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

The stars observed in the universe tend to cluster in huge self-gravitating
systems, being the galaxies among the most noticeable and studied of them.
Galaxies can be described by models whose mass is distributed symmetrically
about an axis to a finite distance of it i.e., the galaxy radius. Particularly
useful models are those restricted to a plane or thin disk, since for many
galaxies like the Milky Way its height is small compared to its radius. For
galaxies in general, the average time between collisions or individual meetings
(mean collision time) is greater than the system's life time. Many of the
current models take Newton's law as their field equations \cite{LB, mestel, T1,
T2, HunterToomre, KAL1, jiang00, jiangmos02, GR, jiang, PRG}. However, many
models have been developed recently under general relativity \cite{Lemos1,
Lemos2, Lemos3, gonzalez-letelier, gonzalez-letelier2, semerak-zacek1,
semerak-zacek2, semerak-zacek3}, being one of the main motivations for including
corrections made by general relativity the actual incompatibility between the
rotation curves of theoretical models and the ones observed.

The post-Newtonian approximation introduces general relativity through a series
over the speed $(v/c)$. For Minkowski's background metric, the first
post-Newtonian corrections (1PN) are included taking the terms
\begin{eqnarray}
g_{00} &\approx& -1 + \stackrel{2 \: \: \: \: }{g_{00}} + \stackrel{4 \: \: \:
\: }{g_{00}}, \\
g_{i0} &\approx& \stackrel{3 \: \: \: \: }{g_{i0}}, \\
g_{ij} &\approx& \delta_{ij} + \stackrel{2 \: \: \: \: }{g_{ij}},
\end{eqnarray}
where the upper index denotes the order of the power of $(v/c)$ of the term.
Using harmonic coordinates, the 1PN order potentials are defined as
\begin{eqnarray}\label{ec_pot_pn_def}
\stackrel{2 \: \: \: \: }{g_{00}} &\equiv & -2\phi /c^2, \\
\stackrel{3 \: \: \: \: }{g_{i0}} &\equiv & \zeta_i /c^3, \\
\stackrel{4 \: \: \: \: }{g_{00}} &\equiv & -2(\phi^2 +\psi) /c^4.
\end{eqnarray}
Henceforth we consider only the stationary case, so the explicit
time-dependent terms along with the potential vector $\boldsymbol{\zeta}$
disappear in all equations.

The stationary field equations in the 1PN approximation are
\begin{eqnarray}
\nabla^2 \phi &=& \frac{4\pi G}{c^2} \stackrel{0 \: \: \: \: }{T^{00}},
\label{ec_campo_pn1} \\
\nabla^2 \psi &=& 4\pi G ( \stackrel{2 \: \: \: \: }{T^{00}} + \stackrel{2 \: \:
\: \: }{T^{ii}} ), \label{ec_campo_pn2}
\end{eqnarray}
where, in the classical limit, potential $\psi$ vanishes and $\phi$ tends to the
Newtonian potential $\phi_N$. Whereas that
\begin{equation}
\frac{\mathrm{d} \mathbf{v}}{\mathrm{d} t} = - \nabla \phi - \frac{1}{c^{2}}
\left[\nabla \left(2 \phi^{2} + \psi \right) + 4 \mathbf{v} (\mathbf{v} \cdot
\nabla \phi) - v^{2} \nabla \phi \right] \label{ecmovimiento1PN}
\end{equation}
is the stationary equation of motion.

A complete statistical description is achieved by knowing the distribution
function (DF) of the system. The DF satisfies a continuity equation in the phase
space called the Boltzmann equation. In the 1PN approximation, the collisionless
Boltzmann equation (CBE) for a many identical particles system is given by
\cite{Rezania}
\begin{equation}\label{ec_general derezania}
v^i \frac{\partial F}{\partial x^i} - \frac{\partial \phi}{\partial x^i}
\frac{\partial F}{\partial v^i}- \frac{1}{c^2} \left( \frac{\partial
\phi}{\partial x^i} (4 \phi + v^2) - \frac{\partial \phi}{\partial x^j} v^i v^j
+ \frac{\partial \psi}{\partial x^i} \right) \frac{\partial F}{\partial v^i} =
0.
\end{equation}
According to Jeans theorem \cite{BT}, the solution of colissionless Boltzmann
equation is any function of the integrals of motion. Now, it is easy to verify
that two isolated integrals a 1PN system with axial symmetry are given by
\begin{equation}\label{ec_ene}
E = \frac{1}{2}v^2 + \Phi,
\end{equation}
where
\begin{equation}
\Phi = \phi + \frac{2\phi^2 + \psi}{c^2},
\end{equation}
and
\begin{equation}\label{lz_pn}
L_z = Rv_{\varphi}e^{-\phi/c^2} \approx Rv_{\varphi}(1-\phi/c^2),
\end{equation}
which can be interpreted as the 1PN generalizations of energy and the $z$
component of angular momentum, respectively.

In addition, the DF must satisfy the condition of self-consistently generating
the macroscopic mean values. In the post-Newtonian approximation, the following
components of the energy-momentum tensor are need,
\begin{eqnarray}
\stackrel{0 \: \: \: \: }{T^{00}}({\bf x},t) &=& c^2\int F({\bf x},{\bf
v},t)d^{3}v, \label{T000} \\
\stackrel{2 \: \: \: \: }{T^{00}} + \stackrel{2 \: \: \: \: }{T^{ii}} &=& 2\int
(v^{2}({\bf x},t) +\phi ({\bf x},t)) F({\bf x},{\bf v},t)d^{3}v. \label{T002}
\end{eqnarray}
Therefore, in the post-Newtonian approximation, self-consistent equilibrium
models are defined by two scalar potentials, $\phi$ and $\psi$, together with a
DF that satisfies 1PN CBE and relations (\ref{T000}) - (\ref{T002}) generating
self-consistenly the 1PN components of the energy-momentum tensor. In this paper
we present a method to obtain post-Newtonian axially symmetric equilibrium
models. The method uses thin disk models, allowing to solve the two differential
equations with the Hunter's method \cite{HUN1}, as shown in the next section.
The solution of the field equations is obtained considering equations in vacuum,
in which case, the energy-momentum tensor vanishes and the content of matter is
expressed as a boundary condition on the fields in the disk, as shown below.
Finally, in section \ref{s_apli_mod} the first axially symmetric models in the
1PN approximation are presented.

\section{Formulation of the method} \label{s_form_met}

For thin disks of finite radius the components of the energy-momentum tensor can
be written as
\begin{eqnarray}
\stackrel{0 \: \: \: \: }{T^{00}} &=& c^2 {\Sigma}(R) \delta(z),
\label{T000-Sigma}\\
\stackrel{2 \: \: \: \: }{T^{00}} + \stackrel{2 \: \: \: \: }{T^{ii}} &=&
{\sigma}(R) \delta(z), \label{Tii02-sigma}
\end{eqnarray}
for $0 \leq R \leq a$, where $\delta$ is the Dirac delta function, and being
zero for $R>a$. Therefore, the field equations reduce to two Laplace equations
for the fields $\phi$ and $\psi$. It is demanded that the fields are even
functions of $z$
\begin{equation}
\phi(R,z)= \phi(R,-z), \qquad \psi(R,z)= \psi(R,-z),\label{reflection1}
\end{equation}
and therefore, that the first derivatives with respect to $z$ are odd functions
of $z$.

Using Gauss' theorem with (\ref{T000-Sigma}) and (\ref{Tii02-sigma}) gives,
\begin{eqnarray}
&& {\Sigma}(R) = \frac{1}{2 \pi G}\left(\frac{\partial \phi}{\partial
z}\right)_{z=0^{+}}, \label{Sigma-phi}\\
&& {\sigma}(R) = \frac{1}{2 \pi G}\left(\frac{\partial \psi}{\partial
z}\right)_{z=0^{+}}. \label{sigma-psi}
\end{eqnarray}
The problem is defined with the following boundary conditions: fields vanish at
infinity, and at $z=0$ its derivatives depend on the energy-momentum tensor
components according to (\ref{Sigma-phi}) and (\ref{sigma-psi}) for $0\leq R\leq
a$ and vanishing for $R>a$. Applying Hunter's method to each of the 1PN field
equations, one can obtain exact analytical expressions for the potentials. The
Hunter's method consists on obtaining solutions of the Laplace equation in
oblate spheroidal coordinates. The oblate coordinates are related to the
cylindrical by
\begin{eqnarray}
&& R = a \sqrt{(1+\xi^{2}) (1-\eta^{2})}, \label{oblatas_R} \\
&& z = a \xi \eta,\label{oblatas_z}
\end{eqnarray}
where $0 \leq \xi<\infty$ and $-1\leq\eta\leq 1$. The disk is placed at $\xi =
0$, where, $\eta^{2}=1-R^{2}/a^{2}$.

Following Hunter \cite{HUN1}, the general solution of each Laplace equation
satisfying previous boundary conditions can be written as
\begin{equation}
\phi(\xi,\eta) = - \sum_{n=0}^{\infty} A_{2n} q_{2n}(\xi) P_{2n}(\eta),
\label{phi1}
\end{equation}
for the $\phi$ potential, and
\begin{equation}
\psi(\xi,\eta) = - \sum_{n=0}^{\infty} B_{2n} q_{2n}(\xi) P_{2n}(\eta),
\label{psi1}
\end{equation}
for the $\psi$ potential, where $A_{2n}$ and $B_{2n}$ are the constants required
for each model, $P_{2n}(\eta)$ are the Legendre polynomials and
$q_{2n}(\xi)=i^{2n+1}Q_{2n}(i\xi)$ are Legendre functions of second kind. Note
that when using classical models, the expression for $\phi$ can be written
taking constants of the form
\begin{equation}
A_{2n} = C_{2n}+D_{2n}/c^{2},\label{constantesA}
\end{equation}
where the $C_{2n}$ constants define the Newtonian potential $\phi_N$ and the
constants $D_{2n}$ define the correction $\phi_{PN}$. So that taking the limit
$c\rightarrow\infty$, $\phi=\phi_{N}+\phi_{PN}$ is reduced to the Newtonian part
only. The corresponding expressions for $\Sigma$ and $\sigma$ in oblate
coordinates are
\begin{eqnarray}
\Sigma = \frac{1}{2\pi a G \eta}\sum_{n = 0}^{\infty} A_{2n} (2n+1) q_{2n+1}(0)
P_{2n}(\eta),&& \label{Sigma1}\\
&&\nonumber\\
\sigma = \frac{1}{2\pi a G \eta}\sum_{n = 0}^{\infty} B_{2n} (2n+1) q_{2n+1}(0)
P_{2n}(\eta).&& \label{sigma1}
\end{eqnarray}
Accordingly, $\Sigma$ can also be writen as the sum of a Newtonian part and a
post-Newtonian correction: $\Sigma = \Sigma_{N} + \Sigma_{PN}$.

