WASHINGTON — When it comes to striking it rich on the lottery, Brody Logan, a reporter at the Fox affiliate in Washington, D.C., does not mince words.
"I want to quit my job if I can," said one woman when asked why she was buying a ticket.
"What you could do is buy a lighter and burn the rest of the ten dollars, and then at least you'd still have a lighter," Logan joked to another woman who was buying $10 worth of tickets.
No winning ticket was sold for the $460 million Powerball drawing so the jackpot jumps to an estimated $550 million for Saturday's drawing.
The Mega Millions jackpot is expected to be $418 million in Friday's drawing.


Finding and working the right problem is often a problem.
Solving problems is like painting. Prepping is ninety percent. That means ensuring we're solving the right problem. It's a common problem.
As example, a call center supported software for sales people. The sales people were giving them poor reviews. Supervisors listened to calls. Support representatives answered questions well. Supervisors were puzzled. However, representatives were answering the right questions to the wrong problems. They weren't qualifying sales people's questions to ensure they were asking the right questions.
Surrounding these are our biases. They encourage us to view problems in ways comfortable to us. We make them fit our experience, expertise, budgets, schedules, understanding and many others.
There are eight generalized biases influencing our perspectives too. They encourage us to view problems in ways we can easily understand, accept and resolve. As a result, we'll end up tackling the easy but wrong problem.
Problems are also like crime scenes. They need enough scope to contain the information and give the perspective we need. Our need for security often as certainty, clarity and simplicity will emotionally trigger us to overemphasize statistics. Expanding our scope means searching and analyzing different types of information, not just the quantifiable.
Details help here. A glass filled with sand looks full. Diving deeper, gaps appear among the sand particles, more spaces to fill. Analogously, they are the gaps hard data leaves to intangible factors. It also means challenging definitions, demanding more specificity and applicability.
Yes, this is work and difficulty, naturally deterring us. This can't deter us from the right problem though. If it does, paint will peel, and we'll soon be painting again.
Brilliant post, Mike. I think it was Aristotle who said: "Well begun is half done." This certainly applies to your wise post.
I firmly believe everyone should develop their personal problem procedure, seeking always to make it better, and using it routinely such that it become habitual – especially in times of stress. Without question, that process must start with the correct problem statement – including what the problem is, what constraints exist, and what criteria will be used to optimize the outcomes. It should surprise no one involved that occasionally the problem statement is that there is no problem to be solved. Two other suggestions, both important during the problem solving process, including developing the problem statement: (1) routinely self-assess; and (2) embrace ambiguity. I'd suggest these help dealing with biases. The last step in problem solving has to be reflection; does it address the problem statement and what, with additional resources, might be done to improve the solution.
Thank you, John, for your insights. Yes, I'm chuckling. Perhaps there is no problem. I do believe as you do that problem solving is highly personal. That's what makes diversity such an important ingredient to innovation. We ensure different perspectives and methods.
Yes, I did read the link – as I always do if I comment and usually do regardless. One of the great positives of the online blogs. Liked the Einstein quote and don't remember seeing it before! I of course believe. One needs to know what problem is to be solved, as does planning. But I also advocate prototyping as quickly as realistic – for testing as refining.
Analytically I think most of us are used to solving problems linearly. We also favor things the we like to do and often avoid things that we are unconfortable with but might be more appropriate. Collaboration helps you work through much of this.
The requirement to be able to think critically, learn effectively, problem solve effectively, and have mastered the appropriate core knowledge does not align with linear approaches AND, I believe, is too infrequently really facilitated in education.
Yes, John, we seriously underestimate the power of looking at undesirable or outlandish solutions. Many times it's those characteristics that help us expand our thinking beyond convention. They might not be the solutions we want, but they might be the paths to the ones we want.
You're right about the linearity of problem solving, Ralph. We usually avoid wandering, tangential or free-response approaches even though they are very successful. Your point about comfort level is very important. Collaboration is a good approach. I qualify it by saying it should have a good level of diversity and conflict. Otherwise, collaboration is nothing more than group think in which everyone is basically looking at the problem in the same way. Nonetheless, the spirit of what you say is important.
I appreciate your insights and stopping by.
Yes, I think the linearity restriction has more to do with time restrictions,dependencies, and tools restrictions. At least in the data analysis part of the problem solving business. And of course linearity is part of the scientific method. I've worked with a few people who have been very creative in the way they approach data problems, yet be unable to express a linear approach to implementing them.
Yes, Ralph, I agree. I've witnessed the same with people's use of data. It seems some are more adept at seeing patterns and connections in data that aren't easily disclosed in more formulaic analyses.


text:
\section{Introduction}

Root-Locus (RL) is a  parametric plot of the roots of the polynomial
$p(s) = d(s) + kn(s)$  over the complex plane, equivalently over the affine plane $\mathbb{R}^2$,
as the parameter $k$ spans $\mathbb{R}$; $d$ and $n$
are fixed coprime polynomials, and $d$ is monic with degree, in general, greater
than the degree of $n$. The polynomial $p$ can represent the denominator of a (proportional) control
feedback loop of a  linear time invariant plant  with transfer function $G(s)=n(s)/d(s)$ (see Figure~\ref{cloop}),
and this makes  the RL a classical approach to study stability and performance of
closed loop feedback systems. The rules for sketching the plot are discussed in most textbooks on
feedback control theory of linear systems (see \cite{dh}).
In a previous paper (\cite{pjrl}) the author showed that the RL plot can be extended
to the  real projective plane ($\mathbb{RP}^2$) and be interpreted as a projective algebraic
variety, that we denominated projective root-locus (PjRL).
In this approach, the RL points, including the ones at infinity,
can be calculated as the solution of a set of homogeneous polynomial equations,
as well as, we can obtain complementary
plots of RL over the different affine planes that make up the projective plane.

\begin{figure}
\begin{center}
\includegraphics{system.pdf}
\caption{\label{cloop}Control Feedback Loop with a Proportional Controller}
\end{center}
\end{figure}

In this paper we use the approach presented in \cite{pjrl} to show how to decompose the RL into several
planes curves that can be plotted independently to form the final RL plot. In fact, at least in some simple cases,
we can easily visualize the RL as a union of several plane curves: for example,
the plot presented in Figure~\ref{rlc}, that represents the RL for $G(s)=(s+1)/s^2$,
is composed by the (parametrized) circle $(x+1)^2+y^2=1$ and by the (parametrized) line $y=0$. In order to deal with this
question in a systematic way, however, we need concepts from algebraic geometry, considering
the RL as an algebraic variety, and the goal is to find its decomposition into {\em irreducible components}
(see \cite[Chap. 4]{clo}).
We cannot, in general, obtain the irreducibles components of an algebraic variety ``by hand",
but considering the curve as the set of zeros of an ideal in a polynomial ring, the question
becomes strongly related to the computation of {\em primary decomposition} of ideals (see \cite[Chaps. 4,7]{am}),
a fundamental topic in abstract algebra, and for which computing algorithms there exists
since a long time (\cite{wiki}). In particular,
Macaulay2 package (\cite{mac}) incorporates a command to
compute the primary decompositon of an ideal.

We also present in this paper, mainly as a matter of mathematical curiosity, a new root-locus plot that we denominate
``Algebraic Dual Root-Locus'' or (ADRL), associated to the conventional RL plot, that is
obtained by computing the dual curve (in projective geometry sense)
for each individual plane curve that makes up the
projective root-locus. We leave the analysis of the properties of ADRL for a possible future work.

Bellow we present some concepts used in the paper:

\begin{figure}
\begin{center}
\includegraphics[scale=1.5]{rlc.pdf}
\caption{\label{rlc} Root-Locus for $G(s)=(s+1)/s^2$}
\end{center}
\end{figure}

\begin{description}

\item[$\pmb{\mathbb R}$, $\pmb{\mathbb C}$] {\bf and} $\pmb{\mathbb R[x_1, x_2, \ldots, x_n]}$:
Represents the field of real numbers, the
field of complex numbers and the ring of polynomials with coefficient's in
$\mathbb R$ and with indeterminates
$(x_1, x_2, \ldots, x_n)$, respectively.

\item [Homogeneous polynomial] A polynomial (in several variables) is
homogeneous when all of its nonzero terms (monomials)
have the same total degree (sum of the degree of each variable). We always
can turn a non-homogeneous polynomial ($q$) into a homogeneous one ($q^h$)
by adding a new variable ($x_{n+1}$), with the following procedure:
$q^h(x_1, \ldots, x_n,x_{n+1}) = x_{n+1}^{d}\;q(x_1/x_{n+1}, x_2/x_{n+1},
\ldots, x_n/x_{n+1})$, where $d$ is the total degree of $q$; this process is
denominated ``homogenization'' of $q$.   We can always ``de-homogenize"
$q^h$ by setting $x_{n+1}=1$ and recover back $q$.

\item[Ideal of Polynomials:] A set of polynomials
$I \subseteq  \mathbb R[x_1, x_2, \ldots, x_n]$ is an ideal when
it satisfies the following properties (\cite{clo}, \cite{am}):
$(i)$ $0 \in I$;
$(ii)$ $p,q \in I$ implies $p+q \in I$; and
$(iii)$ $p\in I$ and $q\in \mathbb R[x_1,x_2,\ldots, x_n]$ implies $pq\in I$.
One important fact about ideals of the ring $\mathbb R[x_1,x_2,\ldots,x_n]$ is that they
are {\em finitely generated}, that is, for every ideal $I$ always there exists a {\em finite} subset of
polynomials in $I$, denoted by $\{p_1,p_2,\ldots, p_t\}$, such that
\[
I = \sum_{i=1}^{t}h_ip_i, \quad h_i \in \mathbb R[x_1, x_2, \ldots, x_n].
\]
The set $\{p_1, p_2, \ldots, p_t\}$ is denominated a {\em generating set for $I$}; in this case
we write $I=\langle p_1, p_2, \ldots, p_t\rangle$. A Grobner Basis for the ideal
$I$ is a particular kind of generating set that allows many important
properties of the ideal to be deduced easily. Given a generating
set $\{p_1, p_2, \ldots, p_t\}$ for $I$, we can obtain a Grobner basis
$\{g_1, g_2, \ldots, g_s\}$ for $I$ algorithmically (see \cite[Ch.~2]{clo}).
The most basic ideals are $\langle 0\rangle$, the zero ideal, and
$\langle 1\rangle$, the ring $\mathbb R[x_1,x_2,\ldots,x_n]$ itself. In fact,
if $1\in I$, we immediatelly conclude $I= \mathbb R[x_1,x_2,\ldots,x_n]$.
We also have that the intersection of any family of ideals results in an ideal.
Another important result related to ideals in Noetherian rings (like
$\mathbb R[x_1,x_2,\ldots,x_n]$) is the ``Lask-Noether Theorem" which
states that every ideal in a Noetherian ring can be written as an finite intersection
of primary ideals.

\item[Variety generated by an ideal:] An (real) algebraic variety is a subset of $\mathbb R^n$
whose elements are the (real) solutions a system of polynomial equations in $n$ variables
 (in $\mathbb R[(x_1,x_2,\ldots,x_n])$.
We can see this set of polynomials as a generating set of an ideal $I$, and so we say
that the variety is generated by the ideal $I$, and represented by $\mathbb V(I)$.
There exists several important relationships between ideals and verieties, in particular:
$\mathbb V(\langle 0\rangle)=\mathbb R^n$, $\mathbb V(\langle 1\rangle)=\emptyset$ and
if $I$ and $J$ are ideals we have that $\mathbb V(I\cap J) = \mathbb V(I) \cup \mathbb V(J)$.

