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

Coupling resonant RF radiation to the spins of atoms in
inhomogeneous magnetic fields allows to locally address clouds of
ultracold atoms with high spatial resolution. This technique is
commonly used in combination with atom chips, where it
offers huge flexibility in the types of potentials that can be
created \cite{Folman:02, Fortagh:07}. Since the RF
fields can also be time dependent, this technique offers the possibility to control the atoms dynamically and has, for
example, been used to split Bose-Einstein condensates (BECs)
\cite{Schumm:05}. By today significant work has been done in the
modelling of RF systems to create highly non trivial trapping
geometries \cite{Lesanovsky:06,Fernholz:07}, including annular
traps \cite{Morizot:06}, examining effects beyond the rotating wave
approximation \cite{Hofferberth:07} and investigating non-linear
Zeeman effects \cite{Sinuco:12}.

The use of multi-frequency fields has recently been suggested to
create multi-well or even periodic potentials
\cite{Courteille:06,Morgan:11}. These can also be time
dependent and in \cite{Morgan:11} a method to coherently control
the centre of mass motion of both, a single atom and a cloud of
interacting atoms, was suggested. While this work highlighted how
versatile multi-frequency RF potentials are for experimentally
realistic parameters, the theoretical model used could only describe limited tunnel coupling strengths between two potential wells, as it required all radio frequencies to be well separated. For large tunnel couplings, however, it is usually necessary to have potentials where the curvature can be controlled over short distances, which, using RF technology, requires two frequencies to be brought close. In such situations the effects of both frequencies have to be considered simultaneously and a more advanced model is necessary.

In this work we address the question of how to accurately deal with near degenerate frequencies  and take full advantage of all degrees of freedom offered by RF fields by using Floquet theory and comparing the results to the currently most common model \cite{Courteille:06}. Floquet theory
allows to describe the interaction between a periodically
oscillating field and a quantum system and its basic idea is to
replace the semiclassical time-dependent Hamiltonian with a
time-independent Hamiltonian of infinite dimensions
\cite{Shirley:63}. We will show that this method allows to obtain highly accurate potentials.

Floquet theory is applicable to single and many-mode systems \cite{Ho:83} and it has been extensively used in
studying multi-photon processes for atoms in strong laser fields
\cite{Ho:84}. For example Drese an Holthaus \cite{Drese:99} used Floquet theory  to
describe adiabatic potentials produced by short laser pulses in
order to stimulate a STIRAP (Stimulated Raman Adiabatic Passage)
process. More recently this was extended to study multiphoton resonance dynamics driven by
intense frequency-comb laser fields using many-mode Floquet
theory \cite{Son:08}. A
comprehensive overview of the application of Floquet theory to
atomic and molecular multiphoton processes in intense laser fields
can be found in \cite{Chu:04}.

The layout of this paper is as follows. In Sec.~\ref{sec:GenRF} we briefly review the solutions of the  Hamiltonian describing a magnetically trapped atom, which is exposed to a single-frequency RF field. In Sec.~\ref{sec:PiecewiseResonance} we discuss the piecewise resonance model for dealing with multiple RF fields, which was developed in
\cite{Courteille:06}, and show how it breaks down when two frequencies come too close. In Sec.~\ref{sec:FloquetModel} we show how Floquet
theory can be used to obtain a more accurate description and in
Sec.~\ref{sec:PotentialGen} we compare the two approaches and discuss the corrections and benefits of the Floquet approach. To demonstrate the power of the approach, we detail in
Sec.~\ref{sec:2dPotential} how an extension to higher dimensions
can be done and show how controlling the orientation of the RF
field can be used to produce non trivial trapping geometries. As an
example, we show how controlling the tunnel coupling in multidimensional RF traps can allow to create ring vortex solitons in Bose-Einstein condensates. Finally we conclude in Sec.~\ref{sec:Conclusion}.

\section{Radio-frequency dressed traps}
\label{sec:GenRF} RF trapping is based on the idea of coupling
magnetic sublevels in the presence of an inhomogeneous magnetic
field. Consider a hyperfine atomic groundstate manifold with total
spin $F$. In the presence of a static magnetic field of modulus
$B_s$, the Zeeman sublevels, $m_F=-F,...,F$ undergo a linear
splitting according to $E_{m_F}=m_F g_F\mu_B B_s$, as long as the
field strength is not too large and second order splitting is
negligible. Here, $g_F$ is the atomic g-factor and $\mu_B$ is the
Bohr magneton. Irradiating such a system with a radio frequency
${\bf B}_\text{RF}(\omega t)$, which can excite atomic Larmor
precession, will couple the sublevels $|F,m_F\rangle
\leftrightarrow |F,m_F\pm 1\rangle$ with spatial selectivity due
to the inhomogeneity of the magnetic field and the spatially varying
Larmor frequency.

For simplicity, let us first consider a one-dimensional situation with
a static field pointing and increasing linearly along the
$z$-direction, i.e. ${\bf B}_s(z)=B_s(z){\bf e}_z=G z{\bf e}_z$ where G is the magnetic field
gradient. Such a situation arises, for example, when an atom
travels along an axis of a quadrupole field. It is convenient to
express the oscillating field in complex spherical components
($\sigma^+$, $\sigma^-$, and $\pi$-polarizations), such that in Cartesian coordinates
\begin{equation}
  \label{eq:rfBdef}
  {\bf B}_\text{RF}(\omega t)=\text{Re}\left[\left(\begin{array}{c}
  \frac{1}{\sqrt{2}}(B_++B_-)\\
  \frac{i}{\sqrt{2}}(B_+-B_-)\\
  B_{\pi}
  \end{array}\right)\cdot e^{-i\omega t}\right]\; .
\end{equation}
The total Hamiltonian for the magnetic interaction can then be
written as
\begin{equation}
\label{eq:Hamiltonian} H(z,t)=\mu_B g_F{\bf \hat{F}}\cdot({\bf
B}_s(z)+{\bf B}_\text{RF}(\omega t))\;,
\end{equation}
where the angular momentum operator is expressed in units of $\hbar$.
Transforming to a frame rotating about the $z$-axis at frequency $\omega$ using
$H_\text{rot}=i\hbar\dot{U}U^{-1}+UHU^{-1}$ with $U=e^{i F_z
\omega t}$ leads to $H_\text{rot}=\mu_B g_F{\bf \hat{F}}\cdot{\bf
B}_\text{eff}$, where the effective field in Cartesian coordinates
is given by
\begin{equation}
  \label{eq:rfBeff}
  {\bf B}_\text{eff}=\left(\begin{array}{c}
  \frac{1}{\sqrt{2}}\text{Re}[B_-e^{-i2\omega t}]+\frac{1}{\sqrt{2}}\text{Re}[B_+]\\
  \frac{1}{\sqrt{2}}\text{Im}[B_-e^{-i2\omega t}]-\frac{1}{\sqrt{2}}\text{Im}[B_+]\\
  \text{Re}[B_\pi e^{-i\omega t}]+B_s(z)-\frac{\hbar\omega}{\mu_B g_F}
  \end{array}\right).
\end{equation}
Expressing this Hamiltonian in the spherical basis ${\bf e}_{\pm}=({\bf e}_{x}\mp i{\bf e}_{y})/\sqrt{2}, {\bf e}_{\pi}={\bf e}_{z}$ then results in
\begin{align}
\label{eq:SphericalHamiltonian}
  H_\text{rot}=\frac{\mu_B g_F}{2}[&(B_s(z)-\frac{\hbar\omega}{\mu_Bg_F})\hat{F}_z+\frac{B_+}{\sqrt{2}}\hat{F}_+\\
   &+\frac{B_-}{\sqrt{2}}\hat{F}_-e^{-i2\omega t}+B_{\pi}\hat{F}_ze^{-i\omega t}]+c.c.\nonumber\;,
\end{align}
with the usual definitions $\hat{F}_{\pm}=(\hat{F}_x\pm i
\hat{F}_y)$.

If the RF field is purely $\sigma^+$-polarized, the effective
field and rotating frame Hamiltonian are time-independent. In
this case, the situation in the rotating frame is fully equivalent
to an atom moving in an inhomogeneous field across a non-zero field
minimum, defined by the resonance condition $\mu_B g_F B_s(z) = \hbar\omega$.
Conversely, the widely used Ioffe-Pritchard type trap,
where the field-zero of a 2D quadrupole field is lifted with an
orthogonal applied field $B_I$, can be viewed as a dressed state trap
with zero coupling frequency. The quasi-energies, i.e., the eigenvalues
of the Hamiltonian in the rotating frame can be obtained straightforwardly as
\begin{align}
    \label{eq:SingleRotExactE}
    E_{m_F} &= m_F \mu_B g_F B_\text{eff}\\
    \nonumber &=m_F \mu_B g_F
    \sqrt{\left( B_s(z)-\frac{\hbar\omega}{\mu_B g_F }\right)^2+ \frac{\left|B_+\right|^2}{2} }\; ,
\end{align}
where the $m_F$ are eigenvalues of the spin component aligned with
the effective field, i.e., rotating in the laboratory frame.

If polarization components other than $\sigma^+$ are present, one
can apply the rotating wave approximation (RWA) by discarding the
fast oscillating terms as long as $|\hbar\omega|\gg
g_F\mu_BB_{\text{eff}}$ \cite{Tannoudji:92}. This however, will neglect shifts in the energy spectrum, which are known as
Bloch-Siegert shifts \cite{Bloch:40}. A second order correction is
caused by a $\sigma^-$ field component, which can be seen as
equivalent to a $\sigma^+$ polarized field at negative frequency, leading to off-resonant coupling between states with $\Delta
m_F=\pm1$ (see Fig.~\ref{fig:SCHEME}). Other higher order effects
can also stem from $\pi$ polarised components.

\begin{figure}[tb]
\includegraphics[width=1\linewidth]{COUPLING_SCHEME.pdf}
\caption{(Color online) A schematic diagram of the eigenvalues of the Hamiltonian
in the rotating frame for both, $\sigma_+$ (green lines) and
$\sigma_-$ (red lines) polarised RF fields irradiating an atom in
a linear static field $B_s(z)=G z$. The blue lines show the bare
Hamiltonian eigenvalues $E_{+m_F}$ and $E_{-m_F}$. The dashed
black lines indicate $z=0$ and $E=0$.} \label{fig:SCHEME}
\end{figure}

\section{Piecewise Resonance Model}
\label{sec:PiecewiseResonance}

More control and complexity can be introduced into RF dressed
potentials by using multiple frequencies $\omega_n$. Using the
method outlined above, one can in principle apply an iterative
procedure by performing consecutive rotating wave approximations
for each frequency. However, it is then necessary at each step to
transform all oscillating fields into the new rotating frame and
determine new spherical polarization components with respect to the
effective field of the previous step. This procedure will lead to
an accumulation of errors and can suffer from a certain
arbitrariness as the order of eliminating individual frequencies
is not defined.

