text:
\section{Introduction}

Coherent excitation influenced by dephasing processes represents an
important topic in quantum mechanics \cite{B.Shore},\cite{A-E}. Applications
of such models are numerious ranging from coherent atomic excitation and
quantum information to chemical physics and solid-state physics. Although a
significant effort have been devoted for studding the Bloch equations
corresponding to specific two-state models, almost all results are related
to some asymptotic regimes as weak dephasing, strong coupling or other
limits \cite{Vitanov}. There are very few exact solutions for the Bloch
equation. The complexity of this problem is due to the difficulty of
deriving an exact solution for third order linear differential equations. In
the case of resonant coherent excitation of a two-state system in the
presence of dephasing, solution can be found in \cite{Kyoseva}.

The original Demkov have been introduced in the theory of atomic collisions
\cite{Demkov}.

\section{Demkov model in the presence of dephasing\label{Sec-background}}

Dephasing processes can be incorporated into the description of resonant
excitation by including a phenomenological dephasing rate $\Gamma =1/T_{2}$,
where $T_{2}$ is the transverse relaxation time, into the Bloch equation,
\begin{equation}
\frac{\text{d}}{\text{d}t}\left[
\begin{array}{c}
u(t) \\
v(t) \\
w(t)%
\end{array}%
\right] =\left[
\begin{array}{ccc}
-\Gamma & -\Delta & 0 \\
\Delta & -\Gamma & -\Omega (t) \\
0 & \Omega (t) & 0%
\end{array}%
\right] \left[
\begin{array}{c}
u(t) \\
v(t) \\
w(t)%
\end{array}%
\right] ,  \label{Bloch-eq}
\end{equation}%
where the components of the Bloch vector $\left[ u(t),v(t),w(t)\right] ^{T}$
are expressed via density matrix elements $\rho _{mn}$ $\left(
m,n=1,2\right) $, as follows

\begin{eqnarray}
u(t) &=&2\text{Re}\rho _{12}(t)  \label{Bloch-vector} \\
v(t) &=&2\text{Im}\rho _{12}(t)  \notag \\
w(t) &=&\rho _{22}(t)-\rho _{11}(t)  \notag
\end{eqnarray}%
Hereafter the language of laser-atom interactions will be used, although the
results apply to any two-state system.The detuning $\Delta =\omega
_{0}-\omega $ is the difference between the transition frequency $\omega
_{0} $ and the carrier laser frequency $\omega $. The time-varying Rabi
frequency $\Omega (t)=\left\vert dE(t)\right\vert /\hbar $ describes the
laser-atom interaction, where $d$ is the electric dipole moment for the $%
\psi _{1}\leftrightarrow \psi _{2}$ transition and $E(t)$ is the laser
electric field envelope. For the Demkov model we have

\begin{eqnarray}
\Delta &=&\text{const,}  \label{Demkov-model} \\
\Omega (t) &=&\Omega _{0}\exp (-\left\vert t\right\vert /T),  \notag
\end{eqnarray}

\begin{equation*}
\Gamma =\text{const}
\end{equation*}%
The constant dephasing rate $\Gamma $ is a positive constant, and $T$ is the
characteristic pulse width. The peak Rabi frequency $\Omega _{0}$ will be
assumed also positive without loss of generality. For $\Gamma =0$, the Bloch
equation Eq.(\ref{Bloch-eq}) is solved exactly and this solution represents
the famous Demkov model \cite{Demkov} introduced in the theory of atomic
collisions.

We shall solve Eq.(\ref{Bloch-eq}) with the initial conditions corresponding
to a system initially in state $\left\vert 1\right\rangle $ i.e. $\rho
_{11}(-\infty )=1$ and $\rho _{22}(-\infty )=0.$ This corresponds to%
\begin{equation}
u(-\infty )=v(-\infty )=0,\text{ \ \ }w(-\infty )=-1.  \label{u-v-w-initial}
\end{equation}%
Our objective is to find the Bloch vector $\left[ u(t),v(t),w(t)\right] ^{T}$
and particulary, the population inversion $w(+\infty )$

\section{Analytic solution of the Demkov model}

Due to the specific form of the Demkov model, it is necessary to consider
the following two cases: $t\in I_{1}(-\infty ;0]$ and $t\in I_{2}[0;+\infty
).$ Let us begin with the first of them. Using Eq.(\ref{Demkov-model}) from
the Bloch system, Eq.(\ref{Bloch-eq}) we obtain third order differential
equation for the population inversion $w,$ which reads.%
\begin{gather}
\dddot{w}_{1}-2(T^{-1}-\Gamma )\ddot{w}_{1}+\left[ (T^{-1}-\Gamma
)^{2}+\Delta ^{2}+\Omega _{0}^{2}e^{2t/T}\right] \dot{w}_{1}+  \label{w-eq}
\\
\Omega _{0}^{2}(T^{-1}+\Gamma )e^{2t/T}w_{1}=0  \notag
\end{gather}%
A subscript "$1$" in the notation for the population inversion $w_{1}$
indicates that the Eq.(\ref{w-eq}) above and all formulas hereafter concerns
the time interval $t\in I_{1}(-\infty ;0].$ The solution of Eq.(\ref{w-eq})
can be expressed in terms of the generalized hypergeometric function $%
_{1}F_{2}(a_{1};b_{1},b_{2};x).$ Using the transformation

\begin{equation}
x=-\frac{1}{4}(T\ \Omega _{0})^{2}e^{2t/T}  \label{x-t}
\end{equation}

Eq. (\ref{w-eq}) is transformed to the following form%
\begin{gather}
x^{2}w_{1}^{^{\prime \prime \prime }}+x(2+T\ \Gamma )w_{1}^{^{\prime \prime
}}+  \label{w(x)-eq} \\
\left[ T\ \Gamma +\frac{(1-T\ \Gamma )^{2}+\Delta ^{2}}{4}-x\right]
w_{1}^{^{\prime }}-\frac{(1+T\ \Gamma )}{2}w_{1}=0  \notag
\end{gather}

Generalized hypergeometric function (GHF) $_{1}F_{2}(a_{1};b_{1},b_{2};x)$
satisfies the equation \cite{Rainville}%
\begin{equation}
x^{2}F^{^{\prime \prime \prime }}+(b_{1}+b_{2}+1)xF^{^{\prime \prime
}}+(b_{1}b_{2}-x)F^{^{\prime }}-a_{1}F=0,  \label{GHF-eq}
\end{equation}%
where $F$ is shortened notation for $_{1}F_{2}(a_{1};b_{1},b_{2};x)$. More
details regarding basic definitions and formulas for GHF are placed in sec.
Appendix. By comparing Eq.(\ref{w(x)-eq}) and Eq.(\ref{GHF-eq}), it is
trivial algebra to determine parameters $a_{1};b_{1},b_{2}$ of the GHF

\begin{equation}
b_{1}=\frac{1}{2}+\frac{T\ \Gamma }{2}+i\frac{T\ \Delta }{2},\
b_{2}=(b_{1})^{\ast },\ a_{1}=\text{Re}(b_{1}),  \label{a1-b1-b2}
\end{equation}%
where as usual the notation "$\ast $" stands for complex conjugation. By
reason to simplify the writing of the formulas, hereafter we use

