text:
\section{Introduction}

Inflation~\cite{Guth:1980zm,Sato:1980yn,Starobinsky:1980te},
the accelerated expansion of the early universe, is an almost perfect idea
for generating seeds for structure formation as well as resolving several issues in
standard Big Bang cosmology.
Valuable information about the physics of inflation is carried by
the power spectrum and bispectrum of primordial perturbations.
The properties of the primordial curvature perturbations, ${\cal R}$,
can be explored through observations of CMB anisotropies~\cite{Ade:2015lrj}
and are characterized primarily by the amplitude and the spectral index,
which can be translated to information about the shape of the inflaton potential.
Some nonstandard inflation models predict strongly non-Gaussian curvature perturbations~\cite{Chen:2006nt},
and hence can be constrained by the bispectrum of ${\cal R}$~\cite{Ade:2015ava}.
In addition to the curvature perturbations, tensor modes, {\em i.e.},
gravitational waves, are also produced during the phase of the inflationary expansion.
Currently, we have only an upper bound on the tensor-to-scalar ratio $r$,
but primordial gravitational waves could be a smoking gun of inflation if observed in future experiments
of direct detection or CMB B-mode polarization measurements.

In this paper, we study primordial non-Gaussianity of gravitational waves
from inflation.
After the seminal work by Maldacena who computed not only
the scalar 3-point correlation function but also
the tensor 3-point function~\cite{Maldacena:2002vr},
several authors have investigated non-Gaussian signatures of primordial tensor
modes~\cite{Maldacena:2011nz,Soda:2011am,McFadden:2011,Gao:2011vs,Gao:2012ib,Huang:2013epa,Bzowski:2011ab,Zhu:2013fja,Cook:2013xea,Sreenath:2013xra,Noumi:2014zqa,Sreenath:2014nka,Fu:2015vja,Chowdhury:2015cma}.
As tensor non-Gaussianity could in principle be measured {\em e.g.}, via the bispectrum of
B-mode fluctuations, it offers us yet another discriminant among an enormous number of different
inflation models. The purpose of the present paper is therefore
to clarify the features of primordial tensor non-Gaussianities
within a framework involving as many inflation models as possible.

Generalized G-inflation~\cite{Kobayashi:2011nu}
is the general framework to study single-field inflation models
based on the Horndeski theory~\cite{Horndeski:1974wa,Deffayet:2011gz},
which is the most general scalar-tensor theory with
second-order field equations and thus is free from Ostrogradsky ghost instabilities.
Within this generalized G-inflation framework,
the general form of the power spectra of curvature and tensor perturbations
has been obtained in Ref.~\cite{Kobayashi:2011nu}, and
the cubic interactions of ${\cal R}$
have been derived in Refs.~\cite{Gao:2011qe,DeFelice:2011uc,RenauxPetel:2011sb,Ribeiro:2011ax,DeFelice:2013ar}
to evaluate primordial non-Gaussianity of the curvature perturbations.
Tensor 3-point interactions in the Horndeski theory have been classified completely in Ref.~\cite{Gao:2011vs}
and it has been shown that there are only two independent contributions:
the ``standard'' one that is present already in general relativity and generates
squeezed non-Gaussianity, and the other ``nonstandard'' one
predicting equilateral non-Gaussianity that
arises from
the coupling between the Einstein tensor and derivatives of the scalar field.
In particular, the former contribution has the fixed non-Gaussian amplitude
irrespective of an underlying model.

Recently, it was noticed that the Horndeski theory can further be generalized
to higher derivative theories that nevertheless preserve the same propagating degrees of freedom,
{\em i.e.}, two polarizations of gravitational waves and one scalar, and hence
remain free of the Ostrogradsky ghost,
giving Gleyzes-Langlois-Piazza-Vernizzi (GLPV) generalization of the Horndeski
theory~\cite{Gleyzes:2014dya,Gleyzes:2014qga}.
The GLPV theory was then extended to a more general, unifying framework of
scalar-tensor theory by Gao~\cite{Gao:2014soa}.
Linear cosmological perturbations in this general class of models have been
investigated in
Refs.~\cite{Gleyzes:2014dya,Gleyzes:2014qga,Gao:2014soa,Kase:2014cwa,DeFelice:2014bma,DeFelice:2015isa,Fujita:2015ymn}
and non-Gaussianity of the curvature perturbations in Ref.~\cite{Fasiello:2014aqa}.
In this paper, we determine the non-Gaussian features
of primordial tensor perturbations in Gao's unifying framework of general scalar-tensor theories.

This paper is organized as follows.
In the next section, we give a brief review of Gao's unifying framework and extract the terms relevant
to tensor perturbations out of all the possible terms.
In Sec.~III, the linear theory of the tensor perturbations
is presented to give the primordial power spectrum.
Then we move to the cubic action and compute the 3-point correlation functions of tensor modes
in Sec.~IV.
We put rough constraints on non-Gaussianities of tensor modes from
CMB observations in Sec.~V.
Finally, Sec.~VI is devoted to discussions and conclusions.

\section{General Lagrangian for tensor perturbations}

Let us begin with a brief review on the unifying framework of scalar-tensor theories.
The most general scalar-tensor theory with second-order field equations
is given by the Horndeski Lagrangian~\cite{Horndeski:1974wa}. As shown in Ref.~\cite{Kobayashi:2011nu},
it turns out that the Horndeski Lagrangian can be written equivalently in the modern form of
the generalized Galileon~\cite{Deffayet:2011gz} as
\begin{align}
\frac{{\cal L}_H}{\sqrt{-g}}=
G_2(\phi, X)-G_3(\phi,X)\Box\phi+G_4(\phi, X)R^{(4)}+
G_5(\phi, X)G_{\mu\nu}^{(4)}\nabla^\mu\nabla^\nu\phi\cdots,\label{Hor-Cov}
\end{align}
where $R^{(4)}$ and $G_{\mu\nu}^{(4)}$ are the (four-dimensional) Ricci scalar and
the Einstein tensor, respectively, and
we have four arbitrary functions of $\phi$ and $X:=-g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi/2$.
Performing an ADM decomposition by taking $\phi=\;$const hypersurfaces as constant time hypersurfaces,
one obtains the Lagrangian of the form
\begin{align}
\frac{{\cal L}_H}{\sqrt{-g}}&=A_2(t,N)+A_3(t,N)K+
A_4(t,N)\left(K^2-K_{ij}K^{ij}\right)+B_4(t,N)R
\notag \\ &
\quad +A_5(t,N)\left(K^3-3KK_{ij}K^{ij}+2K_{ij}K^{jk}K_{k}^{i}\right)
+B_5(t,N)K^{ij}\left(R_{ij}-\frac{1}{2}g_{ij}R\right),\label{Hor-ADM}
\end{align}
where $K_{ij}$ and $R_{ij}$ are the extrinsic and intrinsic curvature tensors
on the constant $\phi$ hypersurfaces.
The functions of $\phi$ and $X\;(=\dot\phi^2/2N^2)$ in the covariant Lagrangian~(\ref{Hor-Cov})
are now regarded as the functions of the time coordinate $t$ and the Lapse function $N$
in the ADM language.
We thus should have four functions of $t$ and $N$, and indeed
$A_4$, $A_5$, $B_4$, and $B_5$ obey
\begin{align}
A_4=-B_4-N\frac{\partial B_4}{\partial N},
\quad
A_5=\frac{N}{6}\frac{\partial B_5}{\partial N},\label{Hor-rel}
\end{align}
leaving four arbitrary functions as expected.
This is the unitary gauge description of the Horndeski theory
which is particularly useful in the study of cosmology.

The scalar degree of freedom is apparently hidden in the unitary gauge description.
However, variation of~(\ref{Hor-ADM}) with respect to $N$ yields a second-class constraint
eliminating one degree of freedom rather than two.
This fact signifies the presence of the scalar degree of freedom.
One notices here that the
relations~(\ref{Hor-rel}) play no role when counting the degrees of freedom.
Therefore, the degrees of freedom remain the same even if one liberates $A_4$ and $A_5$
from~(\ref{Hor-rel}) and considers the theory with six arbitrary functions of $t$ and $N$.
This trick was first used by Gleyzes {\it et al.}~\cite{Gleyzes:2014dya} to
construct the GLPV scalar-tensor theory beyond Horndeski.
Since the GLPV theory is more general than Horndeski,
the covariant equations of motion are of higher order in general. Nevertheless,
the true propagating degrees of freedom are one scalar and two tensors
as in the Horndeski theory~\cite{Gleyzes:2014dya,Lin:2014jga,Gleyzes:2014qga}.
(Note, however, that counting the degrees of freedom using the unitary gauge Lagrangian
involves subtle points~\cite{Deffayet:2015qwa,Langlois:2015cwa}.)
See also Refs.~\cite{Zumalacarregui:2013pma,Ohashi:2015fma} for attempts to extend the Horndeski theory in different
directions.

The GLPV theory can further be generalized while retaining the number of propagating degrees of freedom
as demonstrated by Gao~\cite{Gao:2014soa,Gao:2014fra}.
The key is to notice that one no longer needs to impose the specific
combinations of $K_{ij}$ and $R_{ij}$ as presented in Eq.~(\ref{Hor-ADM}).
Now one arrives at the unifying framework of scalar-tensor theories
which is given by the sum of three dimensional scalars composed of $K_{ij}$, $R_{ij}$, and
$a_i:=\partial_i\ln N$, with coefficients depending on $t$ and $N$:
\begin{align}
\frac{{\cal L}}{\sqrt{-g}}&=
d_0(t, N)+d_1(t, N)R+d_2R^2+\cdots+d_4a_ia^i+\cdots+\left(a_0+a_1R+\cdots\right)K
\notag \\ & \quad
+\left(a_2R^{ij}+\cdots\right)K_{ij}+b_1K^2+b_2K_{ij}K^{ij}+\cdots
+c_1K^3+c_2KK_{ij}K^{ij}+c_3K_{ij}K^{jk}K_{k}^{i}+\cdots.
\end{align}
The ``six-parameter'' subclass of the above Lagrangian with
\begin{align}
& a_0=A_3, \quad  -2a_1=a_2=B_5, \quad b_1=-b_2=A_4,
\notag\\
&c_1=-c_2/3=c_3/2=A_5, \quad d_0=A_2, \quad d_1=B_4,
\notag\\
&{\rm others}\;=0,
\end{align}
corresponds to
the GLPV theory.
By imposing the further restrictions~(\ref{Hor-rel})
we have the ``four-parameter'' subclass which reproduces the Horndeski theory.
Even (the healthy extension of) Ho\v{r}va gravity~\cite{Horava:2009uw,Blas:2009qj}
is included within this framework.
Among possible terms Gao considers 28 operators satisfying the requirements that
(i) there are no derivatives higher than two when going back to the covariant Lagrangian
and (ii) the number of second-order derivative operators does not exceed three~\cite{Gao:2014soa}.
We shall work in Gao's framework to cover a fairly wide range of single-field inflation models,
and evaluate all possible tensor 3-point functions.
As explained below, the number of operators that are relevant to
tensor perturbations is in fact not as large as 28.