However, if the individual frequencies are spaced sufficiently far apart and the coupling is small with respect to the detuning, one can approximate the dynamics locally by considering only the nearest resonance frequency, $\omega(z)=\omega_{n}$. Formally this means that $n$ is chosen such that $\lbrack \mu_B g_F B_s(z) - \hbar \omega_{n} \rbrack$ is minimized at any position $z$. In the language of the above consecutive approach, this is equivalent to approximating the effective field by its $z$-component before decomposing the polarisation components for the next step. In the following, we briefly revisit the method outlined in \cite{Courteille:06} to analyse the resulting potentials.

With the local frequency approximation, and after applying the RWA, the Hamiltonian of Eq.~(\ref{eq:SphericalHamiltonian}) for a system of total spin $F=\frac{1}{2}$ can be expressed as
\begin{equation}
  \label{eq:rfHamiltonian}
  H(z)=\frac{1}{2}
    \left(\begin{array}{cccc}
    \mu_B g_F B_s(z) - \hbar \omega_n &
    \hbar \Omega_n  \\
    \hbar \Omega^*_n &
    \hbar \omega_n-\mu_B g_F B_s(z)
          \end{array}\right) \;,
\end{equation}
where $\Omega_n=\frac{\mu_B g_F}{\hbar\sqrt{2}}B_{n_+}$ is the Rabi frequency of the $n^{\text{th}}$ RF field with $\sigma^+$-polarisation and amplitude $B_{n_+}$ (or $\sigma^-$-polarisation for negative $\omega_n$). For practical reasons, experiments are often performed with linearly polarised RF fields, orthogonal to the static field. In this case, the $\sigma$-components are given by $B_{n_{\pm}}=(B_{n_x}\mp iB_{n_y})/\sqrt{2}$. If only one linear polarisation is used, say $B_x$, each frequency produces two equally strong resonances at $\pm \omega_n$ or $\pm B_s$ with Rabi frequency $\Omega_n=\frac{\mu_B g_F}{2\hbar}B_{n_x}$.

For large detuning the eigenenergies of the two-level RWA-Hamiltonian can be written as
\begin{align}
  E_{\pm}(z) &= \pm \frac{1}{2} \sqrt{ \hbar^2 |\Omega|^2
              + \lbrack \mu_B g_F B_s(z) - \hbar \omega_n \rbrack^2}\\
            &\approx \pm \frac{1}{2} \lbrack \mu_B g_F B_s(z)
                   - \hbar \omega_n \rbrack
                   \pm \frac{\hbar^2 |\Omega|^2}
                   {4 \lbrack \mu_B g_F B_s(z) - \hbar \omega_n \rbrack} \nonumber\;,
\end{align}
where the second step is valid far from the resonance, $\hbar\Omega \ll \lbrack \mu_B g_F B(z) - \hbar \omega_n \rbrack$, and the resulting second term can be viewed as a Stark shift. The effect of all other RF fields which are not closest to resonance can be approximated by creating an effective Stark shift, which is the sum of the shifts of all RF fields of frequency $\omega_j$ ($j \neq n$) \cite{Courteille:06},
\begin{equation}
  L_n(z)=\sum_{j\not=n} \frac{\hbar^2 |\Omega|^2}
         {4 \lbrack \mu_B g_F B_s(z) - \hbar \omega_{j} \rbrack} \; .
\end{equation}
This leads to a correction of the energies, which are now given by
\begin{equation}
  E_{\pm}(z) =\pm\frac{1}{2}\sqrt{ \hbar^2 |\Omega|^2 + \lbrack \mu_B g_F B_s(z)
              - \hbar \omega +2 L_n(z) \rbrack^2}\;.
\end{equation}
From this, and considering that the couplings are strong enough to
yield a Landau-Zener transition probability close to unity, the
resulting adiabatic potential can be written as
\begin{equation}
  V_{ad\pm}(z)=(-1)^{n} \left[ E_\pm(z) \mp \frac{\hbar \omega_{n}}{2} \right]
               \mp \sum^{n-1}_{k=1}(-1)^k \hbar \omega_k \;.
\end{equation}
In Fig.~\ref{fig:PWPotential} we show the adiabatic RF
potentials as seen by an atom in a static field gradient irradiated by two RF fields with frequencies, $\omega_1$ and $\omega_2$, for three
different values of $\Delta \omega=\omega_2-\omega_1$. In order to set scales applicable to typical atom chip experiments, all work presented here assumes a static field in the form of an Ioffe-Pritchard (IP) type trap with radial field profile
\begin{equation}
\label{eq:IP}
  B_s(r)=\sqrt{G^2 r^2 + B_I^2} \; ,
\end{equation}
where we chose a magnetic field gradient $G=1 T m^{-1}$ and an offset field $B_I=1 \mu T$.

While for well spaced frequencies the potential resulting from the above procedure is visually smooth (see Fig.~\ref{fig:PWPotential} (a)), a discontinuity appears for decreasing values of $\Delta \omega$, which grows as the frequencies approach each other. Treating the RF fields independently from each other is therefore no longer appropriate. In order to describe these situations we will explore the advantages a treatment using Floquet theory offers. Situations in which this becomes important are, for example, potentials in which the curvature changes on a small spatial scale.

\begin{figure}[tb]
\includegraphics[width=1\linewidth]{PW.png}
\caption{(Color online) Adiabatic RF potentials for an atom trapped in a IP trap
  irradiated by two linearly polarised RF fields with
  different frequency separation $\Delta \omega$ for
  $\omega_1=1.5\times 10^5$ Hz and Rabi frequencies $\Omega_1=\Omega_2=9.274\times 10^{4}$ Hz. Note that the axis for each plot changes so
  that the important features of each potential are resolved. In all cases $m_F=\frac{1}{2}$ and $g_F=1$.}
\label{fig:PWPotential}
\end{figure}

\section{Floquet Model}
\label{sec:FloquetModel}

Floquet theory provides a practical and powerful nonperturbative method for studying the interaction of a quantum system with an oscillating field, such as ionization and multiphoton excitation processes. It allows to find the solutions of a Schr\"odinger equation with a temporally periodic Hamiltonian by representing it as an infinite matrix \cite{Shirley:63}.
By using a Floquet approach to describe a system containing multiple RF fields we can ensure that higher-order frequency shifts, which are neglected by the piecewise resonance model and other approaches which rely on the RWA, are accounted for.

As in the previous section, we aim to describe the state of an atom confined to a static
magnetic field ${\bf B}_s({\bf r})$ subjected to a radio-frequency field ${\bf B}_{RF}(\omega t)$ with N different frequencies. However, unlike the previous section, we consider linearly polarised fields that can have arbitrary orientation relative to the static field by defining the $\sigma_{+}$ and $\sigma_{-}$ components of the RF field as
\begin{subequations}
\begin{align}
B_{+}&=\frac{\alpha \cos(\theta)- i \alpha \sin(\theta)}{\sqrt{2}}\;,\\
B_{-}&=\frac{\alpha \cos(\theta)+ i \alpha \sin(\theta)}{\sqrt{2}}\;,
\end{align}
\end{subequations}
and requiring the $B_{\pi}$ component to be real. According to Eq.~(\ref{eq:rfBdef}), the $n^{\text{th}}$ RF field can then be written as
\begin{equation}
{\bf B}_{RF}(\omega_n t)=
{\bf B}_n
\cos(\omega_n t)\; ,
\end{equation}
where ${\bf B}_n$ is the RF field vector. It can be decomposed into its components along each Cartesian axis, ${\bf B}_n=\alpha_n \cos(\theta_n)\hat{{\bf e}}_{x}+\alpha_n \sin(\theta_n)\hat{{\bf e}}_{y}+B_{\pi_n}\hat{{\bf e}}_{z}$, and controlling the angle $\theta$ allows to chose orientation of the RF field. Considering $N$ such fields then leads to the Hamiltonian
\begin{equation}
\label{eq:FHamiltonian}
H({\bf r},t)=\mu_B g_F{\bf \hat{F}}\cdot \left({\bf B}_s({\bf r})+\sum_{n=1}^{N} {\bf B}_n \cos(\omega_n t)\right).
\end{equation}

We now move to a frame in which the direction of ${\bf B}_s({\bf r})$ always points along the $z$-axis by applying a rotation matrix $R$ to the Hamiltonian. While this can be done for any static field, here we assume that it is of Ioffe-Pitchard form (\ref{eq:IP}). In this case, the rotation matrix $R$ can be written as,
\begin{equation}
  R=\begin{pmatrix}
      \frac{y}{r}&-\frac{x}{r}&0\\
       \frac{B_I x}{B_s r}&\frac{B_I y}{B_s r}&-\frac{G r}{B_s}\\
      \frac{G x}{B_s}&\frac{G y}{B_s}&\frac{B_I}{B_s}
 \end{pmatrix},
\end{equation}
and we define ${\bf B}'_n({\bf r})$ as the rotated RF field vector such that
\begin{equation}
  {\bf B}'_n({\bf r})=\begin{pmatrix}
  B'_{n_x}({\bf r})\\
  B'_{n_y}({\bf r})\\
  B'_{n_z}({\bf r})
  \end{pmatrix}
  = R\cdot{\bf B}_n \; .
\end{equation}
In the limit $|\mu_B g_F {\bf B}'_{n_z}({\bf r})| \ll \hbar \omega_{n}$ the component that oscillates parallel to the static
field, ${\bf B}'_{n_z}({\bf r})$, can be neglected and only the orthogonal parts, ${\bf B}'_{n_x}({\bf r})$ and ${\bf B}'_{n_y}({\bf r})$, contribute to the coupling between the atomic levels \cite{Hofferberth:07,Pegg:74}. The Hamiltonian (\ref{eq:FHamiltonian}) therefore becomes
\begin{align}
  H({\bf r},t)=\mu_B g_F \Bigg[& B_s({\bf r}) \hat{F}_z
                +\left(\sum_{n=1}^N B'_{n_x}({\bf r})\cos(\omega_n t)\right) \hat{F}_x
                \nonumber\\
  &+\left(\sum_{n=1}^N  B'_{n_y}({\bf r}) \cos(\omega_n t)\right) \hat{F}_y\Bigg] \; .
\label{eq:HamiltonianFinal}
\end{align}

\subsection{Single Frequency Floquet Matrix}
Let us briefly demonstrate the Floquet approach by first explicitly considering the situation where only a single frequency, $\omega_1$, is present. The Hamiltonian is then
periodic in time with a period of $\tau= \frac{2\pi}{\omega_1}$ and the
Floquet theorem states that the time-dependent Schr\"odinger equation
has a complete set of quasi-periodic solutions, which
acquire a phase $\exp(-i \epsilon_n \tau)$ when $t\to t+\tau$. Here the $\epsilon_n$ are
quasi-eigenenergies and the phase factor defines $\epsilon_n$ mod
$\omega_1$.