\end{description}
For more details about the concepts above see (\cite{clo}, \cite{am}).

\section{Decomposing projective root-locus into irreducible components}\label{ic}

In a previous paper (\cite{pjrl}) the author showed how to extended the RL plot
from the affine plane $\mathbb R^2$ to the projective plane $\mathbb{PR}^2$
by considering the parametric plot roots of the ``modified" polynomial
\begin{equation}\label{mpoly}
p(s) = k_dd(s)+k_nn(s)
\end{equation}
over $\mathbb{PR}^2$ as $k_n/k_d$ spans the
projective line $\mathbb{PR}^1$. Considering the ideal $I=\langle u, v \rangle$,
generated by the polynomials
$u=\text{Re}\{p(x+iy)\}$ and $v=\text{Im}\{p(x+iy)\}$,
the projective root-locus (PjRL) is obtained from the
Grobner basis $\{g_{1}, g_{2},\ldots, g_{s}\}$ for the ideal $I$,
defined in the ring $\mathbb R[x,y,k_d,k_n]$,
with respect a graded monomial order. If we define the homogenization
of the ideal $I=\langle u, v\rangle$ as the ideal
$I^h=\langle g_{1}^h, g_{2}^h, \ldots, g_{s}^h\rangle$, where $g_{i}^h$ is the (homogeneous)
polynomial obtained by the homogenization of $g_{i}$, we can obtain the projective root-locus
from the (projective) variety generated by the ideal $I^h$, denoted by $\mathbb V(I^h) $,
where $I^h $ is defined in the ring
$\mathbb R[x,y,z,k_d,k_n]$ (see \cite{pjrl} for details).

To decompose the PjRL into irreducible components we need to obtain
a primary decomposition of $I^h$, in order to write it  as a
finite intersection of ideals, that is
\begin{equation}\label{pdec}
I^h = J_1 \cap J_2 \cap \cdots \cap  J_m,
\end{equation}
where each $J_i$ is a primary ideal (see \cite[Thm. 7.13]{am}).
Based on this, we can write $\mathbb V(I^h) $, the variety generated
by $I^h $, as
\[
\mathbb V(I^h) = \mathbb V(J_1) \cup \mathbb V(J_2) \cup \cdots \cup \mathbb V(J_m),
\]
where $\mathbb V(J_i)$ is the variety generated by the primary ideal $J_i $, and it is
an irreducible component of the variety $\mathbb V (I^h) $. We note that, given a generating set for the
ideal $I^h $, namely the Grobner basis $\{g_{1}^{h}, g_{2}^{h}, \ldots, g_{s}^{h}\} $, we can
obtain a generating set for each primary ideal $J_i $ in (\ref{pdec}) by a computational algorithm,
like the command ``primaryDecomposition" in Macaulay2 package. In this way, we have the
following procedure for finding the irreducible components of the PjRL for an irreducible
transfer function $G (s)=n (s)/d (s) $:
\begin{enumerate}
\item Define $p(s) = k_dd(s) + k_nn(s) $ and taking $s = x + jy $, obtain $p(x+jy) = u(x,y,k_d,k_n) + jv (x,y,k_d,k_n) $;
\item Obtain a Grobner basis for the ideal $I=\langle u, v\rangle $, and denote it by $\{g_1, g_2, \ldots, g_s\} $;
\item Let $I^h = \langle g_{1}^{h}, g_{2}^{h}, \ldots, g_{s}^{h}\rangle $, the homogenization of $I$, and obtain the
primary decomposition of the ideal $ I^h $, as presented in Equation~(\ref{pdec});
\item The zeros of the generating set for each $J_i $ in (\ref{pdec}) is an irreducible variety,
whose union for $i = 1, 2, \ldots, m $ makes up the PjRL.

\end{enumerate}

\subsection{Examples}

In all examples below we used the Macalay2 software (\cite{mac}) to make the calculations
and all polinomials are defined with coeficients in the field of rationals (that is in
$\mathbb Q[x_1,x_2,\ldots,x_n]$) so that we can get infinite precision in calculations.

\begin{example}\label{ex1}\em
Let be $G(s) = (s+1)/s^2$, whose RL plot is shown in Figure~\ref{rlc}, and
\[
p(s) = k_ds^2 + k_n(s+1).
\]
Defining $u={\rm Re}\{p(x+jy)\}$ and $v={\rm Im}\{p(x+jy)\}$ we
have:
\[
u(x,y,k_d,k_n) = k_d (x^2-y^2)+k_n(x+1), \quad
v(x,y,k_d,k_n) = 2k_d xy + k_n y.
\]
Now we compute the Grobner basis for the ideal $\langle u,v \rangle$
using the graded reversed lexicographic order with
$x>y>k_d>k_n$ and obtain $\{g_1,g_2,g_3,g_4\}$, where:
\begin{eqnarray*}
g_1(x,y,k_d,k_n) & = & 2xyk_d+yk_n \quad (= r) \\
g_2(x,y,k_d,k_n)  & = & x^2k_d-y^2k_d+xk_n+k_n \quad (= q)\\
g_3(x,y,k_d,k_n)  & = & x^2yk_n+y^3k_n+2xyk_n \\
g_4(x,y,k_d,k_n)  & =& 2y^3k_d-xyk_n-2yk_n
\end{eqnarray*}
Homogenizing of the polynomials $g_i$, using the
procedure indicated in the Introduction we obtain:
\begin{eqnarray*}
g_{1}^{h} & = & z^3g_1(x/z,y/z,k_d/z,k_n/z) = 2xyk_d + yzk_n \\
g_{2}^{h} & = & z^3g_2(x/z,y/z,k_d/z,k_n/z) = x^2k_d-y^2k_d+xzk_n+z^2k_n \\
g_{3}^{h} & = & z^4g_3(x/z,y/z,k_d/z,k_n/z) = x^2yk_n + y^3k_n + 2xyzk_n \\
g_{4}^{h} & = & z^4g_4(x/z,y/z,k_d/z,k_n/z) = 2y^3k_d - xyzk_n - 2yz^2k_n
\end{eqnarray*}
Now we compute the primary decomposition for the ideal
$I^h=\langle g_{1}^{h}, g_{2}^{h}, g_{3}^{h}, g_{4}^{h}\rangle$ to
obtain $I^h = J_1 \cap J_2 \cap J_3$, where:
\begin{eqnarray}
J_1 & = & \langle y, x^2k_d + xzk_n + z^2k_n \label{j1ex1}\rangle \\
J_2 & = & \langle x^2 + y^2 + 2xz, 2xk_d +zk_n\label{j2ex1}\rangle \\
J_3 & = & \langle k_d, k_n\rangle \label{j3ex1}
\end{eqnarray}
Using the fact that $k_d$ and $k_n$ belong to the set of reals and that they can't be both
simultaneously zero, we have that $1\in J_3$ (suppose $k_n\neq 0$, so $(1/k_n)\times k_n=1\in J_3$)
and then $J_3=\mathbb R[x,y,z,k_d,k_n]$ can be deleted from the primary decomposition of
$I^h$, that is, $I^h=J_1\cap J_2$. Then we have that $\mathbb V(I^h) = \mathbb V(J_1)\cup \mathbb V(J_2)$,
where $\mathbb V(J_1)$ is defined by $y=0$ and $\mathbb V(J_2)$ is defined by $x^2+y^2 + 2xz=0$. To analyze
these varieties in the affine $XY$ plane we set $z=1$ and we obtain the components of the
plot shown in Figure~\ref{rlc}, that is the line $y=0$ and the circle $(x+1)^2 +y^2 = 1$, as desired. Also, from
the ideals $J_1$ and $J_2$ above we can obtain the parametrization of these curves as well as the initial and terminal
points of the PjRL, as was done by the author in \cite{pjrl}:
\begin{description}
\item[Variety $\mathbb V(J_1)$:] Defined by the ideal $J_1$, as shown in Equation~(\ref{j1ex1})
\begin{itemize}
\item Initial Points: $k_d=1$ and $k_n=0$. From (\ref{j1ex1}), we get $y=0$ and $x^2=0$ or $x=0$. Therefore the initial
point
for $\mathbb V(J_1)$ is $(0:0:1)$ or $(0,0)$ in affine plane $XY$.
\item Terminal points: $k_d=0$ and $k_n=1$. We get from (\ref{j1ex1}), $y=0$ and $xz+z^2=0$. Then we have (a) $z=0$ and
$x=1$, which is
the point at infinity $(1:0:0)$ (horizontal lines) and (b) $z=1$ which implies $x=-1$ and the point is $(-1:0:1)$ or
$(-1,0)$ in affine plane $XY$.
\item Intermediary Points: $k_d=1$ and $k_n=\lambda\neq 0$. Again from (\ref{j1ex1}), we have $y=0$ and
$x^2+xz\lambda + z^2\lambda=0$,
and we must have $z=1$ ($z=0$ would imply $x=0$ what is impossible); so, all intermediary points are at finite position
and is given by
$y=0$ and $x^2 + x\lambda + \lambda=0$, $\lambda\neq 0$. Then $x=\frac{-\lambda\pm\sqrt{\lambda^2-4\lambda}}{2}$, which
give us the
RL over $y=0$ line.

\end{itemize}

\item[Variety $\mathbb V(J_2)$:] Defined by the ideal $J_2$, as shown in Equation~(\ref{j2ex1})
\begin{itemize}
\item Initial Points: $k_d=1$ and $k_n=0$. From (\ref{j2ex1}), we get $x^2 + y^2 + 2xz=0$ and $2x=0$ or $x=0$. Then we
have $x^2+y^2=0$
or $y=0$. Therefore the initial point for $\mathbb V(J_2)$ is $(0:0:1)$ or $(0,0)$ in affine plane $XY$.
\item Terminal points: $k_d=0$ and $k_n=1$. We get from (\ref{j2ex1}), $x^2 + y^2 + 2xz=0$ and $z=0$. Then we get
$x^2 + y^2=0$ what
implies $x=y=z=0$ which is not allowed, so this variety has no terminal points.
\item Intermediary Points: $k_d=1$ and $k_n=\lambda\neq 0$. Again from (\ref{j2ex1}), we have $x^2 + y^2 + 2xz=0$ and
$2x + z\lambda=0$,
and we must have $z=1$ ($z=0$ would imply $x=y=0$ what is impossible); so, all intermediary points are at finite
position and is given by
$x^2 + y^2 + 2x = 0$ and $2x + \lambda=0$, $\lambda\neq 0$, which is the parametrized equation of the circle as
shown in RL plot.

\end{itemize}

\end{description}

Now, since the complete PjRL is $\mathbb V(J_1) \cup \mathbb V(J_2)$, we have:
\begin{itemize}
\item Initial points: $(0:0:1)$ (from $\mathbb V(J_1)$) plus $(0:0:1)$ (from $\mathbb V(J_2)$); so we have a duplicate
point at
$(0:0:1)$ or at $(0,0)$ in affine plane $XY$.
\item Terminal Points: $\{(1:0:0), (-1:0:1)\}$, only from $\mathbb V(J_1)$
\item Intermediary points: $\{(x:0:1), x=\frac{-\lambda\pm\sqrt{\lambda^2-4\lambda}}{2}, \lambda\neq 0\}$ from
$\mathbb V(J_1)$ plus
$\{(x:y:1), x=-\lambda/2, \lambda\neq 0$ and $x^2+y^2+2x=0$\} from $\mathbb V(J_2)$.

