text:
\section*{Introduction.}

Let $C\subset \mathbb P^2$ be a reduced curve defined over the field
of complex numbers $\mathbb C$. A curve $C$ is called {\it cuspidal}
if the singular points of $C$ are only the ordinary cusps and nodes.

In modern textbooks on algebraic geometry, classical
Pl$\ddot{u}$cker's formulae are stated as follows (see, for example,
\cite{Br}, \cite{G-H}). \newline {\bf Classical Pl\"{u}cker's
formulae.} {\it Let $C\subset \mathbb P^2$ be an irreducible
cuspidal curve of genus $g$, degree $d\geq 2$, having $c$ ordinary
cusps and $n$ nodes Assume that the dual curve $\hat C$ of $C$ is
also a cuspidal curve. Then
\begin{equation} \label{p1}
\hat d=d(d-1)-3c-2n;
\end{equation}
\begin{equation} \label{p2}
\displaystyle g=\frac{(d-1)(d-2)}{2}-c-n;
\end{equation}
\begin{equation} \label{p3}
d=\hat d(\hat d-1)-3\hat c-2\hat n;
\end{equation}
\begin{equation} \label{p4}
\displaystyle g=\frac{(\hat d-1)(\hat d-2)}{2}-\hat c-\hat n,
\end{equation}
where $\hat c$ and $\hat n$ are the numbers of ordinary cusps and
nodes of $\hat C$ and $\hat d=\deg \hat C$}. \\

Denote by  $V(d,c,n)\subset \mathbb P^{\frac{d(d+3)}{2}}$ the
variety parametrizing the irreducible cuspidal curves of degree $d$
with $c$ ordinary cusps and $n$ nodes.  Very often, if for given
$d$, $c$, and $n$ one of the invariants $\hat c$ or $\hat n$,
obtained as the solution of (\ref{p1}) -- (\ref{p4}), is negative,
then  it is claimed that this is sufficient for the "proof" of the
emptiness of $V(d,c,n)$. However, the correctness of the following
statement is unknown: "{\it the dual curve $\hat C$ of a curve $C$
corresponding to a generic point of $V(d,c,n)$ is cuspidal"}.
Therefore, in general case, it is impossible to conclude the
non-existence of cuspidal curve $C$ if $\hat c$ or $\hat n$ is
negative. Of course, to avoid this problem, it is possible to use
generalized Pl\"{u}cker's formulae including the numbers of all
possible types of singular points of $\hat C$. But, we again have a
difficulty, namely, in this case we must take into account too many
unknown invariables.

To obviate the arising difficulty, in section 1 for any reduced
plane curve $C$ we define the notions of the {\it number} of its
{\it virtual cusps} $c_v$ and the {\it number} of its {\it virtual
nodes} $n_v$ which are non-negative, coincide respectively with the
numbers of ordinary cusps and nodes in the case of cuspidal curves,
and if the dual curve $\hat C$ of an irreducible curve $C$ has $\hat
n_v$ virtual nodes and $\hat c_v$ virtual cusps, then the integers
$c_v$, $n_v$, $\hat c_v$, and $\hat n_v$ satisfy Classical
Pl\"{u}cker's formulae.

In section 2, we investigate the behaviour of the Hessian curve
$H_C$ of a cuspidal curve $C$ at cusps and nodes of $C$, and in
section 3, we give a proof of some inequalities for the numbers of
cusps and nodes of plane cuspidal curves of degree $d$ which was
obtained early in \cite{L} under additional assumption that the dual
curve of a generic cuspidal curve is also cuspidal.

\section{The numbers of virtual cusps and nodes}
Let $(C,p)\subset (\mathbb P^2,p)$ be a germ of a reduced plane
singularity. It splits into several irreducible germs:
$(C,p)=(C_{1},p)\cup\dots\cup (C_{k},p)$. Denote by $m_{j}$ the
multiplicity of the singularity $(C_j,p)$ at the point $p$ and let
$\delta_{p}$ be the $\delta$-invariant of the singularity $(C,p)$.
By definition, the integers
$$c_{v,p}:=\sum_{i=1}^k(m_i-1)$$ and
$$n_{v,p}:=\delta_p-\sum_{i=1}^k(m_i-1)$$ are called respectively the  {\it numbers of virtual cusps}
and {\it virtual nodes} of the singularity $(C,p)$. We have
$\delta_p=c_{v,p}+n_{v,p}$.

\begin{lem} \label{l1} Let $(C,p)\subset (\mathbb P^2,p)$ be a germ of a reduced plane
singularity, $c_{v,p}$ be the number of its virtual cusps and
$n_{v,p}$ be the number of its virtual nodes. Then
\begin{itemize}
\item[($i$)] $c_{v,p}\geq 0$, $n_{v,p}\geq 0$;
\item[($ii$)] if $(C,p)$ is an ordinary cusp, then $c_{v,p}=1$ and
$n_{v,p}=0$;
\item[($iii$)] if $(C,p)$ is an ordinary node, then $c_{v,p}=0$ and
$n_{v,p}=1$.
\end{itemize}
\end{lem}
\proof We prove only the inequality $n_v\geq 0$, since all the other
claims of Lemma \ref{l1} are obvious.  Let
$(C,p)=(C_{1},p)\cup\dots\cup (C_{k},p)$ and $m_i$ be the
multiplicity of its irreducible branch $(C_i,p)$. Then the
multiplicity of $(C,p)$ at $p$ is equal to $m_p=\displaystyle
\sum_{i=1}^k m_i$ and we have
$$\begin{array}{ll} \displaystyle
n_{v,p}= & \delta_p- \displaystyle  \sum_{i=1}^k(m_{i}-1)\geq
\delta_p-
 \sum_{i=1}^km_{i}+1= \\ & \displaystyle \delta_p- (m_p-1)\geq
 \delta_p-\frac{m_p(m_p-1)}{2}\geq 0,\end{array}$$
since $m_p\geq 2$ for singular points and $\displaystyle
\delta_p\geq \frac{m_p(m_p-1)}{2}$. Therefore, we have $$
\displaystyle n_v=\sum_{p\in \text{Sing}\, C}n_{v,p}\geq 0. \qed $$
\\

Let $C\subset \mathbb P^2$ be a reduced curve. Denote by
$\text{Sing}\, C$ the set of its singular points. By definition, we
put
$$c_v:=\sum_{p\in \text{Sing}\, C}c_{v,p},$$
$$n_v:=\sum_{p\in \text{Sing}\, C}n_{v,p}$$
and call these integers respectively the  {\it number of virtual
cusps} and the {\it number virtual nodes} of the curve $C$. If $C$
is an irreducible curve of degree $d$ and geometric genus $g$, then
we have $g=\displaystyle \frac{(d-1)(d-2)}{2}-\delta_C$, where
$\delta_C=\displaystyle \sum_{p\in\text{Sing}\, C}\delta_p$ is the
$\delta$-invariant of $C$. Therefore, we have

\begin{equation} \label{genus} g=\frac{(d-1)(d-2)}{2}-c_v-n_v.\end{equation}

The following proposition is a corollary of Lemma \ref{l1}.
\begin{prop} \label{cl1} Let $c_v$ be the number of virtual cusps and $n_v$ be the number
of virtual nodes of a reduced curve $C\subset \mathbb P^2$. We have
\begin{itemize}
\item[($i$)] $c_v\geq 0$ and $n_v\geq 0$,
\item[($ii$)]
 if $C$ is a cuspidal curve, then
$c_v$ and $n_v$ are equal respectively to the number $c$ of cusps
and the number $n$ of nodes of $C$.
\end{itemize}
\end{prop}
\begin{thm} {\rm (}{\bf Pl\"{u}cker's formulae}{\rm )}. Let $C$ and $\hat{C}$ be
irreducible dual curves of genus $g$, $\deg C=d\geq 2$, $\deg \hat
C=\hat d$, and $c_v$, $n_v$, $\hat c_v$, $\hat n_v$ are the numbers
of their virtual cusps and nodes, respectively. Then we have the
following equalities:
\begin{equation} \label{p11}
\hat d=d(d-1)-3c_v-2n_v;
\end{equation}
\begin{equation} \label{p21}
\displaystyle 2g=(d-1)(d-2)-2c_v-2n_v;
\end{equation}
\begin{equation} \label{p31}
d=\hat d(\hat d-1)-3\hat c_v-2\hat n_v;
\end{equation}
\begin{equation} \label{p41}
\displaystyle 2g=(\hat d-1)(\hat d-2)-2\hat c_v-2\hat n_v.
\end{equation}
\end{thm}
\proof To prove Pl\"{u}cker's formulae, we need the following
\begin{lem} For an irreducible plane curve
$C$ we have
\begin{equation}\label{d^*} \hat d= 2d+2(g-1)-c_v,
\end{equation}
\begin{equation}\label{c^*} \hat c_v= 3d+6(g-1)-2c_v,
\end{equation}
\begin{equation}\label{d} d= 2\hat d+2(g-1)-\hat c_v,
\end{equation}
\begin{equation}\label{c} c_v= 3\hat d+6(g-1)-2\hat c_v.
\end{equation}
\end{lem}
\proof Denote by $\nu: \overline C\to C$ and $\hat{\nu}: \overline
C\to \hat C$ the normalization morphisms, consider generic (with
respect to $C$ and $\hat C$) linear projections $\text{pr}:\mathbb
P^2\to\mathbb P^1$ and $\hat{\text{pr}}:\hat{\mathbb P}^2\to\mathbb
P^1$, and put $\pi=\text{pr}\circ \nu$ and
$\hat{\pi}=\hat{\text{pr}}\circ \hat{\nu}$. We have $\deg\pi=d$ and
$\deg\hat{\pi}=\hat{d}$.

Let $\nu^{-1}(x_i)=\{ y_{i,1},\dots ,y_{i,m_i}\}$ for $x_i\in
\text{Sing}\, C$. For each point $y_{i,j}$ denote by $r_{i,j}$ the
ramification index of $\pi$ at $y_{i,j}$. It is easy to see that
$r_{i,j}$ coincides with the multiplicity $m_{i,j}$ at $x_i$ of the
irreducible germ $(C_{i,j},x_i)\subset (C,x_i)$ corresponding to the
point $y_{i,j}$. Therefore, we have
$$c_v=\sum_{i,j}(r_{i,j}-1).$$

Applying Hurwitz formula to $\pi$ and $\hat{\pi}$, we obtain
\begin{equation}
2(g-1)=-2d+c_v+\hat d\end{equation} and
\begin{equation} \label{p_a}
2(g-1)=-2\hat d+\hat c_v+d\end{equation} which give formulae
(\ref{d^*}) and (\ref{d}).