\begin{equation}
\gamma =\frac{T\ \Gamma }{2};\ \delta =\frac{T\ \Delta }{2};\ \omega =\frac{%
T\ \Omega _{0}}{2}.  \label{g-d-o}
\end{equation}%
Using Eq.(\ref{GHF-f-s}) and Eq.(\ref{a1-b1-b2} ) we obtain the fundamental
set of solutions for the problem%
\begin{widetext}
\begin{gather}
w_{1}(t)=A_{_{-}1}F_{2}\left( \frac{1}{2}+\gamma ;\frac{1}{2}+\gamma
+i\delta ,\frac{1}{2}+\gamma -i\delta ;-\omega ^{2}e^{2t/T}\right)
+B_{-}(-\omega ^{2}e^{2t/T})^{\frac{1}{2}-\gamma -i\delta }\!_{1}F_{2}\left(
1-i\delta ;\frac{3}{2}-\gamma -i\delta ,1-2i\delta ;-\omega
^{2}e^{2t/T}\right) +  \notag \\
C_{-}(-\omega ^{2}e^{2t/T})^{\frac{1}{2}-\gamma +i\delta
}\!_{1}F_{2}\left( 1+i\delta ;1+2i\delta ,\frac{3}{2}-\gamma
+i\delta ;-\omega ^{2}e^{2t/T}\right) .  \notag \label{wtSol}
\end{gather}
\end{widetext}
In Eq.(\ref{wtSol}) $A_{-},$ $B_{-}$ and $C_{-}$ are integration constants.
Next step toward full solution is to determine the integration constants
from the initial conditions given by Eq.(\ref{u-v-w-initial}). Using Eq.(\ref%
{Bloch-eq}) it is straightforward to rewrite the initial conditions given by
Eq.(\ref{u-v-w-initial}) into%
\begin{equation}
w_{1}(-\infty )=-1,\ \dot{w}_{1}(-\infty )=0,\ \ddot{w}_{1}(-\infty )=0
\label{w-initial}
\end{equation}

From the transformation Eq.(\ref{x-t}) we observe that $x(-\infty )=0$ and
keep in mind Eq.(\ref{F(0)}) we will determine the integration constants $%
A_{-},$ $B_{-}$ and $C_{-}.$ One should note that the exponential factors $%
(-\omega ^{2}e^{2t/T})^{\frac{1}{2}-\gamma -i\delta }$ and $(-\omega
^{2}e^{2t/T})^{\frac{1}{2}-\gamma +i\delta }$ oscillate and when $1/2<\gamma
$ diverge in the limit $t\rightarrow -\infty $ $.$ In reason to have finite
value $w_{1}(-\infty )=-1$ we obtain%
\begin{equation}
A_{1}=-1,~B_{1}=C_{1}=0.  \label{A-B-C-initial}
\end{equation}

Finally in the interval $t\in I_{1}(-\infty ;0]$ the solution reads%
\begin{equation}
w_{1}(t)=-\!_{1}F_{2}\left( \frac{1}{2}+\gamma ;\frac{1}{2}+\gamma +i\delta ,%
\frac{1}{2}+\gamma -i\delta ;-\omega ^{2}e^{2t/T}\right) .
\label{w(t)-solution1}
\end{equation}%
Demkov model has a cusp for $\Omega (t)$ at $t=0$. This requires to derive a
solution for the interval $t\in I_{2}[0;+\infty )$, where the new initial
conditions at $t=0$ are obtained using Eq.(\ref{w(t)-solution1}) and Eq.(\ref%
{D-GHF}). We should stress that the initial condition given by Eq.(\ref{w1-2}%
) has not been derived by taking the second derivative of Eq.(\ref%
{w(t)-solution1}) at $t=0$. Because of the specific properties of the Demkov
model, i.e. cusp of the Rabi frequency $\Omega (t)$ at $t=0,$ one should
take the correct derivative of $\Omega (t)$ at $t\rightarrow 0_{+}$ and than
using the Bloch equations given by Eq.(\ref{Bloch-eq}), rigorously to obtain
the initial condition Eq.(\ref{w1-2}).

\begin{widetext}
\begin{eqnarray*}
w_{1}(0) &=&-\!_{1}F_{2}\left( \frac{1}{2}+\gamma ;\frac{1}{2}+\gamma
+i\delta ,\frac{1}{2}+\gamma -i\delta ;-\omega ^{2}\right) \newline
\\
\dot{w}_{1}(0) &=&\frac{2\left( \frac{1}{2}+\gamma \right) \omega ^{2}}{T%
\left[ \left( \frac{1}{2}+\gamma \right) ^{2}+\delta ^{2}\right] }%
\!_{1}F_{2}\left( \frac{3}{2}+\gamma ;\frac{3}{2}+\gamma +i\delta ,\frac{3}{2%
}+\gamma -i\delta ;-\omega ^{2}\right)  \\
\ddot{w}_{1}(0) &=&\frac{4\omega ^{2}\left( \frac{1}{2}+\gamma \right)
(1-T^{2})}{T^{2}\left[ \left( \frac{1}{2}+\gamma \right) ^{2}+\delta ^{2}%
\right] }\left[ _{1}F_{2}\left( \frac{3}{2}+\gamma ;\frac{3}{2}+\gamma
+i\delta ,\frac{3}{2}+\gamma -i\delta ;-\omega ^{2}\right) \right. + \\
&&\left. \frac{4\omega ^{2}\left( \frac{1}{2}+\gamma \right) \left( \frac{3}{%
2}+\gamma \right) }{T^{2}\left[ \left( \frac{1}{2}+\gamma \right)
^{2}+\delta ^{2}\right] \left[ \left( \frac{3}{2}+\gamma \right)
^{2}+\delta ^{2}\right] }\!_{1}F_{2}\left( \frac{5}{2}+\gamma
;\frac{5}{2}+\gamma +i\delta ,\frac{5}{2}+\gamma -i\delta ;-\omega
^{2}\right) \right] \label{w1-2}
\end{eqnarray*}
\end{widetext}
By analogy with Eq.(\ref{w-eq}) for the time interval $t\in I_{2}[0;+\infty
) $ we have the following equation for the population inversion
\begin{gather}
\dddot{w}_{2}+2(T^{-1}+\Gamma )\ddot{w}_{2}+\left[ (T^{-1}+\Gamma
)^{2}+\Delta ^{2}+\Omega _{0}^{2}e^{-2t/T}\right] \dot{w}_{2}+  \label{w2-eq}
\\
\Omega _{0}^{2}(-T^{-1}+\Gamma )e^{-2t/T}w_{2}=0.  \notag
\end{gather}%
The solution can again be expressed in term of GHF, after the transformation%
\begin{equation*}
x=-\frac{1}{4}(T\ \Omega _{0})^{2}e^{-2t/T}.
\end{equation*}%
The solution of the equation for the population inversion $w_{2}$ within the
time interval $t\in I_{2}[0;+\infty ),$ reads%
\begin{equation}
w_{2}(t)=A_{+}f_{1}+B_{+}f_{2}+C_{+}f_{3}.  \label{w2(t)-sol}
\end{equation}%
In this equation by reason to simplify some cumbersome formulas, we will
denote the three linearly independent solutions of Eq.(\ref{w2(t)-sol}) with
$f_{1},$ $f_{2}$ and $f_{3}.$ Adopting the notations introduced by Eq.(\ref%
{g-d-o}) $f_{1},$ $f_{2}$ and $f_{3}$ are given by
\begin{widetext}
\begin{subequations}
\label{f-all}
\begin{eqnarray}
f_{1}(t) &=&\!_{1}F_{2}\left( \frac{1}{2}-\gamma ;\frac{1}{2}-\gamma
-i\delta ,\frac{1}{2}-\gamma +i\delta ;-\omega ^{2}e^{-2t/T}\right)
\label{f1} \\
f_{2}(t) &=&\!(-\omega ^{2}e^{-2t/T})^{\frac{1}{2}+\gamma +i\delta
}\!_{1}F_{2}\left( 1+i\delta ;\frac{3}{2}+\gamma +i\delta ,1+2i\delta
;-\omega ^{2}e^{-2t/T}\right)  \label{f2} \\
f_{3}(t) &=&(-\omega ^{2}e^{-2t/T})^{\frac{1}{2}+\gamma -i\delta
}\!_{1}F_{2}\left( 1-i\delta ;1-2i\delta ,\frac{3}{2}+\gamma -i\delta
;-\omega ^{2}e^{-2t/T}\right)  \label{f3}
\end{eqnarray}%
\end{subequations}
\end{widetext}We have determined the integration constants $A_{-},$ $B_{-}$
and $C_{-}$ by using the asymptotic behaviours of the exponential factors $%
(-\omega ^{2}e^{2t/T})^{\frac{1}{2}-\gamma -i\delta }$ and $(-\omega
^{2}e^{2t/T})^{\frac{1}{2}-\gamma +i\delta }.$ This simple argumentation
cannot be used for Eq.(\ref{w2(t)-sol}) and respectively for $A_{+},$ $B_{+}$
and $C_{+}.$ We will determine the integration constants $A_{+},$ $B_{+}$
and $C_{+}$ using the initial conditions at $t=0$, given by Eq.(\ref%
{w1-2}). The textbook method requires to write a linear system of
equations for the unknown variables $A_{+},$ $B_{+}$ and $C_{+}$.
This is
done using Eq.(\ref{w2(t)-sol}) by taking $w_{2}(0)$ and the derivatives $%
\dot{w}_{2}(0)$ and $\ddot{w}_{2}(0).$ After straightforward albeit tedious
algebra, using Eq.(\ref{w1(0)-all}) and Eq.(\ref{f-all}) we obtain the
solution for the integration constants

