text:
\section{Introduction}
An open and rather controversially discussed topic in high-$T_c$
superconductivity is the role played by phonons for the
low-energy electronic properties and, in particular, the high transition
temperatures $T_c$. A direct way to show the involvement of the lattice
in electronic properties is the study of the isotope effect on
$T_c$. \cite{Franck} Experimentally, the corresponding isotope
coefficient $\alpha$ is very
small in high-$T_c$ cuprates near optimal doping but increases strongly
in the underdoped region attaining values being comparable or even larger
than those in conventional phonon-mediated superconductors. It is often
argued that these large observed isotope effects in the underdoped
region give direct evidence for a large
electron-phonon coupling
in the cuprates. \cite{Franck,Keller,Bornemann}
It even has been suggested that it is so large that
Eliashberg theory breaks down and that non-adiabatic and polaronic features
play an important role in these systems.
\cite{Alexandrov,Buss,Alexandrov1,Jarrell}
Other approaches have suggested that large isotope effects may occur
in the presence of a pseudogap. \cite{Williams,Dahm}

Below we show that the essential features of the isotope experiments on T$_c$
can be explained within a mean-field approximation of the $t$-$J$ model
\cite{Morse,Hsu,Cappelluti,Benfatto}
using very small values for the electron-phonon coupling.
The pure $t$-$J$ model exhibits in mean-field
approximation a competition of $d$-wave superconductivity and a $d$-CDW
with transition temperatures $T_c$ and $T^\ast$, respectively. The
observed pseudogap can be identified with the $d$-CDW phase in this
model. \cite{Cappelluti,Chakravarty} Whereas many experiments support the
idea of two competing phases \cite{Tacon,Lee,Wen,Kondo,Yu,Mook,Liu}
the nature of the additional
phase remains unclear and many proposals besides of the $d$-CDW have been
considered. \cite{Norman} Experiments suggest that its order parameter
has $d$-wave symmetry like that of the superconducting phase. This favors
an unconventional charge- or spin density wave state with internal $d$-wave
symmetry rather than a conventional one with (anisotropic)
$s$-wave symmetry. The $t$-$J$ model
yields at large $N$ ($N$ is the number of spin components) such a
$d$-CDW but its relevance for the physical case $N=2$, for instance
in form of a phase without long-range but strong $d$-wave short-range order,
remains unclear. \cite{Leung,Macridin,Oles}

In section II we introduce our model, its phase diagram and numerical
results for the competing superconducting and CDW order parameters,
and the corresponding transition
temperatures $T_c$ and $T^\ast$. We then add phonons assuming always
that the electron-phonon interaction is very small so that they can be
treated in the weak-coupling approximation. Explicit formulas for the
isotope coefficients $\alpha$ and $\alpha^\ast$ related to $T_c$ and $T^\ast$
will be given. In section III we present numerical results
for the doping dependence of $\alpha$ and $\alpha^\ast$.
In section IV we extend our treatment by including off-diagonal fluctuations
in the $d$-CDW state using the method of Refs. \cite{Lee1,Bartosch,Kuchinskii}.
In this way the pseudogap
phase is treated more realistically because the long-range order is
removed and self-energy effects are included. Our conclusions are
found in section V.

\section{Theoretical framework}

We consider the $t$-$J$ model \cite{Ogata} with the Hamiltonian $H$,
\begin{eqnarray}
H = -t\sum_{\langle i,j \rangle,\sigma} c^\dagger_{i\sigma} c_{j\sigma}
-t'\sum_{\langle i,j \rangle',\sigma} c^\dagger_{i\sigma} c_{j\sigma}
\nonumber \\
+ \frac{J}{2} \sum_{\langle i,j \rangle} {\bf S}_i {\bf S}_j
-\frac{1}{4}(J-2V_C)\sum_{\langle i,j \rangle} n_i n_j.
\label{H}
\end{eqnarray}
$c^\dagger_{i\sigma}, c_{i\sigma}$ are creation and
annihilation operators, respectively, for electrons at site $i$ and
spin projection $\sigma$ subject to the condition that double occupancies
of sites are excluded.
The sums include nearest neighbor $\langle i,j \rangle$ and next nearest
neighbor $\langle i,j \rangle'$ sites on a 2D square lattice, the
corresponding hopping elements are $t$ and $t'$, respectively.
${\bf S}_i$ and $n_i$ are spin and site occupation operators,
$J$ the Heisenberg coupling constant, and $V_C$ a Coulomb interaction
between nearest neighbors.

One way to obtain a mean-field approximation
for $H$ is to introduce $N$ spin components in Eq. (\ref{H}), scale
the coupling constants as $t \rightarrow 2t/N$, $t' \rightarrow 2t'/N$,
$J \rightarrow 2J/N$ etc., and to consider the large $N$
limit. \cite{comment}
As a result $t$ and $t'$ are renormalized yielding the
quasi-particle dispersion $\epsilon({\bf k})$. At the same time the fermionic
operators can be treated as usual creation and annihilation operators.
Explicitly, one obtains
$\epsilon({\bf k}) = -2(\delta t + r J)(\cos(k_x)+\cos(k_y))
-4t'\delta \cos(k_x)\cos(k_y)  -\mu$,
with $r = 1/N_c \sum_{\bf q} \cos({q_x})f(\epsilon({\bf q}))$.
$f$ is the Fermi function, $\delta$ the doping away from half-filling, and
$\mu$ a renormalized chemical potential. Here and in the following
we use the lattice constant $a$ of the square lattice as length unit.
As previously discussed \cite{Cappelluti,Greco} the
relevant order parameters for our mean-field treatment of the $t$-$J$ model
is a CDW order parameter
\begin{equation}
\Phi({\bf k})=-\frac{i}{N_c}\sum_{\bf q}J({\bf k}-{\bf q})
\langle c^\dagger_{{\bf q}\uparrow} c_{{\bf q}+
{\bf Q}{\uparrow}} \rangle,
\label{J}
\end{equation}
with $J({\bf k}) = 2J(\cos k_x +\cos k_y)$,
and a superconducting (SC) order parameter
\begin{equation}
\Delta({\bf k}) = \frac{1}{N_c}\sum_{\bf q}
(J({\bf k}-{\bf q})-V_C({\bf k}-{\bf q}))
\langle c_{{\bf q}\uparrow} c_{{-\bf q}\downarrow}\rangle.
\label{Delta}
\end{equation}
\begin{figure}[b]
\vspace*{-0.5cm}
\centerline{\includegraphics[angle=-90,width=9.0cm]{fig1.eps}}
\vspace{-0.3cm}
\caption{\label{fig:1}
(Color online)
Zero temperature order parameters $\Phi$ and $\Delta$ and the
critical temperatures $T^\star$ and $T_c$ as a function of doping.
}
\end{figure}
$N_c$ is the number of
primitive cells, $\langle...\rangle$ denotes an expectation value,
${\bf Q} =(\pi,\pi)$ is the wave vector of the $d$-CDW, and
$V_C({\bf k}) = 2V_C(\cos k_x +\cos k_y)$. The Coulomb interaction
$V_C({\bf k})$ between nearest neighbors has been introduced to prevent
an instability of the $d$-CDW with respect to phase separation in some
region of phase space. \cite{Cappelluti}
From the self-consistency
condition for the self-energy one obtains
coupled equations for $\Phi$, $\Delta$, the chemical potential and
a renormalization contribution $r$
to the band dispersion due to $J$. \cite{Cappelluti,Greco}
Their most stable
solutions have $d$-wave symmetries in the interesting doping region,
i.e., $\Phi({\bf k})=\Phi \gamma({\bf k})$ and $\Delta({\bf k}) =
\Delta \gamma({\bf k})$ with $\gamma({\bf k})=(\cos k_x-\cos k_y)/2$.

A similar mean-field approximation as above is obtained by
using a slave-boson representation for $H$ in Eq.(\ref{H}),
enforcing the constraint on the average, using usual
mean-field decouplings for the third and fourth term in $H$, and
dropping the antiferromagnetic order parameter. The above expression
for $\epsilon({\bf k})$ as well as Eq.(\ref{Delta}) are in this way exactly
reproduced, Eq.(\ref{J}) with $J/2+V_C$ instead of $J$.

Fig. \ref{fig:1} shows the doping dependence of $\Phi$ and
$\Delta$ at zero temperature,
calculated fully self-consistently for $t'/t=-0.35$, $J/t=0.3$, and
$V_C/J=0.2$. In the overdoped
region $\delta \geq \delta_c \sim 0.14$ $\Phi$ is zero. In the underdoped
region $\delta \leq \delta_c $ $\Phi$ is non-zero and coexists
with $\Delta$. $\Delta$  shows
a maximum near $\delta_c$ and decays approximately
linearly in $\delta$ towards lower and higher dopings.
The two order parameters compete with each other which causes the strong
decay of $\Delta$ with decreasing doping in the underdoped region.
Also shown in Fig. \ref{fig:1} is $T^\star$ (dash-dotted line) and
$T_c$ (dashed line) where $\Phi$ and $\Delta$, respectively, vanish.
$T^\star$ shows near $\delta_c$ a reentrant behavior which has a simple
explanation: The piece of the $T^\star$ line above the $T_c$ curve
is unaffected by superconductivity. Discarding superconductivity
the $T^\star$ line would continue to the right decreasing slowly and
reaching the $x$ axis only at around $\delta \sim 0.25$.
Taking superconductivity
into account $T^\star$ and also $\Phi$ are suppressed by
the presence of a finite $\Delta$, i.e., below the $T_c$ curve.
Since $\Delta$ increases rapidly with
decreasing temperature $T^\star$ even bends back due to the strong
repulsion and reaches the critical doping $\delta_c$ at zero
temperature where $\Phi$ becomes nonzero. The reentrant behavior
thus reflects the strong competition of the CDW and SC order
parameters.
The occurrence of a large coexistence region of $\Delta$ and $\Phi$,
which extends down to
$\delta = 0$,  is plausible because the
Fermi surface consists in the $d$-CDW state of arcs around the nodal
direction \cite{Greco}
which are unstable against the formation of a BCS gap $\Delta$.