The first step towards finding the quasi-eigenenergies is to remove
the time dependence of the Hamiltonian by replacing it with an
infinite matrix of the form
  \begin{equation}
  \begin{scriptsize}
    H_F=\begin{pmatrix}
      .. &.. & .. & .. & ..& .. & ..\\
      .. &H_0+2\hbar\omega_1 & H_{-1} & H_{-2} & H_{-3} & H_{-4}&..\\
      .. &H_{1} & H_0+\hbar\omega_1 & H_{-1} & H_{-2} & H_{-3}&..\\
      .. &H_{2} & H_1 & H_{0} & H_{-1} & H_{-2}&..\\
      .. &H_{3} & H_2 & H_{1} & H_{0}-\hbar\omega_1 & H_{-1}&..\\
      .. &H_{4} & H_3 & H_{2} & H_{1}& H_{0}-2\hbar\omega_1 & ..\\
      .. &.. & .. & .. & ..& .. & ..\\
    \end{pmatrix},
  \end{scriptsize}
  \end{equation}
where the {\it Floquet blocks} $H_n$ (with $n$ integer) are given by
\begin{equation}
  H_n({\bf r})=\frac{1}{\tau} \int_0^\tau \! H({\bf r},t)  e^{in\omega_1 t} \, dt\;.
\end{equation}

This procedure can be interpreted as an expansion of the original
Hamiltonian in terms of the Fourier components of $\omega_1$. For the Hamiltonian \eqref{eq:HamiltonianFinal} the Floquet blocks can be calculated by using the identity $\frac{1}{\tau} \int_0^\tau \! e^{i(m-n)\omega t} d t= \delta_{nm}$, where $\delta$ is the Kronecker delta \cite{Chu:04}. This leads to
\begin{widetext}
  \begin{equation}
    H_F= \begin{pmatrix}
      .. &.. & .. & ..&..& .. & ..\\
      .. &k B_s({\bf r})+2\hbar\omega_1 & 0 & 0 &\hbar\Omega^*_1({\bf r}) & 0 &..\\
      .. &0 & -k B_s({\bf r})+2\hbar\omega_1 & \hbar\Omega_1({\bf r}) &0 & 0& ..\\
      .. &0 & \hbar\Omega^*_1({\bf r}) & k B_s({\bf r})+\hbar\omega_1 &0& 0 & ..\\
      .. &\hbar\Omega_1({\bf r}) & 0 & 0 &-k B_s({\bf r})+\hbar\omega_1 & \hbar\Omega_1({\bf r}) & ..\\
      .. &0 & 0 & 0 &\hbar\Omega^*_1({\bf r}) & k B_s({\bf r}) & ..\\
      .. &0 & 0 & \hbar\Omega_1({\bf r}) &0& 0 & ..\\
      .. &.. & .. & ..&..& .. & ..\\
\label{eq:OurFloquetMatrixInf}
    \end{pmatrix}
  \end{equation}
where the Rabi frequency is given by $\Omega_1({\bf r})=\frac{\mu_B g_F}{4\hbar} \left(B'_{1_x}({\bf r})+i B'_{1_y}({\bf r})\right)$ and $k=\frac{\mu_B g_F}{2}$.

In order to obtain the eigenvalues and eigenvectors of $H_F$, it needs to be
truncated to a finite size, and a consistent way of doing this is to
fix the number of multiples of $\hbar\omega_1$ to include. This
corresponds to limiting the order of the photonic processes that can
occur, i.e.~if we limit the matrix to terms up to $ \pm 2\hbar
\omega_1$, maximally two photons can be absorbed and emitted.
Including higher orders will give a more accurate description, but usually these terms are quickly decreasing in magnitude. To first order, this then leads to

  \begin{equation}
    H_F= \begin{pmatrix}
      k B_s({\bf r})+\hbar\omega_1 & 0 & 0 &\hbar\Omega^*_1({\bf r}) & 0 &0\\
      0 & -k  B_s({\bf r})+\hbar\omega_1 &\hbar \Omega_1({\bf r}) &0 & 0& 0 \\
      0 &\hbar \Omega^*_1 ({\bf r})& k B_s({\bf r}) &0& 0 &\hbar \Omega^*_1{\bf r} \\
      \hbar \Omega_1({\bf r}) & 0 & 0 &-k B_s({\bf r}) & \hbar \Omega_1{\bf r} & 0 \\
      0 & 0 & 0 &\hbar \Omega^*_1 ({\bf r})& k B_s({\bf r})-\hbar\omega_1 & 0  \\
      0 & 0 &\hbar \Omega_1({\bf r}) &0& 0 & -k B_s({\bf r})-\hbar\omega_1 \\
    \end{pmatrix},
  \end{equation}
  \end{widetext}
and diagonalising this matrix gives the quasi-energy spectrum,
which in turn allows the adiabatic RF potential to be calculated. This
process will be detailed in Sec.~\ref{sec:PotentialGen}.

\section{Multi Frequency Floquet Matrix}
In this section we will describe the treatment of an RF field containing several radio frequencies and use the model of Many Mode Floquet Theory (MMFT) \cite{Ho:83}.
We will carry out the calculations explicitly for two different frequencies, $\omega_1$ and
$\omega_2$, with the extension to any number being straightforward. The Hamiltonian follows from
\eqref{eq:HamiltonianFinal} and is given by
\begin{small}
\begin{equation}
  H({\bf r},t)=\mu_B g_F{\bf \hat{F}}\cdot\left({\bf B}_s({\bf r})+{\bf B}_1({\bf r})\cos(\omega_1 t)+{\bf B}_2({\bf r})\cos(\omega_2 t)\right)\;,
\end{equation}
\end{small}
which leads to the basic form for the Floquet matrix
  \begin{scriptsize}
  \begin{equation}
    H_F^{(2)}= \begin{pmatrix}
    .. &..& .. & .. &.. & .. &..\\
      .. &A+2\hbar\omega_r I& P & 0 &0 & 0 &..\\
      .. &P^T & A+\hbar\omega_r I& P &0 & 0& .. \\
      .. &0& P^T & A &P	& 0 & .. \\
      .. &0 & 0 & P^T & A-\omega_r I & P & ..\\
      .. &0& 0 & 0 &P^T & A-2\hbar\omega_r & ..  \\
      .. &..& .. & .. &.. & .. &..\\
    \end{pmatrix}.
  \end{equation}
\end{scriptsize}
Here $I$ is the identity matrix and $\omega_r=\omega_1+\omega_2$ as we want to work in the dressed state picture. The elements of the $H_F^{(2)}$ matrix are matrices themselves and $H_F^{(2)}$ can therefore be thought of as a composite matrix of two single frequency Floquet matrices. The $\omega_1$ frequency terms and
the $\Omega_1({\bf r})$ Rabi frequency terms are contained in matrix $A$, which is
the same matrix as $H_F$ in the previous section.

The off diagonal elements $P$ contain the Rabi frequency of the second field, $\Omega_2({\bf r})=\frac{\mu_B g_F}{4\hbar} \left(B'_{2_x}({\bf r})+i B'_{2_y}({\bf r})\right)$, and are of the form
 \begin{equation}
P= \left(\begin{matrix}
..&.. & .. & .. & .. & .. & ..\\
..&0 & Y & 0 & 0 & 0 &..\\
..& 0 & 0 & Y & 0 & 0& ..\\
..&0 & 0 & 0 & Y & 0 & ..\\
..&0&0& 0 & 0 & Y & ..\\
..&0&0&0&0&0&..\\
..&..& ..&..&..&..&..\\
 \end{matrix}\right)\;,
\end{equation}
where
\begin{equation}
  Y= \begin{pmatrix}
    0 & \hbar\Omega_2^*({\bf r})\\
    \hbar\Omega_2({\bf r}) & 0\\
  \end{pmatrix}\;.
\end{equation}
\begin{widetext}
By following the method outlined above for the single frequency case, one can then evaluate each of these matrices. However, the explicit form of $H_F^{(2)}$ is too large to reproduce here and we only show a small excerpt of it below to highlight
the general structure. The key points of the structure are that the
bare trap eigenenergies are given along the diagonal and each Floquet
block differs by multiples of both $\omega_1$ and $\omega_r$. The
off-diagonal terms correspond to the coupling strengths and contain
terms for $\Omega_1({\bf r})$ and $\Omega_2({\bf r})$

  \begin{equation}
    H_F^{(2)}= \begin{pmatrix}
      k B_s({\bf r})+\hbar\omega_1+\hbar\omega_r & 0 & 0 &.. \\
      0 & -k B_s({\bf r})+\hbar\omega_1 +\hbar\omega_r& \hbar \Omega_1({\bf r})&..\\
      0 &\hbar \Omega_1^*({\bf r}) & k B_s({\bf r})+\hbar\omega_r& ..\\
      \hbar \Omega_1({\bf r}) & 0 & 0&.. \\
      0 & 0 & 0&..\\
      0 & 0 & \hbar \Omega_1({\bf r})&.. \\
      0 & 0 & 0&...\\
      0 & 0 & \hbar \Omega_2({\bf r}) &..\\
      0 & \hbar \Omega_2^*({\bf r}) & 0 &..\\
      \hbar \Omega_2({\bf r}) & 0 & 0&..\\
      0 & 0 & 0 &..\\
      0 & 0 & \hbar \Omega_2({\bf r}) &..\\
      .. & .. & ..& ..\\
    \end{pmatrix}.
\end{equation}
\end{widetext}
\section{Adiabatic Potential Generation}
\label{sec:PotentialGen}
In order to produce the adiabatic potential for the trapped atoms we need to extract the eigenvalues, $\epsilon_{z_n}^i$, and
eigenvectors, $\psi_{z_n}^i$, from the Floquet matrix for every
position on the spatial numerical grid, $z_n$. We do this numerically
as producing analytic expressions becomes quickly unfeasible.
\subsection{1D Potentials}
The quasi-eigenenergies (the eigenvalues of $H_F$) generated when applying a two frequency, linearly polarised, RF field orthogonal to the movement of an atom in a one-dimensional IP trap are shown in Fig.~\ref{fig:Spectrum}. The
spectrum has a periodic structure, which stems from the fact that the
quasi eigenenenergies are defined mod $\omega_1$ and mod
$\omega_r$, and shows the expected avoided crossings (see
Fig.~\ref{fig:Spectrum}(b)). It should be noted that the Rabi frequencies $\Omega_1$ and $\Omega_2$ in this geometry are constant and can be changed independently from each other, which allows to control the size of the avoided crossings
associated with each frequency separately.

\begin{figure}[tb]
\centering
  \includegraphics[width=1\linewidth]{spectrum.jpg}
  \caption{(Color online) (a) The spectrum of quasi eigenenergies for an atom
    trapped in a IP trap irradiated by a two frequency, linearly
    polarised, RF field. The red (bold) line is the adiabatic RF
    potential produced from this spectrum. The inset (b) shows a zoom
    of the highlighted area in (a) where the avoided crossings can
    be seen (dotted circle). The RF fields have the frequencies $\omega_1= 2 \pi \times 1.5
    \times 10^{5}$Hz and $\omega_2= 2 \pi \times 4 \times 10^{5}$Hz
    with Rabi frequencies $\Omega_1=\Omega_2=9.274 \times 10^{4}$Hz. $m_F=\frac{1}{2}$ and $g_F=1$ in all cases.}
  \label{fig:Spectrum}
\end{figure}

The potential seen by the atoms can now be found by identifying
the energy eigenvalue in the centre of the trap which
is closest to the bare trap eigenenergy,  $\epsilon_{z_0}^A$ (normally the
smallest positive quasi-eigenvalue), and following its evolution in space. To find the
potential at the next numerical grid point $z_1$, we take the
eigenvector $\psi_{z_0}^A$ associated with the eigenvalue at
$\epsilon_{z_0}^A$ and calculate $\psi_{z_0}^A \cdot \psi_{z_1}^i$, the dot-product between it and all
eigenvectors corresponding to the eigenvalues $\epsilon_{z_1}^i$. The index of the eigenvector which
maximises this inner product gives the value of the potential at $z_1$. Iterating this process allows the construction of the potential along the whole length of the trap (see red line in Fig.~\ref{fig:Spectrum}).

