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\section{Introduction}

Quantum thermodynamics~\cite{deffner,gemmer} is a research field in the making, with fruitful conceptual implications and a potential
range of applications, mainly in the field of quantum technologies (see, e.g., Ref.~\cite{alexia}). It aims at generalizing the laws of
thermodynamics to the quantum domain, rewriting thermodynamic state functions and processes from the bottom up so that the laws of thermodynamics
can be consistently applied to small systems and scaled up to the classical world~\cite{kosloff,oppenheim, tien,xu,fernando,hoda}. Remarkably, the definition
of thermodynamic variables, such as work and heat, has been challenging,   since they cannot be taken as observables described by Hermitian operators~\cite{peter}.
In the standard framework of quantum thermodynamics~\cite{alicki}, the internal energy change due to state population rearrangement induced by the external environment
has been defined as {\it heat}. On the other hand, the internal energy change due to energy gap variations induced by the coherent dynamics has been defined as {\it work}.
This framework has recently been revisited through an entropy-based formulation for heat and work~\cite{alipour1,alipour2,Ahmadi2020}, with heat identified as the
entropy-related contribution to the internal energy change and work taken as the part unrelated to the entropy change. In particular, this has been applied to the study
of the thermodynamics of a single qubit far from equilibrium~\cite{vallejo}, where a notion of temperature compatible with the classical limit is introduced.
The alternative entropy-based view turns out to motivate an interplay with quantum information, with the interpretation of thermodynamic variables in terms of resources
and correlations in a quantum system.

Indeed, quantum thermodynamics is intrinsically connected with quantum information theory, with quantum resources strongly affecting thermodynamic variables and processes.
This is manifested in a number of situations, such as measurements and their influence on the work performed on/by a quantum system~\cite{peter,william, daniel,michal,chen},
efficiency of thermodynamic tasks in quantum correlated devices~\cite{tien,Zhang:07,Lutz:14,Latune:19}, coherence effects on work and
heat~\cite{Scully:03,philip,Brandner:17,streltsov,bernardo,latune,yuhan,kenza}, among others. By looking at information-based quantifiers,
it is known that quantum coherence plays a relevant role in the characterization of system-bath memory effects. In particular, quantum coherence can be associated
with a measure of non-Markovianity for {\it incoherent} dynamical maps~\cite{cramer,titas,passo,wu}.
Notice that a memoriless (Markovian) behavior is always an idealization, with non-Markovian quantum dynamics being non-negligible
in a number of different scenarios (see, e.g., Refs.~\cite{Apollaro:11,Haikka:12,Chen:15}). From an applied point of view, non-Markovian
dynamics may be also a resource for certain quantum tasks~\cite{Aharonov:06,Bylicka:14}.

In this work, we adopt the entropy-based formulation of quantum thermodynamics to introduce a measure of non-Markovianity based on the heat flow for single-qubit quantum evolutions.
This measure can be applied for {\it unital} dynamical maps that do not invert the sign of the internal energy (energy sign-preserving maps), which is rooted in the idea that von Neumann entropy itself can be used to build a
non-Markovianity measure for unital maps~\cite{haseli}. Under certain conditions, we can also extend this approach to other thermodynamic functions, such as internal energy and work flows. Then, a natural connection between heat and quantum coherence can be observed for dynamical maps that are both unital and incoherent.
In particular, we show that heat and work are monotonically related to quantum coherence for non-dissipative processes. Consequently, both heat and work can witness non-Markovianity for \textit{non-dissipative unital maps}
as well as \textit{non-dissipative incoherent maps}. Moreover, we establish and illustrate the conditions over the system purity and the Hamiltonian such that the thermodynamic variables can be used to provide non-Markovianity measures
throughout the evolution in a decohering environment.

The paper is organized as follows. In Section II, we briefly introduce the entropy-based formulation of quantum thermodynamics, expressing the first law of thermodynamics and
its corresponding thermodynamic variables for a single qubit system. In section III, we discuss the non-Markovian dynamics, where we propose measures of non-Markovianity via
generalized sign-preserving functions. In the section IV, we consider applications in dissipative and non-dissipative evolutions,
illustrating the use of thermodynamic variables as measures of non-Markovianity. In section V, we present our conclusions.

\section{Quantum thermodynamics}

According to the standard framework for quantum thermodynamics~\cite{alicki}, the internal energy $U$ of a system described by a density operator $\rho$ is provided
by the expected value of its Hamiltonian $H$, i.e., $U=\mathrm{tr}\left[\rho H\right]$. In this formalism, the first law of thermodynamics emerges from an infinitesimal change
in the internal energy $dU=\delta Q+\delta W$, with $\delta Q=\mathrm{tr}\left[d\rho H\right]$ and $\delta W=\mathrm{tr}\left[\rho dH\right]$ defining the heat absorbed by system and
the work performed on system, respectively. Considering the density operator as expressed in its spectral decomposition, we have
$\rho=\sum_k r_k \left|r_k\right\rangle\left\langle r_k\right|$, where $\left|r_k\right\rangle$ denotes an eigenvector of $\rho$ and $r_k$ the corresponding eigenvalue. Then,
the thermodynamic quantities $U$, $\delta Q$, and $\delta W$ can be rewritten as
\begin{equation}\label{Eq:energy}
U=\sum_k r_k \left\langle r_k\right|H\left| r_k\right\rangle,
\end{equation}
\begin{equation}\label{Eq:heat}
\delta Q=\sum_k dr_k \left\langle r_k\right|H\left| r_k\right\rangle+\sum_k r_k \left(\left\langle r_k\right|H\,d\left|r_k\right\rangle+h.c.\right),
\end{equation}
\begin{equation}\label{Eq:work}
\delta W=\sum_k r_k \left\langle r_k\right|dH\left|r_k\right\rangle.
\end{equation}
Note that the first term on the right-hand-side of Eq.~(\ref{Eq:heat}) is the responsible for changes in the von Neumann entropy,  $S= -k_{B}\mathrm{tr}\left[\rho\mathrm{ln}\rho\right]$, since $dS= -k_{B}\sum_k  dr_k \mathrm{ln}r_k$.
Therefore, in order to connect the heat flow with the entropy change as in classical thermodynamics, an entropy-based formulation of quantum thermodynamics has recently been introduced in Refs.~\cite{alipour1,alipour2,Ahmadi2020}.
In this framework, heat and work are redefined through
\begin{equation}\label{Eq:heat2}
\delta\mathbb{Q}=\delta Q -\delta \mathbb{W}^*
\end{equation}
and
\begin{equation}\label{Eq:work2}
\delta \mathbb{W}=\delta W +\delta \mathbb{W}^*,
\end{equation}
where $\delta \mathbb{W}^*$ is an additional work contribution given by
\begin{equation}\label{Eq:workd*}
\delta \mathbb{W}^*=\sum_k r_k \left(\left\langle r_k\right|H\,d\left|r_k\right\rangle+h.c.\right).
\end{equation}
The work $\delta \mathbb{W}^*$ is related to the variation $d\left|r_k\right\rangle$ of the density operator eigenvectors. Notice that the entropy-based formalism satisfies the first law of thermodynamics,
i.e., $dU=\delta \mathbb{Q}+\delta \mathbb{W}$, being then equivalent to the standard framework for $\delta \mathbb{W}^{*}=0$. Remarkably, it can be shown that the existence of quantum coherence in $\rho$
in the energy eigenbasis $\{\left|h_k\right\rangle\}$ is a necessary ingredient for a non-zero work $\delta\mathbb{W}^*$ if the energy eigenvectors are fixed (i.e., for
$d\left|h_k\right\rangle= 0$, $\forall k$). Here, we will define coherence through the $l_1$-norm \cite{cramer} of $\rho$ in the energy eigenbasis, reading
\begin{equation}\label{Eq:coherence}
C(\rho)=\sum_{k\neq l}\left|\left\langle h_k\right|\rho\left|h_l\right\rangle\right|.
\end{equation}
Indeed, observe that, if $H$ is constant and $\rho$ and $H$ have a common basis of eigenvectors, then $d\left|h_k\right\rangle = d\left|r_k\right\rangle = 0$. This leads to $ \delta \mathbb{W}^*=0$.
Moreover, since a common basis for $H$ and $\rho$ implies that $\rho$ is diagonal in the energy eigenbasis $\{\left|h_k\right\rangle\}$, we will have $C(\rho)=0$.