\end{itemize}

\end{example}

\begin{example} \em \label{ex2} We now consider a modification of Example~\ref{ex1}
above by defining $\displaystyle G(s)=\frac{s+1}{s^2(s+4)}$, whose RL plot is shown in Figure~\ref{rlwc}. Also
in this case we see that the RL is the union of the line $y=0$ and the ``weird'' curve shown in red. In this case:
\[
p(s) = k_d(s^3+4s^2) + k_n(s+1)
\]
and we have
\begin{eqnarray*}
u={\rm Re}\{p(x+jy)\} & = &k_d(x^3 -3xy^2 + 4x^2 - 4y^2) +k_n(x+1)\\
v={\rm Im}\{p(x+jy)\} & = &k_d(-y^3 + 3x^2y + 8xy) + k_ny.
\end{eqnarray*}
The Grobner basis for the ideal $\langle u,v\rangle$ is $\{g_1,g_2,g_3,g_4,g_5\}$, and the generating set for
$I^h$ is $\{g_{1}^{h},g_{2}^{h},g_{3}^{h},g_{4}^{h},g_{5}^{h}\}$, where:
\begin{eqnarray*}
g_{1}^{h} & = & 3x^2yk_d - y^3k_d + 8xyzk_d + yz^2k_n\\
g_{2}^{h} & = & x^3k_d - 3xy^2k_d + 4x^2zk_d - 4y^2zk_d + xz^2k_n + z^3k_n\\
g_{3}^{h} & = & 2x^3yk_n + 2xy^3k_n + 7x^2yzk_n + 3y^3zk_n + 8xyz^2k_n \\
g_{4}^{h} & = & 24xy^3k_d + 32y^3zk_d + 32xyz^2k_d - 6xyz^2k_n - 5yz^3k_n \\
g_{5}^{h} & = & 24y^5k_d + 160y^3z^2k_d - 128xyz^3k_d - 18x^2yz^2k_n - 24y^3z^2k_n - 39xyz^3k_n - 52yz^4k_n
\end{eqnarray*}
and computing the primary decomposition for $I^h$ we obtain $I^h = J_1\cap J_2\cap J_3$, where
\begin{eqnarray}
J_1 & = & \langle y, x^3k_d + 4x^2zk_d + xz^2k_n + z^3k_n\rangle \label{j1ex2}\\
J_2 & = & \langle 2x^3 + 2xy^2 + 7x^2z + 3y^2z + 8xz^2, 3x^2k_d - y^2k_d + 8xzk_d + z^2k_n\rangle \label{j2ex2}\\
J_3 & = & \langle k_d, k_n\rangle \label{j3ex2}
\end{eqnarray}
Once more, $J_3$ can be removed from the intersection, so $\mathbb V(I^h)=\mathbb V(J_1)\cup \mathbb V(J_2)$,
where $\mathbb V(J_1)$ is defined by $y=0$ and $\mathbb V(J_2)$ is defined by
$2x^3 + 2xy^2 + 7x^2z + 3y^2z + 8xz^2=0$. As in Example~\ref{ex1} above, to analyze
these varieties in the affine $XY$ plane we set $z=1$ and we obtain the components of the
plot shown in Figure~\ref{rlwc}, that is the line $y=0$ and the curve plotted in red whose equation
is $2x^3 + 2xy^2 + 7x^2 + 3y^2 + 8x=0$. We can also
plot these varieties over the projective plane (using Gnomonic projection) as was shown in \cite{pjrl}, as well
as plot them over other components of the projective plane also, as the affine plane $ZY$.

\begin{figure}
\begin{center}
\includegraphics[scale=1.5]{rlwc.pdf}
\caption{\label{rlwc} Root-Locus for $\displaystyle G(s)=\frac{s+1}{s^2(s+4)}$}
\end{center}
\end{figure}

\end{example}

\section{Algebraic Dual Root-Locus -- ADRL} \label{darl}
Duality is a fundamental concept in projective algebraic geometry. In fact, it is a basic
property of the real projective plane $\mathbb{RP}^2$ that a ``point'' with (nonzero) homogeneous
coordinate $(a:b:c)$ can be associated to a ``line'' with equation $ax+by+cz=0$ in and vice-versa.
This kind of duality can be extended from a projective line to a projective plane curve $({\cal W})$
defined by $f(x,y,z) = 0$, where $f(x,y,z)\in\mathbb R[x,y,z]$ is a homogeneous polynomial.
By the natural duality between lines and points in $\mathbb{RP}^2$,
each tangent line to the curve can
be associated to a point with homogeneous coordinate, for instance, $(u:v:w)$, and the main result is that this
set of points is also the solution to some equation $g(u,v,w)=0$, where $g(u,v,w)\in\mathbb R[u,v,w]$ is a
homogeneous polynomial, that represents a curve (${\cal W}^*$) over $\mathbb{RP}^2$ (in fact over the dual
of $\mathbb{RP}^2$, which it is itself). Therefore
${\cal W}^*$ is denominated the {\em dual curve} of ${\cal W}$. Interestingly, we also have that if we take the dual of the
dual of a curve we restore back the original curve, that is $({\cal W}^*)^* = {\cal W}$ (see \cite{gray}). Mathematically,
the dual curve of $f(x,y,z)=0$ is the set of points $(u:v:w)=(\partial f/\partial x:\partial f/\partial y:\partial f/\partial z)$ in
$\mathbb{PR}^2$, or $u=\lambda(\partial f/\partial x)$, $v=\lambda(\partial f/\partial y)$ and $w=\lambda(\partial f/\partial z)$,
for some $\lambda\neq 0$. To find the curve which these points belongs to, we can restate the problem as the one of
eliminating $x,y,z$ and $\lambda$ from the set of equations
$f(x,y,z)=0$, $u-\lambda(\partial f/\partial x)=0$, $v-\lambda(\partial f/\partial y)=0$ and
$w-\lambda(\partial f/\partial z)=0$, which, in turn, can be solved by finding a Grobner basis for the ideal
\begin{equation}\label{dideal}
I = \left\langle f(x,y,z), u-\lambda\frac{\partial f}{\partial x}, v-\lambda\frac{\partial f}{\partial y},
w-\lambda\frac{\partial f}{\partial z}\right\rangle
\end{equation}

In our context, we are primarily interested in obtaining the dual curve for each irreducible component of
the RL, as computed in Section~\ref{ic} above, and collate them to construct a new RL plot that we
denominate ``Algebraic Dual Root-Locus'' (ADRL). So, we will calculate de ideal defined in (\ref{dideal})
for the examples presented in Section~\ref{ic}.

\subsection{Examples}

\begin{example}\label{ex3}\em
Let be $G(s) = (s+1)/s^2$, whose RL plot is shown in Figure~\ref{rlc}, and
we found in Example~\ref{ex1} that the PjRL can be represented by the set
of ideals in Equations~(\ref{j1ex1},\ref{j2ex1}), that is
\begin{eqnarray}
J_1 & = & \langle y, x^2k_d + xzk_n + z^2k_n \label{j1ex3}\rangle \\
J_2 & = & \langle x^2 + y^2 + 2xz, 2xk_d +zk_n\label{j2ex3}\rangle
\end{eqnarray}

To find the dual curve of $\mathbb V(J_1)$, we have to calculate the dual curve of
$f(x,y,z)=x^2k_d + xzk_n + z^2k_n$, and therefore the ideal in Equation~(\ref{dideal})
for this curve is:
\[
I = \langle x^2k_d + xzk_n + z^2k_n, u-\lambda (2xk_d+zk_n), v, w-\lambda(xk_n+2zk_n)\rangle
\]
Finding a Grobner basis for this ideal with ``Lex" monomial ordering with
$x>y>z>k_d>k_n>\lambda>u>v>w$ we eliminate $x,y, z, \lambda$ and obtain the curve:
\[
g(u,v,w) = k_dw^2+k_nu^2-k_nuw
\]
So we can define the ``dual ideal" for $J_1$ as:
\begin{equation}\label{j1dex3}
J_{1}^{d} = \langle v, k_dw^2+k_nu^2-k_nuw\rangle
\end{equation}
and the dual curve for $\mathbb V(J_1)$ is $\mathbb V(J_{1}^{d})$.

To find the dual curve of $\mathbb V(J_2)$, we have to calculate the dual curve of
$f(x,y,z)=x^2 + y^2 +2xz$, and therefore the ideal in Equation~(\ref{dideal})
for this curve is:
\[
I = \langle x^2 + y^2 + 2xz, u-\lambda (2x + 2z), v - \lambda(2y), w-\lambda(2x)\rangle
\]
Finding a Grobner basis for this ideal, to eliminate $x,y,z,\lambda$, we obtain
\[
h(u,v,w) = v^2+2uw-w^2
\]
To find the parametrization for $h$ above we use the ideal
as shown below
\[
I = \langle 2xk_d +zk_n, u-\lambda (2x + 2z), v - \lambda(2y), w-\lambda(2x)\rangle
\]
and finding a Grobner basis for this ideal, to eliminate $x,y,z,\lambda$, we obtain
the (parametrized) curve $h_1(u,v,w) = k_nu + (2k_d - k_n)w$  and then we can define
the again ``dual ideal" for $J_2$ as:
\begin{equation}\label{j2dex3}
J_{2}^{d} = \langle v^2+2uw-w^2, k_nu + (2k_d - k_n)w\rangle
\end{equation}
Now we can define the Algebraic Dual Root-Locus for $G(s)=(s+1)/s^2$ as the union
of the varieties $\mathbb V(J_1^d)$ and $\mathbb V(J_2^d)$ where $J_1^d$ and $J_2^d$
are defined in (\ref{j1dex3}) and (\ref{j2dex3}), respectively. Below we analyse each variety
in order to obtain the complete plot for the ADRL:

\begin{description}
\item[Variety $\mathbb V(J_1^d)$:] Defined by the ideal $J_1^d$, as shown in Equation~(\ref{j1dex3})
\begin{itemize}
\item Initial Points: $k_d=1$ and $k_n=0$. From (\ref{j1dex3}), we get $v=0$ and $w^2=0$ or $w=0$.
Therefore the initial point
for $\mathbb V(J_1)$ is $(1:0:0)$, a point at infinity, or the intersection of horizontal lines in affine $UV$ plane.
\item Terminal points: $k_d=0$ and $k_n=1$. We get from (\ref{j1dex3}), $v=0$ and $u^2 - uw=0$. Then we have (a) $u=0$
and $w=1$, which is
the point $(0:0:1)$, or the point $(0,0)$ in affine plane $UV$ and (b) $u=w=1$ which is the point $(1:0:1)$ or $(1,0)$
in affine $UV$ plane.
\item Intermediary Points: $k_d=1$ and $k_n=\lambda\neq 0$. Again from (\ref{j1dex3}), we have $v=0$ and
$\lambda u^2 - \lambda uw + w^2=0$,
and we must have $w=1$ ($w=0$ would imply $u=0$ what is impossible); so, all intermediary points are at finite position
($w=1$) and is given by
$v=0$ and $u^2 - u +1/ \lambda=0$, $\lambda\neq 0$. Then $u=\frac{1\pm\sqrt{1-4/\lambda}}{2}$, which give us the
ADRL over $v=0$ line in affine $UV$ plane.