In order to obtain self-consistent models of axially symmetric thin disks in
equilibrium, it is used a DF of the form $F = f(R,v_{R},v_{\varphi}) \delta(z)
\delta(v_{z})$, which is zero for $R>a$. The DF reproduces $\Sigma$ and $\sigma$
through the equations
\begin{eqnarray}
{\Sigma}(R) &=& \int \int f(R,v_{R},v_{\varphi}) d v_{R}dv_{\varphi},
\label{relacion-f-Sigma}\\
{\sigma}(R) &=& 4 \int \int E f(R,v_{R},v_{\varphi}) d v_{R}dv_{\varphi} -
2\phi_N \Sigma_N, \label{relacion-f-sigma}
\end{eqnarray}
where $E$ is the integral of motion defined by (\ref{ec_ene}). As in the
Newtonian case, one could define a relative energy and a relative potential as
\begin{eqnarray}
\varepsilon &=& -E + \Phi_0, \label{ec_ene_lz_pn}\\
\Psi &=&-\Phi + \Phi_0, \label{ec_pot efec_lz_pn}
\end{eqnarray}
where $\Phi_0$ is a constant that is chosen so that $\varepsilon$ and $\Psi$ are
always positive, i.e., such that $f>0$ for $0<\varepsilon\leq\Psi$.

The method to obtain self-consistent post-Newtonian models is to take
(\ref{relacion-f-Sigma}) with (\ref{Sigma1}) as the first fundamental equation
and (\ref{relacion-f-sigma}) with (\ref{sigma1}) as the second fundamental
equation. In accordance with the order of magnitude of the approach, the second
fundamental equation is solved using the Newtonian terms and then the first
fundamental equation is solved using the terms up to 1PN order. Finally, note
that for the second fundamental equation, the constants can be obtained directly
by
\begin{equation}
B_{2i}=\frac{4i+1}{4i+2}\frac{2\pi
aG}{q_{2i+1}(0)}\int_{-1}^{1}P_{2i}(\eta)\eta\sigma\mathrm{d}\eta,
\label{alphas_despejadas
\end{equation}
where the integral depends on the particular model. On the other hand, in the
first fundamental equation, the constants also appear on the right side of the
equation (hence, it is necessary to obtain the constants differently for each
model) and, in general, we can not use an explicit expression as done above.
However, it is found that for all models treated it is finally possible to
obtain expressions analog to (\ref{alphas_despejadas}) for the first fundamental
equation, see (\ref{D0}) - (\ref{D4}) and (\ref{consphi1PN-kalnajs2}) -
(\ref{consphi1PN-kalnajs2b}). The DF in the 1PN approximation presents the same
functional dependence on the integrals of motion that in the Newtonian models,
that is, one uses the same DF but now with the 1PN energy and angular momentum.
Of course, this is for the sake of correspondence with the Newtonian limit. Note
that the correspondence principle must be satisfied by both the DF and its
integrals.

It is possible to obtain alternative expressions for $\Sigma$ and $\sigma$
considering in particular the case where the DF depends on a linear combination
of energy and angular momentum called Jacobi's integral, $J=\Omega L_{z}-E$.
Jacobi's integral is interpreted classically as the energy measured from a frame
of reference rotating with angular speed $\Omega$ \cite{BT}. In terms of the
relative energy (\ref{ec_ene_lz_pn}), we can write Jacobi's integral as
\begin{equation}
J = \varepsilon + \Omega L_z - \Psi_e(0), \label{integral-jacobi}
\end{equation}
where $\Psi_e(0)$ is the 1PN relative-effective potential evaluated in $\eta=0$,
defined by
\begin{equation}
\Psi_e = \Psi + \begin{matrix}\frac{1}{2}\end{matrix} \Omega^{2}R^{2}
\left(1-2\phi/c^{2}\right). \label{pot_rel}
\end{equation}
The Jacobi's integral takes values between zero and $J_{max}$, with
\begin{equation}
J_{max}  = \Psi - \frac{1}{2} \Omega^{2} a^{2} \eta^{2} \left(1 -
\frac{2\phi}{c^{2}} \right) - \frac{\Omega^{2} a^{2} \phi}{c^{2}}. \label{Jmax}
\end{equation}
Now, given that $2\pi dJ=dv_{R}dv_{\varphi}$, the relation
(\ref{relacion-f-Sigma}) can be written as
\begin{equation}
{\Sigma} = 2 \pi \int_{0}^{J_{max}} f(J) d J. \label{relacion-f-Sigma-J}
\end{equation}
Then, by using the expression
\begin{equation}
\int\int v_{\varphi} f dv_{R} dv_{\varphi} = 2 \pi \langle v_{\varphi} \rangle
\int_{0}^{J_{max}} f(J) d J,
\end{equation}
the second fundamental equation can be written as
\begin{equation}
{\sigma} = 2(2\Phi_{0}-\Omega^{2}a^{2}-\phi_N+2a\Omega \sqrt{1-\eta^{2}}\langle
v_{\varphi}\rangle)\Sigma_N - 8\pi\int_{0}^{J_{max}}J f(J) d J ,
\label{relacion-f-sigma-J}
\end{equation}
with $\Sigma_N$ given by (\ref{Sigma1}) with $A_{2n} = C_{2n}$.

Finally, the circular speed necessary for the rotation curve can be obtained
considering (\ref{ecmovimiento1PN}) for circular orbits. In that case, the
circular speed is equal to $v_{\phi}$ and perpendicular to the gradient of the
field $\phi$. Therefore, the 1PN equation of motion (\ref{ecmovimiento1PN})
reduces to
\begin{equation}
\frac{v_{\varphi}^{2}}{R} \left[ 1 + \frac{R}{c^{2}} \frac{\partial
\phi}{\partial R} \right]_{z=0} = \frac{\partial}{\partial R} \left[ \phi +
\frac{2 \phi^{2} + \psi}{c^{2}} \right]_{z=0}.
\end{equation}
Then, in accordance with the 1PN order of approximation, the expression for the
circular speed is
\begin{equation}
v_{\varphi} = \left. \sqrt{R \frac{\partial \phi}{\partial R} \left(1 + \frac{4
\phi}{c^{2}} - \frac{R}{c^{2}} \frac{\partial \phi}{\partial R} \right) +
\frac{R}{c^{2}} \frac{\partial \psi}{\partial R}} \right \rfloor_{z=0}.
\label{circular-velocity}
\end{equation}
Note that in the limit $c \rightarrow \infty$, the previous expression reduces
to that of Newtonian theory $v_{\varphi}=\sqrt{R\partial\phi_N/\partial R}$.

\section{Application to the Generalized Kalnajs Disks} \label{s_apli_mod}

We will now apply the previous formalism to the family of Generalized Kalnajs
Disks (GKD) introduced by Gonz\'alez and Reina in \cite{GR}. This family is
characterized by mass densities of the form
\begin{equation}\label{dens-kalnajs}
\Sigma_{N}^{(m)} = \frac{3M}{2\pi a^{2}} \eta^{2m-1},
\end{equation}
where the index $m$ of the model is any positive integer. The potential
$\phi_N^{(m)}$ is given by (\ref{phi1}) by taking the Newtonian limit in
(\ref{constantesA}) and using
\begin{equation}\label{C2n}
C_{2n}^{(m)} = \frac{M G\pi^{1/2} (4n+1) (2m+1)!}{a2^{2m+1} (2n+1) (m - n)!
\Gamma(m + n + \frac{3}{2} ) q_{2n+1}(0)}
\end{equation}
for $n \leq m$, and $C_{2n}^{(m)} = 0$ for $n > m$.

\subsection{The 1PN model for the $m = 1$ GKD}

The first disk of the family, the disk with $m = 1$, is the well known Kalnajs
disk \cite{KAL1}, with the mass distribution
\begin{equation}\label{dens-kalnajs1}
\Sigma_{N}^{(1)} = \frac{3M \eta}{2\pi a^{2}}.
\end{equation}
Then, as was shown by Kalnajs \cite{KAL2}, the DF depends on the Jacobi's
integral as
\begin{equation}\label{DF-kalnajs1}
f(J) = \frac{3M}{4\pi^{2}
a^{3}}\left[2(\Omega_{0}^{2}-\Omega^{2})J\right]^{-1/2}
\end{equation}
where $\Omega_0^{2}=3\pi GM/4a^{3}$. Now, for the Kalnajs disk it holds that
$\langle v_{\varphi}\rangle=\Omega R$, so that the disk spins like a rigid body.

Inserting expressions (\ref{dens-kalnajs1}) and (\ref{DF-kalnajs1}) into the
second fundamental equation (\ref{relacion-f-sigma-J}), and integrating
the DF, one easily obtains the following system of equations
\begin{eqnarray}
B_{0} - B_{2} + B_{4} &=& 0, \label{eq4Kalnajs1PN}\\
3 B_{2} - 10 B_{4} &=& 6 M G a \Omega^{2} - \frac{27 \pi G^{2} M^{2}}{4 a^{2}},
\label{eq5Kalnajs1PN}\\
B_{4} & = & \frac{9 \pi G^{2} M^{2}}{140 a^{2}} - 30 G M \Omega^{2}
a. \label{eq6Kalnajs1PN}
\end{eqnarray}
Likewise, for the first fundamental equation we have
\begin{eqnarray}
D_{0} - D_{2} + D_{4} &=& \frac{9 \pi G^{2} M^{2} \Omega^{2}}{8 a^{2}
(\Omega_{o}^{2} - \Omega^{2})}, \label{eq1Kalnajs1PN}\\
\gamma D_{2} + \vartheta D_{4} &=& B_{2} - \frac{15}{8} B_{4},
\label{eq2Kalnajs1PN}\\
\chi D_{4} &=& \frac{35}{16} B_{4} - \frac{3 \pi G^{2} M^{2}}{4a^{2}} - G M
\Omega^{2} a, \label{eq3Kalnajs1PN}
\end{eqnarray}
where
\begin{eqnarray}
\gamma &=& \frac{24 a^{3}(\Omega_{o}^{2} - \Omega^{2}) - 9 \pi M G}{9 \pi M
G}, \label{gamma}\\
\vartheta &=& \frac{135 \pi M G/8 - 80 a^{3}(\Omega_{o}^{2} - \Omega^{2})}{9 \pi
M G}, \label{vartheta}\\
\chi &=& \frac{70 [128 a^{3} (\Omega_{o}^{2} - \Omega^{2}) - 27 \pi M G]}{864
\pi M G}.
\end{eqnarray}
Therefore, we have a system of linear equations with an upper triangular matrix
for the constants of each potential, $\psi$ and $\phi_{PN}$.