For an arbitrary  single qubit system, the density operator can be written in the Pauli basis $\{I,\vec{\sigma}\}$ as
\begin{equation}
\rho=\frac{1}{2} \left(I+\vec{r}\cdot\vec{\sigma}\right),
\end{equation}
where  $\vec{r}=(x,y,z)$ is the Bloch vector.
For the Hamiltonian, we have $H=-\vec{h}\cdot\vec{\sigma}$.
We observe that $\vec{r}=(x,y,z)$ can be interpreted as a classical magnetic dipole moment immersed in an external magnetic field $\vec{h}$.
Indeed, the quantities in Eqs.~(\ref{Eq:energy}) - (\ref{Eq:coherence}) reduce to \cite{vallejo}:
\begin{equation}\label{Eq:energyq}
U=-\vec{h}\cdot\vec{r},
\end{equation}
\begin{equation}\label{Eq:heatq}
\delta Q=-\vec{h}\cdot d\vec{r},
\end{equation}
\begin{equation}\label{Eq:workq}
\delta W=-\vec{r}\cdot d\vec{h},
\end{equation}
\begin{equation}\label{Eq:heat2q}
\delta\mathbb{Q}=U_rdr,
\end{equation}
\begin{equation}\label{Eq:work2q}
\delta \mathbb{W}=rdU_r,
\end{equation}
\begin{equation}\label{Eq:work*q}
\delta \mathbb{W}^{*}=-rh\,\hat{h}\cdot d\hat{r},
\end{equation}
and
\begin{equation}\label{coherenceq}
C=r\sqrt{1-\frac{U_{r}^2}{h^2}},
\end{equation}
where $r\equiv |\vec{r}|$ is the purity, $U_r\equiv U/r$ is the internal energy per unit of purity, $h\equiv |\vec{h}|$ is the positive energy eigenvalue, $\hat{r}\equiv\vec{r}/r$ is
the dipole direction, and $\hat{h}\equiv\vec{h}/h$ is the external field direction. Note that heat and work in the entropy-based qubit formalism, namely, $\delta\mathbb{Q}$ and $\delta\mathbb{W}$,
are necessarily associated with changes in $r$ (and consequently in $S$) and $U_r$, respectively. On the other hand, the standard contributions for these thermodynamic quantities,
$\delta Q$ and $\delta W$, are required to be associated with variations in $\vec{r}$ and $\vec{h}$, respectively.

An interpretation for $\delta \mathbb{W}^*$ in terms of the behavior of $\vec{r}$ can be obtained through
the relation between $\delta \mathbb{W}^*$ and $C(\rho)$. First, a change in the eigenvectors of $\rho$ is required for non-zero $\delta \mathbb{W}^*$. By imposing $d\hat{h}=0$ (i.e., a fixed energy eigenbasis),
we can express $\delta \mathbb{W}^*$ in Eq.~(\ref{Eq:work*q}) as $\delta \mathbb{W}^*=hCd\theta$, where $hC=|\vec{r}\times\vec{h}|$ denotes the absolute value of the torque
on $\vec{r}$ induced by $\vec{h}$ and $\theta=\text{arcos}(\hat{h}\cdot\hat {r})$ is the angle between $\vec{r}$ and $\vec{h}$~\cite{vallejo}. Therefore, $\delta \mathbb{W}^{*}$ is
equivalent to the energy cost required to rotate a magnetic dipole moment immersed in an external magnetic field, being proportional to coherence.
More generally, $\delta \mathbb{W}^{*}$ represents the departure from the quasistatic dynamics~\cite{alipour1,alipour2}.

\section{Characterizing non-Markovianity}
\label{sec:III}

Let us suppose an open-system dynamical evolution governed by a time-local master equation
\begin{eqnarray} \label{Eq:mastereq}
&&\hspace{-0.2cm}\dot{\rho} = {\cal L}_t \, \rho(t)= -i\left[H(t),\rho(t)\right] \nonumber \\
&&\hspace{0.5cm}+\sum_i \gamma_i (t) \left( A_i(t)\rho(t) A^\dagger_i(t) - \frac{1}{2} \left\{A^\dagger_i(t) A_i(t),\rho(t)\right\}\right),
\end{eqnarray}
where ${\cal L}_t$ is the time-dependent generator, $H(t)$ is the effective Hamiltonian of the system, $A_i(t)$ are the Lindblad operators, $\gamma_i(t)$ are the relaxation rates, and the dot symbol ``$\cdot$" denotes
time derivative.
By taking $\gamma_i(t) \ge 0$, ${\cal L}_t$ assumes the Lindblad form at each instant of time \cite{Gorini1976}. Consequently, the master equation solution $\rho(t)=\Phi_{t,\,\tau}\rho(\tau)$ is obtained through a completely positive trace-preserving (CPTP) map $\Phi_{t,\,\tau} = {\cal T} \exp \left(\int_{\tau}^{t} dt^\prime{\cal L}_{t^\prime} \right)$, with ${\cal T}$ representing the chronological time-ordering operator. In this case, the dynamical map $\Phi_{t,\,\tau}$ satisfies the divisibility condition, i.e.,  $\Phi_{t,\,\tau}=\Phi_{t,\,r}\Phi_{r,\,\tau}$ $(t \ge r \ge \tau \ge 0$), which characterizes the Markovianity of the
dynamical evolution. On the other hand, for  $\gamma_i(t) < 0$, the corresponding dynamical map $\Phi_{t,\,\tau}$ may not be CPTP for
intermediate time intervals and the divisibility property of the overall CPTP dynamics is violated, which characterizes a non-Markovian behavior \cite{Breuer2009,Rivas2010,Chruscinski2014}.