\end{itemize}

\item[Variety $\mathbb V(J_2^d)$:] Defined by the ideal $J_2^d$, as shown in Equation~(\ref{j2dex3})
\begin{itemize}
\item Initial Points: $k_d=1$ and $k_n=0$. From (\ref{j2dex3}), we get $v^2 + 2uw - w^2=0$ and $2w=0$ or $w=0$. Then we
have $v^2=0$
or $v=0$. Therefore the initial point for $\mathbb V(J_2)$ is $(1:0:0)$, a point at infinity (intersection of horizontal
lines) in $UV$ plane.
\item Terminal points: $k_d=0$ and $k_n=1$. We get from (\ref{j2dex3}), $v^2 + 2uw - w^2=0$ and $u-w=0$ or
$u=w$. Then we get $v^2 + u^2=0$ what implies $u=v=w=0$ which is not allowed, so this variety has no terminal points.
\item Intermediary Points: $k_d=1$ and $k_n=\lambda\neq 0$. Again from (\ref{j2dex3}), we have $v^2 + 2uw - w^2=0$ and
$\lambda u +(2 - \lambda)w=0$, and we must have $w=1$ ($w=0$ would imply $u=v=0$ what is impossible); so, all intermediary
points are at finite position and are given by $v^2 + 2u -1 = 0$ and $u = 1 - 2/\lambda$, $\lambda\neq 0$, which is the
parametrized equation of the parabola as shown in ADRL plot.

\end{itemize}

\end{description}

Now, since the complete ADRL is $\mathbb V(J_1^d) \cup \mathbb V(J_2^d)$, we have:
\begin{itemize}
\item Initial points: $(1:0:0)$ (from $\mathbb V(J_1^d)$) plus $(1:0:0)$ (from $\mathbb V(J_2^d)$); so we have a duplicate
point at $(1:0:0)$ or at infinity in affine plane $UV$.
\item Terminal Points: $\{(0:0:1), (1:0:1)\}$ only from $\mathbb V(J_1^d)$; or $(0.0)$ and $(1,0)$ in $UV$ plane
\item Intermediary points: $\{(u:0:1), u=(1\pm\sqrt{1-4/\lambda})/2, \lambda\neq 0\}$ from
$\mathbb V(J_1^d)$ plus $\{(u:v:1), u= 1 -2/\lambda, \lambda\neq 0$ and $v^2+2u-1=0$\} from $\mathbb V(J_2^d)$, in
$UV$ plane.
\end{itemize}
The ADRL plot for $G(s) = (s+1)/s^2$ is shown in Figure~\ref{darlex3}.

It is important to note that if we take the duals of $J_1^d$ and $J_2^2$, defined in Equations (\ref{j1dex3}) and
(\ref{j2dex3}), respectively, we get back, the ideals $J_1$ and $J_2$, as defined in Equations (\ref{j1ex3}) and
(\ref{j2ex3}), respectively. The procedure for doing that is eliminating $u,v,w$ and $\lambda$ in the ideals $I_1$,
$I_2$ and $I_3$ (defined below), using Lex monomial ordering with $u>v>w>x>y>z>k_d>k_n>\lambda$.
\begin{eqnarray*}
I_1 & = & \langle  k_dw^2+k_nu^2-k_nuw, x-\lambda(2uk_n-k_nw), y, z-\lambda(2k_dw-k_nu)\rangle\\
I_2 & = & \langle  v^2+2uw-w^2, x-\lambda(2w), y-\lambda(2v), z-\lambda(2u-2w)\rangle \\
I_3 & = & \langle  k_nu + (2k_d - k_n)w, x-\lambda(2w)y-\lambda(2v), z-\lambda(2u-2w)\rangle
\end{eqnarray*}

\begin{figure}
\begin{center}
\includegraphics[scale=1.5]{drl1.pdf}
\caption{\label{darlex3} Algebraic Dual Root-Locus for $G(s)=(s+1)/s^2$}
\end{center}
\end{figure}

\end{example}

\begin{example} \em \label{ex4} We now consider $\displaystyle G(s)=\frac{s+1}{s^2(s+4)}$,
whose RL plot is shown in Figure~\ref{rlwc} and whose PjRL is represented by the ideals
in Equations~(\ref{j1ex2},\ref{j2ex2}):
\begin{eqnarray*}
J_1 & = & \langle y, x^3k_d + 4x^2zk_d + xz^2k_n + z^3k_n\rangle \\
J_2 & = & \langle 2x^3 + 2xy^2 + 7x^2z + 3y^2z + 8xz^2, 3x^2k_d - y^2k_d + 8xzk_d + z^2k_n\rangle
\end{eqnarray*}

Repeating the reasoning used in Example~\ref{ex3} above, we obtain the ``duals'' ideals:
\begin{eqnarray}
J_1^d & = & \langle v,4k_duw^2 - k_dw^3 + k_nu^3- k_nu^2w\rangle \label{j1dex4}\\
J_2^d & = & \langle f(u,v,w), g(u,v,w)\rangle \label{j2dex4}
\end{eqnarray}
where $f$ and $g$ are the ``astonishing'' polynomials\footnote{In fact, a well known result in projective algebraic geometry
states that if a curve has degree $d$ (and no singularities) its dual has degree $d(d-1)$ \cite[pp.~173]{gray};
in our case the polynomial in the ideal $J_2$ has degree $3$, so its dual has degree $6$.}
\begin{eqnarray*}
f(u,v,w) & = & 216u^5w+144u^4v^2-621u^4w^2-912u^3v^2w+720u^3w^3-352u^2v^4+718u^2v^2w^2 - \\
         &   & 424u^2w^4 -232uv^4w-176uv^2w^3+128uw^5-240v^6+107v^4w^2-8v^2w^4-16w^6 \\
g(u,v,w) & = & 294912k_d^4u^3w-327680k_d^4u^2v^2-798720k_d^4u^2w^2+1671168k_d^4uv^2w+512000k_d^4uw^3-\\
              &    & 1048576k_d^4v^4-675840k_d^4v^2w^2-96000k_d^4w^4+73728k_d^3k_nu^4-448512k_d^3k_nu^3w+\\
              &    & 430080k_d^3k_nu^2v^2+706304k_d^3k_nu^2w^2-788480k_d^3k_nuv^2w-403200k_d^3k_nuw^3+ \\
              &    & 131072k_d^3k_nv^4+300288k_d^3k_nv^2w^2+75600k_d^3k_nw^4-46656k_d^2k_n^2u^4+174816k_d^2k_n^2u^3w-\\
              &    & 68928k_d^2k_n^2u^2v^2-224292k_d^2k_n^2u^2w^2+109920k_d^2k_n^2uv^2w+119040k_d^2k_n^2uw^3- \\
              &    & 6144k_d^2k_n^2v^4-41364k_d^2k_n^2v^2w^2-22320k_d^2k_n^2w^4+8208k_dk_n^3u^4-26172k_dk_n^3u^3w+\\
              &    & 3088k_dk_n^3u^2v^2+30636k_dk_n^3u^2w^2-4764k_dk_n^3uv^2w-15616k_dk_n^3uw^3+ \\
              &    & 128k_dk_n^3v^4+1788k_dk_n^3v^2w^2+2928k_dk_n^3w^4-441k_n^4u^4+1344k_n^4u^3w- \\
              &    & 42k_n^4u^2v^2-1528k_n^4u^2w^2+64k_n^4uv^2w+768k_n^4uw^3-k_n^4v^4-24k_n^4v^2w^2-144k_n^4w^4
\end{eqnarray*}
Remembering that the dual curve for $2x^3 + 2xy^2 + 7x^2z + 3y^2z + 8xz^2=0$ is $f(u,v,w)=0$ and
that $g(u,v,w)=0$ is used just for obtaining a parametrization. The plot for the correspondig ADRL,
obtained by the Scilab package (\cite{scilab}) is shown in Figure~\ref{darlex4}.

\begin{figure}
\begin{center}
\includegraphics[scale=1]{weird.pdf}
\caption{\label{darlex4} Algebraic Dual Root-Locus for $\displaystyle G(s)=\frac{s+1}{s^2(s+4)}$}
\end{center}
\end{figure}

\end{example}

\section{Conclusions}
We have presented in this paper a procedure for isolating the planes curves that makes up
the root-locus plot for an irreducible transfer function. This procedure can be easily implemented
in a computational algebra software package. We also showed how to compute the dual curve
(in projective algebraic geometry sense) to each plane curve and join them to compose what
we denominated ``Algebraic Dual Root Locus'' (ADRL). Some examples were worked out in order to show
the effectiveness of the procedure. We intend to investigatethe properties of the ADRL
more deeply in future works.

\bibliographystyle{plain}

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On 21–22 November 2018 in Кyiv (Ukraine) a lot of experts from 21 countries and 11 Ukrainian universities were share their achievements in fundamental and applied scientific researches with colleagues on the International Conference «SUSTAINABILITY AND LEGACY IN SPORT: CHALLENGES AND PERSPECTIVES». This forum hold under Patronage of International Association of Sport Kinetics International Association of Universities on Physical Culture and Sport.
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text:
Siemiany – polsko-belgijski film krótkometrażowy z 2009 roku w reżyserii Philipa Jamesa McGoldricka.

Opis fabuły
Michał i Andrzej to dwaj nastolatkowie, którzy każde wakacje spędzają razem w miejscowości Siemiany na Mazurach. Lata wspólnych wspomnień scalają ich przyjaźń. Wakacyjna nuda i poczucie wielkiej jedności przeistacza ich przyjaźń w coś więcej.

