation}
 $\text{\rm{ord}}(\mathcal {A}) = 2m$,  which is  elliptic in ${\overline\Omega}$.
Moreover, we assume that  $\mathcal {A}$ is properly elliptic in $\overline \Omega$
(which is automatically satisfied if either $n>2$ or the symbol of
$\mathcal {A}$ is real, cf.\ \cite{LM72}). In addition to \eqref{2.10} we consider its formal adjoint
$\mathcal {A}^{\top} = \sum_{0\le |\alpha|,|\beta|\le m}(-1)^\alpha D^\beta
{\overline{a_{\beta,\alpha}(x)}} D^\beta$, which is also properly
elliptic in ${\overline\Omega}$ (cf.\ \cite{LM72}).

Denote by $A=A_{\min}$ $(A^{\top} = A^{\top}_{\min})$ the minimal operator
associated in $L^2(\Omega)$ with the differential expression
$\mathcal {A}$ (resp., $\mathcal {A}^{\top}$), that is, the closure of $\mathcal {A}$ defined on
$C_0^{\infty}(\Omega)$.  The maximal operators $A_{\max}$ and
$A^{\top}_{\max}$ are then defined by $A_{\max}=(A^{\top}_{\min})^* = (A^{\top})^*$ and
$A^{\top}_{\max}=(A_{\min})^*=A^*$, respectively.
We emphasize that $H^{2m}(\Omega)\subset \text{\rm{dom}}(A_{\max})\subset
H^{2m}_{\text{\rm{loc}}}(\Omega)$, while $\text{\rm{dom}}(A_{\max})\not =H^{2m}(\Omega)$.

After the pioneering work by Vishik \cite{Vi63}, nonlocal boundary
value problems of the form $A_{\max}u = f$,
$(\partial u/\partial n - Ku)\upharpoonright\partial\Omega =0$ for elliptic operators \eqref{2.10}
(with $m=1$) in bounded domains were considered by numerous
authors (see, e.g., \cite{Be65, Gr68} and the references therein). Vishik
was the first to consider these  problems
in the framework of extension theory of dual pairs of operators.
Starting with a formula for the domain $\text{\rm{dom}}(A_{\max})$ of
$A_{\max}$, he applied it to an appropriate regularization of the
classical Green's  formula, using the Calderon operator. The
latter allowed him  to extend the Green's  formula  from
$H^{2m}(\Omega)$ to $\text{\rm{dom}}(A_{\max})$. The next fundamental
contribution to the subject was made by Grubb \cite{Gr68}.
Using the theory of Lions and Magenes \cite{LM72}, Grubb
substantially extended and completed the results of \cite{Vi63}. In particular, Grubb
obtained the (regularized) Green's  formula which (in the special case $m=1$)
reads as follows:
$$
(A_{\max}u, v)_{L^2(\Omega)} - (u, A^{\top}_{\max}v)_{L^2(\Omega)}
 = \big({\widetilde\Gamma}_{\Omega,1} u,{\widetilde\Gamma}^{\top}_{\Omega,0}
 v\big)_{1/2,-1/2}
 - \big({\widetilde\Gamma}_{\Omega,0} u,{\widetilde\Gamma}^{\top} _{\Omega,1}
 v\big)_{-1/2,1/2}.
$$
Here $(\cdot, \cdot)_{s,-s}$ denotes the duality pairing between
$H^{s}(\partial \Omega)$ and $H^{-s}(\partial \Omega)$, $u\in
\text{\rm{dom}}(A_{\max})$, $v\in \text{\rm{dom}}(A^{\top}_{\max})$, and $\widetilde \Gamma_{\Omega,0}$,
$\widetilde \Gamma_{\Omega,1}$, ${\Gamma}^{\top}_{\Omega,0}$,
and ${\widetilde\Gamma}^{\top} _{\Omega,1}$ are regularized trace
operators, having the properties
$$
{\widetilde\Gamma}_{\Omega,1} \colon {\mathcal D}(A_{\max}) \to
H^{1/2}(\partial\Omega), \quad
{\widetilde\Gamma^{\top}}_{\Omega,0} \colon {\mathcal D}(A_{\max})
\to H^{-1/2}(\partial\Omega), \quad  \text{\rm{ran}} \big(
\big({\widetilde\Gamma}_{\Omega,1},{\widetilde\Gamma^{\top}}_{\Omega,0}\big)\big) =
H^{1/2}(\partial \Omega)\times H^{-1/2}(\partial \Omega).
$$
Later, we will use a somewhat different approach (cf.\ Proposition \ref{prop3.2}).

On the other hand, during the past three decades a new approach to
the extension theory, based on the concept of a boundary triple and
the corresponding operator-valued Weyl--Titchmarsh function, was
developed in \cite{DM91} (cf.\ the references therein for the
symmetric case) and in \cite{MM02} (in the case of dual pairs). In
this paper we apply some results and technique from \cite{DM91}
and \cite{MM02} to elliptic operators on unbounded domains. The
most important ingredients from the elliptic theory we need are
the regularized Green's  formula and {\it a priori}
coercivity-type estimates for the elliptic realizations ${\widehat
A}_B$ of $\mathcal {A}$ (see \eqref{2.54} below). To obtain the latter on
unbounded domains one needs additional restrictions on the
coefficients of $\mathcal {A}$, since an elliptic realization is not
necessarily coercive. Here we restrict ourselves to the case of
bounded coefficients $a_{\alpha, \beta}(\cdot)$. Using the
formalism of boundary triples and the corresponding
operator-valued Weyl--Titchmarsh functions in \cite {DM91, MM02},
we investigate the resolvent difference of two realizations and
complement the results of Povzner \cite{Po67}, Birman \cite{Bi62},
and Grubb \cite{Gr83} in this direction. In addition, assuming
$A_{\min}>0$, we compute the number of negative eigenvalues of a
realization $A_K $ and the number of eigenvalues of $A_K $ within
spectral gaps of the Dirichlet realization ${\widehat A}_{\gamma_D}$,
where $\gamma_D =\{\gamma_j\}_0^{m-1}$.

{\bf Notations.}
$\mathfrak{H}$ and ${\mathcal H}$ represent complex, separable Hilbert spaces;
${\mathcal B}({\mathcal H})$, ${\mathcal B}_\infty({\mathcal H})$, and ${\mathcal C}({\mathcal H})$ denote the sets of bounded, compact, and closed linear operators in ${\mathcal H}$; $\text{\rm{dom}}(\cdot)$, $\text{\rm{ran}}(\cdot)$, and $\ker(\cdot)$ denote the domain, range, and kernel of a linear operator, $\rho(\cdot)$ and $\sigma(\cdot)$ stand for the resolvent
set and spectrum of a linear operator.
As usual, $C^{\infty}(\Omega)$ denotes the set of infinity
differentiable functions in the domain $\Omega$,
$C^{\infty}_0(\Omega)$ the subset of $C^{\infty}(\Omega)$-functions of compact support in $\Omega$; $C_b({\Omega})=C({\Omega})\cap L^{\infty}({\Omega})$,
$C_{u}(\Omega)$ the set of uniformly continuous functions  in $\Omega$,
$C_{ub}(\Omega) = C_{u}(\Omega) \cap C_{b}(\Omega)$, and $H^s(\Omega)$ the usual Sobolev spaces.

