text:
\section{Introduction}
Algebraic quartic surfaces are a classical subject of algebraic geometry
and the study of their rich properties has been developed in research
papers and books since the XIX century. Many
different classifications for several classes of quartic surfaces
where introduced (for instance, see~\cite{ROH}, the books~\cite{es}
and~\cite{cn}; for a more complete discussion,
see~\cite{gas},~\cite{pbpt} and the references given there).

In more recent years, many classical results have been reconsidered
and presented in a modern language. In particular, a big effort
has been dedicated to
study the possible singularities on quartic surfaces \cite{Deg},
the number of lines contained in quartic surfaces \cite{gas},
and to study as well the characteristics of monoid surfaces,
as in~\cite{tk1},~\cite{tk2}, where an explicit
description of them in terms of equations can be found
(see also~\cite{jp} and~\cite{bcgm}).
Unlike the well-known case of smooth cubic surfaces, which contain
$27$ lines, the generic quartic surface does not contain lines.
However there are classes of quartic
surfaces which do contain lines, and it has been
shown that the maximum number is
$64$ (see the paper \cite{gas} and its references).

An interesting class of quartic surfaces is given by the quartic monoid
surfaces, that is, surfaces with a triple point. Their
classification in terms of other singularities is given in \cite{tk1} and
\cite{tk2}, while in the forthcoming paper \cite{blt}, it is described
a classification according to the possible configuration of lines they
can contain. In particular, it is shown that a quartic monoid surface
can contain at most $31$ lines; indeed such a result was already obtained by
Rohn in a paper published in 1884 (see \cite{ROH}).

In this paper we aim to study into details the class of quartic monoid
surfaces with $31$ lines. In particular, we want to describe the natural
action of the group $\mathrm{PGL}(4, K)$ on these surfaces, which means
that we are interested in quartic monoid surfaces up to projectivity.
We show that quartic monoid surfaces with $31$ lines
can be parametrized by an open subset $A$
of $\mathbb{P}^1_K$ and, moreover, that for any given points
$a, b \in A$
the corresponing surfaces $Q(a)$ and $Q(b)$ are projectively equivalent
if and only if $a$ and $b$ have the same $j$-invariant.
Furthermore, if $a\in A$ is not a primitive root of $-1$, then the stabiliser
of the corresponding surface $Q(a)$ is a group isomorphic to the
group of permutations $S_3$ of three elements
(which does not depend on the parameter $a$),
while if $a$ is a primitive root of $-1$, then the stabiliser of the
corresponding surface is a group with $18$ elements, isomorphic
to $S_3 \times C_3$, where $C_3$ denotes the cyclic group of order $3$.
If the parameter $a$ is rational, then all the
$31$ lines of $Q(a)$ are rational (i.e. obtained by joining
two points with rational coordinates).
The approach we have followed is quite constructive so that we get (or we
can easily obtain) the explicit equations of all the considered
geometric objects. We have therefore intensively used symbolic
computation tools, and precisely the computer
algebra systems CoCoA~\cite{CoCoA-5} and Sage~\cite{sage}.

\section{Basic properties}
Let $K$ be a characteristic zero field.
By a \emph{quartic monoid of $\mathbb{P}_K^3$} we mean a quartic surface
of $\mathbb{P}_K^3$ which has a triple point (that, w.l.o.g.\ can be assumed
the origin $O=(0, 0, 0, 1)$). Hence the polynomial defining a quartic
monoid is of  the form:
\begin{equation}
Q(x, y, z, t) = t F_3(x, y, z) + F_4(x, y, z)
\end{equation}
where $F_3, F_4 \in K[x, y, z]$ are two forms of degree
three and four, respectively. From now on, for shortness,
we also denote by $Q$
the quartic surface of equation $ Q(x, y, z, t)=0$.

Let $\pi$ be the plane of $\mathbb{P}^3_K$ of equation
$t=0$. We consider on this plane the two curves of equation $F_3=0$
and $F_4=0$, which intersect in $12$ points $P_0, \dots, P_{11}$ on $\pi$.
The quartic
monoid $Q$ contains the $12$ lines given by $O+P_i$. Moreover, if a line
$r$ is contained in the surface $Q$ and does not pass through the origin,
then its projection from $O$ to the plane $\pi$ gives a line
joining three of the points $P_i$'s, see \cite{gas} and \cite{ROH}
(indeed, the intersection
$\{r+O\} \cap Q$ is a quartic planar curve which splits into $r$
and three other lines through the origin, which represent
the three possible collinearities
of three points of $\pi$). This remark has
an immediate consequence: the number of lines a quartic monoid can contain
depends on the collinearities of 12 points of the plane. In particular,
Rohn claimed in~\cite{ROH} that the maximum number of collinear triplets of
points among $12$ points in the plane is $19$,  so that the maximum number of
lines contained in a quartic monoid is $31$ ($19$ from the collinearities,
$12$ from the lines through the singular point). He also gave an explicit
(very elegant) equation of a quartic
surface with $31$ lines, which can be expressed (according to
the formulation of~\cite{gas}) in the form:
\begin{equation}
t\left((x+y+z)^3 +xyz\right)+(x+y+z)(x-y)(y-z)(z-x)
\end{equation}

In the present paper, we want to study into details the quartic monoid
surfaces with maximum number of lines, with particular effort to describe
their possible symmetries.

First of all, the combinatorial problem of finding the maximum number
of collinear triplets of $12$ points of the plane can easily be solved with
the help of a computer. The solution we get (unique, up to permutations
of the labels) is the following (see also Figure~\ref{figA}) (where,
from now on, $(i, j, k)$ is a shortcut to denote the triplet $(P_i, P_j, P_k)$):
\begin{equation}
\begin{array}{l}
(0, 1, 2), (0, 3, 4), (0, 5, 6), (0, 7, 8), (0, 9, 10), (1, 3, 7), (1, 4, 5),\\
(1, 6, 8), (1, 10, 11), (2, 3, 5), (2, 6, 7), (2, 9, 11), (3, 6, 10),\\
(3, 8, 11), (4, 6, 9), (4, 7, 11), (4, 8, 10), (5, 7, 10), (5, 8, 9)
\end{array}
\label{19all}
\end{equation}

\begin{figure}
  \begin{center}
  \includegraphics[height=7cm]{esagono19.pdf}
  \end{center}
  \caption{\small The $19$ collinearities of the
    points described by (\ref{19all}).
    They can be realized starting from
    the $15$ diagonals of an hexagon (of vertices $0, 3, 10, 5, 1, 8$)
    that meet in the further points $4, 6, 7$ and  $2, 9, 11$
    (these last points lie on the line at infinity).}
\label{figA}
\end{figure}

In order to make computations, it is necessary to assign coordinates to
the points.
Up to a projectivity of the plane $\pi$, we can assume that
the coordinates $(x, y, z, t)$ of the points $P_0$, $P_1$, $P_2$, $P_3$, $P_4$
are the following:
\[
P_0,P_1, P_2, P_3, P_4 = (0, 0, 1, 0), (1, 0, 1, 0), (2, 0, 1, 0),
(0, 1, 1, 0), (0, 2, 1, 0)
\]
The remaining points have to satisfy two constraints: they must satisfy
conditions~(\ref{19all}) and they have to lie on a plane cubic curve.
Consequently, the only possible coordinates of the remaining points
turn out to be expressed in terms of  a free parameter $a \in K$ as follows:
\[
\begin{array}{l}
P_5, P_6, P_7 = (1, 1, 3/2, 0), (1, 1, 1/2a + 2, 0), (a + 1, 1, a + 2, 0),\\
P_8, P_9 =  (a + 1, 1, 3/2a + 2, 0), (1, -a + 1, 2, 0),\\
P_{10}, P_{11} = (1, -a + 1, -1/2a + 2, 0), (a + 1, -a + 1, 1/2a + 2, 0)
\end{array}
\]

An easy computation shows the following fact.
\begin{lem}
  The points $P_0, \dots, P_{11}$ are all distinct if and only if $a\not= -1$
  or $a \not= 0$. If the $12$ points are distinct, then they satisfy  the
  collinearities conditions  given by~(\ref{19all}) and no more if and only if
   $a\not= 1/2$, $a\not= 1$ or $a\not= 2$.
\end{lem}

We denote by $D$ the set $\{-1, 0, 1/2, 1, 2 \}\subseteq K$ corresponding to
the degenerate cases of the points.

For a given $a\in K\setminus D$, the cubic curve $C_3(a)$ passing through
the $12$ points $P_0, \dots, P_{11}$ has equation $F_3(a) = 0$, where:
\begin{eqnarray}
  F_3(a) & = & (a - 1)x^3+(2a^2 + 6a - 1)x^2y-3(a-1)x^2z+(a^2 + 4a + 1)xy^2\\
  \nonumber
  & & +  2(a - 1)xz^2 -2a(a+4)xyz+(a + 1)y^3-3(a+1)y^2z+2(a+1)yz^2\nonumber
\end{eqnarray}

In order to construct the quartic monoids, we need quartic curves
of the plane $\pi$  passing
through the $12$ points. For a fixed $a\in K \setminus D$,
let $\mathcal{L}_a$ be the linear system of quartic curves through
the $12$ points.