To prove (\ref{c^*}), note that $\hat c_v=2\hat d+2(g-1)-d$ by
(\ref{d}). Therefore $$\hat c_v=2(2d+2(g-1)-c_v) +2(g-1)-d$$ by
(\ref{d^*}), that is, $\hat c_v= 3d+6(g-1)-2c_v$. Formula (\ref{c})
is obtained similarly. \qed \\

It follows from (\ref{genus}) that
\begin{equation} \label{argen}
2(g-1)+2c_v+2n_v=d(d-3), \qquad 2(g-1)+2\hat c_v+2\hat n_v=\hat
d(\hat d-3)\end{equation} which are equivalent to (\ref{p21}) and
(\ref{p41}). To complete the proof of Pl\"{u}cker's formulae, notice
that formulae (\ref{p11}) and (\ref{p31}) easily follow from
equations (\ref{d^*}) -- (\ref{c}) and (\ref{argen}). \qed

\section{On the Hessian curve of a cuspidal curve}
Let $C\subset \mathbb P^2$ be an irreducible cuspidal curve of
degree $d$ with $c$ cusps and $n$ nodes. It follows from (\ref{p21})
and (\ref{c^*}) that
\begin{equation}\label{eqmain} 8c+6n +\hat c_v= 3d(d-2).\end{equation}

Equality (\ref{eqmain}) has a natural geometric meaning. To explain
it, let the curve $C$ is given by equation $F(x_0,x_1,x_2)=0$, where
$x_0,x_1,x_2$ are homogeneous coordinates in $\mathbb P^2$. Consider
the Hessian curve $H_C\subset \mathbb P^2$ of the curve $C$. It is
given by equation $\det (\frac{\partial^2F}{\partial x_i\partial
x_j})=0$. We have $\deg H_C=3(d-2)$. Therefore the intersection
number $(C,H_C)_{\mathbb P^2}$ is equal to $3d(d-2)$. On the other
hand, it is well-known (see, for example, \cite{Br}) that the curves
$C$ and $H_C$ meet at the singular points and at the inflection
points of the curve $C$. Therefore we have
\begin{equation} \label{int} \Sigma^{\prime}(C,H_C)_{p}+\Sigma^{\prime\prime}(C,H_C)_{p}+
\Sigma^{\prime\prime\prime}(C,H_C)_{p}=(C,H_C)_{\mathbb
P^2}=3d(d-2),\end{equation} where $(C,H_C)_p$ is the intersection
number of the curves $C$ and $H_C$ at a point $p\in C$ and the sum
$\sum^{\prime}$ is taken over all cusps of $C$, the sum
$\sum^{\prime\prime}$ is taken over all nodes of $C$, and the sum
$\sum^{\prime\prime\prime}$ is taken over all inflection points of
$C$.

Let us show that the coefficients involving in equation
(\ref{eqmain}) have the following geometric meaning: {\it equality}
(\ref{eqmain}) {\it is the same as equality} (\ref{int}), that is,
the coefficient $8$ in (\ref{eqmain}) is the intersection number
$(C,H_C)_p$ at a cusp $p\in C$, the coefficient $6$ is the
intersection number $(C,H_C)_p$ at a node $p\in C$, and $\hat
c_v=\sum^{\prime\prime\prime}(C,H_C)_{p}$. Indeed, let $p$ be a cusp
of $C$. Without loss of generality, we can assume that $p=(0,0,1)$
and
$$F(x_0,x_1,x_2)=x_0^2U(x_0,x_1,x_2)+
x_0x_1^2V(x_0,x_1,x_2)+x_1^3W(x_0,x_1,x_2),$$ where $U$ is a
homogeneous polynomial of degree $d-2$ such that $U(0,0,1)=1$ and
$V$ and $W$ are homogeneous polynomials of degree $d-3$ such that
$W(0,0,1)=1$. Put $a=V(0,0,1)$, then in non-homogeneous coordinates
$x=\frac{x_0}{x_2}, y=\frac{x_1}{x_2}$ we have $p=(0,0)$, the curve
$C$ is given by equation of the form
$$x^2+y^3+axy^2+bx^2y+cx^3+ \text {terms of higher degree}=0,$$ and
the curve $H_C$  is given by equation of the form
$$x^2(6y+2ax)+ \text {terms of higher degree}=0.$$ Easy computation
(applying $\sigma$-process with center at $p$) gives the following
inequality:
\begin{equation}\label{1} (C,H_C)_p\geq 8\end{equation} if $p$ is a
cusp of $C$.

Let $p$ be a node of $C$. Again, without loss of generality, we can
assume that $p=(0,0,1)$ and
$$F(x_0,x_1,x_2)=x_0x_1U(x_0,x_1,x_2)+
V(x_0,x_1)W(x_0,x_1,x_2),$$ where $U$ is a homogeneous polynomial of
degree $d-2$ such that $U(0,0,1)=1$, $V$ is a homogeneous polynomial
of degree $3$, and $W$ is a homogeneous polynomial of degree $d-3$.
In non-homogeneous coordinates $x=\frac{x_0}{x_2},
y=\frac{x_1}{x_2}$ we have $p=(0,0)$, the curve $C$ is given by
equation of the form
$$xy+ \text {terms of higher degree}=0,$$ and
the curve $H_C$  is given by equation of the same form
$$xy+ \text {terms of higher degree}=0.$$ Easy computation
(applying $\sigma$-process with center at $p$) gives the following
inequality:   \begin{equation}\label{2} (C,H_C)_p\geq
6\end{equation} if $p$ is a node of $C$.

If $p$ is an $r$-tuple inflection point of $C$ (that is,
$(C,L_p)_p=r+2$, where the line $L_p$ is tangent to $C$ at $p$),
then by Theorem 1 on page 289 in \cite{Br}, we have $(C,H_C)_p=r$.
On the other hand, the branch $(\hat C_i,\hat p)$ of the dual curve
$\hat C$, corresponding to an irreducible branch $(C_i,p)\subset
(C,p)$ at a point $p$ of a cuspidal curve $C$, is singular if and
only if $p$ is an inflection point of $C$; and the branch $(\hat
C,\hat p)$, corresponding to the branch $(C,p)$ at $r$-tuple
inflection point $p\in C$, has a singularity of type
$u^{r+1}-v^{r+2}=0$. The multiplicity $m_{\hat p}$ of this
singularity is equal to $r+1$. Therefore, we have
\begin{equation} \label{3} \Sigma^{\prime\prime\prime}(C,H_C)_{p}=
\sum_{(\hat C,\hat p)} (m_{\hat p}-1) =\hat c_v.\end{equation}

Finally, it follows from (\ref{eqmain}) -- (\ref{3}) that
inequalities (\ref{1}) and (\ref{2}) are the equalities in the case
of cuspidal curves.

\section{Lefschetz's inequalities}
As above, let $C\subset \mathbb P^2$ be an irreducible cuspidal
curve of degree $d$ and genus $g$ having $c$ cusps and $n$ nodes.

In \cite{L},  assuming that for a generic cuspidal curve with given
numerical invariants the dual curve is also cuspidal, Lefschetz
proved the following inequalities
\begin{equation} \label{ineven} c\leq \frac{3}{2}d+3(g-1)
\end{equation} if $d$ is even and
\begin{equation} \label{inodd} c\leq \frac{3d-1}{2}+3(g-1)
\end{equation} if $d$ is odd. It follows from  (\ref{c^*}) that these inequalities
occur for any plane cuspidal curve, since $\hat c_v$ is a
non-negative integer.

Note also that equality (\ref{eqmain}) gives rise to the following
statement: {\it for a plane cuspidal curve of degree $d\geq 2$ the
following inequality holds}: \begin{equation} \label{inmain}
8c+6n\leq 3d(d-2)-\frac{1-(-1)^d}{2}.\end{equation}

\begin{rem}{\rm One can show that} for any $d=2k$, $k\geq 3$, and
for any $g\geq 0$ such that $2\leq 3g\leq k-4$ or $g\leq 1$, there
exist a cuspidal curve of degree $d$ having $c=3(k+g-1)$ cusps and
$n=2(k-1)(k-2)-4g$ nodes for which inequality {\rm (\ref{inmain})}
becomes the equality. If $d=2k+1$, $k\geq 3$, then for any $g$ such
that $2\leq 3g\leq k-4$ or $g\leq 1$, there exist a cuspidal curve
of degree $d$ having $c=3(k+g)-2$ cusps, $n=2(k-1)^2-4g$ nodes, and
for which inequality {\rm (\ref{inmain})} becomes the equality. {\rm
The proof of these statements follows from the fact that the genus
of such curves $C$ is equal to $g$ and for these curves the dual
curves $\hat C$ have degree $\hat d=2(g-1)+7 + \frac{1-(-1)^d}{2}$
and the number of virtual cusps $\hat c_v=\frac{1-(-1)^d}{2}$.
Therefore such curves can be obtained as the image of a generic
linear projection to $\mathbb P^2$ of a smooth curve $\overline
C\subset \mathbb P^{\hat d-g}$ of degree $\hat d$ birationally
isomorphic to $C$. Standard computations (which we leave to the
reader) of codimension of the locus of "bad" projections shows that
in this case there is a linear projection $\text{pr}: \mathbb
P^{\hat d-g}\to \mathbb P^2$ such that $\text{pr}(\overline C)=\hat
C$ is a cuspidal curve with $\hat c=\frac{1-(-1)^d}{2}$ and its dual
curve $C$ is also cuspidal}.
\end{rem}

For completeness, let me remind also the following well-known
inequalities which we have for plane cuspidal curves:
\begin{equation} 3c+2n< d(d-1)-\sqrt{d},\end{equation} \begin{equation} 2c+2n\leq (d-1)(d-2),\end{equation}
\begin{equation} \label{fina} d(d-2)(d^2-9)+(3c+2n)^2+27c+20n\geq 2d(d-1)(3c+2n)\end{equation} which are
consequences of equalities (\ref{p11}) -- (\ref{p41}) and the
inequalities  $\hat d\geq \sqrt d$, $g\geq 0$,  $\hat n_v\geq 0$;
$$16c+9n\leq d(5d-6)$$ ({\it Hirzebruch -- Ivinskis
inequality} (\cite{Hirz})) which is true in the case of even $d$.