\section{Dual pairs, boundary triples, and operator-valued Weyl--Titchmarsh functions}
\label{s2}

\begin{definition} \label{d3.1}
Let  $A$ and $A^{\top}$ be densely defined (not necessarily
closed) linear operators in  $\mathfrak{H}$. Then $A$ and $A^{\top}$ form a
{\it dual pair $($DP\,$)$} $\{A,A^{\top}\}$ in $\mathfrak{H}$ if $(Af,g) =
(f, A^{\top}g)$ for all $f\in \text{\rm{dom}} (A)$, $g\in \text{\rm{dom}} (A^{\top})$.
An operator $\widetilde A$ is called a {\it proper extension of
the DP $\{A, A^{\top}\}$}, and we write $\widetilde A\in Ext\{A, A^{\top}\}$, if
$A\subsetneqq \widetilde A\subsetneqq (A^{\top})^*$.
\end{definition}

\begin{definition} (cf.\ \cite{LS83}, \cite{MM02}) \label{d3.4}
$(i)$ Let $\mathfrak{H}$, ${\mathcal H}_0$, and ${\mathcal H}_1$ be complex, separable Hilbert spaces and
$$
\Gamma^{\top}=\begin{pmatrix}\Gamma^{\top}_0\cr\Gamma^{\top}_1\endpmatrix \colon
\text{\rm{dom}} ((A^{\top})^*)\to {\mathcal H}_0\oplus
{\mathcal H}_1 \, \text{ and } \, \Gamma = \pmatrix\Gamma_0\cr\Gamma_1\end{pmatrix}
 \colon \text{\rm{dom}} (A^*)\to {\mathcal H}_1\oplus {\mathcal H}_0
$$
be linear mappings. Then $\Pi= \{{\mathcal H}_0\oplus {\mathcal H}_1, \Gamma^{\top}, \Gamma \}$  is
called a {\it boundary triple} for the dual pair  $\{A,A^{\top}\}$ if $\Gamma^{\top}$
and $\Gamma$ are surjective and the Green's  identity holds,
$$
\big((A^{\top})^*f,g\big)_{\mathfrak{H}}-(f,A^*g)_{\mathfrak{H}} = \big(\Gamma^{\top}_1 f, \Gamma_0 g\big)_{{\mathcal H}_1}
- \big(\Gamma^{\top}_0 f,\Gamma_1 g\big)_{{\mathcal H}_0}, \quad   f\in \text{\rm{dom}}\big((A^{\top})^*\big),\,
g\in \text{\rm{dom}}(A^*).
$$
We set $A_0 = (A^{\top})^*\upharpoonright \ker (\Gamma^{\top}_0)$ and
$A^{\top}_0 = A^*\upharpoonright \ker (\Gamma_0)$. \\
$(ii)$ The operator-valued function $M_{\Pi} (z )$ defined by
$$
\Gamma^{\top}_1 f_{z }=M_{\Pi}(z )\Gamma^{\top}_0 f_{z }, \quad
f_{z } \in \ker \big((A^{\top})^*-z\big), \;\;  z \in \rho (A_0),
$$
is called the {\it Weyl--Titchmarsh  function}
corresponding to the boundary triple $\Pi$.
\end{definition}

Due to Green's  identity, $(A_{\min}u,v)_{L^2(\Omega)}= (u, A^{\top}_{\min}v)_{L^2(\Omega)}$,
$u, v\in C_0^{\infty}(\Omega)$, the operators $A$ and $A^{\top}$ form a
dual pair $\{A,A^{\top}\}$ of elliptic operators in $L^2(\Omega)$.
Any proper extension $\widetilde A\in \text{\rm{Ext}}\{A,A^{\top}\}$ of $\{A,A^{\top}\}$ is
called a realization of $\mathcal {A}$. Clearly, any realization  $\widetilde A$ of $\mathcal {A}$ is
closable. We equip $\text{\rm{dom}}(A_{\max})$ and $\text{\rm{dom}}(A^{\top}_{\max})$ with the corresponding graph norms. It is known (cf.\ \cite{Be68, LM72}) that if a  domain
$\Omega$ is bounded, then $ \text{\rm{dom}}(A_{\min}) = \text{\rm{dom}}(A^{\top}_{\min}) =
H^{2m}_0(\Omega)$,  where the norms in $\text{\rm{dom}}(A_{\min})$ and
$H^{2m}_0(\Omega)$ are equivalent. Denote by $\gamma_j$ the mappings
$\gamma_j\colon  C^{\infty}({\overline{\Omega}})\to
C^{\infty}(\partial\Omega)$, $\gamma_j u = \gamma_0
({\partial^j u}/{\partial n^j})= {\partial^j u}/{\partial n^j}
\upharpoonright {\partial\Omega}$, $1\le j \le m-1$, $\gamma_0 u=u \upharpoonright {\partial\Omega}$,
where $n$ stands for the interior normal to $\partial\Omega$.
Next we introduce the boundary operators $B_j$ as
\begin{equation}\label{2.17}
B_j u=\sum_{0 \le |\beta|\le m_j}b_{j\beta}\gamma_0(D^\beta u), \quad
b_{j\beta}(\cdot)\in C^{\infty}(\partial\Omega), \quad \text{\rm{ord}} (B_j) = m_j\le 2m-1.
\end{equation}
Here $B_j: C^{\infty}({\overline{\Omega}})\to C^{\infty}(\partial\Omega)$ will eventually be extended to appropriate Sobolev spaces $H^{s}(\Omega)$ and in some cases to
${\mathcal D}(A_{\max})$. $B_j$ in \eqref{2.17} can also be rewritten as $B_ju = b_j\gamma_{m_j}u\  +\  \sum_{0\le k\le m_j-1}
T_{j,k}\gamma_k u$, where $b_j(\cdot)\in C^{\infty}(\partial\Omega)$ and $T_{j,k}$ are
tangential differential operators in $\partial\Omega$ of orders
$\text{\rm{ord}} (T_{j,k}) \le m_j-k$ with $C^{\infty}(\partial\Omega)$-coefficients.

With any elliptic operator $A$ \eqref{2.10} and a system $B =\{B_j\}_{j=1}^{m-1}$
we associate the operator ${\widehat A}_B$   defined by
\begin{equation}\label{2.54}
{\widehat A}_B= A_{\max}\upharpoonright \text{\rm{dom}}({\widehat A}_B), \quad
\text{\rm{dom}}({\widehat A}_B)=H_B^{2m}(\Omega)= \{u\in H^{2m}(\Omega) \,|\, Bu =0\}.
\end{equation}
Our considerations are based on \cite[Thm.\ 2.2.1]{LM72}.
According to this result, for any elliptic differential expression
$\mathcal {A}$ in \eqref{2.10} and any normal system $\{B_j\}^{m-1}_{j=0}$ on
$\partial\Omega$ given by \eqref{2.17}, there exists a  system of
boundary operators $\{C_j\}^{m-1}_{j=0}$,  $\text{\rm{ord}}(C_j) = \mu_j\le 2m-1$, such that the system
$\{B_0,\ldots,B_{m-1},C_0,\ldots,C_{m-1}\}$ is a Dirichlet system
of order $2m$  and  another Dirichlet system of boundary operators $\{B^{\top}_j\}^{m-1}_{j=0}\cup
\{C^{\top}_j\}^{m-1}_{j=0}$, such that the following Green's formula hold
\begin{equation}\label{2.19}
\big(\mathcal {A} u,  v\big)_{L^2(\Omega)} - \big(u, \mathcal {A}
^{\top}v\big)_{L^2(\Omega)} = \sum_{0\le l\le m-1} \big[\big(C_j u,
B^{\top}_j v\big)_{L^2(\partial\Omega)}  - \big( B_j u, C^{\top}_j
v\big)_{L^2(\partial\Omega)}\big], \quad  u,v\in H^{2m}(\Omega).
\end{equation}

Next, following \cite{Gr68} and \cite{LM72}, we introduce the
spaces $D^s_A(\Omega) = \{u\in H^s(\Omega) \,|\,  Au\in H^0(\Omega)\}$,
$s\in {\mathbb{R}}$, provided with the graph norm  $\|u\|_{D^s_A(\Omega)}= (\|u\|^2_s
+ \|A u\|^2_0)^{1/2}$. Clearly,
$D^0_A(\Omega) = \text{\rm{dom}}(A)$ and $D^s_A(\Omega) \hookrightarrow H^s(\Omega)$.

\begin{definition}\label{defellip}
$(i)$ The operator ${\widehat A}_B$ defined by \eqref{2.54} is called
{\it elliptic} and is put in the class $\text{\rm{Ell}}(A)$ if $A$ is
properly elliptic on $\Omega$ and the system $\{B_j\}^{m-1}_{j=0}$ is
normal and  satisfies the covering condition (cf.\ \cite[Sects 2.1.1--2.1.4]{LM72})
at any point of the boundary $\partial\Omega$. \\
$(ii)$ The operator ${\widehat A}_B$ is called {\it coercive} in
$H^{s}(\Omega)$ with $s\ge2m$ if the {\it a priori} estimate (2.25) in \cite{Ag97} (cf.\ also \cite[Sect.\ 2.9.6]{LM72}) holds.
\end{definition}
We note that ${\widehat A}_B$ is a closed operator if $B$ satisfies the
covering condition (cf.\ \cite[Sect.\ 6.5]{Ag97}, \cite[Thm.\ 2.8.4]{LM72}).

