In political campaigns or basketball games, what you see depends on where you sit.
It's too bad that, just as his campaign for governor fades to near irrelevancy, Tallahassee Mayor Andrew Gillum has sparked a discussion of the one never-resolved topic he is uniquely qualified to talk about.
It was probably inevitable that he would eventually have to talk about race. And at a time when the president has Twitter feuds with mostly black football teams and Confederate statues are being removed from public places, it was equally unavoidable that anything Gillum said would please some and upset others.
If you missed it, Gillum went to Tampa last week and said he sees "a truck on my way to work that has a big old Confederate flag" every day. Maybe he takes a different route downtown than most of us – or maybe, as both the mayor and a black citizen, he notices things others disregard, and they hit a bit harder in his memory.
There's also the possibility that, in answering a question on race from a student, Gillum exaggerated. He wouldn't be the first politician (see Trump, Donald J.) to embellish on something that means a lot to him.
In political campaigns or basketball games, what you see depends on where you sit. If you like Gillum, he was speaking forthrightly, even courageously. If you don't, he was playing the race card. The mayor himself referred to race as "the third rail of politics" – touch it at your peril.
But instead of just saying "we should have a conversation about race," Gillum said people of all backgrounds should actually think about how we live, and to speak civilly about how to improve the lives of all Floridians.
It's a theme he's hit on before. Gillum has staked out unflinchingly liberal positions on gun control, gay equality, feminist issues, education, environment, health care and helping ex-cons get their lives on track. Any one of those would give a Republican opponent plenty to work with in a general election, but unrelated events have made it unlikely Gillum will get that far.
He has said, repeatedly, that he's not involved in the FBI investigation of the local Community Redevelopment Agency. But his campaign fundraising has nose dived since subpoenas were served on City Hall last June, and he's had some serious campaign staff turnover.
Florida has never elected a black candidate in a statewide executive race, except for Lt. Gov. Jennifer Carroll, who ran with Gov. Rick Scott in 2010. Education Commissioner Doug Jamerson, who'd been appointed to the Cabinet by Gov. Lawton Chiles, lost in 1994. U.S. Rep. Kendrick Meek finished third in the 2010 U.S. Senate race. Gillum was widely described as "a rising star in the Democratic Party" when he announced early this year, but his campaign sputtered from the start.
True, President Barack Obama carried Florida twice. But before you start thinking a new day has dawned, remember that Trump carried the state last year.
If we could speak honestly, unfettered by political correctness, it would be great to have that "conversation about race." President Bill Clinton tried in 1997, with a seven-member commission headed by the late historian John Hope Franklin, but nothing came of it – for reasons we needn't go into.
Gillum voiced his readiness to make it not about the Old South, but about our lives today.


text:
Stephen Tyng Mather High School (commonly known as simply Mather) is a public 4–year high school located in the West Ridge neighborhood on the north side of Chicago, Illinois, United States. Opened in 1959, Mather is operated by the Chicago Public Schools (CPS) district. Mather is named in honor of Stephen Mather, an industrialist and conservationist who became the first director of the National Park Service.

Background

Campus and Faculty
Mather is a neighborhood high school with a college preparatory emphasis. More than 75% of students speak a language other than English at home. Mather's Bilingual/English as a Second Language (ESL) program is central to the school's curriculum. The faculty and staff reflect the multicultural backgrounds of Mather's students and serve as translators, role models, and mentors. Mather is committed to creating an environment that fosters student achievement. Honors-level classes are available for qualified students. The school campus shares two acres (56,000 m2) with adjacent Mather Park. The school has teachers fluent in languages such as Chinese, Arabic, Assyrian, Spanish, Russian, Serbo-Croat, Gujarati, and Urdu.

Academics
Advanced placement (AP) classes are offered:

Art/Studio Art
English Language and Composition
English Literature and Composition
U.S. History
U.S. Government
World History
Calculus AB
Chemistry
Biology
Statistics
Psychology
Physics
Spanish

Virtual High School classes are offered in a wide variety of subjects at various ability levels.

Athletics
Mather competes in the Chicago Public League (CPL) and is a member of the Illinois High School Association (IHSA). The school sport teams are nicknamed the Rangers. The boys' baseball team were public league champions in 1966–67. The boys' cross country team were regional champs in (2011–12, 2012–13, 2015–16)The girls' soccer team were public league champions in 2000–01. During the 2000–01 season, The girls' softball team were Class AA and public league champions. The girls' volleyball team were Class AA and public league champions twice (1995–96, 2001–02). The school's chess team were Class AA champions in 1991–92. The boys' soccer team were public league champions five times (1983–84, 1985–86, 1988–89, 2000–01, 2011–12) and State champions once (2011–12). The boys' golf team were public league champions in 1974. The boys' tennis team were public league champions twice (1973–74, 1974–75).

Notable alumni

 Robert Berland (1980) – judoka and coach who became the first American to receive as high as a silver medal in Olympic judo, winning the silver medal at the 1984 Olympics.
 Mun Choi – Current President of the University of Missouri
 Stephen Elliott (1990) – brother of William Elliott and author (Happy Baby).
 Noah Falstein (1975) – Pioneer game developer of games such as Sinistar and Indiana Jones and the Fate of Atlantis
 Frank Klopas (1983) – former soccer player, coach, and television broadcaster.  He played on the U.S. national soccer team in the 1988 Olympics and the 1994 FIFA World Cup.
 Qudus Lawal (2012) - Professional soccer player who led Mather to state and city championships.
 Max Levchin (1993) – internet entrepreneur who founded PayPal, Slide.com, and Affirm.
 Harry Rushakoff (1977) - Former drummer for the band Concrete Blonde.
 Ira I. Silverstein (1979) – member of the Illinois Senate (1999–2019).

Bus routes
CTA
11 Lincoln
84 Peterson
93 California/Dodge (Monday–Saturday only)

References

External links
  Official website

Public high schools in Chicago
Educational institutions established in 1959
1959 establishments in Illinois

redpajama_set_name: RedPajamaWikipedia


text:
cychan —
How we got into this mess
This PBS Frontline episode from last month sheds a lot of light on how we ended up in Iraq. From NYMag.com:
Like Nietzsche's eternal recurrence and Freud's return of the repressed, the war in Iraq keeps on coming back to bite us in the pineal gland. We do our best to distract ourselves with the collapse of the American economy or the rehab of pop tarts, but then another suicide bomb explodes in Baghdad and we are made to wonder once again—$3 trillion for exactly what? Bush's War can't tell us exactly "what," except for a fiasco, but this two-night, four-and-a-half-hour Frontline special is the best audiovisual history of who, why, when, and how available to date. Since Frontline has been tracking the metastasis from 9/11 through to the surge, producer Michael Kirk had access to more than 40 previous stories to bolster a fresh batch of interviews. Not only do most of the principals speak for themselves, but because they often had to revise, improve, or repudiate earlier sound bites, they speak against themselves, too.
As a result of watching it, I hate Dick Cheney even more now than I did before, and that's saying something. It's unbelievable how incompetent the Bush administration has been -- how damaging these two presidential terms have been to the world.
If you only have 10 minutes, watch segment twelve of part one.
fusiawol
The truth is sometimes nowhere near The Middle
Plain and simple! I like your work!
cychan
That's a good point. Name-calling environmental activists "crazy tree huggers" has probably undermined the credibility of the green movement to some extent.
ratatosksv
Along the same lines, even when the truth is in the middle, if one extreme succeeds in portraying the middle, or a less extreme view on the other side as "extreme," then that can cause a shift in…
Sensitive female chord progression? ... Really?
I agree, that's got to be a very interesting data set. Like what are the distinguishing factors of each of the clusters of hits? How many clusters are there? Can any (human) sense be made of why…
Yeah, it's my favorite Talk of the Nation in recent memory. I have always fantasized about researching what makes pop music "work." When I first listened to it, I really wanted to be able to…

redpajama_set_name: RedPajamaCommonCrawl


text:
Cette page dresse l'ensemble des armoiries (figures et blasonnements) connues des communes de la Dordogne disposant d'un blason.

A

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H

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T

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U

V

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Notes et références

Notes

Références

Voir aussi

Articles connexes

Liens externes
 La banque du blason – site héraldique sur les communes, collectivités et provinces historiques françaises.
 Armoriale de France : 24 Dordogne

Dordogne
Armorial


text:
\section{Introduction}
Chiral perturbation theory\cite{gl1} provides a low-energy
representation for pion-pion scattering amplitudes that are manifestly
crossing symmetric and have well-known analyticity properties.
In particular, to $O(p^6)$ in the momentum expansion (with the
pion mass $m_\pi^2$ treated as a quantity of $O(p^2)$) the
pion-pion scattering amplitude may be written down in terms of
three functions of single variables $W_I(s),\,
I=0,1,2$\cite{ssf}.
One may then compute the low-energy expansion in the energies and pion
masses in terms of these functions which have now been
explicitly computed\cite{kmsf1,bcegs1}.
Furthermore, the detailed knowledge of the amplitude in field
theory with standard power counting\cite{bcegs1,bcegs2},
is expected to lead to
accurate predictions for the I=0 S- wave scattering length $a^0_0$.
This important physical quantity, whose reported value is
$0.26 \pm 0.05$\cite{nagels} has been measured indirectly only
at the level of $20\%$ accuracy and is expected to be measured
to greater precision\cite{hl1}.

Pion-pion scattering is a problem that is particular
well suited to dispersion relation analysis\cite{gwsv},
rigorously established in axiomatic field theory.
One approach has been to write down fixed-t dispersion relations, with two
subtractions which suffice to guarantee convergence as a consequence
of the Froissart bound, for amplitudes of definite iso-spin.
It has been recognized for a long time that crossing symmetry
in dispersion relations brings in many {\it subtle considerations}.
It is possible to enforce crossing symmetry partially to eliminate
the unknown t-dependent functions in favor of the two S- wave
scattering lengths\cite{smr1}.    We note that it is
the requirement of two subtractions in the dispersion relations
that makes the accurate determination of the S- wave scattering amplitudes
from dispersion relations problematic --- one needs to combine
theoretical inputs with phenomenology in order to extract precise
predictions for these quantities\cite{bcegs1,bcegs2,hl2}.

The two subtractions in the dispersion relations we consider,
leave the S- and P- wave absorptive parts completely unconstrained\cite{bgn}
by crossing symmetry.
One may write down the total amplitude as (a) a part that is
saturated only in terms of these absorptive parts, and (b) a part
that is saturated by the $l\geq 2$ absorptive parts.
In Ref. \cite{ab1} we explictly showed that (a) may be expressed
in a manner whereby the dispersive representation of the
low-energy polynomials in terms of these absorptive parts may
be explicitly produced.
Here we discuss case (b) at some length.