\begin{lem}
  The linear system $\mathcal{L}_a$ of quartic curves through the $12$
  points $P_0, \dots, P_{11}$ has dimension $4$. If $\ell_1$, $\ell_2$, $\ell_3$
  are three fixed, generic lines in the plane and if $r_1$, $r_2$, $r_3$, $r_4$
  are the four lines passing through the triplets of collinear points
  $(P_0, P_1, P_2), $ $(P_3, P_6, P_{10}), $ $(P_4, P_7, P_{11}), $
  $(P_5, P_8, P_9)$, then a basis for the
  linear system $\mathcal{L}_a$ is given by the four quartics:
  \begin{equation}
  C_3(a)+\ell_1, \quad C_3(a)+\ell_2, \quad C_3(a)+\ell_3,
  \quad r_1+r_2+r_3+r_4
  \label{4quart}
  \end{equation}
\end{lem}

\begin{proof}
  To compute the dimension of the linear system, it is enough to take a generic
  quartic curve of $\mathbb{P}^3$ and to impose that it passes through the
  $12$ points. The computation of the rank of the $12\times 15$
  matrix associated to the
  system, gives the dimension of $\mathcal{L}_a$. In order to speed up the
  computation, it is convenient to observe that the points $P_0, \dots, P_5$
  have fixed coordinates. Therefore, to find the dimension of $\mathcal{L}_a$
  we can solve six of the equations in terms of the others, hence it
  suffices to find the rank of a $6\times 9$ matrix (whose entries are
  polynomials in $a$). It turns out that all the maximal minors are zero,
  while the $5 \times 5$ minors are zero if and only if $a=0$, which is
  excluded by our hypothesis. Finally, all the four quartic curves
  of~(\ref{4quart}), contain the $12$ points and they
  are clearly linearly independent.
\end{proof}
The equation of the quartic curve which splits into the lines
$r_1, \dots, r_4$ is:
\begin{eqnarray*}
F_4(a) &=& y(3ax - 2az + x - y)(2ax + ay - 2az + 3x + y - 2z)\\
& & (ax + 2x + 2y - 2z)
\end{eqnarray*}
Thus, as a consequence of the previous lemma one sees  that all
the quartic monoids with $31$ lines (up to a change of coordinates) have
equation:
\[
 tF_3(a) + (\alpha_0x+\alpha_1y+\alpha_2z)F_3(a) + bF_4(a) = 0
\]
where $a$, $\alpha_0$, $\alpha_1$, $\alpha_2, b$ are parameters in $K$. If
we change the coordinates writing $t-\alpha_0x-\alpha_1y-\alpha_2z$
in place of $t$, we finally get that, up to a change of coordinates,
all the quartic monoids with $31$ lines have equation $Q(a, b) = 0$,
where:
\begin{equation}
  Q(a, b) = tF_3(a) + b F_4(a)
  \label{Qab}
\end{equation}
with $a \in  K \setminus D$, $b \not = 0$. Moreover,  starting from the
same given points $P_0, \dots, P_{11}$, different values of
$b$ give different quartic monoids.

We conclude this section with the following proposition, which shows
that the surface~(\ref{Qab}) does not have singular
points (apart from the origin).

\begin{prop}
  If $a \not\in D$ and $b \not= 0$, then the only singular point
  of the quartic surface~(\ref{Qab}) is the origin.
\end{prop}
\begin{proof}
  If $T$ is a singular point of $Q = Q(a, b)$ different from the origin $O$,
  then the line
  joining $O$ and $T$ is contained in $Q$, therefore every singular
  point of $Q$ lies on one of the $12$ lines of $Q$ passing through
  the origin.  Hence we have to look for singular points among the points
  $T_\lambda^{(i)} = O + \lambda P_i$ (where $\lambda$ is a parameter).
  If we substitute $T_\lambda^{(i)}$ into the gradient of $Q$ and we saturate
  the ideal w.r.t.\ the polynomial $a(a-1)(a+1)(a+2)(a+1/2)b$ we
  always get the ideal $(\lambda^2)$ which means that $T_\lambda^{(i)}$
  cannot be singular.
\end{proof}

\section{Convergent sextuples}

In this section we consider a special configuration of points.
\begin{defn}\label{CS}
Let $\mathcal{E} = (E_0, \dots, E_5)$ be six points in
$\mathbb{P}^3$ satisfying the following properties.
\begin{itemize}
\item All the points are distinct and all are different from the origin $O$;
\item The three lines $E_0+E_1$, $E_2+E_3$, $E_4+E_5$ meet in a common,
  new point $A$;
\item There are no other collinearities among the points;
\item The six points are not contained in a plane.
\end{itemize}
The sextuple $\mathcal{E}$ will be called a \emph{convergent sextuple}.
\end{defn}
A simple example of a convergent sextuple is the following:
\begin{eqnarray}
\left((1, 0, 0, 1),\;
 (2, 0, 0, 1),\;
 (0, 1, 0, 1),\;
 (0, 2, 0, 1),\;
 (0, 0, 1, 1),\;
(0, 0, 2, 1) \right)
\label{csBase}
\end{eqnarray}

Convergent sextuples fulfil the following property.
\begin{prop}
If $\mathcal{E}$ and $\mathcal{F} = (F_0, \dots, F_5)$ are
two convergent sextuples, then there exists precisely
one projectivity which sends $E_i$ to $F_i$, $i = 0, \dots, 5$.
\label{unicaProj}
\end{prop}
\begin{proof}
  We call $R_1$ the intersection point of the lines $E_0 + E_3$
  with $E_1+E_2$,  $R_2$ the intersection point of the lines
  $E_0 + E_5$ with $E_1+E_4$, and $R_3$ the intersection point of
  $E_2+E_5$ with $E_3+E_4$. Then it is possible to verify that
  the lines $R_1+E_4$, $R_2+E_2$ and
  $R_3+E_0$ meet in a common point $A_1$. Let $A$ be the intersection
  point of the lines $E_0+E_1$, $E_2+E_3$, $E_4+E_5$
  as in Definition \ref{CS}. Then the five points
  $A$, $E_0$, $E_2$, $E_4$, $A_1$
  are in generic position. Let now $S_1 = (F_0+F_3) \cap (F_1+F_2)$,
  $S_2 = (F_0+F_5) \cap (F_1 + F_4)$ and $S_3 = (F_2+F_5)\cap (F_3+F_4)$.
  Then, as above, the lines  $S_1+F_4$, $S_2+F_2$ and
  $S_3+F_0$ meet in a common point $B_1$. Let $B$ the intersection point
  of $F_0+F_1$, $F_2+F_3$, $F_4+F_5$. Also now the points $B$, $F_0$,
  $F_2$, $F_4$, $B_1$ are in generic position, then, from the
  fundamental theorem of projectivities, there exists exactly one
  proiectively which sends $A$ to $B$, $E_0$ to $F_0$, $E_2$ to $F_2$,
  $E_3$ to $F_3$ and $A_1$ to $B_1$. It is easy to see that, consequently,
  $E_1, E_3, E_5$ are also sent to, respectively, $F_1, F_3, F_5$.
\end{proof}

\begin{rem}
  It is worthy of note a nice geometric property of a convergent sextuple:
  if we compute in the same way the point
  $A_2$ as the intersection of the three lines $R_1+E_5$, $R_2+E_3$ and
  $R_3+E_1$, then the points $A$, $A_1$, $A_2$ are collinear.
\end{rem}

In every quartic surface $Q$ defined by~(\ref{Qab})
we can find convergent sextuples $\mathcal{E}$ with the further
condition that
the six lines $(E_0+E_1, E_2+E_3, E_4+E_5, E_0+E_2,
E_3+E_5, E_1+E_4)$ are contained in the surface. To see this, we can
proceed as follows.
Take three points $P_i$, $P_j$, $P_k$ among the $12$ points of intersection
of $F_3=0$ and $F_4=0$, with the
following properties:
\begin{itemize}
\item $P_i$, $P_j$, $P_k$ are not collinear (i.e. $(i, j, k)$ is not in
the list~(\ref{19all}));
\item for each of the three couples $(P_i, P_j)$, $(P_i, P_k)$, $(P_j, P_k)$
we can find a point $P_{ij}$, $P_{ik}$, $P_{jk}$ such that the
triplets $(P_i, P_j, P_{ij})$, $(P_i, P_k, P_{ik})$, $(P_j, P_k, P_{jk})$
are in~(\ref{19all}).
\end{itemize}
The plane $O+P_i+P_j$ intersects $Q$ along the three lines $O+P_i$,
$O+P_j$, $O+P_{ij}$ and a further line $\ell_{ij}$ which does not pass through
$O$. Similarly, we find a line $\ell_{ik}$ and a line $\ell_{jk}$ of $Q$.
Then a convergent sextuple is given by the points:
\begin{equation}
\begin{array}{ll}
E_0 = (O+P_i) \cap  \ell_{ij}, & E_1 = (O+P_i) \cap \ell_{ik},
\\
E_2 = (O+P_j) \cap \ell_{ij}, & E_3 = (O+P_j) \cap \ell_{jk}, \\
E_4 = (O+P_k) \cap \ell_{ik}, & E_5 = (O+P_k) \cap \ell_{jk}.
\end{array}
\label{sexExc}
\end{equation}
A convergent sextuple of this form is called a \emph{standard
  convergent sextuple}.
For example, we can choose for $i$, $j$, $k$,  the indices $0$, $1$, $3$
(in this order). In this
case the points $E_0, \dots, E_5$ are:
\begin{equation}
\begin{array}{l}
  (0, 0, 1, 0), \; (0, 0, 1, 4ab), \; (1, 0, 1, 0),\;
  (1, 0, 1, -(a + 1)b),\\
  (0, 1, 1, 2(2a + 1)b), \;(0, 1, 1, (2a + 1)b)
\end{array}
\label{bcs013}
\end{equation}

The relevance of the standard convergent sextuples is given by the following
proposition, whose proof is an immediate consequence of
Proposition~\ref{unicaProj}.

\begin{prop}
  Suppose we have two quartic surfaces $Q = Q(a, b)$ and $Q' = Q(a', b')$
  of the family~(\ref{Qab}), for
  $a, a', b, b' \in K$. Then the two quartic surfaces are
  projectively equivalent if and only if we can find a standard convergent
  sextuple $\mathcal{E}$ on $Q$ and a standard convergent sextuple $\mathcal{E}'$
  on $Q'$ such that the projectivity which sends $\mathcal{E}$ into
  $\mathcal{E}'$ (according to Proposition~\ref{unicaProj}) sends $Q$ to
  $Q'$.
\end{prop}

Let us point out another consequence of
  Proposition~\ref{unicaProj}. Fix
a convergent sextuple $\mathcal{E}_0$, as in~(\ref{csBase}), and take a
basic convergent sextuple $\mathcal{E}$ (as in~(\ref{bcs013}))
on the quartic surface $Q(a, b)$. Then the projectivity which sends
$\mathcal{E}$ to $\mathcal{E}_0$ transforms the quartic monoid
$Q$ into a quartic monoid
passing through the convergent sextuple~(\ref{csBase}). In other
words, we can assume that all the quartic monoids pass
through the sextuple~(\ref{csBase}),
and, moreover, that such a convergent sextuple  is a standard one.