\label{A2-B2-C2-all}
\begin{subequations}
\begin{eqnarray}
A_{+} &=&\frac{\left[
\begin{array}{ccc}
w_{1}(0) & f_{2}(0) & f_{3}(0) \\
\dot{w}_{1}(0) & \dot{f}_{2}(0) & \dot{f}_{3}(0) \\
\ddot{w}_{1}(0) & \ddot{f}_{2}(0) & \ddot{f}_{3}(0)%
\end{array}%
\right] }{W[f_{1}(0),f_{2}(0),f_{3}(0)]},  \label{A2} \\
B_{+} &=&\frac{\left[
\begin{array}{ccc}
f_{1}(0) & w_{1}(0) & f_{3}(0) \\
\dot{f}_{1}(0) & \dot{w}_{1}(0) & \dot{f}_{3}(0) \\
\ddot{f}_{1}(0) & \ddot{w}_{1}(0) & \ddot{f}_{3}(0)%
\end{array}%
\right] }{W[f_{1}(0),f_{2}(0),f_{3}(0)]},  \label{B2} \\
C_{+} &=&\frac{\left[
\begin{array}{ccc}
f_{1}(0) & f_{2}(0) & w_{1}(0) \\
\dot{f}_{1}(0) & \dot{f}_{2}(0) & \dot{w}_{1}(0) \\
\ddot{f}_{1}(0) & \ddot{f}_{2}(0) & \ddot{w}_{1}(0)%
\end{array}%
\right] }{W[f_{1}(0),f_{2}(0),f_{3}(0)]}.  \label{C2}
\end{eqnarray}%
The denominator of the expressions for $A_{+},$ $B_{+}$ and $C_{+}$ is the
Wronskian for the three linearly independent solutions $f_{1},$ $f_{2}$ and $%
f_{3}$.

Finally, we can write the solution for the Demkov model, bringing together
the results from Eqs.(\ref{w(t)-sol}), (\ref{A-B-C-initial}), (\ref%
{w2(t)-sol}), (\ref{f-all}) and (\ref{A2-B2-C2-all})
\end{subequations}
\begin{equation}
w(t)=w_{1}(t)\theta (-t)+w_{2}(t)\theta (t),  \label{w1+w2}
\end{equation}%
where $\theta (t)$ is the Heaviside "unit step" function. In the very some
manner the reader could derive solutions for the coherence components of the
Bloch vector $u(t)$ and $v(t).$ Hereafter our main concern will be to
investigate the solution for the population inversion $w(t).$

For variate of applications using exact soluble models, the final transition
probability expressed via $w(+\infty )$ is more important than time
dependent behaviour of the $w(t)$ itself. Having in mind the Demkov model
and its solution given by Eq.(\ref{w1+w2}), it is easy to be seen that only
the expression for $w_{2}(t)$ is important, when the final transition
probability is considered. A closed look to the three linearly independent
solutions $f_{1},$ $f_{2}$ and $f_{3}$ reveal that only $f_{1}$ term will
survive under the limit $t\rightarrow +\infty $. This is due to the
exponential factors $\!(-\omega ^{2}e^{-2t/T})^{\frac{1}{2}+\gamma +i\delta
} $ and $(-\omega ^{2}e^{-2t/T})^{\frac{1}{2}+\gamma -i\delta }$, which tend
to zero at $t\rightarrow +\infty $. Using Eq.(\ref{F(0)}) we arrive at the
following expression
\begin{equation}
w(+\infty )=A_{+}.  \label{w-infinity}
\end{equation}%
Although we have closed analytic result for the time dependent $w(t)$ as
well as $w(+\infty )$, their complexity impose the use of asymptotic
expressions for various limits.

\begin{figure}[tb]
\includegraphics[width=75mm]{expg1.jpg}
\caption{Components of the Block vector. $u(t)$ is plotted with black curve;
$v(t)$ is plotted with blue curve; $w(t)$ is plotted with red curve; Model
parameters are the following $\protect\delta=1.5 $, $\protect\omega_{0}=25 $%
, $\protect\gamma=0.1 $}
\label{blockvector}
\end{figure}

Figure \ref{blockvector} displays the time evolution of the components of
the Block vector for a specific values of the parameters.

\section{Resonant coherent excitation}

Coherent resonant excitation represents an important notion in coherent
quantum processes. Besides from the requirement that the frequency of the
external field must be equal to the Bohr transition frequency i.e the
resonance condition, crucial condition for such processes is also the
coherence. Having derived the analytic solutions for the Demkov model in the
general case it is instructive to investigate the resonant regime. In this
simplified case the Bloch equations take the following form

\begin{eqnarray}
\frac{\text{d}}{\text{d}t}u^{r}(t) &=&-\Gamma u^{r}(t),
\label{Bloch-resonance-u} \\
\frac{\text{d}}{\text{d}t}\left[
\begin{array}{c}
v^{r}(t) \\
w^{r}(t)%
\end{array}%
\right] &=&\left[
\begin{array}{cc}
-\Gamma & -\Omega (t) \\
\Omega (t) & 0%
\end{array}%
\right] \left[
\begin{array}{c}
v^{r}(t) \\
w^{r}(t)%
\end{array}%
\right] .  \label{Bloch-resonance-u-w}
\end{eqnarray}%
In the last formula index "$r$" stands for resonant solution of the Bloch
vector. For the resonant case the Bloch equations factorize to a single
equation for the coherence $u^{r}(t)$ and a system of two equations for the
remaining components of the Bloch vector $\left[ v^{r}(t),w^{r}(t)\right]
^{T}$. Although the solution of the full Demkov problem requires three
linearly independent solutions written in Eqs.(\ref{f-all}), the solution
for the population inversion $w^{r}(t)$ in the resonant case, is derived
from Eq.(\ref{Bloch-resonance-u-w}). This system is reducible to a linear
differential equation of second order, that posses two linearly independent
solutions $f_{1}^{r}(t)$ and $f_{2}^{r}(t)$. Having in mind the symmetry of
the GHF and Eqs.(\ref{f-all}) it is seen that for the interval $t\in
I_{2}[0;+\infty )$, the solutions for the resonant case $\Delta =0,$ are
given by%
\begin{equation*}
f_{1}^{r}(t)=f_{1}(t)|_{\Delta
=0};~f_{2}^{r}(t)=f_{3}^{r}(t)=f_{2}(t)|_{\Delta =0}=f_{3}(t)|_{\Delta =0}
\end{equation*}
Furthermore the condition $\Delta =0,$ lead to significant simplification of
the GHF, which is given by the relation between the GHF and the Bessel
function