Obsada
 Damian Ul jako Andrzej
 Michał Włodarczyk jako Michał
 Aleksandra Radwańska jako Agnieszka
 Kamil Grenda jako Łukasz
 Joanna Opozda jako Dorota
 Mariola Wasińska jako Giza

Linki zewnętrzne

Belgijskie filmy krótkometrażowe
Belgijskie filmy z 2009 roku
Polskie filmy krótkometrażowe
Polskie filmy z 2009 roku

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Millions of people co-own closely held companies, family businesses, and business partnerships, but establishing them and keeping them together is never easy. Here, finally, is the guide they have been waiting for.... Read More
How to Bring the "Family" in Family Business into Focus: The Continuing Challenge
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Posting by Ed Kopf, Ph.D.
Every business can benefit from clearly stating its objectives and, then, understanding the internal and external environment in which it is pursuing those objectives. A well-established approach to examining the environment as part of overall business planning is the SWOT technique. This acronym represents a careful assessment of (internal) Strengths and Weaknesses and (external) Opportunities and Threats.
When a family business undertakes a SWOT analysis, it has a number of family-related factors to consider that other businesses don't. For example, to what extent may personal, spousal, intergenerational, and sibling relationships (long antedating business relationships) strengthen or weaken the organization's ability to reach its objectives? Or, how might management and ownership succession be affected by family-based senses of entitlement and envy? The manner in which these and many similar questions are addressed as part of a planning process could have a significant impact on the success of the business. To what extent do family businesses bring these sorts of questions into clear focus when they think about their future? A recent survey of family business owners offers some insight into the answer to this question as it relates to weaknesses and threats derived from the risk of family conflict.
The PwC Survey
The 2014 Global Family Business Survey commissioned by PricewaterhouseCoopers (PwC) provides insight into the risk perceived by family businesses from conflict within the ownership family – and the degree to which they are prepared to deal with it. Among the nearly 2400 respondents to questions about strengths, weaknesses, opportunities, and threats, one in nine reported the potential for "conflict within the family" as a key challenge facing them in the next five years. In addition, over one in three stated that "company succession planning" – a frequent contributor to family business conflict – would be a key challenge in that same period.
How well prepared are these family businesses to deal with these challenges? When all of the survey respondents were asked what steps they had taken to prevent or deal with the potential for family conflict, the most common responses were that they had in place formal legal agreements such as shareholder agreements (54%), incapacity and death arrangements (43%), and entry and exit provisions (33%).
Legal agreements are part of the fundamental framework families with businesses need to begin to manage their relationships. The fact that nearly half of the businesses surveyed lacked even a shareholder agreement (providing basic rules of governance and ownership rights) clearly should be a source of concern for those firms.
But legal agreements alone can't offer family businesses assurance that the relationships in the owning family will function smoothly. Many key sources of disputes exist outside of a legal framework. Even when there is an issue that can be resolved based on legal rights, the outcome can leave strong feelings of unfairness and bruised emotions. Families are held together by understanding, communication, and a collective sense of fairness – not by law. Resolutions based on a legal adjudication can't assure these.
This is why effective management of family conflict requires robust mechanisms going beyond legal agreements that provide for real transparency, communication, and mutually recognized fair play within the family. However, the proportion of families surveyed reporting the existence of such mechanisms is relatively low: 32% for family councils, 27% for use of third-party mediators, and 22% for a family constitution or charter. Only 16% reported that they had "robust and documented" succession plans in place.
Obstacles to effective preparation for conflict
Why are these critical structures serving family harmony and, therefore, business success, so often given short shrift? There are many plausible explanations. Perhaps the most obvious is the pressure on family business leaders to attend to pressing operational and competitive challenges. In the PwC survey, conflict management and succession planning were on the list of key concerns surfaced by the SWOT-like questions asked. But they ranked well below commercial matters including hiring and retaining key staff, containing costs, innovating, managing competitive change, and coping with globalization. Where can a leader find time to address seemingly less "practical" questions?
In addition, very few family businesses have built-in advocates for attending to family-related issues. According to the American Family Business Surveys (conducted by MassMutual Insurance, Kennesaw State University, and the Family Firm Institute in 2002 and 2007), family business owners' top two most trusted professional advisors were their accountant and lawyer. Under these circumstances, tax strategies get ample attention. So does drafting the legal agreements referred to above and others. However, advisors who are charged with focusing the attention of the owner (or owners) on assessing readiness to deal with family dynamics, potential conflict, and long-term issues such as succession do not even appear on the American Family Business Survey's list of seven key advisors. (The only category of advisors identified that is likely to be highly sensitive to family matters is "spouse!")
Finally, many family business owners are far more comfortable dealing with business issues, narrowly defined, as opposed to complex questions of relationships, interests, and emotions in the interlocking spheres of family and business. Companies, counselors, and individuals often use typologies of personality to explore the "fit" between individuals and the social and professional roles they might play. The most prominent of these typings is the Myers-Briggs Type Indicator — summarized as widely-known (but often misunderstood) groups of four letters. Of course, all successful entrepreneurs don't have the same Myers-Briggs type. But the "ENTJ" type is often identified with business creators and leaders. The ENTJ is, in short, extroverted, imaginative, cogent, and decisive. This certainly fits our intuitive sense of many successful family business founders and leaders and of the qualities required for entrepreneurial success.
Psychologist Robert G. Heyward has described the other side of the coin of these positive traits: the limitations that ENTJ's may bring to a working relationship (see https://www.personalitypage.com/html/ENTJ_per.html), including being unable to understand other people's needs where these differ from their own, becoming petulant or angered when confronted by situations which require feeling judgments, becoming so engrossed in a plan or ambition that personal needs and the needs of others are forgotten, and taking every decision not made in agreement with their rational beliefs as a personal rejection. These shortcomings certainly are not universal among all entrepreneurs or family business leaders, but they may exist in sufficient degree in many instances to cause family and other personal issues to be uncomfortable and to take a backseat to commercial challenges.
Bringing the Family into Focus?
It was a recognition that family businesses needed more help focusing on family-related issues than could be provided by conventional advisors or an owner's instincts that led to the emergence of an advisory category known as "family business consultants." Perhaps the most visible sign of the emergence of this new field was the organization of the Family Firm Institute in 1986, dedicated to "educating, connecting, and inspiring professionals who serve family enterprises." FFI's philosophy highlighted the need for family business consultants to integrate behavioral, financial, legal, and management expertise and experience with a focus on their application to the family enterprise.
The organization, now approaching 30 years of service, encourages academic research on family business and offers training that sensitizes professionals in many fields to the peculiar needs of family businesses. A key function has been the promotion of the highly professionalized, full-time family business consultant — who is fully prepared to help family businesses address their most challenging issues of conflict prevention and resolution, succession, and more.
The emergence of the family business consultant was a creative and positive approach to providing family businesses with the help they needed. But how effective has this initiative been in meeting the special family-related needs of millions of family businesses in the United States? FFI has approximately 800 members in the United States. Many of these are academics or others who do not provide services to families. (For comparison's sake, the U.S. Department of Labor reports over 1.2 million lawyers and 750,000 accountants in the country.) In 2011, Family Enterprise USA estimated that there were 5.5 million family businesses in the United States. If this number were correct, we could estimate a rough ratio of one qualified family business consultant per 10,000 family businesses. This number speaks for itself.
The Family Business Challenge
With the existence of a massive potential market, a critical need for services and the emergence of a profession designed to meet that need, was hasn't the family business consulting field exploded? Why did the family businesses participating in the PwC survey still lack many of the essential tools needed to help them deal with the complex challenges of family conflict and succession?
The answer to these questions is important, not only to these families but also to a national economy which depends so greatly on the success of family businesses. Family business consultants should also be concerned with the answers. The profession would greatly benefit from a dramatic broadening of consciousness of the need for its services — and awareness of its existence — by the great mass of family businesses. Hopefully, FFI and others dedicated to the family business consulting field will place its failure to become a standard component of the vast majority of family businesses' advisory teams high on their agenda.
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Drew University related articles
Nancy Lynne Westfield Appointed Director of the Wabash Center in Crawfordsville, Indiana
Created in 1995 and sustained by grants from the Lilly Endowment, the Wabash Center for Teaching and Learning in Theology and Religion at Wabash College seeks to enhance and strengthen education in North American theological schools, colleges and universities.
Jun 21, 2019 | 0 comments View Post
Calvin O. Butts III Announces Plans to Step Down as President of SUNY Old Westbury
Rev. Butts has led the university since 1999. He will go on study leave for the spring semester of 2020 and plans to return as professor of American Studies in the fall of 2020.
Mar 25, 2019 | 1 comment View Post
Two African American Academics Win National Book Critic Circle Awards
This year, two of the six winners of the National Book Critics Circle Awards are African Americans with current academic affiliations. They are Ross Gay who teaches in the creative writing program at Indiana University and Margo Jefferson who teaches at Columbia University and The New School.
Apr 05, 2016 | 0 comments View Post
Ross Gay to Be Presented With the 2016 Kingsley Tufts Poetry Award
The award, which comes with a $100,000 prize, is given annually to a mid-career poet. Ross Gay teaches in the creative writing program at Indiana University and for the low-residency master of fine arts degree program in poetry at Drew University in New Jersey.
Mar 04, 2016 | 0 comments View Post
The New Dean of Students at Union County College
Dr. Terrence Hardee previously served as vice president for student success at Rowan University in Glassboro, New Jersey, and dean of the University Center at Cumberland County College in Vineland, New Jersey.
Oct 09, 2015 | 0 comments View Post


text:
RECORD: Darwin, C. R. 1883. Charles Darwin on animal mimicry. The Field Naturalist p. 134.
REVISION HISTORY: Scanned, OCRed and edited by John van Wyhe 8.2008. RN1
[page] 134
CHARLES DARWIN ON ANIMAL MIMICRY.
THE death of Charles Darwin has awakened so much interest in his personal character, as well as in his scientific attainments, that the following letter which he recently addressed to one of the workers in zoology in this university,1 is here printed as an excellent illustration of the qualities which were characteristic of the departed naturalist.
The letter was written in reply to a description, sent Mr. Darwin, of a mollusk which closely resembled in colour and form the seaweed upon which it habitually lives.2 This sea-weed is the well known Sargassum, or Gulf-weed, which is found floating at the surface of the sea, sometimes in immense quantity. It has long, narrow, leaflike fronds of a peculiar form, with serrated margins, and is of an olive or reddish brown color, with darker blotches and spots.
The mollusk, which is somewhat like a common garden slug, is provided with three pairs of appendages which exactly resemble in form and color the fronds of the Sargassum, The body is also colored like the sea-weed, and the whole animal is so similar in appearance to the plant on which it lives as almost to defy detection.
This resemblance is an instance of what is called "protective mimicry," many cases of which have been noted in other groups of animals. The mimicry is "protective" because the organism which "mimics" the other is concealed from view, and thus protected from the attacks of enemies. Thus in the present case the mollusk is not distinguished from the plant by fish or other predatory animals, is therefore passed by, and escapes destruction. Some idea of the perfection of the resemblance may be gained from the fact that the mollusks escaped discovery for several hours during which the Sargassum was kept in a large, clear glass jar in the laboratory, and examined several times in the presence of other animals.
The phenomena of mimicry are of interest on account of their clear illustration of the action of natural selection. Obviously there must be a tendency towards the survival of those individuals which are most effectually hidden—that is, those which most nearly resemble the objects with which they are constantly associated—while other individuals will tend to be weeded out. From this tendency has very commonly resulted general resemblances between organisms and their environments, such as the prevailing white color of arctic animals or the tawny colors of desert animals; and now and then have arisen resemblances so special and detailed as to merit the name of mimickry.
Down, Beckenham, Kent,
Dear Sir,—I thank you much for having taken so much trouble in describing fully your interesting and curious case of mimicry. I am in the habit of looking through many scientific journals, and though my memory is now not nearly so good as it was, I feel pretty sure that no such case as yours has been described amongst the nudibranch molluscs.
You perhaps know the case of a fish allied to Hippocampus (described some years ago by Dr. Günther in Proc. Zoolog. Soc.) which clings by its tail to sea-weeds, and is covered with waving filaments so as itself to look like a piece of the same sea-weed. The parallelism between your and Dr. Günther's case makes both of them the more interesting, considering how far a fish and mollusc stand apart. It would be difficult for anyone to explain such cases by the direct action of the environment.
I am glad that you intend to make further observations on this mollusc, and I hope that you will give a figure, and if possible a coloured figure.
With all good wishes from an old brother naturalist, I remain, dear sir, yours faithfully, (Signed), CHARLES DARWIN.
To E. B. Wilson.
John Hopkins University Circulars, August, 1882.
1 Edmund Beecher Wilson (1856-1939), American embryologist and cytologist. This letter appeared, with additional contextual information in Seward 1909 and Poulton 1909.
2 See Calendar 13530.
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text:
package au.id.mcmaster.xlsxlookup;

import org.springframework.boot.SpringApplication;
import org.springframework.boot.autoconfigure.SpringBootApplication;
import org.springframework.context.annotation.Bean;
import org.springframework.context.annotation.Configuration;

import springfox.documentation.builders.RequestHandlerSelectors;
import springfox.documentation.spi.DocumentationType;
import springfox.documentation.spring.web.plugins.Docket;
import springfox.documentation.swagger2.annotations.EnableSwagger2;