The relevant fact is that in this way the equation of
the transformed quartic monoid has a new equation which does not contain
the parameter $b$ (as soon as we assume it is not zero). Therefore, all
quartic surfaces of~(\ref{Qab}) obtained by different
values of $b$ are projectively equivalent.

Here is the family of polynomials giving the quartic
monoids  for which~(\ref{csBase}) is a basic convergent sextuple:
\begin{eqnarray}
  \label{Qa}
  Q(a) & = & 2ax^3y+ 4ax^2y^2+ 2axy^3 -(2a - 1)(a - 2)x^3z+\\ \nonumber
  & & -(5a^2 - 17a + 5)x^2yz -3(a^2 - 4a + 1)xy^2z + ay^3z+\\ \nonumber
  & & -3(2a - 1)(a - 2)x^2z^2 -(7a^2 - 19a + 7)xyz^2+ 2ay^2z^2+\\ \nonumber
  & & -2(2a - 1)(a - 2)xz^3 +ayz^3 -2atx^2y-2atxy^2+ 2(2a - 1)(a - 2)tx^2z+ \\ \nonumber
  & & 4(a^2 - 3a + 1)txyz -2aty^2z+ 2(2a - 1)(a - 2)txz^2 -2atyz^2 \nonumber
\end{eqnarray}
The polynomial  $Q(a)$  is obtained from the basic convergent
sextuple of~(\ref{Qab})
constructed from the triplet $(11, 10, 9)$, since this choice allows us to
obtain a simpler equation for~$Q(a)$. Clearly, we assume
$a \not \in D= \{-1, 0, 1/2, 1, 2 \}$
so that the surface $Q(a)$ is smooth outside the origin and its $31$ lines
do not degenerate.
We have therefore the following:

\begin{thm}
  Let $K$ be a field of characteristic zero and let
  $a\not \in \{-1, 0, 1/2, 1, 2 \}$. Then
  all quartic monoid surfaces of $\mathbb{P}^3_K$  with no other
  singularities outside of the the triple point
  and with the maximum number of lines
  are projectively equivalent to a surface of equation
   (\ref{Qa}).
  \label{teor1}
\end{thm}
Finally, the points $\bar{P}_0, \dots, \bar{P}_{11}$ of
intersection of the $12$ lines of $Q(a)$ passing through
the origin with the plane $t=0$ have now the following coordinates:
\begin{equation}
  \begin{array}{l}
    (0, 1, -1, 0),\ (1, -1, 0, 0),\ (1, 0, -1, 0),\ (1, 2a - 1, -a, 0),
    \ (1, a - 2, 1, 0),\\
    (a, -2a + 1, -1, 0),\ (1, a - 2, -a, 0), \ (a, -a + 2, -1, 0), \
    (a, -2a + 1, a, 0),\\ \ (0, 0, 1, 0), \ (0, 1, 0, 0),\ (1, 0, 0, 0)
  \end{array}
  \label{Pbar}
\end{equation}
They still respect the collinearities given by (\ref{19all}).

\section{Stabilisers}

Starting from relations~(\ref{19all}), it is possible to construct
all the triplets of points $(i, j, k)$
with the property introduced in the previous section,
i.e.\ such that the sextuple $\mathcal{E}$ given by~(\ref{sexExc})
is standard and convergent in the sense of Definition \ref{CS}.
Note that the number of the possible triplets
is $720$ (indeed, any set of points $\{i, j, k\}$ gives six standard
convergent sextuples,
one for each permutation of the indices $i, j, k$).

Let $\mathcal{M} \in \mathrm{PGL}\,(4, K)$.
We consider the natural action of the matrix $\mathcal{M}$
on $\mathbb{P}^3_K$:
given a point $R$ in $\mathbb{P}^3_K$ of
coordinates $(u_0, u_1, u_2, u_3)$, we
send it to the point $\mathcal{M}\cdot R$, whose coordinates are
(the transpose
of) $\mathcal{M} \cdot {}^t(u_0, u_1, u_2, u_3)$.
Hence $\mathrm{PGL}\,(4, K)$ also acts on
homogeneous polynomials in a natural way: if $F(x, y, z, t)$ is a
homogeneous polynomial, then $\mathcal{M}\cdot F$ is the polynomial
$F\left(\mathcal{M}^{-1} \cdot {}^t(x, y, z, t)\right)$.
According to this definition, if a
point $R\in \mathbb{P}^3$
is a zero of $F$, then the point $\mathcal{M}\cdot R$ is a zero of
$\mathcal{M} \cdot F$.

Let us consider the following problem:
given a quartic monoid $Q(a)$ ($a \in K \setminus D$),
compute its stabiliser w.r.t.\ the action of
$\mathrm{PGL}\,(4, K)$, i.e.\ the group
(in the following, by $\mathcal{M} \cdot Q(a) = Q(a)$
we mean that the
surfaces defined  by the equations $Q(a)=0$ and
  $\mathcal{M}\cdot Q(a) = 0$, respectively,  coincide)
\[
  G_a = \mathrm{Stab}_{\mathrm{PGL}(4, K)}Q(a) =
\{\mathcal{M} \in \mathrm{PGL}\, (4, K) \ | \
    \mathcal{M} \cdot Q(a) = Q(a)\}
\]
The quartic monoid surface $Q(a)$ has the convergent sextuple
$\mathcal{E}_0$ as in~(\ref{csBase}) among
its standard convergent sextuples. If $\mathcal{E}$ is
another standard convergent
sextuple of $Q(a)$, let $\mathcal{M}$ be the unique (up to a
multiplicative constant) matrix such that
$\mathcal{M} \cdot \mathcal{E}_0 = \mathcal{E}$ (see
Proposition~\ref{unicaProj}).
If we compute $Q_\mathcal{M} = \mathcal{M}\cdot Q(a)$, we
have to select those matrices $\mathcal{M}$ such that
$Q_\mathcal{M}$ and $Q(a)$ define the same surface
(moreover, we can also check if there are some
specific values of $a$ such that for that specific value
$Q_\mathcal{M}$ and $Q(a)$ coincide).
Of course, this construction has to
be repeated for the $720$ standard convergent sextuples $\mathcal{E}$
of $Q(a)$.
The computations are not too hard; the obvious way to see when
$Q_\mathcal{M}$ and $Q(a)$ define the same surface, is to construct the
$2\times 35$ matrix $W = (w_{rs})$ whose rows are, respectively,
the coefficients of $Q_\mathcal{M}$
and of $Q(a)$ w.r.t.\ the $35$ monomials of degree $4$ in the variables
$x, y, z, t$. The two surfaces coincide if and only if the rank of
this matrix is one. In principle, the number of minors ($595$) might
seem problematic, but the computation can
greatly be reduced by the following observations: (i) in the matrix $W$
we can erase all the columns in which both entries are 0;
(ii) if in the matrix $W$
the element $w_{1s}$ is not zero but the element $W_{2s}$ is zero,
then the two surfaces cannot coincide and no other computations
are needed; (iii) if $w_{1s} = 0$,
then among the equations which test the coincidence of the two surfaces,
we have to add $w_{2s}=0$.

The following result holds true.

\begin{thm} If $a\in K \setminus \{-1, 0, 1/2, 1, 2\}$ is not a root
  of $x^2-x+1=0$,
  then the stabiliser $G_a$ of $Q(a)$ is isomorphic to the group $S_3$,
  and is generated by the following two matrices:
\[
\left(\begin{array}{rrrr}
2 & 2 & \phantom{-}2 & 0 \\
0 & -2 & 0 & 0 \\
-2 & 0 & 0 & 0 \\
0 & 1 & 3 & -2
\end{array}\right), \qquad
\left(\begin{array}{rrrr}
2 & 2 & 2 & \phantom{-}0 \\
0 & -2 & 0 & 0 \\
0 & 0 & -2 & 0 \\
0 & -2 & -3 & 2
\end{array}\right)
\]
If $a=\varepsilon$ is a solution of the equation $x^2-x+1=0$, then
the equation of the quartic monoid surface $Q(\varepsilon)$
becomes $Q'=0$ where:
\begin{eqnarray*}
  Q' & = & x^3y + 2x^2y^2 + xy^3 + 3/2x^3z + 6x^2yz + 9/2xy^2z+ 1/2y^3z
  + 9/2x^2z^2\\
  & & + 6xyz^2 + y^2z^2 + 3xz^3 + 1/2yz^3
  - x^2yt - xy^2t - 3x^2zt - 4xyzt\\
  & & - y^2zt - 3xz^2t - yz^2t
\end{eqnarray*}
In this case, its stabiliser $G_{\epsilon}$
has order $18$, is isomorphic to
$S_3 \times C_3$
and is generated by the following two matrices:
\[
\left(\begin{array}{rrrr}
2 & 2 & 2 & \phantom{-}0 \\
0 & -2 & 0 & 0 \\
0 & 0 & -2 & 0 \\
0 & -2 & -3 & 2
\end{array}\right), \qquad
\left(\begin{array}{rrrr}
0 & 2 \epsilon - 2 & 2 \epsilon - 4 & 0 \\
0 & -4 \epsilon + 2 & 0 & 0 \\
2 \epsilon - 4 & 2 \epsilon - 2 & 0 & 0 \\
-3 & -3 \epsilon & -3 \epsilon & 4 \epsilon - 2
\end{array}\right)
\]
\label{th4.1}
\end{thm}

\medskip
We finally complete Theorem \ref{teor1} answering the
following question: how many vales of $a$ in (\ref{Qa}) give the same
quartic monoid up to a projectivity?

We can answer the question by mean of computations quite similar to
the previous ones. Let $\mathcal{E}_0$ be the convergent sextuples
given by
(\ref{csBase}) (remember that $\mathcal{E}_0$
is a standard convergent sextuple
for all the surfaces of the family (\ref{Qa})). If $Q(a)$ and $Q(b)$
are two surfaces of the family (\ref{Qa}) which are projectively equivalent,
then there exists a standard convergent sextuple $\mathcal{E}$ of $Q(a)$
such that $\mathcal{M} \cdot Q(a)$ and $Q(b)$ coincide, where $\mathcal{M}$
is the $4\times 4$ matrix which sends $\mathcal{E}$ into $\mathcal{E}_0$.