\begin{equation}
\!_{1}F_{2}\left( a;a,b;z\right) =\text{ }_{0}F_{1}\left( \text{ }%
;b;z\right) =\Gamma (b)\left( -z\right) ^{\frac{1-b}{2}}J_{b-1}(2\sqrt{-z}).
\label{GHF-Bessel}
\end{equation}%
Using Eq.(\ref{w(t)-sol}) and Eq.(\ref{GHF-Bessel}) we obtain the solution
for the resonant Demkov model within the interval $t\in I_{1}(-\infty ;0]$%
\begin{equation}
w_{1}^{r}(t)=-\ \Gamma \left( \frac{1}{2}+\gamma \right) \left( \omega \!\
e^{t/T}\right) ^{\frac{1}{2}+\gamma }J_{-\frac{1}{2}+\gamma }(2\omega \!\
e^{t/T}).  \label{wr1(t)-sol}
\end{equation}
By analogy with the initial conditions Eq.(\ref{w1(0)-all}) for the resonant
case we obtain \label{w1r(0)-all}
\begin{eqnarray}
w_{1}^{r}(0) &=&-\ \Gamma \left( \frac{1}{2}+\gamma \right) \omega \!^{\frac{%
1}{2}-\gamma }J_{-\frac{1}{2}+\gamma }(2\omega \!\ ),  \label{w1r-0} \\
\dot{w}_{1}^{r}(0) &=&\frac{2}{T\left( \frac{1}{2}+\gamma \right) }\!\Gamma
\left( \frac{3}{2}+\gamma \right) \omega \!^{\frac{3}{2}-\gamma }J_{\frac{1}{%
2}+\gamma }(2\omega \!\ ).  \label{w1r-1}
\end{eqnarray}

Having in mind the symmetry of the GHF, it is seen that for the interval $%
t\in I_{2}[0;+\infty )$, the solutions for the resonant case are given by
Eqs.(\ref{f-all}), where $f_{2}(t)=f_{3}(t),$ under the constrain $\Delta
=0. $ For the time interval $t\in I_{2}[0;+\infty )$ we have the following
solution of the equation for the population inversion
\begin{equation}
w_{2}^{r}(t)=A_{+}^{r}f_{1}^{r}+B_{+}^{r}f_{2}^{r}.  \label{wr2(t)-sol}
\end{equation}

In Eq.(\ref{wr2(t)-sol}) the following notation were used \label{fr-all}
\begin{eqnarray}
f_{1}^{r}(t) &=&\ \Gamma \left( \frac{1}{2}-\gamma \right) \left( \omega \!\
e^{-t/T}\right) ^{\frac{1}{2}+\gamma }J_{-\frac{1}{2}-\gamma }(2\omega \!\
e^{-t/T}),  \label{f1r} \\
f_{2}^{r}(t) &=&\!(-1)^{\frac{1}{2}+\gamma }\!\left( \omega \!\
e^{-t/T}\right) ^{\frac{3}{2}+3\gamma }\Gamma \left( \frac{1}{2}-\gamma
\right) J_{-\frac{1}{2}-\gamma }(2\omega \!\ e^{-t/T}).  \label{f2r}
\end{eqnarray}%
Integration constants $A_{+}^{r}$ and $B_{+}^{r}$ are given by \label%
{A2r-B2r}
\begin{eqnarray}
A_{+}^{r} &=&\frac{\left[
\begin{tabular}{ll}
$w_{1}^{r}(0)$ & $f_{2}^{r}(0)$ \\
$\dot{w}_{1}^{r}(0)$ & $\dot{f}_{2}^{r}(0)$%
\end{tabular}%
\right] }{W[f_{1}^{r}(0),f_{2}^{r}(0)]},  \label{A2r} \\
B_{+}^{r} &=&\frac{\left[
\begin{tabular}{ll}
$f_{1}^{r}(0)$ & $w_{1}^{r}(0)$ \\
$\dot{f}_{1}^{r}(0)$ & $\dot{w}_{1}^{r}(0)$%
\end{tabular}%
\right] }{W[f_{1}^{r}(0),f_{2}^{r}(0)]}.  \label{B2r}
\end{eqnarray}

\section{Conclusions}

\acknowledgments This work has been supported by the project QUANTNET -
European Reintegration Grant (ERG) - PERG07-GA-2010-268432.

\section{APPENDIX}

For the sake of readers convenience we summarize here some relevant
properties of the GHF. Further details can be found in \cite{Rainville}.
Generalized hypergeometric function $_{1}F_{2}(a_{1};b_{1},b_{2};x)$ can be
introdused as a power series
\begin{equation}
_{1}F_{2}(a_{1};b_{1},b_{2};x)=\sum_{k=0}^{\infty }\frac{(a_{1})_{k}\ }{%
(b_{1})_{k}(b_{2})_{k}}\frac{x^{k}}{k!}.  \label{GHF-series}
\end{equation}%
Here it is assumed that none of the bottom parameters $b_{1}$ and $b_{2}$ is
a nonpositive integer. As usual $(a_{1})_{k}$ , $(b_{1})_{k}$ and $%
(b_{2})_{k}$ are Pochhamer symbols i.e. $(\alpha )_{0}=1$ and $(\alpha
)_{k}=\alpha (\alpha +1)...(\alpha +k-1)$. Series given by Eq.(\ref%
{GHF-series}) converges for all finite values of $x$ and defines an entire
function. Generalized hypergeometric function $%
_{1}F_{2}(a_{1};b_{1},b_{2};x) $ satisfies the differential equation Eq.(\ref%
{GHF-eq}). When neither $b_{1}$ and $b_{2\text{ }}$are integers, nor the
difference $b_{1}-b_{2}$, a fundamental set of solutions of Eq.(\ref{GHF-eq}%
) is given by%
\begin{eqnarray}
w(x) &=&A_{1}F_{2}(a_{1};b_{1},b_{2};x)+  \label{GHF-f-s} \\
&&B\ x^{1-b_{1}}{}_{1}F_{2}(a_{1}+1-b_{1};2-b_{1},b_{2}+1-b_{1};x)+ \\
&&C\ x^{1-b_{2}}{}_{1}F_{2}(a_{1}+1-b_{2};b_{1}+1-b_{2},2-b_{2};x)  \notag
\end{eqnarray}%
We have, in the neighborhood of the origin three linearly independent
solutions. It can be shown \cite{Rainville} that the Wronskian of these
solutions is given by%
\begin{widetext}
\begin{eqnarray*}
&&W\left[
_{1}F_{2}(a_{1};b_{1},b_{2};x);x^{1-b_{1}}{}_{1}F_{2}(a_{1}+1-b_{1};2-b_{1},b_{2}+1-b_{1};x);x^{1-b_{2}}{}_{1}F_{2}(a_{1}+1-b_{2};b_{1}+1-b_{2},2-b_{2};x)%
\right]  \\
&=&(b_{1}-1)(b_{2}-1)(b_{1}-b_{2})x^{-b_{1}-b_{2}-1}
\end{eqnarray*}
\end{widetext}
Some usefull formulas could be derived from the deffinition Eq.(\ref%
{GHF-series}). It follows that%
\begin{equation}
_{1}F_{2}(a_{1};b_{1},b_{2};0)=1  \label{F(0)}
\end{equation}%
The derivatives for the GHF with respect of the independent variable $x$ are
given by
\begin{equation}
\frac{d\!\!^{n}}{dx^{n}}\!_{1}F_{2}(a_{1};b_{1},b_{2};x)=\frac{(a_{1})_{n}\
}{(b_{1})_{n}(b_{2})_{n}}\!_{1}F_{2}(a_{1}+n;b_{1}+n,b_{2}+n;x)
\label{D-GHF}
\end{equation}%
Asymtotic expansion of the GHF is given by%
\begin{gather*}
_{1}F_{2}(a_{1};b_{1},b_{2};z)\symbol{126}\frac{\Gamma (b_{1})\Gamma
(b_{2})\ }{2\sqrt{\pi }\Gamma (a_{1})}(-z)^{\chi }\cos (\pi \chi +2\sqrt{-z}%
)\left( 1+O(1/\sqrt{-z})\right) + \\
\frac{\Gamma (b_{1})\Gamma (b_{2})\ }{\Gamma (b_{1}-a_{1})\Gamma
(b_{2}-a_{1})}(-z)^{-a_{1}}\left( 1+O(1/z)\right) ,\text{ \ }|z|\rightarrow
\infty
\end{gather*}%
where
\begin{equation*}
\chi =\frac{1}{2}\left( a_{1}-b_{1}-b_{2}+\frac{1}{2}\right)
\end{equation*}

