text:
\section{Introduction}

The inflationary paradigm is one of the most successful descriptions
of the early-time evolution of our Universe, in the context of
which, many shortcomings of the Big Bang cosmology are successfully
resolved \cite{inflation2,inflation3,inflation4,inflation5}. In a
recent study \cite{alpha1}, a new class of models was introduced and
these models are now known as $\alpha$-attractors models. These
models are based on a slow-rolling canonical scalar field with a
characteristic functional form of the inflationary potential. The
most appealing feature of this new class of cosmological models is
that the resulting spectral index of primordial curvature
perturbations and the scalar-to-tensor ratio is common to all the
models belonging to the general class of the $\alpha$-attractors
models, for large values of the $e$-foldings number $N$. Later
studies on these models
\cite{alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10,alpha10a,alpha11},
and also some earlier studies in the same context
\cite{slowrollsergei}, indicated that several well-known canonical
scalar field models like the Starobinsky model
\cite{starob1,starob2}, and the Higgs model \cite{higgs}, are
limiting cases of the $\alpha$-attractors models.  In addition, the
fact that the latest Planck data \cite{planck} indicate that the
latter two models are in concordance with the observational
constraints, render the $\alpha$-attractors models quite timely and
intriguing models. Intriguing because there seems to be a common
origin behind all the viable cosmological models of inflation. In
fact, all the $\alpha$-attractors models potentials have a large
plateau, for large values of the canonical scalar field, and all
these models are asymptotically quite similar to the hybrid
inflationary scenario \cite{hybrid}. Another important feature of
the $\alpha$-attractors models is that in many cases these are
supergravity originating, and in most cases supersymmetry breaking
occurs at the minimum of the potential \cite{susybr1}. Interestingly
enough, the late-time acceleration era can find a successful
explanation in the context of $\alpha$-attractors models
\cite{linderefs1,linder}. Also for an interesting approach with
regards to a renormalization group Higgs potential, see
\cite{vernov}.

In this paper we shall present another interesting class of potentials which may lead to the same observational indices with the $\alpha$-attractors. This means that this new class of models, to which we refer to as ``inverse symmetry attractor models'', belongs to the $\alpha$-attractors models, if certain requirements are met. The inverse symmetry attractor models have a symmetry property related to a deformation parameter $\beta$ which appears in the potential. Particularly, the potentials are invariant under the transformation $\beta \to \frac{1}{\beta}$ and this actually justifies the name ``inverse symmetry attractors''. Special cases of this class of models, were originally studied in the context of holographic models \cite{holo1,holo2}, and also see Ref. \cite{hologr} for a recent study. In this paper we are interested in some special cases of these inverse symmetry attractors, which have the interesting property of belonging to the $\alpha$-attractors models. We shall investigate in detail when this property occurs and also we thoroughly discuss all the different cosmological inflationary scenarios that these models imply. In all cases we shall calculate the slow-roll indices and the corresponding observational indices and we compare the results to the latest observational data. As we will show, not all the inverse symmetry models lead to results compatible with the observations. However, it is intriguing that the $\alpha$-attractors related inverse symmetry models are, in most cases, compatible with the observational data. Finally, for the latter models, we shall find the corresponding $F(R)$ gravity equivalent theory and we thoroughly investigate whether the attractor property remains in the Jordan frame too. Finally we study a non-minimally coupled scalar theory which is symmetric under the transformation $\beta \to \frac{1}{\beta}$, and as we show, the attractor behavior occurs in this case too.

This paper is organized as follows: In section II we present the essential features of inverse symmetric attractors and we investigate under which conditions these models can belong to the $\alpha$-attractors class of models. To this end we calculate and study the slow-roll indices and the corresponding observational indices in various limits, and we critically discuss the results. In section III we compare the inverse symmetry attractors to the $\alpha$-attractors and we discuss the qualitative differences of the two classes of models. Also we present another inverse symmetry model and we study its cosmological phenomenological implications. In section IV we study the $F(R)$ gravity corresponding theory of the inverse symmetry attractor model we studied in section II and we investigate whether the attractor property occurs in the Jordan frame too. In section V we study a non-minimally coupled scalar-tensor theory and we demonstrate that the attractor behavior occurs in this case too. Finally, the conclusions follow in the end of the paper.

\section{Essential Features of Inverse Symmetric Attractors and Slow-roll Inflation}

In the following we shall consider a canonical scalar field theory, with the gravitational action being of the form,
\begin{equation}\label{canonocclact}
\mathcal{S}=\sqrt{-g}\left(\frac{R}{2}-\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi -V(\varphi))\right)\, .
\end{equation}
The geometric background we shall use in this paper is a flat Friedmann-Robertson-Walker metric, with line element,
\be
\label{metricfrw} ds^2 = - dt^2 + a(t)^2 \sum_{i=1,2,3}
\left(dx^i\right)^2\, ,
\ee
where $a(t)$ denotes the scale factor. Also we assume that the connection is a metric compatible and torsion-less, symmetric   affine connection, the Levi-Civita connection. Finally we use a physical units system such that $\hbar=c=8\pi G=\kappa^2=1$.

The focus in this paper is on inflationary potentials that depend on a free parameter $\beta$ and have the symmetry $\beta\to \frac{1}{\beta}$. One particularly interesting potential is the following:
\begin{equation}\label{mainpot}
V(\varphi)=\frac{\mu
(\beta+\frac{1}{\beta})}{1-\beta^m}\left(1-\beta^m-2ne^{-\beta\sqrt{\frac{2}{3}}\varphi}+2n\beta^me^{-\frac{1}{\beta}\sqrt{\frac{2}{3}}\varphi}\right)\,
,
\end{equation}
and in the following we shall extensively study the inflationary features of this potential. Also we shall discuss the similarities of this potential with the inflationary attractors described in Refs. \cite{alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10}. The parameter $\mu$ in the potential (\ref{mainpot}) is an arbitrary mass scale, also $n$ is a freely chosen positive real number, while $\beta$ is a free parameter the values of which determine the behavior of the inflationary potential. Also the parameter $m$ is assumed to be a real positive number which satisfies $m\gg 1$. As it can be easily checked, the potential (\ref{mainpot}) is invariant under the transformation $\beta \to \frac{1}{\beta}$, and similar potentials were studied in Refs. \cite{holo1,holo2,hologr}. Actually, potentials with the symmetry $\beta \to \frac{1}{\beta}$ are related to holographic models, see Refs. \cite{holo1,holo2,hologr} and references therein. Let us now discuss the interesting features of the model (\ref{mainpot}), and firstly we discuss two limiting cases of the parameter $\beta$, namely the cases $\beta>1$ and $\beta<1$. Suppose that $\beta=\alpha$, and in the case $\beta=\alpha>1$, since $m\gg 1$, this implies that $\beta^m\gg 1$. In effect, for $\beta>1$ the potential becomes approximately equal to,
\begin{equation}\label{limit1}
V(\varphi)\simeq \mu \alpha \left(1-2ne^{-\frac{1}{\alpha}\sqrt{\frac{2}{3}}\varphi}\right)\, .
\end{equation}
This behavior is due to the fact that the term $e^{-\frac{1}{\alpha}\sqrt{\frac{3}{2}}\varphi}$ dominates over the term $e^{-\alpha\sqrt{\frac{3}{2}}\varphi}$, even for values of $\alpha$ a bit larger than one, for example $\alpha=4$ (we omit the physical units for simplicity). Notice that in this case $\alpha^m\gg 1$, so the limit we obtained is approximately correct. It would be helpful to see why the term $e^{-\frac{1}{\alpha}\sqrt{\frac{3}{2}}\varphi}$ dominates over $e^{-\alpha\sqrt{\frac{3}{2}}\varphi}$, for $\alpha>1$, so let us calculate these terms for $\alpha=11$ and for $\varphi=10^4$, where the canonical scalar field value should be chosen to be large, as it is expected during the inflationary phase, but the value we chose suffices to explain our argument. Then the aforementioned exponentials become,
\begin{equation}\label{expvalues}
e^{-\frac{1}{\alpha}\sqrt{\frac{2}{3}}\varphi}=5.8\times 10^{-11},\,\,\, e^{-\alpha\sqrt{\frac{2}{3}}\varphi}\simeq 2.5\times 10^{-3901}\, ,
\end{equation}
so this behavior clearly explains our argument. Now let us focus on the other limiting case, namely $\beta< 1$ which implies $\beta^m\ll 1$, so let us choose $\beta=\frac{1}{\alpha}$, with $\alpha$ satisfying $\alpha>1$, as in the previous case. In this case then, the potential becomes,
\begin{equation}\label{limit2}
V(\varphi)\simeq \mu \alpha \left(1-2ne^{-\frac{1}{\alpha}\sqrt{\frac{3}{2}}\varphi}\right)\, ,
\end{equation}
which is identical to the limiting case potential of Eq. (\ref{limit1}). Therefore, the two limiting cases, namely $\beta>1$ and $\beta <1$ yield the same potential, a result which to some extent was expected due to the symmetry $\beta\to \frac{1}{\beta}$. The result of the two limiting cases shows us that the limiting potential is identical to the attractor potentials of Refs. \cite{alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10}, however there are some fundamental differences, as we show later on. Before we discuss this issue, let us firstly calculate the slow-roll indices and the corresponding observational indices for the limiting potential (\ref{limit1}).