Solving for the constants explicitly, we obtain
\begin{eqnarray}
B_{0} &=& 2 a G M (\pi-1) \Omega^2 - \begin{matrix}\frac{3 G^2 M^2 \pi  (15 \pi
- 1)}{20 a^2} \end{matrix}, \label{B0}\\
&&	\nonumber	\\
B_{2} &=& \begin{matrix} \frac{2}{7} a G M (7 \pi - 10) \Omega^2 - \frac{3 G^2
M^2 \pi  (21 \pi - 2)}{28 a^2} \end{matrix}, \label{B2}\\
&&	\nonumber	\\
B_{4} &=& \begin{matrix} \frac{18 G M}{35 a} \left(\frac{G M \pi }{8 a} -
\frac{5 a^2 \Omega^2}{3} \right) \end{matrix}, \label{B4}\\
&&	\nonumber	\\
D_{0} &=& \begin{matrix} - \frac{27 G^3 \pi ^2 M^3}{8 a^2 \left(a^3 \Omega^2 - 3
G M \pi \right)} \end{matrix} - \begin{matrix} \frac{47709 G^3 \pi^2 M^3}{448
a^2 \left(128 a^3 \Omega^2 - 357 G M \pi \right)} \end{matrix} \nonumber \\
&& - \begin{matrix} \frac{3 G^2 \pi (1 + 80 \pi) M^2}{320 a^2} \end{matrix} -
\begin{matrix} \frac{9 \left( 28 G^3 M^3 \pi^3 - 95 G^3 M^3 \pi^2 \right)}{28
a^2 \left(8 a^3 \Omega^2 - 21 G M \pi \right)} \end{matrix}, \label{D0} \\
&&	\nonumber	\\
D_{2} &=& - \begin{matrix} \frac{3 G^2 \pi (7\pi - 13) M^2}{28 a^2} \end{matrix}
- \begin{matrix} \frac{9 \left(28 G^3 M^3 \pi^3 - 95 G^3 M^3 \pi^2 \right) }{28
a^2 \left(8 a^3 \Omega^2 - 21 G M \pi \right)} \end{matrix}, \label{D2} \\
&&	\nonumber	\\
D_{4} &=& \begin{matrix} \frac{27 G^2 M^2 \pi \left(184 \Omega^2 a^3 + 39 G M
\pi \right)}{140 a^2 \left(128 a^3 \Omega^2 - 357 G M \pi \right)} \end{matrix},
\label{D4}
\end{eqnarray}
which defines the potential $\psi$, and the correction $\phi_{PN}$,
respectively. Hence we can get all the parameters of interest, in particular, we
observed that the mass correction, $\Sigma_{PN}$, is negligible compared with
the classical mass $\Sigma_N$. In contrast, the 1PN rotation curve obtained with
(\ref{circular-velocity}), is visibly separated from the Newtonian one from a
certain radius, the difference being maximum at the edge of the disk (see Fig.
\ref{gkd1}), where the difference between both reaches $10.3\%$
approximately. Those have been obtained with the typical values of a galaxy such
as the Milky Way.

\begin{figure*}
$$\begin{array}{cc}
\epsfig{width=6.15cm,file=Dens1.eps} &
\epsfig{width=6.15cm,file=CurvRot1.eps} \\
\end{array}$$
\caption{First we plot the Newtonian and 1PN mass density for the $m = 1$ GKD.
The two curves seem to be superposed meaning that the mass correction is
negligible. Then we plot the Newtonian (dashed line) and 1PN (full line)
rotation curves for the same disk. The 1PN corrections are clearly notorious
reaching a maximum at the border of the disc. Parameter values are: $M=4\times
10^{40}kg$, $a=3\times 10^{20}m$, $\Omega=2\times 10^{-13}Hz$. } \label{gkd1}
\end{figure*}

\subsection{The 1PN model for the $m = 2$ GKD} \label{ss_kalnajs2}

The procedure for the second disk is pretty much the same that for the first
one. Again, the DF has a simple form when written as a function of Jacobi's
integral,
\begin{equation}\label{DF-kalnajs2}
f(J) = \frac{2M}{\sqrt{3} a^{2}}\left(\frac{10 a^{3}}{G^{3} M^{3}\pi^{11}
J}\right)^{1/4},
\end{equation}
for a mean circular speed $\langle v_{\varphi}\rangle=\Omega R= \sqrt{15 \pi G
M/32 a^{3}}R$. This DF could be easily integrated to self-consistently obtain
the mass density of the model, which also can be obtained from
(\ref{dens-kalnajs}) with $m=2$,
\begin{equation}\label{dens-kalnajs2}
\Sigma_{N}^{(2)} = \frac{5M}{2 \pi a^{2}} \left(1 - \frac{R^{2}}{a^{2}}
\right)^{3/2} = \frac{5M \eta^{3}}{2\pi a^{2}}.
\end{equation}
the associated gravitational potential is given by the Newtonian limit $\phi_N$
of (\ref{phi1}) with (\ref{C2n}) and $m=2$.

Again, we replace the Newtonian terms into the second fundamental equation
(\ref{relacion-f-sigma-J}) to obtain:
\begin{eqnarray}
\sum_{n = 0}^{4} B_{2n} (2n+1) q_{2n+1}(0) P_{2n}(\eta) = \sum_{n=0}^{4}
\tilde{C}_{2i} \eta^{2i}, \label{ecFundamental2-Kalnajs2}
\end{eqnarray}
where $\tilde{C}_{0} = \tilde{C}_{2} = 0$ and
\begin{eqnarray}
 \tilde{C}_{4} &=& (25\pi^{2}10! G^{2}M^{2})/(160 a^{2}), \\
 &&	\nonumber \\
 \tilde{C}_{6} &=&  - (75\pi^{2}10! G^{2}M^{2})/(160 a^{2}) \\
 &&	\nonumber \\
 \tilde{C}_{8} &=& (75\pi^{2}10! G^{2}M^{2})/(2240 a^{2}).
\end{eqnarray}
Multiplying (\ref{ecFundamental2-Kalnajs2}) with a Legendre polynomial,
integrating with respect to $\eta$, and using the orthogonality properties of
the Legendre polynomials we get
\begin{equation}\label{conspsi-kalnajs2}
B_{2n} = \sum_{i=0}^{4} \frac{\sqrt{\pi} \tilde{C}_{2i} 2^{-2i-1} (4n+1)
\Gamma(2n+1)}{q_{2n+1}(0) (2n+1) \Gamma(i-n+1) \Gamma(i+n+3/2)}.
\end{equation}
We also could have used the expression (\ref{alphas_despejadas}).

After rearranging the terms, the first fundamental equation can be written as
\begin{equation}
\sum_{n = 0}^{4} \{ D_{2n} [ \vartheta_{2n} P_{2n}(\eta) + q_{2n}(0)
P_{2n}(0) ] - B_{2n} q_{2n}(0) P_{2n}(\eta) - \hat{C}_{2n} \eta^{2n}
\} = 0, \label{ecFundamental1-Kalnajs2}
\end{equation}
where,
\begin{eqnarray}
\vartheta_{2n} & = & \pi(2j+1)/(32 a^{2} q_{2n+1}(0) - q_{2n}(0)), \\
 &&	\nonumber \\
\hat{C}_{0} & = & (675\pi^{2} G^{2}M^{2})/(4096 a^{2})+\psi(0,0), \\
 &&	\nonumber \\
\hat{C}_{2} & = & -(1575\pi^{2} G^{2}M^{2})/(4096 a^{2}), \\
 &&	\nonumber \\
 \hat{C}_{4} & = & -(1125\pi^{2} G^{2}M^{2})/(2048 a^{2}), \\
 &&	\nonumber \\
 \hat{C}_{6} & =&  - (2025\pi^{2} G^{2}M^{2})/(4096 a^{2}), \\
 &&	\nonumber \\
 \hat{C}_{8} & = & (2025\pi^{2} G^{2}M^{2})/(8192 a^{2}).
\end{eqnarray}
Integrating and using orthogonality relations, the constants $D_{2n}$ are given
by
\begin{equation}
D_{2n} = \sum_{i=0}^{4} \frac{\sqrt{\pi} \hat{C}_{2i} 2^{-2i-1} (4n + 1)
\Gamma(2j + 1)}{\vartheta_{2n} (2n + 1) \Gamma(i - n + 1) \Gamma(i + n + 3/2)} +
\frac{B_{2n} q_{2n}(0)}{\vartheta_{2n}}, \label{consphi1PN-kalnajs2}
\end{equation}
for $n>0$, and
\begin{equation}
D_{0} = \frac{1}{\vartheta_{0} + \pi/2} \left[\sum_{i=0}^{4} \frac{\sqrt{\pi}
\hat{C}_{2i} 2^{- 2i - 1} \Gamma(2j + 1)}{\Gamma(i + 1) \Gamma(i + 3/2)}  -
\sum_{i=1}^{4} D_{2i} q_{2i}(0) P_{2i}(0) \right], \label{consphi1PN-kalnajs2b}
\end{equation}
which defines the correction $\phi_{PN}$ to the Newtonian potential. The mass
densities and rotation curves are plotted at Figure \ref{gkd2}, note that the
rotation curve is not only cuantitative, but cualitatively different, presenting
its maximum value more closely to the center of the disk and going upwards at
the border. This is due to the fact that the 1PN curve includes more terms than
the Newtonian one.

\begin{figure*}
$$\begin{array}{cc}
\epsfig{width=6.15cm,file=Dens2.eps} &
\epsfig{width=6.15cm,file=CurvRot2.eps} \\
\end{array}$$
\caption{We plot the Newtonian and 1PN mass density, as well as the Newtonian
(dashed line) and 1PN (full line) rotation curves for the $m = 2$ GKD, with
parameter values: $M=4\times 10^{40}kg$, $a=3\times 10^{20}m$, $\Omega=2\times
10^{-13}Hz$. As we can see, the two graphics of mass density appear to be
superposed, while that the 1PN rotation curve behaves completely different to
the Newtonian one.}\label{gkd2}
\end{figure*}

redpajama_set_name: RedPajamaArXiv


Two years on from the launch of the Toyota Kiwi Guardians programme, more than 29,800 Kiwi kids have connected with nature and become guardians of the land and sea.
Toyota Kiwi Guardians is an activity programme that helps kids to connect with nature by encouraging them to go on epic self-guided adventures, undertake conservation actions and earn rewards.
There are now 107 sites located from Whāngārei to Stewart Island, providing Kiwi kids with numerous opportunities to explore their natural surroundings.
More sites and action medal opportunities to reach Kiwi kids across the country are being developed to keep the challenges exciting.
Sites have a mixture of adventures, scenery and activities, encouraging Kiwi Guardians to enjoy the outdoors and gain a better understanding of their natural environment.
The Auckland region recently saw the opening of five new Toyota Kiwi Guardian sites – four in Auckland and one in Whāngārei – coinciding with Māori Language Week from September 10 to 16.
The four Auckland sites, at Ambury Regional Park (Māngere), Te Henga/Bethells Beach, Clevedon Scenic Reserve and Kawau Island, have bilingual maps in Māori and English, which are the forerunners to making more sites bilingual. The Whāngārei site is at Pukenui Forest near Kamo.
Children could also earn limited-edition medals, specific to Māori Language Week; 208 Kiwi Guardians took up the challenge and earned these medals.
In July, 102 Kiwi Guardians achieved the new Toa Manu/Bird action medal, launched to encourage Kiwi Guardians to participate in the annual New Zealand Garden Bird Survey.
There's also been the introduction of a tree planter medal – called Toa Tiaki Rākau – to help New Zealand with its goal to plant one billion trees by 2027. So far, 85 young Kiwi guardians of the land have participated in this action medal initiative.
To earn their medals, the young guardians also had to tell us about the trees they'd planted, where they'd chosen to put them, and how the planting had gone. "We are encouraged that the Kiwi Guardians programme has gained such momentum, with a great increase in participation since its introduction," says Alistair Davis, CEO of Toyota New Zealand.
Alistair says it's fantastic to be working with the Department of Conservation (DOC) on a project that encourages Kiwi kids to conserve our natural environment while having fun doing it.
The programme allows young people to engage with the natural environment and want to care for it now and into the future.
Toyota Kiwi Guardians is about inspiring tomorrow's leaders to protect our land and its birds and animals, says Alistair. It highlights family-friendly activities at specific sites that support kids to engage their senses, take risks and, ultimately, earn themselves medals in the outdoors.
Paparoa National Park on the West Coast.