Fig.~\ref{fig:Comparison} shows the adiabatic RF potentials generated using both the
piecewise resonance and Floquet methods for the same parameters as Fig.~\ref{fig:PWPotential}.
One can see that the Floquet approach produces the same potential for (a) $\Delta \omega=1.5 \times 10^5 Hz$ and avoids the discontinuity for (b) $\Delta \omega=0.4 \times 10^5 Hz$, which is a notable improvement over the piecewise resonant model.

In the extreme case of $\Delta \omega=0.2 \times 10^5 Hz$ shown in Fig.~\ref{fig:Comparison} (c) the Floquet model produces another pair of avoided crossings on either side of the original avoided crossings seen at larger frequency spacing. These extra avoided crossings are the result of the frequencies no longer just coupling the local static field ${\bf B}_s({\bf r})$, where they are resonant. Instead, at this very close frequency separation, each frequency is applied to the effective field created by the static field and the other frequency, which leads to a shift in the resonance position and results in the additional avoided crossings. As one can also see from Fig.~\ref{fig:Comparison} (c), these avoided crossings are not present in the piecewise resonance model, since the rotating wave approximation eliminates the higher order coupling terms.
\begin{figure}[tb]
\centering
  \includegraphics[width=1\linewidth]{comp.jpg}
  \caption{(Color online) Comparison between piecewise resonance model (Dashed Red Line) and the Floquet model (Solid Blue
    Line). All parameters are the same as for Fig~\ref{fig:PWPotential}. See text for discussion.}
  \label{fig:Comparison}
\end{figure}

From this example it is clear that the Floquet approach to modelling adiabatic RF potentials produces highly accurate results with significant corrections to the piecewise resonance approach. It is therefore well suited to accurately describe multi-frequency RF potentials created using closely spaced frequency. In the next section we will show how the Floquet approach can be extend to systems with multiple RF fields where the orientations of the fields are not necessarily perpendicular to the static field.

\subsection{2D Potentials}
\label{sec:2dPotential}
The well known flexibility of RF potentials stems from the large number of parameters (number of frequencies, frequency spacing, field strength and orientation) that can be controlled to modify the geometry of the potentials. These parameters can also be time-dependent, which allows to use the resulting potentials to instigate adiabatic or non-adiabatic dynamics. In the following we consider a multi-dimensional setup and use the Floquet approach to describe some of the features which appear when taking these additional parameters into account.

The main change necessary to extend the model to higher dimensions is to use a multi-dimensional static trapping field $B_s({\bf r})$ which then leads to coupling terms $\Omega({\bf r})$ of the same, higher dimension. This means that the Floquet matrix contains elements that are multidimensional, but its basic structure is unchanged from the one-dimensional case. The added dimension however means that the numerical processing power needed to diagonalise the Floquet matrix is significantly higher.

In the following we will show an example of an interesting potential that can be created using just two frequencies. The numerical approach is similar to the one detailed above, in that we construct the 2D potentials by splitting them into 1D slices and combine them to produce the full 2D potential. To ensure that our minimum rotation method produces 1D slices which are consistent with each other, we use the previously generated 1D slice for each consecutive 1D slice to define an initial quasi-eigenvector and eigenvalue pair.

\subsubsection{Two Frequency Potential}
Two-dimensional RF potentials generated using one frequency have already been demonstrated to study rotating BECs in annular geometries \cite{Morizot:06}. One of the simplest ways to create a more involved structure using two frequencies is shown in Fig.~\ref{fig:2DPotential} (a) where we consider a 2D IP trap and a constant RF field vector which contains a $B_{\pi}$ component only ($\alpha=0$). One can see that the geometry one can create consists of an outer ring and an inner potential, which is actually simply the result from the one-dimensional model of Sec.~\ref{sec:PotentialGen} rotated around the axis along z=0.

However, by controlling $\omega_1$ and $\omega_2$ one can easily change the depth and radius of the inner harmonic well and the outer ring, as well as the size and height of the barrier between them. Performing such a change in a time-dependent way one can then engineer a situation where the tunnel coupling between the ring and inner trap can be increased or decreased with high accuracy.

\begin{figure}[tb]
\centering
  \includegraphics[width=1\linewidth]{2D_2014.pdf}
  \caption{(Color online) The adiabatic potential of an atom trapped in a IP trap irradiated by
  two RF fields with frequencies of $\omega_1=3 \times 10^{5}$Hz and $\omega_2=4\times10^{5}$Hz for (a) $\alpha=0$, $B_{\pi}=8 \mu \text{T}$ (b) $\alpha=10\mu \text{T}$, $\theta=0$, $B_{\pi}=2 \mu \text{T}$ and (c) $\alpha=10 \mu \text{T}$, $\theta=\pi/2$, $B_{\pi}=2 \mu \text{T}$. In all cases $m_F=\frac{1}{2}$ and $g_F=1$ .}
  \label{fig:2DPotential}
\end{figure}

Furthermore, having control over the orientation of the RF fields allows one to break the rotational symmetry and create potentials that are no longer isotropic. In Fig.~\ref{fig:2DPotential} (b) and (c) we show two examples of a 2D potential generated by using constant RF field vectors for (b) $\alpha=10\mu \text{T}$, $\theta=0$, $B_{\pi}=2 \mu \text{T}$ and (c) $\alpha=10 \mu \text{T}$, $\theta=\pi/2$, $B_{\pi}=2 \mu \text{T}$. The resulting potentials display two minima and two maxima on the rings of resonance, which can be understood by considering that the orientation of the $B_{n_x}\hat{{\bf e}}_x$ and $B_{n_y}\hat{{\bf e}}_y$ components of the RF field with respect to the static field is not constant in space. This leads to the variable coupling. Furthermore, controlling the angle $\theta$ allows to create RF fields which point in any direction, which in turn allow the creation of minima and maxima at any position and even in a time dependent fashion.

\subsubsection{Ring Vortex Solitons}
\label{sec:RVS}
As an example of how useful the time-dependent control of the tunnelling interaction between the outer ring and the inner harmonic trap can be, we demonstrate in this section how the potential discussed above can be used to create so-called ring vortex solitions (RVSs) in gaseous Bose-Einstein condensates. These states consist of multiple concentric density-wave rings with a non-zero winding number and they were recently extensively studied by Li {\it et al.} \cite{Li:12}. To create them in a laboratory, one can consider starting out with a single-frequency RF field in a two-dimensional setting, and creating a condensate carrying a persistent current in the resulting annular potential. Adding the second frequency would allow one to create the central  potential and by adjusting all frequencies and intensities appropriately, the current would start to tunnel into the inner potential.

To simulate the creation of RVSs in such a way, the potential must allow large tunnelling strength and therefore the model must be able to deal with situations where two frequencies come close. This makes the Floquet approach the most suitable option.

In Fig.~\ref{fig:RVS} we show a simulations of this tunnelling process using a Gross-Pitaevskii model for the condensate and a potential calculated using the Floquet approach outlined above. The density and phase distribution for the BEC initially confined to the outer ring with $n=1$ can be seen in Figs.~\ref{fig:RVS} (a) and (b), and the density and phase after transfer into the harmonic trap is shown in Figs.~\ref{fig:RVS} (c) and (d). Clearly the resulting state can be identified as a ring vortex soliton.

\begin{figure}[tb]
\centering
  \includegraphics[width=1\linewidth]{rvs.jpg}
  \caption{(Color online) The creation of a RVS in our adiabatic RF potential. The adiabatic RF potential is created by irradiating an IP trap with two RF fields of frequency $\omega_1=27 \times 10^{3}$Hz and $\omega_2=33\times10^{3}$Hz with $ B_{\pi}=0.4219 \mu \text{T}$ for both fields. (a) Shows the density of the BEC of winding number n=1 initially confined to the outer ring and (b) is its corresponding phase plot. (c) Shows the density of the BEC at $t=800 \mu s$ and (d) is corresponding phase plot.}
  \label{fig:RVS}
\end{figure}

\subsubsection{Concentric Ring Potentials}
While we have explicitly shown a 2D adiabatic RF potential generated using two frequencies, this can easily be extended to include more frequencies to create potentials that consist of multiple concentric rings. As in the previous example of just two frequencies, control over the frequency spacing would allow one to adjust the tunnel coupling between the individual rings and can be accurately determined by using a Floquet approach. Such systems are highly desirable as they offer experimentally realistic systems in which one could observe rotational fluxons (Josephson vortices) \cite{Brand:09} or study the Kibble-Zurek mechanism in BECs \cite{Brand:13}.
\section{Conclusion}
\label{sec:Conclusion}
We have shown that using a non-perturbative Floquet approach to calculate radio-frequency potentials for atoms on atom chips leads to good results for multi-frequency situations in one and two dimensions. This approach offers significant corrections to a piecewise-resonant model and can be used to accurately describe situations where two frequencies come close (for example when trying to engineer large tunnel couplings). We have also shown that a Floquet approach can deal with higher dimensions and RF fields of arbitrary field orientation. We have demonstrated the flexibility of the Floquet approach by considering the creation of ring vortex solitons in a 2D adiabatic RF potential which requires that the tunnelling dynamics be determined accurately. Such potentials can be used in a variety of ways, and for example, allow the creation of rotational fluxons and non standard trapping potentials that can connect different topological geometries. This will be the focus of future work.