Our analysis begins with considering fixed-t dispersion relations.
We must expand the Roy version of fixed-t dispersion relations
saturated with certain $l\geq 2$ absorptive parts,
which yield the dispersive representation for the low energy
polynomials in the energies and pion masses.  We immediately encounter
problems that arise from the inadequate implementing
of crossing symmetry by fixed-t disperion relations, which we
discuss at some length.  Results analogous to (a)
as well as (b) with fixed-t dispersion relations have also been discussed
elsewhere\cite{kmsf1,kmsf2}.  The numerical import of these
shows clearly that any attempt to saturate the
dispersion relations with the absorptive parts of
two of the well-known resonances listed by
the Particle Data Group\cite{pdg}, the $I=0,\, l=2$
state $f_2(1270)$(hereafter referred to as the $f$)
and the $I=1,\, l=3$ state $\rho_3(1690)$(hereafter refered to as the $g$)
violates crossing symmetry --- restoration of crossing
symmetry with these would predict a $\pi \pi$ width of
a nearly 110 MeV for the $g$, which falls
short by a factor of almost 3.

We therefore advocate a different approach to (b),
which overcomes the problems posed by crossing contraints.
This is achieved by considering certain manifestly
crossing symmetric dispersion relations. {\it We compute
with the $l\geq 2$ absorptive parts given by the $f$ and
$g$,  what is the manifestly crossing symmetric dispersive representation
for the low-energy polynomials in this approximation,
which constitutes the central result
of this work.}  The technique may be easily extended
to other resonances and also to other models of partial waves.

The manifestly crossing symmetric dispersion relations
are of the type first considered  by Wanders\cite{gw1}
in the context of $\pi^0\pi^0$ scattering and
subsequently by the authors of Ref.\cite{mrw}
for other totally symmetric amplitudes.
The family of dispersion relations
we consider is parameterized in terms of a variable $x_0$;
we concentrate mainly on the special case of $x_0=0$.
Note that crossing constraints on the $l\geq 2$ absorptive
parts cannot disappear altogether:  whereas for
a fixed value of $x_0$ the representation does not entail
any crossing constraints, as $x_0$ is varied, relations are
implied on the absorptive parts of the $l\geq 2$ absorptive
parts.  However, one of our significant findings is
that the low-energy polynomials of the type we are interest in,
can be produced only with $x_0=0$.

We finally note that in
a recent work\cite{gw2}, crossing symmetric dispersion relations
have been employed to fix some of the chiral coupling constants
by comparing the Taylor coefficients of the dispersive and chiral
representations of the pion-pion scattering amplitudes at the
symmetry point $s=t=u=4/3$ in the Mandelstam plane.

In Section 2 we will review the basics of pion-pion scattering
and remark on the structure of the low-energy expansion.  In Section 3
we will consider the form of fixed-t dispersion relations suitable
for saturation with resonances and discuss the deviations from
crossing symmetry.  In Section 4 we will describe the method of
writing down manifestly crossing symmetric dispersion relations
and evaluate the manifestly crossing symmetric low-energy polynomials.
In Section 5 we discuss the numerical import of our work.  In Section 6
our conclusions are presented.

\setcounter{equation}{0}
\section{Pion-Pion Scattering and The Low Energy Expansion}
Pion-pion scattering :
\begin{equation}
\pi^a(p_1)+\pi^b(p_2) \to \pi^c(p_3) +\pi^d(p_4),
\end{equation}
where $a,b,c,d$ label the iso-spin and the $p_i,\, i=1,2,3,4$,
are all incoming momenta,
may be described in terms of a unique function $A(s,t,u)$,
where $s,\, t,\, u$ stand
for dimensionless Mandelstam variables,
\begin{equation}
s=(p_1+p_2)^2/m_\pi^2, \, t=(p_1+p_3)^2/m_\pi^2, \, {\rm and} \,
u=(p_1+p_4)^2/m_\pi^2,
\end{equation}
with $s+t+u=4$.
We shall introduce units of energy squared where ever
necessary in terms of the square of the pion mass, $m_\pi^2$.
The choice of dimensionless squares of energies is very convenient
in producing the low-energy expansion:  we expand out the integrands
of interest in the dispersive representations out in powers of
$m_\pi^2$.

Since the strong interactions conserve iso-spin, it is customary
to write down amplitudes of definite iso-spin in the s-channel:
\begin{eqnarray}
& \displaystyle T^0(s,t,u)=3 A(s,t,u) + A(t,u,s) + A(u,s,t) & \nonumber \\
& \displaystyle T^1(s,t,u)=        A(t,u,s) - A(u,s,t) & \\
& \displaystyle T^2(s,t,u)=        A(t,u,s) + A(u,s,t) & \nonumber
\end{eqnarray}
The scattering lengths $a^I_l$ arise in the threshold
expansion for the partial wave amplitudes ${\rm Re}f^I_l(\nu)=\nu^l
(a^I_l+b^I_l \nu + ...)$, where the partial wave expansion is
given by $T^I(s,t,u)=32 \pi \sum (2l+1) f^I_l(s) P_l((t-u)/(s-4))$,
$\nu=(s-4)/4$ [the normalization of the amplitudes
here differs with that of \cite{mrw} by $32 \pi$].
The $b_l^I$ are the effective ranges.

We present our
results for the case of saturating the dispersive
integrals with the absorptive parts due to the $\rho(770)$
(hereafter referred to as the $\rho$), $f$ and
$g$ in the narrow width approximation.
(We consider the well-known case
of the $\rho$ once more, for two reasons.  Firstly,
since the presence of two subtractions in the dispersion
relations of interest does not constrain the absorptive
part of the $\rho$ from crossing symmetry and our
results will be identical whether we consider
fixed-t dispersion relations or crossing symmetric
ones.  Secondly, the scale of the contribution
to the low-energy coupling constants, or alternatively
the $\beta_i$, from the S- and P- wave absorptive parts
extracted from phenomenology and Roy equation fits to
phase shift and elasticity information, is set by the
$\rho$ as it is the dominant phenomenon in the P- wave
channel in the low to medium energy.)
The quantum numbers for
these states as well as their physical properties
are listed in Table 1\cite{pdg}.
The s-channel absorptive parts due to these resonances
in the narrow width approximation:
\begin{equation} \label{f2abs}
A^I(x,t)=32 \pi \sum_l (2l+1)\, {\rm Im} f^I_l(x)P_l(1+{2 t \, m_\pi^2
\over x-4 m_\pi^2})
\end{equation}
and the narrow width approximation reading
\begin{equation}
{\rm Im} f^I_l(x)=\sqrt{x\over x-4 m_\pi^2} \pi \Gamma^{\pi\pi}_m M_m
\delta(x-M_m^2)
\end{equation}
Note that in the narrow-width approximation, the partial waves,
despite being functions of only the variable $x$ do exhibit the
correct normal threshold behaviour.  We will have to keep this
in mind when expanding out the integrands in our dispersive representations.
It must also be noted that the arguments of the Legendre polynomials
do contain $m_\pi^2$ since they could contain information of
the external energies, parametrized by the dimensionless Mandelstam
variables.

The low-energy representation for the pion-pion scattering
amplitude $A(s,t,u)$, computed to two-loop accuracy in chiral perturbation
theory, may be written down in terms of three functions of
single variables, $W_I,\, I=1,2,3$:
\begin{small}
\begin{equation} \label{lowenergexp}
A(s,t,u)=32\pi\left\{\frac{1}{3} W_0(s)+\frac{3}{2}(s-u)W_1(t)
+\frac{3}{2}(s-t)W_1(u)+\frac{1}{2}W_2(t)+\frac{1}{2}W_2(u)
-\frac{1}{3}W_2(s)\right\}
\end{equation}
\end{small}
These functions are known to have only right hand cuts for
$s>4$ and one then has the dispersion relations for these
functions:
\begin{eqnarray}
& \displaystyle W_0(s)=A_0+B_0 s + C_0 s^2 +D_0 s^3 +{s^4\over \pi}
\int_4^\infty {dy\over y^4 (y-s)} {\rm Im}\, W_0(y) & \\
& \displaystyle W_1(s)=A_1+B_1 s + C_1 s^2  +{s^3\over \pi}
\int_4^\infty {dy\over y^3 (y-s)} {\rm Im}\, W_2(y) & \\
& \displaystyle W_2(s)=A_2+B_2 s + C_2 s^2 +D_2 s^3 +{s^4\over \pi}
\int_4^\infty {dy\over y^4 (y-s)} {\rm Im}\, W_2(y) &
\end{eqnarray}

The coefficients $A_I, \, B_I, \, C_I,\, D_I, \, I=0,2$, and
$A_1,\, B_1,\, C_1$ are the expansion coefficients of the
functions $W_I$ and $W_1$ evaluated at $s=0$, and the
amplitude $A(s,t,u)$ may be written most generally as:
\begin{equation}\label{lowenergyexp}
\beta_1 + \beta_2 s + \beta_3 s^2 + \beta_4 (t-u)^2 +
\beta_5 s^3 + \beta_6 s (t-u)^2 + {\rm integral}.
\end{equation}
The $\beta_i$ are known combinations of the these
Taylor coefficients.
It has been shown that the integral in the expression above
has the same structure as that obtained from dispersion relations
with two subtractions with the neglect of all but the absorptive
parts of the S- and P- waves.   In particular,
the $\beta_i$ are completely expressible in terms
of the two S- wave scattering lengths and certain
integrals over the S- and P- wave absorptive
parts\cite{ab1}, in this approximation. Nevertheless, the absorptive parts
of the $l\geq 2$ states do contribute to the $\beta_i$'s at
this order, although they do not contribute to the integral
in eq.(\ref{lowenergyexp})\cite{ssf,kmsf1,kmsf2}.  The objective
of the present work is, of course, to compute these contributions
for certain $l\geq 2$ absorptive parts.