Arrow Kiteboarding aims to provide the highest quality snowkiting and kitesurfing guided tours and instruction. Arrow offers experienced and high caliber guides, low client to guide ratio, unwavering commitment to safety, on-location skill building in every program and commitment to protect and preserve the mountain and ocean environment.
Come join us this winter for world class guided alpine snowkiting and instruction. Nestled at the foot of the Elk Mountains in Colorado, Arrow capitalize on excellent access to winter terrain in a variety of settings perfect for all levels. We identify safe locations, wind and weather, so that we can plan and carry out exciting, fun and safe backcountry snowkiting tours.
Based out of Provincetown's Long Point Marina at the far tip of Cape Cod during the summer months, Arrow offers boat and beach access wave and flat water kiting at some of Cape Cod's most pristine and unknown locations. Take advantage of warm water, fresh breezes and great surf by booking a guided kiteboarding experience with Arrow.


text:
Football Horse Racing Cricket NFL UFC Boxing NHL
NBA GAA Other Sports More Info Meet the Team
NHL NHL Trade Deadline: 5 acquisitions set to make playoffs impact
NHL Trade Deadline: 5 acquisitions set to make playoffs impact
Guy Giles1
Our NHL expert, Chris Peters, picks out five players who could help their new teams make a splash in the postseason.
Check out the Betway Insider's NHL picks page for best bets throughout the 2020-21 NHL season.
Now that the NHL trade deadline has passed, teams and rosters are mostly set, save for whatever injuries crop up between now and then. The players that moved at the deadline - except for those that have had to go through a quarantine period in Canada after arriving from a U.S. team - are now settling in with their new teams. Some are already making an impact.
As we head into the home stretch of this truncated season, here is a look at the players that appear to have the best chance to make a significant impact on teams headed for the postseason.
Anthony Mantha | Washington Capitals
After being dealt from the Detroit Red Wings in one of the most shocking deals of NHL trade deadline day, Mantha has slid right into the Capitals lineup and made an impact.
He scored goals in each of his first two games with the club and has provided the secondary scoring presence Washington is going to need as they progress towards the playoffs.
Mantha had to be the offensive focal point, or one of them at least, for Detroit. He doesn't necessarily have to be that in Washington, as he'll be behind Alex Ovechkin on the depth chart. Having both Ovechkin and Mantha, however, provides more matchup problems for other teams.
Washington gave up a ton to get Mantha, including two roster players and two draft picks, but they've improved their roster by getting a big scorer like him.
Taylor Hall | Boston Bruins
The opportunity to just be another player was something Taylor Hall wanted after years of being a primary player for his three previous teams.
It really didn't work out for him in Buffalo and he used his no-movement clause to make sure he ended up with the Bruins specifically. Now playing behind Brad Marchand as more of a second-line player, Hall has a little more freedom to loosen up and not put as much pressure on himself to perform.
Despite a shaky first game against his most recent team, Hall scored a goal in his second game to help build a little more confidence in his new surroundings.
Meanwhile, the Bruins are getting a former MVP to help make their second line more potent, giving No. 2 center David Krejci an elite winger, which Hall still can be if he can get things moving in a more positive direction.
Kyle Palmieri | New York Islanders
Acquired days before the deadline activity picked up, Palmieri joined the Islanders from the New Jersey Devils with long-time teammate Travis Zajac.
Islanders GM Lou Lamoriello needed to bring in some veteran talent and found it in some familiar players that he had brought to New Jersey during his time there.
Zajac and Palmieri both have a lot of playoff experience and have gone on deep runs with other teams. Palmieri, meanwhile, may help replace some of the goal-scoring lost when Anders Lee went down with a season-ending injury.
He also has a lot of versatility, which allows the Islanders to move him around their lineup with ease. It's the kind of support the roster needed, and the Isles are in better shape for a deeper run in the postseason.
Mattias Janmark | Vegas Golden Knights
Sometimes the best deals a GM can make are the little ones. Adding a player like Janmark from Chicago at a reasonable price was a solid move for Vegas.
Janmark went on a deep postseason run with the Dallas Stars last year and plays the game at a high speed. He also slots neatly down the Vegas lineup, bolstering a third line that also includes Alex Tuch.
The Golden Knights were already tough to play against, but increasing depth even by one player like Janmark presents more challenges for the opposition because he has some good defensive value, too.
Janmark could also benefit from the move, getting better linemates even though he managed a respectable 19 points in 41 games with Chicago, which was mostly in line with his career norms. Playing alongside a sniper like Tuch could help Janmark pick up some more points, especially assists.
With him on an expiring contract, there's plenty of incentive for him to keep producing, which in turn helps the Golden Knights in this rental situation.
Nick Foligno | Toronto Maple Leafs
One of the more fascinating adds at the deadline was Toronto bringing in Blue Jackets captain Nick Foligno, who remains out for the time being as he clears quarantine protocols before he can start skating with the Leafs.
Raised for a portion of his childhood in Ontario, Foligno gets a chance to make a run at the Stanley Cup not far from home. There are a lot of veterans on the Leafs roster now chasing the Stanley Cup. Maybe that's the kind of desperation Toronto needs right now to enhance their competitiveness in the postseason.
From a more practical standpoint, however, Foligno's scoring had been down this season as Columbus struggled mightily. The 33-year-old brings versatility to Toronto's lineup and will allow them to not have to lean on less-experienced depth players down their lineup.
Foligno also brings a bit of grit and makes Toronto a little heavier, easing some concerns that they don't have enough of that element to compete in the postseason.
Foligno has not often played with a lineup this talented and has been able to produce over the course of his career with less. As he moves into more of a depth role, he might find some more favorable matchups, might get more chances on the power play and have a chance to produce.
If nothing else, Toronto gets a well-liked veteran who won't disrupt what they have going and can provide help in many other ways, even if it's not always going to be on the score sheet.
Visit Betway's NHL betting page.
Tags Toronto Maple Leafs NHL playoffs
NHL picks: 4 best bets for Thursday
NHL picks: 4 best bets for Tuesday

redpajama_set_name: RedPajamaCommonCrawl


text:
You are here: Home / News / Pioneer Theater in Milford raising funds to go digital
Pioneer Theater in Milford raising funds to go digital
February 28, 2014 By Radio Iowa Contributor
A northwest Iowa movie theater will reopen March 7th, but the future of the business depends on fundraising to buy new digital equipment. The movie industry was scheduled to go digital by the end of 2013 and Sharon Mayer, owner of the Pioneer Theater in Milford, closed down in January. However, in the past week Mayer discovered some movies are still available on 35-millimeter film. "I worked hard and my booker worked hard at being able to get a brand new movie," Mayer says. "…I just feel it's important to keep the theater open and as long as I can get film, I'm going to go."
Mayer is still planning to buy a digital projector. "And I'll need the public's help to do that," Mayer says. Mayer says she's can't do it with ticket sales alone. She's planning a local fundraising push for the digital switch. "I'm going to try to keep the Pioneer Theater on the map and be digital and bring us to into the new century here," Mayer says. The town of Milford has nearly 3,000 residents and is sometimes called "the southern gateway" to the Iowa Great Lakes.
Many Iowa movie theaters besides the Pioneer in Milford are struggling with the switch to digital. The Hardacre Theater in Tipton began showing movie pictures in 1919, but closed in August. Those cost of digital equipment and upgrades to the historic opera house are estimated at two million dollars and organizers hope to raise the money and reopen the theater in time for the annual film festival that's held there in August.
In Dubuque, the Mindframe Theaters held local fundraisers and began installing new digital equipment this fall. The largest movie screen in Iowa — in a theater at Merle Hay Mall in Des Moines — will be closing soon, to be replaced by a brew pub with eight smaller screens for movies.
(Reporting by Ryan Long, KICD, Spencer)
Filed Under: News, Recreation / Entertainment


The right accessories can enhance your wine drinking experience. Visit Dover Wine Company for a full array of wine accessories in Dover, NH.
You'll find all of the wine accessories you'll need to look like a true wine connoisseur. Our German wine glasses, one of our featured items, are shatter-resistant. We also offer goat cheese, candles and other items to create gift baskets.
Stop by now to replace your worn, damaged wine accessories.
You can expect superior products at reasonable prices. Talk to one of our associates today to get the best accessories for your needs. Buy wine glasses and other wine accessories. We look forward to helping you!


Here is an example in Python of how to retrieve the system memory usage. This example was adapted from an entry on stackoverflow.
#Example; Get the system memory usage.
Here we have a simple class called MemUsage. The constructor initializes the attributes of the class needed to compute the memory usage. The init_data() method is what MemUsage invokes in order to retrieve the required system data. This is done by using the subprocess module to execute the free command. The resulting data is then mapped to the corresponding attributes. We compute the memory usage as a percentage by subtracting the buffers and cache from the used memory and dividing the result by the total memory.


text:
	<ng-include src="'/modules/hymns/views/info-panel.client.view.html'"></ng-include>

		Hymns

		<form role="form" ng-submit="createHymn()" name="newHymnForm">

New Hymn

						中文名稱
						English Title
						Name
						<input type="text" ng-model="name.name" name="name" />

You must enter at least one name.