\section{Acknowledgements}
The authors would like to thank Igor Lesanovsky for valuable discussions. This work was supported by the European Science Foundation (ESF)
within the framework of the common perspectives for cold atoms, semiconductor polaritons and nanoscience activity and Science Foundation Ireland under project numbers 05/IN/I852 and 10/IN.1/I2979.

redpajama_set_name: RedPajamaArXiv


text:
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Uncle Betty's Diner
Establishment Type
Patio Type
Covered Patio?
Heated Patio?
Mon 8:30a.m. - 9:00p.m.
Tues 8:30a.m. - 9:00p.m.
Wed 8:30a.m. - 9:00p.m.
Thurs 8:30a.m. - 9:00p.m.
Fri 8:30a.m. - 9:00p.m.
Sat 8:30a.m. - 9:00p.m.
Sun 8:30a.m. - 9:00p.m.
About this Patio
Uncle Betty's patio is family-central early on the weekends, but you'll find it evolves to an older crowd as the confines of brunch hour reach their end. This spot is lauded for its unique creation such as its eggs Benny on a doughnut and mac and cheese in a sandwich, which will undoubtedly solicit stares if you indulge out on the patio. A great spot for an ice cream, too.
Find out more in the blogTO restaurants section
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redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Can i make watch ads button in my application? I am making a train android application that user can use while sitting in the train...
I am thinking of adding a button(watch ads) that opens a new Activity that display ads and he can switch between them by a button click...
My question is: is that against the admob privacy policy... or I can do it
thanks in advance

A: no you can not do it , from the official documentation

Repeated or recurring interstitials
  Don't overwhelm users with interstitial ads. Repeated interstitial ads often lead to poor user experiences and accidental clicks.
Examples of non-compliant implementations include but are not limited
  to:
Placing an interstitial ad after every user action, including but not
  limited to clicks, swipes, etc. You should place no more than one
  interstitial ad after every two user actions within your app. Please
  note that this requirement also applies when a user clicks the Back
  button within the app. Placing an interstitial ad immediately after
  another interstitial ad was shown to and closed by the user.

for more information please visit this link

redpajama_set_name: RedPajamaStackExchange


Tears are falling down my face...I can't control them. My eyes just keep leaking.
The news that another MTM boy gained his angel wings last night breaks my heart...the news that it is my dear friend, Lindsey's son Louie, crushes it. At the conference last summer I met this sweet family. They struggled, like we all do, to come to terms with this diagnosis and what it means. Their daughter, Emily, is a doting and special girl, a big sister filled with love. She is comforting her parents now...dealing with this unspeakable loss in the only way many children know how...love those around them.
We joked last summer that Louie was Stesha's boyfriend. They had an immediate and special bond. He would smile and flirt with her. She would hold his hand and talk with him...even though she was years older, these little angels burrow themselves into our hearts.
I hate this disease...I hate that it takes our children like a thief in the night. The last few deaths have been swift and unforgiving. One minute they are fine and then they are not...no explanation, no apologies.
What happens when they are gone? How do you move forward? There is not an instruction manual for the loss of a child. This is not supposed to happen...your child dies before you...we are never prepared, no matter how old we, or our child, is. It is especially difficult your child is a child, not having been able to live a full and complete life.
Being connected with other families is a blessing...feeling that there are others who know your journey, that you are not alone, but then that connection is deeper...you have held and kissed that child, rocked them, smelled their sweet smell...they became a part of you.
Javad has been diagnosed with Myotubular Myopathy for ten years...the diagnosis was a crushing blow since all the news was devastating. We have lived our life...opened the doors for other families, showed them that the world is still their oyster, the limits are only determined by their imagination.
The losses over the years have been devastating...each child lost taking a piece of my heart with them. This one hurts to the core...deep in my heart. I am mourning for my friends, their daughter, my daughter, myself.
There are no answers...I wish there was some sense to it all...I wish there was a cure.
"We have lived our life...opened the doors for other families, showed them that the world is still their oyster, the limits are only determined by their imagination." So many of us are so grateful to you, Shannon, for doing exactly this. Thank you for putting some words to this grief, and for continuing to open your family and heart. Lots of love to you.


When a company produces a good product, they've done so because they followed industry standards and done rigorous testing to ensure that each and every product they're selling is up to industry standards or even beyond. Every industry will have their own product testing methods to ensure that their product is up to par. If the product being tested fails the test, it's back to the drawing board.
The consequences for churning out subpar products can be the livelihood of the business altogether. Some businesses have had to shut their doors because they didn't follow industry standards and as a result turned out inferior products, or worse, turned out products that harmed the individuals using them. Product testing varies by industry. Every industry has its regulations and standards that they set for their products. Ink standards will be different from steel standards and the testing used in each industry will vary.
The rub resistance tester has become one of the industry tests for ink on fabric products. When ink is placed on a fabric material, paper, or other object, it is going to need to be of a certain quality to remain on that material or object without smudging. Smudged labels imply bad quality on the park of both the ink maker and the label company. If ink fades or smudges on a T-shirt, the entire product becomes low quality and even embarrassing to use. Industry leaders use testing like the Sutherland test to see if the ink on the surface will be able to withstand the resistance that occurs during handling and shipping and everyday use.
If the product fails a test, it should be discarded. Selling a subpar or defective product can mean the end of any business. Businesses in general will quickly get rid of a product that doesn't meet their rigorous industry standards. As more tests become available, companies are able to turn out higher quality products and make sure that no defective products leak through with a good batch of products. No matter how good the product is, it's likely that there will be some batches that just don't mix or come together well, and they will need to be put aside. While this might at first seem wasteful, it's not. Imagine a bad batch of ink getting through and attaching itself to designer clothing. People go to buy that clothing and find themselves ink stained. It's likely that the maker of that apparel is going to suffer massive business losses as a result.
Every industry has its own pet regulations and testing measures. It's important for each industry leader to understand the standards expected of them and to make sure that they're leading the way to good quality. Customers depend heavily on different industries and deserve to buy from companies that care for their customers enough to do testing. Any industry leader would be wise to always stay up to date on their latest regulations and standards so that they never turn out defective products.


At Glicky, we will be pro-actively buying a Twitter follower or two. Maybe more. This is part of a Social Media experiment. You might call it a PR Stunt. Either way, we don't advise any businesses to follow suit.
We don't want to glamorise making your business hugely noticeable via Social Media. That would not be a good example to set. Publicity is a terrible, terrible thing. You do not want to go there. Instead, we will go there, and tell you what it was like. We're nice like that.
We will be keeping you updated weekly on our progress. You can follow the hullabaloo, the loving and the hating, and the usual reactions on Twitter using the hashtag #glickly.
By the way, we hate any kind of confrontational reactions too. So in hindsight, it's probably best if this whole thing is forgotten about. Yeah, keep it reaaaaly quiet please.
Get your #smallbusiness or #cottageindustry noticed worldwide #glickly.
Here is the correct blog site for everyone who wants to find out about this kind of topic. You already know much its virtually tough to claim along (not too I just might want?-HaHa). You definitely placed a new spin on a subject matter that's been discussed for many years. Excellent stuff, merely excellent!
Hi- nice site you've got going here. Good luck with the PR!
I beg to differ. Things getting very busy round here recently.
we will be doing an article on social media/stories in our magazine next month. Can we add a link on our blog to this article please? I guess you're not going to have a problem with that lol.
As per usual, we won't be giving any previews, so you'll just have to wait and see what we say about your business.
Self-promotion is the only way to go. Who else is going to tell people about your products? I tried advertising for about six months… It was expensive and it didn't work. Google and Facebook rely on activity on the social networks. It's what gives them more revenue. They are only too happy to turn a blind eye to all of the false traffic and videos on YouTube. And the same goes for Twitter.
I agree entirely with you. Old methods of promotion are becoming obsolete as more people go online to check out businesses and products.
Sorry my English is not good. I see you are on right path to getting to the top. I do not know any company what are not using all the social media to their benefit.
I feel that if my product is good enough, people will enjoy finding me on Google and finding my business to. Personal, I have been rewarded nicely over the use.
First of all, I rock. Second of all, you rock.
This is disgraceful. This is blatant abuse of social media.
Thank you for your comment. I don't share your analysis of the situation.
I'll be checking here again in a few weeks to see how this worked out for you.
It's going pretty good so far!
we are new to all this kind of stuff. Can you help us out? We have a new business selling toys for dogs (yes, for dogs), and we're trying to let people know about us. We have a Facebook account but we don't seem to get many people buying.
We are probably doing something completely wrong, because everybody else seems to be successful at this. We opened a Twitter accounts last month, and we have sent many tweets, but nobody is replying!
Anything that you can do or advise would be appreciated.
I;ll PM you later this week Karren. Thanks.
Wishing you every success in the future Glickly. From all of us here in Texas. You've got balls sir/madam.
How do you expect anybody to trust you if you're creating false information on Twitter? The number one rule in business is to build trust. I don't see you when your business getting very far.
Yup – that's kinda clever.
I think that this is more of a PR stunt than anything else!


DIN member - MAHA Australia Pty Ltd.
Standards provide safety, health and environmental protection and give the German economy 1% of its net domestic product. For companies, the application of standards and the participation in standardisation is a major factor in promoting innovation, market entry, quality assurance and legal certainty.
On 5 June 2013, MAHA Maschinenbau Haldenwang GmbH & Co. KG joined DIN – the German Institute for Standardization. As a DIN member, MAHA undertakes the self-government responsibility of all economic operators involved in standardisation.
For a company that operates internationally, standards are a major criterion for estimating the partnership potential of a supplier or the like and guaranteeing customers compatibility and quality. Standards noticeably simplify worldwide trade and are a strategic competitive instrument. They make it much easier for products and services to enter the market and thus has a positive influence on company profits.


This KVM Switch is the most econmical solution for controlling multiple PCs. This powerful tool is perfect for desktop placement and won't take up critical workspace.
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text:
Q: How to encrypt and sign a file using OpenPGP on Mac I fear I may have sent a message without encryption when I thought it was being encrypted and signed. I don't use OpenPGP on a Mac too often (I can't remember the last time), so I'm trying to understand what is happening.
First, I right click on the file, then Services, and finally OpenPGP: Encrypt File. A window floats in the background with a title Encrypting file.txt:

At Choose Recipients I select and highlight the recipient. I also checked Sign:

The GPGservice runs, flashes a Growl window that encryption is complete, and puts a file on the filesystem named file.txt.gpg.
Next, I double click on file.txt.gpg. GPGservice runs again, flashes a Growl message that decryption is complete, and puts another file on the filesystem named file 2.txt. I then examine file 2.txt, and its the plaintext message.
I've repeated this four or five times now. The first few times was due to disbelief, the other two were to take screen captures. I'm fairly certain I am describing the exact steps I performed. It also is consistent with the GPGTools support article How to encrypt and sign text or files with GPGServices?
How is it possible I am decrypting the file encrypted under another's public key? I know its not possible, so what is really happening?
And more importantly, how do I encrypt and sign file using OpenPGP on a Mac? (I have to ask this dumb question because things don't appear to work as advertised or expected).