If $\Omega$ is bounded, then any elliptic differential expression $\mathcal {A}$ with
$C({\overline{\Omega}})$-coefficients is uniformly elliptic in  ${\overline{\Omega}}$. In this case, ${\widehat A}_B \in \text{\rm{Ell}}(A)$ if and only if ${\widehat A}_B$ is coercive in
$H^{2m}(\Omega)$ (see \cite{ADN59}, \cite[Sect.\ 2.9.6]{LM72}). If $\Omega$ is
unbounded, then the condition  ${\widehat A}_B \in \text{\rm{Ell}}(A)$ is still
necessary for coerciveness in $H^{2m}(\Omega)$, though, it is no
longer sufficient without additional assumptions on $A$.

\begin{hypothesis} \label{h2.5} Assume that $\mathcal {A} $ is a uniformly elliptic
operator, $a_{\alpha, \beta}(\cdot)\in C_b(\Omega)$ for $|\alpha| +
|\beta| \le 2m$ and $a_{\alpha, \beta}(\cdot)\in C_{ub}(\Omega)$ for
$|\alpha| + |\beta| = 2m$.
\end{hypothesis}

\begin{proposition}\label{prop4.2}
Assume Hypothesis \ref{h2.5},  ${\widehat A}_B\in \text{\rm{Ell}}(A)$,  and $0\in
\rho({\widehat A}_B)$. Then for any $s\in{\mathbb{R}}$, the mappings $B$
and $B^{\top}$ isomorphically map
$Z^s_A(\Omega) = \{u\in D^s_A(\Omega) \,|\, A_{\max}u=0\}$
and $Z^s_{A^{\top}}(\Omega) = \{u\in D^s_{A^{\top}}(\Omega)\,|\,  A^{\top}_{\max}u=0\}$
isomorphically onto $\Pi^m_{j=1} H^{s-m_j-(1/2)}(\partial\Omega)$ and
onto $\Pi^m_{j=1} H^{s-2m+\mu_j+(1/2)}(\partial\Omega)$, respectively.
\end{proposition}

\begin{definition} (\cite{Gr68, Vi63}) \label{def3.2A}
$(i)$ Under the assumptions of Proposition \ref{prop4.2}, let
$\varphi\in\Pi^{m-1}_{j=0} H^{s-m_j-(1/2)}(\partial\Omega)$, $s\in{\mathbb{R}}$.
Then one defines $P (z)\varphi$ to be the unique $u\in Z^s_{A-z I_{L^2(\Omega)}}(\Omega)$
satisfying $B u=\varphi$. \\
$(ii)$ The {\it Calderon} operator $\Lambda (z)$ is defined  by
\begin{equation} \label{3.5A}
\Lambda (z) \colon  \Pi^{m-1}_{j=0} H^{s-m_j-(1/2)}(\partial\Omega) \to
\Pi^{m-1}_{j=0} H^{s-\mu_j-(1/2)}(\partial\Omega), \quad
\Lambda (z)\varphi = C P (z)\varphi.
\end{equation}
$(iii)$ Similarly, let $\psi\in\Pi^{m-1}_{j=0} H^{s-2m+\mu_j+1/2}(\partial\Omega)$. Then
$P (z)^\top \psi$ is defined
to be the unique solution in $Z^s_{A^{\top}-z I_{L^2(\partial\Omega)}}(\Omega)$ of $B^{\top} u=\psi$ and
the {\it Calderon} operator $\Lambda (z)^\top$ is defined as
$\Lambda (z)^\top \psi=C^{\top} P^{\top}_z\psi$.
\end{definition}

Let $\Delta_{\partial\Omega}$ be the Laplace-Beltrami operator in
 $L^2(\partial \Omega)$, $-\Delta_{\partial\Omega,1} =  -\Delta_{\partial\Omega}+I_{L^2(\partial\Omega)}$. Then
 $-\Delta_{\partial\Omega,1} = -\Delta_{\partial\Omega,1}^* \geq I_{L^2(\partial\Omega)}$. Moreover,
 $(-\Delta_{\partial\Omega,1})^{-s/2}$ isomorphically maps $H^0 (\partial\Omega)$ onto
 $H^s (\partial\Omega)$, $s\in{\mathbb{R}}$.
Next, we introduce the diagonal $m\times m$ operator matrices
$-\Delta_{\partial\Omega,1,m}$ and $-\Delta_{\partial\Omega,1,\mu}$ with the  $(j,j)$-th entry
$(-\Delta_{\partial\Omega,1})^{(m_{j}/2) +(1/4)}$ (resp., $(-\Delta_{\partial\Omega,1})^{m-(\mu_{j}/2) -(1/4)})$.

\begin{proposition}\label{prop3.2}
Assume Hypothesis \ref{h2.5},  ${\widehat A}_B\in \text{\rm{Ell}}(A)$,  and $0\in \rho({\widehat A}_B)$.
Set
\begin{align}\label{3.10A}
\Gamma_{\Omega,0} u & = (-\Delta_{\partial\Omega,1,m})^{-1}Bu, \quad  \Gamma_{\Omega,1} u =
(-\Delta_{\partial\Omega,1,\mu}) (C u - \Lambda (0) Bu), \quad u\in \text{\rm{dom}}(A_{\max}), \\
\label{3.11A}
\Gamma^{\top}_{\Omega,0} v& =(-\Delta_{\partial\Omega,1,\mu})^{-1}B^{\top}v, \quad
\Gamma^{\top}_{\Omega,1} v= \big(-\Delta_{\partial\Omega,1,m}) (C^{\top}v-\Lambda (0)^\top B^{\top}v\big),
\quad v\in \text{\rm{dom}}(A^{\top}_{\max}).
\end{align}
Then the following holds: \\
$(i)$
$\Pi=\{{\mathcal H}_{\partial\Omega}\oplus{\mathcal H}_{\partial\Omega},\Gamma_{\Omega},\Gamma^{\top}_{\Omega}\}$,
with
$$
{\mathcal H}_{\partial\Omega} = \Pi_{j=0}^{m-1}H^0(\partial\Omega)=
\Pi_{j=0}^{m-1}L^2(\partial\Omega), \quad
\Gamma_{\Omega}=(\Gamma_{\Omega,0},\Gamma_{\Omega,1}), \quad
\Gamma^{\top}_{\Omega}=(\Gamma^{\top}_{\Omega,0},\Gamma^{\top}_{\Omega,1}),
$$
forms a boundary triple for the dual pair $\{A,A^{\top}\}$ of elliptic
operators in $L^2(\Omega)$. In particular, the following Green's  formula holds
$$
(A_{\max}u,v)_{L^2(\Omega)}-(u,A^{\top}_{\max}v)_{L^2(\Omega)}
= (\Gamma_{\Omega,1} u,\Gamma^{\top}_{\Omega,0}
v)_{{\mathcal H}_{\partial\Omega}}-(\Gamma_{\Omega,0} u,\Gamma^{\top}_{\Omega,1} v)_{{\mathcal H}_{\partial\Omega}},
\quad u\in \text{\rm{dom}}(A_{\max}), \, v\in \text{\rm{dom}}(A^{\top}_{\max}).
$$
$(ii)$ The corresponding operator-valued Weyl--Titchmarsh function is given by
$$
M_{\Omega,\Pi}(z)=(-\Delta_{\partial\Omega,1,\mu})\bigl(\Lambda (z)-\Lambda (0)\bigr)
(-\Delta_{\partial\Omega,1,m}), \quad z\in\rho({\widehat A}_B).
$$
\end{proposition}

In the context of operator-valued Weyl--Titchmarsh functions and
elliptic partial differential operators we also refer to the
recent preprint \cite{BGW08} (and the references cited therein).