@SpringBootApplication
@EnableSwagger2
//@ComponentScan(basePackageClasses = {
//		XLSXLookupController.class
//})
public class XSLXLookupSpringBoot {

	public static void main(String[] args) {
		SpringApplication.run(XSLXLookupSpringBoot.class, args);
	}
}

@Configuration
@EnableSwagger2
class SwaggerConfig {
    @Bean
    public Docket productApi() {
        return new Docket(DocumentationType.SWAGGER_2)
                .select()
                .apis(RequestHandlerSelectors.basePackage("au.id.mcmaster.xlsxlookup"))
                .build();

    }
}

redpajama_set_name: RedPajamaGithub


The National Blueberry Festival is only possible through the generous contributions from our sponsors! Please support them and let them know how much their affiliation with the National Blueberry Festival means!
Be sure to check out our blueberry grower partners on the BLUEBERRY page!


text:
import React, {useContext} from 'react';
import AppContext from '../../../utility/AppContext';
import Box from '@material-ui/core/Box';
import {Button, makeStyles} from '@material-ui/core';
import clsx from 'clsx';
import AppContextPropsType, {
  CremaTheme,
} from '../../../../types/AppContextPropsType';

interface AppFixedFooterProps {
  props?: any;
}

const AppFixedFooter: React.FC<AppFixedFooterProps> = (props) => {
  const {footer, footerType} = useContext<AppContextPropsType>(AppContext);

  const useStyles = makeStyles((theme: CremaTheme) => ({
    footer: {
      position: 'fixed',
      left: 0,
      bottom: 0,
      width: '100%',
      zIndex: 99,
      backgroundColor: theme.palette.background.paper,
      color: theme.palette.text.primary,
      margin: '0',
      '& .footerContainer': {
        padding: '5px 20px',
        [theme.breakpoints.up('md')]: {
          paddingLeft: 32,
          paddingRight: 32,
        },
        [theme.breakpoints.up('xl')]: {
          padding: '10px 32px',
        },
      },
    },
  }));

  const classes = useStyles(props);

  return (
    <>
      {footer && footerType === 'fixed' ? (
        <Box className={clsx(classes.footer, 'footer')}>
          <Box
            className='footerContainer'
            alignItems='center'
            flexDirection='row'
            display='flex'>
            <Box>Copy right @crema 2020</Box>
            <Box ml='auto'>
              <Box px={5} clone>
                <Button color='primary'>Buy Now</Button>
              </Box>
            </Box>
          </Box>
        </Box>
      ) : null}
    </>
  );
};

export default AppFixedFooter;


Under general to limited supervision, responds to emergency calls, accidents, and medical emergencies, and/or rescue situations to protect life and property.
High school diploma or general education degree (GED) required; some experience, either paid or voluntary, performing Emergency Medical Technician duties.
Must have a valid State of Arizona E.M.T. certificate at time of hire.
Must have knowledge of first aid, C.P.R. and other basic medical assistance techniques. Must be able to establish and maintain effective working relationships with the staff and the public.
*Must possess strong interpersonal, communication and writing skills.
*Must be a team player; yet be able to work independently when required.
*Must be able to see and remember specific details of incidents and persons involved.
*Must be able to work at a fast pace and in stressful situations.
*Must be able to maneuver in all areas of the casino and a hotel resort, (100,000 and 240,000 square feet respectively).
*Must be physically able to run, ascend and descend 15 flights of stairs multiple times during a shift.
*Must be able to stand and walk for prolonged periods of time regardless of weather conditions.
*Must be able to lift, carry, push or pull the weight needed to perform the duties of the job (e.g. 35 to 50 lb. containers used during drops/fills; large drop carts) on both level and inclined surfaces.
*Must be able to participate in a defensive tactics program which includes self defense and arrest techniques.
*Must be able to bend, stoop, reach, jump, twist, crouch, kneel, twist, raise arms above the head and grip items while working in a patrolled or assigned area.
*Must be able to see, hear and remember the specific details of incidents and persons involved.
*Must respond to visual and aural cues.
*Must be able to wear radio ear pieces and microphones.
*Must be able to respond quickly or run to a medical incident, carrying basic life support bags, AEDS, oxygen and first aid supplies.
*Must be able to use and ratchet Confined Space Entry (CSE) retrieval equipment with a 200 pound person attached.


text:
Le retour du soir by André Brasilier
This highly expressive landscape was composed by French artist André Brasilier
In it, a group of horses and their riders race across the horizon
The artist treats his subjects with a dreamlike quality, using vibrant color and emotive brushwork
Brasilier is famed for his mysterious canvases, especially those featuring horses like this work
Default Title - $228,500 USD
André Brasilier
b. 1929 | French
Le retour du soir
(The Return of the Evening)
Signed "André Brasilier" (lower right); signed and titled "Le retour du soir / André Brasilier" (en verso)
Combining abstract and expressionist elements with dynamic brushwork and pulsating color, this intriguing oil on canvas is the work of the famed French painter André Brasilier. Brasilier's paintings contain a unique blend of entrancing figures, balanced color harmonies and a feeling of intimate communication with the natural world, and this work, entitled Le retour du soir, encapsulates the mysticism and compelling visual language of his distinctive style.
Monumental in size, this painting envelops the viewer, welcoming them into the dreamlike scene of horses and their riders racing through the landscape. Despite the composition's simplicity, it is filled with a dynamic sense of movement, with Brasilier's loose, emotive brushstrokes and vibrant palette revealing his expressionist influences. Silhouetted against the horizon, the horses evoke a profound sense of mystery and lyricism. Horses are a frequent motif in Brasilier's artworks. He has described them as "a superb creation... charged with symbolism, strength, dynamism and beauty," qualities that lend themselves well to the artist's expressive, emotional depictions of nature.
Born to two accomplished artists, Brasilier was naturally drawn to painting, and at the age of 20, he moved to Paris to study at the École des Beaux-Arts. Brasilier has received several prestigious awards, including the 1952 Prix Florence Blumenthal and the 1953 Prix de Rome. He is also one of only two artists (the other being Pablo Picasso) honored with a retrospective at Saint Petersburg's Hermitage Museum during their lifetime. He has exhibited works alongside legends such as Picasso, Braque, Chagall and Miro, and he is represented in the permanent collection of the Metropolitan Museum of Art (New York).
This painting is accompanied by a certificate of authenticity from Alexis Brasilier.
Canvas: 38 1/4" high x 57 1/2" wide
Frame: 46 1/2" high x 65 3/4" wide
Maker: Brasilier, André
Period: 1919-Present
Type: Paintings
Depth: 1.75 Inches
Height: 46.5 Inches
Style: Modernism
Canvas Width: 57 1/2 Inches
Canvas Height: 38 1/4 Inches
A Survey of French Art: Romanticism to the Modern Age
Though largely known by the ephemeral landscapes of the Impressionist frontrunners such as Claude Monet and Pierre-Auguste Renoir, the history of French fine art boasts a vast history that encompasses numerous styles. In fact, ...


Civil society is extremely disappointed with the regressive nature of the access to information provisions in a region which has some of the strongest right to information legislation in the world.
Strengthening the Right to Information for People and the Environment.
Improving transparency of concessions data—the who, what, when and where of commercial activities that drive over 60% of global deforestation—is critical to preventing forest loss.
Jamaicans have greater access to information about infrastructure developments and their environmental impact in the form of Development Alert a new interactive website.
Read more about Development Alert!


text:
Q: How to create an hello world in Java Swing? What is wrong in my code? I am studying Java Swing and I have some problem with the following simple code:
package com.techub.exeute;

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Font;

import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.SwingConstants;

public class Main{

    public static void main(String[] args) {

        JFrame frame = new JFrame("FrameDemo");
        frame.setMinimumSize(new Dimension(800, 400));
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

        JLabel myLabel = new JLabel("Hello World !!!", SwingConstants.CENTER);
        myLabel.setFont(new Font("Serif", Font.BOLD, 22));
        myLabel.setBackground(Color.blue);
        myLabel.setOpaque(true);
        myLabel.setPreferredSize(new Dimension(100, 80));

        frame.getContentPane().add(myLabel, BorderLayout.NORTH);

    }
}

My idea is to create a JFrame object and insert into it an Hello World JLabel object settings some property.
I do it into the main() method. The problem is that when I execute the program I don't see anything !!! Why? What is wrong in my code?
Tnx
Andrea

A: Just add
frame.setVisible(true);

to your code
See the steps to Creating and Showing Java Swing Frames
//1. Create the frame.
JFrame frame = new JFrame("FrameDemo");

//2. Optional: What happens when the frame closes?
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

//3. Create components and put them in the frame.
//...create emptyLabel...
frame.getContentPane().add(emptyLabel, BorderLayout.CENTER);

//4. Size the frame.
frame.pack();

//5. Show it.
frame.setVisible(true);

You missed out #5

A: You need a
frame.setVisible(true);

call in your code.
As others mentioned you should not use the main Thread for gui operations. I suggest you should refer to the official tutorials of SWING, they are rather helpful and you'll see examples there for proper threading.

A: keep this line in your method
frame.setVisible(true);

A: You are creating the frame but you are not displaying it. Call
frame.setVisible(true);

to display it.
Another thing: you should not manipulate GUI components in the main thread. Instead, create a new method for creating the frame and setting up the components, and run that method in the event dispatch thread, like in the example from the official tutorial:
import javax.swing.*;

public class HelloWorldSwing {
    private static void createAndShowGUI() {
        JFrame frame = new JFrame("HelloWorldSwing");
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        JLabel label = new JLabel("Hello World");
        frame.getContentPane().add(label);
        frame.pack();
        frame.setVisible(true);
    }

    public static void main(String[] args) {
        javax.swing.SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                createAndShowGUI();
            }
        });
    }
}