A:
How is it possible I am decrypting the file encrypted under another's public key? I know its not possible, so what is really happening?

As Add to Recipients is checked beneath your own key, the message is not only encrypted for the actual recipient, but also your own key (so you can also decrypt it afterwards).
The safest method to analyze what's contained in an OpenPGP message is probably dropping to the terminal and running gpg --list-packets [filename]. For an encrypted message, you will observe lines like
:pubkey enc packet: version 3, algo 1, keyid CC73B287A4388025

Each of them indicates that a message is encrypted for this public key, referenced by its key ID. There will be additional lines, don't care about them (the output is not really easy to read and understand if you're not familiar with RFC 4880, OpenPGP).

And more importantly, how do I encrypt and sign file using OpenPGP on a Mac? (I have to ask this dumb question because things don't appear to work as advertised or expected).

The method you chose seems like a viable one -- if you prefer dropping to the command line, the equivalent would be
gpg --recipient [key-id] --output file.txt.gpg --sign --encrypt file.txt


text:
Q: Selective inheritance C++ Could you please explain why following code does compile and works fine (checked on gcc-4.3.4). I thought selective inheritance cannot weaken or even strengthen access to members/methods. Doesn't it break encapsulation rules?
#include <iostream>

class A {
protected:
    void foo() { std::cout << "foo" << std::endl;  }
};

class B : private A {
public:
    using A::foo;   //foo() becomes public?!
};

int main() {
    B b;
    b.foo();
    return 0;
}

A: From the language point of view, there's nothing wrong with this (whether it's good design is another matter).
Any class can choose to expose to a wider audience things that it has access to.
In principle, your example is no different to:
class B : private A {
public:
    void bar() { foo(); }
};

except that here foo() is exposed by proxy.
What you can't do is the opposite: a publicly derived class can't restrict access to things that are accessible via the base class.


Low-cost carrier Wizz Air has announced a new baggage policy that it claims will 'ease' the boarding process for passengers. The policy, which comes into effect from 1 November, guarantees one free carry-on with dimensions 40x30x20 cm for all passengers.
Customers will need to purchase the Wizz Priority upgrade, which starts at €5, to be able to bring a trolley bag up to 55x40x23 cm in the main cabin. This also entitles them to priority check-in and boarding. Following in the steps of Irish carrier Ryanair, Wizz is introducing a new checked bag category that will allow passengers to place luggage up to 10kg in the hold, with the fee starting at €7.
The carrier says the change is in response to the growing number of passengers booking shorter trips and packing 'light and smart'. It claims baggage-related delays affect more than 10,000 flights around the world and that the new policy could help reduce disruption.
Wizz is encouraging passengers to purchase the Wizz Priority option, but bookings made before 10 October for travel after 1 November will automatically be upgraded to a free 10kg checked bag and tickets with a checked bag already included will be upgraded to Wizz Priority.


text:
Samsung announces the Galaxy S10e, the first 'budget' Galaxy S device
Kyle Bradshaw
- Feb. 20th 2019 11:40 am PT
@SkylledDev
Many companies are eyeing the market for more budget-friendly devices and releasing slightly lesser versions of their premium flagship phones. At Unpacked 2019, Samsung is the latest to try and tap into the success found by the iPhone XR, with the Galaxy S10e, the first budget-friendly phone in the Galaxy S series.
Like it's bigger siblings also announced today, the S10 and S10+, the Galaxy S10e features an Infinity-O display with its signature holepunch style notch for the front facing camera. Even beyond that, it's very easy to see the Samsung family resemblance among the devices.
The most important difference in the Galaxy S10e is, of course, the price, starting at a retail price of $749, or $150 less than the standard Galaxy S10. This price difference was achieved by downgrading certain specs. For example, the Galaxy S10e has a slightly smaller 5.8-inch display, which measures in at 438ppi, to the S10+'s 6.3-inch 550ppi display. The Galaxy S10e also only uses two rear cameras, compared to the triple-camera arrangement found on the S10 and S10+.
Despite the S10e's clear downsides, the device is still most definitely in the S10 family, sharing major features like fingerprint unlock (though not in-display), wireless power sharing, and WiFi 6 support.
Under the hood, the Galaxy S10e is powered by one of two processors (depending on your region), the same ones used in the S10 and S10+. The first is a 7nm 64-bit Octa-core processor (Max. 2.8 GHz + 2.4 GHz + 1.7 GHz), and the other an 8nm 64-bit Octa-core processor (Max. 2.7 GHz + 2.3 GHz + 1.9 GHz). Exact details haven't been shared yet, but it's likely one is a Samsung Exynos and the other a Qualcomm Snapdragon.
Between the high-powered processor and availability with up to 8GB of RAM and 256GB of storage space, the Galaxy S10e is still placed firmly in the "flagship" category.
The Galaxy S10e will be available for purchase on March 8th, and is available in 6 colors, including the vibrant Canary Yellow to match the Galaxy Buds also announced today.
Samsung is a technology conglomerate based out of South Korea that makes some of the world's most popular smartphones such as the Galaxy S8/S8+ and Galaxy Note 8.
9to5's resident Fuchsia fanatic. Got a tip or want to chat? Twitter or Email. Kyle@9to5mac.com
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Roberto Danesi was born in Bolzano in 1949; he completed his art and architectural studies at the Venice IUAV University. His researches have always been focused, since his apprenticeship years, on office designing.He started his profession in 1980 as a product designer, art director, graphic designer and company advisor for both Italian and foreign office firms.
Mr.Danesi has worked in many other fields, such as house furniture, contract, packaging, graphic and fabric design; lately his activity has expanded in interior and architectural design. Danesi designed multiple collections for Frezza; here are some ofthe most important ones: in the executive area we can find D.O.S., MUX, SILVER and TIPER desks, characterized by a futuristic and technologic aluminium structure. In this area we can also find the "CX collection" desks, which combine the elegance of aluminium with wood and other refined materials. In the operative area we can find the SLAM and INTELL collections.


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Home » Council tax » Exemptions » Overview
If someone has died
Repossessed by mortgage company
By law
Caravans and boat moorings
Other exemptions
Sometimes you might not have to pay council tax. This is called an exemption.
If an adult is living alone or all of the adults in the house fall into any of the areas below then there may not be any council tax bill to pay for some or all of the time.
If you're 18 and your parents are still getting child benefit
If you're a student in full-time education
If you're 18 or 19 and have just left school or further education
If you're caring for someone with a disability who is not a spouse, partner or child under 18
If you're being looked after in a care home
If you're in prison
If you have a mental health condition
If you're an apprentice
If you're a patient in hospital for a long time
If you work for International Headquarters and defence organisation
If you're staying in certain hostels or night shelters
If you're part of a religious community


Salina, a splendid island of the Aeolian archipelagos, is the production center of high quality capers in Italy. For this reason, the Salina capper, still harvested by hand, has been certified one of Slow Food presidiums.
At Salina, capers collection takes place from May until August. The harvested capers are then dried on jute cloths, selected and are placed in containers alternating capers with thick salt water layers. In the following week, capers are poured from one container to another checking the salting process. After about a month, they are ready to be eaten.
When ate, Salina capers are characterized by their compactness, perfume and uniformity.


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☰ Menu | 🔍 Search // Main // 🖖 Prayers & Praxes // 🌔 Prayers for the Moon, Month, and Festival Calendar // Days of Judgement & New Year Days // Hoshana Rabbah
Prayer for the 7th Day of Sukkot (הושענה רבה), by Marcus Heinrich Bresslau (1852)
Aharon N. Varady (transcription) and Marcus Heinrich Bresslau
27 November 2021 under the Creative Commons Zero (CC 0) Universal license a Public Domain dedication
19th century C.E., תחינות teḥinot, 57th century A.M., Jewish Women's Prayers, English vernacular prayer
https://opensiddur.org/?p=41008 Prayer for the 7th Day of Sukkot (הושענה רבה), by Marcus Heinrich Bresslau (1852) 2021-11-27 16:57:43 "Prayer for the Seventh Day of Tabernacles (הושענה רבה)" by Marcus Heinrich Bresslau was first published in his תחנות בנות ישראל Devotions for the Daughters of Israel (1852), p. 37. Text the Open Siddur Project Aharon N. Varady (transcription) Aharon N. Varady (transcription) Marcus Heinrich Bresslau https://opensiddur.org/copyright-policy/ Aharon N. Varady (transcription) https://creativecommons.org/publicdomain/zero/1.0/ Hoshana Rabbah 19th century C.E. תחינות teḥinot 57th century A.M. Jewish Women's Prayers English vernacular prayer
Contribute a translation
Source (English)
O Lord, abundant in goodness and truth!
Animated with pious reflections,
urged by Thy commandment to celebrate this Festival,
I venture to approach Thee this day
which according to custom in Israel
is distinguished by sacred observances
tending to impress us
with our nothingness and our humbleness,
like unto the willow of the brook,
a symbol of plaintiveness, tears, and suffering.
For what is our life,
what is our strength,
and what is our virtue?
We ourselves have as little merit as that willow of the brook,
which has neither taste, nor flavour, nor fragrance.
Be it then a token of deep humility,
to guard us against over-rating our powers,
and over-valuing our merits.
Be this willow a warning to us
not to grow over-bearing and haughty in prosperity,
not to become proud and vain in affluence;
not to boast of our piety,
not to land ourselves for our religious observances;
nor to be intoxicated with joy during these Festivals,
but to allow the injunction of the Psalmist,
"serve the Lord in fear and rejoice in trembling." (Psalms 2:11)
Grant, therefore, O Lord,
that our attention during our Service
may not be distracted by worldly affairs,
that our devotions may not be disturbed,
that our mind be not divided
between the worship of Thee
and that of worldly matters.
Grant that in our rejoicing on these Festivals
at the goodness Thou hast bestowed upon us,
we may tremble also at the punishment which awaits us,
if we abuse Thy kindness and forbearance.
Strengthen us, Omnipotent Father,
to combine this joy and fear,
so that we may not be haughty in prosperity,
nor faint-hearted in adversity.
But that we may be able to attain the golden medium,
in order to walk straightly and uprightly in Thy ways
towards the goal of life,
so that we may merit the blessing of again celebrating this Festival
with that joy and praise to Thee
as our ancestors did in the times of Thy glorious Temple
in Thy holy City.
"Prayer for the Seventh Day of Tabernacles (הושענה רבה)" by Marcus Heinrich Bresslau was first published in his תחנות בנות ישראל Devotions for the Daughters of Israel (1852), p. 37.
In his preface to Devotions, Bresslau is clear that his prayers in English were adapted from traditional teḥinot that had earlier been published in France, Germany, and Poland. If you know of a specific prayer that may have served as the basis for this one, please leave a comment or contact us.
"Prayer for the 7th Day of Sukkot (הושענה רבה), by Marcus Heinrich Bresslau (1852)" is shared by the living contributor(s) with a Creative Commons Public Domain Dedication 1.0 Universal license.
Marcus Heinrich Bresslau
Marcus Heinrich (also Mordecai Ḥayyim/Hyman/Heyman) Bresslau (ca. 1808-15 May 1864) was a Hebraist and newspaper editor. Born in Hamburg, he settled in England when young. For some time from 1834 he was Baal Ḳoreh (reader) at the Western Synagogue. He then taught Hebrew at the Westminster Jews' Free School and went on to tutor privately. A maskil, he became involved with M. J. Raphall's Hebrew Review and Magazine of Rabbinical Literature (1834-6). In October 1844 he was appointed editor of the relaunched Jewish Chronicle by proprietor Joseph Mitchell. Prickly and quarrelsome, he resigned in July 1848 but returned in around September. He remained until about October 1850. After Mitchell's death in June 1854 he became proprietor (his middle name appearing as Heyman) and edited it until February 1855 when new proprietor Abraham Benisch succeeded him. Bresslau, who tried vainly to revive the Hebrew Review, wrote Hebrew poetry, produced a Hebrew grammar and a Hebrew dictionary, and translated various Hebrew manuscripts in the Bodleian Library. Bresslau compiled (we think) the first compilation of teḥinot in English for women. (Much of this information via Bresslau's entry in The Palgrave Dictionary of Anglo-Jewish History)
Please reciprocate for any adaptation or redistribution of this work by (1) properly attributing the work to Aharon N. Varady (transcription) and Marcus Heinrich Bresslau, (2) clearly indicating the date you accessed the resource and whether any changes have been made (and if so, please be in touch with us and leave a comment below so that we might note your adaptation or improvement), (3) providing a link back to this source, and (4) specifying the Creative Commons Zero (CC 0) Universal license a Public Domain dedication under which this work was shared.
Prayer for a woman who is about to become a mother after the [final] blessing over the Etrog, a teḥinah translated by Miriam Wertheimer (1852)
תְּחִנָה זאָגט מען װען מען בּײַסט אָפּ דעם פִּטוּם פוּן דעם אֶתְרוֹג | Tkhine for when biting the pitom from the etrog (Siddur Ḳorban Minḥah, 1861)
Rude are the Tabernacles Now, a hymn for Hoshanah Rabbah by Penina Moïse (Ḳ.Ḳ. Beth Elohim 1842)
Wenn eine Frau den stiel vom Esrog ausbeißt | When a woman bites the pitom from the etrog, by Yehoshua Heshil Miro (1835)
Prayer for the Close of the Sabbath, by Rabbi Moritz Mayer (1866)
A Prayer of Thanksgiving for Friday, by Marcus Heinrich Bresslau (1852)
Prayer for Parents, by Marcus Heinrich Bresslau (1852)
« Seven Hoshanot for Creation, by Rabbi David Seidenberg (neohasid.org)
הושענא להושענא רבה תשפ״א | Save Us! A Hoshana Prayer, by Rabbi Shlomo Zuckier for Hoshana Rabbah 2020 »