\subsection{Slow-roll Era and Inflationary Indices}

Depending on the values of the parameter $\alpha$, the slow-roll era for the potential (\ref{limit1}) can yield quite different resulting expressions for the slow-roll indices and the corresponding observational indices. The slow-roll indices for a canonical scalar theory are equal to,
\begin{equation}\label{slowrollscalar}
\epsilon (\varphi)=\frac{1}{2}\left( \frac{V'(\varphi)}{V(\varphi)}\right)^2,\,\,\,\eta (\varphi)=\frac{V''(\varphi)}{V(\varphi)}\, ,
\end{equation}
and also the $e$-foldings number $N$ can be given in terms of the potential, during the slow-roll regime, so the resulting expression is,
\begin{equation}\label{efoldings}
N\simeq \int_{\varphi_f}^{\varphi_{i}}\frac{V(\varphi)}{V'(\varphi)}\mathrm{d}\varphi \, ,
\end{equation}
where the initial value of the canonical scalar field is $\varphi_i$, which we assume to be the value of $\varphi$ at the horizon crossing, and $\varphi_f$ is the value of the scalar field at the end of the inflationary era. The inflationary era ends when the first slow-roll index $\epsilon$ becomes of order $\mathcal{O}(1)$, so the condition $\epsilon\simeq 1$ yields,
\begin{equation}\label{slowrollend}
e^{\sqrt{\frac{2}{3\alpha^2}}\varphi_f}=2n+\sqrt{\frac{3\alpha^2}{4n^2}}\, .
\end{equation}
By integrating (\ref{efoldings}), for the potential (\ref{limit1}) we get the following expression at leading order,
\begin{equation}\label{leadingn}
N=-e^{\sqrt{\frac{2}{3\alpha^2}}\varphi_f}+e^{\sqrt{\frac{2}{3\alpha^2}}\varphi_i}\, ,
\end{equation}
so by substituting (\ref{slowrollend}) in (\ref{leadingn}) we get,
\begin{equation}\label{noneofthethree}
e^{\sqrt{\frac{2}{3\alpha^2}}\varphi_i}=2n+\frac{4nN}{3\alpha^2}+\frac{\sqrt{3}\alpha}{2n}\, .
\end{equation}
The slow-roll indices calculated at the horizon crossing $\varphi=\varphi_i$ are equal to,
\begin{equation}\label{slowhorexp}
\epsilon=\frac{4 n^2}{3 \alpha ^2 \left(e^{\frac{\sqrt{\frac{2}{3}} \varphi_i }{\alpha }}-2 n\right)^2},\,\,\,\eta=-\frac{4 n}{3 \alpha ^2 \left(e^{\frac{\sqrt{\frac{2}{3}} \varphi_i }{\alpha }}-2 n\right)}\, ,
\end{equation}
so by substituting Eq. (\ref{noneofthethree}) in Eq. (\ref{slowhorexp}), we have,
\begin{equation}\label{oposprepei}
\epsilon\simeq \frac{4 n^2}{3 \alpha ^2 \left(\frac{\sqrt{3} \alpha }{2 n}+\frac{4 n N}{3 \alpha ^2}\right)^2},\,\,\, \eta \simeq -\frac{4 n}{3 \alpha ^2 \left(\frac{\sqrt{3} \alpha }{2 n}+\frac{4 n N}{3 \alpha ^2}\right)}\, .
\end{equation}
We can easily calculate the observational indices of inflation, and particularly the spectral index of primordial curvature perturbations $n_s$ and the scalar-to-tensor ratio $r$, evaluated at the horizon crossing. The analytic expressions of $n_s$ and $r$ in terms of the slow-roll indices are given below,
\begin{equation}\label{spectscalindex}
n_s\simeq 1-6\epsilon+2\eta,\,\,\, r\simeq 16 \epsilon\, ,
\end{equation}
so by substituting (\ref{oposprepei}) in (\ref{spectscalindex}) we have,
\begin{equation}\label{generalobservindices}
n_s\simeq -\frac{8 n^2}{\alpha ^2 \left(\frac{\sqrt{3} \alpha }{2 n}+\frac{4 n N}{3 \alpha ^2}\right)^2}-\frac{8 n}{3 \alpha ^2 \left(\frac{\sqrt{3} \alpha }{2 n}+\frac{4 n N}{3 \alpha ^2}\right)}+1,\,\,\,r\simeq \frac{64 n^2}{3 \alpha ^2 \left(\frac{\sqrt{3} \alpha }{2 n}+\frac{4 n N}{3 \alpha ^2}\right)^2}\, .
\end{equation}
At this point, the resulting behavior of the inflationary observational indices strongly depends on whether $\alpha^2 >N$ or $\alpha^2<N$ and also on the values of $n$. We assume that $N\sim 50$ and also that $n>1$, so the case $\alpha^2>N$ can be realized for $\alpha>8$, in which case the observational indices are approximately equal to,
\begin{equation}\label{observindi}
n_s\simeq -\frac{32 n^4}{3 \alpha ^4}-\frac{16 n^2}{3 \sqrt{3} \alpha ^3}+1,\,\,\, r\simeq \frac{256 n^4}{9 \alpha ^4}\, .
\end{equation}
By choosing for example $(\alpha,n)=(35,8)$, the observational indices are,
\begin{equation}\label{observex1}
n_s\simeq 0.966289,\,\,\ r\simeq 0.0776399\, .
\end{equation}
The latest Planck data \cite{planck} indicate that the spectral index and the scalar-to-tensor ratio are constrained as follows,
\begin{equation}\label{observex1placj}
n_s\simeq 0.966,\,\,\ r< 0.10\, ,
\end{equation}
so the results (\ref{observex1}) are compatible with the Planck constraints (\ref{observex1placj}).

Let us now turn our focus on the case $N>\alpha^2$, and for $N=60$, the parameter $\alpha$ should be chosen to take values in the interval $(1,7)$. In this case, the observational indices of Eq. (\ref{generalobservindices}) are approximately equal to,
\begin{equation}\label{newfnsecondcase}
n_s\simeq 1-\frac{2}{N}-\frac{9 \alpha ^2}{2 N^2},\,\,\,r\simeq \frac{12 \alpha ^2}{N^2}\, .
\end{equation}
We need to note the functional resemblance of the resulting observational indices (\ref{newfnsecondcase}) to the results of the attractors of Refs. \cite{alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10}. We shall discuss this issue in detail in the next section. The observational indices (\ref{newfnsecondcase}) can be compatible with the Planck results (\ref{observex1placj}), for example by choosing $(\alpha,N)=(4.1,60)$, we have,
\begin{equation}\label{observefinalres}
n_s\simeq 0.966667,\,\,\ r\simeq 0.0533\, ,
\end{equation}
which are in good agreement with (\ref{observex1placj}). It is important to note that the values $(\alpha,N)=(4.1,60)$ are not the only ones for which compatibility with the observational data can be achieved. For example by choosing $(\alpha,N)=(1.1,55)$, the observational indices take the following values,
\begin{equation}\label{observefinalresqww}
n_s\simeq 0.963636,\,\,\ r\simeq 0.0048\, ,
\end{equation}
which are in good agreement with the Planck data.

\subsection{Comparison with the Ordinary $\alpha$-attractors}

Let us now compare the results we obtained in the previous section, with the results of the attractor models of Refs. \cite{alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10}. We consider two types of models, namely the T-models and the E-models, with the first models having the following potential,
\begin{equation}\label{tmodels}
V(\varphi)=\alpha \mu \tanh^2 (\frac{\varphi}{\sqrt{6\alpha}})\, ,
\end{equation}
where $\mu$ is a positive mass scale. In addition, the E-models have the following potential,
\begin{equation}\label{potentialemodels}
V(\varphi )=\alpha \mu^2 \left( 1-e^{-\sqrt{\frac{2}{3\alpha}}\varphi}\right)^{2 n}\, ,
\end{equation}
with the parameter $n$ being a positive number. In the case of the E-models, the potential in the small $\alpha$ limit reads,
\begin{equation}\label{smallalphaemodelpot}
V(\varphi )\simeq \alpha \mu^2 \left(1- 2 n e^{-\sqrt{\frac{2}{3\alpha}}\varphi}\right)\, ,
\end{equation}
and it can be checked that the small-$\alpha$ limit of the T-models is a subcase of the potential (\ref{smallalphaemodelpot}). By calculating the observational indices for the limiting potential (\ref{smallalphaemodelpot}), always in the small-$\alpha$ limit, we obtain at leading order,
\begin{equation}\label{observslowroli1}
n_s\simeq 1-\frac{2}{N}-\frac{9\alpha}{2N^2},\,\,\,r\simeq \frac{12\alpha}{N^2}\, .
\end{equation}
By comparing the results of Eqs. (\ref{newfnsecondcase}) and (\ref{observslowroli1}), we can see that these are identical. However, the difference is that the observational indices of Eq. (\ref{newfnsecondcase}) are obtained for the parameter $\alpha$ satisfying $\alpha>1$, while the ones of Eq. (\ref{observslowroli1}) are obtained for $\alpha\ll 1$. This is the main difference between the inverse symmetric attractors and the ordinary attractors of Refs. \cite{alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10}. Another difference is that in the case of the ordinary attractors, for $\alpha=n=1$, the potential (\ref{potentialemodels}) becomes,
\begin{equation}\label{starobmodel}
V(\varphi )=\alpha \mu^2 \left( 1-e^{-\sqrt{\frac{2}{3}}\varphi}\right)^{2}\, ,
\end{equation}
which is the potential of the Starobinsky model \cite{starob1}. In the case of the inverse symmetric attractors, the limit $\beta=1$ cannot be taken, since divergences occur. In the next section we shall discuss this issue in some detail.

\section{Relation of Inverse Symmetric Potentials with the Exponential $R^2$ Model and Other Models}

Unlike the ordinary attractor models of Refs. \cite{alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10}, the inverse symmetric potential of Eq. (\ref{mainpot}) cannot yield, at first sight at least, the Starobinsky model \cite{starob1,starob2}, since the limit $\beta \to 1$ makes the potential (\ref{mainpot}) singular. In this section we shall study the behavior of the potential (\ref{mainpot}), in the limit $\beta \to 1$. To this end we assume that $\beta=1+\varepsilon$, with the parameter $\varepsilon$ being an infinitely small number $\varepsilon \ll 1$. So in order to find the behavior of the potential near $\beta=1$, we will substitute $\beta=1+\varepsilon$ in the potential (\ref{mainpot}) and we expand in powers of $\varepsilon$ for $\varepsilon\to 0$. By doing so we obtain the following expansion,
\begin{align}\label{asxetonbod}
& V(\varphi)\simeq 2 \mu -\frac{8 \sqrt{\frac{2}{3}} \mu  n e^{-\sqrt{\frac{2}{3}} \varphi } \varphi }{m}-4 \mu  n e^{-\sqrt{\frac{2}{3}} \varphi }\\ \notag &
+\frac{\varepsilon ^2 \mu  e^{-\sqrt{\frac{2}{3}} \varphi } \left(-6 \sqrt{6} m^2 n \varphi -36 m n \varphi ^2+18 \sqrt{6} m n \varphi -54 m n+27 m e^{\sqrt{\frac{2}{3}} \varphi }-8 \sqrt{6} n \varphi ^3+72 n \varphi ^2-48 \sqrt{6} n \varphi \right)}{27 m}\, ,
\end{align}
where we omitted higher order terms in $\varepsilon$, since these are subdominant in the limit $\varepsilon\to 0$. By keeping the leading order term, the potential is,
\begin{align}\label{asxetonbod1}
V(\varphi)\simeq 2 \mu -\frac{8 \sqrt{\frac{2}{3}} \mu  n e^{-\sqrt{\frac{2}{3}} \varphi } \varphi }{m}-4 \mu  n e^{-\sqrt{\frac{2}{3}} \varphi }\, ,
\end{align}
and since $m\gg 1$, the last term can be omitted. Hence, in the limit $\varepsilon\to 0$, the potential can be approximated as follows,
\begin{equation}\label{seriespot}
 V(\varphi) \simeq 2 \mu  \left(1-2 n e^{-\sqrt{\frac{2}{3}} \varphi }\right)\, .
\end{equation}
The resulting approximate form of the potential (\ref{seriespot}), functionally looks like the Starobinsky model in the limit $\varphi \to \infty$, however it is different due to the factor ``$2$''. Hence, the functional behavior of the potential (\ref{mainpot}) in the limit $\beta \to 1$, looks like the Starobinsky model functionally, but it is not the same. This behavior of the inverse symmetry potential (\ref{mainpot}) can be regarded as another difference between the ordinary attractors and the inverse symmetry attractor potentials.