redpajama_set_name: RedPajamaArXiv


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Inboard engine version takes from 50 to 300hp. 10hp direct drive gives 10mph or 13mph with 2 to 1 reduction. 100hp direct drive gives 24mph or 27mph at 1.5 to 1 reduction. 200hp direct drive gives 40 mph.
Outboard engine version…takes engines up to 150hp. 10hp gives 10mph. 40hp gives 21mph. Twin 40hp gives 32mph. 50hp gives 25mph.
Inboard-outdrive units give slightly better performance.


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Do you want something a little bit different? This outfit would be perfect for any one wanting to make a statement. The high waisted skirt paired with the cropped top gives the perfect amount of coveraage – only hinting at the midriff.


text:
Q: Can't figure out how to list all the people that don't live in same City as I'd like to list all the people ( Person table ) that don't live in same city as those cities listed in Location table. Thus, if Location table holds a record with City='New York' and State='Moon', but Person table holds a record with FirstName='Someone', City='New York' and Location='Mars', then  Someone is listed in the resulting set, since she lives in New York located on Mars and not New York located on Moon, thus we're talking about different cities with the same name. I tried solving it with the following query, but results are wrong:
SELECT Person.FirstName, Person.LastName,
Person.City, Person.State
FROM Person INNER JOIN Location
ON (Person.City <> Location.City AND Person.State = Location.State)
OR (Person.City = Location.City AND Person.State <> Location.State)
OR (Person.City <> Location.City AND Person.State <> Location.State)
ORDER BY Person.LastName;

Any ideas?

A: Use a left join:
SELECT Person.FirstName, Person.LastName, Person.City, Person.State
FROM Person LEFT JOIN Location
ON (Person.City = Location.City AND Person.State = Location.State)
WHERE Location.City IS NULL
ORDER BY Person.LastName

Left joins include all rows from the "left" table (Person) even if there are no matches in the "right" table (Location). When there are no matches, the columns of the right table are set to NULL.
In this query, the WHERE condition limits the returned rows to those which don't have matches.

A: Try this:
SELECT Person.FirstName, Person.LastName, Person.City, Person.State
    FROM Person INNER JOIN Location
    ON (Person.City = Location.City AND Person.State <> Location.State)
    ORDER BY Person.LastName;

This query finds all people that live in a city that has a matching City in the Location table but where the state is different.  If you want to find People who have no matching Location there see Ayman's answer.

A: Do you mean something like
select person.fn, person.ln, person.city, person.st
from person, location
where person.city not in
(select location.city from location where location.st != person.st)

A: you should do a left outer join on the two tables, and then select the ones where the location is null
something like
select * from Person
left outer join Location
on p.city=l.city and p.state=l.state
where l.id is null

redpajama_set_name: RedPajamaStackExchange


text:
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redpajama_set_name: RedPajamaCommonCrawl


text:
The 1961 All-Ireland Senior Football Championship Final was the 74th All-Ireland Final and the deciding match of the 1961 All-Ireland Senior Football Championship, an inter-county Gaelic football tournament for the top teams in Ireland. A crowd of 90,556 (a record at the old Croke Park) watched the match between Down and Offaly.

Match
The biggest crowd ever to attend Croke Park saw an explosive opening to the match - Offaly's Mick Casey and Peter Daly got goals to put them six points ahead with the match barely begun. Down recovered with three goals by half-time, and led by two points with minutes to go. Har Donnelly had a 21-yard free for Offaly, and took a point when a goal was really needed.

Legacy
This was Down's second appearance in an All-Ireland final, and their second win from two. It was the second of three All-Ireland football titles won by Down in the 1960s, which made them joint "team of the decade" with Galway who also won three.

References

All-Ireland Senior Football Championship Final
All-Ireland Senior Football Championship Final
All-Ireland Senior Football Championship Final, 1961
All-Ireland Senior Football Championship Finals
All-Ireland Senior Football Championship Finals
Down county football team matches
Offaly county football team matches

redpajama_set_name: RedPajamaWikipedia


text:
Q: Repair vs Optimize table in MySQL
*

*Does Optimize include repair table or vice versa internally?

*Is it possible to execute repair table only if found corrupt, any tools can support this?

(I am using MyISAM table engine)

A: *

*REPAIR TABLE Fixes Table Corruption
Issues, such as Open File Handle
Counts, Resolution of Rows with
Variable Length Data, and so forth.

*OPTIMIZE TABLE simply copies the
table to remove unused space. If the
table is MyISAM, ANALYZE TABLE is
also performed to update index
statistics for the sake of the Query
Optimizer. If the table is InnoDB,
ANALYZE TABLE is bypassed.

You could have mysqld auto check and repair all MyISAM tables.
In fact the book MySQL 5.0 Certification Study Guide, Section 30.5, Pages 444,445 state:

The MySQL server can be instructed to
  check and repair MyISAM tables
  automatically. With automatic repair
  enabled, the server checks each MyISAM
  table when it opens it to see whether
  the table was closed properly the last
  time it was used and is not marked as
  needing repair. If the table is not
  OK, the server repairs it.
To enable automatic MyISAM table
  maintenance, start the server with the
  --myisam-recover option, The option value can consist if a comma-separated
  list of one or more of the following
  values:

*

*DEFAULT for the default checking.

*BACKUP tells the server to make a backup of any table that is must
  change.

*FORCE causes table recovery to be performed even if it would cause the
  loss of more than one row of data.

*QUICK performs quick recovery : Tables that have no holes resulting
  from deletes or updates are skipped.

  For example, to tell the server to
  perform a force recovery of MyISAM
  tables found to have problems but make
  a backup of any tables it changes, you
  can put the following lines in an
  option file:
[mysqld] myisam-recover=FORCE,BACKUP

You could also create a file called /root/StartUp.sql and put the REPAIR TABLE commands you want inside. Then add init-file=/root/StartUp.sql to /etc/my.cnf and restart mysql to trigger the init script.


text:
/**
 * Created by Ilkka on 8.4.2016.
 */
"use strict";
var fs = require('fs');