By repeating the above computation for all the $720$ standard convergent
sextuples and by selecting the cases leading to a positive answer
to the question, we get the following result.

\begin{thm} Let $a, b \in K \setminus \{-1, 0, 1/2, 1, 2\}$
  be two elements and consider
  the two quartic surfaces $Q(a)$ and $Q(b)$ from the family (\ref{Qa}).
  Then $Q(a)$ and $Q(b)$ are projectively equivalent if and only if $a$
  has one of the following values:
  \begin{equation}
    b, \quad \frac{1}{b}, \quad \frac{1}{1-b}, \quad  \frac{b}{b-1},
    \quad 1-b, \quad \frac{b-1}{b}
  \label{jinv}
  \end{equation}
\end{thm}

\medskip
We conclude by noticing how conditions (\ref{jinv}) show that
the  action of
$\mathrm{PGL}\, (4, K)$ on quartic monoid surfaces
of $\mathbb{P}^3_K$ with maximum number of lines is quite similar
to the action of $\mathrm{PGL}\, (3, K)$ on cubic curves of
$\mathbb{P}^3_K$ (see \cite{JH}, Lecture 10).
In particular, two quartic monoid surfaces $Q(a)$ and $Q(b)$
are projectively equivalent if and only if $a$ and $b$ have the
same $j$-invariant.

\begin{rem}
  Among the lines of $Q(a)$, the lines $O + \bar{P}_2$,
  $O+\bar{P}_9$ and $O+\bar{P}_{11}$ can be
  distinguished from the others: they are the only three lines
  through the singular point of $Q(a)$ which intersect only $4$ other
  lines of $Q(a)$ (see (\ref{19all}) or figure \ref{figA}).
  The group $G_a$ corresponds to the permutations of
  these three lines.
  Analogously, the group $G_{\epsilon}$ corresponds to the permutations
  of the three lines above and the cyclic permutation of the three lines
  $\bar{P}_1 + \bar{P}_3 + \bar{P}_7$,
  $\bar{P}_0 + \bar{P}_5 + \bar{P}_6$,
  $\bar{P}_4 + \bar{P}_8 + \bar{P}_{10}$.
\end{rem}

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


text:
Q: ESX Server Setup cannot detect my LAN card I want to install esx server on my system that has LAN card, (Realtec RTL-8110sc)
How to install it?
thanks

A: It's quite likely that the Realtec card is not on VMware's Hardware Compatibility List.

redpajama_set_name: RedPajamaStackExchange


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Fired up, Loughborough started off well and it wasn't long before the hosts opened the scoring with some short sharp passing which eventually landed with Lewis Radcliff who hit a reverse stick shot into the top corner.
AFTER a technical loss last weekend, Town were keen to keep the pressure on for the promotion spot and did so in style with a commanding performance and 6-0 victory.
The pressure continued and Loughborough got their second through a short corner which, after an initial save, landed to Hitesh Patel who set up Guest who also hit with his reverse to make it 2-0.
Chesterfield were playing a direct game, trying to hit the ball from the back to their forwards. This didn't really trouble Town but they created a few opportunities which were calmly dealt with by the keeper and defence. Matt Parry made it 3-0 after picking up a loose ball at the top of the 'D', hitting it hard and scoring via a few deflections from the Chesterfield players.
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Overwatch | When Should I Switch My Hero?
Hey guys, today our Overwatch boosting team will be going over tips and advice on switching heroes. Overwatch is unique best it grants players the ability to switch heroes right in the middle of a game. You are able to start off as one character and switch multiple times throughout each and every match. This is novel for many people since the Overwatch release date, because many other similar games only let you play as one character for the entirety of a match. Since this is so new for many players, they have trouble figuring out when to switch.
Different heroes do well under different conditions. In other words, it is best to switch heroes when you are moving to a new area of the map. You will always be moving throughout the entire map, and setting different objectives. In this situation, it makes sense to be switching heroes accordingly. In many cases you will need to fight close combat, and quickly switch to long distance methods. Here, a character switch would be extremely effective. Check out our Overwatch tier list and make a list of which heroes fit where. Match up their abilities, strengths, and weaknesses with different parts of the map to create a strategic masterpiece that can be used in Overwatch boosting.
It is important to take note of when you teammates are changing their heroes too. In the Overwatch beta, I found this tip to be very helpful. Your allies will be swapping characters all the time, making it best for you to adjust to their movements and vice versa. You're on a team, and paying attention to your teammates will definitely benefit you in the long run in the Overwatch beta. If a teammate switches to a new hero, it's often a good idea for you to switch to their old one in order to maintain balance.
It's always a good idea to work as a pair with a friendly team member. If a character such as Zara or Mercy is on your team, try to match up with them for maximum efficiency. They will appreciate your move, and so will you. There's tons of pairs that work well together in an Overwatch boost session. Once again, paying attention to who's switching and when will help out your entire team. In our Overwatch tier list, you can see which heroes work well together, as this can be quite difficult to know on the spot. Experience will only help you get better at making these calls.
Switch to a hero in order to counter an opponent is very obvious, yet essential. There are moments in a match where you feel viciously weak against a certain opponent. Whether they are a tank or an assassin, switching to keep up with counters is key. There's always a way to counter the enemy, and you just have to figure it out. Learn which heroes will be best against others, and memorize these matchups. You'll naturally learn these while in a Overwatch boost too.
Sometimes it is just a grind to play a certain character or you are starting to do poorly. In this case, you'll need to switch in order to make the best out of the match. Find a hero you enjoy playing and can do well as. It will take a while for you to get comfortable as certain heroes, so taking a break is always a great idea. Since the Overwatch release date, players have been constantly switching in order to determine what works best for them, as an individual and unique player.