In order to discuss the isotope effect we consider
a phonon-induced electronic density-density coupling between
nearest neighbors and on the same atom. Approximating
its frequency dependence by a rectangular form, as is often done
in approximate solutions of the Eliashberg equation,\cite{Carbotte}
this effective
electron-electron interaction has in the $d$-wave channel the form,
\begin{equation}
v({\bf q},i\omega_n) = -2V n_d({\bf q},i\omega_n) n_d({\bf -q},-i\omega_n),
\label{v}
\end{equation}
\begin{equation}
n_d({\bf q},i\omega_n) = \frac{1}{N_c}\sum_{{\bf k},\sigma=1,2}
\gamma({\bf k})\Theta_n c^\dagger_{{\bf k}+{\bf q}{\sigma}}
c_{{\bf k}{\sigma}}.
\end{equation}
Similarly, we have in the isotropic $s$-wave channel,
\begin{equation}
w({\bf q},i\omega_n) = -\frac{W}{2} n({\bf q},i\omega_n) n({\bf -q},-i\omega_n),
\label{w}
\end{equation}
\begin{equation}
n({\bf q},i\omega_n) = \frac{1}{N_c}\sum_{{\bf k},\sigma=1,2}
\Theta_n c^\dagger_{{\bf k}+{\bf q}{\sigma}}
c_{{\bf k}{\sigma}}.
\end{equation}
$V$ and $W$ are electron-phonon (EP) coupling constants in the $d$
and $s$-wave channels, respectively,
$\Theta_n$ the cutoff function $\Theta(\omega_D-|\omega_n|)$,
$\omega_n$ the bosonic Matsubara frequency $\omega_n= 2n\pi T$, and
$\omega_D$ the phonon cutoff frequency.
$n_d({\bf q},i\omega_n)$ and  $n({\bf q},i\omega_n)$ are
electronic density operators with $d$ and $s$-wave symmetry, respectively.
Effects due to a small EP interaction can be taken into
account in the curves of Fig. 1 by adding the electronic self-energy  due
to $v({\bf q},i\omega_n)$ and $w({\bf q},i\omega_n)$ in the form of a
Fock diagram.
The resulting self-consistent equations lead to an equation for
the renormalization function $Z({\bf k},i\omega_n)$ due to $W$.
At $T=T_c$ this equation can be solved directly yielding
$Z({\bf k},i\omega_n) \equiv Z = 1 + \lambda_s$ where $\lambda_s$
is the product of $W$ and the electronic density at the Fermi energy
and $T=T_c$, i.e., it refers in general to the $d$-CDW state. A second
equation is obtained
which determines the SC order parameter $\Delta({\bf k},i\omega_n)$,
\begin{eqnarray}
\Delta({\bf k},i\omega_n) =
-4\tilde{J}\gamma({\bf k})\frac{T}{N_c}\sum_{{\bf k}'n'}
\gamma({\bf k}')g_{12}({\bf k}',i\omega_{n'}) - \nonumber\\
-4V\gamma({\bf k}) \Theta_n
\frac{T}{N_c}\sum_{{\bf k}'n'}\gamma({\bf k}')
\Theta_{n'}g_{12}({\bf k}',i\omega_{n'}).
\label{gap}
\end{eqnarray}
$\tilde{J}$ is equal to $J-V_{C}$.
$g_{12}$ is the 12-element of the 4$\times$4
matrix Green's function $g$. Its inverse $g^{-1}({\bf k},i\omega_n)$
is given by,
\begin{equation}
\left(
\begin{array}{c c c c}
i\omega_nZ-\epsilon({\bf k}) & -\Delta({\bf k},i\omega_n)  & -i\Phi({\bf k},
i\omega_n)                      &  0                 \\
-\Delta({\bf k},i\omega_n)    &i\omega_nZ+\epsilon({\bf k})
&   0               &i\Phi({\bf \bar{k}},i\omega_n)      \\
i\Phi({\bf k},i\omega_n)      &   0
&i\omega_nZ-\epsilon({\bf\bar{k}})& -\Delta({\bf \bar{k}},i\omega_n)
 \\
          0         &-i\Phi({\bf \bar{k}},i\omega_n)
&-\Delta({\bf\bar{k}},i\omega_n)&i\omega_nZ+\epsilon({\bf \bar{k}})
\end{array} \right)
\label{matrix}
\end{equation}
with the abbreviation
$\bf {\bar{k}}= {\bf k-Q}$.
$\Phi({\bf k},i \omega_n  )$ is the
$d$-CDW order parameter renormalized by the phonons and given by,
\begin{eqnarray}
i \Phi({\bf k},i\omega_n) = -4J\gamma({\bf k}) \frac{T}{N_c} \sum_{{\bf k'}n'}
\gamma({\bf k'})g_{13}({\bf k'},i\omega_{n'}) \nonumber \\
+2V\gamma({\bf k}) \Theta_n \frac{T}{N_c}\sum_{{\bf k'}n'}
\Theta_{n'}\gamma({\bf k'})g_{13}({\bf k'},i\omega_{n'}),
\label{Phi}
\end{eqnarray}
where $g_{13}$ is the 13-element of the Green's function matrix $g$.

  For the calculation of $T_c$ it is sufficient to linearize the
right-hand side of Eq. (\ref{gap}) with respect to  $\Delta({\bf k},i\omega_n)$.
Furthermore, we may neglect the phonon renormalization for $\Phi$ in this
case: Below we will be interested only in a small EP constant $V$
yielding also only a small renormalization. Moreover, as will be shown below,
this small renormalization is practically independent of the ionic
mass $M$ and thus may be neglected in calculating the isotope effect on
$T_c$. We therefore have solved Eq. (\ref{Phi}) using only the first term
on the right-hand side and use the solution in
Eq. (\ref{matrix}) to obtain $g_{12}$.
Eq. (\ref{gap}) represents an integral equation with two separable kernels
which can easily be solved. Writing Eq.(\ref{gap}) as a condition for $T_c$
we find,
\begin{equation}
(1+F_{11})(1+F_{22}) -F_{12}^2=0,
\label{Tc}
\end{equation}
with
\begin{equation}
F_{11} = -2{\tilde J}\int_0^\infty d \omega
\frac{N_d(Z\omega)}{Z\omega} tanh(\frac{\omega}{2T_c}),
\label{F11}
\end{equation}
\begin{eqnarray}
F_{12} = -2\sqrt{V{\tilde J}}\int_0^\infty d \omega \frac{N_d(Z\omega)}
{Z\omega}\frac{2}{\pi}
\Im[\psi(\frac{1}{2}+{\frac{i\omega}{2\pi T_c}})  \nonumber \\
  -\psi({\frac{\omega_D}{2\pi T_c}}+1 +{\frac{i\omega}{2\pi T_c}})],
\label{F12}
\end{eqnarray}
and $F_{22}=\sqrt{V/{\tilde J}}F_{12}$. $\psi$ is the digamma function and $\Im$
denotes the imaginary part.
$N_d({\omega})$ is given by
\begin{equation}
N_d(\omega) = \frac{2\omega}{\pi N_c} \sum_{\bf k} \gamma^2({\bf k})
\Im [G({\bf k},\omega-i\eta)],
\label{N}
\end{equation}
where $\eta$ is a positive infinitesimal quantity,
\begin{equation}
 G({\bf k},z) = \frac{z^2-\epsilon^2({\bf  \bar{k}})
-\Phi^2({\bf k})}{(z^2-\lambda_1^2({\bf k}))(z^2-\lambda_2^2({\bf k}))},
\label{Pole}
\end{equation}
and
\begin{equation}
\lambda_{1,2} = \frac{\epsilon({\bf k})+\epsilon({\bf \bar{k}})}{2}
\pm \frac{1}{2}\sqrt{(\epsilon({\bf k})-\epsilon({\bf \bar{k}}))^2
+4\Phi^2({\bf k})}.
\label{Pole1}
\end{equation}
\begin{figure}[t]
\vspace*{-0.3cm}
\includegraphics[angle=270,width=9.cm]{fig2.eps}
\caption{\label{fig:2}
Weighted density $N_d(\omega)$ of electronic states for two dopings $\delta$.
}
\vspace{-0.3cm}
\end{figure}
$N_d(\omega)$ represents a weighted density of electronic states at $T_c$
and is shown in Fig. \ref{fig:2} for two different dopings. It consists of a
sharp peak near the energy $\Phi$ due to excitations across the $d$-CDW gap
and a structure at lower energies related to the van Hove singularity.
It is convenient to characterize $V$ by a dimensionless EP coupling constant,
\begin{equation}
\lambda_d = V N_d(0).
\label{lambdad}
\end{equation}

According to the above equations phonons affect $T_c$ in a two-fold
way, namely, via $V=\lambda_d/N_d(0)$ and via $Z=1+\lambda_s$.
$\lambda_d$ and $\lambda_s$ characterize
the phonon-induced pairing interaction of $d$-wave and $s$-wave
symmetry, respectively. Putting $\lambda_s$ to zero $V$ increases $T_c$.
To see this we rewrite Eq. (\ref{Tc}) in the form $1+\hat{F}_{11}=0$.
$\hat{F}_{11}$ is given by Eq. (\ref{F11}) if one makes there the change
${\tilde J} \rightarrow {\tilde J}/(1-F_{12}^2/(1+F_{22}))$.
This means that $V$ increases
${\tilde J}$ and thus increases $T_c$. On the other hand, if we put $V=0$
Eq. (\ref{Tc}) reduces to $1+\hat{F}_{11}=0$ with $\hat{F}_{11}$
given by Eq. (\ref{F11}) modified by ${\tilde J} \rightarrow {\tilde J}/Z$ and
$T_c \rightarrow T_c Z$. Each of these two changes diminishes $T_c$.
Thus phonons may lower or may increase $T_c$ depending which of
the above two effects is larger. Numerical calculations indicate that
generically the second effect dominates and that $T_c$ decreases if
one couples to phonons. \cite{Macridin1} Most important for us is, however,
the following observation. Our aim is not to determine the change in $T_c$
when the electron-phonon coupling is turned on but
when the ionic mass $M$ is changed. It is well known that $\lambda_s$
is independent of the ionic mass $M$, thus there will be no change
in $Z$ by isotope substitutions and $\alpha$ will always be positive.
For small EP couplings we may even
put $Z=1$ and  keep only the linear term in $V$
in the calculation of the isotope coefficient  $\alpha =
-d \ln T_c /d \ln M$.
From Eq. (\ref{Tc}) one finds for $\alpha$ in this limit,
\begin{equation}
\alpha = \frac{\omega_D}{T_c} F_{12} \Bigl(\frac{\partial F_{12}}{\partial
\omega_D} \Bigr) \Bigl(\frac{\partial F_{11}}{\partial T_c}\Bigr)^{-1},
\label{alpha}
\end{equation}
where the derivatives in Eq. (\ref{alpha}) are to be taken at the
$T_c$ without phonons and we also assumed $\omega_D
\sim M^{-0.5}$.