\begin{definition}\label{def3.2}
For any operator $K \colon \text{\rm{dom}}(K) \to \Pi_{j=0}^{m-1} H^{-\mu_j - (1/2)}(\partial\Omega)$,
$\text{\rm{dom}}(K) \subseteq \Pi_{j=0}^{m-1} H^{-m_j - (1/2)}(\partial\Omega)$, we set
\begin{equation}\label{3.22B}
A_K  = A_{\max}\upharpoonright \text{\rm{dom}}(A_K ), \quad
\text{\rm{dom}}(A_K ) = \{u\in \text{\rm{dom}}(A_{\max}) \,|\,  Bu\in \text{\rm{dom}}(K), \  C u
= K B u\}.
\end{equation}
\end{definition}

\begin{definition}\label{def4.1}
Define
${\mathcal S}_p(\mathfrak{H})=\{T\in {\mathcal B}_\infty(\mathfrak{H})\,|\, s_j(T) =O(j^{-1/p}) \, \text{as $j\to \infty$}\}$,
$p>0$, where $s_j(T)$, $j\in{\mathbb{N}}$, denote the singular values of $T$
(i.e., the eigenvalues of $(T^*T)^{1/2}$ ordered in decreasing magnitude, counting multiplicity).
\end{definition}

\begin{theorem}\label{th4.1A}
Assume the conditions of Proposition \ref{prop3.2} and suppose that
$0 \in \rho({\widehat A}_C)$ and $K\in {\mathcal C}({\mathcal H}_{\partial\Omega})$. Then: \\
$(i)$ For any realization $A_K \in {\mathcal C}(L^2(\Omega))$ of the form
\eqref{3.22B}, satisfying $\rho(A_K )\cap\rho({\widehat A}_B)\not =
\emptyset$, the following holds,
\begin{equation}\label{3.90}
\big[(A_{K} - z I_{L^2(\Omega)})^{-l} - ({\widehat A}_B - z I_{L^2(\Omega)})^{-l}\big] \in
{\mathcal S}_{\frac{n-1}{2ml - 1/2}}\big(L^2(\Omega)\big), \quad z\in\rho(A_{K})\cap\rho({\widehat A}_B),
\quad \ell\in{\mathbb{N}}.
\end{equation}
$(ii)$ If $B=\{B_j\}^{m-1}_{j=0}$ is a Dirichlet system, $K \in {\mathcal B}({\mathcal H}_{\partial\Omega})$,
and $\rho(A_K)\cap\rho({\widehat A}_B)\not =\emptyset$, one has
$$
\big[(A_K - z I_{L^2(\Omega)})^{-1} - ({\widehat A}_B -z I_{L^2(\Omega)})^{-1}\big] \in
{\mathcal S}_{\frac{n-1}{2m}}\big(L^2(\Omega)\big),\quad z\in\rho(A_K)\cap\rho({\widehat A}_B).
$$
\end{theorem}

Combining Weyl's theorem with Theorem \ref{th4.1A} one obtains the following result:

\begin{corollary}\label{cor4.4}
Assume the conditions of Theorem  \ref{th4.1A}. Then,
$\sigma_{\text{\rm{ess}}} (A_{K})=\sigma_{\text{\rm{ess}}}({\widehat A}_B)$.
\end{corollary}

In the case of elliptic realizations ${\widehat A}_G\in\text{\rm{Ell}}(A)$, we have the following stronger result:

\begin{theorem}\label{th3.smoothextens}
Suppose that the conditions of Proposition \ref{prop3.2}  are
satisfied and ${\widehat A}_{G}\in \text{\rm{Ell}}(A)$, that is, ${\widehat A}_{G}$ is
the elliptic realization of $A$ with $G=\{G_j\}_{j=0}^{m-1}$. Then for any $\ell\in \mathbb{N}$,
\begin{equation}\label{3.107B}
\big[({\widehat A}_{G} - z I_{L^2(\Omega)})^{-\ell} - ({\widehat A}_B -z I_{L^2(\Omega)})^{-\ell}\big] \in
{\mathcal S}_{\frac{n-1}{2m\ell}}(L^2(\Omega)), \quad z\in\rho({\widehat A}_{G})\cap\rho({\widehat A}_B).
\end{equation}
\end{theorem}

\section{The formally self-adjoint  case, nonnegative elliptic operators, and eigenvalues
in gaps}  \label{s3}

Let $\mathcal {A}$ be a formally self-adjoint  elliptic differential
expression of the form \eqref{2.10},  that is, $\mathcal {A} =  \mathcal {A}^{\top}$
or equivalently, $a_{p,q}= \overline{{a}_{q,p}} \in
C^{\infty}({\overline\Omega})$. In this case $A= A_{\min}=
A^{\top}_{\min} =A^{\top}$, that is, $A$ is symmetric, and
$A_{\max}= (A^{\top}_{\min})^*= A^*$. If a normal system
$\{B_j\}^{m-1}_{j=0}$ is chosen to be formally self-adjoint, that
is, $\hat{A}_B = (\widehat {A}_B)^*$,  then a system
$\{C_j\}^{m-1}_{j=0}$ can be chosen formally self-adjoint  too. In
this case $B_j^{\top}= B_j$ and $C_j^{\top}= C_j$,  and the
Green's  formula \eqref{2.19} holds with $B_j^{\top}= B_j$ and
$C_j^{\top}= C_j$. Moreover, in this case, $ \mu_j = \text{\rm{ord}} (C_j) = \text{\rm{ord}} (C^{\top}_j) = 2m-1-m_j$.
It follows that $\Delta_{\partial\Omega,1,\mu} = \Delta_{\partial\Omega,1,m}$. Hence, Proposition \ref{prop3.2} yields the following result:

\begin{proposition}\label{prop5.1}
Let $\mathcal {A}$  be a formally symmetric elliptic differential expression and assume that
$\widehat {A}_B$ and $\widehat {A}_C$ are  self-adjoint. In addition,  assume the conditions of Propositon \ref{prop3.2} are satisfied. Then: \\
$(i)$ $\Pi=\{{\mathcal H}_{\partial\Omega},\Gamma_0,\Gamma_1\}$ with $ {\mathcal H}_{\partial\Omega} =
\Pi_{j=0}^{m-1}L^2(\partial\Omega)$,  and $\Gamma_{\Omega,0},\, \Gamma_{\Omega,1}$ defined
by \eqref{3.10A}, forms a boundary triple for the operator  $A^*$. In particular,
the following Green's  formula holds
$$
(A_{\max}u,v)_{L^2(\Omega)} - (u,A_{\max}v)_{L^2(\Omega)}
= (\Gamma_{\Omega,1} u,\Gamma_{\Omega,0}
v)_{{\mathcal H}_{\partial\Omega}}-(\Gamma_{\Omega,0} u,\Gamma_{\Omega,1} v)_{{\mathcal H}_{\partial\Omega}}, \quad u, v \in
D(A_{\max}).
$$
$(ii)$ The corresponding Weyl--Titchmarsh operator is given by
$M_{\Omega,\Pi}(z)=(-\Delta_{\partial\Omega,1,m})\bigl(\Lambda (z)-\Lambda (0)\bigr)
(-\Delta_{\partial\Omega,1,m})$.
\end{proposition}

For any self-adjoint operator $T=T^*\in{{\mathcal C}}(\mathfrak{H})$ with associated family of spectral projections $E_T(\cdot)$, we set
$\kappa_{(\alpha,\beta)}(T) = \dim(E_T((\alpha,\beta))\mathfrak{H})$, $-\infty \leq \alpha < \beta$ (these numbers may of course be infinite).