Let us now simplify the Lagrangian before computing
the quadratic and cubic terms of tensor perturbations.
We define the tensor perturbations $h_{ij}$ by
\begin{align}
\textrm{d} s^2&=-\textrm{d} t^2+\gamma_{ij}\textrm{d} x^i\textrm{d} x^j
\notag \\
&= -\textrm{d} t^2+a^2\left(e^h\right)_{ij}\textrm{d} x^i\textrm{d} x^j,
\end{align}
where $(e^h)_{ij}=\delta_{ij}+h_{ij}+(1/2)h_{ik}h_{kj}+\cdots$
and $h_{ij}$ is transverse and traceless.
We simply have $\sqrt{-g}=a^3$ with this definition.
As a consequence of
the traceless and transverse nature of $h_{ij}$, the trace of the extrinsic curvature tensor,
$K\sim \gamma^{ij} \partial_t \gamma_{ij}$, can be written solely in terms of the background quantities.
One sees that the intrinsic curvature scalar $R$ does not contain any first-order terms
up to total derivatives. These facts lead us to
the following 14 terms that are relevant to the tensor perturbations:
\begin{eqnarray}
	\frac{{\cal L}}{\sqrt{-g}}&=&\left(a_1R+a_4R_i^jR_j^i \right)K
	+\left(a_2R_i^j+a_7R_i^kR_k^j \right)K_j^i
	+b_3RK^2+\left(b_2+b_4R \right)K_i^jK_j^i
		\nonumber\\&&
	+\left(b_5KK_i^j+b_6K_i^kK_k^j \right)R_j^i
	+c_2KK_i^jK_j^i+c_3K_i^jK_j^kK_k^i
	 + d_1R+d_3R_i^jR_j^i+d_7R_i^jR_j^kR_k^i.\label{effL1}
\end{eqnarray}
Here, the coefficients may be regarded as the functions of $t$ since we have set $N=1$.
It is convenient to split the extrinsic curvature into the background and perturbation parts as
\begin{eqnarray}
	K_i^j=H\delta_i^j +\delta K_i^j,\label{k-split}
\end{eqnarray}
where $H:=\dot a/a$ and
\begin{eqnarray}
	\delta K_i^j=\frac{1}{2}\dot h_{ij}+\frac{1}{4}\left(h_{ik}\dot h_{kj}-\dot h_{ik}h_{kj}\right)
	+\mathcal O(h^3),
\end{eqnarray}
with a dot standing for differentiation with respect to $t$.
It can be seen directly that $\delta K_i^j$ is traceless, $\delta K_i^i=0$.
Substituting Eq.~(\ref{k-split}) to the Lagrangian~(\ref{effL1})
and extracting the perturbations,
we obtain
\begin{eqnarray}
	\frac{{\cal L}}{\sqrt{-g}}&=&
	\widetilde d_1 R+\widetilde d_3 R_i^jR_j^i + d_7 R_i^jR_j^kR_k^i
	+\widetilde b_2\delta K_i^j\delta K_j^i + c_3\delta K_i^j\delta K_j^k\delta K_k^i
		\nonumber\\&&
	+\widetilde a_2R_i^j\delta K_j^i
	+a_7R_i^jR_j^k\delta K_k^i
	+b_6R_i^j\delta K_j^k\delta K_k^i, \label{eq:relevant action}
\end{eqnarray}
where the coefficients are defined as
\begin{eqnarray}
	\widetilde d_1&=&d_1+\left(3a_1+a_2\right)H+\left(9b_3+3b_4+3b_5+b_6 \right)H^2,
	\\
	\widetilde d_3&=&d_3+\left(3a_4+a_7 \right)H,
	\\
	\widetilde b_2&=& b_2+3\left(c_2+c_3 \right)H,
	\\
	\widetilde a_2&=&a_2+\left(3b_5+2b_6 \right)H.
\end{eqnarray}
Those coefficients are determined
once the concrete form of the Lagrangian is fixed and the background cosmological evolution is obtained.
The reduced
Lagrangian~(\ref{eq:relevant action}) is sufficient for deriving the most general quadratic and cubic
Lagrangians for the tensor perturbations
within Gao's unifying framework of scalar-tensor theories.

In the GLPV subclass, we have only four non-vanishing coefficients,
$\widetilde d_1$, $\widetilde b_2$, $c_3$, and $\widetilde a_2$, all of which are arbitrary.
In the Horndeski case, $\widetilde b_2$ and $c_3$ are fixed by $\widetilde d_1$ and $\widetilde a_2$
via the relations~(\ref{Hor-rel}), and hence we have essentially two functional degrees of freedom,
though all four of these coefficients are still non-vanishing.
Thus, even if one generalizes the Horndeski theory to GLPV,
no new terms appear in the Lagrangian for the tensor perturbations,
though the coefficients can be chosen more freely in the GLPV theory.
The other four terms appear for the first time when going to Gao's framework.
In particular, the $a_7$ and $b_6$ terms are completely new, while
the $\widetilde d_3$ and $d_7$ terms can be found in the specific case of Ho\v{r}ava gravity as well.

\section{Primordial power spectrum with modified dispersion relation}

\subsection{Linear theory}

From Eq.~(\ref{eq:relevant action}) we obtain the quadratic action
for the tensor perturbations~\cite{Gao:2014soa,DeFelice:2014bma,Fujita:2015ymn}:
\begin{eqnarray}
	S&=&\frac{1}{8}\int\textrm{d} t\textrm{d}^3x\;a^3\left[ \mathcal{G}_T\dot h_{ij}^2
	-\frac{\mathcal{F}_T}{a^2}\left(\partial_k h_{ij}\right)^2
	+2\frac{\tilde d_3}{a^4}\left(\partial^2 h_{ij}\right)^2\right],\label{quadaction}
\end{eqnarray}
where
\begin{eqnarray}
	\mathcal{G}_T:=2\widetilde{b}_2,
	\quad
	\mathcal{F}_T:=2\widetilde{d_1}+\dot{\widetilde{a}}_2+H \widetilde{a}_2.
\end{eqnarray}
The third term modifies the dispersion relation.
This term is absent in the Horndeski theory and even in its GLPV generalization,
but it appears
in more general theories in the unifying framework.
The goal of this section is to present the power spectrum of primordial tensor modes
with the modified dispersion relation.
Primordial perturbations with this type of the dispersion relation
have been studied {\em e.g.}, in Refs.~\cite{Martin:2002kt,Ashoorioon:2011eg,Kobayashi:2015gga},
with an emphasis on the curvature perturbation.

Before calculating the linear solution and the power spectrum,
let us comment on the stability conditions derived from the quadratic action~(\ref{quadaction}).
It is required that $\mathcal{G}_T>0$ to avoid ghost instabilities.
We also impose the condition
\begin{eqnarray}
\widetilde d_3\le 0
\end{eqnarray}
in order for the modes with high momenta to be stable.
If ${\cal F}_T>0$ then the tensor perturbations are stable at low momenta as well.
(However, in fact
${\cal F}_T$ can be negative for a short period provided that $\widetilde d_3<0$,
because the instability grows only at low momenta and hence is not catastrophic.)

We move to the Fourier space,
\begin{eqnarray}
	h_{ij}(t,{\bf x})=\int \frac{\textrm{d}^3k}{(2\pi)^3} \tilde h_{ij}(t,{\bf k})e^{i\mathbf{k}\cdot\mathbf{x}},
\end{eqnarray}
and solve the equation of motion for $\widetilde h_{ij}(t,\mathbf{k})$,
\begin{align}
\frac{1}{a^2}\frac{\textrm{d}}{\textrm{d}\eta}\left(a^2{\cal G}_T\frac{\textrm{d}}{\textrm{d}\eta}\widetilde h_{ij}\right)
+\left( {\cal F}_Tk^2-\frac{2\widetilde d_3}{a^2}k^4\right)\widetilde h_{ij}=0,\label{perteq}
\end{align}
where we have introduced the conformal time defined by $\textrm{d}\eta = \textrm{d} t/a$.

To obtain an exact solution to Eq.~(\ref{perteq}) and
manipulate the non-Gaussianity in a tractable way,
we make the following assumptions on the background quantities.
First, the background cosmological evolution is assumed to be exact de Sitter,
so that the scale factor is given by $a=1/H(-\eta)$.
Second, ${\cal F}_T$, ${\cal G}_T$, $\widetilde d_3$, and also
the other coefficients in the Lagrangian~(\ref{eq:relevant action})
are all assumed to be constant.
The second assumption is natural and consistent in view of the first assumption,
though strictly speaking the coefficients of the terms involving $R_{ij}$,
{\em i.e.}, $\widetilde d_1$, $\widetilde d_3$, $\cdots$, can be dependent on time
as the background evolution is insensitive to those coefficients
and is determined by the terms constructed only from $K_{ij}$.

With the above assumptions, the dispersion relation can be written as
\begin{eqnarray}
\omega^2=c_h^2k^2+\epsilon^2k^4\eta^2,
\end{eqnarray}
where we defined the dimensionless quantities
\begin{eqnarray}
c_h^2:=\frac{{\cal F}_T}{{\cal G}_T},
\quad
\epsilon^2:=-2H^2\frac{\widetilde d_3}{{\cal G}_T}.
\end{eqnarray}
The normalized mode solution to the perturbation equation~(\ref{perteq}) is given
in terms of the Whittaker function $W$ by
\begin{eqnarray}
	\psi_{\mathbf{k}}(\eta)=
	\frac{\sqrt{2}}{a}\frac{e^{-\pi c_h^2/8\epsilon}}{\sqrt{-\mathcal{G}_T\epsilon k^2\eta}}
	W\left(\frac{i c_h^2}{4\epsilon},\frac{3}{4},-i\epsilon k^2 \eta^2\right).\label{ex-Whitt}
\end{eqnarray}

In the case of the standard dispersion relation, $\epsilon \to 0$,
which is the case for the GLPV theory as well as Horndeski,
we have
\begin{eqnarray}
\psi_{\mathbf{k}}\to \frac{\sqrt{\pi}}{a}\sqrt{\frac{-\eta}{{\cal G}_T}}H_{3/2}^{(1)}(-c_hk\eta)
\end{eqnarray}
up to a phase factor, where $H_{3/2}^{(1)}$ is the Hankel function of the first kind.
Thus, the familiar mode function is reproduced.
For $\epsilon k^2\eta^2 \gg 1$ with $\epsilon\neq 0$,
$(a\sqrt{{\cal G}_T}/2)\psi_{\mathbf{k}}$ reduces to the positive frequency WKB solution,
\begin{eqnarray}
\frac{a\sqrt{{\cal G}_T}}{2}\psi_{\mathbf{k}}\approx \frac{1}{\sqrt{2\omega}}
\exp\left[-i\int^\eta\omega(\eta')\textrm{d}\eta'\right],
\end{eqnarray}
with $\omega \approx -\epsilon k^2\eta$,
showing that $(a\sqrt{{\cal G}_T}/2)\psi_{\mathbf{k}}$
is indeed canonically normalized. In the opposite, superhorizon limit, $-k\eta\to 0$,
we find
\begin{eqnarray}
\psi_{\mathbf{k}}\to \sqrt{\frac{\pi}{2}}
\frac{e^{-\pi c_h^2/8\epsilon}}{\Gamma(5/4-ic_h^2/4\epsilon)}\frac{H}{{\cal G}_T^{1/2}\epsilon^{3/4}k^{3/2}}
\end{eqnarray}
up to a phase factor.

Using the mode function $\psi_{\mathbf{k}}$, the quantized tensor perturbation can be expanded as
\begin{eqnarray}
	\widetilde{h}_{ij}(t,{\bf k})=\sum_s \left[\psi_{\bf k} e_{ij}^{(s)}({\bf k}) a_s({\bf k})
	+\psi^\ast_{-{\bf k}} e_{ij}^{\ast(s)}(-{\bf k}) a_s^\dagger(-{\bf k})\right],
\end{eqnarray}
where
the transverse and traceless
polarization tensor with the helicity states $s=\pm 2$, $e_{ij}^{(s)}({\bf k})$,
is normalized as
$e_{ij}^{(s)}({\bf k})e_{ij}^{\ast(s')}({\bf k})=\delta_{ss'}$
and has the properties such that
$e_{ij}^{\ast(s)}({\bf k})=e_{ij}^{(-s)}({\bf k})=e_{ij}^{(s)}({\bf -k})$.
The
commutation relation is
given by
$[a_s({\bf k}),~a_{s'}^\dagger({\bf k}')]=(2\pi)^3\delta_{ss'}\delta^{(3)}({\bf k}-{\bf k}')$.
Now we are ready to compute the primordial power spectrum.
First we define ${\cal P}_{ij,kl}(\mathbf{k})$ by
\begin{eqnarray}
	\langle \widetilde{h}_{ij}({\bf k}) \widetilde{h}_{kl}({\bf k}') \rangle= (2\pi)^3\delta^{(3)}({\bf k}+{\bf k}')
	\mathcal{P}_{ij,kl}({\bf k}).
\end{eqnarray}
We have
\begin{eqnarray}
	\mathcal{P}_{ij,kl}({\bf k})=\left| \psi_{\bf k} \right|^2 \Pi_{ij,kl}({\bf k}),
\end{eqnarray}
with
\begin{eqnarray}
\Pi_{ij,kl}({\bf k}):=\sum_s e_{ij}^{(s)}({\bf k})e_{kl}^{\ast(s)}({\bf k}).
\end{eqnarray}
The power spectrum, $\mathcal P_h:=(k^3/2\pi^2)\mathcal P_{ij,ij}$, is then given by
\begin{eqnarray}
	\mathcal{P}_h(k)
	=2 \frac{H^2}{\pi^2} \frac{\mathcal{G}_T^{1/2}}{\mathcal{F}_T^{3/2}}
	|F(\epsilon/c_h^2)|^2 ,
\end{eqnarray}
where we defined
\begin{eqnarray}
F(x):=\frac{\sqrt\pi}{2} \frac{x^{-3/4}e^{-\pi/(8x)} }{\Gamma(5/4-i/(4x))}.
\end{eqnarray}
Since $|F(x)|=1-5x^2/8+{\cal O}(x^4)$, the above expression includes, as the $x\to 0$ limit,
the general result with the standard dispersion relation
derived from generalized G-inflation~\cite{Kobayashi:2011nu}.