2009-08-19 Assigned to ACCESS BUSINESS GROUP INTERNATIONAL LLC reassignment ACCESS BUSINESS GROUP INTERNATIONAL LLC ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: HOPALUK, LIANE B., LAUTZENHEISER, TERRY L., MILES, MICHAEL E.
A fluid filter assembly including a flexible and formable enclosure so as to be useable in many filter applications. The enclosure defines a portion of a fluid flow path residing entirely within the filter assembly, eliminating any fluid contact within the remaining portions of the filter assembly. This flow path is advantageous to reduce the possibility of contamination and to ease in cleaning and maintenance of a device utilizing the filter assembly. The enclosure may be formed of UV-transparent material to allow for UV treatment of fluid passing though the filter assembly. Electronic controls may be combined with the filter assembly to control and monitor fluid flow. Check valves or other closure devices also may be included with the filter assembly to facilitate easy filter changes.
The present invention relates to filters and more particularly to filters for potable water filtration systems.
Fluids are rarely found in nature in a pure state. It is more likely that any fluid has some level of contamination, which may make it undesirable for its intended purpose. There are various methods and apparatuses for removing contaminants from fluids. For example, fluids can be distilled and the condensed vapor resulting in a purified fluid. Another approach is the use of a particulate filter to capture contaminants suspended in the fluid as it flows through the filter.
Water is a fluid that is essential for human life. In many cases, however, naturally occurring water is non-potable (unfit for drinking) due to contaminants contained in the water. Many of these contaminants are particulates, and some are microorganisms. Particulates are easily captured by filters, and UV light is commonly used to deactivate microorganisms.
In many places around the world, water is delivered to customers for consumption in homes, business, and public places. In other situations, water is drawn from local wells, streams, lakes, and other water sources. Naturally, the quality of the water varies widely, even from one municipal system to another, let alone an open body of water. Whether consumers pay for treated water from a municipality, or obtain their water for free from other sources, there is a strong desire for additional water treatment, especially water treatment using filters and UV light exposure.
Water treatment systems, or devices generally consist of a water inlet, a filtering area, a water outlet, and optionally an ultraviolet (UV) light source exposure area for destroying living microorganisms. In many instances, water enters a treatment device and travels a circuitous route within that device before exiting. As a result, water contacts many interior surfaces within such a treatment device. Any surface that drinking water touches must pass a rigorous set of standards to insure that the surface does not contaminate the water. For example, a surface may contain oils from the manufacturing process that could leach into the water being treated. Also, some materials which may be good selections from an engineering standpoint have additional issues that make their use in a water treatment device undesirable, such as aluminum. Aside from defeating the purpose of using a water filter device, removing any contaminants from water-exposed surfaces greatly increases manufacturing cost and overall complexity.
Water filter elements, commonly referred to as "filters", are installed downstream of the water inlet of a treatment device. Filters are generally composed of carbon, various synthetic fibers, or filter membranes. Generally, a compartment is set aside within the device to house the filter, allowing for easy access when the filter is to be replaced. The user/operator of the treatment device may replace the filter manually in order to maintain the intended performance of the device.
Many water filters include a rigid housing, with an internal filtering element designed to trap particles of various sizes. These filters often include components formed of plastic resins. Molding tools for making these filters are expensive, and may require a sizeable production run to be economically viable. Making changes to the treatment device likely results in changes to the filter and may be costly and preferably are avoided.
The aforementioned issues are addressed in the present invention in which the water flow path is constructed of one continuous plastic (such as PTFE) film sleeve, extending through the treatment device, and including a filter element at some point, enhancing the integrity of the water flow path.
In a current embodiment, a film sleeve begins at the water point of entry into the device, whereupon a connection or port would be secured to the front of the sleeve, to provide a watertight seal with the water supply line. Next, the film extends into the device, around and through various internal components, such as a UV light source, before entering the section of the film sleeve containing the filter element. Downstream of the filter element, the film sleeve makes its way through the device until the exit, whereupon the sleeve is terminated with a connection or port using a watertight seal, as used in the entry port. This flow path according to this embodiment also avoids exposing the water to any surface or material within the device, and additionally eliminates any leakage from seals, gaskets, or other means of maintaining water tightness within the device. An added benefit of this embodiment pertains to ease of maintenance and improved serviceability. When the filter element is to be replaced, the user opens the device and removes the entire flow path—the sleeve and the filter element together as a unit—and installs an entirely new flow path with integrated filter element. The result of which is a completely new, water flow path which contrasts with other treatment devices using seals, gaskets or the like which age over time, become brittle, and generally lose their ability to seal, resulting in water leakage.
Alternatively, a flow path using the film sleeve may have a segmented approach. The flow path through the treatment device includes several segments. For example, one segment begins at the entry connection port, where a watertight seal secures the connection to the film sleeve. The sleeve then enters the device and arrives at the filter element, contained in a film sleeve section. Another watertight connection port is secured to the film sleeve to allow the filter element sleeve segment to be detached for replacement. On the other side of the filter element sleeve section is another connection port for connecting to the downstream film sleeve section. A watertight connection secures the film sleeve to the water dispensing line. In this approach, the film sleeve has several segments connected using sonic welding or other plastic-to-plastic joining techniques common in the art. The filter element can then be replaced while the remaining film sleeve sections stay within the device.
The present invention reduces the number of joints requiring watertight seals, or in some instances eliminates them altogether.
As further disclosed, the present invention includes a bag path fluid filter assembly that is the direct fluid water flow path for a water treatment device, and which is made of a plastic formable material, at least some portion of which is UV-permeable, has at least one inlet and outlet flow port connection for water entry and exit, contains a filter element for capturing particles, is optionally equipable with a UV light source and control unit with display, optionally has a flow detector measuring device, and is capable of withstanding varied levels of water pressure. The bag path fluid filter assembly reduces production and material costs, is easier and faster to manufacture, and provides for easy device maintenance.
The present invention optionally includes a flow detector turbine within the flow path.
In at least one embodiment, the plastic film sleeve is preferably made of at least one piece of formable material, such as polytetrafluoroethylene (PTFE), but may be constructed of other plastic materials now known or as may become available or offer physical characteristics which are applicable to film sleeve construction.
In at least one embodiment, the plastic film sleeve material is UV-light permeable, allowing for UV light to permeate the film sleeve to deactivate microorganisms that may be in the fluid flow path. Additionally, the film sleeve material withstands the UV light exposure without degradation. This embodiment isolates the water within the film sleeve that is UV permeable and can withstand the affects of UV light.
In another embodiment, check valves are added to each inlet and outlet connection port to prevent water from escaping and contaminants from entering during filter changes or other maintenance and assembly.
In another embodiment, water flow paths are added to the bag path fluid filter enclosure to accommodate a UV light source. The enclosure with flow paths is made of a material that allows UV light to pass through without degrading the enclosure material. Electronic controls with display are optionally located on enclosure surface, so as to control and measure the UV light source output, water flow, and other parameters.
In another embodiment, the bag path fluid filter assembly contains a filter element, a water flow detector or measurement device, such as a turbine, and is sealed along with a reinforcing sealing band. Water flow fittings are located on the filter element enclosure. One fluid flow path on the enclosure includes a UV light source exposure area and a UV light source (e.g., in a circular or annular bulb shape). Near the UV light source area are located the electronic controls, including an optional user display. A UV transparent pressure window in the UV light exposure area optionally provides additional strength to the water flow area for high water pressure installations and situations while still allowing UV light to contact the water to be treated.
For a better understanding, together with other and further features and advantages thereof, reference is made to the following description, taken in conjunction with the accompanying drawings.
It will be readily understood that the components of the present disclosure, as generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of the embodiments of the apparatus, system, and method of the present disclosure, as represented in FIGS. 1 through 16, is not intended to limit the scope, as claimed, but is merely representative of selected embodiments.
Reference throughout this specification to "one embodiment" or "an embodiment" (or similar) means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment thus described. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment.
Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous details are provided, such as examples of bag path fluid filters, etc., to provide a thorough understanding of the embodiments. One skilled in the art will recognize, however, that the disclosure can be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the disclosure.
The illustrated embodiments of the disclosure will be best understood by reference to the drawings, wherein like parts are designated by like numerals or other labels throughout. The following description is intended only by way of example, and simply illustrates certain selected embodiments of devices, systems, and processes that are consistent with the disclosure as claimed herein.
FIG. 1 is a cutaway view of one embodiment.
FIG. 2 is another cutaway view of one embodiment.
FIG. 3 is an exploded view of one embodiment.
FIG. 4 is a cross-sectional view of one embodiment.
FIG. 5 is a perspective view of one embodiment.
FIG. 6 is a perspective view of one embodiment.
FIG. 7 is a cross-sectional view of one embodiment.
FIG. 8 is a cross-sectional view of one embodiment.
FIG. 9 is a perspective view of one embodiment.
FIG. 10 is a cross-sectional view of one embodiment.
FIG. 11 is a cross-sectional view of one embodiment.
FIG. 12 is an exploded view and complete assembly view of one embodiment.
FIG. 13 is an exploded view and complete assembly view of one embodiment.
FIG. 14 is an exploded view and complete assembly view of one embodiment.
FIG. 15 is a cross-sectional view of one embodiment.
FIG. 16 is a cross-sectional view of one embodiment.
In the present specification, specific embodiments are described. However, one of ordinary skill in the art will appreciate that various modifications and changes can be made without departing from the scope as set forth in the claims. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of the disclosure. The benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential features or elements of any or all the claims.
Referring now to FIG. 1, one embodiment is provided. Bag path fluid filter assembly 1 is shown. Plastic film sleeve 2 is formed by extrusion or other plastic forming techniques, to create a cylindrical or annular shape. Other shapes may be used, such as oval, as is desired. The plastic comprising the film may be any type which is formable into sheet films, preferably PTFE, but other suitable plastics may be used. PTFE is a preferred material for its inert properties and its UV properties. Once the film sleeve is formed in the desired shape, sealing band 3 is placed about the outside diameter of the sleeve 2 in the location where filter element 4 will be located. Sealing band 3 is preferably constructed of a plastic material and is secured to the film sleeve by sonic welding or other appropriate joining method. Once sealing band 3 is located and secured, filter element 4 is positioned within the film sleeve 2 such that sealing band 3 is directly in-line with the filter element 4. Sealing band 3 acts as a reinforcement and strengthening member as the fluid flows through the filter element 4.
Supply water can vary in line pressure, depending upon location and infrastructure, among other reasons. Because of this potential for pressures to be high, low, or varied, the bag path fluid filter must be able to withstand pressure within reasonable limits. Based on research and experimentation, water pressure can vary from a few pounds per square inch (psi) to as much as 120 psi (over 8 atmospheres) in some localities. Thus, the strength of the enclosure material, the sealing band, and the filter preferably are selected to withstand such pressures. The enclosure halves are fused together using traditional plastic joining techniques, such as heat welding, and the sealing band, located about the filter, is joined to the connected halves in a similar manner or other manner as appropriate. As a result, the filter is now watertight, and also importantly, the water path is restricted to the filter and not any other component of the filter device, thus reducing undesirable issues with surface contact and contamination and safety regulations.
Any contaminants are therefore substantially confined, reducing the need to clean the water path (or any other component) of the water treatment device in periodic maintenance or service. A treatment system user simply disconnects the water inlet and outlet connections, discards the exhausted filter and accompanying water path and replaces with a new filter/water path combination. Contaminants within the removed flow path remain in the removed flow path, and the cleanliness of the device is enhanced. Seals or gaskets are eliminated along the water path of the device because the assembly is the sole water path. Thus, the manufacture of a device incorporating the present disclosure can be simpler and less costly, while still providing desired levels of water purification, and can be much simpler to maintain and operate.
FIG. 2 illustrates the construction of another embodiment. Bag path fluid filter assembly 10 is shown. The originally open ends of film sleeve 11 are sealed about inlet/outlet ports 14 using sonic or heat welding or other appropriate plastic joining methods, such as adhesives if desired. Preferably, sonic welding or other plastic-melting type sealing is used to avoid introduction of other components to the fluid flow path. Sealing band 12 is disposed about filter 13 located within the cavity formed by film sleeve 11. Inlet and outlet ports 14 are preferably made of plastic and allow for fluid to flow into and out of the treatment device, and provide locations where fluid pipes or lines may be connected. Additionally, ports 14 may include check valves to prevent fluid from leaking out of the device during service, such as when the device is replaced with a new example (e.g., when the filter element is full).
FIG. 3 illustrates another embodiment. Bag path fluid filter assembly 20 is shown complete, and in an exploded view. In this embodiment, plastic film sleeve 21 is formed in two halves, but may be formed in a plurality of portions as desired for particular applications using plastic forming methods such as pressure molding. Film sleeve halves 21 are formed so as to be adaptably joined together with sealing band 22, also made of a plastic material. Disposed within the two halves of film sleeves 21 is filter element 23 of a shape that coincides with the shape of the film sleeve so that the filter element 23 nests within the two film sleeve halves 21. Attached to either half of film sleeve 21 is an inlet or outlet port 24, which optionally may also include an integral check valve to prevent fluid from leaking out of the filter assembly 20, such as during filter replacements or other service or installation activities.