\setcounter{equation}{0}
\section{Fixed-t Dispersion Relations}
A very convenient form of dispersion relations has been
found\cite{smr1} which eliminates the unknown functions $\mu_I, \, \nu_I$
in favour of the S- wave scattering lengths $a^0_0$ and $a^2_0$,
where  This (Roy) form is:
\begin{eqnarray}
T^I(s,t)&=& \sum_{I'}
\mbox{$\frac{1}{4}$}(s\,{\bf 1}^{II'} + t\,
C_{st}^{II'} + u\, C_{su}^{II'})\,T^{I'}_s(4,0) \label{royform} \\
 &+&\!\!\int_{4 \, m_\pi^2}^\infty \!dx\,g_2^{II'}(s,t,x)\,A^{I'}(x,0)
+\int_{4 \, m_\pi^2}^\infty \!dx\,g_3^{II'}(s,t,x)\,A^{I'}(x,t)\,
.\nonumber
\end{eqnarray}
where the crossing matrices $C_{st},\, C_{su}$ and $C_{tu}$
are defined below:
\begin{eqnarray}
& C_{st}=\left[
\matrix{ {1\over 3} & 1 & {5\over 3} \cr {1\over 3} & {1\over 2} & -{5\over 6}
   \cr {1\over 3} & -{1\over 2} & {1\over 6} \cr  } \right], \, \,
C_{su}=\left[
\matrix{ {1\over 3} & -1 & {5\over 3} \cr -{1\over 3} & {1\over 2} &
  {5\over 6} \cr {1\over 3} & {1\over 2} & {1\over 6} \cr  } \right],
  & \nonumber \\
& C_{tu}=\left[ \matrix{ 1 & 0 & 0 \cr 0 & -1 & 0 \cr 0 & 0 & 1 \cr  } \right],
 &
\end{eqnarray}
and $T^I(4,0)=32 \pi a^I_0,$ and will play no role in
the present discussion.
For our purposes, it is convenient to write the kernels in the form
\begin{small}
\begin{eqnarray}
g_2(s,t,x)&=&-\frac{t \, m_\pi^2}{\pi\, x\,(x-4 \, m_\pi^2)}\,
(u\, m_\pi^2\, C_{st}  + s\, m_\pi^2 \,C_{st}\, C_{tu} )
\left(\frac{{\bf 1}}{x-t \, m_\pi^2}
+ \frac{C_{su}}{x-s\, m_\pi^2-u \, m_\pi^2}\right)\nonumber \\
g_3(s,t,x)&=&-\frac{s\,u \, m_\pi^4}{\pi\,x(x-4 \, m_\pi^2+t \, m_\pi^2)}
\left(\frac{{\bf 1}}{x-s \, m_\pi^2}
+ \frac{C_{su}}{x-u \, m_\pi^2}\right)\;.
\end{eqnarray}
\end{small}

The contribution from the $\rho$ to $A(s,t,u)$
is unambiguous\cite{eglpr} and corresponds to
precisely the form of the amplitude presented in Appendix C of
Ref.\cite{gl1}, as well as with the
dispersion relation evaluation presented in Ref.\cite{ab2}:
\begin{small}
\begin{eqnarray}
& \displaystyle  48 \pi \Gamma^{\pi\pi}_\rho
\sqrt{M_\rho^2\over M_\rho^2-4 m_\pi^2} {1\over M_\rho (M_\rho^2-4 m_\pi^2)}
m_\pi^4
\left( {t(s-u)\over M_\rho^2-t\,  m_\pi^2} +{u(s-t)\over M_\rho^2-u \,
 m_\pi^2} \right)
&
\end{eqnarray}
\end{small}
Retaining the kinematic factor that ensures normal
threshold behaviour, we write the amplitude out to the required order below as:
\begin{eqnarray}
& \displaystyle A(s,t,u)_\rho={12\pi \Gamma^{\pi\pi}_\rho
\over M_\rho^7}\sqrt{{M_\rho^2\over M_\rho^2-4 m_\pi^2}} m_\pi^4
\left( -32 M_\rho^2 -192 m_\pi^2 + 32 M_\rho^2 s +208 m_\pi^2 s-
\right. & \nonumber \\
& \displaystyle \left. 6 M_\rho^2 s^2
 -52 m_\pi^2 s^2 +2 M_\rho^2 (t-u)^2 + 12 m_\pi^2 (t-u)^2 +
 3 m_\pi^2 s^3 +m_\pi^2 s (t-u)^2 \right) \label{arho}&
 \end{eqnarray}
In order to generate the dispersive representation for the
low-energy polynomial, we merely expand the functions $g_2,\, g_3$
and the Legendre Polynomials out in powers of $m_\pi^2$.
A general analysis of the framework considered here has been
discussed earlier\cite{kmsf1,kmsf2}
and will be discussed elsewhere as well\cite{hl2}.

The contribution of the $f$  to the iso-spin amplitudes
resulting from the fixed-t (FT) dispersion relations, to this order read:
\begin{small}
\begin{eqnarray}
& \displaystyle T^0(s,t,u)^{FT}_f=\frac{40\pi \Gamma^{\pi\pi}_f}{3 M_f^7}
\sqrt{\frac{M_f^2}{M_f^2-4 \, m_\pi^2}} \, m_\pi^4 \left(
-32 M_f^2-192 \, m_\pi^2 -48 M_f^2 s -560 \, m_\pi^2 s  \right. &
\nonumber \\
& \displaystyle
\left. +14 M_f^2 s^2 +204 \, m_\pi^2 s^2
 +2 M_f^2 (t-u)^2+ 12 \, m_\pi^2 (t-u)^2
-13 \, m_\pi^2 s^3 + 21 \, m_\pi^2
s (t-u)^2 \right) & \label{f2t0ft} \\
& \displaystyle T^1(s,t,u)^{FT}_f=\frac{40\pi \Gamma^{\pi\pi}_f}{3 M_f^7}
\sqrt{\frac{M_f^2}{M_f^2-4 \, m_\pi^2}} \, m_\pi^4 \left(96 \, m_\pi^2 s
-16 \, m_\pi^2 (t-u) -4 M_f^2 (t-u) s
\right. & \nonumber \\
& \displaystyle
\left.  -24 \, m_\pi^2 (t-u) s-48 \, m_\pi^2 s^2
 + 3 \, m_\pi^2 (t-u) s^2- 6 \, m_\pi^2 (t-u)^2 s+6 \, m_\pi^2 s^3
+\, m_\pi^2 (t-u)^3 \right) & \\
& \displaystyle T^2(s,t,u)^{FT}_f=\frac{40\pi \Gamma^{\pi\pi}_f}{3 M_f^7}
\sqrt{\frac{M_f^2}{M_f^2-4 \, m_\pi^2}} \, m_\pi^4 \left(
-32 M_f^2-192 \, m_\pi^2+2 M_f^2 (t-u)^2-80 \, m_\pi^2 s \right. & \nonumber \\
& \displaystyle \left. -12 \, m_\pi^2 (t-u)^2   + 3 \, m_\pi^2
(t-u)^2 s+2 M_f^2 s^2 +
 60 \, m_\pi^2 s^2
-7 \, m_\pi^2 s^3 \right) & \label{f2t2ft}
\end{eqnarray}
\end{small}

The contribution of the $g$ to the iso-spin amplitudes
resulting from the fixed-t dispersion relations, to this order read:
\begin{small}
\begin{eqnarray}
& \displaystyle T^0(s,t,u)^{FT}_g=\frac{56\pi \Gamma^{\pi\pi}_g}{ M_f^7}
\sqrt{\frac{M_g^2}{M_g^2-4 \, m_\pi^2}} \, m_\pi^4 \left(
-32 M_g^2 -192 \, m_\pi^2 + 32 M_g^2 s +368 \, m_\pi^2 s \right. &  \nonumber \\
& \displaystyle \left.  - 6 M_g^2 s^2 -132 \, m_\pi^2 s^2 +
2 M_g^2 (t-u)^2 + 12 \, m_\pi^2 (t-u)^2
  + 13 \, m_\pi^2 s^3 -9 \, m_\pi^2 s(t-u)^2
\right) \label{g3t0ft} &
\\
& \displaystyle T^1(s,t,u)^{FT}_g=\frac{28\pi \Gamma^{\pi\pi}_g}{ M_f^7}
\sqrt{\frac{M_g^2}{M_g^2-4 \, m_\pi^2}} \, m_\pi^4 \left(- 480 \, m_\pi^2 s
-16 \, m_\pi^2 (t-u)  + 12 M_g^2 (t-u) s +72\cdot \right. &
\nonumber \\
& \displaystyle \left.
\, m_\pi^2(t-u) s +
 240 \, m_\pi^2 s^2+ 30 \, m_\pi^2 (t-u)^2 s
 + 3 \, m_\pi^2 (t-u) s^2 -30 \, m_\pi^2 s^3 + \, m_\pi^2 (t-u)^3\right) & \\
& \displaystyle T^2(s,t,u)^{FT}_g=-\frac{1}{2} T^0(s,t,u)^{FT}_g & \label{g3t2ft}
\end{eqnarray}
\end{small}
Note that the factors $\sqrt{M_m^2/(M_m^2-4 m_\pi^2)}, \, m=f,g$ appear in
the expressions for the amplitudes retaining the memory of the normal
threshold behaviour of the partial waves.

It may be seen from the Roy form of the fixed-t
dispersion relations eq.(\ref{royform}),
that the amplitudes obtained at $O(p^4)$
are manifestly crossing symmetric and thus there are no crossing
constraints at this order.  However, at $O(p^6)$, we immediately
observe the violation of crossing symmetry by considering, say
$T^1(s,t,u)^{FT}_m$, which for $m=f,g$ contains terms that
are even in powers of $(t-u)$.  Note for instance the term
in $T^1(s,t,u)^{FT}_f$,
$$-240 \pi \Gamma^{\pi\pi}_f/(3 M_f^7) \sqrt{M_f^2/(M_f^2-4 m_\pi^2)}
m_\pi^6 (t-u)^2 s$$
and the term in $T^1(s,t,u)^{FT}_g$,
$$840 \pi \Gamma^{\pi\pi}_g/(M_g^7) \sqrt{M_g^2/(M_g^2-4 m_\pi^2)}.
m_\pi^6 (t-u)^2 s$$
One might then
hope that if indeed the width of the $g$ were to be
\begin{eqnarray}\label{finetune}
& \displaystyle
\Gamma^{\pi\pi}_g={2\over 21} \left({M_g\over M_f}
\right)^6 \sqrt{\frac{M_g^2-4 m_\pi^2}{M_f^2-4 m_\pi^2}} \,
\Gamma^{\pi\pi}_f, &
\end{eqnarray}
then these and possibly other
inconvenient terms would be cancelled.  It turns out that
at $O(p^6)$ there is, in fact, only one crossing constraint\cite{kmsf1,kmsf2} which is
the one given by eq.(\ref{finetune}) as we show below.