\begin{theorem}\label{th5.1}
Suppose that  $A> 0$ is a positive definite elliptic operator, and
$\Pi=\{{\mathcal H}_{\partial\Omega},\Gamma_0,\Gamma_1\}$ is the boundary
triple for $A^*$ in Proposition \ref{prop5.1} with $A_0 :=
A^*\upharpoonright \ker(\Gamma_0)  = {\widehat A}_{\gamma_D}$, the Dirichlet
realization of $A$. Assume also that the operator ${\widehat A}_C>0$
is positive definite, $0\in \rho({\widehat A}_C)$. Let  $K$ be a
densely defined $($not necessarily closed\,$)$ symmetric operator
in ${\mathcal H}_{\partial\Omega}$ and $A_K $  the corresponding extension
defined by \eqref{3.22B}. Then: \\
$(i)$ The Calderon operator  $\Lambda (0)$  is self-adjoint  and
negative definite, $\Lambda (0)<0$.  \\
$(ii)$ If  $K$ is  $\Lambda (0)$-bounded with bound strictly less than one, then
$A_K $ is symmetric $($but not  necessarily closed\,$)$.
\hspace*{5mm} If in addition, $\text{\rm{ran}}(K - \Lambda (0))$ is closed, then so is $A_K $,
that is, $A_K \in {\mathcal C}(L^2(\Omega))$.   \\
$(iii)$  If $K$ is  $\Lambda (0)$-compact and self-adjoint, then
$A_K $ is self-adjoint $A_K  = (A_K) ^*$, $\kappa_{(-\infty,0)}(A_K )<\infty $, and
\begin{equation}\label{4.36}
\kappa_{(-\infty,0)} (A_K )
= \kappa_{(-\infty,0)} \big(I_{L^2(\partial\Omega)} + (-\Lambda (0))^{-1/2} K (-\Lambda (0))^{-1/2}\big).
\end{equation}
$(iv)$ If $K$ is  $\Lambda (0)$-compact and sectorial $($resp., $m$-sectorial\,$)$ with vertex $\zeta$ and semi-angle $\omega\in [0,\pi/2)$, then $A_K $ is
sectorial $($resp., $m$-sectorial\,$)$ with vertex $\zeta$ and semi-angle $\omega$ too.
\end{theorem}

\begin{proposition}\label{cor5.4}
Let  $\mathcal {A}$ be formally self-adjoint  and assume the conditions of
Proposition \ref{prop5.1}. Assume also that $A_K  = (A_K) ^*$ is a
self-adjoint  extension of the form \eqref{3.22B} with $K\in
{\mathcal C}({\mathcal H})$. Then the absolutely continuous parts $A_{K, \text{\rm{ac}}}$ and
${\widehat A}_{B, \text{\rm{ac}}}$ of $A_K $ and ${\widehat A}_B$, respectively, are
unitarily equivalent. In particular, $\sigma_{\text{\rm{ac}}}(A_K ) =
\sigma_{\text{\rm{ac}}}({\widehat A}_B)$.
\end{proposition}

\begin{proposition}\label{cor5.5}
Suppose that $A=A_{\min}$ is  symmetric, and let ${\widehat A}_B =
{\widehat A}_{\gamma_D}$ be the Dirichlet realization of $A$. Assume
the conditions of Theorem \ref{th3.smoothextens} to be satisfied
and that ${\widehat A}_{G} = ({\widehat A}_{G})^* \in \text{\rm{Ell}}(A)$ is an
elliptic realization of $A$ with  $G= \{G_j\}_0^{m-1}$. Then  the
absolutely continuous parts ${\widehat A}_{G, \text{\rm{ac}}}$ and ${\widehat
A}_{\gamma_D,\text{\rm{ac}}}$ of ${\widehat A}_G$ and ${\widehat A}_{\gamma_D}$,
respectively, are unitarily equivalent. In particular,
$\sigma_{\text{\rm{ac}}}({\widehat A}_{G}) = \sigma_{\text{\rm{ac}}}({\widehat
A}_{\gamma_D})$.
\end{proposition}

Finally, we turn to eigenvalues in spectral gaps:

\begin{definition}
Let $A$ be a symmetric operator in ${\mathcal H}$. Then
$(\alpha, \beta)$, $-\infty<\alpha < \beta < \infty$, is called a {\it gap of $A$} if
$\|(2A-(\alpha + \beta)I_{{\mathcal H}})f\|_{{\mathcal H}} \ge (\beta - \alpha)\|f\|_{{\mathcal H}}$ for all $f\in\text{\rm{dom}}(A)$.
\end{definition}

By Corollary \ref{cor4.4}, $\sigma_\text{\rm{ess}}(A_K ) = \sigma_\text{\rm{ess}}({\widehat A}_B)$. Therefore,
in the gaps of ${\widehat A}_B$, the point spectrum of $A_K $ can possibly  accumulate  at most at the endpoints of the gaps. Next, we actually show that $\sigma_{\rm p}(A_K)$ cannot accumulate  at the left end point  of any  gap:

\begin{theorem}\label{th5.2}
Suppose that the conditions of Theorem \ref{th5.1}  are satisfied,
and that $K$ is a symmetric $\Lambda (0)$-compact operator in
${\mathcal H}_{\partial\Omega}$. In addition, let $(\alpha, \beta)$ be  a
finite gap of $A_0= {\widehat A}_{\gamma_D}$
and introduce $T_0(z) = \Lambda (z)- \Lambda (0)$.  Then: \\
 $(i)$ $T(z) = \overline{T_0 (z)} \in {\mathcal B}_\infty({\mathcal H}_{\partial\Omega})$ for all
$z\in \rho({\widehat A}_{\gamma_D})$.   \\
$(ii)$ There exists $\varepsilon_0 \in (0, (\beta-\alpha)/2 )$
such that $E_{A_K}((\alpha, \alpha + \varepsilon_0)) =0$,  hence
$\kappa_{(\alpha, \beta- \varepsilon)} (A_K) = \dim(E_{A_K}
((\alpha, \beta-\varepsilon))) < \infty$ for any $\varepsilon\in
(0, \beta- \alpha)$.  Moreover, for any $\varepsilon\in (0,
\varepsilon_0)$ the following equality holds $($with $\Lambda
:=\Lambda (0)$$)$:
\begin{align*}
\kappa_{(\alpha, \beta- \varepsilon)} (A_K) & =
\kappa_{(-\infty,0)} (I_{{\mathcal H}_{\partial\Omega}} + \Lambda^{-1/2}(K +
T(\beta-
\varepsilon))\Lambda^{-1/2})
- \kappa_{(-\infty,0)} (I_{{\mathcal H}_{\partial\Omega}} + \Lambda ^{-1/2} (K
+ T(\alpha + \varepsilon)) \Lambda ^{-1/2}).
\end{align*}
\end{theorem}

\begin{remark}
For Robin-type realizations $[\partial u/\partial n-\sigma
u]\upharpoonright\partial\Omega=0$, $\sigma \in
L^\infty(\partial\Omega)$, of Schr\"odinger operators $-\Delta + q$
on exterior domains $\Omega\subset {\mathbb{R}}^3$, the estimate
\eqref{3.107B} (with $\ell=1$) goes back to the pioneering work by
Povzner \cite{Po67}. For Robin realizations $A_\sigma$ of a
second-order elliptic operator ${\mathcal A}= - \sum_{j,k=1}^n
\frac{\partial}{\partial x_j} a_{j,k}(x) \frac{\partial}{\partial
x_j} + q(x)$, with $q\geq 1$, and
$\sum_{j,k=1}^n \xi_j a_{j,k}(x) \xi_k >0$ for all $\{x, \xi\}\in
\Omega \times ({\mathbb{R}}^n\setminus \{0\})$,
$$
A_\sigma = A_{\max} \upharpoonright\text{\rm{dom}}(A_\sigma),\; \text{\rm{dom}}(A_\sigma) =
\{u\in H^2(\Omega) \,|\,
({\partial u}/{\partial\nu} - \sigma u)\upharpoonright\partial\Omega =0 \}, \;
 {\partial}/{\partial\nu} = \sum_{j,k=1}^n a_{j,k}(x) \cos(n,
x_j) \frac{\partial}{\partial x_k},
$$
$\sigma \in L^{\infty}(\partial\Omega)$, the estimate
\eqref{3.107B} was obtained by  Birman \cite{Bi62}. Moreover, in
\cite[Thm.\ 6.6]{Bi62} it is also proved that
$\kappa_{(-\infty,0)} (A_\sigma) < \infty$. Thus, for $m=1$ and
$A_K  = A_\sigma$, equality \eqref{4.36} with $K$ being a
multiplication operator, $K \colon u\mapsto \sigma u$, yields a
stronger result as it describes the actual number of eigenvalues
in the gap $(-\infty, 0)$.