Note also that inequalities (\ref{inmain}) -- (\ref{fina}) hold for
any irreducible plane curve if we substitute $c_v$ and $n_v$ instead
of $c$ and $n$.


Rubber Ring Shock Absorber Top Aluminum Machine Foot Amplifier Feet Speaker Turntable CD Player Feet 1Set Free Shipping Quantity:1Set 1Set:A pin and a tray The picture is 4 sets. Please buy 4 sets or 3sets Small Foot nail diameter 20, height 20 mm Disc holder diameter 30 mm, height 5 mm With the total height of 24 mm (including the shock absorber rubber ring) Big Pin diameter 31MM, height 28MM Support plate diameter 40MM, height 6MM With the total height of 32 mm (including the shock absorber rubber ring) Delivery details (Free shipping products. We can choose the right way to transport.) 1.We ship Items to USA by China Post E-packet:10-20 work days 2.We ship Items to Spain by Correos Economy:20-45 work days (Less than 20 dollars) 3.We ship Items to United Kingdom by Royal Mail Economy:20-45work days (Less than 20 dollars) 4.Normally,we ship items by CHINA POST AIRMAIL:20-60work days to worldwide. *If you need faster shipping service,please select such as DHL,UPS,EMS,FeDex etc. (the shipping cost is based on weight Dimension weight of your orders) All delivery are with Tracking Number 3.We will ship your items in 3-5 work days as soon as of clearing your payment Terms of sales 1. We will put legal effort to minimize any GST or V.A.T. or other Import Taxes. However, any tax/duty would be excluded from the price. Please afford V.A.T or GST yourself 2. We warmly appreciate your positive feedback, and we will leave positive feedback to you as we complete transaction 3.Import duties, taxes and charges are not included in the item price or shipping charges. These charges are the buyer's responsibility. Please check with your country's customs office to determine what these additional costs will be prior to bidding/buying 4. We ship to PayPal registered address. Please provide your full name & correct address in details in PayPal. A telephone Number may help more accurate delivery 5. We promise each item would be shipped, However, some times, less than 0.5% of packages might be lost on the way, For these items,we'd like to resend the same item or fully refund 6. We warmly appreciate your positive feedback, and we will leave positive feedback to you as we complete transactions About us We sell vacuum tubes, Amplifiers,various tube sockets, audio connectors, triode transformer cover, leather amplifier handles, capacitors, various knobs, aluminum amplifier chassis, etc. Various Parts for tube audio guitar amplifier projects! Contact us We value our customers very much, so, for any questions or problem, please feel free to contact us by E-mail or Ali Message tool, we are always here offering service to you We will reply all of your messages ASAP! We are always here to offer service to you.


text:
NA, Na, na eller .na kan syfta på

 Na (musikgrupp) – en albansk rockgrupp från Gjakova i Kosovo
 .na – nationell toppdomän för Namibia
 Anonyma Narkomaner (NA) – en ideell gemenskap eller förening av män och kvinnor för vilka droger blivit ett allvarligt problem
 Natrium (Na) – ett grundämne (Na)
 Nauruanska – na är ISO 639-kod för språket
 Nederländska Antillerna (NA) – nationalitetsbeteckning för motorfordon därifrån
 Nerikes Allehanda (NA) – en tidning

Se även
 N/A, n/a eller n / a – en engelskspråkig förkortning: not applicable ("inte tillämplig") eller not available ("inte tillgänglig")

redpajama_set_name: RedPajamaWikipedia


The Amigo Aussie Allrounder DiscFront is the perfect paddock sheet for almost all year round use and is back by popular demand!
Made from a water-resistant, lightweight, ripstop, breathable 260gsm polyester fabric that feels soft and comfortable to the touch, the Amigo Aussie Allrounder provides complete UV protection to your horse during the year in warmer weather while also doubling as an under-sheet in colder weather.
Patented Leg Arches allow for freedom of movement and our unique Disc front closure takes the weight out of the neck area, combined with Surefit neck design to relieve pressure on the wither.
Available in White with Green Check and gorgeous Forest Green/Burgundy/Cream binding.


Eggs have the reputation as one of the world's most misunderstood foods.
First we're told to eat eggs, they're a great source of protein. Then we're told don't eat eggs, they contain too much cholesterol. And now it appears that eggs have made it back to the "sunny" side.
Today's holiday celebration is all about helping raise awareness world-wide of the benefits of eggs, and the important role they play in human nutrition.
So let's celebrate the wonderfully, perfectly created egg!


Sugar High Fridays. If you have a sweet tooth (and I admit it, yes, I do), it's hard to ignore this incredibly sumptuous and well-attended monthly sweet fest founded by Jennifer, The Domestic Goddess. But I bake bread, not desserts (Daring Baker challenges notwithstanding).
Even so , when I opened my inbox to discover an invitation from Zorra to participate in this month's event, Pudding, I really wanted to, because, well, it was an invitation from Zorra.
So I thought, let's see, pudding… There's chocolate, although last time I made it, the texture was, shall we say, suboptimal … I love rice pudding and I might not screw that up… or I could probably handle plum pudding for Christmas, but I don't really like it… [Fret, fret] what pudding can I make?