FIG. 4 is a cross-sectional view of an embodiment including a bag path fluid filter assembly 30. Plastic film sleeves 31, formed in half sections in this embodiment, are joined together by sealing band 32, enclosing filter element 33. Sleeve halves 31 and sealing band 32 are joined together to form a watertight seal, using joining methods such as sonic or heat welding or other methods appropriate for water or other fluid connections. On either half of sleeves 31 is at least one inlet/outlet ports 34, allowing fluid to enter and exit the filter assembly 30. Optionally, the ports 34 include a check valve or other quick-connect style attachment for easy installation, service, or maintenance.
FIG. 5 illustrates another embodiment. Bag path fluid filter assembly 40 is shown, with two film sleeves 41 joined together with sealing band 42, enclosing filter element 43. Inlet/outlet ports 44 are shown attached to film sleeves 41 to provide for fluid entry and exit from the enclosed filter element 43. Fluid delivery lines 45 (inbound and outbound) are shown attached to ports 44, which transport fluid to and from the treatment device. The inbound, or supply line, may be attached to a water supply line, for example, as in a residence or restaurant. The outbound line, carrying filtered and treated water, may be attached to a dispenser faucet, cooking apparatus, or ice maker, among many possible uses.
FIG. 6 is another illustration of one embodiment. Bag path fluid filter assembly 50 is shown, with two plastic film sleeve halves 51 joined together with sealing band 52. Enclosed within the cavity formed by the two sleeve halves 51 is filter element 53. At least one inlet and outlet port 54 is provided, attached to film sleeves 51. All connections are fluid and watertight, using joining methods as disclosed above. Ports 54 may optionally include check valves, quick-connects, or other connecting methods that are suitable for fluid connections and prevent leakage. Delivery lines 55 are shown, positioned to be connected to inlet/outlet ports 54. On either end of delivery lines 55 is provided another set of ports 56 that selectively engage ports 54, allowing for fluid to be delivered to the device and to be removed from it as well, after filtering and treatment. Lines 55 may be flexible, and constructed of a material which allows for flexibility while providing strength and durability, such as plastic. Optionally, lines 55 may be located within a treatment device, following the contours and routing within the device, to isolate the fluid from directly contacting the surfaces of the water treatment device. For replacement, the assembly is removed from the device, including the lines 55, and a new assembly of the present disclosure is inserted into the vacated cavity, connected to water supply and delivery (inbound and outbound) lines, and the device is then closed around the assembly disclosed herein and is ready to resume treating and dispensing water for consumption (further illustrated below).
FIG. 7 illustrates another embodiment. Treatment device 60 is shown, with cavity 66. Within cavity 66 is a bag path fluid filter assembly embodiment. Film sleeves 61 joined together by sealing band 62 and enclosing filter element 63 are shown. Inlet/outlet ports 64 are connected to sleeves 61 providing for fluid entry and exit from the enclosure formed by sleeves 61. Delivery lines 65 are shown connected to ports 64. Lines 65 follow the flow path 67 within device 60, isolating the fluid and preventing it from contacting any surface of device 60 directly. Lines 65 may include connection ports of their own, for ease of installation and service, or the lines may be integral to the installation location where device 60 is located (e.g., hard-connected).
FIG. 8 illustrates another embodiment. Treatment device 70 is shown, with cavity 76. Within cavity 76 is an embodiment of the bag path fluid filter assembly. Film sleeves 71 are joined together by sealing band 72 and enclose filter element 73 as shown. Inlet/outlet ports 74 are connected to sleeves 71 providing for fluid entry and exit from the enclosure formed by sleeves 71. Delivery lines 75 are shown connected to ports 74. Lines 75 follow the flow path 77 within device 70, isolating the fluid and preventing it from contacting any surface of device 70 directly. Lines 75 may include connection ports of their own, for ease of installation and service, or the lines may be integral to the installation location where device 70 is located (e.g., hard-connected). Ultraviolet (UV) light source 78 is provided, within device 70 and along flow path 77, exposing fluid in delivery line 75 to UV radiation to deactivate microorganisms contained within.
FIG. 9 illustrates another embodiment. Delivery line 80, which is connected to bag path fluid filter assembly (not shown), includes plastic film sleeve 81 (constructed identically as said assembly), inlet/outlet ports 82, and UV exposure window 83. The connection joints between sleeve 81, ports 82, and window 83 is watertight, using such methods as disclosed above. UV light source 84 emits UV light, which passes through window 83, wherein fluid passing through is irradiated, thus deactivating microorganisms contained therein. Line 80 may be installed in a treatment device flow path (not shown), isolating the fluid within from contacting the surfaces of the device.
FIG. 10 illustrates another embodiment. Film sleeve 90 is shown, including delivery line 91, formed of a plastic. Flow detector 92 is located within line 91, and measures the fluid flow rate passing through line 91. The flow detector may be integrated within any portion of the device disclosed herein, either before or after the filter element, or both, to measure the rate of fluid flow. The measurement of fluid flow is useful for several reasons, such as filter life measurement, fluid pressure, and usage. Flow detector 92 includes a plurality of vanes 93, which are positioned in the fluid flow path, so as to be acted upon by the force of the fluid flowing through line 91. At least one of the vanes 93 includes a measuring device, such as a magnet 94, which allows for a measuring device (not shown) positioned outside and adjacent to line 91 to measure the flow rate electronically. Alternatively, other means for measuring rotational movement and/or velocity may be used, such as a laser, short range radio transmitter, or other rotational velocity detector as appropriate. Flow detector 92 rotates about an axle 95, which is secured to the flow detector chassis (not shown) and allows free rotation within the fluid flow.
FIG. 11 illustrates another embodiment. Film sleeve 100 is shown in cross-section, including delivery line 101, formed of plastic. Flow detector 102 is positioned within line 101, such that no fluid may bypass it. The only path for fluid to follow is to flow through the vaned wheel of flow detector 102, which includes vanes 103. As disclosed previously, at least one vane 103 also includes magnet 104 attached to vane 103. The axle 105 of flow detector 102 allows for the rotation of the vaned wheel. As the wheel rotates, the magnet 104 passes by measuring device 106, located adjacent to flow detector 102 but outside delivery line 101. The passing of the magnet is detected by the device, which records, measures, and outputs the data to the treatment device (not shown). The data may be used to measure filter life, flow rate, or usage, among other relevant data that can be calculated using fluid flow information.
FIG. 12 illustrates a filter assembly 110 according to one embodiment. Filter element (not shown) is enclosed by the two enclosure halves 111 and securely sealed by sealing band 112. A pair of fluid fittings 113 are shown, one on either enclosure half 111 for accepting supply water and allowing treated water to exit the assembly. Ultraviolet light source 114 is disposed within a cavity formed into water flow path 115. A flow detector (not shown) may be located within flow path 115 to measure the flow rate of the treated water. Reflector 116 is disposed adjacent to UV light source 114 to reflect UV light not directed at the water to be treated, and to shield the outside environment from UV light exposure. The reflector 116 may be made of metal, such as aluminum or stainless steel, or any other suitably reflective material, such as plated plastic and is secured about the UV light source 114 using a variety of fastening means. Electronic controls 117 are located adjacent UV light source 114, and may include equipment for monitoring fluid flow rate as measured by the flow detector, and also provide additional controls and displays for operating the treatment device, such as power on/off, filter life remaining display, and other controls and displays as appropriate for a treatment device.
The embodiment shown in FIG. 12 includes UV water treatment and particulate filtering as in the previous embodiment. Incoming water enters a flow path 115, via entry port 113, and is routed through paths adjacent to the UV light source 114. As the enclosure material allows UV light to be transmitted through without degrading the PTFE material, the microorganisms that may be present in the water are deactivated. Before the water passes the UV treatment portion of the flow path, the water enters the enclosure formed by halves 111, is filtered for particulate matter by the filter (not shown), then exits the enclosure through the outlet fitting 113, and to the final dispensing location, such as a faucet or other dispenser. A reflector 116 is positioned outboard of the UV light source 114, to direct any light not originally projecting toward the enclosure and the water flow path back toward the water flow path. Additionally, the reflector prevents any UV light from escaping beyond the filter. Arranged near the UV light source 114 and reflector 116 are the control electronics 117 for the light source and the monitoring device for the flow detector turbine, if so equipped. The control electronics monitor the flow rate of the water, the UV light source, and provide additional functions such as on/off and filter life remaining. A display is located adjacent to the control electronics which provides visual and/or audio information to a user and enables the user to make selections based on desired operational modes.
FIG. 13 illustrates one embodiment, a cutaway view of complete filter assembly 120 with filter element 122 located between enclosure halves 121 and sealing band 123. Water flow path 125 is shown in two halves prior to welding the halves, after which it is connected to a mating pair of holes in one of the halves 121 and aligned parallel to the joined halves as shown.
FIG. 14 illustrates another embodiment, an exploded view and assembled view of filter assembly 130 with filter element 132 and flow detector 141 enclosed by two enclosure halves 131, sealed and reinforced by sealing band 133. A pair of fluid fittings 134 are located one on each enclosure half 131. Each enclosure half 131 also includes an integrated water flow path 136. Ultra-violet light source 135 is disposed around reflectors 137 and UV-transparent pressure windows 140. Flow detector 141 measures and directs water to flow around the pressure windows 140 for UV light exposure and treatment. Controls 138 and display 139 are located within the circular cavity created by the UV light/reflector/flow detector layout for compactness in this embodiment. Controls 138 provide power to the UV light and monitor the flow rate of the fluid, filter life, and other water treatment appropriate information.
Water flows into the fluid inlet fitting of the filter, and enters the flow detector. There, the water moves through the flow detector, which causes it to spin, much like a turbine or a propeller in some embodiments. Sensors in the control electronics monitor the revolutions of the flow detector and use that information to conduct other operations, such as displaying the flow rate for the user. Water enters the filter element where particulate matter is removed. Water then moves around the flow detector and is exposed to UV light from the UV light source that surrounds the flow detector. A reflector directs wayward light back toward the UV transparent pressure window, which separates the UV light source from the water and the flow detector. Treated water then exits the enclosure through the fluid outlet fitting, to a tube attached to a dispensing unit (not shown) for consumption or other purpose by the user.
FIG. 15 is a cross-sectional view according to one embodiment. Bag path fluid filter assembly 150 is shown, with enclosure halves 151 shown banded together and reinforced by sealing band 153. Included in one half of enclosure 151 is flow detector 161. As water flows through sealed enclosure half 151, it causes the vanes, paddles, or other water engagement devices of the flow detector 161 to be disposed in the flow path 156, resulting in the rotation of the flow detector, the speed of which is monitored by electronics 158 and displayed to the user by display 159. Additionally, the flow detector insures that the water flows evenly about the UV light source 155 so that all water is exposed for proper treatment. One portion of enclosure 151 includes UV transparent pressure window 160 which allows ultraviolet light from light source 155 to pass through it and treat the water as it flows through the filter 152. Light from light source 155 is reflected by reflector 157 located outboard of UV light source 155, so as to directed light received from light source 155 back toward UV transparent window 160 and then into the water passing through the UV treatment section. Water enters and exits the assembly through flow ports 154.
FIG. 16 is a cross-sectional view according to one embodiment. Assembly 170 is shown, with enclosure halves 171, enclosing filter element 172, sealed together and reinforced with sealing band 173. Water fittings or ports 174 are shown connected to enclosure halves 171, with at least one for water intake and at least one for water outtake. UV light source 175 is of an annular type in this embodiment, and is shown adjacent to fluid flow path 176. Fluid path 176 also includes a plurality of UV transparent pressure windows 180. In order to enhance the UV light exposure to the fluid to be treated, reflector 177 is used to direct UV light that does not directly project into the water fluid flow path 176, back towards the flow path 176. Reflector 177 also has the additional effect of shielding UV light from escaping the assembly 170. Electronic controls 178 are located adjacent to UV light source 175 along with display 179 which enables a user to operate and monitor the assembly.
Although illustrative embodiments of the present disclosure have been described herein with reference to the accompanying drawings, it is to be understood that the disclosure is not limited to those precise embodiments, and that various other changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the disclosure.
a filter element within the enclosure portion and having a periphery engaging said enclosure portion.
2. The fluid filter assembly of claim 1, further comprising a sealing band about the sleeve, the sealing band sealing the sleeve against the filter periphery and strengthening said enclosure portion against fluid pressure.
3. The fluid filter assembly of claim 1, wherein said filter enclosure portion comprises a plurality of sub-portions, sealably connected to each other.
4. The fluid filter assembly of claim 1, wherein said enclosure portion and said sealing band are made of plastic.
5. The fluid filter assembly of claim 1, wherein said enclosure portion and said sealing band are made of formable material.
6. The fluid filter assembly of claim 1, wherein said assembly further comprises a UV light source and a reflector.
7. The fluid filter assembly of claim 1, wherein said at least one inlet and outlet ports include closure devices.
8. The fluid filter assembly of claim 1, wherein said enclosure portion and said sealing band are selectively connected to each other.
9. The fluid filter assembly of claim 1, wherein said enclosure portion is made of UV-permeable material.
10. The fluid filter assembly of claim 1, wherein said enclosure portion includes a plurality of fluid connections adapted to allow fluid to enter and exit said enclosure portion.
11. The fluid filter assembly of claim 1, further comprising a fluid flow measurement device for measuring fluid flow.
12. The fluid filter assembly of claim 1, further comprising an electronic control unit and a display.
13. The fluid filter assembly of claim 1, wherein the flow of said fluid is measured by electronic means for determining flow velocity.
a flow measuring device for measuring fluid flow.
15. The fluid filter assembly of claim 14, wherein said at least one filter enclosure portion further comprises a plurality of enclosure sub-portions, selectively sealably engagable to each other.
16. The fluid filter assembly of claim 14, wherein said at least one enclosure portion and said sealing band are made of plastic.
17. The fluid filter assembly of claim 14, wherein said at least one enclosure portion and said sealing band are made of formable material.
18. The fluid filter assembly of claim 14, wherein said at least one inlet port and said at least one outlet port include closure devices.
19. The fluid filter assembly of claim 14, wherein said at least one enclosure portion and said sealing band are selectively connected to each other.
20. The fluid filter assembly of claim 14, wherein at least one of said at least one enclosure portion and said sealing band are made of UV-permeable material.
21. The fluid filter assembly of claim 14, wherein said flow measurement device uses electronic means for determining flow velocity.