For positive elliptic realizations ${\widehat A}_G$ of a nonnegative
elliptic operator $A$ of order $2m$ in a bounded domain
$\Omega\subset {\mathbb{R}}^n$, the estimate \eqref{3.107B} is implied by
a sharp estimate due to Grubb \cite[eq.\ (3.22)]{Gr83}.
\end{remark}

Detailed proofs of these results will appear in \cite{GM09}.

\medskip

\noindent {\bf Acknowledgments.}
Mark Malamud is indebted to the Department of Mathematics of the University of Missouri, Columbia, MO, USA, for the hospitality extended to him during his month long stay in April/May of 2007 in connection with a Miller Family Scholarship, which enabled this collaboration.

redpajama_set_name: RedPajamaArXiv


Ms CROZIER (Southern Metropolitan) -- I am pleased to speak on the Victorian Government Aboriginal Affairs Report 2013. I have spoken on this report previously and at that time I was particularly interested in some of the results the report highlights, especially around the Bumps to Babes and Beyond program that is initiated out of the Mildura area. When I was in Mildura some months ago I had the privilege to visit the program, along with the member for Mildura in the other place, Mr Peter Crisp.
I want to come back to the report because there are some very good elements to it.
As the minister states, it is part of the coalition government's reform strategy that we have undertaken since coming to government, and a number of initiatives that we have undertaken, including the strategy released last year -- the Human Services Aboriginal Strategic Framework 2013-2015 -- and also the Victorian Indigenous Honour Roll. The report says that in 2013 a further 14 outstanding Aboriginal Victorians were inducted into the Victorian Indigenous Honour Roll, bringing the total number of inductees to 49.
Mr D. R. J. O'Brien interjected.
Ms CROZIER -- Mr O'Brien is absolutely right that that was under the former Minister for Aboriginal Affairs, Jeanette Powell, the member for Shepparton in the Assembly.
A number of elements I want to address in this report include some very good initiatives, and I note that in the health analysis area the report speaks of the subsidies program for purchasing spectacles, with more than 4000 spectacles being dispensed in the three years to June 2013. I know this program is very well utilised and extremely well supported by the Australian College of Optometry. That scheme, as the report notes, has been highly successful in increasing the number of Aboriginal people accessing eye health services. That is terribly important for any Victorian, noting in particular that Aboriginal people can be at higher risk of certain chronic diseases that lead to eye disease and blindness, which can be devastating.
I am pleased to see that more access will be forthcoming to that very good spectacle service. I note that in July last year the Minister for Health announced further funding of $750 000 to continue the scheme, and I commend him for that.
Blindness is a devastating chronic disease, the effects of which have a real impact, so that will be very well received within the community.
Another area I want to highlight in the report is that of reducing family violence. It is well noted that the Victorian government is very committed to reducing the incidence of family violence, and the Minister for Community Services, Ms Wooldridge, has been at the forefront of providing significant support in this area, and I want to speak to that in relation to an overall focus that she has had. In this year's budget there was a further announcement of $95 million towards addressing the issue. This is a whole-of-government approach, and it has been well highlighted by the minister and the Premier that domestic violence -- physical, emotional and other violence -- is not tolerated at any stage, and that is why we are very committed to stamping it out, educating the community and putting significant funding into the area.
I note that on Friday, 30 May, a further $30 million was invested into strengthening responses to family violence, and that is to be welcomed because it will go not only to the Aboriginal community, where there is unfortunately a high incidence of family violence, but right across the community. This is not in any one particular area in the community; it is right across the Victorian community, and it is something that our government is clearly focused on. That extra $30 million package will expand statewide, strengthening the risk management program. It will fast-track support for women and children who have experienced family violence, expand case management and practical support for women and children fleeing violence and evaluate our family violence initiatives, including perpetrator interventions, to ensure their effectiveness.
These are real, practical solutions that we are putting into the system to support women, children and families who have unfortunately been exposed to family violence. They are practical measures that will make a real difference to those people.


text:
Q: Having trouble with my HTML / PHP form Quite new to the game and trying to put together a form and as the title suggests, I'm having no luck.
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Cheers,
W
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text:
La Comédie française de Sa Majesté le roi de Suède est une troupe de théâtre française active en Suède entre 1781 et 1792.

Composition
Acteurs et chanteurs

Danseurs
 Charles Didelot, père de Charles-Louis Didelot
 Louis Frossard
 Marie-Renée Frossard

Bibliographie
 Fredrik August Dahlgren, Förteckning öfver svenska skådespel uppförda på Stockholms theatrar 1737-1863 och Kongl. Theatrarnes personal 1773-1863. Med flera anteckningar.
 Georg Nordensvan, Svensk teater och svenska skådespelare från Gustav III till våra dagar. Första bandet 1772-1842.
 Ingvar Andersson, Gustavianskt.
 Lars Löfgren, Svensk teater, Stockholm, Natur och Kultur, 2003 .
 Anna Ivarsdotter Johnsson et Leif Jonsson, Musiken i Sverige. Frihetstiden och Gustaviansk tid 1720-1810.
 Ny svensk teaterhistoria. Teater före 1800, Gidlunds förlag.
 Oscar Levertin, Teater och drama under Gustaf III, Albert Bonniers förlag, Stockholm, Fjärde Upplagan, 1920.

Troupe de théâtre française
Théâtre suédois
Histoire du théâtre
Fondation en 1781
Gustave III

redpajama_set_name: RedPajamaWikipedia


Life On Mars star John Simm - who plays a detective involved in a near fatal car crash and wakes up in 1973 - has revealed he is lucky to be alive after walking free from a serious car accident.
The actor was driving to watch his beloved football team Manchester United play Chelsea at Old Trafford, in Manchester, when he had the accident on the M1 motorway.
He injured hurt his wrist and although sporting a heavily bandaged hand, says he is lucky that it was not fatal.
Asked if he would be watching Manchester United in the Carling Cup semi-final against Derby County, he told BBC Radio Five yesterday: 'No not tonight, no chance.
'I was actually travelling up to see them play last week, the Man Utd versus Chelsea game last Sunday when I was involved in a car accident, so I never made it.
'It was on the M1 and that's why my hand is in this bandage.
John, 38, played the role of Sam Tyler in the BBC smash hit show Life On Mars, who wakes up dazed and confused in the year 1973 after being involved in a car crash in 2006.
There he works as a Detective Inspector in the Greater Manchester Police force under Detective Chief Inspector Gene Hunt, played by Philip Glenister.
Over the course of the series, Sam Tyler faces various culture clashes, most frequently regarding the differences between his modern approach to policing and the more traditional methods of his colleagues.
It is unclear whether he is insane, in a coma, or if he really has travelled back in time.
The programme proved a massive hit with viewers and scooped several awards, including two International Emmy Awards for Best Drama Series, Best New Programme category at the Broadcast Magazine awards.
It won two categories, Best Drama Series and the Writers' Award, at the Broadcasting Press Guild Awards.
The first series was nominated for a BAFTA in the Best Drama Series category.
Simm was also nominated as Best Actor for his work on the show. The programme won the audience-voted Pioneer Award.
And it was nominated as the Most Popular Drama at the 2007 National Television Awards.
John married actress Kate Magowan in April 2004 and they have two children; Ryan, seven years and Molly, almost two years old.
He is famed for his passionate support of Manchester United.
Ich verlängere meine Liste von Dingen, von denen er sich fernhalten sollte um "Autos".
Glück gehabt und gute Besserung, John!
Sooooooo dringend braucht John auch wieder nicht einen Oscar, ehrlich....Lieber lebendig an einem Stück als oscar-gekrönt und tot.
Puh, Glück gehabt würde ich sagen. Bin froh, dass das nochmal glimpflich ausgegangen ist.
Zum Glück gehts ihm soweit gut.
Wäre ja eine Horrornachricht,wenn er mags garnicht sagen.