\section{Results for the isotope coefficients}

In deriving the above formulas we assumed that the phonon-induced
interaction $V$ affects only $\Delta$ but not $\Phi$ and thus also
not $T^\ast$. To check this approximation we have calculated
the isotope coefficient $\alpha^\star$ related to $T^\star$
and defined by $\alpha^{\ast} = -d \ln T^{\ast} /d \ln M$.
The calculation of $\alpha^{\ast}$ is very similar to that of $\alpha$.
\vspace{-0.2cm}
\begin{table}[h]
\caption{Isotope coefficient $\alpha^{\ast}$ for different dopings $\delta$
}
\vspace{0.3cm}
\begin{tabular}{c|c|c|c|c|c|c|c}
 $\delta$ & 0.028 & 0.048 & 0.064 & 0.090 & 0.115 & 0.139 & 0.164\\
\hline
$100\cdot\alpha^{\ast}$  & $-0.20$ & $-0.24$ & $-0.27$ & $-0.34$ & $-0.42$
 & $-0.53$ & $-0.66$
\end{tabular}
\end{table}
Numerical values for $\alpha^{\ast}$ as a function of doping throughout the
underdoped regime are given in TABLE I for $V/t=0.04$ and $\omega_D/t=0.1$.
All values for
$\alpha^{\ast}$ are negative, i.e., $\alpha^{\ast}$ shows an inverse
isotope effect. However, this isotope effect is two orders of
magnitude smaller than the usual BCS value of 1/2 and thus tiny. Furthermore,
the absolute value of $\alpha^{\ast}$ decreases with decreasing doping
quite in contrast to $\alpha$ as will be shown below.
The negligible isotope effect on $T^\ast$ which we found
is in agreement with the experiment \cite{Williams} though there
exist also data which have been interpreted in terms of a large
isotope coefficient $\alpha^{\ast}$. \cite{Rubio}
Strictly speaking in our calculation of $\alpha$
the renormalized $d$-CDW order parameter at $T = T_c$ enters the
density of states function $N_d(\omega)$, Eq. (\ref{F11}). Since we have
shown that $T^{\ast}$ is independent of the ionic mass $M$
we may conclude that the $d$-CDW order parameter at $T = T_c$
has also only a negligible isotope effect
justifying the above procedure to calculate $\alpha$.

Fig. \ref{fig:3} shows $\alpha$ as a function of doping for $V/t=0.04$ and
two phonon cutoffs $\omega_D$ corresponding to the buckling and
half-breathing phonon modes in YBa$_2$Cu$_3$O$_7$. \cite{Pintschovius}
In the overdoped region
$\alpha$ is nearly independent of $\omega_D$ and $\delta$ and about
0.03, i.e., very small. In the underdoped region
$\alpha$ monotonically increases with decreasing $\delta$
and reaches appreciable values, for instance, 1/4 at a $T_c$
which is only reduced by a factor 2 from its maximum value.

To understand the increase of $\alpha$ at low dopings better one can rewrite
Eq. (\ref{alpha}) approximately as $\langle N_d(\omega)\rangle/N_d(0)(-F_{22})$,
using a low $T_c$ approximation in the denominator.
\begin{figure}[h]
\vspace*{-0.2cm}
\includegraphics[angle=-90,width=9.0cm]{fig3.eps}
\caption{\label{fig:3}
(Color online)
Isotope coefficient $\alpha$ as a function of doping for
two phonon cutoffs $\omega_D$. Also shown are the curves for
$\Phi$ and $T_c$ from Fig. \ref{fig:1}}.
\end{figure}
$\langle N_d(\omega)\rangle$ is an average of $N_d(\omega)$ around the phonon
frequency $\omega_D$ over an energy
interval of about $\omega_D$. This interval is determined by the
functions $\psi$ in Eq. (\ref{F12}) and caused by the sharp cutoff in
Matsubara frequencies.
According to Fig. \ref{fig:2} $N_d(0)$ decreases rapidly with
decreasing $\delta$
reflecting the fact that $N_d(0)$ is due to the arcs left over
from the Fermi line after formation of the $d$-CDW gap. The length of the
arcs, however, decreases strongly with decreasing $\delta$.
From Fig. \ref{fig:2} it is clear that
for most phonon frequencies the large spectral weight near the
$d$-CDW gap will substantially contribute to this average. As a result
$\langle N_d(\omega) \rangle/N_d(0) \gg 1$ and, since $-F_{22}$ is
a slowly increasing function with decreasing $\delta$, a large
enhancement of $\alpha$ results at low dopings.
A sharp cutoff for real frequencies, usually used in BCS-theory,
would yield
$\langle N_d(\omega)\rangle =N_d(\omega_D)$.
Consequently $\alpha$ would exhibit
strong resonances for $\omega_D \sim \Phi$ or, more generally,
if $\omega_D$ is near well-pronounced peaks in $N_d(\omega)$.
Implementing the phonon cutoff in terms of Matsubara frequencies,
as we did, corresponds to a rather soft cutoff in real frequencies.
Such a procedure is closer to an exact solution of Eliashberg equations,
yields a finite phonon contribution to $Z$ and is also free of the above
unphysical resonances in $\alpha$ if $\omega_D$ and
the gap energy $\Phi$ are of similar magnitude. Another advantage of our
procedure is that $\alpha$ depends only weakly on $\omega_D$, also for
$\delta \leq \delta_c$. If there is no pseudogap $N_d(\omega)$ is
rather constant in the phonon energy region which means that
the above density ratio $\langle N_d(\omega)\rangle/N_d(0)$ is one and $\alpha$
very small for all dopings.

Qualitatively, the curves for $\alpha$ in Fig. \ref{fig:3} are similar to
those in Refs.
\cite{Williams,Dahm} where phenomenological
pseudogaps were used and the problem of resonances was avoided
either by considering only the limit $\omega_D \gg \Phi$ or
by a non-states-conserving pseudogap. This as well as the above
approximate expression for $\alpha$ in terms of
the density ratio $\langle N_d(\omega)\rangle/N_d(0)$ suggests
that the above curves for $\alpha$ are rather independent of the
specific features of our model ($d$-CDW with long-range order) but rather
generic for underdoped cuprates with a pseudogap.

Very remarkable in Fig. \ref{fig:3} is the fact that the tiny
value of 0.04 for the effective EP coupling $V/t$ is able to produce
large values for $\alpha$ comparable to those seen in experiment in the
underdoped region. The LDA yields $\lambda_d \sim 0.022$
in YBa$_2$Cu$_3$O$_7$, \cite{Heid} which
is roughly one order of magnitude smaller than
$\lambda_s$. \cite{Heid1,Cohen} (For a different view on the magnitude
of the EP coupling constants in cuprates, see Ref. \cite{Reznik}).
Using the LDA value
$N_d(0) = 1.108/eV$ from Ref. \cite{Heid}, the relation Eq.(\ref{lambdad})
and $t=0.5 eV$
we get in the LDA $V/t \sim 0.04$ which is the value used in our calculation.
This shows that the
large experimental values for $\alpha$ in the underdoped region
do not contradict, at least in our competing model, the
small LDA values for the EP coupling. The case of overdoped samples
is presently less clear because of conflicting experimental
results. \cite{Franck,Pringle}
An isotope coefficient $\alpha$ which is small throughout the overdoped
region \cite{Pringle} would
agree with our Fig. \ref{fig:3}.

\section{Extension to finite correlation lengths of the $d$-CDW}

In the previous sections our employed mean field treatment yielded a
$d$-CDW with
long-range order and excitations with infinite long lifetimes. Such
idealizations are
certainly not realized in the cuprates and one may wonder to what
degree our previous
results depend on them. Generally speaking we do not expect drastic
modifications because
the strong increase of $\alpha$ with decreasing doping was due to the
rearrangement of spectral
weight due to the $d$-CDW gap. This shift of spectral weight should not be
seriously affected
by fluctuations or  the loss of long-range order as long as the
correlation length is
sufficiently large.  In this section we will investigate this expectation on a
more quantitative
level. To this end we will employ a model\cite{Lee1,Bartosch,Kuchinskii}
which allows to
treat exactly a certain class of semiclassical fluctuations of the off-diagonal
order parameter.