We may wish to enforce the direct constraint on
absorptive parts written down by Roy, which is a three component
equation, for $I=0,1,2$:
\begin{eqnarray}
& \displaystyle \int_{4 m_\pi^2}^{\infty} \, dx \left[ \sum_{I'}
\left\{ g_2^{II'}(s,t,x)-(C_{tu} \, g_2(s,u,x))^{II'} \right\} A^{I'}(x,0)
\right. +
& \nonumber \\
& \displaystyle \left.
\left\{ g_3^{II'}(s,t,x) A^{I'}(x,t)-(C_{tu} \, g_3(s,u,x))^{II'}
A^{I'}(x,u) \right\} \right] = 0 &
\end{eqnarray}

The left hand side of this equation when saturated with the
absorptive part due to the $f$ in the narrow width approximation
and worked out to $O(p^6)$, yields the result
\begin{eqnarray}
{640 \, \pi \Gamma_f \over M_f^7} \sqrt{{M_f^2\over M_f^2-4 m_\pi^2}} m_\pi^6 s\, t\, u
\, \, \delta^{I1},
\end{eqnarray}
while the result for the $g$ yields
\begin{eqnarray}
-{6720\, \pi
 \Gamma_g \over M_g^7} \sqrt{{M_g^2\over M_g^2-4 m_\pi^2}} m_\pi^6 s\,t\, u
\, \, \delta^{I1}.
\end{eqnarray}
This reproduces the result eq.(\ref{finetune}) if these
two states were to guarantee crossing symmetry at this order.

We define below the combination $(T^0(s,t,u)^{FT}_m-T^2(s,t,u)^{FT}_m)/3$
and define it to be equal to $A(s,t,u)^{FT}_m$ (despite the fact that
crossing symmetry is not respected) to obtain the expressions below:
\begin{small}
\begin{equation}\label{af2ft}
A(s,t,u)^{FT}_f=
{80 \pi \Gamma^{\pi\pi}_f \over 3 M_f^7} \sqrt{{M_f^2\over M_f^2-4
m_\pi^2}} m_\pi^4
s(-8 M_f^2 - 80 m_\pi^2 + 2 M_f^2 s + 24 m_\pi^2 s - m_\pi^2 s^2
+ 3 m_\pi^2 (t-u)^2),
\end{equation}
\end{small}
and
\begin{eqnarray}
& \displaystyle
A(s,t,u)^{FT}_g={28 \pi \Gamma^{\pi\pi}_g \over M_g^7}\sqrt{{M_g^2\over
M_g^2-4 m_\pi^2}} m_\pi^4
\left(-32 M_g^2 -192 m_\pi^2 + 32 M_g^2 s +368 m_\pi^2 s -
\right. & \nonumber \\
& \displaystyle
\left.
6 M_g^2 s^2 -132 m_\pi^2 s^2  + 2 M_g^2 (t-u)^2 + 12 m_\pi^2 (t-u)^2
+
13 m_\pi^2 s^3- 9
m_\pi^2 s(t-u)^2 \right) \label{ag3ft} &
\end{eqnarray}

\setcounter{equation}{0}
\section{Crossing Symmetric Dispersion Relations}
In Ref.\cite{mrw}, a remarkable dispersive
representation is provided for a system of three
totally symmetric amplitudes, $G_0,\ G_1$
and $G_2$ constructed out of
the three iso-spin amplitudes that we are familiar
with.  In particular, $G_0$
is the $\pi^0\pi^0$ scattering
amplitude.  $G_1$ is constructed by considering the
$I=1$ s-channel amplitude and dividing it by $(t-u)$ and then
considering the cyclic sum.  This amplitude has all
the analytic properties of $G_0$ and thus all results
applicable to it are also applicable to $G_1$.  $G_2$ is
analogously defined after perfoming a further division.
[Note that as a result of these divisions, $G_1$ and $G_2$
in principle verify dispersion relations with fewer
subtractions than $G_0$.]

The dispersive representation is parameterized
by a parameter, $x_0$.   The crossing symmetric dispersion
relations of interest here, arise from first considering
dispersion relations in the so-called $x-y$ plane, where
the Wanders variables $x$ and $y$, are homogeneous variables
of the type $x\sim (st+tu+us)$ and $y\sim stu$.  One then
writes down dispersion relations on straight lines in
the $x-y$ plane given by $y=a(x-x_0)$.  A one-parameter
family of dispersion relations results, when $a$ is further
restricted to be a certain function of $x_0$.  In Ref.\cite{mrw}
$x_0$ is considered in the range,
$0\leq x_0 \leq 50.41$, in order to generate
a closed system of partial wave equations for pion-pion
scattering, whose rigorous validity is significantly larger than
the original system proposed in Ref.\cite{smr1}.
Note that at fixed $x_0$ crossing
symmetry does not impose any constraints on the
absorptive parts of even the higher waves:  constraints
are obtained by comparing results at differing $x_0$.
One may then
write down the dispersion relations for this case and
extract an expansion in powers of
$m_\pi^2$.   We shall first discuss the case of $x_0=0$
at some length and shall say a few words about $x_0\neq 0$.

\subsection{$x_0=0$}
We shall be interested in the treatment of the following
dispersion relations for the three amplitudes of interest,
for $i=1,2,3$.  Furthermore, in the notation of Ref.\cite{mrw},
we would have to supplement the amplitudes $G_i$ with overlines:
$\overline{G}_i$, but for the present work this is redundant and
shall be omitted.
\begin{eqnarray}
& \displaystyle G_i(s,t,u)=
G_i(4,0,0)+\frac{1}{\pi}\int_{4 \, m_\pi^2}^{\infty} \, d\,x
\, {\rm Disc}\, G_i(x,\tau(x,a)) [x-\tau(x,a)] \cdot
& \nonumber \\
& \displaystyle (2x+\tau(x,a)-4 \, m_\pi^2)
\left[{1\over (x-s \, m_\pi^2)(x-t \, m_\pi^2)(x-u \, m_\pi^2)}-
{1\over x^2 (x-4 \, m_\pi^2)} \right], &
\end{eqnarray}
where
\begin{equation} \label{adef}
a= -{stu  \over 4(st+tu+us)} \, m_\pi^2,
\end{equation}
and
\begin{equation}
\tau(x,a)=\frac{1}{2}\left[-(x-4 \, m_\pi^2)+[(x-4 \, m_\pi^2)^2-\frac{16
a}{x+4a}
(x(x-4 \, m_\pi^2)]^{1/2}\right].
\end{equation}

Note the relations for the discontinuities of the three amplitudes
in terms of the absorptive parts of the three s-channel iso-spin amplitudes:
\begin{eqnarray}
& \displaystyle {\rm Disc}\, G_0(s,t)=\frac{1}{3}(A^0+2 A^2)(s,t) & \nonumber \\
& \displaystyle {\rm Disc}\, G_1(s,t)=
\frac{1}{6 \, m_\pi^2} \frac{3s -4}{(s-t)(2s+t-4)}(2A^0-5A^2)(s,t) + &
\nonumber \\
& \displaystyle \frac{1}{\, m_\pi^2} \left[{1\over 2t+s-4} -{2t+s-4
\over 2 (s-t) (2s+t-4)} \right] A^1(s,t) & \\
& \displaystyle {\rm Disc}\, G_2(s,t)=-{1\over 2 \, m_\pi^4}{1 \over
(s-t)(2s+t-4)} (2 A^0 - 5 A^2)(s,t) + & \nonumber \\
& \displaystyle {3\over 2 \, m_\pi^4} {3s-4 \over (2t+s-4)(s-t)(2s+t-4)}
A^1(s,t) & \nonumber
\end{eqnarray}

Furthermore, our treatment shall concern only the absorptive
parts due to $l\geq 2$ states.  As a result, we have the relations:
\begin{eqnarray}
& \displaystyle G_0(4,0,0)=0 & \nonumber \\
& \displaystyle G_2(4,0,0)={3\over 4 \,
m_\pi^2} G_1(4,0,0) ={1\over \pi}\int_{4 m_\pi^2}^\infty dx
{2x-4 m_\pi^2\over x(x-4 m_\pi^2)} {\rm Disc} G_2(x,0) &
\end{eqnarray}

The s-channel iso-spin amplitudes are now obtained by
employing the relations:
\begin{eqnarray}
& \displaystyle T^0(s,t,u)={5\over 3} G_0(s,t,u) + & \nonumber \\
& \displaystyle {2\over 9} \left[(3s -4)  G_1(s,t,u)\, m_\pi^2 -
{1\over 3}(3s^2-16+6tu)  G_2(s,t,u) \, m_\pi^4 \right] &\\
& \displaystyle
T^1(s,t,u)={(t-u)\over 9}(3  G_1(s,t,u)\, m_\pi^2+(3s-4) G_2(s,t,u)\,
m_\pi^4)& \\
& \displaystyle T^2(s,t,u)={2\over 3} G_0(s,t,u) - & \nonumber \\
& \displaystyle {1\over 9} \left[(3s -4) G_1(s,t,u) \, m_\pi^2 -
{1\over 3}(3s^2-16+6tu) G_2(s,t,u) \, m_\pi^4 \right] &
\end{eqnarray}