/**
 * @param {Array<string>} files
 * @param {Function} cb
 */

function ensureFiles(files, cb) {
  var missingFiles = files.reduce(function(prev, filePath) {
    var fileFound = false;

    try {
      fileFound = fs.statSync(filePath).isFile();
    } catch (e) { }

    if (!fileFound) {
      prev.push(filePath + ' Not Found');
    }

    return prev;
  }, []);

  if (missingFiles.length) {
    var err = new Error('Missing Required Files\n' + missingFiles.join('\n'));
  }

  if (cb) {
    cb(err);
  } else if (err) {
    throw err;
  }
}

module.exports = ensureFiles;

redpajama_set_name: RedPajamaGithub


text:
Q: Group Assignment Java text book I've been doing this program for about 30 minutes now, and I want to make it in this certain format even though I'm pretty sure there are better methods of doing this program!
What I've been trying to do is from alphabet A to I should be placed in group in terms of there first letter of their last name. And, J to S should be group 2 and T to Z should be group 3. I'm not sure how I can make the output equal to group1 and any other groups depending on there last name of course!
import java.util.Scanner;

public class GroupAssignment {

    public static void main(String[] args) {
        String firstName;
        String lastName;
        String output;
        String group1 = "a,b,c,d,e,f,g,h,i";
        String group2 = "j,k,l,m,n,o,p,q,r,s";
        String group3 = "t,u,v,w,x,y,z";
        Scanner input = new Scanner(System.in);

        System.out.print("Enter your first name: ");
        firstName = input.nextLine();
        System.out.print("Enter your last name: ");
        lastName = input.nextLine();

        output = lastName.substring(0,1).toLowerCase();

        if (output.equals(group1)) {
            System.out.println(firstName+ lastName+ "is assigned to Group 1.");
        }
        else if (output.equals(group2)) {
            System.out.println(firstName+ lastName+ "is assigned to Group 2.");
        }
        else if (output.equals(group3)) {
            System.out.println(firstName+ lastName+ "is assigned to Group 3.");
        }

    }

}

Please help me how I can make this work!

A: You should not use .equals: after all the first letter of the lastname cannot be a,b,c,d,.... It can be only one of these. You can use .contains however:
if (group1.contains(output)) {
    System.out.println(firstName+ lastName+ "is assigned to Group 1.");
} else if (group2.contains(output)) {
    System.out.println(firstName+ lastName+ "is assigned to Group 2.");
} else if (group3.contains(output)) {
    System.out.println(firstName+ lastName+ "is assigned to Group 3.");
}

jdoodle demo
Another problem is that your print:
System.out.println(firstName+ lastName+...

I don't know about all cultures, but many add a space between the firstName and the lastName so:
System.out.println(firstName+" "+lastName+...

Is probably a better option.
Note however that this is not the right way to do it. A string is not a collection, it is a sequence. There are faster ways to check if a collection contains an element. I'm thinking about a HashSet<Char> or TreeSet<Char> which can do lookups in average-case constant time or logarithmic time.


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The show airs on WDIY Wednesday evenings, from 6-7 p.m. The show is hosted by Valley National's Laurie Siebert CPA, CFP®, AEP®. Due to Musikfest, this week Laurie will provide a pre-recorded show.
No calls-ins are possible this week. This show will be broadcast at the regular time. Questions may be submitted early through www.yourfinancialchoices.com by clicking Contact Laurie. This show will be broadcast at the regular time. WDIY is broadcast on FM 88.1 for reception in most of the Lehigh Valley; and, it is broadcast on FM 93.9 in the Easton and Phillipsburg area; and, it is broadcast on FM 93.7 in the Fogelsville and Macungie area – or listen to it online from anywhere on the internet. For more information, including how to listen to the show online, check the show's website www.yourfinancialchoices.com and visit www.wdiy.org.