								Hymn Index
								<input type="text" name="hymnIndex" ng-model="newHymn.hymnbookIndex" />

							Languages
							<ui-group-checkbox
								ui-group-checkbox-model="newHymn.lyricLangs"
								ui-group-checkbox-values="lyricLangs.values"
								ui-group-checkbox-labels="lyricLangs.displayNames">

						Publisher
						<select ui-select2 ng-model="newHymn.publisherId">
							<option value=""></option>
						    <option value="{{publisher._id}}" ng-repeat="publisher in publishersList">{{publisher.names|concatNames}}</option>
						</select>

						Hymnbook
						<select ui-select2 ng-model="newHymn.hymnbookId">
							<option value=""></option>
						    <option value="{{hymnbook._id}}" ng-repeat="hymnbook in hymnbooksList | filter:newHymn.publisherId">{{hymnbook.names|concatNames}}</option>
						</select>

					<ui-btn
						ui-btn-type="submit"
						ui-btn-css-class="save-new-hymn-btn"
						ui-btn-btn-css-class="success"
						ui-btn-icon-class="save"
						ui-btn-label="Save">
					</ui-btn>
					<ui-btn
						ui-btn-type="button"
						ui-btn-css-class="cancel-new-hymn-btn"
						ui-btn-label="Cancel"
						ui-btn-on-click="cancelNew()">
					</ui-btn>

		</form>

	<ng-include src="'/modules/hymns/views/filter-hymn.client.view.html'"></ng-include>

						{{hymn.hymnbookIndex}}

							{{nameEntry.name}}

		No hymns yet, why don't you create one?

redpajama_set_name: RedPajamaGithub


You can create printable tests and worksheets from these Grade 5 Baseball questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.
Teams do not have to bat in the same order in the course of the game.
The term used when a player legally crosses home plate.
A batter is given 4 balls and 3 strikes in an official game.
A ball hit between the dugout and third base is a foul ball.
A slow pitch softball game consists of innings.


Research & Polling Inc. conducted a survey of 504 New Mexico likely voters between Nov 1 and Nov 3, 2016. Respondents were contacted by either Cellphone or Landline and instructed by a live operator. The results of this poll were released on Nov 6, 2016.
The poll was sponsored by the Albuquerque Journal.
If the election for president were held today and the candidates were Democrat Hillary Clinton, Republican Donald trump, Libertarian Gary Johnson and Jill Stein of the Green Patty, whom would you vote for?
This question was presented to 504 likely voters from New Mexico who were contacted in some undisclosed fashion. The margin of sampling error is ± 4.4%.
The question wording was provided by Research & Polling Inc. and the Albuquerque Journal.


Roads in FY12 paving list including surface treatment, micro, conversion, and thin overlay.
Roads in FY13 paving list including surface treatment, micro, conversion, and thin overlay.
Roads in FY09 paving list including surface treatment, micro, conversion, and thin overlay.
Roads in FY14 paving list including surface treatment, micro, conversion, and thin overlay.
Roads in FY10 paving list including surface treatment, micro, conversion, and thin overlay.


We did it! Our day, our way and walked down the aisle together!
While a planning wedding is the happiest of occasions, for some it can also be really tricky due to family politics. This week in the news there has been a huge amount of interest about Meghan Markle's Dad and whether or not he is going to be coming to her wedding on Saturday to walk her down the aisle. That is stressful for any bride or groom, but can only imagine how tough it is for Meghan given the additional media scrutiny.
When Mr Ash and I were preparing to marry many moons ago, family politics reared their head on my side of the family. At the time it was deeply embarrassing but I was fortunate that those around us supported and loved us. My parents divorced when I was a teenager. My mother raised us but I still tried to maintain a relationship with my father. At the time when Matt and I got married my relationship with my father and his family wasn't great. It felt right to have my Mum walk me down the aisle but I didn't want to upset my father further.
Also in some ways I am fiercely independent and challenge convention. I couldn't get my head around the fact that traditionally the father gives his daughter away. While that feels right for some - it just didn't feel right for me. I'm my own person and no one can 'give me away!' So instead, Mr Ash and I walked down the aisle together! In the end I don't know why I stressed over walking down the aisle because us walking down together turned out to be so sweet and just right for us.
Over the years I've come across similar challenges for some of the couples I have had the honour of working with. Keep in mind that while you still love your parent etc, this is your day. Don't be afraid to be non-traditional if you can't or don't want to do the conventional thing with regards to certain traditions such as who will walk you down the aisle. Don't stress over it either. This is just one small part of your day, your way! By the way - there is no rule book…you could even walk yourself down the aisle!


The 2018 Youth Flag Football League is now underway with players in grades 3-6. Games will take place over the next four Sundays at 5pm. 3rd and 4th grade players will remain in Brown City, while 5th and 6th grade players will compete against teams in BC, Marlette, and Sandusky.
The Green Devil Junior Varsity Team began their season with an impressive 28-12 victory at Durand High School on Wednesday night. Congratulations to Coach Schindler and the JV's for getting off to a great start to the season. The JV's team next contest will be at home on Wednesday August 29th at 6:30pm. Come support the Green Devils.
The BC Varsity Football Team received their opening week win via a forfeit. Unfortunately Burton Atherton was unable to field a team as the opening game approached and they notified the MHSAA of their need to forfeit. The Green Devil Varsity will prepare for their first action against Sandusky which will take place on Thursday August 30th in Sandusky.
REMINDER...... ALL athletes (grades 7-12) need to have a physical completed and on file in the school office in order to participate in official practices. For HS football that deadline is August 6th. For Jr. High Football, the deadline is August 23rd.
The annual youth football camp for players in grades 2-6 was a success. Around 25 young players participated in the camp learning a variety of football skills and competing in multiple tasks and games.
The Brown City Football 2017 Senior Class finished their football careers with a BIG win on Friday night against Capac High School with a score of 52-7. All of the seniors played hard and contributed to the victory. The Brown City Football Program is extremely grateful for the effort and work ethic that this group of young men have shown. We wish our seniors the best of luck moving forward.
The 2017 Pink Out Game against rival Marlette HS took place on Friday Sept. 29th. Both teams wore custom Pink Ribbon uniforms to honor individuals who have battled cancer. It was a great football game with our Green Devils coming out on top by a score of 28-20.
There was a Community Tailgate Party catered by Brower Farms, and money was raised for a tremendous cause.
All proceeds from this event went to MRH- BCUPS program (breast cancer screening and prevention).
We still have some Discount Cards left.............. For a $20 donation, you will receive the following discount card which includes many great local deals. The card can help save you hundreds of dollars over the next year at places such as Treve's Pizza, Taco Bell, Subway, Holly Meadows Golf, Dairy Queen, and many others. Cards can now be purchased via credit or debit card as well as with cash or check. The donation helps us continue to grow and update our football program.
If you are interested in a card please contact a player or coach, or message us and we will make sure to get one delivered ASAP.
Please consider supporting BC Football....... Go Devils!


text:
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Correcting six common types of lens aberrations
In optical design, aberrations occur when light from one point of an object doesn't converge into or diverge from a single point after transmission through the system. The non-linear terms in Snell's Law cause deviations from perfect imagery: optical systems that form images will produce images that aren't as sharp. Optical engineers must correct the aberrations to produce the sharpest images possible.
Six common types of optical aberrations
Defocus: The optical system is out of focus, reducing the sharpness of images produced by the system.
Radial distortion: Images with radial distortion usually have symmetric distortion due to the symmetry of a lens. There are three types of radial distortion: barrel, in which image magnification decreases with distance from the optical axis; pincushion distortion, in which image magnification increases with distance from the optical axis; and mustache distortion, which is a blend of the two types. Chromatic aberration is radial distortion that depends on wavelength.
Astigmatism: Rays that propagate in two perpendicular planes have different foci. Where the horizontal and vertical axes cross, the axes will be in sharp focus at two different distances. There are two forms of astigmatism: third-order aberration, which occurs for objects away from the optical axis; and when the optical system is not symmetric about the optic axis.
Coma: Defined as a variation in magnification over the entrance pupil, coma is seen often in telescope design, resulting in stars or other objects appearing to have a tail.
Spherical aberration: This occurs when there is increased refraction of light rays striking a lens or when there is a reflection of light rays striking a mirror near the edge versus closer to the center.
Petzval field curvature: Named after physicist Joseph Petzval, one of the founders of geometrical optics, this is an aberration in which a flat object cannot be brought into focus on a flat image plane.
Solving optical aberrations with optical design software
Many optical aberrations can be easily solved with the right optical design software. OpticStudio has many features and functionalities that help correct common aberrations.
For example, OpticStudio offers the Full-field Aberration Analysis feature, which allows optical engineers to improve freeform designs by analyzing how various aberrations degrade the image or beam quality of a system across the full field of view. Freeform optical surfaces are a key element in many modern optical systems, used for example, in virtual and augmented reality designs. This analysis feature displays aberrations and contributions to image degradation across the full XY field of view. Users can analyze freeform systems in the same way they would with any other regular sequential system, identifying the change in aberrations across the field of view and getting an indication of how to correct these.
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Government, Public Sector
Canada: Positive Economic Impacts For First Nations Are Relevant For Decision Makers
by Jeremy Barretto , Arend Hoekstra , David Bach , Neil Burnside and Aaron Cressman
Cassels
The Alberta Court of Appeal released its decision in AltaLink Management Ltd. v Alberta (Utilities Commission)1 on October 15, 2021. The majority held that positive economic impacts for First Nations are relevant factors to be considered by the utilities commission in evaluating the public interest. This decision follows a recent trend among decision makers to consider not only mitigation and accommodation measures on the negative impacts projects may have on Indigenous peoples, but also positive economic outcomes for Indigenous peoples, in considering regulatory approvals.
AUC: First Nation Participation Costs Not Eligible for Rate Recovery; Savings on Shorter Route not Considered
The Alberta Utilities Commission's (AUC) predecessor, the Alberta Energy and Utilities Board, approved an expansion of Alberta's electrical transmission system in May 2005. To meet this demand, AltaLink Limited Partnership (AltaLink) applied for permission to construct and operate a new 240 kV transmission line, running approximately 100km between Pincher Creek and Lethbridge. The project was approved in March 2009, and the line was constructed and operational by October 2010.
The shortest and lowest cost route crossed two reserves: Piikani Indian Reserve No. 147 and Blood Indian Reserve No. 148. As part of its negotiations with landowners, AltaLink entered into agreements with the First Nations to give them an option to acquire up to a 51% interest in the operation of the portions of the transmission line crossing their reserve land, and setting out the relationship between AltaLink and the First Nations with respect to the operation of the transmission line. These options were exercised in February 2014 and October 2012, respectively.
AltaLink, in its capacity as general partner of the 51% Indigenous-owned limited partnerships that would own and operate the transmission line (First Nation LPs), filed transfer applications with the AUC in 2017.
The AUC reviewed the application under subsection 17(1) of the Alberta Utilities Commission Act, which requires that the AUC consider whether the operation of the transmission line is in the public interest, and applied a "no-harm test" to weigh the positive and negative impact of AltaLink's transfer applications.2 The AUC approved the applications in November 2018 but in doing so included a condition that the First Nation LPs could not pass hearing and auditing costs on to ratepayers. The AUC found these were additional costs that would not exist but for the transfer of the assets, and they could not consider savings from routing the transmission line through the First Nations or intangible benefits arising from the partnership with the First Nations as offsetting the additional costs.
Court of Appeal: Savings from Reserve Routing Relevant to the "No-Harm Test"
The Alberta Court of Appeal granted leave to appeal, and the majority considered whether the AUC erred by failing to consider all relevant factors as part of the "no-harm test" when reviewing the application.
The Court held that the AUC erred by failing to consider the cost savings from the initial construction phase as relevant. AltaLink's partnership with First Nations allowed for a route with lower maintenance, increased operational capacity, and a reduced environmental impact - all of which would offset any hearing and audit costs. The Court also noted that the AUC has previously allowed applicants to recover the cost of fostering relationships with First Nations.
The majority decision went on to note that projects that increase the likelihood of economic activity on a reserve are in the public interest.3 It reasoned that addressing the employment gap between Indigenous and non-Indigenous Canadians is a benefit to society, and cited two examples of energy companies partnering with Indigenous people for mutual gain.
Having concluded that the AUC erred by failing to consider a relevant factor in its application of the "no-harm test," the majority decision declined to answer whether the public interest included the honour of the Crown and the principle of reconciliation. In a concurring decision, Justice Feehan described the honour of the Crown as the guiding principle that Crown representatives must conduct themselves with honour when engaging with Indigenous peoples on behalf of the Crown. Justice Feehan noted that in contrast, reconciliation referred to the work in progress of rebuilding the relationship between Indigenous peoples and the Crown following injustices by the Crown against Indigenous peoples. Much of the submissions before the Court had focused on whether the AUC was obligated to consider these factors, which would subsequently require the AUC to also consider the First Nation LPs' involvement in reaching its decision.
Justice Feehan agreed with the rest of the Court's ruling but also addressed whether the AUC's assessment should be informed by the principle of the honour of the Crown and the imperative of reconciliation.4 Justice Feehan held that statutory decision-makers with a broad public interest mandate must consider the honour of the Crown and reconciliation when engaging in decision-making that has the potential to impact Indigenous peoples.
Implications for Resource Development and Infrastructure Projects: Greater Consideration of Positive Economic Impacts for First Nations
The AltaLink decision suggests that decision makers with public interest mandates should consider benefits that go to Indigenous peoples and benefits that working with Indigenous peoples can foster, such as a more direct and economical route.
This decision provides proponents with additional incentive for benefits such as preferential contracting and employment opportunities, and equity positions for Indigenous peoples, which are becoming increasingly common in the resource and energy sectors.
The economic benefits going to a community may take different forms. In this instance, the Court found that increased economic activity on a reserve and involvement in the workforce for Indigenous people were public interest benefits. It would appear reasonable that financial participation, spending on Indigenous-owned businesses, and equity interests in projects would also contribute to the public interest.
This decision follows on other recent jurisprudence holding that the Crown should consider negotiated socio-economic project benefits for Indigenous communities in making a decision. In Ermineskin Cree Nation v Canada (Environment and Climate Change) the Federal Court found that the loss of negotiated economic benefits to a First Nation could trigger the Crown's duty to consult.5
1 2021 ABCA 342 [AltaLink].
2 Alberta Utilities Commission Act, SA 2007, c A-37.2, s 17(1).
3 AtlaLink, supra note 1, at para 59.
4 AtlaLink, supra note 1, at paras 81-83.
5 2021 FC 758, at paras 6-10.
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text:
Q: Callback в Телеграм боте на Google apps script Бот отправляет меню но не отвечает на клики по нему. Подскажите, пожалуйста, что я делаю не так? В инете искал искал. Так и не могу разобраться никак
https://docs.google.com/spreadsheets/d/1XPbjxWH1sL-rLF-rGPOI08KvNNCBKTt5DPev2i_Vums/edit?usp=sharing