\subsection{Small $\epsilon$ expansion of the mode function with modified dispersion relation}

\begin{figure}[tb]
  \begin{center}
    \includegraphics[keepaspectratio=true,height=80mm]{anvsap.eps}
  \end{center}
  \caption{The real part of the exact solution~(\ref{ex-Whitt}) (solid lines) versus
  that of the approximate expression~(\ref{approx}) (dashed lines) as functions of $y\,(=c_hk\eta)$.
  We take (a) $\delta=10^{-2}$ and (b) $\delta=10^{-3}$. It can be seen that
  the approximation is good for $\delta\times y^2\lesssim 1$.
  }%
  \label{fig:anvsap.eps}
\end{figure}

In the next section we compute the 3-point functions
by means of the in-in formalism~\cite{Maldacena:2002vr}.
To do so, one has to integrate products of $\psi_{\mathbf{k}}$ with respect to time.
Unfortunately, this turns out to be impossible in an analytic way if
one directly uses $\psi_{\mathbf{k}}$ written in terms of the Whittaker function.
Therefore, we assume that the modification to the dispersion relation is small,
and expand $\psi_{\mathbf{k}}$ in terms of $\epsilon$.
The approximation allows us to calculate the 3-point functions analytically
in a perturbative manner.

To second order in $\epsilon$, we find, up to a phase factor,
\begin{eqnarray}
	\frac{a{\sqrt{{\cal G}_T}}}{2}\psi_{\mathbf{k}}
	=F(\delta)\frac{e^{-iy+i\delta y^2/2}}{\sqrt{2c_h k}}
	\left[-\frac{i}{y}+1-\frac{\delta}{2}\left(y +iy^2\right)-\delta^2
	\left(\frac{5}{12}y^2+\frac{i}{24}y^3+\frac{1}{8}y^4 \right)+{\cal O}(\delta^3)\right]
	,\label{approx}
\end{eqnarray}
where $y:=c_hk\eta$ and $\delta:=\epsilon/c_h^2$.
The approximation is valid as long as $\delta\times y^2 = \epsilon k^2\eta^2\lesssim 1$,
as is clearly seen from Fig.~\ref{fig:anvsap.eps}.
We use this formula in the following calculations of the 3-point functions of the tensor perturbations.
The same approximation was used in Ref.~\cite{Ashoorioon:2011eg}
to evaluate the effects of nonstandard dispersion relations
on non-Gaussianities of the curvature perturbations.

\section{Cubic interactions and 3-point correlation functions}

\subsection{The cubic action}

Expanding Eq.~(\ref{eq:relevant action}) to third order in $h_{ij}$,
we obtain the following cubic action,
\begin{eqnarray}
S&=&\int\textrm{d} t\textrm{d}^3x\,a^3\biggl\{
\frac{c_3}{8}\dot h_i^j\dot h_j^k\dot h_k^i
+\frac{\mathcal{F}_T}{4a^2}
\left(h_{ik}h_{jl}-\frac{1}{2}h_{ij}h_{kl}\right)h_{ij,kl}
+\frac{a_7}{8a^4} \dot h_k^i \partial^2 h_j^k \partial^2 h_i^j
-\frac{b_6}{8a^2}\dot h_k^i \dot h_j^k \partial^2 h_i^j
\nonumber\\&&\qquad \qquad \quad
+\frac{\widetilde{d}_3}{a^4}\partial^2h_{ij}
\left[
\frac{1}{2}h_{ik,l}h_{jl,k}+h_{kl}\left(h_{ik,lj}-\frac{1}{4}h_{kl,ij}-\frac{1}{2}h_{ij,kl}\right)
\right]
-\frac{d_7}{8a^6}\partial^2 h_i^j\partial^2 h_j^k\partial^2 h_k^i
\biggr\}.\label{3action}
\end{eqnarray}

At this stage, several comments are in order.
It is easy to see that $\widetilde b_2\delta K_i^j\delta K_j^i$
does not contribute to the cubic action.
It is also noted that $\widetilde d_1 R$ and $\widetilde a_2 R_i^j\delta K_j^i$
give rise to the identical terms even at cubic order, leading to
the single combination having the coefficient ${\cal F}_T$.
We are thus left with the above 6 combinations out of the 8 terms in Eq.~(\ref{eq:relevant action}).
If the gravitational sector of the theory is described only by the Einstein-Hilbert term,
only the terms with the coefficient ${\cal F}_T$ remain, and therefore
all the other terms signal theories beyond general relativity.

Now let us look at the Horndeski and GLPV subclass by taking
$a_7=b_6=\widetilde d_3=d_7=0$:
\begin{eqnarray}
S\to\int\textrm{d} t\textrm{d}^3x\,a^3\biggl[
\frac{c_3}{8}\dot h_i^j\dot h_j^k\dot h_k^i
+\frac{\mathcal{F}_T}{4a^2}
\left(h_{ik}h_{jl}-\frac{1}{2}h_{ij}h_{kl}\right)h_{ij,kl}
\biggr].\label{H-GLPV}
\end{eqnarray}
As shown in Ref.~\cite{Gao:2011vs}, we have two independent cubic interactions
in the Horndeski theory. Those correspond to the two contributions displayed in the above action.
We see that no new contributions appear and
we have only the above two even in the GLPV theory beyond Horndeski.
Thus, we conclude that
{\em the tensor bispectrum in the GLPV theory reduces to a combination of
the shapes obtained within the Horndeski theory}~\cite{Gao:2011vs}.

The other four interaction terms newly appear in Gao's framework.
Among them the $\widetilde d_3$ and $d_7$ terms have also been studied
in the context of Ho\v{r}ava gravity~\cite{Huang:2013epa},
though the modification of the mode function due to the nonstandard dispersion relation
has been ignored for simplicity.
It is worth noting that in the case of the standard dispersion relation, $\widetilde d_3=0$,
the $b_6$ term can be recast in the form of the $c_3$ term
by the use of the linear equation of motion and integration by parts.

\subsection{3-point correlation functions}

We turn to evaluate the 3-point correlation functions of the tensor modes.
Although some of the 3-point functions have already been obtained in the literature~\cite{Gao:2011vs,Huang:2013epa},
below we present all the results for completeness. We also evaluate the corrections
arising from the nonstandard dispersion relation.
Using the in-in formalism~\cite{Maldacena:2002vr}, the 3-point functions can be
computed as
\begin{eqnarray}
	\langle
	\widetilde{h}_{i_1j_1}({\bf k}_1)\widetilde{h}_{i_2j_2}({\bf k}_2)\widetilde{h}_{i_3j_3}({\bf k}_3)
	\rangle
	=-i \int_{t_0}^t \textrm{d} t' \left\langle\left[\widetilde{h}_{i_1j_1}(t,{\bf k}_1)
	\widetilde{h}_{i_2j_2}(t,{\bf k}_2)\widetilde{h}_{i_3j_3}(t,{\bf k}_3)
	,~H_\mathrm{int}(t') \right]\right\rangle,
\end{eqnarray}
where $H_{\rm int}$ is the interaction Hamiltonian obtained from the cubic action~(\ref{3action}).
Actually, integration with respect to time is to be performed using the conformal time rather than $t$
from $\eta=-\infty$ to $\eta=0$.
As mentioned earlier, this cannot be done analytically using the exact mode function
written in terms of the Whittaker function~(\ref{ex-Whitt}).
To make this step feasible, we use instead the approximate expression~(\ref{approx}).

For convenience we introduce the non-Gaussian amplitude ${\cal A}_{i_1j_1i_2j_2i_3j_3}$
defined by~\cite{Gao:2011vs}
\begin{eqnarray}
	\langle
	\widetilde{h}_{i_1j_1}({\bf k}_1)\widetilde{h}_{i_2j_2}({\bf k}_2)\widetilde{h}_{i_3j_3}({\bf k}_3)
	\rangle
	=(2\pi)^7 \delta^{(3)}(\mathbf{k}_1+\mathbf{k}_2+\mathbf{k}_3) \frac{\mathcal{P}_h^2}{k_1^3k_2^3k_3^3}
	\mathcal{A}_{i_1j_1i_2j_2i_3j_3},
\end{eqnarray}
where $\mathcal{A}_{i_1j_1i_2j_2i_3j_3}$ is written as a sum of each contribution,
which we compute to order $\epsilon^2$.
It turns out that the corrections due to the nonstandard dispersion relation
start at ${\cal O}(\epsilon^2)$, so that we write
\begin{align}
 \mathcal{A}_{i_1j_1i_2j_2i_3j_3}=\sum_{\bullet = c_3, a_7, \cdots} \left(
 \mathcal{A}^{(\bullet)}_{i_1j_1i_2j_2i_3j_3}+
 \frac{\epsilon^2}{c_h^4}\mathcal{C}^{(\bullet)}_{i_1j_1i_2j_2i_3j_3}
 \right),\label{A-divide}
\end{align}
where $\bullet = c_3, a_7, \cdots$ denotes the corresponding term in the cubic action.

First, the non-Gaussian amplitude arising from the cubic interaction
with the coefficient ${\cal F}_T$ is given by
\begin{align}
{\cal A}_{i_1j_1i_2j_2i_3j_3}^{({\cal F}_T)}&=
\widetilde{\cal A}
	\left\{
	\Pi_{i_1 j_1,ik}({\bf k}_1)\Pi_{i_2 j_2,jl}({\bf k}_2)
	\left[k_{3k}k_{3l}\Pi_{i_3 j_3,ij}({\bf k}_3)-\frac{1}{2}k_{3i}k_{3k}\Pi_{i_3 j_3,jl}({\bf k}_3)\right]
	+\mathrm{5~permutations~of~1,2,3}
	\right\},\label{eq:AGR}
	\\
{\cal C}_{i_1j_1i_2j_2i_3j_3}^{({\cal F}_T)}&=
\widetilde{\cal C}
	\biggl\{
	\Pi_{i_1 j_1,ik}({\bf k}_1)\cdots\biggr\},\label{eq:CGR}
\end{align}
where in ${\cal C}_{i_1j_1i_2j_2i_3j_3}^{({\cal F}_T)}$ the structure constructed from $\Pi_{ij,kl}$
is identical to that in ${\cal A}_{i_1j_1i_2j_2i_3j_3}^{({\cal F}_T)}$ and
\begin{align}
	\widetilde{\mathcal{A}}
	&=\frac{K_t}{16}
	\left(-1 +\frac{K_2}{K^2_t} +\frac{K_3}{K^3_t}\right),
	\\
\widetilde{\cal C}&=\frac{K_t}{8}
 \left(1-\frac{K_2}{K^2_t}+3\frac{K_3}{K^3_t}
	- 2 \frac{K_2^2}{K^4_t} -6 \frac{K_2 K_3}{K^5_t}+6 \frac{K_3^2}{K^6_t}\right).
\end{align}
Here, we introduced the notations
$K_t:=k_1+k_2+k_3$, $K_2:=k_1 k_2+k_2 k_3+k_3 k_1$, and $K_3:= k_1 k_2 k_3$.
Note that ${\cal A}_{i_1j_1i_2j_2i_3j_3}^{({\cal F}_T)}$
is the only term present in the case of general relativity.
Interestingly, this term has the fixed and universal form
and is insensitive to an underlying theory and the inflationary energy scale.
This result strengthens
the statement originally made in the Horndeski theory in Ref.~\cite{Gao:2011vs}.