The most beautiful thing about music is that it touches the soul like nothing else. That has been the key for Grammy award winning songwriter Adonis Shropshire as he's been able to impact the lives of many with his approach to music. Starting out under Bad Boy in the early 2000's, Adonis has become one of the most prolific writers of our generation as he's worked with everyone from Usher to Mariah Carey to Jennifer Lopez. YouKnowIGotSoul had a chance to speak with Adonis about his past work with Bad Boy, his new artist Georgia Reign and his thoughts on the state of R&B. He also reflected on some of his biggest hits and talked about the process behind some of his favorite songs.
YouKnowIGotSoul: I read that you originally started out working with the group Blaque on their debut album. Talk about that whole experience and how it came about.
Adonis Shropshire: I was in a singing group that was trying to do a production deal with Left Eye from TLC, so during that time we were performing at this club and Left Eye was frequent in that club with the girls. My group and that group became friends. I was the only one that expressed interest in being a producer and songwriter from my group and one of the girls' dad in their group was the vocal producer for the album. I guess he took a liking to me and he invited me in their sessions. He had me vocal produce a few records by teaching and guiding me.
YouKnowIGotSoul: Unfortunately we lost Natina Reed not too long ago. What do you remember about working with her?
Adonis Shropshire: Just the craziness. She was definitely the character of the group. She was funny and always cracking jokes. She was really creative and brilliant with songwriter. She wrote most of the records as well. She was a very good songwriter. I was really sad to hear that because we were all kids growing up in this game and it kind of shocked me. I wish her family well and I'm praying for her son and everyone that's involved.
YouKnowIGotSoul: You started out working with Bad Boy afterwards. Talk about working with Diddy and that whole experience.
Adonis Shropshire: That is probably the biggest learning experience I've ever encountered in my whole life. I think the knowledge that he passes on just from you being around him is amazing. For him to take a chance on a kid that had never had written a record for anybody professionally, that speaks volumes about his brilliancy in the music industry. I really appreciate him for that. Those were the greatest moments as far as learning that I've had in my career.
YouKnowIGotSoul: Since you wrote both of these songs, which song do you think is better: "I Need a Girl" Part 1 or Part 2?
Adonis Shropshire: That's typical to say. *Laughs* We wrote both songs at the same time in the same session. Wow, I don't know. I guess it's like choosing if your son or daughter is your favorite. I'll say both for different reasons. I'll say the first is better because it was my first time hearing a song I wrote on the radio, but the second one beats the first one because that's the one everybody really remembers. Both of them just have that special place in my heart.
YouKnowIGotSoul: What would you consider to be your greatest success? Your first placement was on Jennifer Lopez's "J.Lo", you had consecutive hits with "I Need a Girl", you had "My Boo" by Usher which won a Grammy and you also had a lot of placements from 2005-2007.
Adonis Shropshire: Probably the Usher record. More so not because that was by far the longest number one I've had. That song was number one for 14 weeks. I would say "My Boo" is the greatest success not only because it was the longest number one I had at 14 weeks, but Usher's album subsequently went onto sell 25 million records worldwide. I think that coupled with the fact that the album at one point had stalled and then they put that record out and it went onto do what it did. It makes me feel like I was vital in the record sales of that album. Maybe not the whole thing, but for the part that I played a part in. I think that really speaks volumes about what one record can do for an album.
YouKnowIGotSoul: I've had a chance to speak with your production partners Bryan-Michael Cox and Kendrick Dean. They both mentioned that the writing process when you guys worked together starts out with a conversation. Talk about that process.
Adonis Shropshire: A lot of times an artist will come in and they'll be going through something. We'll just start talking about a real situation that they're going through and in the middle of it, there are certain things that they'll say and I'll be like "That'll be good for a song." Of course with their permission, I'll be like "Let's write about that." I'll go in the booth and I'll write about whatever it is and it becomes more real to them because it's something that they're going through. A lot of times different situations that you go through are the same. The key to song writing is to write something that is personal, but the entire world can understand because that's the whole point. You want to speak to the fans or the multitude. I think those real situations always resonate more than fabricated ones, so that's why we do it that way.
YouKnowIGotSoul: Even though we know you as a songwriter, you've also had a hand in producing tracks. Talk about that because a lot of writers stick to just writing but you've dipped into the production side of things.
Adonis Shropshire: When I first started working with Puff, Mario Winans, Rodney Jerkins and K-FAM, I used to love the way they would come up with tracks because they were all musical first. Rodney and K-FAM play piano classically and Mario Winans plays every instrument known to man. They all were real musicians but they knew how to craft beats. I got to a point where I wanted to stop asking people for music. I played piano myself, so I wanted to figure that out as well. It's kind of like if you're on a football team and Chris Carter can catch balls with one hand, if you're Randy Moss, you can catch hands with two hands but you want to catch with one hand because it's an added skill. So that's where it came from. I just wanted to add another skill to my creativeness so that in the event that we can't get a producer in a session or in the event that we're in a session and the artist wants to create a brand new song on the spot, I don't have to call another guy to come in and do something that I could do.
YouKnowIGotSoul: As far as the state of R&B right now, sales are really low. Has that affected you as a writer?
Adonis Shropshire: It has especially for me because I'm a volume writer. I may have three or four songs on an album versus another writer who may one song on the album, but that's one of the singles. For me I'll get the third single but I'll have three or four songs on the album, so album sales really generate a lot of money for me. Now that album sales are not selling, then of course you don't generate a certain amount. It affects you in different ways and even the guys who were getting singles, now that one song that they're placing that's the single, they're not even getting that placement now. You just have to be creative about the ways you get on this album and that you sell your records because it definitely affects the way that the labels look at it because records are not selling the way that they're used to.
YouKnowIGotSoul: I've spoken to other producers that instead of chasing placements, they're more so into developing artists. Is that something you're looking to do?
Adonis Shropshire: It's interesting that you ask me that because right now we have an artist named Georgia Reign. She has followers on Twitter and she has two or three videos on YouTube that are at 200,000 views. It's something that we really are developing. I think she's an amazing talent, she's a songwriter as well. She wrote the Chris Brown "2012" record with me that's on "Fortune". She's Grammy nominated now so I want to say congratulations to her. I'm very excited about what we're doing with her and we're just ready to shock the world. I think it's time for new artists to come through. Every so often, every decade, new artists come through and a few of them really have staying power and I think she's one of those that will have staying power.
YouKnowIGotSoul: What is it about her that makes you want to work with her? You've worked with so many big artists already.
Adonis Shropshire: I think it's her independence with her creativity. She really doesn't need me to write records with her, but the way we create is incredible when we create together. I can also give her music and she can do it on her own. Secondly she's a star. There's no question about and maybe that should be the first thing, but there's no question about her superstardom. It's really something that I've never seen before from somebody who hasn't been trained or has had teaching from labels. It's just naturally in her and that right there was the most important thing to me. Besides the fact that her voice is beautiful and she's pretty and all of that, it's the fact that she doesn't need me to make hits. She's a bona fide star.
Adonis Shropshire: Me and Makeba wrote that record together. We had already been doing some work for B2K and Chris Stokes expressed that he was working with Omarion's little brother. They brought him in the studio and we did that record on the spot.
YouKnowIGotSoul: Next is B2K's "One Kiss".
Adonis Shropshire: That was a record me and Johnta Austin did together. Me and Johnta wrote another record together for something else and he found out I did tracks, so I gave him a track and he wrote it. Chris Hicks placed the record for us and I went out to record it on B2K and that's how I developed a relationship with them.
YouKnowIGotSoul: How about Mariah Carey "For The Record"?
Adonis Shropshire: That was actually a great experience. That was me, Bryan-Michael Cox and Mariah. We all sat down, we had been working with Mariah for about a week. We were just coming up with different ideas. Mariah is a star who is probably talked about the most and there's a lot of rumors. She wanted to at least set the record straight so that's how the song came about. She just wanted people to know "Listen, this is really what it is." She's a brilliant songwriter as well. The melody she chooses and the way she goes about writing her records, it was an astonishing process just being involved with that record with her.
YouKnowIGotSoul: Then we've got Ginuwine "Last Chance".
Adonis Shropshire: That was me and Bryan-Michael Cox. We were working with Ginuwine. We had done a few other ballads and Ira Dewitt who was his label head expressed that she wanted to go with a ballad as the first single. Once she said that, of course me and Bryan, over the years a lot of our singles have been ballads. We knew exactly what she was trying to ask us to do, so that's how we came up with that record. It's basically a man pleasing for his last opportunity to show a woman that he's serious about being with her. That's how that record came about.
YouKnowIGotSoul: What about the single you did for Mario Winans, "Never Really Was"?
Adonis Shropshire: Mario had a beat and it was that sample in the beginning. He showed me the sample first and was like "Yo I think I got a verse." He showed me his verse and I wrote the hook. A lot of these joints just come out. It's not even a struggle because it's just real life situations.
YouKnowIGotSoul: Then we've got Faith Evans "Don't Cry".
Adonis Shropshire: Oh man, that was one of my favorite records. Faith and Meelah from 702 were coming up with verses and melodies. I came in with the hook and the bridge. Actually if you listen to the record, you can hear me singing on the bridge. That was a great process too. Faith is another talented songwriter that I enjoyed working with. It was very interesting working with her after growing up listening to her and then finally being in the studio with her. It was incredible to me.
YouKnowIGotSoul: Finally, Brandy's unreleased song "Cry".
Adonis Shropshire: At the time Brandy was going through management change. Her management that she was with was also managing Bryan, so they wanted her to go in with me and Bryan. We went in with her at Track Record in Los Angeles and it was during the time when she was going through the whole thing with being married or not being married. It was a very vulnerable time for her, so we just came up with something that we felt was indicative of the time period that she was going through. We were supposed to do her whole album at the time. We spent a lot of time with her, so those records that came out of those sessions are still some of my favorite records that I've worked on. Even though they'll probably never come out, I love those records.
YouKnowIGotSoul: How does it feel for you as a writer when a song you write doesn't come out because of label politics? I know you spend a lot of time working on these songs.
Adonis Shropshire: It doesn't bother me because you have to understand that just because they don't buy it doesn't mean it won't get sold. There's a lot of records that I may have written on Joe but I ended up placing it on Mario. It's not a waste of time because it's still property that can still be monetized. If they don't take it, you just have to be creative about who else you can send the record to. I know it bothers some people, but it doesn't bother me.
YouKnowIGotSoul: We haven't really heard much from you aside from the Chris Brown's "2012". Who else have you been working with?
Adonis Shropshire: I'll tell you the things that I've done in the last year. I did two records on Mary J. Blige's latest album. I did the "Fa La La" record for Justin Bieber and Boyz II Men. I did a record on Joe Jonas' album that came out. I also did a record on Bobby V. Jin Akanishi who is a Japanese artist, I did his single on his album that came out this year. As of recently, I've been in the studio with Omarion. He's doing an album with Maybach Music. I did like four records on Starshell, she's signed to Mary J. Blige's label. Kayla Smith who is signed to Interscope. She's Kenny Smith's daughter. I did two records for her. A lot of other things I have been doing have been video game related or television related. I've been trying to add that into my repertoire as well as placing records. It's been a fun time for me this year.
YouKnowIGotSoul: I wanted to ask you about something that you and a bunch of other writers started out a couple years ago and that's Nodeci. What happened with Nodeci?


Turbomeca do Brasil (Safran group) has signed a five year GSP (Global Support Package) contract with the Brazilian Ministry of Defense, to cover the support of 100 Makila 2A gas turbines. The engines power the EC 725, operated by all three Brazilian armed forces and the Presidential transportation group.
The GSP, a maintenance lease based on predicted fleet flight hours, is the first to be signed across the Brazilian armed forces. It demonstrates the confidence of Brazilian military customers in Turbomeca's capacity to support them, earned over 20 years of experience.
The contract covers initial provisioning, technical support on-site, fleet and pool management and training.
The Brazilian armed forces have operated Turbomeca engines since 1980. Today, the fleet includes 230 Arriel & Makila engines and, with the delivery of a new EC 725 fleet, is set to grow.
In 2008 Brazil ordered 50 EC 725 helicopters, powered by Makila 2As to be assembled, tested and overhauled at Turbomeca do Brasil, Rio de Janeiro.
Furthermore, in 2010, the Army launched a programme to update the Army's Pantera fleet with the Arriel 2C2CG.
Turbomeca do Brasil, together with Turbomeca Sud Americana at Montevideo, provides support services for 500 customers operating over 1,400 engines across Latin America.