A similar model to the one appearing in Eq. (\ref{mainpot}) is the following canonical scalar field model, with its potential being,
\begin{equation}\label{alternpot}
V(\varphi)=\frac{2\mu}{3(1-\beta^m)}\left( e^{-\beta \sqrt{\frac{2}{3}}\varphi}-\beta^m e^{-\sqrt{\frac{2}{3}}\frac{1}{\beta}\varphi}\right)\, ,
\end{equation}
where $m\gg 1$ and the parameters $\mu$ and $\beta$ being chosen as the ones of the model (\ref{mainpot}). The model (\ref{alternpot}) is almost identical to the holographic-inspired model of Ref. \cite{hologr}, so in this section we shall investigate the phenomenological implications of this model. The model (\ref{alternpot}) is symmetric under the transformation $\beta\to \frac{1}{\beta}$, and in the case $\beta>1$, and by assuming that $\beta=\alpha$, with $\alpha>1$, the potential can be approximated as,
\begin{equation}\label{approx1}
V(\varphi)\simeq \frac{2\mu}{3}e^{-\frac{1}{\alpha}\sqrt{\frac{2}{3}}\varphi}\, ,
\end{equation}
and in the case $\beta<1$, where in this time $\beta=\frac{1}{\alpha}$, the potential is again approximated by the expression in Eq. (\ref{approx1}). So the two different limits of the parameter $\beta$ yield the same resulting limiting potential, and this is due to the fact that the potential is symmetric under $\beta\to \frac{1}{\beta}$. Let us now calculate the slow-roll indices for this limiting potential and also the corresponding observational indices. The slow-roll indices for the limiting potential (\ref{approx1}) have a particularly simple form,
\begin{equation}\label{symmetr}
\epsilon \simeq \frac{1}{3 \alpha ^2},\,\,\,\eta\simeq \frac{2}{3 \alpha ^2}\, ,
\end{equation}
and the corresponding observational indices are,
\begin{equation}\label{observfin}
n_s\simeq 1-\frac{2}{3 \alpha ^2},\,\,\, r\simeq \frac{16}{3 \alpha ^2}\, .
\end{equation}
It is obvious that the case at hand is much more constrained in comparison to the model (\ref{mainpot}), since the resulting observational indices depend solely on one parameter $\alpha$. For $\alpha=4.5$ the spectral index $n_s$ and the scalar-to-tensor ratio read,
\begin{equation}\label{spectral}
n_s\simeq 0.963944,\,\,\,r\simeq 0.288444\, ,
\end{equation}
so in this case it is not possible to obtain compatibility with the Planck data. However, for $\alpha\gg 1$, one obtains an exactly scale invariant spectrum with an extremely small scalar-to-tensor ratio. In Table \ref{table1} we have gathered the results for the models (\ref{mainpot}) and (\ref{alternpot}).
\begin{table*}[h]
\small
\caption{\label{table1}Two Inverse Symmetric Canonical Scalar Field Models and Their Phenomenology}
\begin{tabular}{@{}crrrrrrrrrrr@{}}
\tableline
\tableline
\tableline
Canonical Scalar Field Potential  & Limiting Potential for $\beta>1$ and $\beta<1$ & Observational Indices
\\\tableline
 $V(\varphi)=\frac{\mu (\beta+\frac{1}{\beta})}{1-\beta^m}\left(\beta^m-1-2ne^{-\beta\sqrt{\frac{2}{3}}\varphi}+2n\beta^me^{-\frac{1}{\beta}\sqrt{\frac{2}{3}}\varphi}\right)$ & $V(\varphi)\simeq \mu \alpha \left(1-2ne^{-\frac{1}{\alpha}\sqrt{\frac{3}{2}}\varphi}\right)\,\,\,\,\,\,$ & $n_s\simeq 1-\frac{2}{N}-\frac{9 \alpha ^2}{2 N^2},\,\,\,r\simeq \frac{12 \alpha ^2}{N^2}$
\\\tableline
$V(\varphi)=\frac{2\mu}{3(1-\beta^m)}\left( e^{-\beta \sqrt{\frac{2}{3}}\varphi}-\beta^m e^{-\sqrt{\frac{2}{3}}\frac{1}{\beta}\varphi}\right)$  & $V(\varphi)\simeq \frac{2\mu}{3}e^{-\frac{1}{\alpha}\sqrt{\frac{2}{3}}\varphi}$ & $n_s\simeq 1-\frac{2}{3 \alpha ^2},\,\,\, r\simeq \frac{16}{3 \alpha ^2}$
\\\tableline
\tableline
\tableline
 \end{tabular}
\end{table*}
As a conclusion, we can firmly say that not all the inverse symmetric models result to an attractor behavior, but it is certain that the models which in some limit are equal to the potential of Eq. (\ref{limit1}), then it is possible that these lead to the attractor observational indices (\ref{newfnsecondcase}).

\section{The $F(R)$ Gravity Description of Symmetric Attractors}

Having described the Einstein frame picture, let us now investigate the $F(R)$ gravity \cite{reviews1,reviews3,reviews4} equivalent theory corresponding to the potential (\ref{limit1}). Before going to the details of the calculation, let us recall in brief some essential features of the Einstein-Jordan frame correspondence, for details we refer to Refs. \cite{reviews1,slowrollsergei,sergeioikonomou1,sergeioikonomou2,sergeioikonomou4} and references therein. We consider the following $F(R)$ gravity action,
\begin{equation}\label{pure}
\mathcal{S}=\frac{1}{2}\int\mathrm{d}^4x \sqrt{-\hat{g}}F(R)\, ,
\end{equation}
with $\hat{g}_{\mu \nu}$ being the metric tensor in the Jordan frame. By introducing the auxiliary scalar field $A$ in the gravitational action (\ref{pure}), the action can be written as follows,
\begin{equation}\label{action1dse111}
\mathcal{S}=\frac{1}{2}\int \mathrm{d}^4x\sqrt{-\hat{g}}\left ( F'(A)(R-A)+F(A) \right )\, .
\end{equation}
Varying Eq. (\ref{action1dse111}) with respect to the auxiliary field $A$, we obtain the solution $A=R$, so in effect, the actions (\ref{action1dse111}) and (\ref{pure}) are mathematically equivalent. Then, in order to connect the Jordan to the Einstein frame, we perform the following canonical transformation,
\begin{equation}\label{can}
\varphi =\sqrt{\frac{3}{2}}\ln (F'(A))
\end{equation}
where $\varphi$ is the canonical scalar field in the Einstein frame. By making the following conformal transformation in the Jordan frame metric $\hat{g}_{\mu \nu }$,
\begin{equation}\label{conftransmetr}
g_{\mu \nu}=e^{-\varphi }\hat{g}_{\mu \nu }
\end{equation}
we can obtain the Einstein frame canonical scalar field action,
\begin{align}\label{einsteinframeaction}
& \mathcal{\tilde{S}}=\int \mathrm{d}^4x\sqrt{-g}\left ( R-\frac{1}{2}\left (\frac{F''(A)}{F'(A)}\right )^2g^{\mu \nu }\partial_{\mu }A\partial_{\nu }A -\left ( \frac{A}{F'(A)}-\frac{F(A)}{F'(A)^2}\right ) \right ) \\ \notag &
= \int \mathrm{d}^4x\sqrt{-g}\left ( R-\frac{1}{2}g^{\mu \nu }\partial_{\mu }\varphi\partial_{\nu }\varphi -V(\varphi )\right )
\end{align}
The detailed form of the canonical scalar field potential $V(\varphi)$ is equal to,
\begin{align}\label{potentialvsigma}
V(\varphi )=\frac{1}{2}\left(\frac{A}{F'(A)}-\frac{F(A)}{F'(A)^2}\right)=\frac{1}{2}\left ( e^{-\sqrt{2/3}\varphi }R\left (e^{\sqrt{2/3}\varphi} \right )- e^{-2\sqrt{2/3}\varphi }F\left [ R\left (e^{\sqrt{2/3}\varphi} \right ) \right ]\right )\, .
\end{align}
Then it is easy to find the $F(R)$ gravity which corresponds to the potential (\ref{potentialvsigma}), and this can be done by combining Eqs. (\ref{potentialvsigma}) and (\ref{can}). So by taking the derivative of Eq. (\ref{potentialvsigma}), with respect to the Ricci scalar, we obtain the following differential equation,
\begin{equation}\label{solvequation}
RF_R=2\sqrt{\frac{3}{2}}\frac{\mathrm{d}}{\mathrm{d}\varphi}\left(\frac{V(\varphi)}{e^{-2\left(\sqrt{2/3}\right)\varphi}}\right)
\end{equation}
with $F_R=\frac{\mathrm{d}F(R)}{\mathrm{d}R}$. By solving this with respect to $F_R$, yields the resulting $F(R)$ gravity which generates the potential $V(\varphi)$. By substituting the potential (\ref{limit1}) in Eq. (\ref{solvequation}), we obtain the following algebraic equation,
\begin{equation}\label{algegeneralalpha}
F_R =\frac{R}{4\alpha \mu}-F_R^{1-\frac{1}{\alpha}}(\frac{n}{\alpha}+2n)\, .
\end{equation}
This algebraic equation can be solved at leading order with respect to the Ricci scalar, and the parameter $\alpha$ plays a crucial role. Since $F_R\gg 1$ during the slow-roll inflationary era (this can be seen by looking at the canonical transformation (\ref{can})), we can see that since $\alpha>1$, the the exponent of the second term in the right hand side of Eq. (\ref{algegeneralalpha}), satisfies the following inequality $1-\frac{1}{\alpha}<1$. In effect, the second term in Eq. (\ref{algegeneralalpha}) is subleading, hence at leading order $F_R\simeq \frac{R}{4\alpha \mu}$. By substituting this in Eq. (\ref{algegeneralalpha}), we obtain that,
\begin{equation}\label{fr}
F(R)\simeq \frac{R^2}{8\alpha \mu}-\frac{\frac{n}{\alpha}+2n}{(2-\frac{1}{\alpha})(8\alpha \mu)^{}}R^{2-\frac{1}{\alpha}}+\Lambda\, ,
\end{equation}
where $\Lambda$ is an integration constant. In the following we shall assume that the $F(R)$ gravity at leading order is,
\begin{equation}\label{fror}
F(R)\simeq \frac{R^2}{8\alpha \mu}\, .
\end{equation}
Having the approximate expression for the $F(R)$ gravity, we can calculate the approximate expression for the Hubble rate in the slow-roll regime and eventually we can compute the observational indices. The equations of motion corresponding to the action  (\ref{pure}), for the FRW metric (\ref{metricfrw}), are equal to,
\begin{align}\label{cosmoeqns}
& 6F_RH^2=F_RR-F-6H\dot{F}_R ,\\ \notag &
-2\dot{H}F_R=\ddot{F}_R-H\dot{F}_R\, ,
\end{align}
Using the first differential equation in Eq. (\ref{cosmoeqns}), and by differentiating with respect to the cosmic time, we obtain the following differential equation,
\begin{equation}\label{oneofthefinals}
\frac{9 \gamma ^2 H(t) H^{(3)}(t)}{\mu }+\frac{27 \gamma ^2 H(t)^2 H''(t)}{\mu }+\frac{54 \gamma ^2 H(t) H'(t)^2}{\mu }=0\, ,
\end{equation}
and therefore by dividing with $H(t)^2$, we obtain,
\begin{equation}\label{enyaex}
\frac{9 \gamma ^2 H^{(3)}(t)}{\mu  H(t)}+\frac{27 \gamma ^2 H''(t)}{\mu }+\frac{54 \gamma ^2 H'(t)^2}{\mu  H(t)}=0\, .
\end{equation}
During the slow-roll era, the only dominant term in the above differential equation is the second one, so by solving the resulting equation we obtain the Hubble rate during the slow-roll era, which reads,
\begin{equation}\label{quasidesitter}
H(t)=H_0-H_i (t-t_k)\, ,
\end{equation}
which is a quasi-de Sitter evolution, as it was probably expected. Notice that $H_0$, $H_i$ in Eq. (\ref{quasidesitter}) are arbitrary integration constants, and $t_k$ is the time instance that the horizon crossing occurs during the inflationary era. Having the Hubble rate at hand, we can easily calculate the slow-roll indices, which in terms of the Hubble rate for a general $F(R)$ gravity are equal to \cite{noh},
\begin{equation}\label{slowrollparameters}
\epsilon_1=-\frac{\dot{H}}{H^2},\,\,\,\epsilon_2=0,\,\,\,\epsilon_3=\simeq \epsilon_1,\,\,\,\epsilon_4\simeq -3\epsilon_1+\frac{\dot{\epsilon}_1}{H(t)\epsilon_1}\, .
\end{equation}
In addition, the spectral index $n_s$ and the scalar-to-tensor ratio $r$ read,
\begin{equation}\label{nsdf}
n_s\simeq 1-6\epsilon_1-2\epsilon_4\simeq 1-\frac{2\dot{\epsilon}_1}{H(t)\epsilon_1},\,\,\,r=48\epsilon_1^2\, .
\end{equation}
Then by following the same description as in Ref. \cite{attractorsI}, we obtain the leading order $N$ observational indices, which are,
\begin{equation}\label{jordanframeattract}
n_s\simeq 1-\frac{2}{N},\,\,\,r\simeq \frac{12}{N^2}\, .
\end{equation}
The resulting picture is identical to the one obtained for the ordinary $R+\gamma R^2$ model at leading order. We need to note that the resulting observational indices are independent of $\alpha$.