The concrete expressions for the other amplitudes are obtained as
\begin{align}
\mathcal{A}^{(c_3)}_{i_1j_1i_2j_2i_3j_3}
	&=
	\frac{3 c_3}{8}
	\frac{H}{\mathcal{G}_T}
	\cdot \frac{K_3^2}{K^3_t}
	\Pi_{123},\label{eq:Ac3}
	\\
\mathcal{A}^{(a_7)}_{i_1j_1i_2j_2i_3j_3}
	&=
	\frac{3 a_7}{8}
	\frac{H^3}{\mathcal{G}_T c_h^4}
	\cdot \frac{K_3^2}{K^3_t}
	\left(3+4\frac{K_2}{K^2_t}\right)\Pi_{123},
\label{eq:Aa7}
	\\
\mathcal{A}^{(b_6)}_{i_1j_1i_2j_2i_3j_3}
	&=
	-\frac{3 b_6}{4}
	\frac{H^2}{\mathcal{G}_T c_h^2}
	\cdot \frac{K_3^2}{K^3_t}
	\Pi_{123},\label{eq:Ab6}
	\\
	\mathcal{A}^{(d_7)}_{i_1j_1i_2j_2i_3j_3}
	&=
	\frac{3 d_7}{2}
	\frac{H^4}{\mathcal{G}_T c_h^6}
	\cdot \frac{K_3^2}{K^3_t}
	\left(1+3\frac{K_2}{K^2_t}+15 \frac{K_3}{K^3_t}\right)\Pi_{123},\label{eq:Ad7}
\end{align}
and
\begin{align}
\mathcal{C}^{(c_3)}_{i_1j_1i_2j_2i_3j_3}
	&=
\mathcal{A}^{(c_3)}_{i_1j_1i_2j_2i_3j_3}\cdot 2
\left(1-12 \frac{K_2}{K^2_t}+15 \frac{K_3}{K^3_t}\right)
,
\label{eq:Cc3}
	\\
\mathcal{C}^{(a_7)}_{i_1j_1i_2j_2i_3j_3}
	&=
 \mathcal{A}^{(a_7)}_{i_1j_1i_2j_2i_3j_3}\cdot 2
 \left(27-14 \frac{K_2}{K^2_t}+30\frac{K_3}{K^3_t}
	- 240 \frac{K_2^2}{K^4_t} +210 \frac{K_2 K_3}{K^5_t}\right)
	\left(3+4\frac{K_2}{K_t^2}\right)^{-1}

	,
\label{eq:Ca7}
	\\
\mathcal{C}^{(b_6)}_{i_1j_1i_2j_2i_3j_3}
	&=
\mathcal{A}^{(b_6)}_{i_1j_1i_2j_2i_3j_3}\cdot 2
\left(7-29 \frac{K_2}{K^2_t}+30\frac{K_3}{K^3_t}\right)

	,\label{eq:Cb6}
	\\
	\mathcal{C}^{(d_7)}_{i_1j_1i_2j_2i_3j_3}
	&=
\mathcal{A}^{(d_7)}_{i_1j_1i_2j_2i_3j_3}\cdot 20
\left(1+3 \frac{K_2}{K^2_t}+51\frac{K_3}{K^3_t}
	- 18 \frac{K_2^2}{K^4_t} -126 \frac{K_2 K_3}{K^5_t}+126 \frac{K_3^2}{K^6_t}\right)
	\left(1+3\frac{K_2}{K^2_t}+15 \frac{K_3}{K^3_t}\right)^{-1}

	,\label{eq:Cd7}
\end{align}
where we introduced the shortened notation for the common factor:
$\Pi_{123}:=\Pi_{i_1j_1,ij}({\bf k}_1) \Pi_{i_2j_2,jk}({\bf k}_2) \Pi_{i_3j_3,ki}({\bf k}_3)$.
We see that ${\cal A}_{i_1j_1i_2j_2i_3j_3}^{(c_3)}$ and ${\cal A}_{i_1j_1i_2j_2i_3j_3}^{(b_6)}$
have the same momentum dependences as expected.
Finally,
the $\widetilde d_3$ term itself is a small correction of ${\cal O}(\epsilon^2)$ in our approximation,
so that ${\cal A}_{i_1j_1i_2j_2i_3j_3}^{(\widetilde d_3)} =0$ and
\begin{align}
\mathcal{C}^{(\widetilde d_3)}_{i_1j_1i_2j_2i_3j_3}&=
	\frac{1}{4K_t}\left[1 +\frac{K_2}{K^2_t} +3\frac{K_3}{K^3_t}\right]
	\biggl\{-k_3^2\Pi_{i_3j_3,ij}(\mathbf{k}_3)
	\biggl[\frac{1}{2}\Pi_{i_2j_2,jl}(\mathbf{k}_2) \Pi_{i_1j_1,ik}(\mathbf{k}_1)k_{2l}k_{1k}
	\notag\\& \quad
	+\Pi_{i_2j_2,kl}
	\left(\Pi_{i_1j_1,ik}k_{1l}k_{1j}-\frac{1}{4}\Pi_{i_1j_1,kl}k_{1i}k_{1j}
	-\frac{1}{2}\Pi_{i_1j_1,ij}k_{1k}k_{1l}\right)\biggr]
	+\mathrm{5~permutations~of~1,2,3}\bigg\}.\label{eq:Ad3}
\end{align}

Let us investigate the 3-point correlation functions
between each polarization mode of gravitational waves.
The two polarization modes are expressed as
\begin{eqnarray}
	\xi^{(s)}({\bf k})=\tilde h_{ij}({\bf k}) e_{ij}^{\ast (s)}({\bf k}).
\end{eqnarray}
For the 3-point functions $\langle \xi^{(s_1)}\xi^{(s_2)}\xi^{(s_3)}\rangle$
its amplitude can be evaluated by computing
\begin{eqnarray}
\left\{
\begin{array}{c}
\mathcal A^{s_1s_2s_3}_{(\bullet)} \\
\mathcal C^{s_1s_2s_3}_{(\bullet)}
\end{array} \right\}
=
	e_{i_1j_1}^{\ast (s_1)}({\bf k}_1)
	e_{i_2j_2}^{\ast (s_2)}({\bf k}_2)
	e_{i_3j_3}^{\ast (s_3)}({\bf k}_3)\times
	\left\{
\begin{array}{c}
\mathcal A_{i_1j_1 i_2j_2 i_3j_3}^{(\bullet)}\\
\mathcal C_{i_1j_1 i_2j_2 i_3j_3}^{(\bullet)}
\end{array} \right\}.
\end{eqnarray}
It is straightforward to obtain the following amplitudes,
\begin{align}
	\mathcal{A}^{s_1 s_2 s_3}_{({\cal F}_T)}
	&=
	\widetilde{\mathcal{A}}
	\cdot F^{s_1 s_2 s_3}_{({\rm GR})},
	\\
	\mathcal{A}^{s_1 s_2 s_3}_{(c_3)}
	&=
	\frac{3 c_3}{8}
	\frac{H}{\mathcal{G}_T }
	\cdot \frac{K_3^2}{K^3_t}
	F^{s_1 s_2 s_3}_{({\rm H})},
	\\
	\mathcal{A}^{s_1 s_2 s_3}_{(a_7)}
	&=
	\frac{3 a_7}{8}
	\frac{H^3}{\mathcal{G}_T c_h^4}
	\cdot \frac{K_3^2}{K^3_t}
	\left(3+4\frac{K_2}{K^2_t}\right)
	F^{s_1 s_2 s_3}_{({\rm H})},
	\\
	\mathcal{A}^{s_1 s_2 s_3}_{(b_6)}
	&=
	-\frac{3 b_6}{4}
	\frac{H^2}{\mathcal{G}_T c_h^2}
	\cdot \frac{K_3^2}{K^3_t}
	F^{s_1 s_2 s_3}_{({\rm H})},
	\\
	\mathcal{A}^{s_1 s_2 s_3}_{(d_7)}
	&=
	\frac{3 d_7}{2}
	\frac{H^4}{\mathcal{G}_T c_h^6}
	\cdot \frac{K_3^2}{K^3_t}
	\left(1+3\frac{K_2}{K^2_t}+15 \frac{K_3}{K^3_t}\right)
	F^{s_1 s_2 s_3}_{({\rm H})},
\end{align}
and
\begin{align}
\mathcal{C}^{s_1 s_2 s_3}_{{\cal F}_T}
&=
\widetilde {\cal C}\cdot F_{({\rm GR})}^{s_1s_2s_3},
\\
	\mathcal{C}^{s_1 s_2 s_3}_{(c_3)}
	&=
\mathcal{A}^{s_1 s_2 s_3}_{(c_3)}\cdot 2
\left(1-12 \frac{K_2}{K^2_t}+15 \frac{K_3}{K^3_t}\right)
,
	\\
	\mathcal{C}^{s_1 s_2 s_3}_{(a_7)}
	&=
 \mathcal{A}^{s_1 s_2 s_3}_{(a_7)}\cdot 2
 \left(27-14 \frac{K_2}{K^2_t}+30\frac{K_3}{K^3_t}
	- 240 \frac{K_2^2}{K^4_t} +210 \frac{K_2 K_3}{K^5_t}\right)
	\left(3+4\frac{K_2}{K_t^2}\right)^{-1}
,
	\\
	\mathcal{C}^{s_1 s_2 s_3}_{(b_6)}
	&=
\mathcal{A}^{s_1 s_2 s_3}_{(b_6)}\cdot 2
	\left(7-29 \frac{K_2}{K^2_t}+30\frac{K_3}{K^3_t}\right)
,
	\\
	\mathcal{C}^{s_1 s_2 s_3}_{(d_7)}
	&=
	\mathcal{A}^{s_1 s_2 s_3}_{(d_7)}\cdot 20
 \left(1+3 \frac{K_2}{K^2_t}+51\frac{K_3}{K^3_t}
	- 18 \frac{K_2^2}{K^4_t} -126 \frac{K_2 K_3}{K^5_t}+126 \frac{K_3^2}{K^6_t}\right)
		\left(1+3\frac{K_2}{K^2_t}+15 \frac{K_3}{K^3_t}\right)^{-1}
,
	\\
	\mathcal{C}^{s_1 s_2 s_3}_{(\widetilde d_3)}
	&=
	\frac{1}{4K_t}\left(1 +\frac{K_2}{K^2_t} +3\frac{K_3}{K^3_t}\right)
	F^{s_1 s_2 s_3}_{(\widetilde d_3)},
\end{align}
where we defined
\begin{eqnarray}
	F^{+++}_{({\rm GR})}
	&:=&
	\frac{1}{128} \cdot \frac{K^8_t}{K_3^2}\left(1 -4\frac{K_2}{K^2_t} +8\frac{K_3}{K^3_t}\right),
	\\
		F^{+++}_{({\rm H})}
	&:=&
	\frac{1}{64} \cdot \frac{K^6_t}{K_3^2}\left(1 -4\frac{K_2}{K^2_t} +8\frac{K_3}{K^3_t}\right),
	\\
	F^{+++}_{({\widetilde d_3})}
	&:=&
	\frac{1}{256} \cdot \frac{K^{10}_t}{K_3^2}
	\left(1 -10\frac{K_2}{K^2_t} +28\frac{K_3}{K^3_t} +24\frac{K_2^2}{K^4_t}
	-128\frac{K_2 K_3}{K^5_t} +160\frac{K_3^2}{K^6_t}\right),
\end{eqnarray}
and when spins are mixed the corresponding functions can be derived from
$F^{++-}_{({\rm GR}, {\rm H}, \widetilde d_3)}(k_1,k_2,k_3)=F^{+++}_{({\rm GR}, {\rm H}, \widetilde d_3)}(k_1,k_2,-k_3)$.
Note the relations
\begin{eqnarray}
	F^{+++}_{({\rm GR})}&=&\frac{K^2_t}{2}F^{+++}_{({\rm H})},
	\\
	F^{+++}_{({\widetilde d_3})}
	&=&\frac{K^{10}_t}{4}\left(1-6\frac{K_2}{K^2_t}+20\frac{K_3}{K^3_t}\right)F^{+++}_{({\rm H})}.
\end{eqnarray}
Since theories in Gao's framework do not violate the parity symmetry, we have the properties
$F^{++-}_{({\rm GR}, {\rm H}, \widetilde d_3)}=F^{--+}_{({\rm GR}, {\rm H}, \widetilde d_3)}$ and
$F^{---}_{({\rm GR}, {\rm H}, \widetilde d_3)}=F^{+++}_{({\rm GR}, {\rm H}, \widetilde d_3)}$.
In the equilateral configuration, we have
\begin{align}
	&F^{++-}_{({\rm H})}=F^{+-+}_{({\rm H})}=F^{-++}_{({\rm H})}=\frac{1}{9}F^{+++}_{({\rm H})},
	\\
	&F^{++-}_{({\rm GR})}=F^{+-+}_{({\rm GR})}=F^{-++}_{({\rm GR})}=\frac{1}{81}F^{+++}_{({\rm GR})},
	\\
	&F^{++-}_{(\widetilde d_3)}=F^{+-+}_{(\widetilde d_3)}=F^{-++}_{(\widetilde d_3)}
	=\frac{13}{189}F^{+++}_{(\widetilde d_3)},
\end{align}
while in the squeezed limit ${\bf k}_3\to 0$ we find
\begin{align}
	&F_{({\rm GR},\widetilde d_3)}^{+++} \approx  F_{({\rm GR},\widetilde d_3)}^{++-}\approx -\frac{k_1^2}{2},
	\\
	&F_{({\rm GR})}^{+-+} \approx F_{({\rm GR})}^{-++}\approx -\frac{k_3^4}{32k_1^2},
	\\
	&F_{(\widetilde d_3)}^{+-+} \approx  F_{(\widetilde d_3)}^{-++}\approx -\frac{7k_3^4}{32k_1^2}.
\end{align}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{AGR+++.eps}
\caption{$\mathcal A^{+++}_{({\cal F}_T)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:AGR+++}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ac3+++.eps}
\caption{$\mathcal A^{+++}_{(c_3)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Ac3+++}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Aa7+++.eps}
\caption{$\mathcal A^{+++}_{(a_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Aa7+++}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ab6+++.eps}
\caption{$\mathcal A^{+++}_{(b_6)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.}
\label{fig:Ab6+++}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ad7+++.eps}
\caption{$\mathcal A^{+++}_{(d_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Ad7+++}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{AGR++-.eps}
\caption{$\mathcal A^{++-}_{({\cal F}_T)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:AGR++-}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ac3++-.eps}
\caption{$\mathcal A^{++-}_{(c_3)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Ac3++-}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Aa7++-.eps}
\caption{$\mathcal A^{++-}_{(a_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Aa7++-}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ab6++-.eps}
\caption{$\mathcal A^{++-}_{(b_6)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Ab6++-}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ad7++-.eps}
\caption{$\mathcal A^{++-}_{(d_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Ad7++-}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{CGR+++.eps}
\caption{$\mathcal C^{+++}_{({\cal F}_T)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:CGR+++}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cc3+++.eps}
\caption{$\mathcal C^{+++}_{(c_3)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Cc3+++}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ca7+++.eps}
\caption{$\mathcal C^{+++}_{(a_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Ca7+++}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cb6+++.eps}
\caption{$\mathcal C^{+++}_{(b_6)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	.}
\label{fig:Cb6+++}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cd7+++.eps}
\caption{$\mathcal C^{+++}_{(d_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Cd7+++}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cd3+++.eps}
\caption{$\mathcal C^{+++}_{(\widetilde d_3)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Cd3+++}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{CGR++-.eps}
\caption{$\mathcal C^{++-}_{({\cal F}_T)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:CGR++-}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cc3++-.eps}
\caption{$\mathcal C^{++-}_{(c_3)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Cc3++-}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Ca7++-.eps}
\caption{$\mathcal C^{++-}_{(a_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Ca7++-}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cb6++-.eps}
\caption{$\mathcal C^{++-}_{(b_6)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Cb6++-}
\end{figure}