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I'm extremely excited to be back with Environment for the Americas. I had an amazing experience interning with EFTA in 2013 and I am very proud to be a returning intern. When I was informed that the internship training was going to be held in San Diego, CA this year I was excited to go birding in such a new and amazing place. The warm weather California has to offer this time of year was also rather enticing since the San Luis Valley was covered in a couple of feet of snow.
The San Diego, CA shorebird training was an awesome experience. It was really neat to see how the EFTA shorebird training program has evolved and improved over the last two years. Even though this was my second shorebird training I have participated in, I still found the information they presented to us extremely helpful. It was amazing to work alongside so many people who truly have a passion for what they do, our environment, and the wildlife. EFTA interns are always some of the best people I have met. I was an EFTA intern in 2013, I worked alongside the SLV EFTA interns from last year and I could not be happier to work with the interns of 2015. I cannot wait to see what new and exciting opportunities this summer to brings us!


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text:
Q: upgrade no longer appears My updates reminder used to suggest upgrade to Ulyana from Tricia, but no longer does so.  I think I've switched something off.  Can I get it to revert to offering,Which looked a lot easier) or do I have to upgrade from the internet now?

A: You should be able to go to the Application Menu -> "Administration" -> "Update Manager", and use the update using that. Here is an article that will give you a step-by-step run-through of what to do. Specifically at step 3. If that is confusing to you, see the video at the end of the article that will show you.


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Khabarovsk kraj, (, ) er en kraj i Rusland og en af de 83 føderale enheder i den russiske føderation. Krajens areal er på 787.633 km² og har  indbyggere. Krajens administrative center er placeret i Khabarovsk, der med sine  indbyggere er krajens største by. Andre større byer er Komsomolsk ved Amur med  indbyggere og Amursk, der har  indbyggere.

Khabarovsk kraj ligger primært ved den nedre del af Amur-flodens bækken, men har også et stort bjergrigt område langs kysten af Okhotske Hav, en arm af Stillehavet.

Byer
 Amursk
 Khabarovsk
 Komsomolsk ved Amur

Referencer

Eksterne henvisninger

redpajama_set_name: RedPajamaWikipedia


text:
Social-Class Discrimination Contributes to Poorer Health
Health Effects of Stress
Discrimination felt by teenagers based on their social class background can contribute to physiological changes associated with poorer health, according to a new study published online in Psychological Science, a journal of the Association for Psychological Science.
Lead author Thomas Fuller-Rowell, a researcher at the University of Wisconsin-Madison and a Robert Wood Johnson Foundation Health & Society Scholar, says that while the link between poverty and poor health has long been known, this is one of the first studies to consider the impact of class discrimination.
"The findings of our study suggest that the stress caused by social-class discrimination may be an important factor in explaining the negative influence of poverty on health,'' says Fuller-Rowell.
The study looked at 17-year-olds from upstate New York enrolled in a long-running Cornell University study of rural poverty. The vast majority of the 252 teens were white, so the study did not look at the effect of race.
"Experiences of discrimination are often subtle rather than blatant, and the exact reason for unfair treatment is often not clear to the victim," says Fuller-Rowell. For these reasons, rather than asking the study participants if they had experienced discrimination specifically based on their class background, the study measured general perceptions of discrimination. For example, they were asked: "How often do people treat you differently because of your background?"
Then researchers took overnight urine samples, and other tests to assess stress on the body, including measures of blood pressure and stress-related hormones such as epinephrine, norepinephrine, and cortisol. Together, these factors can measure a person's "allostatic load," a term that describes the negative health changes caused by a frequent exposure to stress.
The study found that teenagers who grew up in poverty reported higher levels of discrimination, and that discrimination, in turn, predicted allostatic load. In other words, the poorer the teens, the more they experienced discrimination, the worse their health measures were. Fuller-Rowell's model suggests that about 13 percent of the negative health effects of poverty on health can be attributed to perceived discrimination.
"Our findings suggest that the stigma associated with poverty can lead to class discrimination, which, over time, can impact an individual's health,'' Fuller-Rowell says.
He says the researchers were interested in the question because despite research showing that negative stereotypes about the poor are pervasive, research has failed to consider the impact of social class discrimination on the poor. Furthermore, discussion of social class discrimination is generally not present in the public discourse in the same way as racial discrimination.
This suggests some possible avenues for helping poor children cope with discrimination. In the same way minority children are often alerted by their parents to possible racial discrimination they may encounter, Fuller-Rowell says, that all Americans may need to get better at talking about class discrimination and its effects.
"Americans tend not to be comfortable talking about social class, because this is supposed to be a class-less country,'' he says. "But in terms of mitigating the effects of class discrimination, talking about it in schools and in the media is a beginning."
Fuller-Rowell's co-authors on the study are Gary Evans and Anthony Ong, both of Cornell University. Support for the study came from the Robert Wood Johnson Foundation Health & Society Scholars program, the W. T. Grant Foundation and the John D. and Catherine T. MacArthur Foundation Research Network on Socioeconomic Status and Health.
News > Latest Research News > Social-Class Discrimination Contributes to Poorer Health
Thomas E. Fuller-Rowell
Hired, Fired, or Stopped by Police: The Discriminatory Stew of Intersectionality and Stereotypes
Perceptions of gender and race combine into unique stereotypes and complex patterns of discrimination. More
Richeson Receives SAGE-CASBS Award for Research on Discrimination and Diversity
A social psychologist at Yale University, Richeson uses a broad range of empirical methods to examine the potential cognitive "costs" and mutual misperceptions associated with intergroup interactions. More
Recent research highlights from APS journals. More

redpajama_set_name: RedPajamaCommonCrawl


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People tend to pay too much attention to the "face problem", so the skincare for the face is always in place, but it ignores the skin care work in other parts of the body. It seems that there is no problem, but the real beauty should be for yourself rather than for Others, and not paying attention to maintaining some parts of their skin, such as the neck, can easily expose your age. Therefore, perfect skin should pay attention to the whole body care. Today, the focus is on introducing the method of exfoliating the body. Only by removing the old dead skin cells can you create a more fair and smooth skin.
Does the body need to exfoliate?
February 14, 2019 February 14, 2019 Categories Beauty & Personal care, Skin care, Women1 Comment on Does the body need to exfoliate?
It is only necessary to exfoliate when the following conditions occur: The skin looks a bit dull, and the touch is also rough and unsmooth; After using the essence and cream, it feels that for a long time, the skin care products "float" on the skin surface and cannot be quickly absorbed by the skin. Exfoliation work is performed for up to 2 weeks. Frequent exfoliation removes the useful stratum corneum, causing the skin to dry out and even become allergic due to loss of protection.


text:
Q: The variance of linear regression estimator $\beta_1$ Can we say
$$\text{Var}(\beta_1) = \text{Var}\left(\frac{\sum (x_i-\bar x)y_i}{\sum (x_i- \bar x)^2}\right) = \left(\frac{\sum (x_i-\bar x)}{\sum (x_i- \bar x)^2}\right)^2 \text{Var}(y_i) \;\;??$$
I am not sure if I can separate the $x$'s i from $\sum (x_i-\bar x)y_i$. This expression seems like a linear combination of $y_i$'s. Is this legit because every $y_i$ follows the same distribution?