Now, assume $F_{\alpha}(t) = F_{\alpha}(\rho(t))$ represents an arbitrary monotonic function of $t$ under divisible dynamical maps, where $\alpha=+1$ and $\alpha=-1$ indicate increasing and decreasing behaviors,
respectively. Then, a sign change in $\dot{F}_{\alpha}(t)$ works as a witness of non-Markovianity. From this breakdown of monotonicity, we propose a measure of non-Markovianity as
\begin{equation}\label{Eq:NF}
N_{F_{\alpha}}[\Phi]=\text{max}_{\rho_0}\int_{\text{sgn}\dot{F}_{\alpha}=-\alpha}{\left|\dot{F}_{\alpha}(t)\right|dt}.
\end{equation}
The maximization in Eq.~(\ref{Eq:NF}) is performed over all sets of possible initial states, $\rho_0$, and the integration  extends over all time intervals for which the sign of $\dot{F}_{\alpha}(t)$ is $\text{sgn}\dot{F}_{\alpha}=-\alpha$.  If $\{(t_i^k, t_f^k)\}$ represents the set of all time intervals for which $\text{sgn}\dot{F_{\alpha}}=-\alpha$, then we can write
\begin{equation}\label{Eq:NF2}
N_{F_{\alpha}}[\Phi]=\text{max}_{\rho_0}\sum_{k\, :\, \text{sgn}\dot{F}_{\alpha}=-\alpha}\left|F_{\alpha}(t_f^k)-F_{\alpha}(t_i^k)\right|.
\end{equation}
We can employ different functions $F_{\alpha}$ depending on the dynamical map. First, let us consider the case of operations over incoherent states. By choosing a fixed basis $\{|i\rangle\}$ in a $d$-dimensional
Hilbert space, incoherent states are defined by density operators $\rho_{inc}$ that are diagonal when expressed in the basis $\{|i\rangle\}$, namely, $\rho_{inc}=\sum_i c_i \, |i\rangle\langle i|$, with $c_i$ denoting an
arbitrary complex amplitude. Then, it follows the notion of an {\it incoherent map}, which is a dynamical map
leading any incoherent state to another incoherent state. For the case of incoherent quantum operations, it can be shown that quantum coherence $C(\rho(t))$ can witness non-Markovianity through  $F_{-1}(t)=C(\rho(t))$~\cite{titas}.
We can also consider the case of a {\it unital map}, which maps the identity operator to itself, $\Phi(I)=I$. In this case, it can be shown
that the von Neumann entropy can witness non-Markovianity through $F_{+1}(t)=S(\rho(t))$~\cite{haseli}.
An operational approach to determine whether or not a dynamical map is unital or incoherent can be established through the {\it{sufficient conditions}} obtained from Eq.~(\ref{Eq:mastereq}): (i) if $[A_i,A_i^{\dagger}]=0$ then $\Phi$ is a {\it{unital map}};
(ii) If $\left\langle h_n\right|A_i\left|h_k\right\rangle\left\langle h_k\right|A^{\dagger}_i\left|h_m\right\rangle=0$ for all $k$ and $n\neq m$ then $\Phi$ is an {\it{incoherent map}} in the energy eigenbasis $\{\left|h_k\right\rangle\}$~\cite{titas}.
There are several well known quantum channels that are both incoherent and unital, such as phase flip, bit flip, bit-phase flip, among others~\cite{Nielsen-Book}. For further applications of Eq.~(\ref{Eq:NF2}) as a non-Markovianity measure and its relationship with correlation measures, see also Ref.~\cite{Paula2016}. Notice that, in this generalized approach, $\alpha$ may depend on the initial state, enabling the use of thermodynamic quantities such as internal energy, heat, and work to characterize non-Markovianity.

The use of the von Neumann entropy to witness non-Markovianity for unital maps suggests that heat flow, as defined by the entropy-based formulation of quantum thermodynamics, is also able to detect non-Markovian processes for unital maps.
Indeed, the expression $\dot{\mathbb{Q}}=U_r\dot{r}$ obtained from Eq.~(\ref{Eq:heat2q}) reveals that heat is {\textit{monotonically}} related to the purity (consequently to the entropy) for single qubit energy sign-preserving dynamics i.e., quantum
evolutions such that the internal energy $U$ is either a non-negative or a non-positive function of the time $t$. Notice that the purity does not increase under unital Markovian quantum processes \cite{Streltsov2018}. Then, we can establish the following measure of
non-Markovianity:
\begin{itemize}
\item [(\textit{a})] \textit{$N_{\mathbb{Q}}[\Phi]$ is a measure of non-Markovianity if $\Phi$ is a single-qubit energy sign-preserving unital map.}
\end{itemize}
In this case, heat can witness non-Markovianity via $F_{\alpha}(t)=\mathbb{Q}(\rho(t))$ with $\alpha=\text{sgn}U\neq 0$.  As an illustration, the sign of $U$ does not change under \textit{isochoric} processes, with heat a monotonic function of the purity
\begin{equation}\label{Eq:isochoric}
\mathbb{Q}=\Delta U=U_r\left(r-r_0 \right)\,\,\,\,(\dot{U}_r=0),
\end{equation}
where $r_0$ represents the initial purity. Then, we can employ either $\mathbb{Q}$ or $U$ to quantify the degree of non-Markovianity for \textit{isochoric unital maps}. Other examples include \textit{non-dissipative}  processes, where heat and work are monotonically related to the quantum coherence,
\begin{equation}\label{Eq:nondissipative}
\mathbb{Q}=-\mathbb{W}=U\mathrm{ln}\sqrt{\frac{C^2+U^2/h^2}{C_{0}^2+U^2/h^2}}\,\,\,\,(\dot{U}=0),
\end{equation}
being $C_0$ the initial quantum coherence. Consequently, we can use either $\mathbb{Q}$ or $\mathbb{W}$ to characterize the non-Markovianity of \textit{non-dissipative unital maps} as well as \textit{non-dissipative incoherent maps}.
Regardless of $\mathbb{Q}$, we can use $U$ and $\mathbb{W}$ for characterization of non-Markovianity if $\vec{h}(t)\cdot \vec{r}(t)$ and $U_r(t)$ are monotonic functions of $t$ for $\gamma_i (t)\geq 0$ ($\forall \, t\geq 0$), respectively.
As a special case, let us provide sufficient conditions for the thermodynamical variables to witness non-Marovianity for a time-independent Hamiltonian. In this scenario, we take $H=\omega_0\sigma_z$ and
denote $\vec{r}=[x(t),y(t),z(t)]$. Moreover, let us define $z_r\equiv z/r = \text{cos}\theta$. Then, it follows that
\begin{equation}\label{Eq:energy-z}
U(t)=\omega_0z(t),
\end{equation}
\begin{equation}\label{Eq:heatflow-z}
\dot{\mathbb{Q}}(t)=\omega_0 z_r(t)\dot{r}(t),
\end{equation}
\begin{equation}\label{Eq:workflow-z}
\dot{\mathbb{W}}(t)=\dot{\mathbb{W}}^*(t)=\omega_0r(t)\dot{z}_r(t).
\end{equation}
Hence, from Eq.~(\ref{Eq:heatflow-z}), we can establish that:
\begin{itemize}
\item [(\textit{b})] \textit{$N_{\mathbb{Q}}[\Phi]$ is a measure of non-Markovianity for a time-independent Hamiltonian $H=-\omega_0\sigma_z$ if $\Phi$ is a single-qubit unital map that does not invert the sign of $z(t)$.}
\end{itemize}
Furthermore, it follows from Eq.~(\ref{Eq:energy-z}) and Eq.~(\ref{Eq:workflow-z}) that $N_U$ and $N_{\mathbb{W}}$ are measures of non-Markovianity if $z(t)$ and $z_r(t)$  are monotonic functions of time for $\gamma_i (t)\geq 0$ ($\forall\, t \geq 0$), respectively.