Following the procedure of expanding out the integrands in powers
of $m_\pi^2$ and inserting the narrow-width approximation for the
absorptive parts of the partial waves, we first evaluate
the contribution of the $f$  to the iso-spin amplitudes
resulting from the crossing symmetric (CS)
dispersion relations, to this order read:
\begin{small}
\begin{eqnarray}
& \displaystyle T^0(s,t,u)^{CS}_f=\frac{40\pi \Gamma^{\pi\pi}_f}{3 M_f^7}
\sqrt{\frac{M_f^2}{M_f^2-4 \, m_\pi^2}} \, m_\pi^4 \left(
-32 M_f^2-192 \, m_\pi^2 -48 M_f^2 s -496 \, m_\pi^2 s +\right. &
\nonumber \\
& \displaystyle
\left. 14 M_f^2 s^2
+172 \, m_\pi^2 s^2+2 M_f^2 (t-u)^2+ 12 \, m_\pi^2 (t-u)^2
-9 \, m_\pi^2 s^3+ 17 \, m_\pi^2 s(t-u)^2  \right) & \label{f2t0cs} \\
& \displaystyle T^1(s,t,u)^{CS}_f=\frac{40\pi \Gamma^{\pi\pi}_f}{3 M_f^7}
\sqrt{\frac{M_f^2}{M_f^2-4 \, m_\pi^2}} \, m_\pi^4 (t-u)\left(
-16 \, m_\pi^2 - \right. & \nonumber \\
& \displaystyle
\left. 4 M_f^2  s -24 \, m_\pi^2  s
 + 3 \, m_\pi^2  s^2 +\, m_\pi^2 (t-u)^2\right) & \\
& \displaystyle T^2(s,t,u)^{CS}_f=\frac{40\pi \Gamma^{\pi\pi}_f}{3 M_f^7}
\sqrt{\frac{M_f^2}{M_f^2-4 \, m_\pi^2}} \, m_\pi^4 \left(
-32 M_f^2-192 \, m_\pi^2 -112 \, m_\pi^2 s +2 M_f^2 s^2 +
 \right. & \nonumber \\
& \displaystyle \left. 76 \, m_\pi^2 s^2 +2 M_f^2 (t-u)^2+12 \, m_\pi^2 (t-u)^2
-9 \, m_\pi^2 s^3 + 5 \, m_\pi^2 s(t-u)^2 \right)\label{f2t2cs} &
\end{eqnarray}
\end{small}
The contribution of the $g$  to the iso-spin amplitudes
resulting from the crossing symmetric dispersion relations, to this order
read:
\begin{small}
\begin{eqnarray}
& \displaystyle T^0(s,t,u)^{CS}_g=\frac{56\pi \Gamma^{\pi\pi}_g}{ M_f^7}
\sqrt{\frac{M_g^2}{M_g^2-4 \, m_\pi^2}} \, m_\pi^4 \left(
-32 M_g^2 -192 \, m_\pi^2
+ 32 M_g^2 s
+ 208 \, m_\pi^2 s \right. &  \nonumber \\
& \displaystyle \left.- 6 M_g^2 s^2 -52 \, m_\pi^2 s^2 + 2 M_g^2 (t-u)^2
+12 \, m_\pi^2 (t-u)^2 + 3 \, m_\pi^2 s^3 + \, m_\pi^2 s (t-u)^2
   \right) \label{g3t0cs} &
\\
& \displaystyle T^1(s,t,u)^{CS}_g=\frac{28\pi \Gamma^{\pi\pi}_g}{ M_f^7}
\sqrt{\frac{M_f^2}{M_f^2-4 \, m_\pi^2}} \, m_\pi^4 (t-u) \left(
-16 \, m_\pi^2  + 12 M_g^2  s  +72
\, m_\pi^2  s +  \right. & \nonumber \\
& \displaystyle \left.
 \, m_\pi^2 (t-u)^2+ 3 \, m_\pi^2  s^2  \right) & \\
& \displaystyle T^2(s,t,u)^{CS}_g=-\frac{1}{2} T^0(s,t,u)^{CS}_g \label{g3t2cs}&
\end{eqnarray}
\end{small}

From the $I=0,2$ iso-spin amplitudes, we now write down
\begin{small}
\begin{equation}\label{af2cs}
A(s,t,u)^{CS}_f=
{160 \pi \Gamma^{\pi\pi}_f \over 3 M_f^7} \sqrt{{M_f^2\over M_f^2-4 m_\pi^2}}
m_\pi^4
s(-4 M_f^2 - 32 m_\pi^2 + M_f^2 s + 8 m_\pi^2 s + m_\pi^2
(t-u)^2)
\end{equation}
\end{small}
and
\begin{eqnarray}
& \displaystyle
A(s,t,u)^{CS}_g={28 \pi \Gamma^{\pi\pi}_g \over M_g^7}\sqrt{{M_g^2\over
M_g^2-4 m_\pi^2}} m_\pi^4
\left(-32 M_g^2 -192 m_\pi^2 + 32 M_g^2 s +208 m_\pi^2 s -
\right. & \nonumber \\
& \displaystyle
\left.
6 M_g^2 s^2 -52 m_\pi^2 s^2 + 2 M_g^2 (t-u)^2 + 12 m_\pi^2 (t-u)^2+
3 m_\pi^2 s^3
+m_\pi^2 s(t-u)^2 \right) \label{ag3cs} &
\end{eqnarray}
The expressions in eq.(\ref{af2cs}) and eq.(\ref{ag3cs}) constitute
some of the most important results in this work.  Also
note the  striking feature that the amplitude
$A(s,t,u)^{CS}_g$ is identical in structure to eq.(\ref{arho})
$A(s,t,u)_\rho$, upto their respective angular momentum
multiplicites of 7 and 3 respectively.

A check to our results arises from considering the sum of
the contributions from the resonances $f$ and $g'$, where $g'$
is a hypothetical resonance whose mass is equal to that of
the $g$, but whose width is tuned to agree with eq.(\ref{finetune}).
The sum of these amplitudes from fixed-t dispersion relations,
{\it viz.}, eq.(\ref{f2t0ft})-eq.(\ref{f2t2ft}) and
eq.(\ref{g3t0ft})-eq.(\ref{g3t2ft}) the latter evaluated
with the width given by eq.(\ref{finetune})
is identical to those from the crossing symmetric dispersion
relations, {\it viz.}, eq.(\ref{f2t0cs})-eq.(\ref{f2t2cs}) and
eq.(\ref{g3t0cs})-eq.(\ref{g3t2cs}) the latter evaluated
with the width given by eq.(\ref{finetune}).  This is due to
crossing constraints being satisfied by the
former in this event.

\subsection{$x_0\neq 0$}
The dispersion relations for $x_0 \neq 0$ for the $G_i$ turn
out to be far more complicated.  Furthermore, the analog of
eq.(\ref{adef}) for non-zero $x_0$ is now:
\begin{equation}\nonumber
a(x_0)=-{stu \over 4(st+tu+us + 16 x_0)} m_\pi^2.
\end{equation}
Furthermore, the are expressions analogous to $\tau(a)$ of
the previous subsection and dispersive representation for
the $G_i$ has been listed explicitly in Ref.\cite{mrw}.  We have
considered these representations and worked out the
contributions of our resonances at $O(m_\pi^6)$.
Consider for instance, the contribution of the $f$ at $O(m_\pi^6)$
to the low-energy expansion:
\begin{small}
\begin{eqnarray}
& \displaystyle A(s,t,u)^{CS,x_0}_f=
{{160\,\pi \,{\it \Gamma_f}\,{\sqrt{{{{{{\it M_f}}^2}}\over {{{{\it M_f}}^2}-4 m_\pi^2}}}}\,
      {{{\it m_\pi^4}}}\,\left( -4 + s \right) \,s}\over
    {3\,{{{\it M_f}}^5}}} + & \nonumber \\
    & \displaystyle
    {{160\,\pi \,{\it \Gamma_f}\,
      {\sqrt{{{{{{\it M_f}}^2}}\over {{{{\it M_f}}^2}-4 m_\pi^2}}}}\,{{{\it m_\pi^6}}}\,
      s\,\over
    {3\,{{{\it M_f}}^7}\,\left( 16 + 8\,s - 3\,{s^2} -
        {{\left( t - u \right) }^2} + 16\,{\it x_0} \right) }} }\cdot
      \left( -512 - 128\,s + 160\,{s^2} - 24\,{s^3} +
        48\,{{\left( t - u \right) }^2} -  \right. & \nonumber \\
        & \left.
        3\,{s^2}\,{{\left( t - u \right) }^2} - {{\left( t - u \right) }^4} -
        1216\,{\it x_0} + 480\,s\,{\it x_0} - 44\,{s^2}\,{\it x_0} +
        60\,{{\left( t - u \right) }^2}\,{\it x_0} \right)  &
\end{eqnarray}
\end{small}
While with $x_0=0$, the low-energy polynomial
was produced by the repeated use of the identity $s+t+u=4$,
for the case at hand, the appearance of the parameter $x_0$ prevents the
factorizing of a series in $m_\pi^2$ into a sum of terms
that is a polynomial in $s$ and $(t-u)^2$ for $A(s,t,u)$.
The result above illustrates our remark.  We also
note that the answer at $O(m_\pi^4)$ is independent of $x_0$
as expected.  Furthermore, it may be easily checked that in
the limit of $x_0\to 0$, we recover our results of the
previous subsection.
It appears, therefore, that only the choice with $x_0=0$
can produce a low-energy polynomial that is manifestly
crossing symmetric.

The analogous result for the $g$ at this order in $m_\pi$
corresponds to the $x_0=0$ answer even at non-zero $x_0$.
The dependence on this parameter manifests itself at the
next order.

\setcounter{equation}{0}
\section{Numerical Results}
We discuss the numerical import of our work in this section.
We first discuss the case of resonance saturation at $O(p^4)$.
It may be seen by inspection that at this order no crossing
constraints arise.  As a result, we may unambiguously compute
the contributions of the $\rho$, $f$ and $g$  respectively.
The primary reason for our consideration of the $\rho$  is that
it sets the scale for the contributions that arise from the
S- and P- wave absorptive parts.  Crossing symmetry dictates
that the presence of the $\rho$ necessarily
implies contributions to the low-energy polynomials of a similar
order of magnitude from the S- waves; here we do not embark on
a detailed numerical analysis.
We insert the values of the parameters listed in Table 1,
with $\Gamma^{\pi\pi}$ given by $\Gamma_{tot} \cdot BF$, where
$\Gamma_{tot}$ is the total width and $BF$ is the
$\pi\pi$ branching fraction, into the terms of
$O(p^4)$ of eq.(\ref{arho}), eq.(\ref{af2ft}) and eq.(\ref{ag3ft}).
Comparing with eq.(\ref{lowenergyexp}), we isolate the
$\beta_{i}, \, i=1,2,3,4$ and tabulate the results in Table 2.
An inspection of the Table 2 shows
that at $O(p^4)$ the contributions from the $f$ certainly cannot
be neglected even in comparison with the contribution of the
$\rho$.  The contribution of the $g$ is an order of magnitude
lower to $\beta_i$.  It is then a standard exercise
to translate these results and read off the
contributions of the resonances to the the one-loop chiral
coupling constants, the $\overline{l_i},\, i=1,2$, which
are also tabulated in Table 2.  Pion-pion
scattering also involves the coupling constants $\overline{l_i},\, i=3,4$.
Resonance saturation does not contribute to these coupling constants
at this order.
It is also instructive to compare our results with those from effective
lagrangian comptuations of Ref.\cite{dt,bgs,hl2} which are
found to be in agreement, when the constraints from the
Froissart bound are enforced on the latter.

At $O(p^6)$ we compile the contributions of the resonances
of interest to the $\beta_i$.  This comparison is performed between
eq.(\ref{arho}), eq.(\ref{af2ft}),
eq.(\ref{ag3ft}) and eq.(\ref{lowenergyexp})
and then between eq.(\ref{arho}),
eq.(\ref{af2cs}), eq.(\ref{ag3cs}) and
eq.(\ref{lowenergyexp}), upon inserting the values of the parameters
listed in Table 1.  This procedure yields the results tabulated
in Tables 3 and 4 respectively.
One sees that the contributions from the fixed-t
and the crossing symmetric dispersion relations have important
and interesting discrepancies.  However, if the width of the
$g$ is tuned to satisfy eq. (\ref{finetune}),
(we have referred to such a
hypothetical resonance as the $g'$), then the sum of the contributions
of $f$ and $g'$ to each of the $\beta_i$ is the same no matter
if we compute them from the fixed-t or the crossing symmetric
dispersion relations as indeed it should be.