First we consider only the $d$-CDW part of $g^{-1}$, i.e., the first and third
rows and columns of Eq.(\ref{matrix}) where we may put $Z=1$
considering again the weak-coupling case. Transforming the part induced by the
variation of the order parameter into $\bf r$-space we get,
\begin{eqnarray}
g_{CDW}^{-1}({\bf k}-i\nabla,i\omega_n) = \nonumber \\
\left(
\begin{array}{c c }
i\omega_n -\epsilon({\bf k}-i\nabla)  & -i\gamma({\bf k})\Phi_0 e^{i\beta}  \\
i\gamma({\bf k})\Phi_0 e^{-i\beta}   & i\omega_n -\epsilon({\bf \bar{k}}-i\nabla)
\end{array} \right),
\label{matrix1}
\end{eqnarray}
with $\beta = {\bf p}{\bf x} +\phi$ and ${\bf {\bar{k}}} = {\bf k}-{\bf Q}$.
${\bf p}$ is a random variable with cartesian components
distributed according to a Lorentzian. $\phi$ is a random phase which will not enter
our final expressions and thus its distribution function has not to be specified.
We apply now the unitary transformation
\begin{equation}
 U_1({\bf x}) = e^{i\beta \sigma_3 /2},
\label{U}
\end{equation}
to Eq.(\ref{matrix1}), where $\sigma_3$ is a Pauli matrix. After some algebra we find,
\begin{eqnarray}
\tilde{g}_{CDW}^{-1}\hspace{-0.3cm}&(&\hspace{-0.3cm}{\bf k}-i\nabla,i\omega_n) =
U^\dagger_1({\bf x}) g_{CDW}^{-1}({\bf k}-i\nabla,i\omega_n) U_1({\bf x}) \nonumber \\
&=&\left(
\begin{array}{c c }
i\omega_n -\epsilon({\bf k}) +\epsilon_1  & -i\gamma({\bf k})\Phi_0   \\
i\gamma({\bf k})\Phi_0    & i\omega_n -\epsilon({\bf \bar{k}}) +\epsilon_2
\end{array}
\right),\nonumber \\
\label{matrix2}
\end{eqnarray}
with the abbreviations $\epsilon_1 = {\bf v}({\bf k}){\bf p}/2 $ and
$\epsilon_2 = -{\bf v}({\bf {\bar{k}}}){\bf p}/2$. $v_{x,y}({\bf k})$ are given by
$\partial \epsilon({\bf k})/\partial {k_{x,y}}$. In deriving
Eq.(\ref{matrix2}) we also expanded  $\epsilon({\bf k}-i\nabla)$ up to first order
in $\nabla$ assuming that the changes in one-particle energies induced by the
variation of the order parameter vary slowly in space.
To simplify the following we will take
$\epsilon_1=\epsilon_2=\epsilon$ which holds exactly for the case $t'=0$.

The matrix in Eq.(\ref{matrix2}) can be diagonalized by a second unitary
transformation $U_2$
yielding,
\begin{eqnarray}
 U_2^\dagger({\bf k}) \tilde{g}_{CDW}^{-1}({\bf k},i\omega_n) U_2({\bf k}) = \nonumber \\
\left(
\begin{array}{c c }
i\omega_n -\lambda_1({\bf k}) +\epsilon  &     0   \\
        0                            & i\omega_n -\lambda_2({\bf k}) +\epsilon
\end{array}
\right),
\label{U2}
\end{eqnarray}
with the eigenvalues $\lambda_{1,2}({\bf k})$ of the unperturbed $d$-CDW,
given by
Eq.(\ref{Pole1}).
Taking also superconductivity into account we note that the Heisenberg
interaction is invariant under the gauge transformation $U_1$. Applying the
second unitary transformation $U_2$ to the Heisenberg interaction
and using the BCS factorization
the transformed matrix $g^{-1}$ splits into two 2x2 matrices and the
resulting gap equation can easily be calculated. Adding also phonons one
finds that Eqs.(\ref{Tc})-(\ref{F12}) still hold if the density
$N_d(\omega)$ of
Eq.(\ref{N}) is replaced by the expression,
\begin{equation}
\frac{\omega}{\pi N_c} \sum_{{\bf k},\beta} \gamma({\bf k})^2
\Im \frac{1}{(\omega-i\eta+\epsilon)^2-\lambda_\beta^2({\bf k})}.
\label{N2}
\end{equation}
Finally,
\begin{figure}
\vspace*{-0.2cm}
\includegraphics[angle=270,width=9.0cm]{fig4.eps}
\caption{\label{fig:4}
Weighted density of electronic states $\bar{N}_d(\omega)$ for two
dopings $\delta$ for a correlation length $\xi = 250$.
The inset shows $\bar{N}_d(0)$ at low dopings.
}
\end{figure}
Eqs.(\ref{Tc})-(\ref{F12}) have to be averaged over the distribution
function $P({\bf p})$,
\begin{equation}
P({\bf p}) = \frac{\kappa^2}{\pi^2(p_x^2 + \kappa^2)(p_y^2+\kappa^2)},
\end{equation}
where $\kappa = 1/\xi$ and $\xi$ is the correlation length of the off-diagonal
order parameter fluctuations. According to Eq.(\ref{matrix1}) $\Phi_0$
is the equilibrium $d$-CDW order parameter after omitting the factor
$\gamma({\bf k})$. It thus varies in $\bf r$-space with the momentum $\bf Q$
because it connects electron states with momenta $\bf k$ and $\bar{\bf k}$.
The random variable $\bf p$ modulates the equilibrium total momentum $\bf Q$
of the $d$-CDW in an additive way and it is distributed according to a
Lorentzian. It is sufficient to apply the necessary average over
$\bf p$ just to the expression of Eq.(\ref{N2}) yielding,
\begin{eqnarray}
\bar{N}_d(\omega) = \frac{\omega}{\pi N_c} \sum_{{\bf k},\beta} \gamma({\bf k})^2
\nonumber \\
\Im \frac{1}{(\omega-i/(2\xi)(|v_x({\bf k})|+|v_y({\bf k})|))^2 -\lambda_\beta^2({\bf k})}.
\label{N1}
\end{eqnarray}
It is easy to see that the above
expression can formally be obtained from $N_d(\omega)$ if one
replaces there
the infinitesimal $\eta$ by the finite, $\bf k$-dependent imaginary part
$ (|v_x({\bf k})|+|v_y({\bf k})|)/(2\xi)$. The latter quantity is in
Eq.(\ref{N1}) averaged over
the Fermi line in the pure $d$-CDW state, i.e., for $\beta =1$ over the arc
around the nodal line
and for $\beta = 2$ over the remaining small piece near the antinodal point
which however, vanishes
for our two considered dopings. Thus the $\beta = 2$ contribution in Eq.(\ref{N1}) is
negligible small. In the $\beta = 1$ contribution
$ (|v_x({\bf k})|+|v_y({\bf k})|)/(2\xi)$
varies only little along the arc so we may replace this quantity by its average over the
arc and obtain for $\delta = 0.085$ the value  $1.15 v_F/\xi$
where $v_F \sim 4.6t$ is
the square root of the Fermi surface average of ${\bf v}^2({\bf k})$ in
the normal state. This allows to describe phase
correlations with a finite correlation length $\xi$ as an inverse life time effect with
energy $\Gamma/t = 1.15 v_{F}/(t\xi)$.
\begin{figure}
\vspace*{-0.2cm}
\includegraphics[angle=270,width=9.0cm]{fig5.eps}
\caption{\label{fig:5}
Isotope coefficient $\alpha$ as a function of doping for
two phonon cutoffs $\omega_D$ calculated in the presence of
short-ranged correlated phase fluctuations with correlation length
$\xi = 250$.
}
\end{figure}

Fig. 4 shows $\bar{N}_d(\omega)$ for the two dopings of Fig. 2
and for the case of a correlation length $\xi = 250$, corresponding to an
inverse lifetime of about $0.02t$. Though such a large correlation length
may seem to simulate a rather well-ordered state most of the fine structures in
Fig. 2 are wiped out by phase fluctuations.  In particular, the two peaks
seen in Fig. 2
have merged into one broad and rather structureless peak. At low
frequencies the changes introduced by phase fluctuations are rather minor.
In the inset
in Fig. 4 the static value $\bar{N}_d(0)$ is plotted as a function of doping
showing the pronounced decrease of $\bar{N}_d(0)$ with decreasing $\delta$
similar as in the case without phase fluctuations in Fig. 2. This behavior
for the density is rather robust as function of $\xi$ as long as
$\xi \gg 1$ holds.

Fig. 5 shows the doping dependence of the isotope coefficient $\alpha$
using the same parameter
as in Fig. 3 but $\bar{N}_d(\omega)$ instead of $N_d(\omega)$.
Comparing Figs. 3 and 5 reveals
that this change of densities does hardly affects $\alpha$ so that
corresponding curves in these
two figures are practically identical. This demonstrates that
the steep increase of $\alpha$ with decreasing doping is not related or
even caused by
the sharp peaks present in $N_d(\omega)$ or by special values for the
phonon cutoff $\omega_D$.
Instead, it is a rather universal property caused by the large shift of
spectral weight towards higher frequency due to the pseudogap.
If the correlation length $\xi$ is decreased from large to small values of the
order of the lattice constant
the depletion in the density $\bar{N}_d(0)$ at
low energies becomes smaller and smaller. In accordance with the decreasing
shift of spectral weight from low to high energies the isotope coefficient
$\alpha$ also decreases approaching a similar small value as
in the absence of a pseudogap, i.e., in the overdoped region.

Fig. 5 can qualitatively be understood in a simple way considering our
previously approximate expression $\langle N_d(\omega)\rangle/{N_d(0)}$
for $\alpha$. The numerator
is essentially given by the area under the density curve in Figs. 2 and 4.
Its value thus
is independent of the shape of the  density curve, i.e., whether it has sharp or
broad  peaks, as long as the area below the curve is constant. This area
is practically
the same in Figs. 2 and 4.  On the other hand the $\omega =0$ values of
the densities
both decrease strongly
and in a similar way with decreasing $\delta$.  As a result $\alpha$
should be of similar
magnitude in both cases and, in particular, show a strong increase
towards low dopings
in agreement with Fig. 5. The above approximate expression for
$\alpha$ may also explain
why the calculated values for $\alpha$ of Ref. \cite{Jarrell} are for our
electron-phonon
coupling $V$ much smaller than ours: Their density of
state function at $\lambda_d = 0$,
plotted in their Fig. 4, is large at $\omega=0$ compared to the modulation
due to
the pseudogap which implies only a small redistribution of spectral weight
by the pseudogap.