A: У вас блоки условий идут не в том порядке.

*

*Обновил ваш код

*Добавил перехват ошибок и лог в Таблицу (не забудьте выдать права)

*поменял местами блоки условий. Блок с message для /start стал вложенным

Скорее всего, вам просто нужно заменить код файла doPost.gs на следующий:
/*
ниже – пример сообщения, которое отправит бот нам как только ему что-то напишут
это – объект, в коде мы его парсим, достаём имя отправителя, никнейм, само сообщение и записываем в наш лог

 {"updateid":000000000,
   "message":{"messageid":00,
     "from":{"id":000000000,"isbot":false,"firstname":"<your name>","lastname":"<your surname>","languagecode":"en"},
     "chat":{"id":000000000,"firstname":"<your name>","lastname":"<your name>","type":"private"},
     "date":0000000000,
     "text":"<текст сообщения>",
     "entities":{"offset":0,"length":11,"type":"bot_command"} // в случае если это команда
   }
 }

*/

function doPost(e) {
  try {
    var contents = JSON.parse(e.postData.contents),
      contents_s = JSON.stringify(contents);

    SpreadsheetApp.openById(ssID).appendRow([new Date(), 'doPost', contents_s]);
    if (contents.message) {

      const msg = contents.message,
        chatType = msg.chat.type,
        messageText = (msg.text || '') + (msg.caption || ''), //или само сообщение или подпись к файлу / фото
        user = msg.from.hasOwnProperty('username') ? msg.from.username : '',
        userId = msg.from.id,
        userFirstName = msg.from.first_name,
        userLastName = msg.from.last_name,
        chatId = msg.chat.id,
        src_msg = msg.hasOwnProperty('reply_to_message') ? msg.reply_to_message.text : '',
        src_sender = msg.hasOwnProperty('reply_to_message') ? msg.reply_to_message.from.username : '';

      if (messageText == "/start") {
        var title = "Заголовок/вопрос меню 1 уровня";
        var inlineKeyboard = [
          [{ "text": "Опция1", 'callback_data': 'option1' }],
          [{ "text": "Опция2", 'callback_data': 'option2' }]
        ];
        sendMessageInlineMenu(chatId, title, inlineKeyboard);
        return;
      }

      const checkPm = chatType == 'private',
        chat = checkPm ? '' : msg.chat.username,   //если отправлено не ЛС, то добавляем username чата
        chatTitle = checkPm ? '' : msg.chat.title; //и название чата

      const checkFile = msg.hasOwnProperty('document'),
        fileId = checkFile ? msg.document.file_id : msg.hasOwnProperty('photo') ? msg.photo[1].file_id : '',
        fileMime = checkFile ? msg.document.mime_type : '',
        fileName = checkFile ? msg.document.file_name : '';

      var answer = "нет данных";

      //==========================================================================================================================

      sendMessage(chatId, JSON.stringify(e));
      return;
    }

    if (contents.callback_query) {
      var callback_query_id = contents.callback_query.id;
      var callback_userId = contents.callback_query.from.id;
      var callback_data = contents.callback_query.data;

      answerCallbackQuery(callback_query_id, "Ура работает!"); // по факту нихера не работает)))

      sendMessage(contents_s);
      if (callback_data == 'option1') {
        sendMessage(callback_userId, "Ответ на пункт меню 1 уровня");

      } else if (callback_data == 'option2') {
        var title = "Заголовок/вопрос меню 2 уровня";
        var inlineKeyboard = [
          [{ 'text': 'Подопция1', 'callback_data': 'suboption1' }],
          [{ 'text': 'Подопция2', 'callback_data': 'suboption2' }]
        ];
        sendMessageInlineMenu(chatId, title, inlineKeyboard);

      } else if (callback_data == 'suboption1' || callback_data == 'suboption2') {
        sendMessage(chatId, 'Ответ на пункт меню 2 уровня');
      }

      // Если отправлено сообщение а не callback
    }
    SpreadsheetApp.openById(ssID).appendRow([new Date(), 'doPost', 'nothing']);
  } catch (err) {
    console.error(err.stack, err.message);
    SpreadsheetApp.openById(ssID).appendRow([new Date(), err.stack, err.message]);
  }
}

Должно заработать.

redpajama_set_name: RedPajamaStackExchange


I could write an entry about the various things I've been doing lately, but frankly they're all rather boring (well, apart from winning a quiz night at Justin's tennis club). So instead I've compiled a timeline of Dan Abnett's Gaunt's Ghosts series.
(Hey, I didn't go to Supanova – I had to do something spectacularly nerdy with the weekend).
~500.M35: Birth of Saint Sabbat.
~515.M35: Start of Sabbat's Crusade.
~620.M35: Saint Sabbat martyred on Harkalon.
~220.M41: Birth of Golesh Constantine Pheppos Heldane.
~235.M41: Heldane apprenticed to Inquisitor Commodus Voke.
240.M41: Heldane horribly scarred during investigation of House Glaw. He later (prior to 338.M41) has surgery to enhance the resulting terrifying appearance.
251.M41: Three Astartes of the Iron Snakes are sent to Formal Prime to investigate a warp incursion. Only two return to Ithaka.
278.M41: Heldane rises to the rank of full Inquisitor.
304.M41: Birth of Gideon Ravenor.
338.M41: Ravenor horrifically injured in the Thracian Atrocity and confined to a Force Chair.
386.M41: Heldane suffers terrible injuries while facing the daemonhost Cherubael. He undergoes extensive augmetic reconstruction and takes many years to recover.
600.M41: Chaos attacks on the Sabbat Worlds increase notably.
~702.M41 Birth of Ayatani Zweil.
707.M41: Birth of Tolin Dorden.
~717.M41: Birth of Hlaine Larkin. Birth of Macaroth.
~722.M41: Birth of Veynom Blenner.
724.M41: Birth of Ibram Gaunt.
732.M41: Slaydo writes A Reasoned Approach to the Reconquest of the Sabbat Territories.
735.M41: Death of Gaunt's father on Kentaur (Gaunt aged 11).
736.M41: The 12 year old Gaunt is sent to the Schola Progenium on Ignatius Cardinal.
741.M41: The Civitas Imperialis is officially suspended across the Sabbat Worlds. The worlds are officially considered lost. Birth of Thuro of NorthCol on Verghast.
745.M41: Twenty-one year old Cadet Commissar Gaunt fights separatists on Darendara with the Hyrkans under Commissar Oktar. He encounters a Psyker who makes numerous predictions about his future.
747.M41: The 23 year old Gaunt fights Orks with the Hyrkans and Oktar on Gylatus Decimus. He is promoted to full Commissar on the death of Oktar by Ork poisons.
749.M41: The 25 year old Commissar Gaunt avenges his father on Khedd 1173. Birth of Dermon Caffran. Birth of Kolding.
750.M41: Birth of Brin Milo.
755.M41: Slaydo is promoted to Warmaster and appointed to lead the Crusade to liberate the Sabbat Worlds.
755.M41: Commissar Gaunt and a team of Hyrkans investigate an ancient shrine on Formal Prime.
757.M41: Thirty-three year old Gaunt is assigned to the newly founded 8th Hyrkans.
~762.M41: On Verghast, Thuro moves from Ferrozoica Hive to NorthCol.
765.M41: The assault on Balhaut. Gaunt (aged 40) and the 8th Hyrkans bring down the Tower of the Plutocrat. Slaydo is mortally injured defeating Archon Nadzybar but promotes Gaunt to Colonel Commissar on his deathbed. Urlock Gaur assumes the position of Archon.
765.M41: Three new regiments are raised on Tanith. Gaunt is sent to take command and rescues around half of them from the planet's destruction on the day of Founding.
765.M41: The Tanith first and Only engage in their first action on Blackshard.
765.M41: The Tanith assault Voltis City on Voltemand and are then redeployed to the ruins of Kosdorf.
765.M41: A Vermillion level message is relayed by ships scouting the Nubila Reach.
765.M41: The Tanith fight on Fortis Binary and Menazoid Epsilon, then are deployed to Bucephalon and Caligula.
767.M41: The Tanith fight Orks on Typhon 8, then Chaos on Nacedon and Ramillies 268-43.
768.M41: The Tanith take part in the assault on Sapiencia and are then deployed to Monthax. On Verghast, Thuro of NorthCol carves a frieze for the portico of the NorthCol Imperial Hospice.
769.M41: The Tanith defend Vervunhive on Verghast. House Chass commissions Thuro of NorthCol to sculpt a memorial to the victory. Many Verghastites join the Tanith First under the Act of Consolation.
770.M41: The Tanith fight on Hagia.
771.M41: The Tanith take part in the liberation of Phantine.
772.M41: The Tanith fight on Aexe Cardinal.
773.M41: Saint Sabbat is reborn on Herodor. The Tanith are redeployed at her request and fight alongside her. The Phantine Air Corps fight on Ouranberg.
774.M41: A specialist team of 12 Ghosts led by 50 year old Commissar Gaunt are sent to the Chaos held world of Gereon.
~775.M41: The under-strength Tanith First and Only is merged with the Belladon 81st Recon to form the 81st/1st Recon, and the new regiment is deployed to Ancreon Sextus.
776.M41: Gaunt's team return from Gereon and are reunited with the 81st/1st on Ancreon Sextus. Gaunt re-assumes command and the Tanith First and Only is reformed, absorbing the Belladon personnel from the 81st.
777.M41: The Tanith assist in the liberation of Gereon.
778.M41: The Tanith defend the Hinzerhaus on Jago.
779.M41: The Tanith and 55 year old Gaunt arrive on Balhaut after being rotated off the front line.
779.M41: Titan Legio Invicta diverts from the Crusade to assist the Forge World of Orestes against a Chaos invasion.
780.M41: Gaunt and the Tanith battle a unit of Blood Pact infiltrators on Balhaut.
791.M41: The Ghosts defend Urdesh against the Sons of Sek. Gaunt is appointed Lord Executor.
829.M41: Thuro of NorthCol records his memoirs. The remains of Vervunhive have been completely demolished.
Edit March 2014: Updated the timeline with some info on the background of Inquisitors Heldane and Ravenor (author of Gaunt's beloved Spheres of Longing). Added Salvation's Reach to the timeline and reading list.
Edit July 2015: Updated the timeline to include stories from the Sabbat Crusade Anthology.
Congratulations on winning the quiz night, and give my regards to Commissar Gaunt.
Great work though, I love it. What got me in general is always how Abnett has little snippets and lines about people's past that don't really fit into this timeline (unless people would want to read specifically page x of volume y). For example I was re-reading Warmaster today and there's a bit where Abnett shoehorns in when Kolea took his wife and a babe-in-arms Dalin onto the Curtain Wall at Vervunhive. Relevant to the story, but would anyone be willing to skip around like that to get a perfectly linear narrative? Just a thought, love the work.