\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cd7++-.eps}
\caption{$\mathcal C^{++-}_{(d_7)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Cd7++-}
\end{figure}
\begin{figure}[H]
\centering\includegraphics*[width=6.0cm,keepaspectratio,clip]{Cd3++-.eps}
\caption{$\mathcal C^{++-}_{(\widetilde d_3)}(1,k_2/k_1,k_3/k_1) (k_2/k_1)^{-1}(k_3/k_1)^{-1}$
as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to 1
for equilateral configurations $k_2/k_1=k_3/k_1=1$.	}
\label{fig:Cd3++-}
\end{figure}

The configuration dependences of all the ``$+++$'' and ``$++-$''
amplitudes and the corresponding ${\cal O}(\epsilon^2)$ corrections
are shown in Figs.~\ref{fig:AGR+++}--\ref{fig:Cd3++-}.
At leading order in $\epsilon$ expansion, we find that only
the contribution from ${\cal F}_T$ term, {\em i.e.},
${\cal A}_{({\cal F}_T)}^{+++}$,
peaks in the squeezed limit, while all the other
${\cal A}_{(\bullet)}^{+++}$'s peak in the equilateral configuration.
We emphasize again that ${\cal A}_{({\cal F}_T)}^{+++}$ {\em is a fixed and universal feature
even for single-field inflation models beyond Horndeski}.
In other words, it is impossible to suppress or enhance ${\cal A}_{({\cal F}_T)}^{+++}$ even in
the present general framework beyond Horndeski as long as the effect of the modified
dispersion relation is small.
It would therefore be of great interest to explore this ``consistency relation''
with CMB B-mode observations such as LiteBIRD~\cite{Matsumura:2013aja}.
When spins are mixed, the momentum dependences of
${\cal A}_{(\bullet)}^{++-}\;(\bullet = c_3, a_7, b_6, d_7)$ are
similar to each other and their peaks
are located between the equilateral and squeezed configurations.
As for the corrections of ${\cal O}(\epsilon^2)$,
it can be seen that they have momentum dependences similar to
their leading order counterparts, namely,
the relative changes in the amplitudes have mild momentum dependences,
as is also the case for the curvature perturbation~\cite{Ashoorioon:2011eg}.
However, ${\cal C}_{(\widetilde d_3)}^{+++}$
shows the peak at a squeezed shape, breaking
the uniqueness of ${\cal A}_{({\cal F}_T)}^{+++}$'s momentum dependence at this order.
Therefore, it would be interesting to investigate the case
where the effect of the modification to the dispersion relation
cannot be treated perturbatively.\footnote{The 3-point function of the
curvature perturbations has been evaluated
when the $k^4$ term is dominant in the context of ghost inflation~\cite{ArkaniHamed:2003uz}.}

\section{Constraints from CMB observations}

We can roughly estimate the constraints on the parameters of the theory by comparing
the results obtained in the previous section with the Planck results~\cite{Ade:2015ava,Ade:2015lrj}.
Schematically, one has
\begin{eqnarray}
	\frac{\langle hhh\rangle}{\langle hh\rangle\langle hh\rangle}
	\sim \sum\frac{{\cal A}_{(\bullet)}^{s_1s_2s_3}}{k_1 k_2 k_3}
	=\sum\frac{{\cal A}_{(\bullet)}^{s_1s_2s_3}(1,k_2/k_1,k_3/k_1)}{(k_2/k_1)(k_3/k_1)},
	\label{eq:plotted}
\end{eqnarray}
where the quantities in the right hand side are presented in the previous section.
It is reasonable to assume that
\begin{eqnarray}
	 \langle hhh\rangle  \lesssim \langle \mathcal R\mathcal R\mathcal R\rangle,
\end{eqnarray}
where ${\cal R}$ is the curvature perturbation. (Otherwise,
the dominant source of non-Gaussianity in the CMB comes from the tensor modes,
but if so $\langle hhh\rangle$ can be constrained directly from CMB observations.)
Then, using the tensor-to-scalar ratio $r=\langle hh\rangle/\langle {\cal R}{\cal R}\rangle$
and the nonlinearity parameters $f_{\rm NL}^{\cal R}$, we have
\begin{eqnarray}
	\frac{{\mathcal A}_{(\bullet)}^{s_1s_2s_3}}{k_1 k_2 k_3}\lesssim
	\frac{\langle \mathcal R\mathcal R\mathcal R\rangle}{\langle hh\rangle\langle hh\rangle}
	=\frac{1}{r^2}
	\frac{\langle \mathcal R\mathcal R\mathcal R\rangle}
	{\langle\mathcal R\mathcal R \rangle\langle \mathcal R\mathcal R\rangle}
	\sim \frac{f_\mathrm{NL}^{\mathcal R}}{r^2},
\end{eqnarray}
where we have made the second assumption that different ${\mathcal A}_{(\bullet)}^{s_1s_2s_3}$'s
do not cancel each other.
Thus, we obtain the constraint
\begin{eqnarray}
	\frac{{\mathcal A}_{(\bullet)}^{s_1s_2s_3}}{k_1 k_2 k_3}\lesssim \frac{f_\mathrm{NL}^{\mathcal R}}{r^2}
	\sim 10^3 \left(\frac{r}{0.1}\right)^{-2}\left(\frac{f_\mathrm{NL}^{\mathcal R}}{10}\right),
\end{eqnarray}
which is translated to
\begin{align}
\frac{c_3H }{{\cal G}_T},\;
\frac{a_7H^3}{{\cal G}_Tc_h^4},\;
\frac{b_6H^2}{{\cal G}_Tc_h^2},\;
\frac{d_7H^4}{{\cal G}_Tc_h^6}
\lesssim
10^3 \left(\frac{r}{0.1}\right)^{-2}\left(\frac{f_\mathrm{NL}^{\mathcal R}}{10}\right),
\end{align}
or, equivalently,
\begin{align}
\frac{c_3c_h}{H},\; \frac{a_7H}{c_h^3},\;\frac{b_6}{c_h},\;\frac{d_7H^2}{c_h^5}
\lesssim
10^{13} \left(\frac{r}{0.1}\right)^{-3}\left(\frac{{\cal P}_{\cal R}}{10^{-9}}\right)^{-1}
\left(\frac{f_\mathrm{NL}^{\mathcal R}}{10}\right),
\end{align}
where ${\cal P}_{\cal R}$ is the power spectrum of the curvature perturbation.
Note the mass dimensions of the coefficients: $[c_3]=1,~[b_6]=0,~[a_7]=-1,$ and $[d_7]=-2$.
Thus, the current constraints are very weak.

\section{Discussions and Conclusions}

In this paper, we have clarified primordial non-Gaussianities of tensor modes
by computing the tensor 3-point functions within the unifying framework of
scalar-tensor theories~\cite{Gao:2014soa}.
The framework includes the Horndeski theory and recent GLPV generalization
as specific cases.
We have shown that no new terms appear in the cubic Lagrangian
even if one goes to the GLPV theory beyond Horndeski.
In more general theories beyond GLPV, we have found four new interactions, one of which
is related to the modification of the dispersion relation in the linear theory.
The impact of this modification of the dispersion relation can be parametrized
using a small parameter $\epsilon$,
and we have computed the 3-point functions analytically by
treating $\epsilon$ as a small expansion parameter.
Two of the four new terms beyond GLPV have already been studied
to leading order in $\epsilon$ in the context of Ho\v{r}ava gravity~\cite{Huang:2013epa},
and our results are in agreement with those in Ref.~\cite{Huang:2013epa} where they overlap.
In Ref.~\cite{Gao:2011vs} it was found that
there are only two independent terms in the cubic Lagrangian within Horndeski:
the standard one present already in general relativity
generating squeezed non-Gaussianity with the {\em fixed} amplitude
and the other nonstandard one predicting equilateral non-Gaussianity.
We have strengthened this statement by showing that
at leading order in the $\epsilon$ expansion
the squeezed non-Gaussianity is only generated by
this ``standard'' cubic term and has the fixed amplitude, ${\cal A}_{({\cal F}_T)}^{+++}$,
even in the general unifying framework of scalar-tensor theories.
At leading order in $\epsilon$ all the other non-Gaussian amplitudes
peak at equilateral shapes.
The ``standard'' interaction is quite likely to be present
in the cubic Lagrangian because it can easily be generated from
the term linear in the Ricci scalar.
The fixed and universal nature of ${\cal A}_{({\cal F}_T)}^{+++}$
thus provides us the ``consistency relation'' in the primordial tensor sector.
Any detection of the equilateral tensor non-Gaussianity
would imply the nonstandard interactions between gravity and the scalar degree of freedom,
though it is difficult to distinguish among different contributions.
Note that the inverse is not true;
even in the absence of equilateral non-Gaussianity,
gravity could be modified significantly from general relativity,
because one can consider various nonstandard interactions that
do not affect the tensor sector, as well as $R_i^j\delta K_j^i$.