Oh, right. Depends on who you ask… one version of the story says it started as a German phrase, "alle alle auch sind frei," which loosely translates to "everyone, everyone is free." Another side says it was "all ye all ye outs in free," essentially saying, "it's safe to come in." We know it from years of hide 'n' seek.
When and where can I get the game?
Night School is a new independent studio founded by cousins Sean Krankel and Adam Hines, former Disney and Telltale developers respectively. Based in Los Angeles, Night School's focus is on the cross section between story and games.
What in the world is up with that radio?
It starts out innocuous enough. Alex brings the radio because there's an inlet on the beach that emanates weird sounds when frequencies are tuned nearby. But it quickly becomes the catalyst of the rift, and Alex's only hope for survival. We can't say much more beyond that.
Is the game set in the 80s? How 'bout the 90s?
OXENFREE is set in present day, but we're glad it's rekindling fond / mortifying memories.
But that music! It feels like a scarier version of my childhood!
Our soundtrack is all original tunes, courtesy of scntfc. He is doing an incredible job creating our score, and we are brainstorming cool ways to bring you the music outside of the game. Stay tuned.


Tayside Aviation is one of the UK's leading flight training organisation, who have been training pilots for over 40 years, and has a solid operation based at Fife Airport.
The company operates a fleet of well-maintained four-seater Piper Warrior aircraft from Fife available for training and private hire.
Trial lesson flights are available for a taster of learning to fly or as a unique gift, along with full flight training.
For more information, please visit the Tayside Aviation website.


This annual SHOUT event is held the last Saturday of June. Each year hundreds of people visit five or six area homes and summer cottages. It is like walking through a three dimensional version of Architectural Digest.
This event is held the last Saturday in June, noon until 5:00 p.m, with advance tickets on sale at the Visitors Bureau and select merchants. Tickets are also for sale on Cottage Walk day at the park opposite City Hall. The cost is $15.


Recent repairs to the 2015 shape Bentley Continental GT have been completed. The GT had been booked in for accident damage to the offside front wing, front bumper and rear bumper and whilst on site a niggling wheel refurbishment.It is most important for a vehicle of this calibre to have perfect, unnoticeable repairs to maintain aesthetics and also residual value, you can trust Bentley Conversions to meet those requirements. You can see the completed repairs on our website soon.


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Home / POLITICS / President Akufo-Addo Eulogises Dr. Busia
President Akufo-Addo Eulogises Dr. Busia
Adwenpa-Hene August 30, 2022 POLITICS 373 Views
Ghana's President Nana Akufo-Addo has paid glowing tribute to the late Prime Minister, Dr. Kofi Abrefa Busia.
Born in Wenchi in the then Brong Ahafo region on 11 July 1913 and died on 28 August 1978), Busia was a Ghanaian political leader and academic who became Prime Minister from 1969 to 1972.
As a nationalist leader and Prime Minister, he helped to restore civilian government to the country following military rule.
At a book launch in Accra Monday evening, he described the man as a far-sighted think tank.
The audiobook was compiled by children of the late Dr. K.A. Busia titled "The Prof" A Heart of Faith, from "Poor Boy" to Prime Minister".
President Akufo-Addo indicated that but for the overthrow of Busia in 1972, the story of Ghana's rural development would have been different from what it is today.
"As the eldest child of my father, Edward Akufo-Addo, then President of the 2nd Republic, I had the privilege to witness at first hand his excellent leadership skills, his vision for the development of our country, and the sacrifices he made towards the creation of the free, democratic Ghana in which we now live", he said.
He, therefore, noted that "as we celebrate his legacy, we commemorate also the 109th anniversary of his birth, the 44th anniversary of his death, and the 53rd anniversary of the famous victory of the Progress Party he led in the 1969 general elections. I dare say our nation, and indeed, Africa has not seen a more far-sighted political thinker tank like Professor Kofi Abrefa Busia."
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For President Akufo-Addo "the overthrow of the Second Republic and the Progress Party government meant that our country was deprived of the full impact of his agenda for development."
"The case has gone to show that we turned out to be the poorer for it. We can imagine for example, where our nation would have been now if he had been allowed to develop his visionary programme of rural development", he emphasised.
"Some of the ills of contemporary Ghana such as rural-urban migration which has been the source of much current social tension could well have been avoided", he insisted.
The audiobook is a compilation of letters that Professor Kofi Abrefa Busia exchanged with his lifelong friend and mentor, Reverend William Whittle.
Dr. Busia's daughter, Akosua Busia, authored the book.
He was born in the traditional kingdom of Wenchi, in the then Brong Ahafo Region, one of the four Gold Coast Territories, then under British rule and now called Ghana.
He was educated at Methodist School, Wenchi, Mfantsipim School, Cape Coast, then at Wesley College, Kumasi, from 1931 to 1932.
The late Prime Minister taught at Wesley College and left to study at Achimota College in 1935 and taught there.
He gained his first degree with Honours in Medieval and Modern History from the University of London, through correspondence during this period.
e then went on to study at University College, Oxford, where he was the college's first African student.
Busia returned to the Gold Coast in 1942.
He took a BA (Hons) in Philosophy, Politics, and Economics (1941, MA 1946) and a DPhil in Social Anthropology in 1947 at Nuffield College, Oxford, with a thesis entitled "The position of the chief in the modern political system of Ashanti: a study of the influence of contemporary social changes on Ashanti political institutions." He was a Fulbright scholar in 1954.
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He served as a District Commissioner from 1942 to 1949 and was appointed the first lecturer in African Studies.
He became the first African to occupy a chair at the University College of the Gold Coast (now the University of Ghana).
In 1951, he was elected by the Ashanti Confederacy to the Legislative Council. In 1952, he was the Leader of the Ghana Congress Party, which later merged with the other opposition parties to form the United Party (UP).
As the leader of the opposition against Kwame Nkrumah, he fled the country because his life was under threat.
In 1959 Busia became a Professor of Sociology and Culture of Africa at the University of Leiden near the Hague, Netherlands.
From 1962 until 1969, he was a Fellow of St Antony's College, Oxford.
He returned to Ghana in March 1966 after Nkrumah's government was overthrown by the military to serve on the National Liberation Council of General Joseph Ankrah, the military head of state; and was appointed as the Chairman of the National Advisory Committee of the NLC.
In 1967/68, he served as the Chairman of the Centre for Civic Education.
He used this opportunity to promote himself as the next Leader.
Busia was also a Member of the Constitutional Review Committee. When the NLC lifted the ban on politics, Busia, together with Lawyer Sylvester Kofi Williams and friends in the defunct UP formed the Progress Party (PP).
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In 1969, the PP won the parliamentary elections with 105 of the 140 seats.
This paved the way for him to become the next Prime Minister. Busia continued with NLC's anti-Nkrumaist stance and adopted a liberalised economic system.
There was a mass deportation of half a million Nigerian citizens from Ghana, and a 44 percent devaluation of the cedi in 1971, which met with a lot of resistance from the public.
While he was in Britain for a medical check-up, the army under Colonel Ignatius Kutu Acheampong overthrew his government on 13 January 1972.
Busia remained in exile in England and returned to Oxford University, where he died from a heart attack in August 1978.
Along with J. B. Danquah and S. D. Dombo, Busia's name is associated with Ghana's right-wing political party, the NPP.
The New Patriotic Party (NPP) has claimed the Danquah-Busia-Dombo mantle in the Fourth Republic.
Dr. Kofi Abrefa Busia. Nana Akufo-Addo 2022-08-30
Tags Dr. Kofi Abrefa Busia. Nana Akufo-Addo
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