text:
46 - Interesting sundial, Cosmological conundrum, Moon & Apollo missions
An Interesting Sundial
This sundial was seen at the Port of Alcudia on the island of Majorca
The two photographs on the cover of this issue of MIRA are of an unusual sundial I saw while on holiday in Majorca, they where taken at the port of Alcudia. This is an old town situated on the north east side of the island of Majorca where my wife and I had our summer holiday this year. Most evenings after dinner we would walk from our hotel, along the beach up to the port area, inspect the boats in the harbour and them have a welcome cup of coffee at a lovely harbour side cafe. One evening, feeling more energetic than usual, we walked around the whole of the harbour and discovered this interesting sun dial in the far corner. A few days later we returned with my camera to find that the sun was already setting behind a water front tree casting a shadow on the sun dial.
I have never seen a round sundial before so it was interesting to examine it. One side of the column had an unusual time index engraved on it to show the time before or after the sun had moved round from the south facing side. This northern side of the column reads only the early morning and evening time during summer when the sun passes the equinox and moves north of the east and west points on rising and setting.
On the front was the interesting time and sun position scale showing the height of the sun at various months of the year with the zodiacal constellations around the side and along the bottom of the scale. This left hand photograph is a composite of two photographs, cloned together to show both sides of the front. This is why the image looks a little odd in the centre where it joins. The gnomon pointed to the pole position at a shallow angle and is not shown. The position given on the reverse of the column was Latitude 39.51° N Longitude 3.08° E. On top of the column was a seahorse wind vane. The sundial side of the column faces due south so the shadow cast by the gnomon points to the correct time and also shows the height of the sun during the year as it goes from winter to summer solstice and back. How does the constellations scale work around the edge of the dial? Do they show where the sun is along the ecliptic during the year? Any ideas?
Here is a little puzzle for all you budding astrophysics out there to have a go at on a cloudy night this autumn. !f was first put to the members of the Hinkley & District Astronomical Society by Dennis Spratley who was, with Peter Wise, one half of the C&WAS, January 1998 meeting presentation on problems in the big bang theory and cosmology in general. This question at Hinkley drew almost a blank with only one incorrect reply! So common guys, put the grey matter to work. We can do better than Hinkley, can't we? I have already had a go and you can read my own (nearly correct, well ok, wrong) answer over the page. Dennis has sent to me the correct answer which I'll print after I receive a few replies. Please have a go, write your answer down and give it to me at the next meeting. The more the merrier. Don't forget that your support will encourage authors to contribute other work to MIRA so that it stays a regular publication.
Suppose that the Universe we inhabit is indeed one that will continue to expand for ever. That is, we consider the situation of a model universe that expands without limit unlike the model that collapses back into a final singularity.
There are two classes of objects that we may have to account for in such a universe: those which are now 'visible' to the astronomer and those which can never be 'visible', the latter class being further away. These two classes of objects are separated by a boundary, which may be moving: it can be static depending on the model we choose. This boundary, called the event horizon, is spherically symmetric about us. But every observer in this universe has his, or her, own horizon. For any observer in this universe staying say, in his own galaxy, events occurring beyond this horizon are for ever beyond his powers of observation. Due to the cosmological expansion away from any observer, objects cross his horizon at the speed of light.
Consider a quasar, Q, emitting, as is to be expected, its vast outpouring of radiation, a proportion of which, regarded as a stream of photons, is heading in the direction of the Earth situated at O, which we regard as the origin. Due to the universal cosmic expansion, when this radiation is received at O it has a high red-shift. Suppose that somewhere between O and Q is a galaxy G, which may be taken as a member of a cluster that is receding from O. The quasar Q and galaxy G are seen with very small angular separation in the night sky. Radiation from G also arrives at O with red-shift, but this red-shift is less than that of the radiation from Q. From the view obtained from G, however, the radiation arriving at G from Q will have less red-shift than that of the radiation arriving at O from Q.
This is the general picture. Suppose now that Q is just on the event horizon of O which will be taken as static for simplicity. That is, the event horizon for any observer in the space is at a fixed distance from him: consequently this is so for O. No information about Q can be received by O: the light from the quasar has infinite red-shift on its arrival at O. Now a photon PQ ejected from quasar Q towards O leaves Q with no red-shift. On its journey to us at O, the photon PQ passes the galaxy G where it has a finite red-shift, and we may imagine that at this time a photon PG is emitted by G at exactly the same frequency as that of PQ and that both PQ and PG (an identical pair) head towards O. Photons PQ and PG arrive at O together, but we have arranged that on arrival PQ has infinite red-shift. Since photons PQ and PG can be regarded as starting from G together with identical frequencies should not PG also have infinite red-shift on arrival at O and thus the galaxy G, like Q, cannot be seen from O?
What is the answer and why?
Submissions, please, in writing to the Editor.
An answer to A COSMOLOGICAL CONUNDRUM?
Right, here is my attempt at Dennis Spratley's A COSMOLOGICAL CONUNDRUM, I wrote this and sent it to him before receiving his answer. . .
The main point of this conundrum is, I believe, that if Q is on the event horizon, then it will be invisible to us, as stated in paragraph three, because an object on the event horizon has infinite red-shift and so is invisible because no radiation reaches us, nor can reach us, (the same as any other object at the same distance).
A photon from Q arriving at an (it?) observer at G is visible to G even if the photon is very red-shifted. If G emitted a photon PG of the same energy as a passing PQ photon, then that photon will also be unobservable when it arrives at O because of its red-shift into lower frequencies. However most of the light emitted from G is not at a red-shifted frequency, it is normal light at the start of the journey, exactly as is the case of light emitted from Q at the start of its journey, and this light only gets red-shifted during its passage through space and time to us. So the idea of two photons having the same frequency from two independent sources, one being away across the universe at the limit of detection, and the other much nearer, and then travelling to reach us together, is not correct because it will not happen. The light energy from G will be red-shifted depending on its distance, not just because of a passing photon from a distant quasar has a similar frequency. If any light from G started out with the same frequency as a passing PQ photon then when it gets to us, we won't know its there because we can't see it!
The Universe is a ^ Dangerous Place Cynthia
Over the last few years the universe has suddenly became a very dangerous place for any life form to live in, and this includes us. It has always been like that of cause, but we just didn't know.
For thousands and thousands of years mankind has looked on the heavens as a static star filled dome, with only the odd comet and the planets drifting across the night time sky. Meteors where a mystery like thunder and lighting.
The sun and the stars formed the base for the calendar because they where consistent and reliable. Every year the same constellations filled with the same stars would show themselves again above the horizon so that farmers would knew when to plant the seeds for next years crop. Nothing changed from year to year but the weather.
Only a few years ago we knew nothing of Earth crossing asteroids and comets, chaos theory, gamma ray bursts and other nasty things the universe can throw at us. We all lived in peace with the universe content in the knowledge that life had gone on for thousands of years without any problems from outer space!
The recent impacts of the little comet Shoemaker-Levy 9 crashing into Jupiter causing Earth size blemishes on that planet's clouds have, maybe, at last brought home to the general public that perhaps the Earth is in danger of being hit by an object someday. Just consider the panic if the comet Hale-Bopp had been just a few months (three or four) earlier on its 3,500+ year orbit. It could have passed us only 3,000,000 miles inside our orbit. What a sight that would have been! The recent scare of the newly discovered Dooms-Day asteroid 1997 XF11, which was found to be in an Earth crossing orbit and on 2028 Oct 26 would pass very close to the Earth made the headlines around the world. For a short while it seemed to be coming very close, within the orbit of the moon. But now that more data has been collected on its orbit by spotting it on older photographs, so that a better orbit fit could be predicted, it appears it will miss us by over half a million miles.
Still it made people think. People with the money and power realise that even they will be in the same boat as the rest of us if a large object hits Earth. And no one knows just what is out there.
For only now in the last few decades has mankind realised how near we have come to destruction. Only recently have we had the technology to find the small bodies whizzing around in the solar system and map their orbits. Only now have we the computers to calculate quickly the orbits of the tiny streaks of light found on the photographic plates and fit them into the known solar system. How many asteroids are out there? Anybody's guess is as good as anyone else. We don't know. More are found almost every night by the NASA Space Guard program, in the last few months 3,000 more asteroids have been added to the list.
One of the problems is that these tiny bodies don't follow exactly the path calculated for them after they have been discovered. All the other planets in the system pull on them subtlety and because they have such a small mass they are easily moved. A small alteration in the orbit will eventually lead to a shift in the predicted position and over time, just a few orbits unseen because we are far from it or on the other side of the sun, it is lost again. It must be remembered that we are talking about thousands of these objects which with present day technology can only be seen during darkness when fairly close to Earth. We can't see them very well, if at all, if they are orbiting inside our own orbit. They are small, most are very dark, so don't reflect much light, and hide in the zodiacal light.
With the coming of the new satellites observing the sun such as the SOHO spacecraft, astronomers have been surprised how many comets they have detected crashing into the sun, ones we have never seen! In 1910 Comet Halley passed between Earth and the sun and no sign of it was detected even though the time of passage was known and was looked for. So what chance would we have of a comet coming at us from out of the sun?
Other problems have started to raise their heads in the distance universe. Supernova can fry us if too close. When the light pulse reached us in February 1987 from the supernova in the Large Magellanic Cloud it was followed very closely by trillions upon trillions of neutrinos which passed through every one on the planet. Only a dozen or two registered in detection equipment. The rest swept through Earth as if it was a sheet of glass. But this supernova was 150,000 light years away. Suppose it was only 100 light years, well I wouldn't be writing this and you wouldn't be reading it. The solar system would be sterile. The radiation from an explosion of that magnitude would be fatale to all life within about 250 light years of the star.
What might help is the Earth's magnetic field, this would protect us from a lot of the charged particles by directing them away from the surface and trapping them in the Van Allan Belts. But the really powerful particles, the high energy cosmic rays and gamma particles which do the damage would not be so easily detracted by Earths magnetic field and would reach us through the atmosphere. Any supernova within say 1,000 light years would cause eyesight problems to anyone daft enough to look at it through a telescope, it would be like looking down a laser beam. The light energy in the explosion would light up the night sky of all the planets within hundreds of lightyears.
Over the period of time that the Earth has existed, a nova or a supernova must have happened near by once or twice in the distance past. Maybe this caused one or more of the mass extinctions which have occurred in the last billion years. During these episodes 85% to 95% of the different species alive at that moment have disappeared within a short space of time.
One of the problems with extinctions in the distant past is that no effects (luckily for us), remain from such catastrophes, to tell us what did the killing. Mind you, I heard the other day that we are killing off different species almost as fast as it has ever happened!!!