\section{Non-minimal Coupling Description}

The approach we adopted for the Einstein frame theory can be extended in the case of a non-minimally coupled theory, in which case the gravitational action reads,
\begin{equation}\label{graviactionnonminimal}
\mathcal{S}=\int \mathrm{d}^4x\sqrt{-g}\left( \frac{f(\phi)R}{2\kappa^2}-\frac{1}{2}g^{\mu \nu}\partial_{\mu}\phi\partial_{\nu}\phi-V(\phi) \right)\, ,
\end{equation}
where the function $f(\phi)$ will be chosen to be symmetric under the transformation $\beta\to \frac{1}{\beta}$. The gravitational equations of motion for the action (\ref{graviactionnonminimal}), for a FRW metric, are equal to,
\begin{align}\label{gravieqnsnonminimal}
& \frac{3f}{\kappa^2}H^2=\frac{\dot{\phi}^2}{2}+V(\phi)-3h\frac{\dot{f}}{\kappa^2}\, ,\\ \notag &
-\frac{2f}{\kappa^2}\dot{H}=\dot{\phi}^2+\frac{\ddot{f}}{\kappa^2}-H\frac{\dot{f}}{\kappa^2}\, ,\\ \notag &
\ddot{\phi}+3H\dot{\phi}-\frac{1}{2\kappa^2}R\frac{\mathrm{d} f}{\mathrm{d}\phi}+\frac{\mathrm{d} V}{\mathrm{d}\phi}=0\, ,
\end{align}
where the ``dot'' denotes differentiation with respect to the cosmic time. For a non-minimally coupled scalar-tensor theory, the slow-roll indices are equal to,
\begin{equation}\label{slowrollnonminimal}
\epsilon_1=-\frac{\dot{H}}{H^2},\,\,\,\epsilon_2=\frac{\ddot{\phi}}{H\dot{\phi}},\,\,\,\epsilon_3=\frac{\dot{f}}{2Hf},\,\,\,\epsilon_4=\frac{\dot{E}}{2HE}\, ,
\end{equation}
where the function $E$ is in this case equal to,
\begin{equation}\label{epsilonparameter}
E=f+\frac{3\dot{f}^2}{2\kappa^2\dot{\phi}^2}\, .
\end{equation}
In terms of the slow-roll indices, and during the slow-roll era, the observational indices read,
\begin{equation}\label{observatinalindices1}
n_s\simeq 1-4\epsilon_1-2\epsilon_2+2\epsilon_3-2\epsilon_4,\,\,\,r=8\kappa^2\frac{Q_s}{f}\, ,
\end{equation}
where it is assumed that $\epsilon_i\ll 1$, $i=1,..,4$, and the parameter $Q_s$ is equal to,
\begin{equation}\label{qs1nonslowroll}
Q_s=\dot{\phi}^2\frac{E}{fH^2(1+\epsilon_3)^2}\, .
\end{equation}
We shall use the slow-roll conditions in order to find a simplified expression for the scalar-to-tensor ratio $r$, valid during the slow-roll era, so we will calculate $Q_s$ during the slow-roll era. The gravitational equations (\ref{gravieqnsnonminimal}) during the slow-roll era, are simplified as follows,
\begin{equation}\label{gravieqnsslowrollapprx1}
\frac{3fH^2}{\kappa^2}\simeq V(\phi)\, ,
\end{equation}
\begin{equation}\label{gravieqnsslowrollapprx2}
3H\dot{\phi}-\frac{6H^2}{\kappa^2}f'+V'\simeq 0\, ,
\end{equation}
\begin{equation}\label{gravieqnsslowrollapprx3}
\dot{\phi}^2\simeq \frac{H\dot{f}}{\kappa^2}-\frac{2f\dot{H}}{\kappa^2}\, ,
\end{equation}
where the ``prime'' denotes differentiation with respect to the scalar field $\phi$. The the parameter $Q_s$ takes the following form,
\begin{equation}\label{qs2}
Q_s=\frac{\dot{\phi}^2}{H^2}+\frac{3\dot{f}^2}{2\kappa^2fH^2}\, ,
\end{equation}
and by using the slow-roll equation (\ref{gravieqnsslowrollapprx3}), the parameter $Q_s$ is approximately equal to,
\begin{equation}\label{qs3}
Q_s\simeq \frac{H\dot{f}}{H^2\kappa^2}-\frac{2f\dot{H}}{\kappa^2H^2}\, .
\end{equation}
So by combining Eqs. (\ref{observatinalindices1}) and (\ref{qs3}), the scalar-to-tensor ratio finally reads,
\begin{equation}\label{rscalartensornoniminal}
r\simeq 16 (\epsilon_1+\epsilon_3)\, .
\end{equation}
Also in terms of the slow-roll indices, the spectral index of primordial curvature perturbations $n_s$ takes the following form,
\begin{equation}\label{nsintersmofslowroll}
n_s\simeq 1-2\epsilon_1\left (\frac{3H\dot{f}}{\dot{\phi}^2}+2 \right)-2\epsilon_2-6\epsilon_3\left( \frac{H\dot{f}}{\dot{\phi}^2}-1\right)\, .
\end{equation}
Having the above at hand we can proceed and specify the function $f(\phi)$ and we discuss the relation of the non-minimally coupled theory with the inverse symmetric attractors of the previous sections. A convenient choice for the function $f(\phi)$ is the following,
\begin{equation}\label{frphispec}
f(\phi)=\frac{1+\xi \left( e^{-\beta n\phi}+e^{-\frac{1}{\beta}n\phi}\right)}{2}\, ,
\end{equation}
where $\xi>0$ and $n>0$, while $\beta$ is chosen as in the previous sections. Also, the potential $V(\phi)$ can be chosen in such a way so  that it contains higher powers of the exponentials appearing in the function $f(\phi)$ in Eq. (\ref{frphispec}), but for the purposes of this paper, it suffices to choose the potential to be simply a constant, that is $V(\phi)=\Lambda$, with $\Lambda>0$. The function $f(\phi)$ in Eq. (\ref{frphispec}) is symmetric under the transformation $\beta \to \frac{1}{\beta}$, so by using the slow-roll formalism we developed in this paper, we shall calculate the slow-roll indices and the corresponding observational indices of this theory. We shall use a physical units system where $\kappa^2=1$ and also we assume that $\xi=1$ for simplicity, but the results are robust towards the choice of $\xi$. If $\beta>1$, then the function $f(\phi)$ is approximately equal to,
\begin{equation}\label{fphifirstmainapprox}
f(\phi)\simeq \frac{1+ e^{-\frac{n}{\beta}\phi}}{2}\, ,
\end{equation}
so by using the slow-roll approximated equations of motion, we have,
\begin{equation}\label{slowrollapproxeqnsofmotion}
\dot{\phi}\simeq -H\frac{n}{\beta}e^{-\frac{n}{\beta}\phi}\, .
\end{equation}
Also $\dot{f}$ in the slow-roll approximation reads,
\begin{equation}\label{slowrollapprxofdot}
\dot{f}\simeq \frac{n^2e^{-2\frac{n}{\beta}\phi }H}{2}\, .
\end{equation}
The first slow-roll index is,
\begin{equation}\label{firstdslowrollapproxanalyt}
\epsilon_1\simeq \left(\frac{\dot{\phi}}{H} \right)^2\frac{1}{2f}-\frac{\dot{f}}{2fH}\, ,
\end{equation}
so by using (\ref{slowrollapproxeqnsofmotion}) and (\ref{slowrollapprxofdot}), the first slow-roll index becomes,
\begin{equation}\label{epsilon1afteranalysis}
\epsilon_1\simeq \frac{n^2e^{-2\frac{n}{\beta}\phi }}{2\beta^2}\, .
\end{equation}
In the same way we can calculate the slow-roll indices $\epsilon_2$ and $\epsilon_3$, which are approximately equal to,
\begin{equation}\label{slowrolllast}
\epsilon_2\simeq \frac{n^2}{\beta^2}e^{-\frac{n}{\beta}\phi }+\epsilon_1,\,\,\,\epsilon_3\simeq \epsilon_1\, .
\end{equation}
So by combining Eqs. (\ref{rscalartensornoniminal}),  (\ref{nsintersmofslowroll}), (\ref{epsilon1afteranalysis}) and (\ref{slowrolllast}), we have,
\begin{equation}\label{nsandrprefinal}
n_s=1-2\frac{n^2}{\beta^2}e^{-\frac{n}{\beta}\phi },\,\,\,r\simeq 16 \frac{n^2}{\beta^2}e^{-2\frac{n}{\beta}\phi }\, .
\end{equation}
We can introduce the $e$-foldings number in the final expression for the observational indices (\ref{nsandrprefinal}), by using the following relation,
\begin{equation}\label{efolidngsanalyticresults}
N=\int_{t_k}^{t_f}H(t)\mathrm{d}t=\int_{\phi_k}^{\phi_f}\frac{H}{\dot{\phi}}\mathrm{d}\phi\simeq \frac{\beta^2}{n^2}e^{\frac{n}{\beta}\phi }\, ,
\end{equation}
where $t_k$ is the horizon crossing time instance and $\phi_k$ the value o the scalar field at that time, $t_f$ the time instance that inflation ends and $\phi_f$ the corresponding value of the scalar field. Also for the derivation of (\ref{efolidngsanalyticresults}) we used the fact that $\phi_k\gg \phi_f$, which is justified since during the slow-roll inflationary era, the values of the scalar field are quite large. From Eq. (\ref{efolidngsanalyticresults}) we have $\frac{n^2}{\beta^2}e^{-\frac{n}{\beta}\phi }=\frac{1}{N}$, so by substituting in Eq. (\ref{nsandrprefinal}), we have,
\begin{equation}\label{nsandrprefinal1}
n_s=1-\frac{2}{N},\,\,\,r\simeq  \frac{16\beta^2}{n^2N^2}\, .
\end{equation}
Finally, for $n=\frac{2}{\sqrt{3}}$, the observational indices read,
\begin{equation}\label{nsandrprefinal2}
n_s=1-\frac{2}{N},\,\,\,r\simeq  \frac{12\beta^2}{N^2}\, ,
\end{equation}
which are identical to the resulting observational indices of Eq. (\ref{newfnsecondcase}). Hence as we demonstrated, it is possible to have the attractor behavior even with a suitably chosen non-minimally coupled theory. Finally, we need to note that the non-minimally coupled theory we chose is different from the strongly coupled non-minimally coupled theory of Ref. \cite{lindelast}, where the function $f(\phi)$ has to satisfy a different class of criteria, and also $\xi$ should be quite large.

\section{Conclusions}

In this paper we studied some inflationary potentials with a special inverse symmetry. As we demonstrated, it is possible that these inverse symmetry models can belong to the more general class of $\alpha$-attractors models. As we showed, this is possible in some limits of the theory, however, there are some quantitative differences with the $\alpha$-attractors models. We investigated various limiting cases of the inverse symmetry models and we showed that in all cases, compatibility with the observational data is achieved. We discussed in some detail all the qualitative features of the inverse symmetric models of inflation and also we investigated whether these models can be limiting cases of the Starobinsky model, with the answer lying in the negative. Also we showed that not all inverse symmetric potentials yield quantitatively viable results, and as we showed, it seems that when the limiting inverse symmetric potential is identical to the one corresponding to the $\alpha$-attractor models, then compatibility with the observations can be achieved. Moreover, we found the $F(R)$ gravity theory corresponding to the inverse symmetry model and we calculated the observational indices in order to see if the attractor property remains. As we showed, the resulting indices are identical to the ones corresponding to the $R+\gamma R^2$ model, so the $R^2$ model is the attractor of this kind of potentials in the Jordan frame. Finally, we showed how the attractor behavior can occur in the case of a non-minimally coupled scalar-tensor theory.