redpajama_set_name: RedPajamaStackExchange


text:
Ontario Premier Doug Ford announces the government's plan for reopening schools at Father Leo J. Austin Catholic Secondary School in Whitby, Ont., on July 30, 2020. THE CANADIAN PRESS/Nathan Denette
Empathetic incompetence? Ontario's Doug Ford government at 2 years
August 25, 2020 11.55am EDT
Mark Winfield, York University, Canada
Mark Winfield
Professor of Environmental Studies, York University, Canada
Mark Winfield receives funding from the Social Sciences and Humanities Research Council and the Natural Sciences and Engineering Research Council of Canada
York University provides funding as a member of The Conversation CA-FR.
York University provides funding as a member of The Conversation CA.
Now into the third year of its mandate, the Ontario government under Premier Doug Ford is being assessed for its handling of the COVID-19 crisis. The impressions are mixed.
On a personal level, the premier's responses to the pandemic have generally been regarded favourably. He has at times conveyed deep personal empathy for those affected by COVID-19 and their families.
At the same time, the province has struggled to provide effective responses to the COVID-19 crisis, seemingly uncertain of what direction to take or of the scope of its own authority and capacity.
Controversies over the government's plans to reopen elementary schools without reducing class sizes are the latest in series of stumbles in managing the crisis.
'Have fun'
The Ontario government was initially slow to recognize the scope of the pandemic and the risks it posed. COVID-19's global spread was apparent by early March, yet the premier confidently advised Ontarians to "go away" and "have fun" over the March break holiday.
By the time a provincial lockdown was imposed on March 18, most of those travellers were already back in Ontario. Some brought the virus with them, where it began to spread into the community, most critically to long-term care facilities.
The disaster that ensued in long-term care centres has been well-documented. More than 1,450 long-term care residents have died of COVID-19. More may have perished due to neglect as portions of the care system, particularly in for-profit facilities, effectively collapsed.
Read more: The coronavirus exposes the perils of profit in seniors' housing
The province was again slow to respond, despite well-known risks in the sector, especially its increasing reliance on part-time itinerant staff, and more general concerns over the quality and level of care being provided in long-term care facilities. Many of these issues had been highlighted less than a year earlier in the July 2019 report of the inquiry into the murders of nursing home residents by nurse Elizabeth Wettlaufer.
Elizabeth Wettlaufer is escorted by police from the courthouse in Woodstock, Ont., in June 2017. THE CANADIAN PRESS/Dave Chidley. THE CANADIAN PRESS/Dave Chidley
The province's promise of an "iron ring of protection" for care facility residents failed. The government then studiously avoided a formal judicial inquiry into the COVID-19 care home disaster, opting for a less formal commission, which will lack public testimony, under oath, by key officials in system.
Early warning bells were also sounded around the potential risks to large numbers of temporary foreign farm workers employed in Ontario. Crowded, unsanitary living conditions, as well as the vulnerability to deportation for workers who lack permanent resident status if fired by their employers, were again well-known long before the arrival of COVID-19.
Read more: Migrant workers face further social isolation and mental health challenges during coronavirus pandemic
Yet the province failed to take proactive action, despite having substantial legal authority to set and enforce standards and practices for farm operators under occupational health and safety, public health and agricultural legislation.
Those responsibilities were left to the ad hoc efforts of local health units, most notably in Windsor-Essex. The result was more than 1,000 cases of COVID-19 among temporary farm workers and at least three deaths.
School reopenings
The government's latest missteps have been around the reopening of schools in September. Major concerns are being raised by health experts, school boards, teachers and parents about the government's approach to opening elementary schools.
Read more: Coronavirus outbreaks are inevitable as Ontario plans to reopen schools
The government seems to be proceeding on a largely business-as-usual model with normal, pre-pandemic class sizes. Personal protective equipment will be provided for teachers, and masks are required for students in grades 4 to 8, and are recommended for younger children.
But health experts and public health authorities have highlighted the need to reduce class sizes to control COVID-19 in schools. With smaller classes, any outbreak would be limited to a smaller group. Teachers are also far more likely to be able to manage the behaviour of their students in smaller classes.
The Ford government, overall, has presented an image of deep concern and empathy for the victims of the pandemic. But it's flailing when it comes to delivering the kinds of concrete, proactive measures that COVID-19 requires. The premier's own management style remains more like that of a city councillor — someone who is genuinely trying to help his constituents, but suggests he's up against forces beyond his control.
'Final sign-off'
This is an odd stance for a premier who once declared that he had "final sign-off on everything in this province." At times the government has seemed unable to grasp the scope of the many tools at its disposal to deal with the pandemic.
The province is spending nearly $6 billion annually to keep hydro rates artificially low. In that context, it should be able to find the means to implement a safer and more effective plan for reopening public schools, where there are significant risks of triggering a second wave of COVID-19.
Despite its challenges in dealing with COVID-19, the province has been quietly efficient in the ongoing pursuit of its pro-business agenda. In fact, in many ways, that agenda has accelerated under the cover of the pandemic.
The land development industry continues to be a favourite of the government. Proposed revisions to the Growth Plan for the Greater Golden Horseshoe region released in June would compel municipalities to make land available to developers to accommodate doubtful projections of population growth to 2051.
Migrant workers in Leamington, Ont., wave hello at one another. The Ford government has failed to ensure temporary foreign farm workers were safe from COVID-19 duing the pandemic. THE CANADIAN PRESS/Rob Gurdebeke
The same proposed amendments would permit aggregate extraction operations (for example, gravel pits and quarries) in the habitat of endangered and threatened species. The province's environmental assessment process, in place since the mid-1970s, was largely dismantled through the government's omnibus "Economic Recovery Act" pushed through the legislature in July.
Read more: The erosion of Ontario's Endangered Species Act threatens iconic Algonquin wolf
Where the government's combination of empathy, administrative ineptitude and responsiveness to whatever developers and other industries seem to ask of it will lead is unknown. But that doesn't serve the interests of Ontario residents very well. Nor does it provide a very strong basis on which to head into an election less than two years away.
Ontario government
Ford government


Torkard Hill Medical Centre is an approved training practice and we have GP Registrars attached to the practice for either 4 or 12 months. The Registrars are under the supervision of Dr Dalton and Dr Bilkhu. The GP Registrars are fully qualified doctors undergoing training in general practice.
You may be asked on occasions if a Registrar may video his or her consultation with you. These videos will be treated in a confidential manner and will be used for training purposes only. If, however, you do not wish to be videoed, please let the reception staff know.
We also train F2 doctors as part of their hospital training. They are attached to the Pactice for 4 months under the supervision of Dr French.
The Practice is involved in the teaching of medical students from Nottingham University. You may be asked if you will allow medical students to sit in on your consultation with your doctor. If you do not wish to see medical students, please let our reception staff know.
We are always looking for volunteer patients to help with the medical student "Community Follow Up Project" for those with chronic disease. If you are interested please get in contact with Dr Brodie.


text:
Pa Qaleh (, also Romanized as Pā Qal'eh; also known as Pā'īn Qal'eh, Pāi Qal'eh, and Pa yi Qal'eh) is a village in Pa Qaleh Rural District, in the Central District of Shahr-e Babak County, Kerman Province, Iran. At the 2006 census, its population was 138, in 37 families.

References

Populated places in Shahr-e Babak County


you are here // Nor-Cal Vans » Nor-Cal Vans Blog » Ford Transit » 2015 Ford Transits Have Been Released!
2015 Ford Transits Have Been Released!
It's the middle of June 2014 and Transits are starting to arrive at Ford dealers. The cargo vans shipped out first, and Wagons will ship out in August 2014.
We have traveled to Detroit to examine the Transit, and unfortunately, we have determined that we will not be doing a lowered-floor modification on this vehicle.
Ford will continue to produce the E-Series Wagon, Cargo, and RV Converter through the 2014 model year without changes to the current design.


The Diary of a Nouveau Soccer Mom: Happy Halloween from F&B!
We did trick or treating tonight, then took the kids to this new little pizza place by our house.
They had a blast and we have candy coming out our ears. We'll sort it out tomorrow, then we may be taking a lesson from Chantel's Candy Witch story!


text:
Таскола () — місто () в США, в окрузі Тейлор штату Техас. Населення — 742 особи (2010).

Географія
Таскола розташована за координатами  (32.210629, -99.799295).  За даними Бюро перепису населення США в 2010 році місто мало площу 1,94 км², уся площа — суходіл.

Демографія

Згідно з переписом 2010 року, у місті мешкали 742 особи в 290 домогосподарствах у складі 210 родин. Густота населення становила 382 особи/км².  Було 322 помешкання (166/км²).

Расовий склад населення:

До двох чи більше рас належало 1,5 %. Частка іспаномовних становила 7,8 % від усіх жителів.

За віковим діапазоном населення розподілялося таким чином: 27,8 % — особи молодші 18 років, 56,2 % — особи у віці 18—64 років, 16,0 % — особи у віці 65 років та старші. Медіана віку мешканця становила 39,2 року. На 100 осіб жіночої статі у місті припадало 89,3 чоловіків;  на 100 жінок у віці від 18 років та старших — 86,1 чоловіків також старших 18 років.

Середній дохід на одне домашнє господарство  становив  доларів США (медіана — ), а середній дохід на одну сім'ю —  долари (медіана — ). За межею бідності перебувало 8,3 % осіб, у тому числі 15,5 % дітей у віці до 18 років та 0,0 % осіб у віці 65 років та старших.

Цивільне працевлаштоване населення становило 336 осіб. Основні галузі зайнятості: освіта, охорона здоров'я та соціальна допомога — 33,6 %, роздрібна торгівля — 13,1 %, сільське господарство, лісництво, риболовля — 8,6 %, будівництво — 8,3 %.

Джерела

Міста Техасу
Населені пункти округу Тейлор (Техас)


As the nights draw in, the weather is cooling and thoughts turn to the changing seasons of autumn and winter, many holidaymakers will be visiting their holiday homes on Abergele Caravan Parks for long weekend breaks. Although the daylight hours are less, there are still many adventures to be had in the Abergele region of North Wales. Within a short time, you can be shopping in Cardiff City centre, having an enthralling weekend adventure or maybe even getting out your bucket and spade, depending on the weather. The end of the month of October brings us spooky Halloween. Here are some ideas for spine-tingling events being held around Static Caravan Parks, North Wales.
Ride the Ghostly Train to Waunfawr from Caernarfon and return, in fancy dress and enjoy the scary surprises and competitions. It is advisable to book advance tickets.
Halloween events commence on Saturday, 25th, with craft workshops to make a lantern, a mask, a Harry Potter style broomstick or the chance to bring a witch's pet to life. Hot chocolate is on offer, free to those who come in fancy dress outfits.
Other events are on Monday, see a lifelike dinosaur in the park; Tuesday, Ricardo's Halloween show; Friday, a spooky chamber of lights.
Take a ghostly tour, if you dare, of Llandrillo cemetery where you could meet ghouls and ghosts and characters such as Harry the Old Sea Captain, or the Professor, to guide the way.
It is recommended that you bring a torch and wear fancy dress, on your visit to see fairy tale creatures with a twist at Anglesey Sea Zoo. Book in advance, with free entry for children in costumes and season ticket holders.
This historic castle built between 1812 and 1822 and inhabited initially by the Hesketh family, before falling into disrepair. During World War II, the castle was used to house 200 refugees and after, was sold in 1948 when it was opened to the public and known as The Showplace of Wales. During the 1970s, it hosted jousting competitions and medieval markets, also being marketed as a bar and restaurant. After 1996, Gwrych Castle was left to the elements when it became derelict. It is alleged that the castle is haunted, possibly by a young girl.
Maybe you prefer to spend your long weekend break relaxing at Static Caravan Parks, North Wales coast region, where there are plenty of activities and facilities onsite to keep the family happy, with no need to leave the Park unless you want to. Maybe hollow out a pumpkin lantern and take a walk around the Park grounds with the children. So why not have a Spooky Halloween at Whitehouse Leisure Park. In addition to the Children's Play Park, we have an Amusement Arcade, a Snooker Room, Cabarets, Discos, Game Shows, Quizzes and Bingo. A family restaurant serves delicious food at reasonable prices, offering a menu of family favourites. Or why not visit our Coffee lounge, The Living Room, where you can enjoy speciality coffees whilst relaxing next to our feature fireplace.