We have found that the effects of the modified dispersion relation
appear in the non-Gaussian amplitudes at ${\cal O}(\epsilon^2)$.
The momentum dependences of the correction $\mathcal{C}_{(\bullet)}^{s_1s_2s_3}$
are similar to their leading order counterparts $\mathcal{A}_{(\bullet)}^{s_1s_2s_3}$.
It should be noted that the correction to the squeezed non-Gaussianity,
$\mathcal{C}_{({\cal F}_T)}^{s_1s_2s_3}$, breaks its fixed and universal nature.
Therefore, detection of squeezed tensor non-Gaussianity whose amplitude
is different from ${\cal A}_{({\cal F}_T)}^{+++}$ would
imply a significant higher order term in the dispersion relation
or the tensor modes of non-inflationary origin.

Let us mention here some other sources of gravitational waves from the early universe,
as it would be interesting to explore tensor non-Gaussian signatures of such origin
in order to contrast them with the results in this paper.
A spectator scalar field other than inflaton can produce gravitational waves~\cite{Biagetti:2013kwa},
though it is difficult to expect large amplitudes~\cite{Biagetti:2014asa,Fujita:2014oba}.
Large tensor modes are produced, {\em e.g.}, by
self-ordering of multi-component scalar fields after a global phase
transition~\cite{JonesSmith:2007ne,Fenu:2009qf,Giblin:2011yh,Figueroa:2012kw,Kuroyanagi:2015esa}.
Vector fields can also source gravitational waves during inflation~\cite{Mukohyama:2014gba,Barnaby:2010vf}.
We hope that we will come back to the issue of
non-Gaussian signatures of those gravitational waves in future publications.

Finally, it should be noted that by construction the present analysis
does not cover multi-field inflation models. Though the multi-field effects
in the tensor sector are expected to be small, it would be interesting
to investigate whether one can discriminate single- and multi-field models
using primordial non-Gaussianity of tensor modes.

\acknowledgments
This work was supported in part by the JSPS Grant-in-Aid for Scientific
Research Nos.~24740161 (T.K.) and
MEXT KAKENHI No.~15H05888 (T.K.).

redpajama_set_name: RedPajamaArXiv


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text:
package com.buglee.dailysentence;

import android.app.Application;
import android.content.Context;

/**
 * Created by LEE on 2017/7/24 0024.
 */

public class App extends Application {
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    @Override
    public void onCreate() {
        super.onCreate();
        mContext = getApplicationContext();
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    public static Context getContext() {
        return mContext;
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}

redpajama_set_name: RedPajamaGithub


"The samadhi naturally experienced at rebirth comes to the videha yogis (who die after perfecting the ecstatic meditation) and prakriti-laya yogis ( who have accomplished the meditation accompanied by "I-am-ness") having dissolved the awareness of matter but without the final self-realization." Swami Veda Bharati.
Explanation: There are some practitioners of yoga who attain very advanced levels of meditative experience. Those who naturally and easily enter samadhi are re-born very accomplished yogis from birth. Yet, being born with the ability to enter samadhi does not mean that the yogi has attained the final enlightenment. Such yogis then can take up practice again to move farther toward complete union with the Ultimate.
Explanation: After attaining the previous, samprajñata samadhi, and through supreme non-attachment, Para-vairagya, the practitioner may attain a arrested state of mind known as nirvîja samadhi, in which the concentration is without an object. When the concentration on arrested state of mind becomes habitual, it is called asamprajñata samadhi and this may lead to kaivalya, in which the Seer rests in its own nature without the presence of the I-sense—the state of liberation.
Explanation: As was stated previously, when the mind becomes still, the Seer rests in his own nature. But so long as the mind is attached to nature, the stillness of mind, though attained, is broken again as the mind craves. As a practitioner practices vairagya, his/her non-attachment slowly extends to more things. When the practice of dispassion/non-attachment extends all the way to the most subtle building-blocks of nature (called gunas), so that the practitioner does not crave even them, that is called paravairagya, supreme dispassion. It is this supreme non-attachment that allows the mind to finally remain still without seeking the satisfaction of cravings. This is the culmination of knowledge and the entrance to liberation.
A further very good explanation is given Here.
Explanation: This sutra defines vairagya, dispassion or non-attachment. Non-attachment is built up through a process. At first one seeks to begin building strength to resist attraction and attachment by limiting indulgence. Once that is successful, then one can eliminate certain sensual enjoyments and strengthen a spirit of renunciation. As the practitioner becomes increasingly aware of the benefits of this practice, the will strengthens, and one can further increase his dispassion. This sutra makes it clear that mastery means not being attached to not only sensual enjoyment experience but also things heard about from the scriptures. Direct experience of the effects of attachment and of the peace when there isn't attachment increases the strength of detachment.


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Baka (or Baq'a) is a beautiful, green neighbourhood located in the South West of Jerusalem. Whilst Baka is mainly residential, it is fantastically well located in terms of local amenities, being within a short walk/drive to many local points of interest. Nearby attractions include the First Station (a complex of restaurants, cafes and shops), the Park HaMesila (the former train track, now converted to a great park), The Jerusalem Theatre, not to mention the close proximity to the Old City (30-40 min walk or free shuttle bus from the First Station).
Baka was somewhat rundown for many years, but has seen a resurgence, with some of the most luxurious developments and homes in the city being built and renovated there. That being said, there are still plenty of large blocks that have apartments that can be obtained at reasonable prices, though these tend to be somewhat older blocks.
As a quiet residential area there's not much of note within, but Baka is bordered on all sides with some great amenities. To the West; the "Rakevet" (see below) and the German Colony's Emek Refaim Street with its shops & restaurants. The North; The First Station and Yes Planet (cinema complex), to the East the trendy shops and cafes that line Derech Beit Lechem and finally to the south, the shops and supermarkets of Talpiot.
The streets of Baka are named for the twelve tribes, plus a sprinkling of other Biblical figures that managed to sneak in (Shimshon, Gidon and Boaz).
For around 60 years, Baka was home to the 'famous' Ulpan Etzion, the hebrew language school that has had it's doors open since the founding of the state. The end of 2008 saw the transfer of the school to it's new facility in the Beit Canada centre in Armon HaNetziv in the south east of the city..
Baka has developed a reputation for luxurious property, and rightly so, but affordable apartments do exist within the area too. The neighbourhood is home to what can only be referred to as mansions, often located in Baka's quiet leafy backstreets. These properties can command 7-8 figure prices in both shekel and dollar amounts and having been lucky enough to visit many of these, the price is certainly justified for those that have the budget.
Baka has a number of new construction projects, such as Bustan Baka and Park8 with additional projects in the pipeline. We are also seeing a number of TAMA 38 projects being undertaken in the neighbourhood. These projects see brand new apartments being added to existing buildings in return for upgrading them to current earthquake resistance standards. These properties can often be obtained at a discount if you are willing to buy them 'off-plan' but have construction schedules that are significantly faster than a development that is being planned and built from scratch.
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Baka is a largely residential zone and as such, there's not much in the way of entertainment here, but that's not to say it can't be found close by with both the 'Tachana Rishona' and the Yes Planet cinema complex being located within easy walking distance of the area.
Derech Beit Lechem Street is also home to a lively cafe scene, with some great options like Grand Cafe or Kalo. The street is also home to an annual street fair, which shuts the road down to car traffic and brings in food stands, street performers and musicians for a fun filled evening.
Way back when, Jerusalem used to have a train line that ran through Baka. When the train stopped running, the track was abandoned and left desolate as a scar running through the neighbourhood, but in 2010, work commenced to turn the tracks into a park. Now spanning over 7km with a bicycle path and a running track, the park is always busy, particularly in the evenings, when the city's exercise fanatics are out in force.


Peru face Scotland in the first of three friendlies before they head to Russia for the World Cup, where they will kick off their tournament against Denmark.
As for Scotland, after being denied a playoff spot during their qualifying campaign, The Tartan Army have turned to former boss Alex McLeish to help rebuild a very inexperienced squad. With the likes of Stuart Armstrong, Allan McGregor, Matt Ritchie, and Ryan Fraser all withdrawing from the squad, Alex McLeish will travel to the Estadio Nacional de Lima with an incredibly young team. Although Scotland are coming off the back of a 1-0 win against Hungary, The Scots have now only managed to win two of their last six.


text:
Prosecutor Maizitis warns of further criticism
By The Baltic Times
RIGA 's Prosecutor General Janis Maizitis, under increasingly intensive fire from a local newspaper, said on Wednesday that prosecutors may face increased counter-actions and "attempts to upset their psychological balance."
Speaking at a meeting of top prosecutors, Maizitis repeated that he himself had received warnings and "opinions about which course of action I should take as regards to work of the prosecutor's office and its further development."
If he had heeded those warnings, he said, he would have violated basic principles of prosecutors' ethics. "I responded as was proper for a prosecutor general in such situation. The reaction was a promise of very negative publicity about my work," he said.
Maizitis said recent reports on his activities had been biased but pointed out that prosecutor general must be prepared to hear criticism.
Most of the criticism has come from the Neatkariga Rita Avize daily, which is generally supportive of the interests of a group of Ventspils-based businessmen and politicians, particularly Mayor Aivars Lembergs. The paper is hounding Maizitis for sharing information on an investigation that concerned a U.S. company with a former U.S. ambassador, though the real source of dissatisfaction, many observers believe, has to do with the prosecutor's attempts to solicit information about the owners of a number of offshore shell companies from Swiss authorities.
Maizitis stressed that no major investigation in past or present had been stopped as a result of the pressure he has felt. "This year I also hope for specific results in cases entailing great public interest," he said.
"We must not forget that most mass media in Latvia are privately-owned as befits a democratic country," he added.
Baltic Security Foundation established to promote regional defense synchronization
Estonian PM in Georgia for Eastern Partnership 10th anniversary conference
Lithuanian MPs to consider their response to Russia's PACE return
Two Russian Tu-160 strategic bombers carry out patrolling mission over Baltic Sea
Lithuanian president to meet with Mission Siberia team
Defense Ministry has approached 12 countries regarding armored vehicles procurement
Estonian MEP Paet: Turkey's missile purchase from Russia creates tensions with NATO

redpajama_set_name: RedPajamaCommonCrawl


Stout Foundation; Polytechnic Advantage. Board Regents System Educational Communications. Research teaching materials collected Politiken about matters both world individual. Kira Sopsic River Falls Over winter. Short range minute minutes long. Madison photos, pictures, views. Offering free tampons MEN'S.


This water resistant product has all the characteristics to help add both charm and value to any home! It is the perfect laminate flooring for all living areas, it's hygienic, durable and easy to care for and is perfect for bathroom or kitchen use. With an AC4 heavy domestic rating, and a 4-sided v-groove to help define each individual plank, this Oak floor will complement many interiors.
The product is ideal for heavy domestic use and moderate commercial use and can also withstand the use of steam cleaners and other heavy water exposure without running the risk of de-laminating.
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Review Summary - 4.6 out of 5 based on 9 ratings.
The colour is very nice and matches perfectly with what I have in the other rooms. The packs have arrived on the specified day and some of them were damaged. I have called the company and said that they will send a replacement packs.
It matches with the colour of flooring from the other rooms.
Good quality laminate. Realistic oak effect with a slightly textured surface. Excellent service from Discount Flooring.
I ordered three laminate floor samples to get an idea of colours for my flooring. It's always hard to tell what things look like online so I was pleased this service was offered. So quick and easy! Free samples and delivery. Arrived in less than 48 hours, no problems at all. The flooring looks good quality, realistic wood effect. This colour is a classic oak effect that you see frequently, seems very popular. Not too dark but quite warm in tone. I have similar in my home at the moment and wanted to lean to a more neutral look. I was glad I got to see a sample in order to make that decision.
This laminate is a medium light oak. Definately honey brown not orangey. Dull not glossy. Looks good like real wood and sample was cut so that you could see how easy it was to connect to other laminate sample pieces. Just marginally lighter than 'Northline'.
This was one of a sample of three pieces of hydro guard laminate and looks to be of very good quality and gives a good idea of colour. Thank you.