Most of the extinctions have happened at regular intervals of around 200 million years, this happens to be the average amount of time when the Sun along with the Earth travels into one of the spiral arms of our galaxy as we orbit around. These arms are more crowded with stars and dust than the place we now occupy between the Perseus and the Sagittarius arms. When we travel through an arm the sun and planets would sometimes be bombarded with dust and debris from clouds in the arms. These are the clouds in which stars form and many are light years wide, dense enough to diminish the light from the Sun in some patches, so causing cooling to the Earth to say nothing of the amount of meteoric material falling into the atmosphere.
Once in an arm the density of stars in the night sky would increase with some coming closer than the ones today. Many more stars would be visible to our human eyes in the night sky with new constellations to name. That is unless we happened to be in a dust cloud when the night sky would be very boring to say the least! Even through the galactic arms appear bright and thick with stars, the danger of a collision or near miss is extremely slight. Stars are very small relative to the amount of space around then. But the biggest factor would be the amount of bright blue stars shining near by. These are what makes the spiral arms so visible in other galaxies along with the star forming regions. In these regions are the nova and supernova we observe in distant galaxies owing to the higher star density and the effects of shock waves on the interstellar material. Luckily for us this is still a long way into the future.
Gamma-Rays
A new threat lies with the recently discovered gamma rays bursts. Since 1973 it has been known that flashes of intense gamma-ray radiation happen in space. The Compton Gamma Ray Observatory has seen hundreds of these bursts from every possible direction which implies they all lie in the far universe at huge distances from us in space and time. As of now we have no idea as to the cause of this radiation which in some cases lasts for only a few seconds before it disappears. Theories abound of collapsing black holes, neutron stars colliding, but none can generate the kinds of energy seen, ie. the output of billions of galaxies from a single point. If this energy was released in the centre of our galaxy or a near one we would be fried to a burnt crisp in seconds. A charming thought to end on.
As always I try to stay at least within sight of the boundaries of known science - see the September 1995 edition of Sky and Telescope for a discussion of the much sought after chemical properties of giant molecular clouds
You might remember my friend Clive, allegedly of the Interplanetary Dangerous Sports Club. The last time we met he was going out with the beautiful Clarissa. Over a pint or two Clive had spun me a yarn about how, on an early date, he had almost ended up dumping Clarissa, emotionally and gravitationally, into a rather large black hole. Then Clarissa turned up and spoilt his story by revealing that in reality the two of them had never got any further than Majorca.
I was annoyed. I had spent several very enjoyable evenings filling in Clive on the scientific aspects of his exploits, and now it seemed to me that my so-called friend had simply been stringing me along, setting me up to provide background for his stories. Worse, I couldn't see how he could invent the tales without knowing at least as much astrophysics as I did. Was he simply winding me up with his so-called adventures?
So I was not exactly pleased when he got into my carriage on the train. I tried to look inconspicuous, but it didn't work.
"Oh Hi Frosty!" he cried and came bounding over.
"Hello Clive", I said, off-handedly. He sat down opposite me. I wasn't going to start a conversation.
Diddly-dum diddly-dee diddly-dum diddly-dee....
"So what's new, Frosty!"
"Nothing much. How's Clarissa?" That knocked the smile off his face.
"Dunno..". I should have guessed, he was back in trainers and T-shirt. I wondered what had happened to her. No, I wasn't going to ask.
We both said nothing.
Clive perked up suddenly. "Did I ever tell you about the time we climbed the anti-Matterhorn?"
"CLIVE, I'M NOT INTERESTED IN YOUR STUPID STORIES!!". Everyone in the carriage looked round at me.
"Be miserable, then" said Clive sulkily, and looked out of the window. "See if I care."
This was ridiculous. I didn't want to hear another of Clive's outrageous adventures, but it would be impolite, not to mention uncomfortable, to ignore him for the entire journey.
"So what happened with Clarissa, then?"
"Oh, she's in prison...."
"PRISON?!" Everyone looked at me again. "What's she doing in prison?"
"About ten years, I think. Less with remission..."
"No, I mean, what's she in for?"
"Smuggling"
"SMUGGLING?" Only the gossipy types looked round this time.
"Oh, all right - tell me the story!"
Clive brightened up and leaned forward confidentially.
"Clarissa and I had hired a space yacht to go cruising round the galaxy"
I interrupted him. "Oh no! This isn't going to be another astronomical yarn, is it?"
Clive looked hurt. Then annoyed. "Look, Frosty, I don't know why you think I'm making these stories up. You know I was part of The Interplanetary Dangerous Sports Club - you saw us off at the spaceport when we went event horizon bungee jumping..."
That was true. But... "...but Clarissa said the story about you and her and the black hole was made up.."
"Well she would, wouldn't she? She was embarrassed by the whole thing... me having to save her from the black hole..."
That wasn't quite how I remembered the story. Nevertheless. "OK. OK. I'll give you the benefit of the doubt. So you went off cruising."
"Well at first it was great. Just me and her in our cosy space yacht. But after a while we started getting on each others' nerves. And there was a problem...."
I hardly dared ask. Fortunately Clive answered the question for me. "…Booze. Clarissa didn't like me drinking. In fact, she forbade it altogether!"
"How long was the cruise?!"
"Two months."
I could hardly imagine it. Two months without a drink.
"Of course, I managed to smuggle on-board a few crates of beer, but they hardly lasted a week. From then on it was torture... Eventually, I had to take desperate action."
Clive sat back in his seat. "I'll tell you how things were, by the last week of the cruise. We'd had so many arguments that we dared not disagree with each other. So we ended up being ever so polite. 'I thought we might pay a visit to the giant molecular cloud on the Aquila-Serpens border, Clarissa dear, so we can refuel in preparation for the journey home'.
'Anything you want, Clive darling. You do just that while I take a nap. Then I'll plan our course back to Earth. I'd like to stop off at that neutron star on the way home, I'm told their surface composition is most interesting...'
'All right, dear' I said, 'Mind you don't get too close. I don't want to be pulled apart by the tidal forces again, thank you.'"
Clive looked smug. "She played right into my hands. I was delighted to get her into her boudoir and out of my way. I made straight for the star formation region on the outskirts of the molecular cloud."
He looked very pleased with himself. "As you know, Frosty, when the radiation of young stars ionises a giant molecular cloud, the primary chemical reaction is the formation, and sublimation of... pure alcohol."
I did know. I also noted that Clive knew; how much more astronomy did he know and not let on to?
Clive continued. "Our space cruiser worked on a ramjet principle, gathering fuel from the interstellar medium to act as propellant. The molecular clouds are still pretty much vacuum by terrestrial standards, but if you move through them at speed you can suck in surprising quantities of matter. We had a mass spectrometer, of course, and so I tuned it to accumulate just the right atomic weight." (More physics, I noted)
Clive licked his lips as he remembered. "I drained off some of the contents of the starboard fuel tank, then lips trembling, took a sip. Frosty, it was wonderful! Like neat vodka, only stronger..."
He sighed in remembrance. "I must have drunk gallons of the stuff, it tasted so good. I certainly remember toasting Clarissa, The Dangerous Sports Club, you, the molecular clouds, bungee jumping... After that, it got a bit blurred."
"You passed out?"
He looked a bit sheepish. "Well, it was very strong, there was a lot of it, and I hadn't had a drink in weeks. When I came to, there was a siren going off in my ear. It felt like my brain was exploding. I managed to crawl to the intercom. 'TURN THAT NOISE OFF!!!' Or words to that effect....."
"Clarissa answered sweetly, 'I'm afraid I can't darling. This is the docking siren. We're back in Earth orbit.'"
"I was astonished.", Clive said, still rubbing away an imaginary hangover, "How long had I been unconscious for? Somehow I made my way up to the flightdeck. 'Did you enjoy your little snooze dear?' said Clarissa, 'you've been down in engineering for forty eight hours...' She must have suspected something, but I think didn't think she wanted an argument until the cruise was finally over. I had to say something.... 'Did you enjoy the fly by of the neutron star?'"
The train was approaching the station. Hopefully Clive knew how to time his stories.
"Well, she seemed amazingly cheerful. 'The neutron star fly-by was wonderful! Pity you weren't around to see it. Neutron star crusts are amazing things, aren't they? Most of star is degenerate neutronium but on the surface there are very thin layers of almost totally pure elemental material - metallic hydrogen, then lithium, then....'"
The train was pulling in to the platform. "Get on with it!" I cried.
"Exactly what I said!," said Clive. "I had the mother of all hangovers - why should I be interested in pure element crusts of neutron stars. Then something terrifying occurred to me.
'Clarissa dear,' I said, gingerly, '....have we been through customs yet?'
We got up and went to the door. "Clarissa looked at me like thunder and took a sniff of my breath. 'Have you been drinking, Clive?' I nodded, sheepishly, 'Have you still got booze aboard this vessel' I nodded again. 'Clive, darling, how far over the customs limit are we?'
'About eight million gallons, dear. But it's all for my own consumption....'"
We stepped on to the platform and walked towards the station exit. "I thought quickly." Clive continued, "'There's a way out' I said. 'My surfboard. We can blast away from the ship on it, then escape by surfing into the upper atmosphere. The ride might be a bit hairy, but no worse than the time we....'"
We joined the ticket queue. "Clarissa stopped me. 'Your plan has two flaws. First, as you well know, your surfboard only has room for one. So what would I do, thank you? In any case, it's an academic question. Your surfboard isn't there any more. I fired it straight at the neutron star.'"
As he handed in the ticket, Clive's eyes filled with tears in remembrance of his beloved surfboard. "'YOU DID WHAT!' I yelled. 'Well', she said, 'I told you I was interested in the elemental crust of the neutron star. I wanted to blast some off as a souvenir...'"
"Frosty", Clive said, "at that moment I knew we were finished. Fancy shooting my beautiful surfboard into a neutron star."
"I'm sure you were distraught", I said, "but what happened with the customs?"
"Oh, the customs. Well, I declared the alcohol, and they confiscated it all. I heard they had a great party that evening!"
"But what happened to Clarissa?"
"Well," said Clive, as we strolled out of the station, "I think we would have been OK if they hadn't searched us."
"Why, what did they find?"
"Well, it was the samples Clarissa had blown off the neutron star. I was too hung over to take in what she was saying. Metallic hydrogen - fine, it vaporised before she could scoop it up. Lithium - great for depression, but you can get it on prescription. Beryllium, boron, who cares? But elemental carbon...."
"Who wants soot?"
Clive looked at me, "Diamonds, Frosty, diamonds! She had ten million pounds worth of the things hidden in her handbag."
He sniffed. "...And I thought I was her best friend."
Opposite the station was a pub. "Fancy a drink?" I said.
Clive looked at his watch. "Go on, just a quick one. I promised to tell you about the anti-Matterhorn."
The alcohol in giant molecular clouds is a mixture of ethyl alcohol, the sort we drink, with methyl alcohol - poisonous to the human metabolism. But I didn't care.
The Moon & The Apollo Missions
by J. Workman
The Moon is the sixth largest satellite in the solar system. lt is one quarter the diameter of the Earth and eighty times less massive. The surface gravity is one sixth that of our own world, so if you stood on the Moon you would weigh six times less.
The Moons surface is peppered with impact craters of varying size, with the largest being over 200 miles across. There are long snaking rift valleys, one called Schröter's Valley is about two hundred miles long and several miles wide and at least a mile deep. Many impressive mountain ranges skirt the surface. The highest of these are the Apennine mountains, which border the Sea of Rains (Mare Imbrium). This is unusual because most of the other satellites in the solar system have fairly smooth surfaces.
The large seas on the Moon are impact basins, which have been filled in by lava. This lava appears rather runny and is not at all like the more viscous lavas of the Earth, Venus and Mars. Evidence for volcanism has been shown, so it is certain that this process took place on the Moon very early on in its history. The lunar maria is testament to that.
Structurally the Moon has a crust of light silicate rock, with a mantle of heavy silicate material. There is no direct evidence for an iron core, because the Moon appears to lack a magnetic field. The overall density of the Moon is roughly three and a half times denser than water. This value is very similar to the density of compressed rock.
Interestingly there appear to be mass concentrations on the lunar surface called mascons for short. These are particularly noticeable over the lunar maria. What has probably happen is that the heavier and lighter silicate material has separated out, by some unknown process. These mascons were picked up when the speed of the orbiting Apollo spacecraft varied from place to place.