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Ackworth School has, as one of its founding aims, to support 'Friend' children not in affluence. The School today strives to support 'Friend and non-Friend' children who would benefit from an education at Ackworth School.
Ackworth School recognises the exceptional gifts and talents of young people through the award of scholarships. Therefore, scholarships are awarded on the basis of merit. In cases of need, bursaries are available but they are all means tested. The School will consider applications to supplement a scholarship with a bursar. The number and size of scholarships is at the discretion of the Head. The award of a scholarship will remain solely on merit in any of the categories described below and the financial implications of this award will be a fee remission of 5% of the annual day fee.
The School does not have a foundation scholarship or bursary fund. The School has a limited amount of bursary funding held in trust. It also has access, along with the other Friends' Schools, to the Joint Bursary Scheme which provides some support for applications from members of the Society of Friends. All other support for scholarships and bursaries is derived from the annual fee income and this imposes a restriction on the amount of funding available for scholarships and bursaries in any given year. The number and size of scholarships is at the discretion of the Head. The award of a scholarship will remain solely on merit.
Scholarships will be awarded at three points in a student's progression through the school or on entry. The three points are at ages 11+, 13+ and 16+. The school may approach parents having judged a student worthy of consideration for assessment for scholarship. Parents are welcome to approach the school to ask for their child to be assessed for a scholarship. Ultimately the school's decision is final. Scholarships are usually tenable until the end of Fifth form providing the holder's academic progress and general conduct remains satisfactory and provided that the holder continues enthusiastically to fulfil the obligations associated with the scholarship.
Scholarships are reviewed annually, at the end of each academic year. Sixth Form Scholarships are tenable for two years but are reviewed after the completion of the first year. There is a separate process for application for a Sixth Form Scholarship.
The award of any scholarship carries with it privilege and responsibility; every scholarship holder is expected to set an example for the other pupils in their conduct and approach to academic study, and to participate in the fuller life of the School through commitment to extra-curricular activities. All scholarships are liable to be rescinded in the case of the student not meeting their potential or obligations explicitly stated in the granting of the scholarship.
Academic Scholarships
Academic Scholarships on entry at First form (11+) and Third form (13+) are assessed by an overall performance in the three Entrance tests, i.e. the English, Maths and Non- Verbal Reasoning (NVR) papers. School references are also obtained from the feeder school. The top performing students will be invited to an interview with the Head. This interview may involve a presentation by the student.
Sixth Form Academic Scholarships are through a Sixth Form Scholarship examination which is normally sat in February. Students performing well on this paper will be invited to attend an interview with the Head. Entry into the Sixth Form is also dependent upon a student meeting the entrance criteria as set out in Ackworth's Admission Policy.
Music Scholarships
Music Scholarships are assessed by auditions and through practical assessments. The financial implications of a Music Scholarship will provide for individual lessons on one instrument, or voice. Any conditions pertaining to the award of this Scholarship are stated in the letter offering the Scholarship. A pre-audition is highly recommended.
Sixth Form Music Scholarships are awarded during the Spring term of the Fifth form following recommendation, consultation and practical assessment by the Director of Music along with an interview with the Head. A letter inviting all Fifth Form students wishing to be considered for a Music Scholarship is sent to Fifth Form parents and also to external applicants for Sixth Form places.
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Art Scholarships are assessed by the presentation of a portfolio and through practical assessments. The financial implications of an Art Scholarships will be a fee remission of 5% of the annual day fee. Any conditions pertaining to the award of this Scholarship are stated in the letter offering the Scholarship. Presentation to the Head of Art of a portfolio of recent work prior to the application for an Art Scholarship is highly recommended.
Sixth Form Art Scholarships are awarded during the Spring term of the Fifth Form following recommendation, consultation and practical assessment by the Head of Art and an interview with the Head. A letter inviting all Fifth Form students wishing to be considered for an Art Scholarship is sent to Fifth Form parents and also to external applicants for Sixth Form places.
Drama Scholarships
Drama Scholarships may be awarded to students who show exceptional potential in drama. Drama Scholarships are assessed by auditions and through practical assessments. The financial implications of a Drama Scholarships will be a fee remission of 5% of the annual day fee. Any conditions pertaining to the award of this Scholarship are stated in the letter offering the Scholarship. A pre-audition is highly recommended.
Sixth Form Drama Scholarships are awarded during the Spring term of the Fifth Form following recommendation, consultation and practical assessment by the Head of Drama along with an interview with the Head. A letter inviting all Fifth Form students wishing to be considered for a Drama Scholarship is sent to Fifth Form parents and also to external applicants for Sixth Form places.
Sports Scholarships may be awarded for students who show exceptional potential in team and individual sports offered within the curriculum. Sports Scholarships are assessed through practical assessments. The financial implications of a Sports Scholarship will be a fee remission of 5% of the annual day fee. Any conditions pertaining to the award of this Scholarship are stated in the letter offering the Scholarship. A pre-assessment is highly recommended.
Sixth Form Sports Scholarships are awarded during the Spring term of the Fifth Form following recommendation, consultation and practical assessment by the Head of Sport along with an interview with the Head. A letter inviting all Fifth Form students wishing to be considered for a Sports Scholarship is sent to Fifth Form parents and also to external applicants for Sixth Form places.
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For those currently at the School entering the Sixth Form, scholarships may be awarded for entry on the basis of outstanding GCSE results, and these will be known as GCSE Scholarships. They will be honorary, but parents will then have the opportunity to apply to supplement the Scholarship by a Bursary, based upon the financial circumstances of the candidate's parents.
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The Highest Scholarship Award, a single payment, is made to recognise excellence in A Level final examinations. Normally two awards are offered but in exceptional circumstances awards may be split. The Award is at the discretion of the Head.
In order to ensure that funding is fairly, socially, responsibly and most effectively employed, all bursaries are means assessed. The award of a bursary will remain solely dependent on the completion and assessment of a bursary form. The use of means testing for bursaries allows the award of bursaries to be up to the value of 100% fee remission, although this level of support is extremely rare with between 10% and 50% of day fees being the normal range. The financial value of a means tested bursary award is reassessed annually to ensure the ethical distribution of funds is maintained.
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Requests for information and applications for support from members of the Religious Society of Friends or Attenders, in good standing, or for support from the Friends Schools' Joint Bursary Scheme should be directed to the Bursar.
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All other requests for bursarial support should be addressed to the Head in the first instance.
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After a few days of rain and cold, today's change in weather was welcome! And it seemed fitting to change up my birding adventures by heading out to some new territory. With Black Vultures as my target, Doug Happ and I birded through the Lewiston and Niagara Falls areas.
Three Sisters Islands in Niagara Falls was powerful and scenic - and very birdy. We ran into Jim Pawlicki who gave us a tip on where to find some warblers and for later on, Black Vultures. We did well with the warblers, finding at least 12 identifiable species in the park, a Warbling Vireo, a Greater Black-backed Gull, and... and something I never expected, one of my two nemesis birds: a YELLOW-BILLED CUCKOO! As we were in the park area enjoying all the warblers, I noticed a larger, light breasted bird fly into a tree up ahead. I nearly dismissed it, as I was totally wrapped up with all the little jewels flitting all around us. Thankfully, I raised my binoculars and nearly fell over - a Yellow-billed Cuckoo was sitting there big as life! Stunned, I somehow managed to get a few photos of him before he flew off. Shortly after that, Doug spotted a Black-billed Cuckoo. How often does THAT happen?!
Finally, pulling ourselves away from all the warblers, we set out in search of a Black Vulture, stopping at a few places that had been recommended to us. It wasn't until we got to our last spot that we found not only saw one but FIVE Black Vultures. I honestly can't say I was enamored with these birds, their black, featherless face looked downright ugly to me. But that's just my humble opinion - and beauty IS in the eye of the beholder; right?!
Yellow-billed Cuckoo - a life bird!
Sounds like a very satisfying and fun day. The Warblers look very similar to me. I'm impressed that you can identify them so easily. It was a beautiful day yesterday. Good that you're taking advantage of Fall migration on these pleasant days.