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Farm Sanctuary's 'Fashion Loves Animals' Benefit + Fashion Show
Gene Baur, Farm Sanctuary President and Co-Founder and me
Farm Sanctuary held a 'Fashion Loves Animals' benefit and fashion show at Stage 37 in New York City. It's the very hot spot where the Kardashians launched their Bebe line and Mac launched Viva La Glam.
The evening also honored VAUTE Couture President and Creative Director Leanne Mai-ly Hilgart, who made history this year with the first all-vegan label to show at New York Fashion Week.
For the event I wore a Cachet sequin dress and shoes by Jeffrey Campbell. The sequins on the dress and metallic in the shoes really gave my look a festive feel which was perfect to celebrate such a fun evening.
Farm Sanctuary works to protect farm animals from cruelty, inspire change in the way society views and treats farm animals and promotes compassionate vegan living. It's the nation's leading farm animal protection organization which promotes legislative, policy and individual lifestyle changes to help farm animals. They operate three shelters in New York and California that provide lifelong care for nearly 1,000 rescued farm animals.
The evening started with a cocktail reception where Fashion editors, Farm Sanctuary supporters, and VIP guests, including Miss New York City Acacia Courtney and Miss Metropolitan Melissa Philips, mixed and mingled to music by renowned DJ Princess Superstar.
Guests enjoyed a delicious assortment of drinks and vegan hors d'oeuvres by 20-year-old vegan "wunderkind" chef Jay Astafa. One of my favorites of his concoctions were the above puréed green soup 'shots'.
Photo Credit: Max Gordon www.maxgordonphotography.com
Symbolizing the night's message that fashion and animals can co-exist in a peaceful, non-exploitative way, many of the models strutted the runway holding adorable dogs which are currently available for adoption from the New York Humane Society.
After the show, Farm Sanctuary President and Co-Founder Gene Baur spoke about the organization's more than 25 years of work to protect farm animals from the abuses of the food and fashion industries, explaining that it's standard practice for the wool, leather, fur, and down industries to treat animals in ways that would warrant felony cruelty charges if done to a dog or cat.
Gene then presented Leanne Mai-ly Hilgart, VAUTE Couture President and Creative Director with an award honoring her accomplishments in fashion and commitment to pushing the industry in a more compassionate direction.
A live auction followed, giving guests the opportunity to bid on amazing fashion packages from the night's designers and a chance to have Chef Jay Astafa cook for them and their friends in their own home.
One of the most memorable moments of the evening was a performance from singer/songwriter Rosi Golan, who sang some of her most popular songs.
Rosi's music has been featured on The Vampire Diaries, Grey's Anatomy, In Plain Sight, Dollhouse, and Ghost Whisperer.
Rosi Golan performed so many beautiful songs but my favorite was definitely Fly Away. Click the above video to play the song!
The event concluded with vegan desserts by famed author and pastry chef Fran Costigan.
Thank you Farm Sanctuary for inviting me to be a part of such a wonderful evening.
For more information about Farm Sanctuary visit: www.farmsanctuary.org
Tags Doggy fashion show, Events, Farm Sanctuary, Farm Sanctuary benefit, Farm Sanctuary's Fashion Loves Animals Benefit and Doggy Fashion Show, Gene Baur, New York Humane Society, Rosi Golan


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100th Anniversary of the Russian Revolution - past, present, & future
On Arts Express at WBAI radio, Prairie Miller interviews journalist Caleb Maupin who shares his ideas about the October Revolution, the Soviet Union, 'not-Capitalism' and much more!
Caleb's points:
October was " a rare moment in history", "an anomaly" where the Bolsheviks were able to become the ruling party, which changed world history
"I don't think anyone in October 1917 knew what was going to happen"
The actions of the Bolsheviks in October and after split the political Left; some forces on the Left denounced it after-the-fact
In October, it was not clear at all what Soviet power and the Revolution would proceed in
While they are romanticized in Soviet Historiography, "these were bad times", with hardship, famine, invasion, "some of the hardest times in Russian history"
Recorded by Arts Express with host Prairie Miller on WBAI radio
100th Anniversary of the Russian Revolution


With a hefty RockShox Lyrik RCT3 fork and all-new Super Deluxe RC3 shock in back, the Transition Patrol GX evo Complete Mountain Bike eats bumps for breakfast and smashes through chunky rock gardens for dinner. You're worried about the climb up though? Don't be! The Patrol relies on Transition's award-winning Giddy Up suspension system to adapt that plush travel into powerful and efficient pedal strokes on the climb. Epitomizing what it means to be an enduro-worthy pedal pony, this evo exclusive Transition Patrol GX evo Complete Mountain Bike was built out specially for gravity enthusiasts who still find themselves putting in work to earn every air and power slide on the way down.


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Since graduating from HVGS (2005) – Melissa-Kelly Franklin, an alumni student has taken the world by storm. After completing her studies, she moved to London and is now chasing her dreams. She is a prime example of how anything is possible if you set your mind to it! Melissa-Kelly took a (quick) break from her busy schedule to have a chat with us about what's next, what a typical day in her life is like and more.
Read about Melissa-Kelly Franklin's story below.
What made you decide to go into writing & directing as a career?
It's difficult to pinpoint a precise moment, because I've been involved in storytelling in some form since I was quite young. My love of stories is the reason why I studied English Literature and History at university. It wasn't until I finished my degree and moved to London that I really started taking my first steps towards a career in film and theatre-making – born from undertaking a Diploma of Classical Acting at LAMDA, and then combining both my academic and creative selves to write and direct plays and films. Sometimes it's leaving places that you're comfortable that is the perfect catalyst!
What motivates you? Keeps you going?
My work is often driven by political themes, such as women's reproductive rights, climate change, refugee rights. I find that as a result there is a sense of urgency intrinsic to my work that motivates me to keep going with it, regardless of its eventual destination. It's a way that I can use my skills to contribute to political conversations about social justice and respond to the world around me. My plays in particular all engage in political issues through a creative lens – We'll Dance on the Ash of the Apocalypse is about climate change, Reclaim the Night examines gender-based violence and women's rights, and Paradise Lost reckons with Australia's inhumane offshore refugee processing policies. I think the arts can be a powerful tool for inviting us to empathise with people outside our usual spheres, and wrestle with challenging social and political ideas.
What's your big dream?
In many ways, I'm living it! I always wanted to live overseas, and London is one of the great cities to live and work if you're in the creative sector. I love the rich cultural life here, and the diversity of people and places – London feels like a city with many personalities. I'm also working in a field I love and I have the privilege of meeting and working with so many fascinating, talented people from different backgrounds. This constantly inspires me.
I recently returned from the Australian Theatre Festival in New York, where my latest play Paradise Lost received a staged reading as part of the Australian Theatre Festival NYC New Play Award 2022. The plan is to showcase the play again with staged readings in both London and Australia, with the aim of finding it a home in full production.
I have a few other projects cooking – some new play ideas, and I'm also working on the script of my debut feature film. I usually have several projects going at varying stages of development.
What does a day in your life look like?
That really depends on the time of year. I'm an associate lecturer at the University of Greenwich, and teach English and Writing for Theatre periodically throughout the academic year, so when I'm doing that I'm usually juggling my own projects at the same time. When I'm not lecturing, my days vary depending on whether I'm writing a script, rehearsing a play, or prepping for a shoot. Sometimes I'll be working with actors on character development, or discussing mood boards and visual style with my cinematographer or production designer. If I'm writing, it's very much solo; writing from home or in a café. The variety is one of the things I love about what I do – no two days are the same. All of them involve a morning coffee though!
What advice would you give students at HVGS?
Do what you love, not what you think is expected of you. If you study what you love, you'll naturally excel at it and that joy and positivity will permeate all aspects of your life.
If you'd like to learn more about Melissa-Kelly's work, visit her website:
www.melissakellyfranklin.com
Alumni profile: Sarah Dockrill


New Delhi: The Delhi government has issued a circular making it mandatory for all hospitals to ascertain and certify brain death-irreversible loss of brain function due to any disease or trauma. This, the government says, is not just necessary for boosting organ donation. It will also check incidences where patients with irreversible brain function are kept in hospitals causing anxiety and financial burden on their families.
According to the circular issued by state health secretary Dr Tarun Seem, many medical practitioners are not following the prescribed procedure in all cases of brain stem death.
"All clinicians, when facing a situation where 'brain stem death' is suspected, must follow the procedure mentioned in Section 3(6) of Transplantation of Human Organs and Tissues Act, 1994 to ascertain and certify brain stem death in Form 10," the circular says.
Once a patient is certfied brain-dead, multiple organs and tissues can be harvested, including heart, kidney, lung, liver and pancreas, for transplantation. Dr S K Sarin, director of Institute of Liver and Biliary Sciences, said the move by the Delhi government will increase the organ pool and help save many lives.
Sources said the Delhi Organ Transplant Cell, which is headed by Dr Anil Aggarwal, held several meetings with forensic experts, police and transplant surgeons before deciding that brain stem death assessment is mandatory. The government is also contemplating nominating experts, who can assist hospitals in this, said sources.
As per the provision of Transplantation of Human Organs Act (THOA), once the brain stem death is declared, the doctor is required to make a request-to let the patient's kin know about the option to authorise or decline the donation of organs or tissues or both.
Dr Aarti Vij, chief of Organ Retrieval and Banking Organisation at AIIMS, said "Our hospital has put a lot of focus on identiying such cases and then requesting the family of such patients to donate the organs.