What we did not address in this paper is the relation of the inverse symmetric attractors with supergravity superpotentials. The motivation for this study is that some of the inverse symmetric models are directly related to supergravity superpotentials \cite{holo1}, so what now remains is to investigate whether the $\alpha$-attractor related inverse symmetric potentials can be derived by supergravity. We defer this task to a future work.

\section*{Acknowledgments}

This work is supported by MINECO (Spain), project
 FIS2013-44881 (S.D.O) and by Min. of Education and Science of Russia (S.D.O
and V.K.O).

redpajama_set_name: RedPajamaArXiv


text:
Q: Unable to display information using ajax django i am trying to display sizes using ajax but it does not show up after the ajax success
here is ajax script

here is the template
    <form id="form" action="{% url 'storeView'  user=store.user %}" method="post"  />
                      {% csrf_token %}

                      {% for size in sizes %}

                      {{size}}:
                      <input type = "number" name="quantity" value="{{product.quantity}}">
                      <input type = "hidden" name = "size" value="{{size}}">
                      <input type = "hidden" name = "productid" value = "                              {{product.id}}">
                       {% endfor %}

                      <input type="submit" value="submit" id="submit"/>
                     </form>

here is views.py
if request.user.is_authenticated():
        productid = request.GET.get('productId')
        if request.is_ajax():
            try:
                sizes = StoreProduct.objects.get_size(productid)
            except:
                sizes = None

            sizes = list(sizes.values())

            data = {
            "sizes" : sizes
            }

            return JsonResponse(data)

i am able to console log the sizes but how do i display them in forloop?
based on Hybrid's answer the following traceback is generated
File "C:\Python27\lib\site-packages\django\core\handlers\base.py" in get_response
  132.                     response = wrapped_callback(request, *callback_args, **callback_kwargs)
File "C:\Users\lenovo\Desktop\plump\Plumpin\src\store\views.py" in StoreView
  61.           return render(request , "store/storeform.html" , {'sizes' : sizes})
File "C:\Python27\lib\site-packages\django\shortcuts.py" in render
  67.             template_name, context, request=request, using=using)
File "C:\Python27\lib\site-packages\django\template\loader.py" in render_to_string
  99.         return template.render(context, request)
File "C:\Python27\lib\site-packages\django\template\backends\django.py" in render
  74.         return self.template.render(context)
File "C:\Python27\lib\site-packages\django\template\base.py" in render
  209.                     return self._render(context)
File "C:\Python27\lib\site-packages\django\template\base.py" in _render
  201.         return self.nodelist.render(context)
File "C:\Python27\lib\site-packages\django\template\base.py" in render
  903.                 bit = self.render_node(node, context)
File "C:\Python27\lib\site-packages\django\template\debug.py" in render_node
  79.             return node.render(context)
File "C:\Python27\lib\site-packages\django\template\defaulttags.py" in render
  507.                         six.reraise(*exc_info)
File "C:\Python27\lib\site-packages\django\template\defaulttags.py" in render
  493.             url = reverse(view_name, args=args, kwargs=kwargs, current_app=current_app)
File "C:\Python27\lib\site-packages\django\core\urlresolvers.py" in reverse
  579.     return force_text(iri_to_uri(resolver._reverse_with_prefix(view, prefix, *args, **kwargs)))
File "C:\Python27\lib\site-packages\django\core\urlresolvers.py" in _reverse_with_prefix
  496.                              (lookup_view_s, args, kwargs, len(patterns), patterns))

Exception Type: NoReverseMatch at /store/storeView/zara/
Exception Value: Reverse for 'storeView' with arguments '()' and keyword arguments '{u'user': ''}' not found. 2 pattern(s) tried: ['store/storeView/(?P<user>[\\w-]+)/$', 'store/storeView/(?P<user>[\\w-]+)/$']

A: So what you are trying to do requires you to merge the AJAX response with a for-loop, so you would need it processed by Django. The only way to do this is to return a render() response instead of a JSONResponse, and then append that to your html. For example:
Create a new HTML file called _store-form.html:
<form id="form" action="{% url 'storeView'  user=store.user %}" method="post"  />
                  {% csrf_token %}

                  {% for size in sizes %}

                  {{size}}:
                  <input type = "number" name="quantity" value="{{product.quantity}}">
                  <input type = "hidden" name = "size" value="{{size}}">
                  <input type = "hidden" name = "productid" value = "                              {{product.id}}">
                   {% endfor %}

                  <input type="submit" value="submit" id="submit"/>
</form>

In your views.py, instead of the last line return JsonResponse(data):
return render(request, '_store-form.html', {'sizes': sizes})

and now amend your JS to append the new returned html into your page:

A: Django template variables are passed from views.py through the context, while ajax is fetching value from somewhere else. Django template variable and javascript variables are two different things, you cannot expect them to work together. You need to use javascript to render the form manually. Take a look at jquery doc for details.

redpajama_set_name: RedPajamaStackExchange


text:
The doubt that the school has lost the opportunity to educate today is widespread, among school people and also in public opinion. The lack of trust in the scholastic institution, reflected in the more general distrust of all educational realities, accompanies teachers and students and influences their behavior and motivations. The information of the mass media contributes to the lack of authority of the educational institution, every time it shows the impotence or publicizes, often in great detail, those episodes that seem to sanction the ineffectiveness of the school's action.
It is therefore opportune to question whether the school can still constitute an important reference point for their growth for the new generations.
2. Is there an educational emergency in the school?
There is an insistence on an educational emergency. Pope Benedict also returned to the topic in the speech made to the bishops of the Italian Episcopal Conference on May 28, 2009:
As I have repeatedly stated, this is a constitutive and permanent need (that of education) in the life of the Church. , which today tends to take on the features of urgency and, even, of the emergency.
What is the educational emergency measured by? From the behavior of the boys – bullying, bravado, provocation … -? They would seem to sanction the failure of the educational action, or show an uneasiness and suffering in the face of which the adults seem powerless. The educational emergency can be grasped in the school even in the effort to get in communication with the boys? Their interests, their languages, their cultural categories, their tastes seem to be so far from those of adults, to discourage those who want to understand them. Unless they belong to that kind of adults whose sympathy for the young and whose attention to them makes it possible to grasp in the folds of certain behaviors the glimmers of a positive search that can open the door to dialogue.
When we observe social phenomena we can not help but stop at the objectivity of the facts; but this reading does not allow us to grasp the nuances that open the way to less obvious evaluations of reality.
It seems to me that this is what is happening for the educational emergency: we are content to judge from facts that are not sufficiently understood; not contextualized; not always caught in their changing complexity.
Faced with those events that lead us to talk about an educational emergency, I think it is very appropriate to find out what the real underlying problems are, also in order not to be paralyzed by that defeatism which, in fact, takes responsibility for itself.
We can not make any useful reflection if we do not take into account the social complexity in which the school is immersed and affected, to understand thoughts and choices originating from the climate of widespread uncertainty, identifying drives for change and tracks for reorientation.
It is necessary to take into account these elements from which today the school can not disregard, both to educate the younger generations to grow in it, and to prepare to enter it as protagonists. Boys and young people are immersed in this context: one can not deny it, nor imagine a different one, placing itself in an attitude of sterile conflict.
Society, with its contradictions and its riches, enters the classroom through what children, young people and young people live outside of it. The fragility of families enters the classroom through the emotional fragility of the little ones; the pluralism of cultures enters, through the multiplicity of the origins; enter the cultural and social weight of new media, through the quantity of information – fragmented and without an order, but numerous – of the children …
The company enters the classroom also through the requests that it addresses to the school and whose answer helps to determine the social consideration of the school itself. Enter the classroom through the kind of culture that is developed outside the school and with which it must enter into a relationship.
To stay in the school in a planning way, giving value to the action that it is called to perform, we need to acquire awareness of being in transition from mass society to the planetary one in a process still in progress, in which we are involved and from which not always we have the necessary distance to judge.
3. The answers from the school
The school has been displaced by this new situation. His disorientation is not very different from that of the family, the Christian community or other educational agencies that are struggling to assume their own function, in a full and at the same time renewed way. Even the school often seems to look back on the past: its not a naive regret, but in fact it is a reductive interpretation of its task in the face of today's complexity, in an attempt to return to school life patterns that have characterized other seasons of the culture of our country. I quote two signs of this attitude:
– first of all the return to the notionism and the refuge in the transmission of cultural contents, that the boys almost always feel as far away from their life, their interests and their curiosity, ineffective in order to help their growth, to open their horizons of meaning and hope;

redpajama_set_name: RedPajamaCommonCrawl


text:
Nieman Fellowship
The Nieman Foundation for Journalism at Harvard University awards multiple types of fellowships.
1 Nieman Fellowships for journalists
1.1 The Nieman–Berkman Fellowship in Journalism Innovation
1.2 The Abrams Nieman Fellowship for Local Investigative Journalism
1.3 The Knight Visiting Nieman Fellowship
Nieman Fellowships for journalists
A Nieman Fellowship is an award given to journalists by the Nieman Foundation for Journalism at Harvard University. The fellowship is a transformative learning opportunity open to candidates working in all media in every country around the world.
Nieman Fellowships are awarded to reporters, editors, photographers, producers, filmmakers, editorial writers, cartoonists, digital innovators and other journalists with at least five years of full-time, professional experience in the news media.
At Harvard, Nieman Fellows attend seminars, shop talks, master classes and journalism conferences designed to strengthen their professional skills and leadership capabilities. Those selected for the program spend two full semesters at Harvard auditing classes with some of the university's greatest thinkers, participating in Nieman events and collaborating with peers. The fellowship home is at Lippmann House in Cambridge, Massachusetts.
Each fellow is free to design an individual course of study. Some pursue classes in a reporting specialty. Others explore the breadth of Harvard's schools and departments. With the knowledge they gain on campus and the relationships they build, fellows often return to work as journalism entrepreneurs, industry innovators and top managers in their newsrooms.
Some two dozen fellowships are awarded annually, half to Americans and half to non-Americans.[1]
As part of each class, specialized fellowships are also available:
The Nieman-Berkman Fellowship in Journalism Innovation
The Abrams Nieman Fellowship for Local Investigative Journalism (open to U.S. candidates)
The Knight Visiting Nieman Fellowships
Additionally, "during years in which a watchdog journalist or investigative reporter from the United States is selected for a fellowship from the general application pool, the Nieman Foundation may offer the Murrey Marder Fellowship in Watchdog Reporting."
The Nieman–Berkman Fellowship in Journalism Innovation
This joint fellowship, awarded for the first time in 2012, is a joint fellowship between the Nieman Foundation and the Berkman Klein Center for Internet & Society that is awarded to U.S and international candidates with project proposals related to innovation in journalism.
The Abrams Nieman Fellowship for Local Investigative Journalism
Funded by the Abrams Foundation, the Abrams Nieman Fellowship for Local Investigative Journalism was created in 2018 to bolster deeply reported local and regional news stories in underserved areas throughout the United States. Candidates selected for the fellowship spend two semesters at Harvard and then receive financial support for up to nine months of fieldwork to develop an investigative project that will provide better, more in-depth coverage of issues important to the communities they serve.
The Knight Visiting Nieman Fellowship
Funded by the John S. and James L. Knight Foundation, this fellowship offers a short-term research opportunity to individuals interested in working on special projects designed to advance journalism in some new way. Candidates need not be practicing journalists, but must demonstrate the ways in which their work at Harvard and the Nieman Foundation may improve the prospects for journalism's future. This may be related to research, programming, design, financial strategies or another topic. Both U.S. and international applicants are invited to apply.
John S. Knight Fellowship (Stanford)
Knight–Wallace Fellowship (University of Michigan)
Knight–Bagehot Fellowship (Columbia)
^ "Nieman Foundation Visiting Fellowships". Nieman Foundation. Retrieved 10 November 2013.
Nieman Fellowship eligibility requirements
List of Nieman fellows by year since 1939