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BCS Review Series: 1999, FSU Dynasty vs. Michael Vick
Part 2 of a series: Over the next few weeks, I will be reviewing each of the 16 seasons since the Bowl Championship Series came into existence in 1998. Here is a look back at who got lucky, who got robbed, what could've been, what should've been and other controversies of the day. The series will appear throughout December and January.
Part 1: 1998, A New Beginning for College Football
Give yourself a big pat on the back, BCS. You deserve it. You got it right.
You matched up the only two undefeated major conference teams in the national championship game. Brilliant! Couldn't have done it without ya!
What's was left unsaid was: "Whew!"
Despite the obvious—only Florida State and Virginia Tech emerged from the regular season unbeaten—there were doubts about whether they'd face each other in the Sugar Bowl for the national championship. In the end, Virginia Tech had a barely comfortable margin to hold off one-loss No. 3 Nebraska to play in the title game.
But in the 16-year history of the BCS, 1999 was one of the most uneventful. The Seminoles went wire-to-wire as the No. 1-ranked team, their place in New Orleans never in question. Upset losses by Penn State and Tennessee in the first two weeks of November paved the way for Virginia Tech to seize the No. 2 ranking.
The Hokies, led by redshirt freshman quarterback Michael Vick, had to sweat out the final four weeks of the regular season mostly because of a soft schedule. With strength of schedule still a separate component accounting for nearly one-third of the BCS standings, Virginia Tech had a hard time gaining breathing room from the Cornhuskers, finishing just 1.30 points ahead in the final standings.
Just as in 1998, an undefeated non-BCS conference team finished the regular season unbeaten. And just like Tulane, a 12-0 Marshall team was shut out of a BCS bowl despite finishing No. 12 in the final standings. And one more thing like the Green Wave: The Thundering Herd, quarterbacked by Chad Pennington, completed a perfect season with a victory over BYU, in the Motor City Bowl.
In the Sugar Bowl, Vick rallied the Hokies to take a 29-28 lead at the end of the third quarter. But the Seminoles scored the game's final 18 points in the fourth quarter, giving Bobby Bowden his second and final national championship.
Complete Final BCS Standings
Rank Team Poll Avg. Computer SoS Loss BCS
1 Florida State 1.0 1.00 6 0 2.24
2 Virginia Tech 2.0 2.00 53 0 6.12
3 Nebraska 3.0 2.86 14 1 7.42
4 Alabama 5.5 4.57 1 2 12.11
5 Tennessee 5.5 5.57 16 2 13.71
Alternative Methods
Using post-2003 BCS formula: 1. Florida State, 2. Virginia Tech.
Likely four-team playoff: Florida State vs. Alabama; Virginia Tech vs. Nebraska.
The top four teams also won their respective conferences, making the selections fairly simple.
Kansas State snub II: Well, it wasn't quite as egregious as the one in 1998, but the Wildcats once again earned the dubious honor of being the highest-ranked team not invited to a BCS bowl. K-State, ranked No. 6 with its only loss to Nebraska, was passed up by the Fiesta Bowl (No. 5 Tennessee) and Orange Bowl (No. 8 Michigan). But unlike the previous year, the Wildcats managed to hold it together and win the Holiday Bowl, 24-20, over Washington.
Marshall snub: With today's arrangement, the Herd would've earned an automatic BCS berth. But with strength of schedule a key component in the formula at the time, Marshall was doomed by its 98th-place schedule. The MAC champs, however, would become the last undefeated team not to play in a BCS bowl.
1999 BCS Bowl Matchups
Game Score Attendance TV Rating
Sugar Bowl* #1 Florida St. 46, #2 Va. Tech 29 76,503 17.5
Rose Bowl #7 Wisconsin 17, Stanford 9 93.731 14.1
Orange Bowl #8 Michigan 35, #4 Alabama 34 (OT) 70,461 11.4
Fiesta Bowl #3 Nebraska 31, #5 Tennessee 21 71,526 9.6
BCS formula review: Five more computer rankings were added to the formula—Billingsley, Dunkel, Massey, Matthews and Rothman—bringing the total to eight. The lowest ranking among the eight was dropped, and the remaining seven averaged to produce the computer ranking. Also, a "Kansas State clause" was added, guaranteeing any team finishing in the top four a BCS bowl spot, but the Wildcats weren't in position to benefit from it.
Final analysis: Two years in, the BCS appeared to be producing the desired results. The title games matched deserving teams, and the other BCS bowls featured interesting matchups. But this was only the calm before the storm, as raging controversies were about to envelope the BCS, forcing major changes almost annually in the coming years.
Posted by Samuel Chi at 1:05 PM
Labels: BCS, BCS Years in Review, Florida State, Nebraska, Virginia Tech
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Academia Censorship Corruption Freedom of Speech Political Weaponization Twitter
Aspen Institute's New "Commission on Information Disorder"
by JMBK.NEWS July 11, 2021 July 13, 2021
Leave a Comment on Aspen Institute's New "Commission on Information Disorder"
America's next pandemic may be misinformation. In fact, Aspen Institute's latest privately funded endeavor "Commission on Information Disorder". vows to combat misinformation, no matter the risk.
The Commission pledges to empower the federal government to promote fact based information. Using words like "protect underrepresented groups" and "who have lost faith in evidence-based reality" raise questions. Will giving the federal government more power and control over free speech "protect" "underrepresented groups"? Should Americans be looking to the federal government for "faith"?
Relative to Communism, the government suggests they are a source of faith, above religion. Atheism is pushed in Communistic countries, as citizens may be willing to die to uphold their religious beliefs. Without religion, the population will obey the government as if it were God. This means there will be a lower percentage of rebellion among the oppressed. This is the reason why the Communist Party of China has the highest population of Atheism in the world.
The Aspen Institute's Commission of Information Disorder's website states "The Commission on Information Disorder aims to identify and prioritize the most critical sources and causes of information disorder and deliver a set of short-term actions and longer-term goals to help government, the private sector, and civil society respond to this modern-day crisis of faith in key institutions."
"The most effective policy solutions and stakeholders to address those most damaging near-term disinformation threats"
"The lawful and ethical means by which the federal government can promote fact-based information to counter the most dangerous disinformation campaigns"
"How government, private industry, and civil society can work together in the short term to help protect underrepresented groups, and engage disaffected populations who have lost faith in evidence-based reality"
"The longer-term, more foundational challenges that will require deeper societal engagement to address"
"The Commission on Information Disorder consists of three co-chairs and 15 commissioners, representing key perspectives drawn from government, research and academia, civil society, public service, and private industry. The composition of the Commission is intended to represent a diversity of expertise, backgrounds, and lived experience. We also draw upon both formal and informal expert advisors and additional research as needed."
What is Information Disorder? The term is so ambiguous, that the Aspen Institute actually calls for "submissions" from "stakeholders" to "identify and prioritize" the sources of information disorder to help "government" respond to this "crisis of faith".
Members include Prince Harry, Nevada Attorney General Dr. Aaron Ford, Former Texas Congressman Will Hurd, Dr. Herb Lin of Stanford, Prof. Deb Roy of MIT, Chris Krebs Director of Cyber Security at the Department of Homeland Security.
Could this be a step closer to the transfer of power over free speech? Why has mass censorship become a political center focus? Should Americans have the right to decide what source is considered "information"? By providing the government access to gain deeper control of our lives, we ultimately lose more of our own private liberty.
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Q: Some Extra Words In an Embedded Question I have seen the following sentence:

They reported whatever it was he did.

I wonder whether "it was" should not be removed to have a grammatical structure.
If the sentence is grammatical, what is the semantic difference between the sentence and the one without "it was"?

A: While Seowjooheng's answer is good, it may not be complete.
As a native Englishman, I interpret the two sentences differently.

*

*They reported whatever he did.

This means, they watched him (over a period of time), and every single thing he did, they reported. "First he sat down, then he pulled a handkerchief out of his pocket, then he blew his nose, then he ..."

*

*They reported whatever it was he did.
This means:
"He did something specific, but we (who read the sentence) don't know what that something is. But what we do know is: Whatever that (reportable) thing was, they reported it."

A:
[1] They reported whatever it was [that] he did.

[2] They reported whatever he did.

Both have similar meanings but their sentence structures are different.
whatever it was he did is a subordinate interrogative clause functioning as direct object of reported.  it and was are the subject and linking verb respectively. I have inserted [that] to show that he did is a reduced relative clause within this subordinate clause.
whatever he did similarly is a subordinate interrogative clause functioning as direct object of reported.  he and did are the subject and action verb respectively.


Bachelorette parties are a lot of fun, but planning the event can be a stressful task for bridesmaids, family members, and friends. The following guide focuses on unique, non-traditional ideas to help you plan an event tailored to the taste of the bride-to-be and her bridesmaids. The Pittsburgh area has plenty of options for creative bachelorette parties, no matter the theme.
Find out how involved the bride-to-be would like to be. She may want to be surprised by the festivities, or she may want to help plan every detail. Either way, start planning early.
Discuss the invitation list with the bride. Does she want to invite just the bridesmaids? Or family, too? Or an even larger group?
It's her big celebration, so consider her personal style. Does she like to party or be pampered or something else entirely? Plan an event that will be true to her.
Finally, remember to bring a camera to chronicle your memories of the festivities.
Wedding planning is stressful. Help the bride relax with a day of pampering. Massages, manicures, pedicures, and facials are a great way to unwind. The bright and inviting Spa Jema, located downtown, is among the best in Pittsburgh. Or take pampering to the next level with a weekend at Nemacolin Woodlands Resort, known for its lavish spa. Nemacolin's spa packages feature yoga, meditation, and traditional spa treatments.
Create a piece of art to remember the party for years to come. There are several options in the area for paint nights, including Painting with a Twist, Corks and Canvases, and Paint Monkey. You bring the wine and a creative spirit, they'll provide the canvas and the instructor. The instructors provide detailed directions, so even those without art experience can create something beautiful.
For the foodie bride, try a cooking class at Gaynor's School of Cooking. The school offers several menus and varying levels of involvement in the cooking process. Wine aficionados, check out a wine tasting at Dreadnought Wines in Lawrenceville.
Sip spirits in the most regal place downtown—the Omni William Penn Hotel. The grand hotel's lobby is a great place for group photos (don't forget to look up at the stunning chandeliers). Then, head downstairs to the Speakeasy, a genuine Prohibition-era bar, for drinks.
Grab your dancing shoes, and head to piano bar Howl at the Moon in downtown or party spot Buckhead Saloon in Station Square. Pro tip: Check out the bachelorette party specials at Buckhead.
Try a group fitness class at Iron City Circus Arts in Brentwood. An aerial circus party or a pole dance night would certainly make for a memorable (and endorphin-filled) bachelorette evening. Or drive to Seven Springs for a weekend full of biking, swimming, and zip-lining.