\section{Applications}

\subsection{A dissipative quantum evolution}
Let us first consider  a dissipative single-qubit dynamics described by a time-local master equation given by Eq.(\ref{Eq:mastereq}), with $H=\omega_0\sigma_z$, $A_i =\delta_{1,i}\, \sigma_x$, and $\gamma_i=\delta_{1,i}\,\gamma$, such that $\omega_0>0$ and $\gamma>0$. Then
\begin{equation} \label{Eq:mastereq-markov}
    \dot{\rho}(t)=-i\omega_0\left[\sigma_z, \rho(t)\right]+\gamma
    \left[\sigma_{x}\rho(t)\sigma_{x}-\rho(t)\right].
\end{equation}
This master equation generates a Markovian quantum process $\rho(t)=\Phi_{M}\,\rho_0=(I+\vec{r}(t)\cdot\vec{\sigma})/2$, where $\vec{r}(t)=[x(t),y(t),z(t)]$,
whose solution for the Bloch vector is given by
\begin{equation}
x(t) =\frac{e^{-\gamma t}}{2 \omega}\left[\alpha_x e^{\omega t}+\beta_x e^{-\omega t} \right],
\end{equation}
\begin{equation}
y(t) =\frac{e^{-\gamma t}}{2 \omega}\left[\alpha_y e^{\omega t}+\beta_y e^{-\omega t} \right],
\end{equation}
\begin{equation}
z(t)= z_0 e^{-2\gamma t},  \label{Eq:BlochVectorExample1}
\end{equation}
where
\begin{equation}
\alpha_x= \omega x_0 + \gamma x_0 - 2 \omega_0 y_0,
\end{equation}
\begin{equation}
\beta_x= \omega x_0 - \gamma x_0 + 2 \omega_0 y_0,
\end{equation}
\begin{equation}
\alpha_y= \omega y_0 - \gamma y_0 + 2 \omega_0 x_0,
\end{equation}
\begin{equation}
\beta_y= \omega y_0 + \gamma y_0 - 2 \omega_0 x_0,
\end{equation}
with
\begin{equation}
\omega=\sqrt{\gamma^2 - 4 \omega_0^2}
\end{equation}
and $\vec{r}_0=[x_0,y_0,z_0]$ denoting the initial state. The Markovian map $\Phi_M$ is both unital and incoherent, since the Lindblad operators $A_i =\delta_{1,i}\, \sigma_x$ satisfy the conditions (i) and (ii) described in Sec.~\ref{sec:III}. Moreover, $\Phi_M$ is also a map that preserves the sign of $z(t)$ (note that $\text{sgn}z(t)=\text{sgn}z_0$ $\forall\, t\geq 0$). Consequently, we can use the monotonicity of $\mathbb{Q}(t)$ or $C(t)$ as functions of $t$ to observe the Markovianity of Eq.~(\ref{Eq:mastereq-markov}). Then
\begin{equation}\label{Eq:NF1}
N_{F_{\alpha}}[\Phi_M]=0,
\end{equation}
where $F_{\alpha}= \mathbb{Q}$, with $\alpha=\text{sgn}z_0\neq 0$ or $F_{\alpha}=C$ with $\alpha=-1$. Indeed, Fig. \ref{fig:1} illustrates the sign preservation of $\dot{F}_{\alpha}(t)$ for the initial state $\vec{r}_0=[1/2,0,1/2]$,
where the heat and coherence flows reduce to
\begin{equation}
\dot{\mathbb{Q}}(t)=\frac{\omega_0 \gamma \left[2\omega_0^2(1-\cosh{(2\omega t)}) -\omega^2 e^{-2\gamma t}\right]e^{-2 \gamma t}}{\omega^2 e^{-2 \gamma t}+\gamma^2 \cosh{(2 \omega t)}+\omega \gamma \sinh{(2\omega t)}-4 \omega_0^2},
\end{equation}
\begin{equation}
\dot{C}(t)=\frac{2\omega_0^2 \gamma e^{-\gamma t}\left(1-\cosh{2 \omega t}\right)}{\omega \sqrt{\gamma^2 \cosh{(2 \omega t)}+\omega \gamma \sinh{(2\omega t)}-4\omega_0^2}}.
\end{equation}
The Markovianity of Eq.~(\ref{Eq:mastereq-markov}) can also be observed by the behavior of the internal energy and work  (see plots for $U$ and $\mathbb{W}$ for $\vec{r}_0=[1/2,0,1/2]$ in Ref.~\cite{alipour1}).

\begin{figure}[ht!]
\centering
\includegraphics[scale=0.32]{fig1}
\caption{(Color online) Heat (dotted black line) and quantum coherence (solid red line) flows as a function of time for $\vec{r}_0=[1/2,0,1/2]$, in units such that $\gamma=0.1$ and $\omega_0=1$.}
\label{fig:1}
\end{figure}

\subsection{A non-dissipative quantum evolution}

Let us consider now the dynamics of a single qubit under \textit{dephasing}, whose master equation is given by
\begin{equation}\label{Eq:mastereq3}
    \dot{\rho}(t)=-i\omega_0 \left[\sigma_z, \rho(t)\right]+\gamma
    \left[\sigma_{z}\rho(t)\sigma_{z}-\rho(t)\right],
\end{equation}
This master equation can be derived from Eq.(\ref{Eq:mastereq}) by taking $H=\omega_0\sigma_z$, $A_i =\delta_{1,i}\, \sigma_z$, and $\gamma_i=\delta_{1,i}\,\gamma$. The solution is given by a map $\Phi_{D}$ such that $\rho(t)=\Phi_{D}\rho_0=(I+\vec{r}(t)\cdot\vec{\sigma})/2$ with \cite{titas}
\begin{equation}
\vec{r}(t)=[x_0\Gamma (t), y_0\Gamma (t),z_0],
\end{equation}
where
\begin{equation}
\Gamma(t)=\exp[-\int_0^t{\gamma(t) dt}].
\end{equation}
In this case, the internal energy and the quantum coherence are given by
\begin{equation}\label{Eq:U-deph}
U(t)=U_0\, , \,\,\,\,\,\,\text{with}\,\,\,\,\,\,U_0=\omega_0z_0 ,
\end{equation}
and
\begin{equation}\label{Eq:C-deph}
C(t)=C_0\Gamma (t)\, , \,\,\,\,\,\,\text{with}\,\,\,\,\,\,C_0=\sqrt{r_{0}^2-z_{0}^2},
\end{equation}
respectively. The  map $\Phi_D$ is both \textit{non-dissipative unital} and \textit{non-dissipative incoherent}. Consequently,  we can use $\mathbb{Q}(t)$, $\mathbb{W}(t)$, or $C(t)$ to
characterize the non-Markovianity of Eq.(\ref{Eq:mastereq3}). Inserting Eqs.~(\ref{Eq:U-deph}) and (\ref{Eq:C-deph}) in Eq.~(\ref{Eq:nondissipative}), we can express heat in the form
\begin{equation}\label{Eq:Q-deph}
\mathbb{Q}(t)=\omega_0z_{r0}r_0\ln \sqrt{\Gamma(t)^2+\left(1-\Gamma(t)^2\right)z_{r0}^2}.
\end{equation}
The non-Markovianity measure in Eq.~(\ref{Eq:NF2}) then reads
\begin{eqnarray} \label{Eq:Nmax}
&&\hspace{-0.5cm}N_{\mathbb{Q}}[\Phi_D]=\text{max}_{\rho_0}\sum_{k:\text{sgn}\dot{\mathbb{Q}}=\text{sgn}U_0}\left|\mathbb{Q}(t_f^k)-\mathbb{Q}(t_i^k)\right| \nonumber \\
&&\hspace{-0.5cm}=\omega_0\text{max}_{|z_{r0}|,r_0}r_0\sum_{k:\gamma < 0}|z_{r0}|\ln \sqrt{\frac{\Gamma(t_f^k)^{2}+(1-\Gamma(t_f^k)^{2})|z_{r0}|^2}{\Gamma(t_i^k)^{2}+(1-\Gamma(t_i^k)^{2})|z_{r0}|^2}} \nonumber \\
&&\hspace{-0.5cm}=\omega_0\text{max}_{|z_{0}|}\sum_{k:\gamma < 0}|z_{0}|\ln \sqrt{\frac{\Gamma(t_f^k)^{2}+(1-\Gamma(t_f^k)^{2})|z_{0}|^2}{\Gamma(t_i^k)^{2}+(1-\Gamma(t_i^k)^{2})|z_{0}|^2}}.
\end{eqnarray}
Note that a pure initial state (i.e., $r_0=1$) results from the maximization procedure in Eq.~(\ref{Eq:Nmax}). In order to enable a numerical comparison with the coherence-based
measure of non-Markovianity, let us consider a typical example of a zero-temperature bosonic reservoir with an Ohmic-like spectral density, where the time-dependent dephasing
rate presents the specific form \cite{Haikka2013, Shekhar2015, titas}
\begin{equation}\label{Eq:gamma}
\gamma(t,s)=[1+(\omega_c t)^2]^{-s/2}\Gamma [s]\sin[s\arctan(\omega_c t)],
\end{equation}
being $s\geq 0$ the ohmicity parameter, $\Gamma[s]$ the Euler Gamma function, and $\omega_c$ the cutoff spectral frequency. In this case, $\gamma(t,s)<0$ occurs for
$t_i^k=t_{2k-1}$ and $t_f^k=t_{2k}$, where $t_{k}=\tan[k\pi/2s]/\omega_c$, being $k$ an integer such that $0\leq k \leq \lfloor s\rfloor$ ($\lfloor s\rfloor$  is the floor function of $s$).
Thus, we can conclude that $0\leq s \leq 2$ and $s> 2$ correspond to the Markovian and non-Markovian regimes of this model. In terms of the ohmicity parameter, $N_{\mathbb{Q}}[\Phi_D]$ takes the form
\begin{equation}\label{Eq:NQ-s}
N_{\mathbb{Q}}(s)=\omega_0\ln\left[\prod_{k=1}^{\lfloor s/2 \rfloor}\frac{\Gamma(t_{2k})^{2}+(1-\Gamma(t_{2k})^{2})z_{max}^2}{\Gamma(t_{2k-1})^{2}+(1-\Gamma(t_{2k-1})^{2})z_{max}^2}\right]^{\frac{z_{max}}{2}},
\end{equation}
where $z_{max}$ represents the value of $|z_0|$ that maximizes the last expression in Eq.~(\ref{Eq:Nmax}). The coherence-based measure $N_{C}[\Phi]$ has been employed
to quantify the degree of non-Markovianity of the incoherent map $\Phi_D$ for the dephasing rate described in Eq.~(\ref{Eq:gamma}) \cite{titas}. As function of the $s$-parameter, $N_C[\Phi_D]$ reduce to
\begin{equation}\nonumber
N_{C}(s)=\text{max}_{\rho_0}\sum_{k:\text{sgn}\dot{C}=+1}\left|C(t_f^k)-C(t_i^k)\right|
\end{equation}
\begin{equation}\label{Eq:NC-s}
=\sum_{k=1}^{\lfloor s/2 \rfloor}\left[\Gamma(t_{2k})-\Gamma(t_{2k-1})\right],
\end{equation}
where a maximally coherent state (i.e., $C_0=1$) emerges from the maximization process.