At CEL, our nationally recognized experts work with educators to build both leadership capacity and instructional expertise. CEL does not have a "one-size-fits-all" professional development model. We meet with you, help you target school or district needs, and work with you to find the most powerful services to address them, based on your resources and requirements.
Unlike traditional investments in teacher professional development that have not consistently yielded results for students, CEL's approach to professional learning develops teacher collective efficacy — a long-term, sustainable approach to addressing persistent challenges of student learning. Our partnership methodology ensures that your investment will be aligned with ESSA's requirement for professional learning activities that are sustained, intensive, collaborative, job-embedded, data-driven and classroom-focused.
AASA, the school superintendents association, has partnered with the University of Washington Center for Educational Leadership to bring CEL's Principal Supervisor Professional Development Program to all central office leaders who support principals' instructional leadership growth as their primary responsibility. Applications are due May 15, 2019 for the 2019-2020 academy.
This training helps principals, central office leaders and teachers recalibrate their understanding of the teaching and learning practices described by each indicator, transitioning from version 2 to version 3 of the 5D+ Rubric 5D+™ Rubric for Instructional Growth and Teacher Evaluation.
The Measures of Instructional Leadership Expertise provides independent measures of one's expertise in observation and analysis, providing feedback to teachers, leading professional learning and one crosscutting skill of adopting an inquiry stance in one's leadership.
The Instructional Leadership Academy is a yearlong professional development program that CEL delivers directly within a school district. Through the academy, a school district's principals, instructional coaches, teacher leaders, and central office leaders become stronger and more effective instructional leaders.
The Center for Educational Leadership offers Principal Supervisor Professional Development to school districts seeking to increase the capacity of principal supervisors to improve principal instructional leadership. Using team learning and job-embedded coaching, principal supervisors develop and practice skills critical to their actual work with principals.
The Center for Educational Leadership works side by side with your leadership team to ensure you are recruiting, selecting and retaining the very best principal supervisors. CEL offers customized services including Coaching Supervisors of Principal Supervisors, Principal Supervisor Hiring Process, and Principal Supervisor Pipeline Development.
The Center for Educational Leadership offers a variety of services focused around the 4 Dimensions of Instructional Leadership (4D™) framework. Through professional development opportunities, school leaders and their supervisors develop a clear understanding of the instructional leadership practices that will help them increase student achievement in their schools.
Instructional Leadership Teams professional development increases school leaders' and instructional leadership team (ILT) members' abilities to improve teaching and learning in a results-focused learning environment. Participants will walk away with a viable, customized plan to develop and maintain ILTs at their school. All participants will have access to an ILT toolbox that includes online resources for sustaining the work of the ILT.
Research and practitioner experience have deepened our understanding of the most salient practices of instructional leaders. We believe that when school leaders consistently put these practices into action, instructional practice improves. When instruction improves, student academic performance improves.
The Center for Educational Leadership offers a professional learning series designed to help school leaders develop their understanding and skill in developing and evaluating professional development, including creating professional development plans that align with student and teacher needs. Through this professional learning series, principals, assistant principals and instructional leadership team members will develop the skill to identify professional development needs, and understand what effective professional development looks like and how it will help them improve instructional practice and student achievement.
The Center for Educational Leadership offers a year-long training series for new and aspiring leaders during which participants learn the critical aspects of instructional leadership. Participants are provided an opportunity to delve into their own practice, learn from others, apply new skills and receive feedback on their developing practices.
The Center for Educational Leadership offers training designed to help educators learn how to use learning walkthroughs as a process for improving instructional practice. Leaders sharpen their ability to observe, analyze and discuss issues of student learning and teaching practice.
Side by side, we work with teachers and leaders to improve the quality of education for all students.
Our content area-focused professional development helps district leaders, administrators, coaches and teachers build content knowledge and hone pedagogical skills.
CEL's nationally recognized faculty, staff and consultants have expertise that supports schools, districts and states in strengthening instructional practice and leadership to improve student learning. We believe that teacher evaluation is an ongoing process that goes hand in hand with deepening the expertise of teachers to engage students in high-quality learning while simultaneously increasing the expertise of school leaders to guide and support teachers in this improvement process.
The University of Washington Center for Educational Leadership offers school districts a two-day institute, "Targeted Feedback for Teacher Growth: Tools and Processes to Support Teacher Evaluation." The Targeted Feedback Institute supports principals, teachers and central office leaders in learning the skills for giving feedback and creating a culture that results in effective teacher evaluations centered on growth of teacher practice and improvement of student learning.
CEL's one-day Creating Focused Goals Institute helps school leadership teams learn a process to enable teachers' professional goals to be strategic, with a greater impact on student learning. This institute addresses how adults learn best, how to create goals that align with student needs in the classroom and how a school leadership team can support teachers in growing in their practice based on a focused goal. Participants in this institute learn a process to create focused goals and ensure that teachers' goals positively influence student learning and their own instructional practice.
The Teaching Tune-up Institute helps teams of principals, instructional coaches and teachers to work together in analyzing data, so that they can decide if they should keep their instructional goals or set new ones.
The one-day Leading Professional Learning Institute supports school leadership teams in determining what kind of professional learning to provide for teachers and why. Effective professional learning needs to address the highest-leverage instructional strategies that are focused on the specific needs of instructional staff as identified by the school leadership team through instructional analysis. School leaders will learn about ways to plan and deliver professional learning that supports those highest-leverage instructional strategies.
We realize how critical it is to provide leaders and teachers with the skills necessary to support excellent classroom practice and we also know that this work needs to be thoughtful, intentional, and focused. That's the intent of our research-based instructional framework, the 5 Dimensions of Teaching and Learning™ (5D), composed of the core elements that constitute high-quality teaching.
The Center for Educational Leadership offers a two-stage training program designed to help educators develop their understanding of the 5D+ Teacher Evaluation Rubric and the 5 Dimensions of Teaching and Learning™ instructional framework. Training participants learn how to effectively use these tools in daily classroom practice.
Stage I Online Training presents learners with an overview of the 5 Dimensions of Teaching and Learning™ instructional framework and the 5D+ Teacher Evaluation Rubric. Through the online training, learners will develop their skills in the use of the inquiry process during teacher evaluation to support teacher growth. Stage I Online Training is an ideal support for principals, teachers and central office staff as they learn how the new model of teacher evaluation is different from the old model.
5D+ Stage II Online Training develops and deepens learners' knowledge of the 5 Dimensions of Teaching and Learning™ instructional framework, the 5D+ Teacher Evaluation Rubric (Version 2), and the 5D+ Inquiry Cycle. 5D+ Stage I Online Training introduced participants to the Classroom Environment & Culture dimension of the framework and rubric as well as the 5D+ Inquiry Cycle. 5D+ Stage II Online Training provides learners an opportunity to develop a deeper understanding of each of the remaining four dimensions.
5D+ Summative Scoring Training develops the summative part of the 5D+ teacher evaluation process. It provides participants with the opportunity to learn how to analyze the formative instructional practice data that has been collected over the course of the school year and determine indicator and overall instructional practice scores using a four-point scale. 5D+ Summative Scoring Training is ideal for principals and principal supervisors.
Developing reliable evaluators of teachers is a key component to the success of any school district's teacher evaluation system. Teachers and students benefit from principals and evaluators who are trained and certified to observe, analyze and rate instruction, before they ever step into a classroom to observe a teacher for the purpose of evaluation.