It turns out that the requirment that crossing symmetry be restored at
this order by the $f$ and the $g$, eq.(\ref{finetune}), with
the known masses of the $f$ and $g$  and the width of
the $f$ from Table 1, predicts
for the $\pi\pi$ width of the $g$ $\Gamma^{\pi\pi}_g$,
the value of 109 MeV.
This is to be compared with its experimental value
of 38 MeV.   It is precisely this problem which led us to consider
the crossing symmetric representations:
the problem of the mismatch between the ``predicted''
and observed widths of the $g$ resonance
is evaded by considering resonance saturation
with manifestly crossing symmetric dispersion relations.  From
Table 4 we can unambiguously read off the contributions of the
$f$ and the $g$ to the low-energy polynomials. {\it Thus the results
of Table 4 constitute the central results in this work.}
Somewhat improved values for the $\beta_i$ can
be obtained by replacing the narrow-width approximation
by other phenomenological models of these and higher partial waves.
Since the resonances considered
here essentially dominate the pion-pion phenomenology, the
present work gives a realistic estimate of the contributions of
the relevant partial waves.

\setcounter{equation}{0}
\section{Conclusions}
In this work, we have shown that $l\geq$ states contribute to
the low-energy polynomial in a manner that can be computed explicitly
from the dispersion relations with two subtractions.  Whereas
fixed-t dispersion relations require us to satisfy crossing constraints,
the problem can be avoided through the use of manifestly crossing
symmetric dispersion relations.  We have shown that, since the
width of the $g$ is smaller by a factor of nearly 3 than the requirement
of crossing constraints of the fixed-t dispersion relations, it
is practical to evaluate the contributions of the $f$ and $g$ states
using the crossing symmetric dispersion relations.
We conclude with the remark that the subtle property of crossing symmetry
in field theory and dispersion relations must be treated with great
care in matters of principle and practice.

\medskip
\noindent {\bf Acknowledgements:}  It is a pleasure to thank
Prof. H. Leutwyler for discussions.  I also thank P. B\"uttiker and
D. Toublan for a careful reading of the manuscript, and D. Toublan for
useful correspondence on tensor meson dominance.

\bigskip

\newpage

redpajama_set_name: RedPajamaArXiv


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LAS VEGAS, N.M. — Sunbury Press has released Mela Suse Vigil Duran Carvalko's memoir of her childhood titled Maybe Tomorrow.
A FAMILY THAT CONFRONTS THE FORCES OF MENTAL ILLNESS, AND LEARNS THAT NO BURDEN IS SO HEAVY AS TO DEFEAT AN ETERNAL LOVE.
Quite apart from other memoirs, the author captivates the reader's attention, by painting a portrait of mental illness through the eyes of a child. As a child growing up during the 40s and 50s, in the rural Spanish farming communities of New Mexico/Colorado, she recounts her father's courage and refusal to accept the finality of his wife's mental illness, and how he single-handedly raised four daughters, teaching them what it means to survive, drawing strength from the pride of self-worth, and the humility of self-reliance.
I have come full circle to the land of my father's birth, Rociada, New Mexico, where I breathe in the aspirations of my ancestors, where I hear the swish of their scythe against the wheat, their plough turning a stubborn, bounteous earth, where I see the rutted and hooved reliefs of wagons and beasts, burdens, which led directly to a remarkable life, one guided by a dream of an angel sitting on my shoulder, watching over me.
The screams frightened me beyond verbal description, but this fright was quickly supplanted by the even greater one of not knowing where I was going and what waited for me at the top. We climbed the metal grated stairs, each step causing vibrations that made me feel they would collapse at any moment. The higher we climbed, the louder the screams became. I was afraid to go on, but afraid of what was behind me. As we ascended, my heart beat faster with each step. I felt sick to my stomach wondering what evil waited for me, but I never complained, and did what was expected of me. By the age of three I had learned to control my emotions, and as I grew older, I found that self-control in the face of the unknown would help me survive.
As we neared the top, I could hear doors creak open in front of us and slam shut behind us. When we reached the final step, we came to a lobby with a long hallway. The door closings reverberated off the high ceiling and masonry walls; harsh lights overhead reflected off shiny, off-white, dirty-beige, and pea-green walls. The floors were covered with hard linoleum squares, worn, scuffed, and cracked, and though polished to a high sheen, every square was embedded with the dirt of half a century.
MELA SUŚE VIGIL DURAN CARVALKO has spent many years investigating the genealogy of Spanish families that settled in San Miguel/Mora counties, New Mexico. In addition to documenting her accounts of the life and times during the mid-twentieth century, she devotes time as an artist and musician. She studied art at Sacred Heart University and mentored under impressionist artist Albert Werner. Currently she lives between New Mexico and the east coast with her husband, three cats and dog Leila.
Dysfunctional Kansas family battles it out in April Knight thriller "Nobody Dies in Kansas"
LAWRENCE, Kan. — Sunbury Press has released April Knight's psychological thriller Nobody Dies in Kansas.
"Something bad always happens," she answered without turning around. She wiped the kitchen counter with a dirty dishrag and hung it up to dry.
"I mean, is something bad going to happen to us?" Linda asked.
Mother turned around and looked at her daughter with annoyance.
"Have you done something that is going to embarrass and humiliate me? Like the time you picked flowers out of the churchyard?" Mother put her hands on her hips.
"No, I haven't done anything and I didn't know I couldn't pick the flowers. I thought since they were growing in the churchyard they belonged to God and it was OK to pick them because God has lots of flowers," Linda explained again. She'd been explaining ever since she'd picked the flowers two years ago when she was six.
"Well, to answer your question, yes, I'm sure something bad will happen to us. I'm a very unlucky woman," Mother said.
"Do you think something bad is going to happen to me, too?" Linda asked.
She knew something bad was going to happen. She thought about what Mother had said: she was going to die, she was going to be kidnapped and cut up and thrown into the river.
She wondered who she'd miss after she was gone and decided there wasn't anybody. Nobody liked her at school, nobody liked her at home. No, she wouldn't miss anybody and nobody would miss her, not even Sue. Maybe Mother wouldn't even notice she was gone. Maybe she'd be gone for a month before Mother missed her.
It would be nice if somebody missed her. It would be nice if somebody cried because she was gone forever. She couldn't think of anybody who would cry.
Thinking about it made her cry for herself.
Linda Davison is tall, beautiful, powerful, and strong enough to escape from dangerous snares and defeat evil monsters … in her dreams. The eight-year-old Kansan dreams of someday becoming just like her silver screen heroine, Tandaleah, Fire Goddess of the Volcano—a gorgeous conqueror of the jungle and its many pitfalls and villains. In her real life, however, Linda is what her mother tells her she is: skinny, scrawny, scraggly, and scared—not at all like the queen of the jungle.
Dave Davison has successfully spent most of his life cruising along, not making waves, flying under the radar. Just the way his family expects. His one mistake—marrying his cold, selfish wife—however, has slowly snowballed over the years, resulting in an unwanted child, a hateful marriage, and a general sense of not having met his full potential.
The Davisons take steps toward their ideal lives and away from each other in this psychologically demented family story. Only one Davison will achieve their goal—who will it be … and will the adage ring true that "Nobody dies in Kansas"?
April Knight decided at the age of nine she would be a writer and live on the crater rim of a volcano and be called Tandaleah, Fire Goddess of the Volcano. At the age of thirteen she sold her first story to anational magazine and her first book became a best seller. She moved to Hawaii and lived near the Kilauea volcano but failed to become Tandaleah the Fire Goddess.
April has been a missionary in New Mexico, a barrel racer in rodeos in Colorado, panned for gold in the Yukon and has ridden camels in the outback in Australia. She is currently living a nice quiet, respectable life in Seattle where she writes about blood awful murder.


text:
Dipoena linzhiensis är en spindelart som beskrevs av Hu 200. Dipoena linzhiensis ingår i släktet Dipoena och familjen klotspindlar. Inga underarter finns listade i Catalogue of Life.