\begin{figure}[ht!]
\centering
\includegraphics[scale=0.3]{fig2}
\caption{(Color online)  $\mathbb{Q}$ as a function of $\omega_c t$ for $s = 1.5$ (black dashed line) and $s = 3.5$ (red solid line), with $\omega_0=1$, $r_0=1$, and $z_0=0.05$.}
\label{fig:2}
\end{figure}
In order to witness non-Markovianity, Fig.~\ref{fig:2} shows the time evolution of the heat $\mathbb{Q}$ for an initial pure state under the single-qubit dephasing channel in both Markovian and non-Markovian regimes.
Note that $\mathbb{Q}$ is a monotonically decreasing function of time for $s = 1.5$. On the other hand, a non-monotonic behavior arises due to the backflow of heat from the
environment to the system for $s = 3.5$. The behaviors of the non-Markovianity measures $N_\mathbb{Q}$ and $N_C$
as functions of $s$ are illustrated in Fig.~\ref{fig:3}, with the inset showing $z_{max}$ versus $s$. These measures are monotonically related,
i.e., $N_C(s)\approx 2.0 \, N_\mathbb{Q}(s)$, with both assuming non-zero values only for $s > 2$, a maximum value at $s=3.2$, and negligible values for $s > 5$. From the behavior of $z_{max}(s)$,
notice that a maximally coherent state (where $z_0=0$) does not optimize the expression in Eq.~(\ref{Eq:NQ-s}) for all $s$.

\begin{figure}[ht!]
\centering
\includegraphics[scale=0.3]{fig3}
\caption{(Color online) $N_\mathbb{Q}$ (green solid line) and $N_C$ (blue dashed line) as functions of $s$ for $\omega_0=1$ and $\omega_c =1$. Inset: $z_{max}$ as a function of $s$.}
\label{fig:3}
\end{figure}

\section{Conclusions}

We have introduced a characterization of non-Markovianity by using the entropy-based formulation of quantum thermodynamics.
Specifically, by looking at the divisibility property of the overall CPTP dynamics, we derived a measure of non-Markovian behavior
through the relationship between entropy and heat in a thermodynamic process. This result supports the
entropy-based approach, since it provides utility for the definition of heat by exclusively taking the entropy change contribution
in the internal energy balance.

The analysis of the heat flow can be a useful tool from an experimental point of view to provide a thermodynamic assessment of the memory effects of the bath.
Based on the heat flow behavior, we can design an environment engineering approach to induce the desired amount of memory in a system-bath interaction
for a suitable physical architecture. Moreover, from a conceptual point of view, it would be interesting to establish to what extent a thermodynamic characterization of non-Markovianity beyond single-qubit maps can be achieved. These are left as perspectives for future investigations.

\section*{Acknowledgments}
J.M.Z.C. acknowledges financial support from  Conselho Nacional de Desenvolvimento Cient\'{\i}fico e Tecnol\'ogico (CNPq).
M.S.S. is supported by Conselho Nacional de Desenvolvimento Cient\'{\i}fico e Tecnol\'ogico (CNPq) (307854/2020-5).
This research is also supported in part by Coordena\c{c}\~ao de Aperfei\c{c}oamento de Pessoal de N\'{\i}vel Superior (CAPES) (Finance Code 001) and by the Brazilian National Institute for Science and Technology of Quantum Information (INCT-IQ).

redpajama_set_name: RedPajamaArXiv


text:
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redpajama_set_name: RedPajamaCommonCrawl


Make this furry creature happy by serving your finger foods out of Arthur Court's Small Squirrel Nut Bowl.
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Once the grand downtown Menlo Hotel, and home to the oldest [still] working elevator in Oakland, the towers have had their fair share of historic moments, including scandal and tragedy, before being converted into an apartment building, and an underground art space.
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text:
Economic Win Conditions in Prismata?
This entry was posted in Banter on April 15, 2016 by Elyot Grant
Before I get to the main article, I wanted to mention a few experimental things we're trying out on the alpha server right now:
Bots that resign when they think they're losing.
Bots that use emotes.
Coloured usernames in the chat boxes.
These are not final, but we're trying them out for now to see what people think. Let us know if you love or hate them, or would like to see changes!
On with the main topic, which relates to TODAY'S EVENT…
Economic Victory?
A number of turn-based strategy, tactics, and board games include so-called economic victory conditions, which provide a mechanism for players to win the game without eliminating their opponents. The Civilization series is perhaps the most well-known example, with the standard rules allowing a number of alternate victory conditions, including scientific, diplomatic, and cultural victories. There are a number of nuances involved, but the key point is the following: it's possible to win without fighting your opponent, simply by collecting tons of resources and upgrading/teching your way to victory.
A simple question naturally arose: could such a mechanic work in Prismata?
Unfortunately, a naive implementation of economic victory never really panned out in Prismata's ruleset. Games with rules like "first to 100 gold wins" turned out to be a snooze-fest. Prismata has no territory to capture, resources to fight over, or neutral creatures to fight, and without these incentives for interaction, economic battles turn into 2-player solitaire. Worse, that specific form of 2-player solitaire is often quite uninteresting.
It didn't take us long to give up on the idea. However, a related idea held some promise.
Economic Almost-Victory
Early on in Prismata's history, when we were still figuring out the exact implementation of our technology tree, we contemplated the existence of ultra-powerful high-tech units that didn't win the game outright, but would have such a powerful effect on the board state as to "almost win", and thus would strongly incentivize players to go for them. Our design goal was somewhat similar to that of the ultimate spells used by planeswalkers in Magic: the Gathering—we didn't want units that had a pure "buy this and you win" effect, but instead said something that roughly translated to "buy this and you probably win, unless something crazy happens!"
One such ultimate unit was the infamous "Fire Spinner", which was briefly reintroduced on April Fools Day in 2015.
Yes, its cost is *20 red*. That means you'll likely need to exhaust your Animus supply to get it.
These types of designs never really worked. Balance was problematic. If an ultimate unit was too weak, nobody would go for it. If it was too strong, then players would race to purchase them, and whoever got there first would often have a huge lead and win the game outright. Unfortunately, there isn't much design room in between the two extremes of too weak and too strong; the situational nature of Prismata unit sets tends to add a lot of game-to-game variance in the power level of units like Fire Spinner. Accordingly, we witnessed some pretty degenerate games when Fire Spinner was really good, and we couldn't prevent these degenerate situations from arising without nerfing the unit until it was terrible.
We even experimented with special rules like "you can only level up your tech once per turn" to find balance in these types of unit designs, but we kept hitting problems with player advantage and never really found something that worked.
Alas, the power level of these ultimate units had to come down to what we now see in units like Odin, Lucina Spinos, and Zemora Voidbringer (though we had better luck when experimenting with units like Arka Sodara that provided a small benefit to the player who buys it second).
That said, we're not done with Fire Spinner entirely…
This Week's Event
Even though Fire Spinner proved to be too degenerate to make the final roster of competitive Prismata units, a lot of players had fun exploring the possibilities with Fire Spinner when we ran it last year during April Fool's Day. Many of our players have requested that we bring Fire Spinner back, so we've decided to do so, along with a few of his friends. As per tradition, I requested that Alex provide the illustrations, and you can witness his exquisite artistic flair below:
In theory, you can buy this thing off of a single Conduit, if the game goes long enough…
Is this the largest blocker in Prismata? Is he throwing two Blastforges?
Today's event will feature all three units in all event games. As usual, the event starts at 4pm Eastern, and there will be an encore next Tuesday.
About Elyot Grant
A former gold medalist in national competitions in both mathematics and computer science, Elyot has long refused to enjoy anything except video games. Elyot took more pride in winning the Reddit Starcraft Tournament than he did in earning the Computing Research Association's most prestigious research award in North America. Decried for wasting his talents, Elyot founded Lunarch Studios to pursue his true passion.
View all posts by Elyot Grant →
← Tales from Prismata development: The Shift Bug
Annotated Prismata Openings by Will Ma →