\section{Conclusions}

We have shown that a mean-field treatment of the $t$-$J$ model which
identifies the pseudogap with the gap of a $d$-CDW state is able
to explain the large isotope effect in underdoped cuprates.
Interestingly,
a very small EP coupling constant $V/t \sim 0.04$ is sufficient
to explain the experimental data. This value is very close to that calculated
for YBa$_2$Cu$_3$O$_7$ within the LDA. This shows that the large values for
$\alpha$ of order 1 found in the underdoped region are, at least in our
competing model, compatible with the small EP coupling constants predicted
by the LDA.
The obtained huge increase of the isotope coefficient $\alpha$ with
decreasing doping is rather independent of the phonon cutoff frequency
$\omega_D$ and the spectral properties of the excitations in the pseudogap
state. The latter information is obtained by considering a simple phase
fluctuation model where the $d$-CDW state has only short-range correlations.

Most important for the large increase of $\alpha$ with decreasing doping
is in our calculation the large depletion of spectral weight at low frequencies
and its shift to high energies by the pseudogap. Because of this we conjecture
that our results are not specific to the employed $d$-CDW
providing the pseudogap but also
hold for other order parameters such as the antiferromagnet order parameter
as long as they lead to a strong depletion of spectral weight at low
frequencies.
Our calculation shows, in particular, that it is not necessary
to assume a large EP interaction in cuprates or extrinsic effects such as
pairbreaking due to impurities \cite{Tallon,Bill}
to explain the observed isotope effect of $T_c$.

The authors thank O. Gunnarsson for discussions and A.M. Ole\'s for a
critical reading of the manuscript.

redpajama_set_name: RedPajamaArXiv


On the night before Christmas, two strangers connected.
Was all it took for Christian to fall in love.
Was all it took for Eve to give in to her deepest desires.
But as fate would have it, they were destined to meet again.
Only this time, Christian's not going to let his Angel slip through his fingers.


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text:
Home / Celebrities / 10 Filthy Rich Stars Who Were Caught Stealing
10 Filthy Rich Stars Who Were Caught Stealing
By KK Angus, 2 January 2018
Hollywood's penchant for shoplifting and petty theft is not unknown. It doesn't matter how rich a celeb is, taking something that's not theirs is always a thrill to the stars, apparently. From youth icons Lindsay Lohan to Britney Spears, to prolific actors like Winona Ryder, they have all been charged with stealing. Now, you may ask why they need to shoplift or steal, when they earn millions. But nobody knows…
1Lindsay Lohan
Mean Girls star and your definite early 2000s crush Lindsay Lohan has had a troubled life. From addiction issues to abusive relationships to a shaky career, Lindsay has had it tough. But things went ugly in 2011 when she was accused of stealing a gold necklace worth $2,500 from a swanky California boutique.
Image Source: www.aol.com
Lindsay had the most hysterical response to these charges. The actor said that she was simply borrowing the jewellery, and would have returned it. Though many designer stores have a lending policy in lieu of deposits, the store Lindsay stole from had no such records claiming that the actor had ever requested for borrowing the item.
In 2009, during one of Lindsay's magazine photoshoots, £250,000 worth of Christian Dior jewellery went missing. Lohan was obviously the prime suspect after the magazine staff overheard Lindsay repeatedly asking if she could keep the Dior jewellery used in the shoot.
2Britney Spears
In 2007, one of the biggest pop stars of the century had a famously crazy year. Britney Spears had a number of public meltdowns, had hilarious gaffes on-stage, went through tumultuous personal problems, shaved off her head and had to go to multiple rehabs.
Image Source: www.usmagazine.com
It was during that year that Britney was seen stealing a lighter from a gas station. It is possible that the pop sensation was just doing it for fun. "I stole something. Oh, I'm bad," Britney was heard saying into the camera after she took the lighter. It was also reported that Britney stole a wig from a shop after the staff wouldn't let her try some underwear.
3Megan Fox
One of the hottest Hollywood actors also had a pretty rough childhood. Not only did her parents split up when she was very young, but she was also bullied a great deal in middle school. As a teenager, maybe as a way to vent out her angst, Megan started to grow a penchant for shoplifting and petty stealing.
Image Source: www.hawtcelebs.com
As a teen, Megan would steal candies and small goods from gas stations and small convenience shops. Although she did not face charges and escaped the law several times, she was once caught stealing a tube of lipgloss from Walmart. Upon being held, the Transformers star came clean about her crime and burst into tears. She is reportedly still banned from Walmart.
Britney Spears Amanda Bynes Lindsay Lohan Courtney Love Big Sean Stealing Shoplifting
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10 Hollywood Celebrities Who Had Their Smartphone Hacked
10 Amazing facts about the Tom and Nicole Relationship you never knew about
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The Top 10 Hottest Female Athletes as Never Seen Before
Remember Carmen From Spy Kids? Well This Is How She Looks Now and It's Amazing
Adam West, The First Man To Play Batman Dies at Age 88, Read Ten Interesting Facts about Him
10 Famous and Loved Actors Who Are Just Too Sick To Work in Films Anymore

redpajama_set_name: RedPajamaCommonCrawl


text:
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On the Border, Buying Clothes by the Pound at Ropa Usada Shops
McALLEN, Texas — A mountain of clothes swallowed half of Juani Lira's petite body, from the waist down. But the 67-year-old did not seem to mind. Ms. Lira closely inspected a pair of black shorts studded with rhinestones and tossed them behind her, unimpressed. Too flashy for her teenage granddaughter, […]
McALLEN, Texas — A mountain of clothes swallowed half of Juani Lira's petite body, from the waist down. But the 67-year-old did not seem to mind. Ms. Lira closely inspected a pair of black shorts studded with rhinestones and tossed them behind her, unimpressed. Too flashy for her teenage granddaughter, she murmured.
Ms. Lira then spotted a long-sleeved, pearl-colored blouse, still with a tag intact. Bingo. She looked around her, as if she were getting away with something, and tucked the blouse at the bottom of a duffle bag. At a price of 71 cents a pound, Ms. Lira was on her way to collecting a haul big enough to clothe most of her 13 grandchildren at Ludy's Ropa Usada in downtown McAllen.
The sight of people, mostly women, rummaging through large heaps of fabric inside sweltering warehouses is hardly unusual in the Rio Grande Valley.
While used clothing stores operate all over the country, in one of the nation's poorest regions, giant ropa usada stores — sort of thrift shops on steroids — have been part of the cultural and commercial landscape of border life for decades.
With the added economic dislocation caused by the coronavirus pandemic, the shops have become both places to shop and part of the social and economic mix of El Valle, as locals call the region. Shoppers can spend hours digging, literally, for bargains, and may score the occasional Aeropostale or Polo garment. Some of them resell choice items at flea markets.
An endless parade of trucks with deliveries from recycled-clothes suppliers drop loads from all over the country, including discarded items from big-box retailers. The clothing is then dumped on floors, some the size of basketball courts.
Whatever is not sold on the premises is piled into categories — winter wear, baby clothes, men's shirts, women's sweaters — and shipped in plastic containers and bales to bulk buyers around the world, as near as Mexico or as far away as Japan.
The businesses, which generally charge shoppers between 35 and 71 cents a pound for whatever they find, are hard to miss. Just past the International Bridge from Reynosa, Mexico, the imposing warehouses appear on the horizon, heralded by towering painted signs that seem to scream "ROPA USADA" at motorists and announce the sale of "Pacas," or bulk quantities. Despite their larger-than-life presence in the valley, though, the shops operate in relative obscurity.
Because many transactions are made in cash, a paper trail is often hard to come by, said Salvador Contreras, director of the Center for Border Economic Studies at the University of Texas Rio Grande Valley.
Still, their popularity is evident in a part of the country where multigenerational families often live under the same roof and need to stretch very modest resources. (The unemployment rate in the McAllen region recently soared to past 8 percent, nearly twice the rate in the rest of Texas).
During several visits to ropa usada warehouses, some of them just a mile from the Rio Grande, store operators were protective of their businesses and their clients' privacy. Signs prohibiting photos were often posted at the entrance, a reminder that the stigma of shopping for discarded clothes persists. Some people hid their faces in the piles of clothing, and some avoided eye contact.
But others, like the longtime ropa usada shopper Angelica Gallardo, 64, felt there was no shame in struggling to make ends meet and doing the best you could to clothe your growing clan. Ms. Gallardo spends hours at a time meticulously inspecting an endless heap of potential purchases. "You have to dig in!" she said.
Ms. Gallardo said it made no sense to spend $20 to $30 for a single item of clothing at a chain store like Wal-Mart or Target. "'Ta' muy caro" — it's too expensive — she said, gesturing with her hands. She does not have money to spare. Ms. Gallardo makes $9 an hour working part-time, cleaning offices in McAllen.
Ms. Gallardo, who said she has been shopping at ropa usada outlets since the 1970s, has developed a keen eye for "the good stuff" from the "pila" — the pile. "The items with holes, or the ones that look really used, stay here," she said.
Bright colors catch her eye. So do images of popular culture characters imprinted on clothing. On a day in late March, Ms. Gallardo sat on the cold concrete at the edge of the clutter and painstakingly picked up one item at time with her 11 grandchildren in mind, including one who is getting ready to celebrate a quinceañera.
She found a single sock with an image of a droid from "Star Wars." "My grandson would love this," she said. "Where's the other?"
She thrust her arm into the pile and shared a victorious smile. "Ahí 'ta'," here it is, she said when she found it.
She took a break from her search and scanned the room for a familiar face, but could only see random moving arms and the tops of bobbing heads amid the sea of cotton, polyester, denim, lace and leather.
But then her cheer caught the attention of Ms. Lira. Other women lifted their heads.
Ms. Gallardo unfolded a skirt that resembled a tablecloth decorated with roses.
"That's a great for the quinceañera," Ms. Lira offered, referring to Ms. Gallardo's granddaughter.
It only took seconds for Ms. Lira to find her own gems, a black bikini bottom and white top. Summer is around the corner, she said.
"I don't wear those!" Ms. Gallardo said. "I'm a grandma."
"I do, at the beach," Ms. Lira replied, hugging the garments. They both shared a laugh.
Ms. Gallardo paid $24 for around 30 pounds of clothes. Ms. Lira settled for eight pounds for about $6.
Not everyone who shops at ropa usada stores does so for economic reasons. On this day, a 29-year-old visitor from Austin, Christian French, said he shops there when visiting the border to do his part for the environment.
"There is so much waste in this world, you know?" he said, holding a stack of clothing for friends and family, including a plaid skirt, T-shirts and other items. "They have made enough clothes in this world to last us until the sun burns out. There is just so much here."
The owner of Ludy's, Umair Pariyani, said his business goes beyond providing locals with bargains. Mr. Pariyani pointed at more than 10 women and men who were sorting discarded items or returns from big-box stores into plastic containers or bales by category for export.
His task includes deciding what styles have a better chance of selling in which parts of the world. Miniskirts do well in Japan, he said. Conservative items that cover up most of the body fare well in places like Pakistan.
Over at Dos Imperios, a large warehouse with a clear view of a border fence, many customers are Mexican citizens planning to resell their wares back home.
During the height of the pandemic, most Mexicans were not permitted to travel to the United States. But when the Biden administration lifted travel restrictions for vaccinated foreigners late last year, many, like Carmen Martinez, 53, who lives in the city of Reynosa, Mexico, rediscovered a financial lifeline.
On this day Ms. Martinez found herself eyeing a forklift pushing a jumble of used clothing into a pile. Once the machine cleared the floor, Ms. Martinez and several others climbed on top of the pile, trying to get first dibs on the best items. She made out with a rug, a bedsheet, a blue tank-top and a pair of summer shorts.
At 35 cents a pound, she planned to spend about $40, and hoped for a net profit of maybe $10. "I sell them from my home," she said. "People want to buy American brands. Every dollar helps."
She gathered her pila and got ready for her long trek home. She said that the next day, she planned to do it all over again.
Pfizer Names David M. Denton Chief Financial Officer | Business & Finance
Mon Apr 11 , 2022
NEW YORK–(BUSINESS WIRE)–Apr 11, 2022– Pfizer Inc. (NYSE: PFE) today announced that David M. Denton will join the Company as Chief Financial Officer (CFO) and Executive Vice President effective May 2, 2022. Mr. Denton will be a member of Pfizer's Executive Leadership Team reporting to Chairman and Chief Executive Officer, […]
Trending Spring Fashion On Secondhand Shopping Sites
14 Amazon customers' most-loved fashion for summer
How to Save Money on the Latest Fashion Clothing Online Shopping
'Hi-tech', underwhelming: Amazon's IRL clothing store misses the point of shopping | Amazon
How to buy clothes without ruining the planet