Källor

Klotspindlar
linzhiensis


My husband has been on 4-month drug holiday from Sprycel 50 mg due to shortness of breath. Because SOB has diminished but not gone away entirely, he will likely switch to 300 mg Bosulif if/when his PCR goes above .1. It is at .026. Would like to hear from others on Bosulif with advice for how best to take drug, what to avoid, etc. For example, time of day, what kind of food/water amounts, etc. And he does enjoy beer or wine with dinner. Has this been a problem?
Our hope is that on this "lower" dose of 300 there will not be severe side effects. My husband has been very responsive to TKI's since diagnosis 2012 and in MMR the whole time. A previous TFR failed after 3 months and he returned to MMR almost immediately.
I plan to also post this on the LLS community forum since I'm a bit confused about the level of activity on the two forums at this time. As always, am extremely thankful to others who share experience and advice on this journey.
TTT this was posted right before the forum went offline for a day or two, so hoping may get some responses.
UPDATE: He will start on 100 mg Bosulif and perhaps titrate up, NOT on 300 mg as I had originally posted.
Bosutinib is a powerful TKI. The 100mg dose seems low. I was on it for a while at a starting dosage of 400mg and felt good. But had to change off it recently due to my liver enzymes (ALT/AST) being to high. I think I was an exception that couldn't work through that issue. No alcohol while the liver values were high. It should be taken with food. No grapefruit. I took it in the morning with breakfast. Otherwise Bosutinib is usually well tolerated.
The thing to know is it can give some very bad diarrhea issues at the start, but if you can ride that out it usually gets better.
similar situation as your husband. Severe PEs on Sprycel after 5 very successful years. Intolerable at lower doses as well.
just switched to 200mg Bosulif 3 days ago. Going to 400mg by adding 100 every week.
Thanks, Mike B. I am being moved over to Bosulif in a few weeks after not being able to tolerate Gleevec, Tasigna or Sprycel. I can deal with the gastro issues so if that's all I have to deal with I'll consider myself lucky! Have a great day.
Update: my husband is no longer in TFR and will likely go on Bosulif. Would like to hear from others on Bosulif — especially those after TFR. Beginning dosage? How quickly titrate up? Current dosage? Side effects?
I recently came off Bosutinib (my third line therapy) due to intolerance. I have switched back to Dasatinib (my second TKI), since although my PCR results on Dasatinib were sub-optimal, they weren't that bad (no higher than 0.233%) and I didn't fancy the prospect of Nilotinib, which my Consultant was suggesting, due to potential cardiovascular adverse events and having to fast twice a day. I also have Ponatinib left to try (definitely a last resort).
From my experience on Bosutinib, I would suggest you speak to your husband's Consultant to try a lower starting dose than the 500mg indicated for patients previously treated with another TKI, since this will lower the risk of diarrhoea and abnormal Liver Function Tests (LFT). Make sure he has a monthly LFT for the first 3 months. I had to come off Bosutinib due to elevated ALT readings and this is the first TKI I have failed due to intolerance.
I hope your husband has success with Bosutinib if this is the TKI he chooses next. Apart from the ALT issue, I didn't have any other major side effects and the diarrhoea wasn't as bad as I feared (it was worse on Dasatinib, as I'm starting to experience again!) I also achieved MMR, which made it particularly difficult to accept the decision to have to come off Bosutinib.
@James thx so much for the reply. I am curious about your statement about starting dose of 500mg for those coming off another TKI? I believe they will start at 100 and titrate up. My husband went into MMR very quickly on both Tasigna and Sprycel and sustained MMR on lower doses. Sprycel was great drug for him except when he experienced breathlessness. I wish he had tried even lower dose. He went off Tasigna because of concern of cardiovascular events. Thx for sharing your experience and hope your new drug regime works well. If any advice to share to keep diarrhea at minimum or treat it would appreciate it. Again many thanks.
@chigi could you please post how you did on Bosulif and how quick was the titration? Any advice for when and how to take the drug? side effects? thanks. Wish there was a PM feature!
@liamsdad would love to hear more about your experience. dosage? side effects? wish there was a private message tool.
I started on a 300mg dose of Bosutinib for 2 weeks and then increased to 400mg. I hit MMR in less than 2 months, so didn't need to increase to 500mg (newly diagnosed patients will increase to 400mg, however, previously treated patients will increase to 500mg - these are the manufacturer's recommended dose guidelines). However, my Liver Function Test result at 3 months showed my ALT level had increased to 270, so I had a treatment break for over 2 weeks to allow this to recover. I restarted again on 300mg, however, after 4 days my ALT level increased again, so I had to come off Bosutinib. My Consultant stated doses less than 300mg aren't effective.
Diarrhoea wasn't a particular problem for me on Bosutinib. I only had to take Loperamide twice, which did the trick. I experienced nausea during the first few weeks. Although I was prescribed Ondansetron, this didn't really help. I found stem ginger cookies were more effective and tasted much better! I also switched from taking Bosutinib at breakfast (the manufacturer's instructions specified this) and took it in the evening after dinner (as I have done with the other 2 TKIs I have previously taken). My Consultant was happy for me to do this and it also helped to reduce the nausea.
Hi, Alison. I was given your email so I hope you got my message. If not let me know here and I'll check back here. I've been away for a few weeks and haven't been online as much lately.
@James thx for another detailed reply. My husband has been fortunate that he remained undetectable at low doses of both Tasigna and Sprycel. That's why we are hoping he can start on lower dose of Bosulif. Good luck on your journey and thx for the tips.
TTT in case anyone has any recent advice/experience about Bosulif. If PCR again above .1 my husband will go on 100 mg Bosulif and titrate up from there. Hoping 200 or 300 will do the trick without bad side effects. Would love to hear from others on Bosulif.
I was switched to Bosulif from Sprycel after rejecting the latter. My doctor and Dr. Kantarjian (MD ANderson location) decided to put me on 100mg Bosulif and eased me into the the new drug slowly. Dosage was raised every 2 weeks till I hit 300mg. My last bone marrow showed fast response so I was not moved to 400mg. I take my TKI about 1/3 into my breakfast drink 1/2 bottle of water and my supplements about 3/4 into breakfast and drink the rest of my water. A cup of coffee for liver counts and try to eat foods to promote liver health. Rest of supplements later in day with a healthy fat. Diarrhea has not been an issue. You will experience much softer constitutions for sure if you get by the diarrhea side effect. I do not eat as spicy foods as I use to. No need to rock the boat there. By taking my pills in the morning, the bathroom time has been just after breakfast everyday. I did read up on the Bosulif diet and I started eating a diet of what was suggested. I lost 15 pounds unintentionally but as I eased in to more variety of food I got back to my normal/healthy weight. I am not sure if I over reacted by cutting out regular food stuff but I was never nauseous. I feel I could have eaten regular food faster than I did.
Hi Alison - sorry for delayed response. I started with 100mg, then 200mg after 3 days, then 300 mg after 3 days.
@chigi, how about any side effects? and are you still on 300 mg? thanks.
@Steff, thanks so much for all that info. Good to hear you are doing well on 300. It seems that most of the really bad side effects are at 400 or 500 dosages.


text:
Wacky Water Towers Across the South
What is that off in the distance? Is that a giant peach?
By Nellah Bailey McGough
Credit: Courtesy of the Richards Group
Water towers don't have to be boring. In fact, some towns have come up with creative disguises that will surely put a smile on the faces of passers-by. In 1995, "Eat Mor Chikin" appeared for the first time on an Atlanta billboard being painted by a pair of rebel cows. In 2008, the renegade Chick-Fil-A cows painted their first water tower. And it's located at the Chick-Fil-A Headquarters in Atlanta, GA.
Credit: Courtesy of Hilton Mom Voyage
Ever wonder who paints these enormous structures? We spoke with Jim Kelly, owner of Industrial and Commercial Signs in Conehatta, MS, who has painted water towers from Albuquerque to Miami. Jim and his team paint on average about 20 towers each year. One of his favorites is the Hollywood, Florida tower. He sketches the images on these massive water towers mathematically. Some of his most difficult and time-consuming jobs were water towers in Panama City, FL and Luling, TX. The tower in Luling was painted in camouflage as a tribute to the Troops. Another of Jim's works can be found at Pensacola Beach, FL.
Luling, TX, also has another fun water tower that is painted like a watermelon. Luling's "Watermelon Thump" is a yearly festival which began in 1954 to celebrate the watermelon farming heritage of this small town.
According to Brian West, Media and Community Relations Manager of Publix Grocery Stores, the "cake" water tower in Lakeland, FL was built and dedicated in 1982, and still exists as a working water tower today. The design was the idea of Publix founder, George Jenkins (Mr. George) and President, Joe Blanton. There are 11 candles on the cake which are on a timer to light up at dark. The center candle also serves as an aerial beacon for planes.
pIn the South, we're so smitten with produce that we write songs about it, name beauty queens after it, and even make it our team mascots. (Go, Fighting Okra!) But perhaps the ultimate declaration of love is to put a fruit or vegetable on a water tower, flaunting it high in the air for all to see. In 1981, Gaffney, South Carolina, showed its abiding affection for peaches by erecting a 1 million-gallon water tower just off I-85, between Exits 90 and 92. The artist, Peter Freudenberg, worked to make it look like an actual peach, and his efforts with the cleft were so successful that The Peachoid is now jokingly referred to as the
| Credit: Photo: Art Meripol
In 1958, the Dixie Cup Corporation located in Lexington, KY, decided to build a water tower to look like the little Dixie Cup synonymous with the company. The current owners of the property wanted to remove the tower but the city refused as it serves as a navigation device for the nearby airport.
In Tipton, MO you'll find an "8 Ball" water tower that was built in 1968 by Ewald Fisher, owner of Fischer Manufacturing Company. The billiard table manufacturer has since closed but the citizens of Tipton voted to keep it up for visitors to enjoy. The tower is generally regarded as the world's largest eight ball and is registered on the list of World's Largest Things.
Credit: Courtesy of the City of Ruleville, MS
According to DeWayne Griffin, Public Works Director for Ruleville, MS, these tanks were built in the early 1920's to serve a local cotton compress. Though not in use today, they were cleaned and painted in 2010 by Alderman Billy Marlow who added the Hot & Cold labels simply for good humor and a conversation starter. We agree! (Photo credit: City of Ruleville)
(photo of hot and cold water towers here)
Located in the heart of the Shenandoah Valley, Mount Jackson, VA is easily identified from I-81 exit 273 by the water tower painted as a basket of apples which celebrates the apple industry of this area.
Credit: Courtesy of Maker's Mark; Artist: Eric Henn
Home of Maker's Mark Distillery and a stop on the Kentucky Bourbon Trail, Lebanon, KY officials came up with a brilliant idea of changing the local water tower to look as if bourbon is spilling out of this 135 ft. structure. This brand new attraction will be a fun photo op for visitors and the only place to get the "largest Maker's pour in the world!"
If you're in Alexandria, LA around the holidays, check out their creatively decorated water tower. Thousands (2700 red, 3800 blue, and 650 white, to be exact) of twinkle lights are draped over it making it resemble a big, beautiful jelly fish. This tradition began in the early 1970s. It is lit the beginning of Thanksgiving week and stays illuminated until New Year's Day.
Credit: Courtesy of the City of Alexandria, LA
If strawberries are your thing, head to Poteet, TX and Plant City, FL to see their sweet strawberry water towers.
The Groom, TX water tower has taken many travelers by surprise who think the tower is about to topple over. In fact, in 1980 owner Ralph Britten built it that way on purpose. Mr. Britten obviously has a good sense of humor.
These festively painted water towers often have a story behind them, which makes them doubly interesting. If you're traveling the byways and highways this summer, keep an eye out for these and other wacky water towers. We'd love to see others across the South so please post pictures if you run across any.