The Apollo missions were originally conceived in July 1960. With greater emphasis being placed on them in May 1961. This was immediately after Alan Sheperds fifteen minute flight into space. The Americans had been pipped at the post a number of times by the Russians. So they were determined to get to the Moon before their rivals.
The aim was to get a man on the Moon before the end of the decade and then return him safely to the Earth. The first initial missions from Apollo 7 through to Apollo 10 paved the way for the first official manned lunar landing.
The dream was realised on 21st July 1969, when Neil Armstrong stepped on to the sea of Tranquility and spoke the now famous words "that's one small step for a man, but one giant leap for mankind." He was shortly followed onto the Moons surface by Edwin Aldrin, leaving Michael Collins behind in the command module orbiting the Moon.
The astronauts spent about two hours on the lunar surface doing scientific experiments. This included collecting moon rock and dust, putting a laser reflector into the lunar soil (to measure the Earth to Moon distance) and testing for Moonquakes. Both Armstrong and Aldrin made a number of observations, which were later confirmed by other astronauts.
1 There was an eerie silence (sound cannot travel in the vacuum of space).
2 The sky was very black (this could eventually be an ideal place to do Astronomy from particularly the optical variety).
3 The horizon was very small, close and appeared to dip downwards (this is because the Moon is a smaller body).
4 The lunar soil appeared to have a distinctly bad odour (maybe the powdered silicates had been scorched by the Sun).
The site of Apollo 11 had really been chosen for its safety. Future missions would land in more interesting and daring places. Furthermore the scientific testing would be more rigorous and longer. Despite the astronauts relatively brief visit to the surface, the mission was a resounding success.
The Apollo 12 mission landed only two hundred metres away from an earlier craft called Surveyor 3. This showed that the Apollo crew had a lot of control over where they landed in a particular area. The target area was in a large lava basin called the Ocean of Storms, near a 56 mile wide crater called Copernicus. Scientists believed that there would be impact ejecta from this crater in the landing area, which could of course be collected and then brought back to Earth for analysis.
The Apollo 13 spacecraft failed to land on the Moons surface, because the engine exploded about 50,000 miles from the lunar surface. This led to a dramatic recovery, which resulted in all three of the astronauts being brought back safely to the Earth.
The Apollo 14 mission included two rookies (new boys) Edgar Mitchell and Stuart Roosa, coupled with that they had an experienced member Alan Shepard (who was the first American in space). Shepard at the time was forty seven and was by far the oldest crew member on any of the Apollo flights.
Touchdown was near a collapsed crater called Frau Mauro, where samples were taken. Shepard and Roosa actually got lost on the Moon trying to find Cone crater. For much of the time they were within reach of the rim, but were unaware of it.
The last three missions Apollo's 15, 16, 17 saw the introduction of a roving vehicle, this enabled the astronauts to travel wider a field and collect a larger variety of rock samples. More adventurous landing sites were chosen, including highland regions. The three week quarantine operation was stopped because it became apparent that the Moon was completely sterile and devoid of any kind of biological material. Nothing could survive there.
The Apollo 15 mission landed in the Hadley Rille area, this feature is a long winding rift valley about one hundred miles long and probably half a mile deep. The target area was within reach of Hadley mountain (a 7000 foot high feature). This was visited by the astronauts.
The Apollo 16 mission visited the lunar highland region called Descartes. It was by far the most dangerous terrain encountered. This time astronauts had the opportunity to collect highland material, which is lighter in colour than the lava plains.
The Apollo 17 mission studied the Taurus-Littrow region and for the first time a professional geologist was on board.His name was Harrison Schmitt but was called Jack for short. Schmitt had problems with his balance and took many tumbles. He did have an exciting time amongst the lunar rocks.
The site had been chosen because the area had dome shaped features, thought to be volcanic. On closer inspection they turned out to be less volcanic than expected. Also some orange soil was found, this turned out to be shocked silicate material which had become glassy by rapid heating.
With each new mission we were seeing:-
1 An increase in the time, that the astronauts were spending on the lunar surface, collecting rocks and doing scientific investigations. Compare Apollo 11 (2 hours), with Apollo 17 (22 hours).
2 An increase in the amount of lunar rock collected from the surface. Compare Apollo 11 (48 pounds), with Apollo 17 (250 pounds).
3 An increase in confidence and know how of the astronauts on the lunar surface and a greater awareness by mission control of the lunar environment.
The six different lunar landing sites, were all carefully planned in advance. With each set of rocks turning up there own little mysteries. There were chemical and physical differences, but basically the rocks contained mixtures of silicates, which are found on the Earth.
These Apollo missions uncovered some but certainly not all of the Moons secrets. It is still not certain where the Moon originated from, many still think that it could have formed from the Earth. It is likely however that it formed as a separate body, because there are many rare elements contained within the rocks. These are much less abundant in the Earths crust.
Undoubtedly humans will set foot on the moon again, but probably this time to establish colonies. it is still not certain when this will occur, as plans are still on the drawing board. Certainly there is plenty of potential for the different aspects of astronomy to be studied in minute detail on the lunar surface.
What Will The European Eclipse Weather
Be Like On August 11, 1999?
By Jay Anderson, NASA / Goddard Space Flight Center
Adapted by Ivor Clarke
To witness a total eclipse of the Sun is a privilege that comes to but few people. Once seen, however, it is a phenomenon never to be forgotten. The black body of the Moon standing out... in sinister relief between Sun and Earth, the sudden outflashing glory and radiance of the pearly corona which can be seen at no other time, the scarlet prominences rising from the surface of the hidden Sun to heights of many thousand miles, the unaccustomed presence of the brighter stars and planets in the daytime, the darkness of twilight and the unusual chill in the air. There is something in it all that affects even the strongest nerves and it is almost with a sigh of relief that we hail the return of the friendly Sun.
Isabel M. Lewis, 1924 A Handbook of Solar Eclipses
The British Isles
Of all of the countries of Europe, the British Isles is the most exposed to the varying weather from the mobile westerly air flows of the North Atlantic. While blessed with mild winters, the dampness, cool summers and meteorological exposure to the westerlies has lead to the pronouncement that the British Isles have "no climate, only weather." Historically, Britain has appealed more to invading northern peoples rather than those from the south. The former found the warm moist climate an improvement on their homelands, while to the latter, especially the French, it appeared illogical to covet such a cloudy, damp and windy land. While good for the 'English lawn', the damp grey skies will not find favour at eclipse time.
But fairness dictates that we note the eclipse comes at the height of summer over the sunniest parts of the English countryside. Land's End and the south coast of England offer the best prospects for sunshine anywhere in the Isles, and so by good fortune the eclipse track is located to its best advantage.
The upper air currents which carry the weather systems onto the islands are predominantly westerly. The main track of invading low pressure centres is north of Scotland, but trailing cold fronts frequently drag across England as these disturbances pass, bringing persistent cloudiness and precipitation. The cooler, drier high pressure systems following these fronts do not always improve the sky conditions, as the colder airmass is often unstable and speckles the afternoon landscape with showers or thunderstorms.
Periodic blocking patterns occasionally interrupt the alternating stream of highs and lows, bringing episodes of stable unchanging weather. This interruption in the variable weather pattern may or may not favour the eclipse observer depending on where the block develops. If the circulation over the islands is anticyclonic, as when a high builds northward from the Azures anticyclone or takes up residence over western France, then sunny dry weather will dominate, likely for several days. However, when cyclonic circulations settle in, especially if the low centre lingers over England, dull grey skies will dominate.
Long term studies suggest that a variable westerly flow can be found about 28% of the time, cyclonic blocking for 24% and anticyclonic patterns for 23%. Suitable eclipse-viewing weather will be found during anticyclonic days and possibly in the wake of cold fronts during the changeable westerly weather. In the wake of a cold frontal passage, coastal areas are more likely to have sunshine than interior locations as the cooling effect of the nearby ocean suppresses the development of convective cloud. This distinction is often enhanced by the formation of sea breeze circulations which can bring a zone of clear skies along the waterfront to an otherwise cloudy day. The zone of clearing will extend inland at best for only a few kilometers depending on the precise nature of the onshore winds.
Realistically, however, climate statistics suggest that England is the least suitable land location from which to view the eclipse except for parts of India and Pakistan where monsoon cloudiness dominates. The satellite-derived climatology shows a mean cloud cover of 50% to 65% across southern England. Surface observations show an average of 5.8 to 6.5 days of the month with scattered cloud and good visibility, slightly lower than much of the rest of western Europe, but only a third of the cloud-free days available in Bulgaria and Romania, and a quarter to a fifth the number of days in the best locations in Turkey and Iran. This rather heavy cloudiness culminates in a meagre 43% of the possible sunshine at Land's End and The Lizzard, which are among the sunniest spots in England thanks to the suppression of convective cloud by sea breezes and a slightly closer position to the semi-permanent anticyclone over the Azures. The effect of these two factors is minor but detectable and can be seen by comparing statistics for Plymouth and The Lizzard. Data collected at the former show a frequency of scattered cloud and good visibility of 5.8 days per month. At The Lizzard this statistic improves slightly to 6.5 days per month. Most climatological studies concede a five to ten percent increase in sunshine to the coastal sites over those inland, but much of this advantage is only realized during unstable convective days, such as those found behind a cold front. This promises a stationary observer only a 45% chance of seeing the eclipse in southern England.
Whatever the cause, low level stratiform clouds are the most likely type of cloud along the south coast. These clouds form as warm maritime air approaches from the south and moves over the colder waters of the nearby English Channel. Such clouds typically cover three-quarters of the sky when present, making a clear patch difficult to find. The best location to find a gap in this kind of cloud cover is to seek shelter against the southerly flow behind the low range of hills which define the spine of Cornwall so that low level winds are flowing downhill and dying the air. The hills near the centre line between Penzance and The Lizard do not accord much protection, in part because they are not quite oriented to lie across the likely direction of the wind. In the event of a heavy layer of low cloud, the eclipse watcher is best advised to sacrifice some of the duration of the eclipse and head northeast along the highway toward Bodmin, leaving the centre line behind. It's a small chance, but the best that can be offered under the circumstances.
France. Germany & Austria
Crossing the English Channel the eclipse track touches down in France over Dieppe and continues across northern France over Amiens and Beauvias, just missing Paris and EuroDisney and continuing on over the cities of Reims, Metz, Saarbruken and Strasbourg.
During the summer months, the 'European monsoon' sets in across the western half of the continent, this is a period of cloudy and showery weather which begins with the onset of westerly winds in mid June and continues into September. At other times of the year the prevailing wind direction aloft is more variable, bringing alternating spells of warm and cold weather. This does not imply that cold air does not spread southward in summer, for cold spells with unstable weather come at intervals of a week or two with frequent weak disturbances bringing showers and thunderstorms. Intervals between disturbances often come with fine and dry weather. Prolonged dry weather in Europe comes when a high pressure system builds northward from the Azures anticyclone.