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X SPEAKS is a performance-based social practice project conceived and led by artist Nsenga Knight. In February 2015, Knight invites members of the Black Muslim community to collectively perform or present Malcolm X's final speeches and reflect on his continuing pertinence on the 50th anniversary of his death. Everyone is invited to watch the live performances and participate in the following discussions here on YouTube and Twitter using #XSpeaks . X Speaks takes place on February 3rd, 4th, 8th, 11th, 14th, 15th, 16th and 18th @6pm EST and the speech dates follow Malcolm X's original 1965 lecture dates. Please check www.nsengaknight.com/xspeaks regularly for information and updates on this project.
#XSpeaks #BlackLivesMatter #LegacyX #BeingBlackAndMuslim
X is a mathematical symbol for the unknown. In the early part of the 20th century thousands of Black people began replacing their last names with an X to symbolize their identity as Muslims – Malcolm X being the most notable X in our history. The "X" in X Speaks represents Malcolm X and the X Speaks project collaborator. As X, he or she symbolizes a present or potential embodiment of Malcolm X's legacy and an activator for his speech. As a variable, X changes each day within the X Speaks project. Knight provides the speaking material to each X Speaks collaborator. This project is sponsored in part by Muslim Anti Racism Collaborative.
Malcolm X was an African-American Muslim minister and a human rights activist. In 1964, a year before his assassination, he went on a religious pilgrimage to Mecca and was forever changed, on February 15th 1965 stating, "While I was in Mecca among the Muslims, I had a chance to meditate and think and see things with a great deal of clarity — with much greater clarity than I've achieved from over here…" He had renounced the anti-white views that he preached as a minister in the Nation of Islam, stating in a February 14th 1965 speech given in Detroit, "The real religion of Islam doesn't teach anyone to judge another human being by the color of his skin." He promoted unity amongst all people, and an increased international outlook to solve the human rights violations against Blacks in America. Because his death occurred when he was on the brink of his evolved philosophical and spiritual orientation, his later philosophy is less known. He has been called one of the greatest and most influential African Americans in history and his legacy holds a special place in the hearts and imaginations of Black Muslims for whom he stands as a model for leadership, social change, and community engagement.
X Speaks collaborators embody Malcolm X's speech by activating it through performance in a disembodied digital form – the internet; bringing him into the present imaginations of diverse audiences via smartphones, tablets, laptops and desktop computers.


There were Surfboard prizes aplenty being given out at this year's Teen Choice Awards to the wild bevy of talented young musicians, actors and celebrities that America's teens love and voted for. One celeb who really shined was Demi Lovato, who won three awards and performed live.
The two-hour award show was stuff to the brim with live performances, guest presenters, and a riled-up, screaming crowd of teenage fans who couldn't get enough of the celebs they love.
The show kicked off with a performance by One Direction that could barely be heard over the deafening roar of the audience. Then, Glee's Darren Criss and Pretty Little Liars' Lucy Hale took over as hosts.
RELATED: One Directions Best Song Ever Music Video!
The show featured other performances by Paramore and Florida Georgia Line, as well as Demi Lovato, who performed her new single Made In The U.S.A.
Lovato also won several awards including Choice TV Personality for her work on The X Factor, along with Choice Female Artist and Choice Single by a Female Artist, for her song Heart Attack.
Notable moments included a tearful Lea Michelle dedicating her win to the late Cory Monteith and Ashton Kutcher being celebrated with the Ultimate Choice Award.


Kingsnake.com - Herpforum - RE: Experts, I need your medical advice.
RE: Experts, I need your medical advice.
Emysbreeder makes a good point here. In doing a complete evaluation you should (the vet) have checked the stool by doing a direct microscope slid inspection of the stool and a float for worms. In any case Flagyl (Metronidazole) is not a bad place to start as it is an appetite stimulant and he is right, as soon as they get stressed it is not unusual to see Protozoa.
What do the stools look like, If he is having any? I used Amakacin extensively at one time its not a big gut flora killer.
Basically you're all the way back to the beginning without the test results you have no idea what you're dealing with.
Not only that, if you do need to dose him with Flygel you will probably find he will not eat it, even in food so you have to tube him.
If you don't have experience Tubing a turtle or Tortoise you are getting in over your head.
Try to find someone competent to help you.


Great carpeting can make a big difference in a room. Carpeting has the ability to turn a home into a comfortable, relaxing place to live. In fact, new flooring can be a huge improvement in any home. That is why your Punta Gorda, Florida Carpet One carries a wide array of options in high-quality flooring. At Carpet One, we take pride in our ability to provide the very best selection of carpet, hardwood, ceramic tile, luxury vinyl, and laminate flooring.
Your Carpet One in Punta Gorda knows that choosing flooring that suits your home can be tricky. We are home to sales professionals who are specially trained with the expertise to pick the perfect flooring for you from our wide selection. Our sales professionals will work with you to choose the flooring material and style that's best for the conditions in your home. There is a variety of materials, warranties, and brands to select from, including many brands of flooring that are made exclusively for Carpet One. From stain resistance to odor protection, no need is ignored when it comes to our wide range of Punta Gorda flooring. Carpet One can supply you with affordable Punta Gorda flooring that is beautiful, comfortable, and held to the highest industry standards. Additionally, thanks to our multiple easy-to-understand levels of SelectAFloor™ warranty options, you can protect the quality of your Punta Gorda floors over time. What's more, Carpet One can help make the installation of your new carpet a breeze. Our installation professionals are experts in carpet installation, so you know it will be done right.
Want to know more about how to change your flooring? With selections of hardwood, laminate, vinyl, carpet, and ceramic tile flooring at great prices, Carpet One is here to help with whatever flooring changes you need. For additional information about the ways that Carpet One can improve your Punta Gorda home's flooring, contact your nearest Carpet One location. Call or come in to your Carpet One today to shop for the best in Punta Gorda carpeting and flooring!