I understand that if given the option, you'd probably want to get laid right here and right. Gauging when you should leave can be difficult. You'll never believe where these people hooked up - top 8 places revealed. Dress to impress, am I right? Sure, we all know plenty of people who've used it for actual dating, but let's be totally honest: That's totally up to you. Why not start with the fun part?


text:
Southwark Bridge ( ) is an arch bridge in London, for traffic linking the district of Southwark and the City across the River Thames. Besides when others are closed for temporary repairs, it has the least traffic of the Thames bridges in London.

History

A previous bridge, designed by John Rennie the Elder, opened on the site in 1819. On the 1818 Cary map of London, it was labelled as Queen Street Bridge. All subsequent maps label it as Southwark Bridge.  The bridge consisted of three large cast-iron spans supported by granite piers. The bridge was notable for having the longest cast iron span, , ever made. Unsurprisingly, it became known colloquially as "The Iron Bridge" as mentioned inter alia in Charles Dickens' "Little Dorrit". The iron spans were cast in Masborough, Rotherham. It was a commercial tolled operation which was trying to compete with the toll free Blackfriars and London bridges nearby, but the company became bankrupt and its interests were acquired by the Bridge House Estates which then made it toll free in 1864.

A new bridge on the site was designed by Ernest George and Basil Mott. It was built by Sir William Arrol & Co. and opened on 6 June 1921.

Halfway along the bridge on the Western side is a plaque which is inscribed:
 Re-built by the Bridge House Estates Committee
 of the Corporation of London
 1913-1921
 Opened for traffic by their Majesties
 King George V and Queen Mary
 6th June 1921
 Sir Ernest Lamb CMG, JP Chairman
 Basil Mott, CB Engineer
 Sir Ernest George RA Architect

The bridge provides access to Upper Thames Street on the north bank and, due to the ring of steel, there is no further road access to the City and the north. The bridge is owned and maintained by Bridge House Estates, a charitable trust overseen by the City of London Corporation. The current bridge was given Grade II listed structure status in 1995.

Nearby

At the north-west side is Vintners' Court, a 1990s office block which has a classical façade of columns and pediment; this was developed on the site owned by the Worshipful Company of Vintners whose hall is behind it on Upper Thames Street.

The south end is near the Tate Modern, the Clink Prison Museum, the Globe Theatre, and the Financial Times and Ofcom buildings. Below the bridge on the south side are some old steps, which were once used by Thames watermen as a place to moor their boats and wait for customers.

Below the bridge on the south side is a pedestrian tunnel, part of the Queen's Walk Embankment, containing a frieze depicting the Thames frost fairs.

Cycle Superhighway 7 runs along the bridge.

Popular culture
Southwark Bridge appears in many films, including Harry Potter and the Order of the Phoenix (2007).
The cream painted houses on the south side of the bridge, Anchor Terrace, just after the FT building, were used for the exterior shots of the shared house in This Life.
The 1819-1920 "Iron Bridge" is mentioned in the first sentence of "Our Mutual Friend" by Charles Dickens, and several times in his "Little Dorrit", where in Chapter 24 he identifies the toll as being one penny.
In the 1964 Disney film Mary Poppins, the Banks family mistakenly think that George W. Banks has committed suicide by jumping off the bridge after he is fired from his job at the bank.
DCI Luther and Alice Morgan meet at Southwark Bridge in the season 3 finale of the BBC crime drama Luther.
The bridge appears in the final scene of Lock, Stock and Two Smoking Barrels with Tom leaning over the bridge with his cell phone in his mouth set to drop antique guns in the Thames River.

See also
List of crossings of the River Thames
List of bridges in London

References

External links

Bridges completed in 1819
Rebuilt buildings and structures in the United Kingdom
Bridges completed in 1921
Bridges across the River Thames
Grade II listed bridges in London
Transport in the London Borough of Southwark
Bridges in the City of London
Former toll bridges in England
Grade II listed buildings in the City of London
Grade II listed buildings in the London Borough of Southwark
Bridges in London
Bridge light displays

redpajama_set_name: RedPajamaWikipedia


text:
Celebrity Spouse
Home » People » Alexis Del Cid Height, Wiki, Fired, KCTV5, Husband, Legs, Married
Alexis Del Cid Height, Wiki, Fired, KCTV5, Husband, Legs, Married
By pushpanjaliin Peopleon July 4, 2019
Alexis Del Cid is a versatile American news anchor and reporter. She was previously presenter of "Better Kansas City" that airs on KCTV5 Kansas while she currently serves for NBC-affiliate WOAI where she is part of morning and midday newscast. She joined WOAI in August 2018 and has invested over two decades in news media.
Birthday: N/A
Ethnicity: Mexican-American
Profession: News Anchor and Reporter
Alexis Del Cid Personal and Family Life: Who Is Her Husband?
Alexis Del Cid is married to a handsome man named Sal. The couple began dating in early 2000 when they both were immature and young and 19 years later, they still are very beautiful and adorable.
The couple doesn't have any children of their own, however, they have an adopted son named Kingston whom they adopted from Guatemala. Alexis is extremely active in social media where she often flaunts the picture of her family and their trips.
Recently, she resides in San Antonio, Texas along with her husband, son, and a lovely boxer named Buster.
Born and raised in Chicago, Alexis holds American nationality and is of Mexican-American heritage. A self-proclaimed Midwest girl at heart, she has stated that she was in love with Kansas City where she served for KCTV5.
Parents: N/A
Husband: Sal Del Cid
Marital Status: Married
While growing up in Chicago, she used to spend her summers by ski in northern Wisconsin which she still indulges into. After completing her high school, she joined the University of Iowa from where she graduated with a bachelor degree in broadcast journalism.
Following, she began her career at Chicago-based radio station WMAQ; there she worked as a general news reporter. Then after, she went to work on television, joining KPLC in Lake Charles as a general reporter and host.
In 2012, she signed a contract with KCTV5 in Kansas City and worked until 2018 as Emmy Award-winning reporter and anchor. Currently, she works WOAI-TV, anchoring on News 4 Today and News 4 San Antonio at Noon.
Alexis Del Cid Age, Height, and Weight
Alexis Del Cid is a striking journalist with a model height and appropriate weight. She has an attractive hourglass figure and intriguing facial features that helped her to get an easy entry in the broadcasting industry.
A real professional who helps to bring authentic essence in journalism, Alexas is a gorgeous diva on television with outstanding knowledge of news and great presentation skills. Moreover, she can make anything look good on her with her exquisite face and hot figure.
Body Measurement: N/A
Plastic Surgery: N/A
Hasn't revealed her exact birthday, whatever age she is of, she still has got splendidly carved well-toned hourglass physique and glowing skin which makes her appear as if she is on her mid-twenties. She has brown hair, big brown eyes, and fair skin tone.
A fitness fanatic, Alexis performs hardcore physical workouts and eats a healthy diet to retain her smoldering figure. She enjoys water skiing, reading books, traveling, photography, eating, and cuddling with her son at the weekend.
Alexis Del Cid Net Worth and Salary
Alexis Del Cid net worth and salary are still to be disclosed, however, this veteran news personality has surely accumulated the notable amount of money through her burgeoning career in the broadcast industry.
Known as a former host of "Better Kansas City", Alexis's long-run career as a journalist has surely earned her the whopping fortunes along with numerous prestigious accolades.
Salary: N/A
Net Worth: N/A
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1927 House Bill 1119. An Act Relative To Sittings Of The Second District Court Of Southern Worcester.
Title 1927 House Bill 1119. An Act Relative To Sittings Of The Second District Court Of Southern Worcester.