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Most Washington teens reject alcohol and other drugs
Healthy Youth Survey explores attitudes and behaviors of middle and high school students
Contact: Kelly Stowe • Department of Social and Health Services • 360-902-7739 • Kelly.Stowe@dshs.wa.gov
OLYMPIA-Results for the 2016 Washington Healthy Youth Survey (HYS) show that teen rates of substance use in our state have remained mostly unchanged since the last survey was taken in 2014, and that most teens avoid alcohol, marijuana, tobacco and other drugs.
"The health, safety and economic impacts of substance use disorders affect many individuals, families and communities in our state, and a wide range of organizations at all levels are partnering to prevent them," said Governor Jay Inslee. "A big thank you goes out to all of the students who took time out of their busy school days to take the Healthy Youth Survey. This survey provides crucial information on adolescent health, behaviors and perceptions. It helps us in making the right decisions to ensure that the next generation is the Healthiest Next Generation."
The HYS is taken every two years by students in grades 6, 8, 10 and 12, who voluntarily answer a wide variety of questions about their health behaviors. In the fall of 2016, over 230,000 students in over 1,000 schools from 236 school districts in all 39 counties took part. The survey provides state and community organizations with needed information about which teen health issues to focus on.
One of the concerning changes since the last survey is that the percentage of 8th graders who believe there is great risk in using marijuana has declined from 53 to 48 percent. Since marijuana is now more visible in communities with advertising and retail stores, state and community organizations and schools have increased education and prevention efforts to discourage underage use. These efforts may be helping to prevent an increase in use, with 17 percent of 10th graders reporting use in the past month, which has not changed since 2014.
Preventing underage drinking has long been a statewide priority, and alcohol use by 10th graders has dropped by 12 percentage points since 2006. However, the number of students who use alcohol has not changed since 2014. In 2016, one out of five 10th graders (a total of about 16,737 students) drank alcohol in the past month. Alcohol plays a significant role in all three leading causes of death among youth: injuries, suicides and homicides.
The number of teens who said they drove a car after using alcohol or marijuana is cause for alarm. More than half (51 percent) of the 12th graders who reported marijuana use in the past 30 days said they had driven within three hours of using marijuana.
E-cigarette/vapor product use significantly dropped from 2014 to 2016, but remains a concern because of its prevalence and association with other tobacco and substance use. E-cigarette use in the past month among 10th graders dropped from 18 percent in 2014 to 13 percent in 2016. Over twice as many 10th graders reported vaping (13 percent) as smoking cigarettes (6 percent), and 65 percent of 10th graders who vaped reported using marijuana.
"Growing up is difficult. The issues facing our youth today are big and have serious life consequences. Parents, teachers and agencies all help guide youth when facing these challenges" said Pat Lashway, Acting Secretary for DSHS. "This information will help the 'helpers' drive home the true impact of drugs on the young developing brains before it's too late." Because the teen brain is still developing, alcohol and other drug use can cause more severe and permanent damage compared to those who start using at age 21 and older. National data identifies the risks such as poor grades and not graduating, due to problems with memory and concentration; serious injuries and death from driving under the influence; unwanted and/or unplanned sexual activity; addiction; depression and anxiety with long-term use.
Parents and guardians are the number one influence on children's decisions about alcohol and other drugs. All adults can help teens avoid the negative consequences of substance use by talking with them early and often about the risks, locking up any alcohol, marijuana or prescription drugs in the home, reminding them that most of their peers are making healthy choices, and having clear rules and consequences to discourage use. Visit StartTalkingNow.org for proven tips on how to talk, monitor and bond with teens. For more information about the survey, including other results and fact sheets, visit the HYS website.
Washington state is recognized nationally as a leader in supporting evidence-based prevention practices and collaborating with community-based prevention organizations. Survey results for mental health, nutrition, physical activity and school engagement will be analyzed and released over the next few months.
The survey is a collaborative effort between DSHS and the Department of Health (DOH), the Office of Superintendent of Public Instruction (OSPI) and the Liquor and Cannabis Board (LCB). The results provide state and local organizations with needed information to plan, implement and evaluate publicly funded programs.
data and evaluationhealthy youth developmentmental healthsubstance abuseteens


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Dr. Dominic F Dixon®
Executive Director @ UNADAP
Expertise: UN Geopolitical Foreign & Public Policy
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Dominic Dixon
Living for the Audience of One!
NATURE, GOD'S NATURAL BEAUTY!
DOWNLOAD/ READ PDF HERE
Nature is one of God's most beautiful, living creations. Through nature, God is able to teach us, speak to us, and provide for us. Psalms 95:4-5 reminds us about God who created nature. "In his hand are the depths of the earth, and the mountain peaks belong to Him. The sea is His, for He made it, and His hands formed the dry land."
During the lockdown of 2020, we felt nature reclaiming its space with the nostalgic chirping of birds, cool weather and the non-verbal melodic chanting of Mother Nature; "The heavens declare the glory of God; the skies proclaim the work of His hands." (Psalms 19:1); which was silenced over the decades with the noise of the industrial revolution and climate change.
Greenhouse gas emissions may perhaps have dipped during this season of humans being in lockdown, but, sadly, our dreaded history of pumping of indiscriminate amounts of CO2 into the atmosphere with the industrial revolutions, mainly, mass production; will come back to haunt us, post the lockdown, and perhaps increase as we continue our greed to over consume whilst being under judicious. Now, with the fourth industrial revolution of social media, mobile, Internet of Things (IoT) and artificial intelligence (AI), Isaiah 24:4-5 gives us the bitter reality of what we've done to the earth: "The earth dries up and withers, the world languishes and withers, the heavens languish with the earth. The earth is defiled by its people; they have disobeyed the laws, violated the statutes and broken the everlasting covenant."
Both Bitcoin and NFTS (Non-Fungible Tokens) which are the digital equivalents of cash and collectibles, generates the same amount of carbon emission and footprint per transaction, equivalent to 680,000 plastic card transactions at super markets, or an equivalent of over 51,000 hours of YouTube gorging.
India has constantly committed to its responsibilities and obligations to the United Nations Framework Convention on Climate Change (UNFCCC). India is a forerunner in Climate Action, and the Climate Action Tracker has rated the India's efforts as '2 degree compatible', which means that if all countries made efforts like India's, the average global temperature rise could be limited to 2°C by the year 2100, in keeping with the Paris Agreement and Kyoto Protocol. According to Babul Supriyo, MoS Climate Change, GOI, "India is the world's only major economy to be rated so. India's intensity of GDP reduced to 12% between 2005 and 2010 while a reduction of 24% was achieved between 2005 and 2016."
Therefore, let us be mindful that we are stewards on God's green planet, and we must take care of it, as Mother Earth takes care of us.
Dr. Dominic F Dixon
EDUCATION - a powerful weapon against poverty!
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Home » News » Serbia's government: Europe or Russia?
Serbia's government: Europe or Russia?
posted by Cioce News | October 16, 2014 | In News
Not the best way to play the game
UNDER Aleksandar Vucic, Serbia's prime minister, the country is caught between its European ambitions and his autocratic drift. This week's visit by Russia's president, Vladimir Putin, highlights Serbia's dilemmas. Its main strategic goal is to join the European Union, yet it is refusing to apply EU sanctions on its traditional ally, Russia. Indeed, to celebrate Mr Putin's arrival, a military parade to mark the 70th anniversary of the liberation of Belgrade was brought forward by four days, with Russian fighter jets flying over the capital.Mr Vucic's treatment of the Serbian media also has a Russian hue. Discussing a sensitive topic, a senior editor slips her phone under a cushion, fearful that the secret services are listening. One of her journalists went to interview a man who refused to talk after being warned off by the secret police. A popular interview show has been taken off the air. Anyone asking critical questions of Mr Vucic risks a savaging by tabloids loyal to him.According to Serbia's Independent Journalists' Association, free speech and criticism "are dying in the Serbian media" and…
Link to article: www.economist.com/news/europe/21625793-vladimir-putins-visit-and-football-match-rekindle-rows-serbia-europe-or-russia?fsrc=rss|eur
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French public finances: Budget, fudge it
Harold Ramis, 'Ghostbusters' actor, 'Groundhog Day' director dies at 69
Italian politics: Bickering and back-stabbing
Maduro government 'occupies' Venezuela electronics chain
UK trade deficit edges down in November, helped by exports to recovering EU


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Epiphany Cathedral
Diocese of Venice in Florida
http://www.epiphanycathedral.org Facebook
nault@epiphanycathedral.org +19414843505
The Church of Epiphany in Venice, Fla., was founded as a mission of St. Martha Church in Sarasota in 1935. The parish was established in 1950 and the current Church was dedicated in 1980. When St. Pope John Paul II established the new Diocese of Venice in Florida in 1984, the Church of the Epiphany was elevated to Epiphany Cathedral. Epiphany Cathedral has hosted numerous events including the installation of two bishops and the ordination of dozens of priests.
Weekdays 8 a.m. to 11:30 a.m. and 12:30 p.m. to 4:30 p.m.
Mass: Monday through Friday 7 a.m. and 8:30 a.m., Saturday 8:30 a.m., 4 p.m., 5:30 p.m., 6:30 p.m. (Spanish), Sunday 7:30 a.m., 9 a.m., 11 a.m., 12:30 p.m. (Polish), 5:30 p.m.
Eucharistic Adoration: Fridays noon to 7 p.m.
Saturdays 3 p.m. to 3:45 p.m., and the Thursday before the first Friday after the 7 a.m. and 8:30 a.m. Masses.
Those making a pilgrimage to the Cathedral during non-Mass hours are encouraged to call ahead to arrange a tour. The Holy Door is located by the south entrance to the Cathedral - the entrance closest to the Post Office.
350 Tampa Ave. W., Venice, Vereinigte Staaten von Amerika


Those who know me best know of my love for minigolf. It goes way back to my childhood, playing at the local courses and trying to find a new courses on almost every family vacation. So when I saw there was a minigolf game on Nintendo Switch, I was excited. Yes, Infinite Minigolf not the same as actually playing, but maybe like you, I was curious if the great game designers over at Zen Studios could make something good enough to satisfy my desires until the next real course.
On the surface, it does a great job of recreating the look and feel of minigolf. The only unfortunate thing is that the graphics could be more crisp and take advantage of the high definition output of the Switch. They aren't horrible, by any means, but I have definitely seen better on the system. Similarly, the music is not bad, but it can get old after a long session of play.
Once you finish your download, you'll see the game contains a ton of crazy holes. Some of them could be found on a real-life course, while the majority of them could probably only be pulled off in a video game. The game's physics usually work exactly as you would expect with only a few hiccups along the way. Similarly, putting is usually spot-on, but every once in awhile, you might be left scratching your head about why you didn't hit the ball as hard or soft as you thought you did.
What I didn't know going into the game was why the game is, in fact, called Infinite Minigolf. I originally thought there was no way they could really have an unlimited number of courses in the game. How they ended up pulling it off was by outsourcing creation to the players themselves. In fact, the game has quite a toolset for creating your very own course, which you can upload to share with the entire community. This is what will continue to bring minigolf fans back for more. Whether you enjoy creating or you love playing what others have made, the fun will only stop when the creativity stops.
Whether you play on your own or with up to seven of your friends, you will pretty much never run out of courses, which means it's quite the steal. And if you want even more, you can download two free DLC packs (Tortuga and Hangar 37), each containing 108 new holes, four tournaments, tiles, objects, and avatar items. If you're like me and love minigolf, I highly recommend picking up Infinite Minigolf for your Switch.