text:
70th parallel north
The 70th parallel north is a circle of latitude that is 70 degrees north of the Earth's equatorial plane, in the Arctic. It crosses the Atlantic Ocean, Europe, Asia and North America, and passes through some of the southern seas of the Arctic Ocean.
On Victoria Island, Canada, part of the border between Northwest Territories (green) and Nunavut (white) is defined by the 70th parallel north
At this latitude the sun is visible for 24 hours, 0 minutes during the summer solstice and Civil Twilight during the winter solstice.
Around the worldEdit
Starting at the Prime Meridian and heading eastwards, the parallel 70° north passes through:
Country, territory or sea
70°0′N 0°0′E / 70.000°N 0.000°E / 70.000; 0.000 (Prime Meridian)
Norwegian Sea
70°0′N 18°40′E / 70.000°N 18.667°E / 70.000; 18.667 (Norway)
Troms - islands of Rebbenesøya, Ringvassøy, Reinøya, Karlsøya and Kågen; mainland; island of Skorpa; mainland
Finnmark (mainland)
70°0′N 27°22′E / 70.000°N 27.367°E / 70.000; 27.367 (Finland)
Passing about 10 km south of the northernmost point of Finland, which is located at 70°05.537′N 27°57.335′E / 70.092283°N 27.955583°E / 70.092283; 27.955583 in the village of Nuorgam
70°0′N 28°2′E / 70.000°N 28.033°E / 70.000; 28.033 (Norway)
70°0′N 29°30′E / 70.000°N 29.500°E / 70.000; 29.500 (Barents Sea)
70°0′N 58°44′E / 70.000°N 58.733°E / 70.000; 58.733 (Russia)
Vaygach Island
Kara Sea
Yamal Peninsula
70°0′N 72°30′E / 70.000°N 72.500°E / 70.000; 72.500 (Gulf of Ob)
Gulf of Ob
70°0′N 159°53′E / 70.000°N 159.883°E / 70.000; 159.883 (East Siberian Sea)
East Siberian Sea
70°0′N 168°13′E / 70.000°N 168.217°E / 70.000; 168.217 (Russia)
Ayon Island
70°0′N 177°56′E / 70.000°N 177.933°E / 70.000; 177.933 (Chukchi Sea)
Chukchi Sea
70°0′N 162°27′W / 70.000°N 162.450°W / 70.000; -162.450 (United States)
70°0′N 142°34′W / 70.000°N 142.567°W / 70.000; -142.567 (Beaufort Sea)
Beaufort Sea
70°0′N 131°2′W / 70.000°N 131.033°W / 70.000; -131.033 (Canada)
Northwest Territories - Tuktoyaktuk Peninsula
70°0′N 128°18′W / 70.000°N 128.300°W / 70.000; -128.300 (Canada)
Northwest Territories - Cape Bathurst Peninsula
70°0′N 126°54′W / 70.000°N 126.900°W / 70.000; -126.900 (Amundsen Gulf)
Amundsen Gulf
Northwest Territories - Parry Peninsula
On Victoria Island:
- Northwest Territories
- Northwest Territories / Nunavut border
- Nunavut
70°0′N 100°48′W / 70.000°N 100.800°W / 70.000; -100.800 (Victoria Strait)
Victoria Strait
70°0′N 98°50′W / 70.000°N 98.833°W / 70.000; -98.833 (Larsen Sound)
Larsen Sound
Passing just north of King William Island, Nunavut,
70°0′N 97°35′W / 70.000°N 97.583°W / 70.000; -97.583 (James Ross Strait)
James Ross Strait
Passing just north of the Clarence Islands, Nunavut,
70°0′N 96°17′W / 70.000°N 96.283°W / 70.000; -96.283 (Canada)
Boothia Peninsula, Nunavut
70°0′N 92°1′W / 70.000°N 92.017°W / 70.000; -92.017 (Gulf of Boothia)
Gulf of Boothia
Nunavut - Crown Prince Frederik Island
70°0′N 86°27′W / 70.000°N 86.450°W / 70.000; -86.450 (Fury and Hecla Strait)
Fury and Hecla Strait
Nunavut - Baffin Island
70°0′N 81°9′W / 70.000°N 81.150°W / 70.000; -81.150 (Murray Maxwell Bay)
Murray Maxwell Bay
70°0′N 78°39′W / 70.000°N 78.650°W / 70.000; -78.650 (Steensby Inlet)
Steensby Inlet
70°0′N 67°20′W / 70.000°N 67.333°W / 70.000; -67.333 (Baffin Bay)
Baffin Bay
Northern limit of the Davis Strait
70°0′N 53°39′W / 70.000°N 53.650°W / 70.000; -53.650 (Greenland)
Disko Island
70°0′N 52°30′W / 70.000°N 52.500°W / 70.000; -52.500 (Sullorsuaq Strait)
Sullorsuaq Strait
Nuussuaq Peninsula
70°0′N 50°37′W / 70.000°N 50.617°W / 70.000; -50.617 (Torsukattak Fjord)
Torsukattak Fjord
Sermeq Kujalleq
70°0′N 27°20′W / 70.000°N 27.333°W / 70.000; -27.333 (Gaasefjord)
Gaasefjord
Geikie Plateau
70°0′N 22°18′W / 70.000°N 22.300°W / 70.000; -22.300 (Arctic Ocean)
Greenland Sea
71st parallel north
Retrieved from "https://en.wikipedia.org/w/index.php?title=70th_parallel_north&oldid=730803097"


text:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace StoryTeller.DataModel.Model
{
    public enum SceneTagType
    {
        None,
        Location,
        Character,
        Custom,
    }
}

redpajama_set_name: RedPajamaGithub


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« Salt vs. Sugar ~ How to Choose the Right Body Scrub!
Omg I need the hair products! I absolutely LOVE tropical smelling products!
Me too! There's nothing better than fresh, amazing smelling hair!
I hear ya. The Baby Bum products are mineral based so they are really gentle on the skin.
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I had to google Melasma Doesn't sound fun, I'm sorry you got it. Happy to hear you managed to get it clear and keep it clear!!
You still look amazing Victoria! Great post, thanks for the tips!
My aunt has Melasma so I'm always careful about being out in the sun. These sunbum products I will check out, I'm always looking for newer better sun protection.
That' so great that you're already taking the right precautions. Let me know if you pick up any Sun Bum products and let me know what you think!
Definitely going to try the face cream. I find products with SPF so greasy on my skin so this sounds pretty good.
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That's awesome! Definitely get the leave-in conditioner! You will love it!