Oh yeah — the CSA box comes to about $17 per week/$35 per box. It takes us the full two weeks to get through the whole box.
All that and a sack of potatoes!
Thank you for being patient. Just one more week to go! Can you make it?
Then I'm out — my real name, my face and everything!
I'll send you details soon about the reveal, but know this: It's going to be on TV and in print.
How am I holding up? Most of the time I'm not thinking about it at all. I'm good at compartmentalizing. I have a lot going on. When I remember "oh yeah, it's next week," I feel a surge of nerves/fear/anxiety/excitement. A big mess of emotion. I'm just taking it one day at a time –for my own sanity.
When I blogged about the book a few weeks ago, many of you asked if it would be available via Kindle/Nook/ebook, etc and at the time I had no idea. The answer is yes!
Everything will be available on October 5th (Amazon, Barnes and Noble, Chronicle Books).
Did you see this article? This is the kind of stuff that gives me shivers. I'm so happy they caught this before it hit the lunch line! It reminds me of this guest blog post about "super bugs." It's all very disturbing.
I'm already sick of packing my son's lunch. September is not even over!
I did not pickle those beets myself. I bought them from a stand at the farmer's market already in jars. My son loved them. Child care menu: Salisbury steak (!), mashed potatoes, diced carrots, orange and wheat bread.
That's tilapia with a sweet red chile sauce (Thai Kitchen brand). It was a hit all around. Child care menu: BBQ chicken, rice, salad greens, pear and wheat dinner roll.
I crumbled and sent chicken nuggets. I asked my son if he wanted leftover lamb or chicken nuggets in his lunch and big surprise — he wanted chicken nuggets. I shouldn't have given him a choice. I had to dig out the gluten free, extra special ones from the freezer but still. What has it been? Chicken nuggets maybe twice in 2011? I feel like a hypocrite since I do rail on chicken nuggets. At least these ones are not 50% or more fillers. Sometimes I just feel bad for the kid, you know? At least he loves spinach. Child care menu: Chicken tenders, cheesy mashed potatoes, broccoli, applesauce, and rye bread.
It was after this lunch that I was told that I'm not packing enough food for my little guy. So I'm trying to bulk up the lunches. Frankly, that shocks me because I pack more that I imagine he'll actually eat. Portion-wise he might eat two of these containers at lunch. Child care menu: Cheese ravioli with meat sauce, cucumber slices with dip, and watermelon.
Well, at least I won't be accused of packing too little. Child care menu: Turkey hot dog, baked beans, salad and an apple.
I love egg salad. It's so delicious.
That fish was so good. The potatoes are an odd accompaniment, I know.
I decided that if you can do "fried rice," that you must be able to do "fried quinoa" so I tried mixing up egg in the quinoa and I thought it turned out great. The true test is the husband and he thought the quinoa was good. He likes the plain quinoa, not the black quinoa (at least not straight), so I mixed them up.
Nachos can be made healthy and delicious! I also want to note here that I have always hated pickles, but these "bread and butter" pickles I bought at the farmer's market are to die for! Who knew?
By Friday I'm usually so sick of packing lunches. Luckily I could repeat the nachos again.
This summer we took a trip to a farm that is affiliated with our CSA. I found the experience to be life-changing.
But first, a little background. Before I started this blog, my son was very sick. He was getting ear infections every two weeks. He had a constant runny nose and a rattle in his chest. No one was sleeping. I started the blog after the Christmas where we took him to the ER twice. Throughout the first month of January 2010 when I was eating school lunch, my son was eating day care food and was ill all the time. Finally in February 2010 he had ear tubes put in. I thought they would be the magic cure I had been waiting for. They weren't (but they can be for a lot of families — listen to your doctor). My son continued getting ear infections, though they were occurring less frequently, averaging once per month. By age 16 months my son had had eight ear infections and eight rounds of antibiotics.
In April 2010 I talked to my doctor about taking my son off of cow's milk. Our pediatrician, who I adore, told us that the cause of my son's troubles was child care and not the food. I couldn't ignore what I thought was going on with my son, especially because I had started this blog and discovered that food really did have an effect on people. My son was already drinking lactose-free cow milk. One of my friends mentioned goat milk to me and I found some at the regular old grocery store. I compared the nutritional facts between cow milk and goat milk. The milks are virtually identical in nutrition (goat's milk is slightly lower in fat content), but goat milk costs around $4.00 a quart. I thought I'd give it a try in spite of the cost.
All this to say I guess I have a particular fondness for goats.
I thought that was a strange idea because a hoofed animal strikes me as way more work that backyard fowl and insects. But my husband was thinking about it economically: we spend a small fortune on goat milk.
When we got the flyer from our CSA saying that they were offering a two-hour session onsite entitled "Making Goat Milk Ice Cream," I highlighted it with a bright yellow. It would be something that my son would enjoy as he loves animals and farms and, the best part, he could eat the fruits of his labor without worry.
Weeks later we drove to the farm. We were in the car for a very long time. I had to use my phone's GPS when we found ourselves on a dirt road. I was sure it couldn't be that rural. We almost drove right past a field with lines and lines of produce just coming up. That green stuff was headed for my CSA box!
Who wouldn't fall in love with a farm like this?
We got a tour of the farm and the animals. At first I was interested. We all enjoyed hanging around in the little goat paddocks letting the goats come up and sniff us. A goat even tried to eat my small metal key chain that I had left hanging out of my pocket. They were curious, friendly, and ready to eat anything — really endearing animals. But after about an hour, I was getting a little impatient. I was there to milk a goat. This was a relatively short session and I wanted to have plenty of time for goat milking. Luckily my son and husband were enjoying themselves and were unaware of my getting slightly annoyed at the wait.
Finally our guide told us that we all were going to go ahead and make goat milk ice cream. As we followed her inside, I run up and quickly asked about the actual milking of the goats and she explained that the goat milk we were using to make the ice cream had been milked previously and pasteurized. We were not going to be able to use raw goat milk to make ice cream so we would make the ice cream first, while the ice cream machine was making the ice cream we would milk goats, and then we would sit down and eat the ice cream.
At least the goat milk we were about to use to make the ice cream was from the goats that we met — the farm has pasteurizing equipment. I had been interested in maybe trying raw goat milk, but that was not going to happen. Why would I want to try raw goat milk you ask? Because people like me (who have figured out they can't drink any kind of dairy product without having "problems") sometimes respond well to raw goat or cow milk. It's great that my son can drink goat milk from the store and be ok. Me? I realized that my body gets mad at both cow and goat milk. Frustrating. I miss dairy and I'm only dairy free because I don't want to be in the bathroom all the time (like I used to be).
Oh boy, I thought. Well, now our son is going to have trouble with this ice cream. My husband told me to relax and I tried to shrug it off.
After we got everything going with the ice cream machines, we went outside to the barn to milk the goats. The guide instructed us that milking a goat is not like what you see on TV when people milk a cow. She told us we had to pinch with our thumb and forefinger and then squeeze with our remaining fingers, sort of like wrapping the other fingers around the teet. No pulling down.
My son was so excited seeing all of the adults and kids moving their hands and learning the correct hand motion that he was practicing, too. I looked down at him moving his hands and I had to snap a shot of his adorable attempts.
Finally, it was our family's turn so we went up to the goat. The instructor held the goat's rear hooves. My husband milked the goat, my son got the hand movement right and milked him too! I was shocked and a little choked up. Then it was my turn and I didn't get it right. I was trying to milk a cow I guess so the instructor reminded me "pinch and squeeze" and then I got it. Yeah me!
When we finished milking, the group went back to get the ice cream, bowls, and spoons. We set up on some picnic tables and the instructor started serving everyone up. I decided that I would try a spoonful and just suffer through any "after effects." We were not going to deny our son at all. I told the instructor to "just put a little in my bowl" and she obliged.
I put the spoon to my mouth. I tasted the ice cream. The rich taste of dairy swirled in my mouth and oh the honey. It was dark and and astonished my last taste bud.
It was the best ice cream I ever had. Immediately I wanted a second helping. And thankfully there was a lot to go around. My son had three helpings and, well, I had at least two. Maybe three. I don't know.
I got choked up. The ice cream made my eyes water because I didn't know that ice cream could be that wonderful. Just pure and sweet. Just thinking about that moment brings tears to my eyes.
Leaving the farm was tough. We had a great time and we all felt connected to the animals. An hour later I waited for my son and I to have "digestive issues." Two hours went by. Nothing happened. Five hours went by. Nothing at all.
Everything agreed with both of us. I'm still stunned.
Now I want to 1) Move to a small farm 2) Get a goat 3) Make goat milk ice cream as much as I can.
Still in the process of convincing my husband that we need to move more rural. The fact that he also thought the goat milk ice cream was divine is working in my favor!
Dreaming of my next spoonful….
*In September 2010 I took him off all day care food and cow's milk-based yogurt and cheese. Finally in October all gluten. There went the chronic diarrhea and asthma!
Pack tomato and lettuce separately from sandwiches, as they can make sandwiches soggy and unappealing to kids.
Making the switch from chocolate milk to 1% white milk can be easier than you think. To enforce this, you can take the hard line and make it the only thing you're going to offer. A second thing is to make sure to educate your kids on how important it is for them to have the nutrients in white milk as opposed to strawberry and vanilla milk. Education and reinforcement are the best tools you have as a parent. And, finally, make every effort to keep milk very cold. Do this by keeping it in the refrigerator until morning and packing it right by the ice pack.
At the grocery store, look for low-sodium and low-fat deli meats.
To convince your kids to eat fruits and veggies at lunch, cut them into small, easy-to-eat pieces. If you cut up apples, douse with a little lemon juice to prevent them from turning brown.
If your child is a picky eater, substitute classics for healthier options. For example, if your child is a big peanut butter and jelly fan, you can give him or her a no-trans-fat sunflower-seed spread with a no-sugar fruit preserve.
If my kids eat their healthy food, I feel that they can have a treat. Sometimes I buy baked multi-grain chips or vegetable chips in small packages. Look for reduced salt varieties. Also there are 100-calorie cookies that make a nice treat. We discuss the fact that their lunch comes first and then the treat.
When packing your child's lunch, include them in the process. This is the most important step in making healthier lunches for kids. Talk about what ingredients are going in, you need to gain buy-in. If the kids don't like what's in the lunchbox, they simply will not eat it. You have to educate your children that what they have for lunch matters. My girls have taught me that it's important to urge them to try new things and to compromise as we start the new school year.
You are still very young, but I'm already thinking about your education. Part of the reason why we changed daycare centers was that we wanted to make sure your needs were being met. I wanted more structure for you in a school-like setting. The transition has not been easy, but I think you are doing great.
When I was a little girl, I went to a lot of different schools because my parents moved all over the country. It was very hard, especially in middle school and high school. My parents made decisions to move based upon financial motivations, not educational ones. In college, I was envious of some of the high school education experiences of my peers. Thankfully I was prepared for college, but I want more for you.
I can't promise that we won't move and there won't be difficulties in your young life. Growing up is tough. However, I will tell you that I will make sure that you are challenged at school as well happy and healthy.
What I have learned in my work is that there is no "do over" for childhood. Every school year must be another opportunity for new growth. Now is a critical period of development for you, little guy. Dad and I love watching you grow and mature — it's such a joy.
All you get is one shot at an education. It better be damn good because you're all I got! We are so proud of our terrific little boy.
Join Parenting's Mom Congress on Education and Learning on Facebook at www.facebook.com/momcongress to connect with parents around the country who are standing up for great schools. Want to make your school great right NOW? Enter the Mom Congress School Transformation Grant contest to win $20,000 for your school.
To make the sauce, I found her recipe online and used it as a guide. My kid ate everything, but left some of the mac and cheese. One of you guys reminded me that I should use egg molds. I bought and used them back in December (during the Eat Along Challenge) and promptly shoved them in the back of the silverware drawer. They are a huge hit. Also — "day care" or "daycare" ?? — every week I can't be sure! Day care menu: Chicken cacciatore, pasta, mixed veggies, peach applesauce and rye bread.
Half of a bagel with goat cheese, peaches (farmer's market), tomato soup, tomatoes, breadsticks.
My son saw the baby tomatoes at the grocery store and told me he wanted to buy them. I don't like to refuse him veggies he requests, but I should have. He only ate two of the four. Day care menu: Mac and cheese, salad with French dressing, and apple.
Too small of a lunch. He was ravenous when I picked him up from daycare. Those potatoes were terrible! Whoops! Day care menu: Turkey hot dog, au gratin potatoes, peas, banana, and wheat bun.
Big hit of a lunch. Only the pepitas came back. Day care menu: Chicken marinara, pasta, "winter blend," peaches, Italian bread. A lot of pasta and bread on their menu for the week, eh?
I used corn tortillas and ground bison for a twist. I also used the sauce I made myself. My husband was in heaven. My son? Not so much. Just ate the bison meat. I couldn't send it in his lunch because I didn't want him to waste the precious enchiladas.
Not enough food! The potatoes were so bad that I couldn't eat them.
I have decided that rice is a permanent FAIL in the crockpot. I tried to mix up potatoes, squash, wild rice, and pinto beans (with water, etc) in the crockpot and cook it all day. It turned out TERRIBLE. I could get through it all. Mark my words, I will never do rice in the crockpot again!