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Cloudbank
Cloudbank Books 2022
Cloudbank 15
This issue includes new poems and flash fiction from Maya Janson, Mark Terrill, Fred Muratori, Gary Fincke, Nancy Keating, and many others, as well as reviews of No Day at the Beach by John Brehm and Long Voyage Gathering Light by John Kooistra.
To order this issue click here.
Issue introduction by Michael Malan
Le beau temps
For many, 2020 was The Year of the Pandemic. For others it was a year of peace, contemplation, and freedom from anxiety. As Charles Bukowski said, "It's not that I don't like people; it's just that I feel better when they aren't around."
For introspective writers and artists, 2020 was a banner year. No in-person parties, poetry readings, weddings, and funerals. No face-to-face uncomfortable social interactions. "No more teachers' dirty looks." Refugees from Facebook and other social media could spend their time reading, writing, and "counting flowers on the wall."
"Every cloud has a silver lining" or, as they might say in France, Après la pluie, le beau temps! What a blessing it's been to be in touch with so many people via Zoom and email. Over the years, Cloudbank has been assisted (and nourished) by bright young poetry students enrolled in Oregon State University's MFA in Poetry program. They stayed with us for a year and then, after graduation, they drifted away and we never heard from them again.
Now, thanks to Zoom, all that has changed. Every other week I meet online with former Cloudbank interns who live in North Dakota, Alaska, and Portland, Oregon, (as well as seasoned veteran poets here in Corvallis and Eugene). We share poems, offer helpful comments, and chat about the weather. You know, heaven on earth. And Linnea Nelson, Karah Kemmerly, and Ben Swimm, all OSU MFA graduates, are continuing to support the press as associate editors.
I'll mention three other people who have been instrumental in the growth and flourishing of Cloudbank. My co-editor Peter Sears, who started the press with me in 1999. We published several books, and then in 2008, I decided to start a journal. At first he was hesitant; he said he didn't want to read a lot of "unaccomplished" (or something like that) poetry. But when I told him I would go it alone, he was all in.
One fine day, Peter and I were eating lunch at the Valley Restaurant (now Evergreen Restaurant) and we made up a list of possible names for the press. He suggested Cloudbank. I liked it and we were off and running.
The first issue stumbled out of the starting gate. It didn't look as though we would have a enough good poetry and flash fiction to put together a quality journal. I held all the checks that people had sent with their submissions for several months so that I could easily refund their money if we decided not to launch the magazine.
And then we got a submission from Christopher Buckley. He was always drawn to cloud imagery, he said, and liked the title of our magazine. We accepted "In Memory of the Winos at the Moreton Bay Fig Tree, Santa Barbara CA" and "New Clouds," in which he wrote:
Here they are again, wadded across the length
of the washboard blue, napkins flung
from the afterlife. . . . How open to suggestion
they have always been, carrying nothing
with them of the past, content to leave almost
everything behind. . . .
I cashed the checks and Cloudbank 1 was published a few months later.
And then there was Dennis Schmitz. Back in the day, long before Peter and I started the press, I had enrolled in a poetry workshop with Dennis at Cal State Sacramento (then affectionately known as "Sac State"). Shortly after the workshop was concluded, I moved to New York, and Dennis and I corresponded a few times, then we lost touch.
Flash forward to 2010. While I was working on Cloudbank 3, I wrote Dennis and said, "You probably don't remember me but . . ." He wrote back and said, "Of course, I remember you. The picture comes in, but it's a bit fuzzy around the edges. I last heard from you when you were doing the Cornell workshops with [A.R.] Ammons and Robert Morgan. I'm glad that you're Westcoast and back to poetry. Cloudbank is a handsome magazine—I enjoyed the poems. Peter Sears I know from FIELD poems—good writer—say 'hello.'" Dennis submitted several poems—we accepted "Bad Dog!" for Cloudbank 3 and he judged the first two Vern Rutsala Book Prizes (2015 and 2016).
And now here we are in 2021 and the dark clouds of the pandemic are beginning to lift. Are we looking to a brighter future, "carrying nothing / . . . of the past, content to leave almost / everything behind. . . "?
PRIZE-WINNING POEM
Perchakucha Divided by Four by David James
Note: A Perchakucha presentation is a format that uses 20 slides or images that are displayed for 20 seconds each.
This day is made from hope, light, wind and a blue sky swirling around a few clouds traveling east. The cedars shake up and down, waving to me, so I wave back. I blow a kiss in their direction and they blush, not pink, but a lighter green. I love their smiles.
My four-year old grandson, Henry, is having a meltdown because he doesn't want to go home for dinner. His mother says, "Watch your attitude." His younger brother, Simon, announces, "I'm watching my attitude." Then this sweet boy looks up to me, straight-faced, and asks, "What's an attitude?"
It's hard to believe it was 65 degrees today, March 27. T-shirt weather for Michiganders. But snow is predicted for the weekend, shocking the hell out of the robins. I opened the windows to let spring in. We had some tea and biscuits and then she begged off, you know, buds to create, flowers to make.
Smoked two cigars today as I cut wood for shelves in the basement, stained the mailbox for the first time in twenty years. Finished a poem, revised another. Mahi-mahi for dinner with a baked potato. Sometimes I forget where I live and how blessed I am.
Half-moon up there, peeking behind wisps of clouds. A train barrels through town, on schedule, its horn echoing off stars. It's good to be in love after forty years, three kids, six grands, and three parents still walking the earth. This day goes down and, with luck, another will be born into my open arms.
Poets and writers in Cloudbank 15
R. A. Allen
Aaron Angello
Amy Bagwell
Laurie Blauner
Don Boes
John Brehm
Cory Brown
Claudia Buckholts
Rebecca Buller
Jim Daniels
Margaret Diehl
Diana Donovan
Deborah H. Doolittle
Jennifer Dorner
Jeff Ewing
Ken Fifer
Gary Fincke
Diane Frank
Alice Friman
John Harn
Alison Hicks
Maya Janson
Keith Jones
Nancy Keating
Kamal E. Kimball
John Kooistra
Gary Lark
Rebecca Lilly
Nina Lindsay
George Looney
Daniel Lusk
Richard Lyons
Katharyn Howd Machan
Linda Malnack
Fred Muratori
Allan Peterson
Anne Randolph
Mike Schneider
Bradley Samore
Marc J. Sheehan
Ben Swimm
Mark Terrill
J.P. White
Sharon White
Dan Wiencek
Bruce Willard
Paul Willis
← Long Voyage Gathering Light
Book of Years →


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Home » Entertainment » Lawsuit against him admitted: Prince Andrew fails in court
Lawsuit against him admitted: Prince Andrew fails in court
January 12, 2022 January 12, 2022 by Admin
Lawsuit against him admitted
Prince Andrew fails in court
Lawsuit against him admitted Prince Andrew fails in court
Agreement is of no use to Andrew
Virginia Giuffre accuses Prince Andrew of sexually abusing her when she was a minor. For a long time the prince hopes to get away with a black eye. Now, however, a judge rejects his lawyers 'motion to dismiss Giuffres' lawsuit.
If it were up to Prince Andrew and his lawyers, he would escape a civil lawsuit in the United States for the sexual abuse of Virginia Giuffre, who was then underage. This should ensure a deal between his alleged victim and the former puller Jeffrey Epstein. But now nothing will come of it. A New York judge has ruled to admit the lawsuit.
Giuffre accuses the British prince of abusing her in 2001 when she was only 17 years old. The meeting was arranged by Epstein, who was convicted and who died in prison in 2019 by suicide, or his ex-girlfriend, Ghislaine Maxwell, who is also now convicted. An accusation that Andrew has always dismissed. In an interview with the BBC in 2019, he said that he could not remember ever meeting Giuffre. And certainly he hadn't had sex with her, according to the Queen's second oldest son at the time.
His lawyers now argued that Giuffre agreed in court in 2009 not to sue anyone associated with Epstein when she settled her lawsuit for damages against the billionaire sex offender. During the virtual hearing, they said the Duke of York was a "potential defendant" within the meaning of the agreement, so the case should be "closed". Giuffre had forfeited her right to a lawsuit with the out-of-court settlement. The plaintiff's lawyer, however, found that only the parties to the settlement agreement could benefit from it themselves, but not a "third party".
Judge Lewis A. Kaplan saw it similarly. In his decision, he said the agreement of silence could not be used to serve the Duke of York. It had failed twice before trying to stop the lawsuit. For one thing, he had evaded service of the application for weeks by avoiding his residence on the grounds of Windsor Castle.
On the other hand, he tried to thwart the lawsuit by letting his lawyers argue that Giuffre, who now lives in Australia, could not go to court in the USA. With Judge Kaplan's decision, nothing stands in the way of the civil process.
It wasn't until late last year that Epstein's confidante, Ghislaine Maxwell, was found guilty of five out of six sex trafficking charges of minors. The prosecution accused her of having procured underage victims for Epstein's sex ring as the right hand man.
Demet Özdemir: the biggest flaw that the Turkish actress confessed before ending her relationship with Oğuzhan Koç
Sofia Cerveira updates fans about her daughter's health after the operation: "Another day of pampering…"


Reddy, D S S (2012) 3d Object Reconstruction from Multiple Views: A Compressive Sensing Framework. Masters thesis, Indian Institute of Technology Hyderabad.
Automatized life like representation of natural objects has been a cherished goal for humanity. Towards achieving this goal we propose a novel framework for the reconstruction of the 3D object. We laid the foundation for the representation of the signal by a developing a theory which deals with different sampling techniques(both Uniform and Non-uniform) for signals in the euclidean space, finite element method(Interpolative basis) for signals in the topological domain and finally the compressive sampling using which we can capture and represent the compressible signals by exploiting the sparsity.


text:
Immerse yourself in the stunning scenery of the Game of Thrones sets with a Game of Thrones Tour from Belfast.
Go from Winterfell to Storm's End
Experience the Game of Thrones' world of Westeros with a private tour around some of the spectacular locations used to film the popular show. Stand on the spot where the Lannisters schemed, and stroll in the footsteps of the Starks.
Iconic & Unforgettable
Visit Winterfell Castle and Ballycastle (the real home of both Conleth Hill (Lord Varys) and Michelle Fairley (Catelyn Stark)) and meet the real-life Dire Wolves. Go to Storm's End, The King's Road and Pyke Harbour and see for yourself why the makers of Game of Thrones chose Ireland for most of their sets.
Our suggested itinerary for your Game of Thrones Tour can be tailored to suit your needs. Whether you choose a private guided tour, or handpicked self-drive itinerary, we put together a unique trip, designed around your favourite Game of Thrones location sets, for the perfect private travel experience.
Belfast's iconic political murals paint a picture of the city's troubled past. A private tour will show you some of the most striking, and give you a flavour of this now-booming city. Visit the Titanic Experience to imagine life onboard and explore the shipyard where the infamous ship was built.
Antrim Coast
Visit Ballycastle, The King's Road and the beaches where Lady Melisandre burned the gods of Westeros, and Jaime and Bronn approached the gates of the Water Gardens. See the harbour that was transformed into the Iron Islands for Theon's homecoming, Storm's End and the turreted ruins of the House of Greyjoy.
Winterfell and Mourne Mountains
Practise your archery within the sprawling medieval walls of Winterfell Castle, used extensively as a set for the Game of Thrones' Stark family home. Take a private tour around the Mourne Mountains, including The River Quoile, where the Riverrun scenes were filmed, The Haunted Forest and locations sets for Vaes Dothrak.