An excipient is an inactive substance formulated with the active ingredient of a medication for the purpose of bulking-up Route of Administration that contain potent active ingredients. These substances improve bulkiness and dissolution rate of the drug and are crucial in drug delivery within the body. A sugar-based excipient is required if the conventional tablet contains a bitter drug substance or, more importantly, if the tablet is chewable. Sweeteners are added in tablets to impart sweetness to the drugs. Sucrose is the standard against, which all sweeteners, both artificial and natural, are measured. Apart from being sweeter than sucrose, artificial sweeteners have the advantage of not disturbing blood sugar levels of pre-diabetic or diabetic patients, and they are considered to be non-cariogenic. Sugar-based excipients are widely used as ingredients in pharmaceutical tableting. They are used for taste masking of bitter drugs and as bulking agents. Dextrose, fructose, mannitol, sorbitol, and xylitol are few examples of sugar-based excipients that are mainly used.
Increasing use of co-processed excipients and rising development of orally disintegrating tablets (ODTs) are major factors that are expected to boost growth of sugar-based excipients market over the forecast period. ODTs are solid dosage forms containing medicinal substances, which disintegrate rapidly, generally in few seconds, when placed on the tongue. Research on delivering biological molecules through the oral route have widened the scope of ODT technology, which further drive growth of the market. According to the American Pharmaceutical Review 2016, over 35 products have been launched using Zydis ODT technology in over 60 countries worldwide. Furthermore, rising use of sugar alcohols such as mannitol in a wide range of oral dosage and high adaptability in formulation technologies such as ODTs are expected to drive the sugar-based excipients market growth over the forecast period. Sugar alcohol is granular and white like sugar, and is used as a sugar alternative. The sugar alcohols differ in calorie content and sweetness level. Their sweetness level ranges from 50% to 100% that of sugar.
Demand for oral Route of Administration due to increased use of tablets, capsules, solutions, and emulsions for various therapeutic areas is anticipated to drive market growth. Oral route of administration form the largest category of pharmaceutical dosage. Although an excipient is pharmacologically inactive and does not interact with the active drug ingredients or other excipients, few excipients meet the criteria. Some sugar-based excipients can cause side effects and therefore should be avoided. For instance, Aspartame, which is used as a sweetener in drugs are not prescribed to patients with phenylketonuria.
However, all sugar-based products do not have fast dissolution rate and good compatibility or compressibility. Incompatibility with stringent government regulations for drug manufacturing and excipient usage are expected to hinder sugar-based excipient market growth. For instance, as per the European Medicines Agency, the usage of an excipient should be well reasoned, explaining its role and justification for inclusion of the amount used.
On the basis of region, the global sugar-based excipients market is segmented into North America, Latin America, Europe, Asia Pacific, Middle East, and Africa. North America sugar-based excipients market is expected to hold a dominant position over the forecast period, owing to increased usage for generic drugs in the region. Increasing investments in drug development and rising production of generic drugs will drive growth of sugar-based excipient market in Europe. Significant growth in the healthcare and pharmaceutical industry, favorable government policies, low-cost manufacturing, and increasing demand for generic drugs, especially in emerging economies directly contributes to the market growth. According to the Food and Drug Administration (FDA) data, in 2017, Indian firms received around 40% of the new U.S. approvals for generics with a wider base of companies.
Some of the key players operating in the global sugar-based excipients market include Ashland Inc., Associated British Foods Plc, BASF SE, Colorcon, Inc., Cargill, Inc., DFE Pharma, FMC Corporation, MEGGLE AG, Roquette Group, and The Lubrizol Corporation.


CONWAY, Ark.--The Birmingham-Southern softball team split on the road today with Hendrix on day one of the series, winning game one 8-1 but losing in the nightcap 5-4 at Warrior Field in Conway, Ark.
The Panthers move to 20-10 overall and 11-3 in the Southern Athletic Association, while the Warriors move to 18-8 overall and 8-4 in league play.
In game one, BSC scored its first two runs in the top of the first inning on a Hendrix error and an RBI single by sophomore Bethany Fronk. The Warriors put up their lone run in the bottom of the first, and BSC added three more in the bottom of the fourth, with two scoring on another Hendrix error and another courtesy of an RBI from sophomore Joanna Jernigan, putting the Panthers up 5-1.
Sophomore Taylor Bassett led off the top of the fifth with a home run to put BSC up 6-1, and RBIs from sophomore Alyssa Statham and Fronk in the top of the seventh put the Panthers up 8-1.
BSC recorded 12 hits, led by senior Brittany Berkopec who was 3-4. Freshman Deanna Creps was 2-3 and Statham and Fronk were both 2-4.
Fronk started in the circle and threw the complete game, getting the win to move to 15-7 on the season. She gave up four hits and one earned run with five strikeouts.
In game two, BSC got off to another quick start, scoring twice in the top of the first on another Bassett home run, this time good for two on the scoreboard. Bassett recorded another RBI in the top of the second on a single to put the Panthers up 3-0.
Hendrix got on the board in the bottom of the second, scoring on two RBI singles, and then took the first lead of the day in the bottom of the third with three runs scored on an RBI single and a two-run double, putting the Warriors up 5-3.
BSC cut it to 5-4 in the top of the sixth on a Statham RBI double, but the Panthers weren't able to score again to overcome the Warriors' single-run lead.
Both teams recorded 10 hits; Bassett led BSC, going 3-3 at the plate with three RBI. Statham and Jernigan were 2-3 and Fronk was 2-4.
Creps started in the circle and went 1.2 innings, giving up four hits and two earned runs before Fronk came in for the final 4.1 innings. She allowed six hits and three earned runs with two strikeouts, taking the loss to fall to 15-8.
The four-game series will conclude tomorrow with a noon doubleheader.


The call is now open for case studies on "Reading for health and wellbeing in libraries and information services" to be published by Facet Publishing.
Final chapters will be 3000-4000 words.
Interested applicants should send an abstract (200-300 words) and a brief biographical statement to s.mcnicol@mmu.ac.uk by the 3rd March 2017.
Brief project description: what are you doing? Are you following a particular model of bibliotherapy? Who is the audience?
Aims: What do you hope people will gain from participating?
Outcomes: What have people actually gained from participating?
Reflections: What are you most proud of? What would you do differently?


Labeling software with installed libraries of nursery stock, indoor plants, etc. Enables to edit descriptions, add/delete items.
Gardenware Labeling Software Reviews Recently Reviewed!
Pros: Extremely easy to use. There is absolutely no effort to use this gardening software program. Need to put your name and logo on a label? Type in in the ino box and it's there. Want to change the installed info about a product? Use the edit button, make changes and save. DONE! This is the best gardening program available and it's extremely reasonably priced.
Cons: There is nothing we dislike about this software!
Overall: We have used this software program for nearly 20 years and love it.
Comments: We have used Gardenware labeling software since it was developed. It's without doubt, labeling software that every nursery, large or small should own.
Our firm has on occasion had a need to call and reference an available product. They have always answered all our questions and provided customer service that most other software sellers only talk about.