Description ROCK2 Full-Length MS Protein Standard (NP_004841), Labeled with [U- 13C6, 15N4]-L-Arginine and [U- 13C6, 15N2]-L-Lysine, was produced in human 293 cells (HEK293) with fully chemically defined cell culture medium to obtain incorporation efficiency at Creative-Proteomics. The protein encoded by this gene is a serine/threonine kinase that regulates cytokinesis, smooth muscle contraction, the formation of actin stress fibers and focal adhesions, and the activation of the c-fos serum response element. This protein, which is an isozyme of ROCK1 is a target for the small GTPase Rho.


text:
Oleg Valeryevich Kukhta (, born 27 December 1970) is a Russian singer-songwriter, actor, former Spetsnaz GRU officer, and military intelligence man. He was titled an Honored Artist of Russia in 2008.

Early life
Oleg Kukhta was born 27 December 1970 in Kinel-Cherkassy, Samara Oblast, Russian SFSR. When he was four years old, his family moved to Pervouralsk in Sverdlovsk Oblast.

Military career
In 1988, he began his studies at the Higher Airborne Command School (Military Institute) in Ryazan. In 1990–1992 he interrupted his studies for service in the army. 1992–1993 he took part in the peacekeeping mission in the Republic of Serbian Krajina. 1994–1996 he continued his studies at the Higher Airborne Command School in Ryazan and at the Military Command Academy in Novosibirsk. He then took part in the First Chechen War (1994 to 1996) as commander of Spetsnaz GRU group. During the war he carried out many military operations, suffered a severe wound and was awarded the Order of Courage and medals. In 1999, he finished his military career and became a senior lieutenant in the Spetsnaz reserve.

Musical career
He began his artistic career as an amateur singer during military service. In 1994, he became the first winner and 1995 Grand Prix winner of the All-Russian Military Song Festival "Victoria". In 1999, he performed in the International Festival "Slavyanskiy Bazar" in Vitebsk, and was awarded with a diploma. After completion of the military career he went from 1999 to 2012 as a soloist of the Academic song and dance ensemble of Internal Forces of Ministry of Internal Affairs. In 2005 he graduated from the Russian Academy of Theatre Arts in Moscow and got the same year the title of Honored Artist of North Ossetia-Alania. In 2008, he was titled an Honored Artist of Russia. Since 2011 he is soloist of the Orchestra of Russian Interior Ministry and began his solo career.

Discography
2000: "Армейский сборник 2" (Song Шинели)
2003: "Doswidanja. Ich komm wieder" (Song O Happy Day)
2003: "Академический ансамбль песни и пляски внутренних войск МВД России" (Song Be My Love)
2008: "Академический ансамбль песни и пляски внутренних войск МВД России" (Songs Be My Love, O Happy Day, The Prayer, На дальнем берегу, Piu Che Puo)
2010: "Помяни меня, поле. 65 лет Победы в Великой Отечественной войне" (Album)
2010: "Русское поле. 65 лет Победы в Великой Отечественной войне" (Album)

Filmography
 2005: "Not Born Beautiful" / "Не родись красивой"
 2007: "The Unknown Country" / "Незнакомая земля"
2007: "The Teacher in Law" / "Учитель в законе"
2011: "The Prosecutor's Investigation" / "Прокурорская проверка»
2011: "The Family Dramas" / "Семейные драмы»
2011: "Before The Court" /"До суда»

Awards
Honored Artist of North Ossetia–Alania
Honored Artist of Russia
Order of Courage
Medal "For service in the North Caucasus»
Medal "Army General Margelov"
Medal "For Participation in Counterterrorism Operations"
Medal "200 Years of the Ministry of Internal Affairs"
United Nations Special Service Medal
Medal "80 Years of Airborne Forces of Russia»

References

External links

Official blog
Oleg Kukhta on MySpace
Oleg Kukhta on Twitter
Oleg Kukhta on Facebook

1970 births
Living people
People from Samara Oblast
Russian male singer-songwriters
Russian pop singers
Russian military personnel
People of the Chechen wars
Recipients of the Order of Courage
Honored Artists of the Russian Federation
21st-century Russian male singers
21st-century Russian singers

redpajama_set_name: RedPajamaWikipedia


The report presents the radio consumption among adults of 25 to 54 years old in the United States. It studies, among others, different types of radio broadcast, e.g. AM/FM, satellite of internet radio, time spent listening to the radio, radio's reach and places where radio programs are heard.


text:
Shelby Davidson to Donald A. Glaser
Hans Dehmelt Biography (1922-)
Hans Dehmelt has devoted his career as a physicist to developing means of performing highly precise, accurate atomic measurements. In pursuit of this goal, Dehmelt devised a trap that for the first time isolated a single electron,which in turn made possible the precise experimental measurements that verified the theory of quantum electrodynamics. For his work, Dehmelt was honored with a share in the 1989 Nobel Prize in physics.
The son of Georg Karl and Asta Ella Klemmt Dehmelt, Hans Georg Dehmelt was born on September 9, 1922, in Görlitz, Germany. An early interest in the workings of radios led Dehmelt to the study of physics, which was interruptedby service in the German army and a period as a prisoner of war in France during World War II. After the war, Dehmelt continued his studies in physics atthe University of Göttingen, financing himself in part by repairing broken radios. During one college course, Dehmelt became interested in the possibility of isolating the electron, something theorists said couldn't be done.
Dehmelt earned his Ph.D. from Göttingen in 1950 and stayed on for postdoctoral work until 1952, concentrating on nuclear magnetic resonance, and using his skill in electronics to make up for a postwar lack of conventional experimental equipment. He continued these studies from 1952 to 1955 at Duke University in the United States, and became a professor at the University of Washington in 1955, where he remains today. While at Washington, Dehmelt returnedto his original interest in isolating the electron in order to measure it accurately. Although the electron's mass and charge could be measured preciselywith existing methods, its spin and magnetism could not be. Quantum electrodynamics (QED) did predict the electron's spin and magnetism, as part of QED'sexplanation of all interactions between electrically charged particles, butuntil spin and magnetism were actually measured on existing electrons, QED remained an unproven theory.
In 1959, Dehmelt's electronics background once again came into play. He usedan electronic component called a Penning discharge tube to build what he called a Penning trap: a vacuum tube with a strong magnetic field and a weak electric field that trapped and held electrons. Throughout the 1960s Dehmelt andhis colleagues tried to devise ways of measuring the gyromagnetic ratio, or g-factor, of an electron, which had been calculated theoretically via quantum mechanics. Dehmelt and his team found that by manipulating voltage, they could drive electrons out of the trap until only a single one remained. This breakthrough was accomplished in 1973, and soon the team was able to capture and hold single electrons for extended periods of time. Two years later, Dehmelt worked out a way to cool the trapped electron, which slowed its motionand made accurate measurement easier. In 1976 Dehmelt and his coworkers usedtheir trap to observe the quantum jump of a single ion, again confirming a prediction of quantum mechanics.
Soon Dehmelt and his team were able to measure the g-factor to ten times its previously calculated value. Driven by his goal for ever more accurateatomic measurements, Dehmelt applied a number of refinements to his trap sotheg-factor could be measured to 12 decimal places by 1991. Dehmelt and his colleagues have also trapped positrons (antielectrons). One of these positrons, which he named Priscilla, was held for three months, performing itsquantum jumps and thus allowing the first experimental measurement of the g-factor for antimatter. Dehmelt also initiated and guided an experimentat the University of Heidelberg in 1974 to trap and observe a single barium ion. This eventually produced the first photograph, in black and white, of a charged atom. With his long-time collaborator Robert Van Dyck, Dehmelt later was able to take a color photograph of a blue barium ion they named Astrid.
For his particle-trapping work, Dehmelt shared half of the 1989 Nobel Prize in physics with Wolfgang Pauli of the University of Bonn, who also devised anion trap. The work of Norman Foster Ramsey of Harvard University, the other 1989 Nobel physics laureate, led to the development of the atomic clock. The precise measurement methods made possible by the work of these three men madeit possible "to conduct experiments that might force us to reconsider some basic physical laws," according the Nobel Committee.
Late in his career, Dehmelt noted the discrepancies between the theoretical g-factor predicted by QED and the actual g-factor he had measured. Although the discrepancy was minuscule, Dehmelt speculated that it might indicate that the electron could be broken down into smaller and smaller particles, or subquarks, finally ending in the "cosmon." A linked cosmon and anticosmon, Dehmelt theorized, spontaneously came into being out of nothingness ina quantum jump and then instantly decayed, creating the Big Bang that beganthe universe.
Dehmelt became a naturalized U.S. citizen in 1962. He acted as a consultant to Varian Associates of Palo Alto, California, from 1956 through 1976, and hascontributed numerous articles to professional journals. He was elected to the National Academy of Sciences in 1978 and remains on its Physics and Astronomy Board. Dehmelt also won the 1995 National Medal of Science.


text:
St Brigid's College recognises the contribution that students from other countries and cultures make to its community.
St Brigid's College recognises the contribution that students from other countries and cultures make to its community. It is with this in mind, that programmes are designed specifically to meet the needs of overseas students while ensuring their gentle integration into the life of the College.
Overseas students participate fully in all areas of College life, combining academic rigour with spiritual, cultural and physical growth. Such involvement encourages personal excellence in a broad spectrum of subjects as well as nurturing a life-giving respect for different cultural backgrounds in all students of the College.
Important Information for Overseas Students
Living in Perth, Western Australia
Western Australia is the largest Australian State occupying about one-third of the continent. The State contains approximately 12 500 kilometres of coastline and covers an area of more than 2.5 million square kilometres. With the State being so vast, Western Australia contains many different climatic regions including tropical conditions in the North to temperate conditions in the South-West.
Perth itself experiences a Mediterranean climate of warm to hot, dry summers and cool, wet winters. Perth skies are often clear of cloud and a beautiful blue and Perth boasts the highest number of average daily sunshine hours of any major Australian city. With an extensive coastline of white sandy beaches, it is easy to understand why Perth's lifestyle is enjoyed by so many. The temperature ranges from a mean monthly maximum of approximately 17ºC in July to 29ºC in January and February. The majority of Perth's 853mm of rainfall falls in the winter months of June, July and August. Perth has a population of over 1.6 million which represents about three-quarters of Western Australia's total population.
On Western Australia – go to http://www.westernaustralia.com/
On Perth – go to http://www.countrywide.com.au
The St Brigid's College campus is magnificently situated in the Hills of Perth, some 30 kilometres from the city of Perth. Our unique setting allows our School to present an almost rural atmosphere combined a comprehensive education for our 1300 plus students.
In addition to the standard curriculum, our campus also includes a heated swimming pool and fully maintained Gymnasium, playing fields, computer and language laboratories, Library Resources Centre, Food Technology Rooms and our magnificent Heritage Chapel, whilst our Junior School children enjoy their learning in close proximity to the Senior School.
Transportation links are also on our door step with bus services to and from Kalamunda and the City of Perth. The main highways to the State's north and east are less than 15 kilometres from our campus while the Domestic and International Airports are only a short distance away.
SBC Application Form
SBC International Fees and Charges 2023
SBC International Student Handbook
SBC Written Agreement 2023
SBC Refund Policy for International Students
SBC Pastoral Care Policy
SBC Privacy Policy
SBC Guidelines for Guardians & Guardian Nomination Form
SBC Deferment, Suspension and Cancellation Policy
SBC International Students Complaints and Grievances Policy
SBC Standard Collection Notice
SBC Uniform Price List