The varied topography through Germany and Austria creates a wealth of climatic sub-regions, but these are defined more by temperature and precipitation differences than in cloudiness. Cloud patterns are strongly modified by the higher mountain ranges, particularly the Alps and Jura Mountains to the south of the eclipse track, but the main effect of these barriers is to create cloud rather than dissipate it. The prevailing westerly and northwesterly winds are forced to rise up these slopes, cooling and causing clouds to form. Southerly winds, flowing over the mountains toward the eclipse track, would tend to dissipate the cloud and bring dry sunny weather on the downhill side (a process known as a foehn wind in Europe), but southerlies are relatively rare during August and the benefits of the mountain barrier are not likely to be realised.
In spite of the influence of the Alps, there is a steady trend to sunnier skies as the eclipse track proceeds across Europe, and the distance from the Atlantic moisture source increases. The percent frequency of clear skies is about 18% over Normandy on the Channel coast and barely rises above 20% throughout the length of the eclipse track over the rest of France. However, beyond this point the maritime character of the westerly winds becomes more continental, and sunshine frequency begins a slow climb through Germany and Austria. This improving trend is interrupted briefly through central Austria where a branch of the Alps reaches down to the eclipse track and brings an increase in cloudiness. The effect is quite dramatic in the number of hours of sunshine in summer drops nearly 25% across middle of Austria in comparison with its eastern and western borders.
Mean August cloudiness decreases from 60% near Cornwall to 50% near Paris. The mean number of hours of sunshine grows from 6.5 over France to just over 8 hours in Austria, with a matching increase in the frequency of scattered cloud conditions. There is little difference in the prospects between Land's End and Paris, but then a slowly growing probability of seeing the eclipse through Germany and Austria.
There is not much to recommend one part of the track over another other than to suggest that eclipse viewers head eastward to take advantage of the slow climatological improvement. A much more reliable option is to simply await the weather forecasts in the days ahead of the eclipse and pick a site which is forecast to be sunny. While long range forecasts are available out to ten days, they do not become particularly reliable until about five days in advance of the event.
Summing up then, and extracting the smallest details from the statistical record, the best sites along the center line in France will be found from Compiegne, past Reims, to Metz, though the advantage gained is very small. In Germany the most suitable climatology is found from Ulm past Munich to the Austrian border. I n Austria, climatology favours a location near the Hungarian border south of Vienna, though a location near the German border comes in as a close second.
Eastern Europe to the Black Sea
As the track leaves Austria, it also draws away from the influence of westerly winds which have controlled the meteorology up to this point. In summer, the Danubian plains over southern Hungary are affected more by the Mediterranean climate advancing northward from the Adriatic Sea than from the march of Atlantic disturbances. The pronounced effect on cloud cover and the amount of sunshine leaves little doubt that the best European eclipse conditions will be found in Hungary, Romania, and Bulgaria.
For the most part the path follows the lowlands along the Danube River and is protected from stronger weather systems by the Carpathian Mountains in the north and the Balkan Mountains in the south. Prevailing winds blow lightly from the north or northwest, being drawn into a large low pressure system which forms over Iran in the summer. These etesian winds bring dry invigorating air which is constant in direction and speed. Precipitation is mostly in the form of showers and thunderstorms, and tends to be greatest where the winds blow upslope - generally on the northern slopes of the Balkan Mountains.
From Hungary, the eclipse track begins to cross the cloud isotherms at a sharper angle eastward with the result that the mean August cloud amount has dropped to about 45% at the shores of the Black Sea. The amount of sunshine climbs above ten hours per day, more than 70% of the maximum possible. The number of days with scattered cloud or less at eclipse time rises from about half the month near the Austrian border to nearly two-thirds over Bulgaria. The probability of seeing the eclipse reaches 63% at the Black Sea ports of Vama and Constanta, popular summer destinations with beaches and fine Roman ruins to attract visitors and eclipse-seekers.
Thunderstorms have a relatively high frequency of occurrence in eastern Europe and bring considerable cloudiness when present. But this convective cloud relies on the heating of the ground for much of its development, unless pushed by cold fronts or other weather disturbances. Because of this, cloud cover statistics tend to underestimate the chances of seeing an eclipse which takes place in the morning hours or in the early afternoon. The maximum time of thunderstorm development occurs at 6 pm local time, well after the noon hour date for the eclipse. Indeed, the cooling associated with the eclipse may delay the onset of convection for another hour or two. The path crosses Hungary's Lake Balaton, a popular resort area of warm water and sandy beaches. At one time the border between the Ottoman and Hapsburg empires ran down the centre of the lake, and a number of ruined castles dot the northern hills above the lake. The location is easily reached from Budapest. The weather in Hungary is normally stable in summer with occasional long periods (3-4 weeks) of high pressure, cloudless skies and a dry atmosphere. The last 20 years of weather records for the week on either side of the eclipse date have only three days out of the 300 were without sunshine at stations along the track. Sunshine is the overwhelming character of the day, with nearly two thirds of the records showing more than ten hours each day. This is mirrored by statistics for Keszthely ('cast-eye'), a resort and service town on the western shore of Lake Balaton. The 14 days of the month in which scattered cloud is reported at eclipse time at this location is the best in Hungary and comparable with sites in Romania and Bulgaria. Lake Balaton seems to have more than its share of sunny weather, likely a result of the protection afforded by the surrounding heights.
Just after its point of maximum eclipse, the Moon's shadow crosses Bucharest, the capital of Romania. This city of two million promises to be a prime eclipse-viewing site, in part because of the comfort and ease of access, and partly because of the excellent weather prospects and the long eclipse duration. Since the centre line neatly bisects the city, eclipse-viewing can be done from the wide boulevards or one of the many city parks.
The Black Sea and Turkey
The sum of all of the climatological measures points to Hungary, Bulgaria and Romania as the choicest locations in Europe for viewing this event. The shores of the Black Sea offer the greatest prospects of success, with a generous sunny climate enhanced by sea breeze circulations. Other suitable spots can be found all along the track from Lake Balaton eastward. To get any better weather prospects, the eclipse location will have to move to the other side of the Black Sea.
Once across the Black Sea, the lunar shadow's eastward mach moves into the best weather conditions. Weather in the region is dominated by an extension of the large monsoon low over India and Pakistan. While low pressure systems are normally associated with cloud and rain, this particular low lies beneath an upper level high which suppresses the formation of cloud. A weak frontal system extends from northern Iran to the Mediterranean coast, separating moderate temperature and moisture on the north side from the semi-arid airmasses to the south. Upper level winds tend to flow from the west in northern Turkey and from the east in more southerly parts along the track. The narrow coastal plain along the Black Sea coast of Turkey has a Mediterranean climate and represents the airmasses north of the front. This area has sufficient moisture to grow figs, olives, tea and tobacco. Most of the rain falls in winter, but steady northwest winds in the summer season bring occasional convective clouds with showers and thunderstorms.
The eclipse comes ashore at a remote part of the Turkish coastline near the town of Cide. To the east of the shadow path is Sinop, an ancient city of Greek and Byzantine origins. Its most famous native son was Diogenes the Cynic, who is reputed to have replied to Alexander the Great when asked what Alexander could do for him, "Yes, stand aside, you're blocking my light" - a perfect quotation (though not sentiment) to go with a solar eclipse. The scenic road to the center line winds closely along the coast, forced to the edge of the sea by a range of 2000 meter mountains which line the Black Sea coast. Cide, a few kilometers inland from the sea, has a 10 km long pebbly beach nearby which could provide a site to watch the eclipse. Travel time from Sinop to Cide is about two hours. West of the centre line is the regional capital Zonguldak, slightly closer than Sinop, and with good transportation connections to Ankara.
The steady onshore winds along the coast promote the development of convective cloudiness as they rise up the mountain slopes which line the sea, but cloud statistics for Cide and Sinop promise weather at least as favourable as on the Bulgarian coast. Farther south, the track reaches Sim on the eastern edge of the Anatolian Plateau. This city of magnificent monuments has a long history. Cloud rises rapidly here as downslope winds from the surrounding mountains dry the air. Much of the meagre cloudiness is due to occasional summer thunderstorms, though the incidence of rainy days is dwindling rapidly. Nevertheless, some of these thunderstorms can bring violent weather with widespread cloudiness. As in eastern Europe they are primarily an afternoon event, but because the eclipse is later in Turkey and the heating of the ground more pronounced, thunderstorms are more likely here than in Europe at eclipse time. Beyond Sivas the shadow bounces across the eastern limb of the Taurus Mountains, with gradually improving prospects for good eclipse weather.
From Turkey the track passes over both Iraq and Iran where the weather will be superb, but too dangerous to go to. So you will have to take your chance with the sky where you are because travel will be difficult all over Europe on the day of the last eclipse of the millennium.
The Unwanted Menace
By Clive Rogers
The continuing fight against light pollution has led really nowhere fast, no one said it was going to be easy. The more people that write to Councillors, MP's and MEP's the better, the fight is being won slowly but surely as the latest from Bob Mizon in Astronomy Now demonstrates but with your support more could be done.
Some arguments that could be used in correspondence about light pollution are set out below.
May I bring to your attention a growing problem through out the country that I believe needs to be addressed as soon as possible, that is the growing menace of the bright light syndrome. You may already be aware that sky glow is caused by dust and moisture particles illuminated by unguarded lighting seeping into the night skies, thus causing the horrible glow over our cities.
Quite a lot of street lighting is wasted by going upwards into the night sky, where as all the light is needed down near the ground. This could easily be achieved by fitting better reflectors, hoods, shrouds and / or skirts. Thus directing the light downwards, with this done maybe a smaller wattage light (tube or bulb) could be used. This would cause less dazzle and be cheaper to run. I am not suggesting for a moment that all lighting should be switched off as that would be foolish to say the least.
The security lighting that can be bought relatively cheaply from the high street are becoming more common in back gardens etc. These could be fitted with passive infra-red, heat and / or motion sensors to detect / deter any anti-social elements on the prowl. If security lighting must remain on during the hours of darkness simply by directing the light below the horizontal would help.
Astronomers lighting needs are the same as everyone else's. We are not a special breed that shy away if caught in bright lights. What we really are, are ordinary people with a hobby or pastime that takes us out side during the hours of darkness to gaze at the wonders of the cosmos.
Do you realise that the light from the nearest star has taken years to us, so really we are looking at history unfolding.
The reason for my writing is an article in the magazine Astronomy Now, July 1994 issue pages 18-20. I believe the article speaks for itself, especially the picture on page 19 showing England and Europe lit up like a Christmas tree during the hours of darkness.
I am an amateur astronomer who enjoys the company of the stars, but, because my hobby takes me out side during the hours of darkness to observe the richness of the cosmos only to find the night skies an orange colour and most of the faint glories beyond my grasp. I am not the only one suffering this problem, in fact most, if not all amateur astronomers do suffer this problem.
The natural resources of OUR PLANET will not last forever, so is it not logical to conserve them now. Meaning the fossil fuels with which each of us use to warm our homes, cook with and light our surroundings when needed. My point being is in 1992 Britain spent £150 million operating 5.5 million street lights and as much as £40 million was wasted lighting up the night sky.
May I bring to your attention the Campaign for Dark Skies (CfDS) who are trying to save our night skies now before it is too late and our children's children miss out on the glories to be seen. Would you add your voice to ours in asking the people who matter to act now.