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Beta Omicron Chapter alumnus recognized for 30 years of service to NSU
Longtime NSU Sports Information Director Doug Ireland was among the faculty and staff members recognized with milestone awards during the annual Faculty/Staff Lunch on Monday, August 13.
Ireland has been in charge of athletic media relations at his alma mater since January 1989 and was acknowledged for 30 years of employment.
An alumnus of Pi Kappa Phi Fraternity, he has served as Beta Omicron Chapter Advisor since 2008, working closely with student leaders.
For the university, Ireland coordinates publicity efforts for Northwestern's 14 intercollegiate sports teams through local, regional and national media outlets in print, broadcast, television and the internet.
He also serves in the volunteer role of chairman of the Louisiana Sports Hall of Fame. Ireland assumed that post in April 1990.
He was chosen as the 2016 recipient of the Southland Conference's Louis Bonnette Sports Media Award, named for the iconic retired McNeese SID.
His 1992 Demon Football Media Guide won "Best in the Nation" in FCS Division from the College Sports Information Directors of America. A 1997 story on Joe Delaney, "The Guy We Called Joe D," won a national second-place award in a CoSIDA writing contest. Ireland has won dozens of awards as SID from the Louisiana Sports Writers Association, including 31 this century.
Several of his assistant SIDs and graduate assistants have advanced to prominence in sports. Former NSU sports information staffers under Ireland include Bruce Ludlow, associate commissioner for operations of the Southland Conference; Bill Magrath, media relations manager for the Sports Business Daily; Mike Morrison, former co-editor of the ESPN Information Please Almanac; Daucy Crizer, assistant AD and business manager at Lamar; Erik Cox, former SID at Lamar; Dart Volz, former SID at Southeastern Louisiana; Melissa Reynaud, former assistant SID at LSU; Kenny Lannou, associate AD for communications at Kansas State; Matthew Bonnette, assistant AD and SID at McNeese, and Troy Mitchell, SID at Henderson State. Dustin Eubanks, NSU's assistant AD/director of NCAA compliance, worked in the NSU SID office as a graduate assistant and for two years as the full-time assistant, and Adam Jonson, athletics director at LSU-Alexandria, was a student and graduate assistant in the SID office.
In 1981-82, while an undergraduate at Northwestern, Ireland worked as chief of the Shreveport Times Natchitoches Bureau, coordinating news coverage of an eight-parish region along the Red River. From 1982-85, he was assistant SID at Southwestern Louisiana (now UL Lafayette), working with a men's basketball program that made three straight postseason tournament appearances. He won CoSIDA publications and writing awards while at USL. Ireland was the sports editor of the Natchitoches Times in 1985-86 and attended graduate school at Northeast Louisiana (now UL Monroe) before joining the Alexandria Town Talk sports staff in 1987. In 18 months at the Town Talk, he covered both NSU and LSU sports and won 15 writing awards from the Louisiana Sports Writers' Association.
In 2001, the LSWA presented its prestigious Mac Russo Award to Ireland for his contributions to the organization. In 1999, Ireland was awarded honorary membership in the Graduate N Club at NSU by the university's group of athletic lettermen for his service to Northwestern and its athletic program, and in 2003 he was given full membership. He was appointed by President Dr. Randall Webb to serve a two-year term on the inaugural University Planning Council in 1997-99.
In 2008, he was awarded the Northwest Louisiana's National Football Foundation "Distinguished American" award and in 2012 he was honored by the Alexandria Town Talk by being named the "CENLA Sportsman of the Year" award for his work as an SID and toward the completion of the $23 million Hall of Fame Museum.
Louisiana Lt. Gov. Jay Dardenne presented a special award to Ireland at the grand opening of the museum on June 28, 2013, for his "tireless work and dedication to the creation" of the museum. The Louisiana Association of Museums gave him its Lois Wyatt Bannon "Heart and Soul" Service Award in April 2014 for his work with the museum.
A member of the Blue Key National Honor Fraternity and a student government senator while completing a journalism degree from Northwestern, Ireland was editor of the student newspaper "Current Sauce" as a sophomore before going to work for the Shreveport Times. He was an all-district baseball player and the student body president at Jonesboro-Hodge High School, where he was a wingback for the Tigers' 1977 Class AA state football finalists coached by the late Don Shows.
Pi Kappa Phi alumnus announces retirement after three decades as NSU Sports Information Director
Pi Kappa Phi alumnus featured in ESPN '30 For 30′ film
← NSU Pi Kappa Phi member completes cross-country construction marathon
Pi Kapp alum, NSU professor honored as teacher of the year →


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Le Trogon citrin (Trogon citreolus) est une espèce d'oiseau de la famille des Trogonidae.

Cet oiseau fréquente le littoral pacifique du Mexique.

Liens externes

Trogoniformes
Oiseau du Mexique

redpajama_set_name: RedPajamaWikipedia


is the mean ionic activity coefficient, I is the ionic strength of the solution, and are the charges of cation and anion, respectively.
m is the molality, and are the stoichiometric coefficients of cation and anion, respectively, in the dissociation reaction of the electrolyte.
is the standard potential of the cell, and Q is the reaction quotient, and n is the number of moles of electrons involved in the net cell reaction.


Now this is getting ridiculous. When I say this is the last one, I absolutely 10000000000% mean it this time. I shall not explore further. But this one's pretty cool.
They're separated by genre, and each part is in chronological order.
Last edited by StevieFan13 on Wed May 24, 2017 5:00 am, edited 1 time in total.
Henrik wrote: Great find, Stevie!


#1356: When you live for over a thousand years, it redefines long-term planning.
#1356: When you live for over a thousand years, it redefines long-term planning. published on December 7th, 2012 Read more posts by the author of #1356: When you live for over a thousand years, it redefines long-term planning., Miss MabNo Comments on #1356: When you live for over a thousand years, it redefines long-term planning.


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« Autodesks SketchBook | Main | ANA's charter 787 flights »
Tidal Power
"Off the northernmost tip of Scotland, where the turbulent waters of the Atlantic Ocean meet those of the North Sea, sits a chain of 70 mostly uninhabited islands collectively known as Orkney. Best known for its wildlife and Neolithic historical sites, it isn't the first place you think of as a centre for cutting-edge science. Yet it is at the heart of what could soon be a renewable energy renaissance.
The strong tides around these islands have led the European Union-funded European Marine Energy Centre (EMEC) to use Orkneys' waters as the world's largest testbed for a renewable energy source that has been stalled for years: tidal power.
If new turbine designs being tested here can survive the pitiless Scottish swells, they will finally tame one of the world's most promising sources of renewable energy. But that's not all. Some of these designs could go far beyond tapping tides along the coast, reaping energy from the most powerful phenomena in the oceans - the world's major ocean currents. Harness these powerhouses, and tidal power would help smash all previous predictions of how much energy the oceans can provide."
New Scientist (subscription required)
The article discusses various turbine and other designs including SeaGen in photo.
September 28, 2011 in Alternative Fuels | Permalink


Critics have highlighted the potential for "overblocking", in which cautious algorithms censor content even when it does not breach copyright law, and warned of the cost that such a requirement would have for smaller publishing platforms.
Critics - including the internet's creator, Sir Tim Berners-Lee - say the rules would lead to information on the internet being more hard to access. "[The warnings] are correct, but exaggerated".
Critics fear the legislation being brewed up in Brussels could stop people from sharing memes and news articles online.
More than 80,000 people were already without power as the storm began buffeting the coast, and more than 12,000 were in shelters. The typhoon is expected to make landfall in the Philippines Saturday before barreling toward China, Vietnam and Laos.
De Bruyne, once of Chelsea, is considered one of the world's elite midfielders and signed a six-year deal at City in January. He won three La Liga titles, two Champions Leagues and two Club World Cups during four seasons in charge.
Julia Reda, an Internet activist and German member of European Parliament, said the decision was "a severe blow to the free and open Internet" and that the parliament was putting "corporate profits over freedom of speech". Jean-Claude Moreau, chairman of the Society of Authors, Composers and Publishers of Music, which supports the reform, said artists would "prefer no directive to a bad directive". YouTube said it spent over $100 million on an existing content ID system that identifies copyrighted material after it's published.
YouTube, which is owned by Google, has campaigned against the new law. Among them are exceptions to the new copyright laws for small businesses, open-source platforms such as GitHub and online encyclopedias. "We've always said that more innovation and collaboration are the best way to achieve a sustainable future for the European news and creative sectors".
Article 11 introduces a so-called "link tax" which would mean that social media platforms, such as Google and Facebook, could have to pay news organisations to use their headlines on their sites.
Despite the amendments, some still view the laws as hindering freedom of expression online. If search engines are required to pay licensing fees for every bit of text, some results will inevitably be removed when a certain publisher proves untraceable, links or outlets are not considered viable enough to contend with, or a publisher refuses to license their content for any reason.
Previous efforts to make sure publishers are paid have backfired in Europe.


Steelers have won six of eight in series. … Bengals RB Cedric Benson (837 yards) needs 163 yards rushing for second consecutive 100-yard season. Steelers have allowed one 100-yard rusher in 46 games, and lead NFL by limiting opponents to 62.3 yards rushing per game. Only one team (New England) has rushed for 100 yards against them this season.
Bengals QB Carson Palmer needs two TD passes to join Ken Anderson (197) and Boomer Esiason (187) as only players in Bengals history with 150 TD passes. … Bengals WR Terrell Owens had 10 catches for 141 yards and two TDs when teams met last month. Owens has five TD catches in six games against Pittsburgh. Owens (961 yards receiving) needs 39 yards to join Jerry Rice and Randy Moss as only receivers with 10 1,000-yard seasons.
Owens also needs one more TD catch for ninth season with 10-plus TD receptions. … Bengals have lost nine in row. Club record is 11 during 1992-93 seasons. … Steelers QB Ben Roethlisberger is 10-4 against Cincinnati. He has thrown three TD passes in each of last three home games. … Steelers WR Hines Ward has 15 career TD catches against Cincinnati, most against any opponent.
Steelers can clinch playoff spot with win and help from variety of teams. … Pittsburgh an NFL-best 225-87-1 (.720) at home since 1970 merger. … Steelers starting first three-game homestand since 1986. This is first time in franchise history they have played three home games in so short a span (12 days). They meet Jets on Dec. 19 and Panthers on Dec. 23. … LB James Harrison needs 1 1/2 sacks for 50 for his career.
2 Comments on "Streaks, Stats and Notes for Sunday vs Cincinnati"
Didnt the Steelers play a 3 game homestand in 2008? Losing to the Colts 20-24, then beating the Chargers 11-10 and then on a Thursay night beating the Bengals 27-10? I think all of those games were in Pittsburgh, unless the Bengal game was on the road?


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Q: Schematic Feedback I am looking for design feedback regarding the following schematic.
The idea is very simple.
The Controller board pulls the relay coil terminal low on the relay board to activate the relay.The relay board is 6 feet away from the controller board.
Once the relay is activated the brushless pump turns on.
The 220uf caps on the 12v line is used to keep the voltage high enough momentarily to have the microcontroller save a value in EEPRom before shutting down.
Looking to hear your comments/feedback.
The relay contact  generates a bit of contact noise upon closure. Attached is the scope shot taken across the relay Common contact as it forms contact with the pump 12v line.
Will the contact noise interfere with the microcontroller function at some point?
Thank you

A: that should work ok.
one possible improvement would to separate the 330uF used before the 5V regulator from the 12V supply using a diode, this stops the the pump sdtart-up current from draining the capacitor, and reduces wear on the relay contacts.

simulate this circuit – Schematic created using CircuitLab


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Q: Can a 2k thermistor be converted to a 10k output? I have a 2k ohm sensor that fits properly but I can not find a proper 10k that fits a M14 hole for the water temperature on my car.
The gauge I am using only reads the NTC 10k thermistor so I was wondering if it was possible to convert the resistance. Bit new to the thermistor world.

A: Simpler idea (thanks, Circuit fantasist), although this version requires that the 2k thermistor be "floating" with respect to ground. See my other answer if that isn't possible.

simulate this circuit – Schematic created using CircuitLab
By reducing the voltage across the actual thermistor to 1/5 of the applied voltage, it draws 1/5 the current from the measuring circuit, and therefore appears to have 5× the resistance.
The current through R1 and R3, while nonzero, will be negligible (less than 1% of the thermistor current).

A: Okay, inspired by Dave (+1), a generic answer that works if one side of the sensor is grounded is to use a Generalized Impedance Converter (GIC), a configuration much beloved by my old professor Adel Sedra. It will work even if the sensor is energized by AC.

simulate this circuit – Schematic created using CircuitLab
As should be obvious from the configuration, the same voltage appears across the 2K sensor as appears across the simulated 10K sensor, so self-heating will be 5x worse.
The impedance as seen at the left port is
\$Z_{in} = \frac{Z_1 Z_3 Z_5}{Z_2 Z_4}\$, in the case of the above circuit R5*5.

A: Generally speaking, no. If you made it read correctly at one temperature it would be very inaccurate at other temperatures.

A: Assuming the resistance-vs-temperature curves are proportional between the two thermistors, it is possible to make a ground-referenced 2k sensor behave like a ground-referenced 10k sensor. It just requires a bit of trickery with current mirrors.

simulate this circuit – Schematic created using CircuitLab
OA1 keeps the voltage across the 2k thermistor (R3) the same as the terminal voltage of the sensing circuit represented by V1. This causes a certain amount of current to flow through R2 and R3.
OA2 keeps the voltages across R1 and R2 the same. Since R1 is 5× the value of R2, this means that only 1/5 the current is required through R1, controlled by Q3.
Q4 mirrors the current through Q3 (these need to be matched transistors, kept at the same temperature, etc.). So, whatever voltage the sensing circuit applies to Q4, it behaves like R3, except with 5× the resistance.