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Home » News » In tit-for-tat, Malaysia bans North Korean embassy officials from leaving country
Datuk Seri Ahmad Zahid Hamidi
In tit-for-tat, Malaysia bans North Korean embassy officials from leaving country
All North Korean embassy officials are barred from leaving Malaysia with immediate effect.
Deputy Prime Minister Datuk Seri Ahmad Zahid Hamidi made the announcement today in an immediate reaction to Pyongyang's ban against Malaysians from leaving North Korea.
"As a response to foreign minister of North Korea, the Home Ministry via Immigration has released an immediate ruling that not one officer in Malaysia is to leave the country.
"This is effective immediately to all exits of immigration nationwide," he told a news conference here.
Ahmad Zahid also said the Cabinet will meet this Friday and discuss if it is to sever all ties with North Korea.
He reiterated that Malaysia will not tolerate being accused of a murder conspiracy without proof.
"We have no intent to take any reciprocating action. But after this has been done by a country with diplomatic ties with Malaysia outside of the normal conventions of bilateral relationships, Malaysia is forced to take a similar action as they have manipulated the murder case here.
"We want to send a clear message, 'Don't point fingers at us and don't look down upon Malaysia as (a) sovereign nation," he said.
Deputy Foreign Minister confirmed separately that 11 Malaysians are currently stranded in North Korea after its government imposed a ban on them leaving the country.
Among them are two Malaysians with the UN Food Programme, three embassy staff and their six family members.
– See more at: http://www.themalaymailonline.com/malaysia/article/in-tit-for-tat-malaysia-bans-north-korean-embassy-officials-from-leaving-co#sthash.aCM737Xl.dpuf
← 11 Malaysians stranded at Pyongyang airport Malaysian family in Pyongyang stopped from taking flight home →


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ACC: Potent Quotables
By - March 10, 2007
Some more notes from tonight's twinbill to come but in the meantime, here's a sampling from the post-game pressers:
"In the first half we were letting them dictate what we were doing on offense and we weren't being really aggressive with our cuts and our screens. In the second half we came out and took what we wanted instead of taking what they gave us." --North Carolina State's Brandon Costner on his team's offensive adjustments in the second half
"We came here to win the tournament, we didn't come because we had to be in the tournament. We beat Carolina this year, we beat Virginia Tech twice, and those are two teams that were at the top of the league. I thought throughout the year we were immature at times and that's why we lost a couple of games we shouldn't have lost. But guys like Brandon [Costner] and Ben [McCauley] and Courtney [Fells] are really maturing in front of our eyes and that's why we were able to win a lot of games." --State's Gavin Grant on team morale through Coach Lowe
"All you have to do is look around at games that are going on now and will be going on next week. As we've been talking about for two days, this game today, games yesterday and the day before, tomorrow -- whenever -- are not games that are played on paper. They're not played with records. They're played with competitiveness. If you don't compete, I can guarantee you the other team is going to figure that out and they're going to compete. We stopped competing, they kept competing and they never gave up down 14. As a result, they put it to us." --Virginia coach Dave Leitao on his team's lack of energy
"They just did things better. Fatigue was not a factor." --Wake Forest coach Skip Prosser on Virginia Tech's taking control in the second half. (The Demon Deacons had played a double-overtime game that ended in the wee hours of Friday morning.)
"I hope it's not. When I was sitting on the bench thinking that this could be the last time I wear the uniform, it's ... I don't know ... I hope it's not. It's out of our hands now." --Wake Forest senior Kyle Visser on Friday's game potentially being his last
Posted by at 12:14 AM on March 10, 2007
The Sloggers...
Josh Herwitt
Josh Herwitt is CSTV.com's basketball editor and writes a weekly national column
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Jerry Palm looks for the angles from the world of college hoops.
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The golden rule is to always ask for receipts when paying rent or bond. If you collect rent or bond from your housemates, always give receipts.
If you're the co-tenant responsible for paying rent to your landlord, you should ask for receipts from your landlord.
If you're the head-tenant, you should give rent receipts to your housemates when they pay their rent. If they pay you bond at the beginning of the tenancy, you should give them a receipt and lodge it with Renting Services at the Office of Fair Trading.
If you're a sub-tenant paying your rent to the head-tenant, make sure they give you receipts, and keep them somewhere safe. This will ensure that if confusion arises about who's paid, you can prove you have paid your share.
If you're moving in and you pay a tenant who is leaving their share of the bond, make sure you lodge a "Change of Shared Tenancy Arrangement" form with Renting Services. This form is available on the NSW Office of Fair Trading website. The bond that is lodged already will be transferred to your name, which will simplify things when you vacate the premises (see Looking for a new housemate).
TIP: Always get a receipt for any rent or bond you pay!
It is a good idea to pay your rent by electronic funds transfer. That way, you can keep track of how much money you have paid to whom. You can also set up an automatic transfer online, which will make sure you pay the rent on time. If you do, check you have sufficient funds in your bank account to pay the rent.
If one person is in charge of paying the rent on behalf of the other housemates, you may want to create a separate bank account from which to pay the rent. That way, everyone can keep track of the rent payment and make sure that the person doesn't accidentally spend the rent money on something else.
Share houses vary enormously in the way they purchase food. Some housemates do cooking and groceries shopping together, while others prefer to do it alone.
Sharing food with your housemates can be difficult, as you are likely to have different tastes, dietary requirements, portion sizes and cooking skills. Your budget-conscious housemate might consider your chicken salad a luxury, or your foodie roommate may not enjoy the home brand vanilla ice cream as much as you do!
If you decide to share food with your housemates, start by sharing basic foodstuffs such as milk, bread and butter. Once you get used to each other's cooking and grocery shopping, you can share the food and cooking responsibilities.
Some share houses have a 'kitty' to cover basic foods, cleaning products and other household items. Having a kitty is a good idea if you want to avoid a scene over who finished that last roll of toilet paper, but make sure you don't use it as an emergency fund for cigarettes and alcohol. While the quickest way to disrupt domestic bliss is to abuse the kitty system, it's also important to realise that everyone has different ideas about what is a vital household purchase, it doesn't help to become obsessive about how the kitty is spent.
Like it or not, there are certain tasks which have to be done for a household to continue functioning. The toilet is not self-cleaning, the garbage has to go out eventually and disposable plates are not the answer to the washing-up saga. Floors, bathrooms and lawns also need looking after.
Many households find that a roster for certain tasks, especially cooking and washing-up, is the best way to ensure that chores are completed fairly. Others find that a more flexible honour system is sufficient. In some share houses, people put down a tick every time they do the washing-up or some other chore.
Again it's necessary to realise that if you want the advantages of having housemates, you will have to do your share in the upkeep of the household. If you find that one or more of your housemates is falling in their duties, remind them politely that jobs have to be done. Rude notes left under people's doors are probably unproductive. If you think there is a problem, it's a good idea to get together and discuss before things get out of hand. Try not to let this discussion turn into a hunt for someone to blame.
Living in a happy household means finding people who have similar ideas about cleanliness and domestic arrangements. If the differences are too great, it may be difficult to continue living together.
A major conflict in a share house often arises over the payment of bills. When you move in, it is important to decide who will be paying bills and how the bills are to be divided. Generally, bills such as gas, electricity and water are divided equally between all members of the household.
In some share houses, people decide to set aside some money each week to pay for bills. That way, you don't have to worry about paying extra when a $1000 electricity bill lands on your doorstep.
If the bills aren't included in the rent, it's a good idea for each housemate to organise different services in order to spread the financial responsibility around. That way, one person is not left with a huge debt and a bad credit rating if things go wrong.
Bills for electricity, gas, phone, and Internet usually arrive either every month or three months. Often these can be quite large and housemates on tight budgets can sometimes have difficulties paying their share all in one hit – which is why bills cause so many problems.
You can decide to set aside some money each week to cover the bills, or you could arrange a pre-payment plan with these services. Pre-payment means that you pay a certain amount each week or month, which gets credited your account. When the bill is issued, the credit will be taken off and you will only have to pay the remainder.
TIP: If you're worried about your housemates running up a huge phone bill making interstate or international calls without paying for it, you can ask your telephone provider to restrict out-going calls, so that these more expensive type of calls can not be made from the home phone. Contact your telephone provider for more information.
If you are responsible for paying for the water, the landlord must give you a copy of the bill within three months of the issue of the bill for those charges by the water supply authority. The landlord must give you at least 21 days to pay. Water bills usually come quarterly.
If there is a dispute over payment of an account, call the Energy and Water Ombudsman NSW (see Contact Points).
If your housemate is leaving without paying the bills, you might be able to come to an agreement to keep all or part of their bond to cover the bills. Legally, you do not have the right to use bond without the permission of a housemate to cover anything but rent arrears and damage to the house. This is because the bond is part of the tenancy agreement and does not cover household bills.
If your housemate and you can't reach an agreement, and you have applied to the Tribunal to terminate the housemate's co-tenancy (see Moving Out), the Tribunal may make an order that the housemate pays for the outstanding utilities if it thinks that it is appropriate to do so.
Alternatively, you may be able to to sue through the Local Court to recover the money. This can be time-consuming and expensive. A Local Court chamber magistrate or community legal centre can give you advice about what you need to do. Sometimes you might decide it is cheaper and less troublesome to write the debt off, rather than going to court.
If you have guests over, be mindful of your housemates and keep the noise to a minimum. If you have guests who stay overnight, let your housemates know in advance.
Some share houses like to have regular parties and gatherings, while others prefer everyone to 'party outside the house' and keep the house relatively quiet. If you want to have a house party, tell your housemates in advance and don't forget to invite them to the party. Be flexible – your housemates might have an exam or an assignment over the weekend you have organised a house party.
If you're a tenant, you also have an obligation under the residential tenancy agreement not to disturb your neighbours or damage the property. This includes disturbance or damage caused by your guests. Make sure you keep the noise to a minimum and set a reasonable end time to avoid any potential breach of the residential tenancy agreement.
Make sure you speak to your housemates before getting a pet. Your housemates may dislike pets or be allergic to certain types of animals. You may breach your tenancy agreement with the landlord if the tenancy agreement does not allow you to keep pets. If you decide to get a pet, generally you will need written consent from the landlord. Unless you agree otherwise, you will also have to pay for carpet cleaning when you decide to move out.


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Q: Unable To Install Symfony Windows 7 I am trying to install Symfony, but unable to find how can we start with symfony with Xampp. I have already tried on google but there is no proper solution for installation and configuration of Symfony.
As I want to edit a project which is already developed using symfony CMS.

A: Symfony is not a CMS.
If you need to run a symfony app locally, all you have to do is to copy all files into a project subdirectory inside your Xampp (for example htdocs/symfony).
I assume existing project will have a database, so be sure to import your database locally or use external database. You need to tweak your symfony config file: http://symfony.com/doc/current/configuration.html

A:
I am trying to install Symfony, but unable to find how can we start with >symfony with Xampp. I have already tried on google but there is no proper >solution for installation and configuration of Symfony.
  As I want to edit a project which is already developed using symfony CMS.

Hi, for begin Symfony is not a CMS but a framework ^^, it's a little bit (alot) different.
For install Symfony WHY use google O_o ----> http://symfony.com/doc/current/setup.html
After, why Xampp ? for windows use Wamp who do the local server it's more performing :/
And if you want you don't have necessary to install symfony if it's an existing project -> just clone it (if he is on github) ... and just open the complete folder with your IDE or text editor.
You can modify the file without problems, (just you can have a prob for use command php bin/console.
Good luck i hope it's answering all you questions :)