redpajama_set_name: RedPajamaCommonCrawl


text:
Obasanjo Working Towards forming a New Political Party – Source
July 4, 2021 BACLAD TV News, POLITICS 0
Former Nigerian President Olusegun Obasanjo is said to be working on forming a new political party to represent disgruntled members of the All Progressives Congress (APC) and the Peoples Democratic Party (PDP).
According to Vanguard, Obasanjo believes that the two major political parties are likely to be entangled in serious legal and political disputes, putting them in jeopardy of contesting and winning the upcoming elections and forming a national government.
According to the source, while the former president may have declared his retirement from politics, he is still involved in people mobilization, notably in choosing who will win significant offices in the 2023 elections.
The source said: "Even as the name for the hybrid party has not been made public as we speak, Baba (Obasanjo) is seriously mobilising his keen loyalists and die-hard supporters across the country to actualise his dream of installing a government that would be answerable to him."
The source also noted that Obasanjo is hoping to harvest many key members of the two major political parties into his new party as a result of the forthcoming preparations for 2023.
The source said Obasanjo is increasingly becoming worried over what he described as the overbearing influence of a South-South governor in the PDP and his simmering altercation with the National Chairman of the party, Prince Uche Secondus.
"Baba is afraid of the growing personalisation of the party by one man and the growing rancour with other stakeholders of the PDP and he does not want to put all his eggs into the troubled ship," the source added.
"In fact, it was for these reasons that the former President has been moving round and consulting with those he believes can help in realising the new political thinking."
The source said Obasanjo has already scheduled a strategic meeting with his loyalists and associates to assess the progress made by the new group for Tuesday, July 13.
It is expected that three former governors of Osun, Jigawa and Kwara states and other coordinators drawn from across the six zones of the country, as well as the structure of the fledgling political movement, would be unveiled.
"The three former governors are to subtly coordinate the activities of the hybrid party in the North-West, North-Central and South-west zones, while efforts are being made to name more coordinators for the remaining areas of the country," the source added.
I was Evicted from Miss Nigeria Contest – Linda Ikeji Share Story
Court Of Appeal Sacks Ned Nwoko, Reinstates Nwoboshi
May 30, 2019 BACLAD TV News, POLITICS 0
Another Person Dead In Ibadan After Sugar's Death Was Pronounce
March 11, 2019 BACLAD TV CRIME, News, POLITICS 0
Court Grants PDP's Sen. Ademola Adeleke N2m Bail
May 7, 2019 BACLAD TV POLITICS 0


Darrin Wright of Wright Chiropractic was the guest speaker at Payson High School's Windows on the Workplace, April 20. Wright spoke to the students about the difference between being a medical doctor and a chiropractor and the benefits of the two. Among other things chiropractors learn about nerves and bones in a way a doctor does not. Wright also shared the enjoyment of his profession with the students.
The PHS tennis team uses being a young team to their advantage by using their quickness and high energy to shut down their opponent. Sitting second in region is a very hard earned spot. With only four seniors on this year's team, most of their players will return next year. The seniors are Jordan Wood first singles, Connor Hart second singles, and doubles Jakob Johnson and Bryce Clyde.
Payson High School Dance Company is excited to announce their upcoming dance concert titled "Tangents". The concert will be held on Thursday and Friday, May 3rd and 4th at 7:00 p.m. in the Payson High School Auditorium. General admission is $5.00, Student admission is $4.00, or $20.00 for an immediate family pass.
Coach Marjie Jo Ralph a speech and debate coach at Payson High School has been awarded a Coach Workshop Scholarship by the National Forensic League to Whitman College. The scholarship, which covers all fees was awarded competitively to outstanding speech and debate coaches based on applications to the program. Coach Ralph is one of just 66 Coach Workshop Scholarship recipients from across the country.
first region match they played at Spanish and showed the Dons how to play some real Tennis.
team captains this year are Jordan Wood and Conner Heart.
"We are definitely ready to take region this year!" said Bryce Clyde.
big assembly that was on March 13.


text:
February 17th, 2015 11:49 am| by admin
For the first time in the station's history, Radio Shalom did not broadcast its usual blend of programs about Jewish culture, music and history on Monday evening.
The control board located in a basement in Nørrebro was silenced for what host Abraham Kopenhagen called "security reasons".
"PET says it's too dangerous," Kopenhagen told DR Nyheder. "We do not feel that it is too dangerous, but we respect the information we are given."
No cops in the doorway
Kopenhagen said that Radio Shalom will be back on the air when PET tells them that it is safe. The security agency offered to protect the station while it was on air, but Kopenhagen turned them down.
"We must do as instructed, but we will not have police standing outside the door," he said. "We would rather close down until it is quiet again. I do not know how long that will take."
The radio station was not the only Jewish institution in Copenhagen that chose to shut its doors following the weekend's attacks, which included the fatal shooting of 37-year-old Dan Uzan, a guard standing in front of the synagogue on Krystalgade by Omar Abdel El-Hussein. The Jewish school Carolineskolen was also closed yesterday.
Calls for greater protection across Europe
Jews across Europe are fearful and calling for better protection in the wake of the Copenhagen attacks. Rabbis in both Britain and France called for better protection at synagogues and schools.
"There is much fear; people are afraid to go to synagogue," Rabbi Menachem Margolin from the organisation European Jewish Community told DR Nyheder.
Rabbi Barry Marcus from London Central Synagogue called the weekend's attacks "very uncomfortable, very disturbing and extremely troubling".
A war on democracy
Margolin said he was "not surprised" by the Copenhagen attacks and wants all Jewish institutions in Europe to be given 24/7 police protection.
"We are disappointed that European governments still do not listen to our cries for help and ensure that all Jews are protected," he said.
READ MORE: Danish imam encourages followers to kill Jews
Rabbi Marcus said that simply beefing up security is not enough.
"For us it is very clear what is happening in Europe," he said. "There is an attack on western European democracy and its values."


text:
package org.seasar.doma.wrapper;

/**
 * A visitor for the {@link Wrapper} interface.
 *
 * @param <R> The result type
 * @param <P> The first parameter type
 * @param <Q> The second parameter type
 * @param <TH> The error or exception type
 */
public interface WrapperVisitor<R, P, Q, TH extends Throwable> {

  default R visitArrayWrapper(ArrayWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitBigDecimalWrapper(BigDecimalWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitBigIntegerWrapper(BigIntegerWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitBlobWrapper(BlobWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitBooleanWrapper(BooleanWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitBytesWrapper(BytesWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitByteWrapper(ByteWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitClobWrapper(ClobWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitDateWrapper(DateWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitDoubleWrapper(DoubleWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default <E extends Enum<E>> R visitEnumWrapper(EnumWrapper<E> wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitFloatWrapper(FloatWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitIntegerWrapper(IntegerWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitLocalDateWrapper(LocalDateWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitLocalDateTimeWrapper(LocalDateTimeWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitLocalTimeWrapper(LocalTimeWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitLongWrapper(LongWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitNClobWrapper(NClobWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitObjectWrapper(ObjectWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitPrimitiveBooleanWrapper(PrimitiveBooleanWrapper wrapper, P p, Q q) throws TH {
    return visitBooleanWrapper(wrapper, p, q);
  }

  default R visitPrimitiveByteWrapper(PrimitiveByteWrapper wrapper, P p, Q q) throws TH {
    return visitByteWrapper(wrapper, p, q);
  }

  default R visitPrimitiveDoubleWrapper(PrimitiveDoubleWrapper wrapper, P p, Q q) throws TH {
    return visitDoubleWrapper(wrapper, p, q);
  }

  default R visitPrimitiveFloatWrapper(PrimitiveFloatWrapper wrapper, P p, Q q) throws TH {
    return visitFloatWrapper(wrapper, p, q);
  }

  default R visitPrimitiveIntWrapper(PrimitiveIntWrapper wrapper, P p, Q q) throws TH {
    return visitIntegerWrapper(wrapper, p, q);
  }

  default R visitPrimitiveLongWrapper(PrimitiveLongWrapper wrapper, P p, Q q) throws TH {
    return visitLongWrapper(wrapper, p, q);
  }

  default R visitPrimitiveShortWrapper(PrimitiveShortWrapper wrapper, P p, Q q) throws TH {
    return visitShortWrapper(wrapper, p, q);
  }

  default R visitShortWrapper(ShortWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitStringWrapper(StringWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitSQLXMLWrapper(SQLXMLWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitTimestampWrapper(TimestampWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitTimeWrapper(TimeWrapper wrapper, P p, Q q) throws TH {
    return null;
  }

  default R visitUtilDateWrapper(UtilDateWrapper wrapper, P p, Q q) throws TH {
    return null;
  }
}

redpajama_set_name: RedPajamaGithub


I have wanted to write a jazz waltz for a long time and when Mary suggested a collaboration I knew this was the right occasion because I have admired Mary's jazz vocal since I joined iCompositions.
Mary agreed to write lyrics. This is her first lyrics. And her first jazz waltz. And I am very amazed with the result.


Set stove top to medium heat.
Sautee onions in olive oil until slightly browned.
Add cashews and raisins and sautee for a minute or so.
Add Chickpea Masala and combine thoroughly with onion, cashew and raisin mixtuer.
Add olive oil as needed to make a dense sauce out of the masala mixture.
Take off heat and add fully cooked rice.


text:
Bakery firms top global sustainable palm oil list
A number of the UK's leading bakery manufacturers and retailers have been named as the most responsible buyers of certified sustainable palm oil in the world.
The World's Wildlife Foundation has scored Allied Bakeries and Burton's Foods with the top score of nine in The Palm Oil Buyers' Scorecard 2011, which asseses companies using certified palm oil in a sustainable way. In addition, Warburton's, United Biscuits and Premier Foods were among the top performers in the report.
In total, 132 food and personal care product businesses from Europe, Asia and Australia were scored out of nine, marked on their commitment to using the product and their pledge to the public to only use palm oil certified by the Roundtable on Sustainable Palm Oil (RSPO) by 2015 or earlier. In addition, the report took into account whether businesses has disclosed the total volume of palm oil it uses and whether this information is published.
Biscuit manufacturer Burton's Foods, which uses between 10,000 and 50,000 tonnes of palm oil a year, has made a commitment to using sustainable palm oil until 2013. Allied Bakeries, known for its Kingsmill and Sunblest brands, uses between 1,000 and 10,000 tonnes per year pledging a commitment to using the product until 2014.
United Biscuits, who produce such brands as Jaffa Cakes and McVitie's biscuits, signed a deal in 2009 to purchase certified palm oil from New Britain Palm Oil for a minimum of two years. The company has said it uses up to 100,000 tonnes of the product each year.
Both Warburton's and Premier Foods have stated that they will use certified sustainable palm for another four years.
Sales of sustainable palm oil more than tripled from 0.4 million tonnes in 2009 to about 1.3 million tonnes in 2010.