I have two SSG550M in a Active/Passive configuration. After a couple hours the 2950G shuts down the interface the SSG is connected to. Below are log entries from the switch. It looks like the SSG is bouncing some packets back to the switch confusing it. Any ideas on this? These entries make it look like the switch is seeing its own BPDUs and keepalives.
39w5d: %SPANTREE-2-RECV_PVID_ERR: Received BPDU with inconsistent peer vlan id 13 on FastEthernet0/6 VLAN1.
39w5d: %SPANTREE-2-BLOCK_PVID_PEER: Blocking FastEthernet0/6 on VLAN0013. Inconsistent peer vlan.
39w5d: %SPANTREE-2-BLOCK_PVID_LOCAL: Blocking FastEthernet0/6 on VLAN0001. Inconsistent local vlan.
39w5d: %SPANTREE-2-UNBLOCK_CONSIST_PORT: Unblocking FastEthernet0/6 on VLAN0013. Port consistency restored.
39w5d: %SPANTREE-2-UNBLOCK_CONSIST_PORT: Unblocking FastEthernet0/6 on VLAN0001. Port consistency restored.
39w5d: %SPANTREE-2-RECV_PVID_ERR: Received BPDU with inconsistent peer vlan id 61 on FastEthernet0/6 VLAN1.
39w5d: %SPANTREE-2-BLOCK_PVID_PEER: Blocking FastEthernet0/6 on VLAN0061. Inconsistent peer vlan.
39w5d: %SPANTREE-2-UNBLOCK_CONSIST_PORT: Unblocking FastEthernet0/6 on VLAN0061. Port consistency restored.
39w5d: %SPANTREE-2-RECV_PVID_ERR: Received BPDU with inconsistent peer vlan id 12 on FastEthernet0/6 VLAN1.
39w5d: %SPANTREE-2-BLOCK_PVID_PEER: Blocking FastEthernet0/6 on VLAN0012. Inconsistent peer vlan.
39w5d: %SPANTREE-2-UNBLOCK_CONSIST_PORT: Unblocking FastEthernet0/6 on VLAN0012. Port consistency restored.
39w5d: %ETHCNTR-3-LOOP_BACK_DETECTED: Loop-back detected on FastEthernet0/6. The port is forced to linkdown.
The switch has VLANs 1,12,13, & 61 configured. The SSG only has sub-interface or 12. I also just discovered spanning tree is disabled for 12 on the second switch. I have SSG A&B attached to switch 1&2 respectively. SSG A is supposed to be the master under normal conditions. Switch 1&2 have 2 - gig connections between them, trunking and etherchanneled. Switch 2 has spanning tree disabled for VLAN 12. Not sure why original IBM contractors did that. I have had SSG B active for a day now and it has some of the BPDU errors but not the loopback error yet.
OK, so where's that "13" coming from? I seem to remember some funny business about where "zero" is when doing 802.1Q on Cisco's. Perhaps an 'off-by-one' error?
I failed to mention the switch port is set to dot1q trunking and I have one subinterface for the SSG tagged with VLAN 12.


text:
borders migration peter pellegrini Serbia slovakia Viktor Orbán
Orbán to Pellegrini: 'It's forbidden to say so in Europe, but migration is an organised invasion'
Prime Minister Viktor Orbán on Thursday warned of increasing migration pressure on Hungary's southern border and an expected rise in the number of organised groups of migrants attempting to enter the country as the weather improves.
Speaking to reporters after inspecting Hungary's border fence with Peter Pellegrini, his Slovak counterpart, Orbán said the fence was also protecting Slovakia's border.
"This is hard work which we would have a hard time doing without help and our allies," Orbán said, expressing his gratitude for Slovakia's support.
Slovakian PM Peter Pellegrini and Hungarian PM Viktor Orbán at the border. Photo by Zsolt Szigetváry/MTI
The prime minister said depictions of the situation at the Hungarian border in the international media were inaccurate, arguing that 95 percent of the migrants arriving at the border were "military-age men". Orbán said
It's forbidden to say so in Europe, but this is an organised invasion,"
Orbán said the reason he had invited Pellegrini to inspect the border was that there had been a sharp rise in the number of illegal border crossings recently. More than 5,000 migrants have attempted to enter Hungary illegally so far this year, he said, adding that a lot of organised migrant groups were also coming to the border. Orbán said there were some 100,000 migrants currently on their way to Europe via the Balkan route and if Hungary let them, they would enter the country and even reach Slovakia.
Orbán expressed his gratitude to the Slovak government for the assistance it has provided to Hungary with its border protection efforts. Orbán said he and Pellegrini had strengthened their agreement under which Slovakia will be prepared to assist Hungary again if migration pressure were to rise on its border.
Photo by Zsolt Szigetváry/MTI
In response to a question, Orbán said Hungary's border was not closed, arguing that if someone wanted to enter Hungary's territory, they were free to "knock", and follow the proper procedure. Those who opt for this method, he said, have to wait in the transit zone for the end of the legal procedure. During that time migrants are looked after and if their application is approved they are free to enter Hungary, but otherwise they must leave the transit zone, he added.
"If everyone acted this way life would be nice," Orbán said. "But the majority don't, but instead choose the illegal path." He said that recently groups of migrants had tried to break through the fence recently, noting that at one point warning shots had to be fired.
Migrants Storming Röszke Border Fence Receive Prison Sentences
He said cooperation between Hungary and Serbia was good, adding that the two countries could handle the migrant situation through fair cooperation.
Orbán said Hungary's secret service was monitoring the situation and had a clear view of "how the movement of migrants is being organised".
Orbán insisted that the migrants were backed by organisations claiming to be NGOs operating similarly to people smuggling groups. These organisations had significant financial resources and considerable logistical capabilities, he added.
In response to another question, he said Brussels "isn't going to give us a single cent to finance the fence because we're on the wrong list". Hungary was the first to build a fence on its border, "so we're the number-one culprits", he added.
Pellegrini stressed the importance of protecting the Hungarian-Serbian border, noting that it was also the southern border of the European Union's passport-free Schengen zone. He said Slovakia, too, would be in trouble if the border were to be breached by migrants.
Slovakia is handling the protection of its eastern border with Ukraine but needs Hungary's help regarding its southern border, he said.
Pellegrini said Slovakia was prepared to keep assisting Hungary with its border protection efforts with a view to keeping migrants at bay.
In the featured photo (from left to right): Slovakian PM Peter Pellegrini, Hungarian PM Viktor Orbán, Slovakian Interior Minister Denisa Saková, and Hungarian Interior Minister Sándor Pintér (behind). Photo by Zsolt Szigetváry/MTI


Warsaw is the home of several shoemakers, who handmake shoes to measure. You will also find a bunch of bespoke tailors of varying quality. Zaremba, though, seems like the real deal. Located on the corner of Nowogrodzka and Kruzca, Zaremba provides bespoke suits and jackets following Italian and English tradition of fittings, handsewing, fine interlining and no fusing.
Maciej Zaremba, a young man at 32, runs the family business. He took over in 2005, when his father died. Maciej employs four or five cutters and tailors.
I met Maciej in Florence in January. He is a pleasant fellow. He told me that he enjoys to keep an eye on fashions, and that he is very keen to bring Zaremba to speed with younger customers, without loosing the older ones, of course.
I believe the current price for a two-piece suit is around 2.000 Euros.


2. Take a screenshot of your first voting screen!
3. Take a screenshot of where/what top are we!
4. Then post the screen shot here with the Following Format below!
Staffs can join! @Staffs: You must used your normal character!
*This event will be approve if we go to top 40! So vote now. Don't waste your time!
*You can enter so many entries though you can! We don't have limit in posting your vote advertise/support!
We will pick 5 Person/Player every month!
3. [Third Prize]Red pet + full trade of Jewel of Soul!
w8 for further announcement about the event when the server is fixed!


Many motorists falsely assume that drivers of trucks and buses can see the road better because they sit twice as high as the driver of a small vehicle. While trucks and buses do enjoy a better forward view and have bigger mirrors, they have serious blind spots into which a small vehicle can disappear from view.
The "No-Zone" represents danger areas around trucks and buses where crashes are more likely to occur.
1. The area approximately up to 20 feet directly in front of a large vehicle is considered a No-Zone. When small vehicles cut in too soon after passing or changing lanes, then abruptly slow down, trucks and buses are forced to compensate with very little room or time to spare.
2. Unlike small vehicles, trucks and buses have deep blind spots directly behind them. Avoid following too closely in this No-Zone. If you stay in the rear blind spot of a large vehicle, you increase the possibility of a traffic crash. The driver of the bus or truck cannot see your vehicle and your view of the traffic ahead will be severely reduced.
3. Large vehicles have much larger blind spots on both sides than cars do. When you drive in these blind spots for any length of time, the vehicle's driver cannot see you. When passing, even if the vehicle's driver knows you are there, remaining alongside a large vehicle too long makes it impossible for the driver to take evasive action if an obstacle appears in the roadway ahead.
4. Truck and bus drivers often cannot see vehicles directly behind or beside them when they are attempting to safely negotiate a right turn. If you cut in between the truck or bus and the curb or shoulder to the right, this maneuver greatly increases the possibility of a crash in this "right turn squeeze."
If your fleet utilizes any large trucks like the ones mentioned in these tips, make sure that your drivers are aware of their vehicles' limitations and are trained to drive safely and do their part to avoid these costly accidents.
Photo courtesy of Cliff Cooper and re-used under the Creative Commons license.


In the midle month of March 2015 we installed biogas system to maximize the utilisation of the waste from the toilet of about 85 childen.
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This is a very simple way of allowing users to be authenticated via Shibboleth but to be a part of Django groups and users. This is accomplished by using Apache mod_shib to protect the provided view. If the user is able to authenticate then we extract certain details from the data provided by Shibboleth. The view will create Django Users and Groups as necessary.
This code has only been tested with mod_shib for Apache.
You may want to tweak or remove the Require line depending on your needs. As it is, it requires users to be a member of group staff in order to be able to authenticate.
Note that we use shibboleth-sso both here and in the Apache config.
# HTTP_xxx variables which are derived from the HTTP request headers.
IDP_ATTRIBUTE defines which Apache environment variable carries the name of the IdP.
AUTHORIZED_IDPS is a list of IdPs that we trust. The full URL may vary for your setup – please check this with whomever runs your IdP..
USER_ATTRIBUTES a list of tuples which are used to map from the attribute names provided by the IdP to fields to be used with the Django User model. The format is (idp_attribute, django_model_attribute, required).
GROUP_ATTRIBUTE is the name used by the IdP to provide group membership. The user will be added to each group listed in the group attribute. If the group does not already exist it will be created. Groups are assumed to be separated by a semicolon (;) in the data provided by the IdP.
GROUPS_BY_IDP this is a dictionary mapping an IdP (from AUTHORIZED_IDPS) to a list of groups. If the user is authenticated to the named IdP then the user will be added to each of the groups, creating the groups as necessary.
DJANGO_STAFF_GROUP is the name of the group presented by the IdP that will be used to determine if the user has the is_staff bit set or not.
We assume the the IdP is the source of truth for groups and for whether or not a user should have Django staff privileges. This means that the set of groups the user will be a member of will be exactly the set of groups that the IdP sends. This also means that if the user is no longer a member of DJANGO_STAFF_GROUP that they will lose their staff privileges.


ZTE USA, today debuted the ZTE Blade Max View, enhancing its award-winning Blade smartphone series to deliver top-range features and functionality for under $200. Offering the latest and greatest in display, multimedia, audio, and battery functionality, consumers looking for a smart investment should look no further than the latest additions to the ZTE Blade portfolio.
For under the cost of some wireless headphones—the new ZTE Blade Max View device dramatically outperforms other smartphones in their respective price points with top-of-the-line smartphone features and functionality.
With dual Dolby® speakers, the Blade Max View becomes a pocket-sized sound system that can go anywhere—enabling consumers to enjoy superior audio wherever they go.
The ZTE Blade Max View will be available starting today, October 31, via ZTE's online store, ZTEUSA.com; Newegg.com; and B&H.
ZTE USA has committed to update this device to Android Oreo by end of 2018.
Is what I'm reading correct? The phone comes with Nougat?
It comes out of the box with Nougat 7.1.1 but WILL be updated to Oreo before years end(2018).
This device seems solid. I will know next week when I get it.
This question is for ZTE, does the Max View come with any sort of Warranty like Passport? Or I guess a better question is what IS the warranty on the Max View? Thanks!
hollap The Blade Max View comes with a 1 year manufactures limited warranty.
Iove the specs vs price, dual Dolby speakers and to top it all off support with AT&T, T-Mobile and... Verizon!! Lots to love with this one!