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package pl.java.scalatech;

import lombok.Data;
import lombok.EqualsAndHashCode;
import lombok.NoArgsConstructor;

import org.joda.money.Money;

import pl.java.scalatech.entity.user.BaseUser;

/**
 * @author Sławomir Borowiec
 *         Module name : basicEntity
 *         Creating time : 27 lut 2014 15:19:35
 */
@Data
@EqualsAndHashCode(callSuper = true)
@NoArgsConstructor
public class ConcreteUser extends BaseUser {

    public ConcreteUser(ConcreteUserBuilder concreteUserBuilder) {
        super(concreteUserBuilder);
        this.salary = concreteUserBuilder.salary;
    }

    /**
         *
         */
    private static final long serialVersionUID = 1L;

    private Money salary ;

    public static class ConcreteUserBuilder extends UserBuilder<ConcreteUser> {

        public ConcreteUserBuilder(String firstName, String lastName, String login, String password) {
            super(firstName, lastName, login, password);
        }

        private static final long serialVersionUID = 3095189519520925314L;
        private Money salary;

        public ConcreteUserBuilder salary(Money salary) {
            this.salary = salary;
            return this;
        }

        @Override
        public ConcreteUser build() {
            return new ConcreteUser(this);
        }

    }

}

redpajama_set_name: RedPajamaGithub


This week a CBC Ontario Today broadcast featured an open lines show with Danah Boyd, author of It's Complicated: The Social Lives of Networked Teens.
This week, our Tuesday night live voice discussion will take a look at the parent perspective. We recommend that you take time to listen to the CBC podcast of When Keeping an Eye on Kids Becomes Spying prior to Tuesday night.
The session (June 3rd, 2014 at 8 p.m. EDT) will be hosted [here] to share your insights,ideas and ask questions. The meeting room will be open at 7:30. If you are joining us for the first time, allow a few minutes for the necessary plugins to download.
We look forward to connecting with you for sharing and discussion.
Modelling connected leading and learning is a critical element in our digital learning world. Connected learners need connected teachers and leaders. Try the OSSEMOOC experience where you can participate in connected leadership with a group which offers a supported approach.
Based on the positive feedback and interest in the 30 Days of Learning in Ontario collaborative blogging project, OSSEMOOC will be running another collaborative blogging project during the month of June. The theme will be "a picture and post" based on what catches your attention on social media. We would be delighted to include you on the OSSEMOOC blog.
Participating is: as easy as 1 2 3.
1. Watch for interesting education related posts on Twitter, Google Plus, Facebook and/or any other social media sites you read.
2. Screen capture the tweet or post, and write a short paragraph (even 2 or 3 sentences) explaining why the tweet or post resonated with you.
We look forward to connecting and leading with you as you share your learning.
Interacting with your personal learning network (PLN) means great learning opportunities every day. A case in point is represented in this tweet I read from @ScottMcKenzie27.
The approach Scott is taking with digital citizenship in his classroom really brings it to life through relationships, conversation, collaboration and a real world connected learning experience as evidenced through this screen capture of his tweet.
Of course, not all our learning comes from our online connections. We learn from our f2f co-workers as well, when we take the time to sit down (or go for a walk) and talk about our work.
I am very fortunate to work in a center that highly values the building of personal relationships and the informal sharing of our work and learning.
We take time each month to celebrate birthdays and eat a special lunch together. It amazes me how much learning and how many new projects arise after we take this time to share the work we are doing in our different branches.
Thank you so much to my colleague, Yvonne Morrison (EO, Aboriginal Education) for sharing her learning with me.
I hope you find this topic as fascinating and engaging as I did.
Have your say!!! On Monday May 26th (8:00 – 9:00 p.m. EDT), we will be providing an opportunity for you to learn more about the OSAPAC project on digital citizenship resources and provide feedback to the project team.
The online meeting room will be open at 7:30 p.m. EDT. If you are joining us for the first time, please allow a few extra minutes to allow for the necessary downloads (plugins).
During the last few weeks, we have focused on the topic of digital citizenship. The discussions and sharing of insights and personal experiences have been very rich.
Our professional learning sessions for the next two weeks will be special events.
On Tuesday May 20th, TEDxKitchenerED is presenting an event (7:30 – 9:30 p.m. EDT) centred around "the idea of Fostering Connectivity in the educational space can take on a variety of meanings. While its name leads many to the digital space, it simply means the state or capability of being connected. TEDxKitchenerED will look to highlight the many ways connectivity can be fostered in education." Check out the speaker list [here].
We hope you will join us for this "OSSEM" event. Watch for a special OSSEMOOC connection!
Mark your calendar: On Monday May 26th (8:00 – 9:00 p.m. EDT), we will be providing an opportunity for you to learn more about the OSAPAC project on digital citizenship resources and provide feedback to the project team. Additional details will be provided in a future blog post.
Our Tuesday discussion this week (May 13, 2014 at 8 p.m. EDT) will continue our look at the evolving and complex area of Digital Citizenship. Join our live voice conversation [here] to share your insights,ideas and ask questions. The meeting room will be open at 7:30.
Continue exploring the #digitalcitizenship and #digcit hashtags on Twitter as well as resources on the Scoop.it page here. The Digital Citizen, a weekly paper.li publication, may have resources of interest as well.
30 Days of Learning in Ontario: What Did We Learn Today?
As the 30 Days of Learning in Ontario OSSEMOOC project comes to a close, we want to thank, and congratulate, all of the educators who took the opportunity to share their learning. For some, it was their very first time posting their thinking in the blog format. We thank you for taking the time to let others learn from you. We hope that you will continue to share your learning and connect with others doing the same.
Thank you as well to everyone who took the time to comment on the blog. You shared your response and your feedback, and kept the thinking and conversations going.
One of our goals in OSSEMOOC is to have people connect and then create, to go off and learn and share, to sustain those connections and that learning. We were excited to see Deborah McCallum's efforts to collate the 30 Days of Learning in a new format.
Collaborative blogs give ownership to a group rather than an individual. As co-owners, we all anticipate the next learning. We are motivated to comment and continue the conversation as we are invested in this community of learners. Collaborative blogs encourage new thinking, invite new participants, expand our world and our learning. They give us a focus for reading and sharing.
We learn by watching others. We teach by modelling the practices we value. Collaborative blogging allows us to model the action of making thinking visible.
We all have a story to tell, and we learn from each other. Together we are stronger and wiser. Connected learning takes many forms: observing, reading, asking, reflecting, writing, speaking, audio, video and collaborating. Connected learning and leading is a participatory culture. It takes time, time to jump in, time to create new routines and time to build comfort. Courage is needed to put yourself "out there" and find your voice. It is worth the risk to gain insight, broader perspectives and recognize that "the smartest person in the room is the room".
In our technology enabled learning environments, connected students need connected teachers and leaders. As educators, I believe each of us owns nurturing those around us and role modelling. As pointed out in one of the blog posts, value encouragement and supporting each other with "just right" feedback is important for adult learners too.
Each of the 30 days of learning bloggers has taken the leap of faith, put themselves "out there" to share their reflections and ideas. Congratulations to all for openly participating in the collaborative learning process.
We often wonder why it is so hard to change thinking in education, to bring people into the world of connected learning. We learned from Tim's comment that perhaps focusing on the changing world, while validating the work that has been done, is a key component of making this change happen.
It's hard to hit publish. But opportunity can be fleeting. Don't be afraid to share.
Be more dog and grab the frisbee when it comes your way. Carpe diem!


Spanish house prices are going to continue falling for 2 years before turning up again, if the past is anything to go by (charts).
There are some fascinating charts in the Bank of Spain's latest monthly economic bulletin, published today. They illustrate the drama of the Spanish property crash, and give us a hypothesis of where house prices might go from here.
First of all, a couple of charts showing how the supply of new homes outstripped demand for most of the last decade (left-hand chart), leading to today's glut, which the bank estimates at somewhere between 700,000 and 1,200,000 homes (right-hand chart).
Now comes a map showing where the glut is concentrated, measured as a percentage of the local housing stock. The biggest glut is to be found in The Valencian Community, Murcia and Cantabria (all in blue), where the glut is over 6% of the housing stock. Andalucia is in the second group with a glut of 3.6pc of the housing stock.
Turning to house prices, the next chart on the left shows how official house prices have fallen back to where they were around 2005, which is not to say they won't fall further (in reality, official figures belie the true extent of the crash – prices have fallen significantly more than they suggest).
The chart on the right is the one I find most interesting. It compares the price evolution today to previous property slumps (1979 & 1991). In both previous cases prices fell for about 4&1/2 years before bottoming out. So if the past is anything to go buy, prices today will continue sliding for another 2 years, and could fall another 10pc if this turns out to be a repeat of 1979.
And finally, a map showing peak-to-present price falls by province, all according to official figures, of course. Biggest falls marked in blue, lowest falls in yellow. Most of the provinces where foreigners tend to buy holiday homes – the islands, Malaga, Almeria, Murcia, and Alicante – are in blue, with price falls above 15pc.
The biggest decline of all goes to Malaga, home of the Costa del Sol, down 20pc sine the peak.
Did the BoS actually suggest prices will fall for another two years, or is that your take on the numbers?
Its very significant is they did state that prices will fall. It will have the effect of pushing prices further south and the BoS wouldnt be ignorant of that effect. So should we take it that the BoS are trying to push down house prices?
I've changed the title from '….suggests BOS' to '….if the past is any guide'.
Your comment made me realise that the title could be misleading. The BOS said no such thing, it was my take on the numbers.
No problem, thanks for clarifying.
Great blog and that comparison to previous falls is remarkable.
However, after skimming the report via my admittedly very shaky Spanish I'm wondering how comparable this period is to earlier price drops. One chart in the report (not shown in your blog) seems to show that the investment in property only fell in real terms by about 10% in 1991-5, but this time has dropped off by 40% already and still falling.
Have I interpreted this correctly? If so, can we really expect this time round to have the same pattern moving forward?


After ten years of dentistry in the Seattle's Pike Place Public Market, I decided to seek my fortune and bought the Tugboat Winamac in 1988. After hauling the Winamac out on the hard--the planks fell off and I was more or less committed to a full hull restoration. Not being afraid of a hard day's work, I spent the next three years restoring the 1909 tug only to have it sunk on it's maiden voyage by Harken #6 in the Fraser River.
The 1933, 42 foot bridgedeck cruiser, "Betty B" was my second boat--a "temporary" boat to float about on while I searched for that perfect tugboat. The Tug Katahdin (ex Catherine Foss) was offered for sale in 1994 and was purchased that October. And then the work and lawsuits began...."


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