A: This appears to be simple linear regression. If the $x_i$'s are treated as deterministic, then things like "variance" are not associated with them, and so the expression holds, under the additional assumption that the the error term (and hence $y$ also) has identical distribution for all $i$, and also, that the error terms (and hence $y$ also) are independent for all $j\neq i$.
For compactness, denote
$$z_i = \frac{x_i-\bar x}{\sum (x_i- \bar x)^2}$$
Then
$$\text{Var}(\beta_1) = \text{Var}\left(\sum z_iy_i\right)$$
The assumption of deterministic $x$'s permits us to treat them as constants. The assumption of independence permits us to set the covariances between $y_i$ and $y_j$ equal to zero. These two give
$$\text{Var}(\beta_1) = \sum z_i^2\text{Var}(y_i)$$
Finally, the assumption of identically distributed $y$'s implies that $\text{Var}(y_i)= \text{Var}(y_j) \;\; \forall i,j$ and so permits us to write
$$\text{Var}(\beta_1) = \text{Var}(y_i)\sum z_i^2$$

A: There are a few way to approach this. Alecos' method is simple and clear. Here's another:
$\hat{\beta}_1=\frac{\sum (x_i-\bar x)y_i}{\sum (x_i- \bar x)^2}=\frac{\sum (x_i-\bar x)y_i}{S_{xx}}=\frac{\sum d_iy_i}{S_{xx}}$
$\text{Var}(\hat{\beta}_1) = \text{Var}\left(\frac{\sum (x_i-\bar x)y_i}{\sum (x_i- \bar x)^2}\right)=\frac{1}{S_{xx}^2}\text{Var}\left(\sum d_iy_i\right)=\frac{1}{S_{xx}^2}(\sum d_i^2)\text{Var}\left(y_i\right)$
You can then inspect $\sum d_i^2$ in order to do some cancelling out in the formula, and you can substitute a value for the variance of the observations.
Compare with the sample estimate of the standard error, $s_{\hat\beta}$ here, which should be similar up to the two obvious differences.


text:
Elio Motors Starts Work On 5th-Gen Prototype
June 12, 2015 June 12, 2015 Steve Hanley 0 Comments 3 cylinder engine, 84 mpg, Elio, Elio Motors, fifth generation prototype car, paul elio
Elio Motors has begun work on its 5th generation prototype. It plans to build 26 prototypes before production begins in mid-2016. The three wheeled car will sell for $6,800 and get 84 miles per gallon, according to the company.
The 5th generation car includes a number of upgrades over the 4th generation prototype. Some styling changes have been made to improve aerodynamics and a multi-mode manual transmission has been sourced from Aisin. But the big news is the newest prototype is fitted with the company's bespoke 0.9 liter 3 cylinder gasoline engine. This represents the first time in 60 years that a start-up car company has designed and built its own engine, according to Green Car Reports.
Elio Motors has formed a partnership with Comau to build the car at a manufacturing facility in Shreveport, La., where General Motors previously built the Hummer H3 and Chevy Colorado. Comau is part of the FCA group that builds FIAT, Chrysler and Alfa Romeo automobiles, so they have a fair bit of experience in how to manufacture an automobile.
To date, 43,000 people have said they want to buy an Elio when it goes on sale. That's about double the number who have signed up for the Tesla Model X. When production begins, the company will employ 1,500 workers at the Shreveport factory. The car contains 90% North American content, which will fuel the creation of another 1,500 jobs at the companies who supply parts for it. Combined, the new jobs are expected to create another 18,000 jobs for people who are indirectly involved in manufacturing or supply parts.
With all the buzz in the auto industry focused on electric and plug in hybrid cars, will there be a place for an inexpensive, basic car that gets great gas mileage? The last company to try that was a little Korean manufacturer nobody in America had ever heard of. Its name was Hyundai and things worked out pretty darn OK for it, didn't they?
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Steve Hanley
Closely following the transition from internal combustion to electricity. Whether it's cars, trucks, ships, or airplanes, sustainability is the key. Please follow me on Google + and Twitter.
Elio Motors Finally Responds … What's Next? You Decide!
June 6, 2014 Jo Borrás 0
The 11 Best Fuel Efficient Motorcycles You Can Buy in 2016
March 23, 2016 Jo Borrás 0
Jo Borras Returns to Gas 2


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Media reports: New redistricting lawsuit filed over congressional districts
In Courts & the Law, News
There has apparently been a new redistricting lawsuit filed — voters from 13 congressional districts across the state are alleging lawmakers unconstitutionally drew maps to benefit Republicans, according to several media outlets.
The lawsuit comes a week and a day after North Carolina lawmakers submitted remedial state House and Senate districts to a three-judge panel after they ordered a redraw because of partisan gerrymandering. It was filed in the same Wake County Superior Court, according to reports.
WRAL posted a copy of the lawsuit online. The court has not yet officially released a copy of the lawsuit.
Senate President Pro Tem Phil Berger, House Speaker Tim Moore, Sen. Ralph Hise (R-Mitchell) and Rep. David Lewis (R-Harnett) — who are all named as defendants in the document — did not respond to a request for comment Thursday from NC Policy Watch.
The suit is over the 2016 congressional map, which is described in the document as possibly "the most extreme and brazen partisan gerrymander in American history."
"There is no dispute that the 2016 congressional map reflects an extreme and intentional effort to maximize Republican advantage," it states. "Legislative Defendants proudly admitted it at the time. They adopted 'Partisan Advantage' as an official criterion, directing that the districts be constructed to 'maintain the current partisan makeup of North Carolina's congressional delegation,' namely '10 Republicans and 3 Democrats.'"
The U.S. Supreme Court heard a similar lawsuit earlier this year but ultimately ruled that partisan gerrymandering was out of the reach of federal courts. That ruling, followed by the successful state challenge to partisan gerrymandering in North Carolina this summer and another previous lawsuit in Pennsylvania has set a roadmap for similar disputes.
The lawsuit filed Friday is being backed by The National Redistricting Foundation. The question of whether lawmakers' remedial state legislative maps enacted last week will stand under court review is still pending.
North Carolina Democratic Party Chair Wayne Goodwin did not respond to requests Thursday about the lawsuit from NC Policy Watch but released a public statement Friday about believing strongly in fair maps.
For more information about the lawsuit, read the full document here.
More In Courts & the Law
Lawmakers will hear public comment on Congressional maps tomorrow
Congressional redistricting at the North Carolina legislature appears to be nearing an end, and the public will have their chance to ...
Voters, Congressional candidate file federal lawsuit over decision to halt use of 2016 map
A group of North Carolina voters and man campaigning for Congress filed a federal lawsuit this week asking the court not ...
Courts & the Law immigration News
Twice defeated, Republicans to try again for forced sheriff-ICE cooperation bill
For the third time, Republicans will try to enact a law that would require sheriffs across North Carolina to cooperate with ...
NC Republicans want Supreme Court opinions that went against them tossed
North Carolina Republican legislators have asked the state Supreme Court to throw out last year's opinions on voter ID and redistricting ...
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There has apparently been a new redistricting lawsuit filed -- voters from 13 congressional districts across the state are alleging lawmakers unconstitutionally drew maps to benefit Republicans, according to several media outlets. The lawsuit comes a week and a day after North Carolina lawmakers submitted remedial state House and Senate districts to a three-judge panel after they ordered a redraw because of partisan gerrymandering. It was filed in the same Wake County Superior Court, according to reports. WRAL posted a copy of the lawsuit online. The court has not yet officially released a copy of the lawsuit. Senate President Pro Tem Phil Berger, House Speaker Tim Moore, Sen. Ralph Hise (R-Mitchell) and Rep. David Lewis (R-Harnett) -- who are all named as defendants in the document -- did not respond to a request for comment Thursday from NC Policy Watch. The suit is over the 2016 congressional map, which is described in the document as possibly "the most extreme and brazen partisan gerrymander in American history." "There is no dispute that the 2016 congressional map reflects an extreme and intentional effort to maximize Republican advantage," it states. "Legislative Defendants proudly admitted it at the time. They adopted 'Partisan Advantage' as an official criterion, directing that the districts be constructed to 'maintain the current partisan makeup of North Carolina's congressional delegation,' namely '10 Republicans and 3 Democrats.'" The U.S. Supreme Court heard a similar lawsuit earlier this year but ultimately ruled that partisan gerrymandering was out of the reach of federal courts. That ruling, followed by the successful state challenge to partisan gerrymandering in North Carolina this summer and another previous lawsuit in Pennsylvania has set a roadmap for similar disputes. The lawsuit filed Friday is being backed by The National Redistricting Foundation. The question of whether lawmakers' remedial state legislative maps enacted last week will stand under court review is still pending. North Carolina Democratic Party Chair Wayne Goodwin did not respond to requests Thursday about the lawsuit from NC Policy Watch but released a public statement Friday about believing strongly in fair maps. For more information about the lawsuit, read the full document here.


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HBO Max looks to woo new subscribers with free episodes
August 3, 2021 In Media and Marketing, Media Production, Motion Pictures and Film, Online Media By Catie Keck
HBO Max is offering free content to potential users. | Image: HBO Max
HBO Max is offering free episodes to potential new subscribers in-app and free of charge so they can take its more popular series for a test drive before committing to yet another streaming service.
The company announced that, starting today, new viewers mulling a subscription can watch a selection of 13 pilots from HBO and HBO Max without having to sign up for the service. Normally, subscribers would pay $10 per month for HBO Max's ad-supported tier or $15 per month to go ad-free and get special perks like 4K streaming and day-and-date releases for Warner Bros films. (HBO Max does not currently offer a free trial.) The full list of series whose pilots can be streaming for free is as follows:


It was a tough year for investors in 2018, with broad declines in stock and bond prices affecting their returns. Sustainable funds, however, demonstrated resilience. This report provides an update on the state of the sustainable fund universe in Europe and looks at how these funds stacked up against peers.