Jigsaw puzzle of the Statue of Liberty standing with her torch on Liberty Island.
Beautiful. Saw this when we were at the World Trade Center a few weeks ago. My grandfather had to go thru Ellis Island when he came over from Sweden. Would love to see it. On my bucket list--hope I get to do it while I can.
The World Trade Center? Maybe the memorial - those are the two buildings that were destroyed in the 911 attacks. One of my neighbors is a pilot and he was schedule to fly one of those planes. He switched at the last moment with a colleague. He was suppose to fly the plane that crashed in PA that day. My neighbor said he was so crushed when he learned the news - they went to flight school together.
That tragedy happened two days after I moved in here, still like yesterday and almost 15 years ago. Hugs.
I can still recall that am when it happened. Arrived at work and was informed that there was a hijacking. Then was told that there was another plane. I said to the receptionist "This isn't a coincidence - this is terrorism. Worked in an architects office and the boss who went to school asked another co- worker how the buildings melted. This co worker told me about this bosses comment and said omg he (boss) should know.
For some reason I still say "World Trade Center". It was the memorial and very impressive. Last time I saw it was when it was "raw" ground and they were working there.However, it does seem like yesterday! So awful and this country is not much better now.
Even with all of its flaws (who said life is perfect? ), the U.S. is my home and it is definitely the best place to be! God bless America!
You have to love this puzzle! She welcomes all to the US!
I lived in NJ 25 years and never took the time to visit this statue.
I would not trade USA for any other country.
She is so Beautiful! this is one place I have been so many years ago when I lived in New York!
For a couple of minutes I have silver. the colour of the sky sets of the statue beautifully. what else is there to say except God bless you all and keep you safe.
We are moving into autumn and it is cold and wet the worse 2 combination for me, hope we might get an indian summer to make the winter shorter. Have a great and blessed day.


text:
Massasoit CC Athletics
Dropdown Logo
Concussion Management Plan
Field House Information
PASS Program
Survey - EADA
Peter Asiaf Field House
Louis R. Colombo Field
Warrior Soccer Field
Massasoit Softball Field
Massasoit Track
Massasoit Athletics Hall Of Fame
Online Nomination Form
NJCAA Hall Of Fame
NJCAA Championships
Region 21 Championships
Team Archives
Watch Games
Region XXI
MASSASOIT.EDU
Cross Country Questionnaire
NJCAA - Cross Country
John Mantia Named Massasoit Cross Country Head Coach
BROCKTON, Mass. ---- Former UMass Amherst cross country and track student-athlete John Mantia was recently named the next Massasoit CC cross country head coach for the 2016 season.
Mantia competed for the Minutemen from 2011-2015, racing in a number of different events during his time in Amherst.
"We are excited for John to take the reins of our cross country program," Athletics Director Julie Mulvey said. "He has a true passion for running and can take his knowledge and recent experiences as a student-athlete and apply it here at Massasoit. John is a great fit for our department."
A long distance specialist, Mantia ran anything from the 400-meter to the 10k and everything in between during his time with the Minutemen. He also raced on in the 4x400 relay team and in the 3,000m steeplechase, which he finished 11th at the Atlantic 10 Championships in 2014 in a personal best time of 9:29.48.
"I'm beyond excited for the opportunity to coach cross county here at Massasoit," Mantia said. "I love the idea of being able to work with students and help make them better with regards to running. It's rare you get to do a job that coincides with something you are passionate for, something you dedicated years to doing and something that you've studied (kinesiology). I could not be more excited about this opportunity."
Mantia graduated from UMass in 2016 with a degree in kinesiology and was an All-scholastic All-Star at Coyle & Cassidy High School. He is currently taking classes at Massasoit with plans to attend physical therapy school in the future.
In addition to coaching cross country, Mantia will assist track & field head coach Matt Jordan in the spring.
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Things can quickly go from bad to worse when you're working in some of the conditions that David Manson from Manson Machinery finds himself. At the moment he's racing to stay ahead of the rain as he works on an awkward site in Lynfield, west of the central Auckland City. Thankfully his Komatsu PC18MR-3 will help.
"I did my due diligence and looked at a number of different brands," says Manson. "There was another brand that I was keen on, but kept coming back to Komatsu. Looking at the others kept me honest."
What he is talking about is the two Komatsu excavators – a PC35MR-3 and a PC18MR-3 – that he has purchased over the last six months. These replaced his MR-2 model Komatsus that had clocked up a few thousand hours.
The machine we are here to look at today is the 1.8-tonne PC18MR-3. This nifty little excavator is proving popular with operators and hire companies, being the reason that Manson had to wait in a holding pattern until his machine was delivered.
The grin on his face as he shows us around his latest acquisition easily tells that the wait was worth it. He's very happy with the purchase but there are a couple of changes he would have done if he was in charge of the Komatsu design studio.
So, what's the PC18MR-3 all about? For starters it's big (or small) enough to fit on a ute-towed trailer, so that explains the interest from hire companies. The expandable tracks – 900mm to 1200mm – mean that tight urban access problems are easily solved, so that explains the interest from contractors and drainlayers.
Manson has JB Attachment hydraulic hitches fitted to both his Komatsus and he says this adds to the versatility of the machines and means he doesn't get lazy about changing buckets when the job at hand calls for different tactics.
Different tactics are certainly what is needed in Manson's daily grind, as most of his jobs are on tight, steep sites that frequent the area that he predominately works. Stuff like this is not for the faint hearted and many a digger operator that I've seen boasting about their prowess wouldn't survive more than a day in conditions that Manson works, before going home crying to their mamas.
One benefit, as Manson explains, is the low centre of gravity that the excavator affords. He points out the side counterweights that, in addition to the rear counterweight, make the machine very stable.
This particular area was one of the reasons Manson forked out more money than he would have on some other brands to buy a Komatsu, as he points out the extra space available for the operator.
"Yes, I could have saved a few grand and bought something cheaper that may have done a similar job. But when I'm spending all day on a machine for weeks on end, the extra space it gives means that money becomes insignificant."
Another important feature are the two entry/exit points. Most other brands have only one of these, so again, the versatility of the machine is noted.
This area however does come into some criticism from Manson, as we previously alluded to. On the PC18MR-2 model, the left-hand control console pivots up and out of the way to provide a wider gap for an exiting or entering operator.
On this new model, the controls are fixed and although there is a decent amount of space (some 560mm), there is a definite chance of getting shorts, especially the thigh pocket of cargo pants caught, which can easily throw someone off balance. It is difficult to understand why this has been done, but no doubt a plausible explanation is out there.
The other change Manson would like to see is the replacement of the steel canopy with a plastic one. I was wondering if he was referring to a noise problem during heavy rain? "No," he says. It was the damage these types of canopies incur when working in tight areas – heavier plastic being the preferred choice, due to its ability to 'pop' back into shape.
After talking to Manson for a while, I had almost forgotten that the reason for looking at the machine was to give it a test run. Seeing it was already set-up on a stockpile, it was a simple matter of climbing aboard and giving the engine some revs.
One thing I noticed immediately was the intuitive layout of the controls, and even though this was the first time I had operated a small Komatsu excavator, my hands intuitively landed in all the right places.
Another noticeable difference I picked up on was the stability, and despite the front of the tracks being firmly planted in the stockpile of soil and the rear of the tracks hanging in mid-air, being lifted there by the blade, I was able to operate comfortably without the machine pitching and rocking my internal organs as much as I would have expected.
Power supply to the hydraulics was more than adequate, and to be fair I wouldn't have expected less considering the work the machine was undertaking.
Having finished my stint aboard, I did come away from the PC18MR-3 genuinely impressed with its stability, comfort and operating capabilities.
I did agree with David Manson's observations about the machine. After all, he should know, as his last model had done over five-and-a-half-thousand hours when he upgraded.
Granted, these machines carry a heftier price tag than some other brands, but Manson does make a very strong case for that cost difference. If I was spending as much time aboard a smaller machine as he does, I'm quite sure I'd be thinking the same way.
For more information contact Komatsu on 0800 566 2878.
Deals on Wheels puts a Komatsu PC18MR-3 excavator to the test in this video.


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Waves of a Global Slowdown come Ashore in the U.S.
Tomoko Iwakawa
Earlier this week Paul Single, our colleague at City National Rochdale, focused his Economic Perspectives video on weakness in Europe.
The news from Europe got even worse during the course of this week. German industrial orders declined at the fastest rate since 2012 and the Italian economy posted slightly negative GDP in the last two quarters of 2018, officially putting that country into recession.
In our morning commentary earlier this week, we talked about developments in Australia. A day after its central bank issued a rate decision that was considered a "hawkish hold," the governor warned markets that the next move could be a cut, due to fears of a global slowdown.
In today's interdependent global economy, these developments will obviously wash back up on our shores. The transformation of the U.S. Federal Reserve's outlook in the last three months seems to have a certain finality to it. Just a little over three months ago, the central bank seemed to be set on autopilot when it came to raising rates and shrinking its balance sheet. Now, it seems to be firmly on hold and waiting for data to inform it of its next move.
Federal Reserve Chair Jay Powell is already juggling equity market volatility, winding down the fed's balance sheet and questions about executive interference in the economy. Add to all that weak foreign economic data, and the troubles multiply.
If the global economy moved in sync, monetary policy could be applied with less concern about the effects in certain markets. But with many U.S. companies' earnings tied in with foreign economies, a lot of unintended consequences can result.
With this last round of corporate earnings releases, we saw how that works. Caterpillar and Nvidia were two of the U.S. companies that had disappointing quarters, and they specifically cited Chinese weakness as a major problem. General Motors reported pretty good results, but they were the result of cost-cutting the company undertook to offset poor sales outside of the U.S.
For the Fed, this results in U.S. businesses needing looser credit conditions, while at the same time the U.S. economy continues to add jobs. It also multiplies the amount of economic analysis the Fed must consider when backing into U.S. monetary policy
Our View: We're only a month into the year and already we are seeing shifts away from what we were expecting for 2019. These changes could bleed over into our expectations about the U.S. dollar, which we thought would drift lower over the course of the year on U.S. weakness. Now, it is looking like we may get outdone in that weakness by a few other countries.
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text:
The Birds and The Bees är en sång med Jewel Akens skriven av Barry Stuart. Låten var en hit 1965, och nådde plats två på Cash Box magazine lista och plats 3 på Billboard Hot 100  samt plats 29 på Record Retailer lista i England.

Coverversioner

 En cover av låten är inspelad av Alma Cogan i England. Denna version blev en större hit i Skandinavien än Akens version. En komplicerande omständighet kring låten är att Cogan 1956 spelade in en helt annan låt med samma titel.
 En svensk text med titeln "Blommor och bin" skrevs av Keith Almgren och spelades in av Sten & Stanley på albumet "Musik, dans & party 8" 1993

Listplaceringar, Jewel Akens

Listplaceringar, Alma Cogan

Referenser

Sånger 1965
Musiksinglar 1965
Engelskspråkiga sånger


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Well - you can always dream! We have had a calm and relaxing Christmas but NO snow! Still - a white card can never be bad - right?
I love how this turned out. It was pretty hard to capture it on a photo cause it truly is white. Different shades of white and silver. The stamping with seasonal stamps from IndigoBlu and then transformed into magic shimmer with Mega Flakes in the color "Sheffield Steel". Splatters of Baseboard Mist "Sandy Beach" gives an other tone of white to the background.
I have used products from IndigoBlu (stamps & Mega Flakes), Tattered Angels (Mist), Petaloo (Flowers), 7 Dots Studio (tag), Prima Marketing (pearls & word stickers).