Tender girl, I want carefree dating of a sexual nature. Do it, dial my phone number and come to me, i will do everything, as you want!
Sluts Hillsborough these are real beauties, who know everything ways satisfaction men.


This is a film about the growing movement to transform economics education.
There is an increased criticism of economics and economists not adequately dealing with our societal issues, as most recently demonstrated by the global financial crisis. Voices are calling for change, and among that chorus there is a strong plea to make economics education more pluralist and related to the real world, giving economists-to-be a bigger toolbox and wider range of perspectives when dealing with increasingly complex economies and societies.
Around the world there is a growing movement working to change how we educate economics. This project attempts to tell the story of this movement, and asks why and how students, academics, educational institutions and citizens are working to make economics education more pluralist, updated and related to the real world.
The movement to change economics education is broad and diverse, with a variety of motivations and visions for change. A sample of these engaged people and organizations have participated in the film, and you can read about them at "Meet the Movement".
"OIKONOMOS: transforming economics education" is a joint film and research project, made as part of Ingrid M. Rieser's dissertation in the Economics for Transition MA at Schumacher College.


Portal addresses that require knowing up to the 9th glyph (hex: 8).
System Name KICKERSSTADION AM DALLENBERG!
Base Description A beachfront base close to a portal in an Elkupalos gateway system. Occasional storms, otherwise a very nice planet.
Notes There is another player's base on this planet.
Base Description A small production base on a planet with high security sentinels. Radon collection facilities are available. This is an Elkupalos gateway system. There are a few of my bases in this system.
Base Description Base right next to portal with resources to build 39 circuit boards.


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Lake Geneva: Winterfest | February 2-6, 2022
Harlem Globetrotters | January 2nd, 2022 at Alliant Energy Center in Madison, WI
We've partnered with the Harlem Globetrotters to share about this event. We love partnering with brands and businesses that add value to our community!
(Madison, WI): The World-Famous Harlem Globetrotters are bringing their newly reimagined Spread Game tour to the Coliseum at Alliant Energy Center in Madison, WI on January 2, 2022. The Spread Game Tour is a basketball event like no other. Ankle-breaking moves, jaw-dropping swag, and rim-rattling dunks are only some of the thrill you can expect from this fully modernized show. Part streetball from the players who defined it, part interactive family entertainment, the new tour will show off the best of the Globetrotters in a dazzling exhibition of talent and game.
January 2, 2022 at 3pm
Alliant Energy Center in Madison, WI
NEW Dunk Contest – The Globetrotters always rattle the rim – even breaking a backboard or two! All-new for the Spread Game Tour, the stars go head to head with the Generals in a dunk contest. Which dunk will be your favorite?
NEW Laugh-Out-Loud Funny Characters – The Globetrotters teamed up with award-winning experts from Broadway and renowned comedians to bring you all-new on-court characters who bring the funny to every game, including the Globetrotters' Day 1 fan.
NEW Access To The Stars – After the game, get an autograph from your favorite stars during our 5th Quarter. Want even more interactions with the stars? Check out the Premium Fan Add-On Experiences like the pre-game Magic Pass and the all-new 1:1 Meet & Greets available in limited quantities.
Full-Court Family Fun – These players are bringing ball handling, dunking, and big plays all four quarters. It's the team your entire family can cheer for. If you're seated near the court, you and your family may even get pulled into the action!
Grab your tickets here!
Madison Moms Blog is written by and for moms who live in the Madison Area. We strive to connect local moms by sharing personal experiences, fun ideas and useful information as well as promoting local businesses. Our community begins online, but doesn't stop there! We offer Mom's Night Out events, play groups and other opportunities to connect offline, with and without kids.
Where to Get a COVID Vaccine | In + Around Madison, WI
5 Free Indoor Spots This Winter Around Madison for Babies and Toddlers


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News on Cuvier Street vacation may give crucial lift to La Jolla Recreation Center renovation plans
A preliminary brochure design shows the proposed La Jolla Recreation Center renovation.
(Courtesy of Trace Wilson)
By Elisabeth FraustoStaff Writer
A requested vacation of part of Cuvier Street — considered a critical step in the planned renovation of the La Jolla Recreation Center — will return to the La Jolla Community Planning Association for possible approval soon, local architect Trace Wilson told the La Jolla Community Recreation Group, the Rec Center's advisory board, during its meeting last week.
Under the proposed vacation, the city of San Diego would relinquish part of its right of way on Cuvier Street to the adjacent Rec Center and The Bishop's School.
The vacation of Cuvier, which also would involve a lot-line adjustment to split the land widthwise instead of down the middle of the street, has been approved by several community groups but was held up at LJCPA in July as questions arose about who actually owns the land.
Wilson said he heard before the Sept. 22 CRG meeting from San Diego Parks & Recreation Department Director Andy Field that "the underlying land of Cuvier is not dedicated parkland," which means the vacation of the street can proceed, giving the Rec Center the frontage along Prospect Street — about 11,106 square feet — with the south portion, 8,061 square feet, going to Bishop's.
"We will be clear to go back to the CPA and ask for approval and move forward," Wilson said.
Steve Hadley, representing San Diego City Councilman Joe LaCava, whose District 1 includes La Jolla, said the request for vacation and accompanying requests for the lot-line adjustment and a coastal development permit will go before LJCPA in October or November.
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Laurel Hanson, a graphic artist and marketing strategist, presented the CRG with a brochure she designed for the Visioning Committee to send to potential donors as part of fundraising efforts for the Recreation Center renovation.
"All images are a work in progress," Hanson said as she reviewed the brochure, which lays out the history of the building and grounds and illustrates the planned refurbishments, such as a new roof deck and auditorium, "and also just highlighting the fact that they're going to be great places to hold meetings and classes and different events for the community."
The brochure also is designed to highlight "the community leaders behind the project and their varying expertise," Hanson said.
Wilson said there will be a website for information and that all funds raised will go to Friends of La Jolla Recreation Center, a nonprofit that supports the center.
He said the renovation plans themselves are "really at a schematic level, which gives us the opportunity to get to a cost so we know what we're talking about here to fundraise to."
Wilson said the Visioning Committee is working with Minnesota-based Landscape Structures Inc. to design the playground and that representatives of the company will tour La Jolla and the Rec Center to discuss ideas.
"There's great momentum overall on the project," he said.
Other CRG news
La Jolla Community Recreation Group members meet Sept. 22 online.
(Elisabeth Frausto)
Rec Center operations: San Diego Parks & Recreation Department area manager Rosalia Castruita said masks are still required inside the Rec Center, regardless of a person's COVID-19 vaccination status.
Rec Center Director Jesse DeLille said the new fall program is out and "we pretty much have the same schedules we had before."
"Our adult classes aren't back yet because the volunteers just aren't comfortable yet coming back," he said. However, "our PeeWee sports class, since we opened back up, has completely filled up every time" to its 12-person capacity. "It's been very popular."
Celebrating Walter Munk: CRG Chairwoman Mary Coakley Munk said a celebration of the 104th birthday of her late husband and famed oceanographer Walter Munk will be held at The Map of the Grand Canyons of La Jolla at Kellogg Park at 4 p.m. Friday, Oct. 15. There will be activities for children and a short program, she said.
Next meeting: The La Jolla Community Recreation Group next meets at 5 p.m. Wednesday, Oct. 27, online. For more information, call (858) 552-1658. ◆
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Elisabeth Frausto
Elisabeth Frausto is a reporter for the La Jolla Light.
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