Every year sees energy storage build on the success of the preceding one, it seems, and this year we were able to carry insights and opinions from some of the best placed participants and observers. Here's our picks for the content most representative of the year it's been, as well as the 10 most read news stories on the site.
Covering the energy storage market has been an interesting – if occasionally bumpy – ride so far and we can expect it to be an even more vibrant and action-packed space from here on in. From the top five most-read news stories to some great interviews via our regular guest blogs, we've rounded up some highlights from our year.


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Jack Whitehall Gets Around at SSE Arena, Wembley London.
Jack Whitehall on scandal, public school privilege and new BBC drama Decline and Fall The actor and comedian leads the cast of Evelyn Waugh's high-society satire on the BBC Share on Facebook.
A home in Lambeth plays the posh residence of Jack Whitehall in his new comedy series for Sky One, Bounty Hunters. Take a look at the trailer for the show here. Location manager Simon Scott has said the production filmed there for a week in May this year. FilmFixer manages the film office service for Lambeth Council. FilmFixer director Andrew Pavord explains, "The series is a great farce.
Determined not to let lockdown spoil Father's Day, Jack sets up outside his Dad's house to spend some quality time together. They reminisce, catch up with some celebs and surprise some key workers who can't be with their loved ones.
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Jack Whitehall Photos - Image has been converted to black and white) Jack Whitehall attends the EE British Academy Film Awards at The Royal Opera House on February 14, 2016 in London, England. - EE British Academy Film Awards - Portraits.
Bad Education follows Alfie Wickers, the worst teacher ever to (dis)grace the British Education system and a bigger kid than the pupils he teaches. Along with his class of wayward teens, Alfie is never far from trouble as he strives to prove that he knows best. Jack stars as Alfie Wickers.
Crowned the 'King of Comedy' at 2012's British Comedy Awards, comedian of the moment Jack Whitehall is now venturing on his first solo stand-up arena tour, 'Jack Whitehall Gets Around'. Having also delved into acting and writing - he stars in the award-winning Channel 4 series 'Fresh Meat' and writes for the BBC sitcom 'Bad Education' - this will be Whitehall's first show since the 2011.
Companies House does not verify the accuracy of the information filed (link opens a new window). Jack WHITEHALL. Filter appointments Filter appointments Current appointments Total number of appointments 1 Date of birth July 1988. JACKPOT PRODUCTIONS LIMITED (06785902).
Jack Whitehall has said he was "terrified" he had given his father coronavirus during the first weeks of lockdown. The comedian, who often appears with his 80-year-old father Michael on screen, developed symptoms of the virus shortly after lockdown began, days after he had visited his parents.
From the moment you drive up to the The Whitehall Hotel Darwen, you realise that the claim to be the perfect venue for any occasion is well-founded. A majestic Victorian manor house lovingly transformed into a traditional country house hotel in Darwen.. The foundations of the house are as solid as the pursuit of customer care. As a privately owned hotel we pride ourselves on a professional.
Jack Whitehall: 30 of his best jokes and quotes as he presents Brit Awards The Manchester University alumnus is set to present the 40th Brit Awards. By Alex Nelson. Tuesday, 18th February 2020, 3.
Jack's new national arena tour Jack Whitehall Gets Around played to sell-out audiences across the country and will be available on DVD this Autumn. Michael Whitehall as a theatrical agent has been involved in the careers of many eminent actors, including Colin Firth, Richard Griffiths, Angela Thorne, Michael Fassbender, Daniel Day Lewis, Nigel Havers and Judi Dench. He is also a television and.
The country-folk singer and songwriter died at the Vanderbilt University Medical Center in Nashville, Tennessee, U.S., at the age of 73 On March 20, his wife Fiona had revealed that he had tested.
Actor and comedian Jack Whitehall and his father Michael Whitehall will record a bespoke video message for father's day. Two generations of Whitehalls can serenade your father with humour.
Jack Whitehall is a hugely influential and exciting British comedian. He has entertained television and stage audiences with his endearing personality, cynical views and quick wit for many years. One of the UK's favourite comedians, there are few who have the same appeal as the posh comedian. Book Jack Whitehall Today!
Catch Jack Whitehall as he tries out new material for his upcoming arena tour. A great opportunity to catch Jack in a theatre near you. Show includes tour support. Jack is a Joy to watch on stage and a comedian who is firmly on the road to becoming a global megastar, this show is not to be missed.
JACK Whitehall, known as the posh boy of comedy, is one of the UK's best known comedians thanks to his meteoric rise to fame. His next TV project, Jack Whitehall's Father's Day, will air TONIGHT (June 19) in BBC One. Who is Jack Whitehall? Jack Whitehall was born on July 7, 1988, in London and is a comic and actor. His father, Michael Whitehall, was an agent for Judi Dench and Colin Firth.
A League Of Their Own: Jack Whitehall and Freddie Flintoff are the new Brokeback Mountain and it's so heartwarming - smouldering romantic tension between Jack Whitehall and Freddie Flintoff on finally boiled over on A League Of Their Own's roadtrip special - May 2016.


What you might have seen in a GP record circa 1980, if you could have read the handwriting!
Things got easier you could get a 10Mb hard disk for under £5k and we could afford a bit of free text – "Tonsillitis (probably) Pen .V and thus was born the computerised GP record that survives to this day. A structure coded, record, with text used occasionally to clarify or maybe confuse what w e meant by the code "Carcinoma of the Broncos (B192) Excluded (Text)" an approach driven by the limitations of the hardware but one that fitted with the GP approach to record keeping and led us to discover the power and flexibility of a structure record built on a terminology – What to record some new stuff, no need to change the software just add a few codes to the terminology.
This paradigm has served GPs well and continues to do so, codes first, text an afterthought. However, trying to extend this approach into other areas of healthcare where there is a need to record a richer narrative has been a challenge, spawning ever more complex terminologies (SNOMED) and complex structures (ENV 13606, HL7 V3, OpenEHR……) the holy grail has been semantic interoperability, computable, interoperable records. In my view this remains a noble pursuit but one that fits poorly with the alternate paradigm in much of secondary care where the clinical narrative (text) comes first and coding is an afterthought, probably done by someone else for purpose not directly related to the delivery of care.
Today I detect a new zeitgeist, which might provide a way to combine these two worlds. The priority now seems to be to put the right information in front of the right person at the right time in an eye-readable form. This takes us to a document-centric view where all you need is some computable metadata to route the document. However, while this approach offers many benefits over paper, it perpetuates records based on forms, scales, assessments and unstructured clinical correspondence which hardly unleashes the power of computerised records. Those leading the development of records in secondary care understand this and we are now seeing the development of records standards which apply some high level structure (headings) to create semi-structured clinical narrative. For those in secondary care this is useful progress and will hopefully facilitate the electronic sharing of clinical records but also, and more excitingly, help them understand the clinical benefits of coding parts of this clinical narrative.
What I hope to see as the next phase in the development of electronic records are records which support a rich clinical narrative, structured so that we can get the right information, in front of the right person at the right time, but also coded, where this is useful and practical, so that we can start to explore the possibilities that flow from computable semantically interoperable records.


Villa Santa Teresa Medical Imaging Ltd and the Center of Nuclear Medicine San Gaetano Srl constitute an ambulatory health center accredited by the Regional Health System.
becoming, in recent years, a landmark of great significance in the delivery of health services in view of the fact that benefits paid specialties are characterized by high and can count on a park electrical equipment, technologically advanced and constantly updated the light of the gradual evolution of electro-technology.
Finally, the administration has always paid attention to and protection of medical skills, and technical assistance center, helping to enrich it with new resources and training to ensure the upgrade, allowing it to reach a certain level of preparation and professionalism.


Davy Chou is a young French filmmaker and producer, whose parents were born in Cambodia. Between 2001 and 2004, he managed a film and video workshop for high school students. In 2005 he founded CQN Productions, which produced 9 short films. Davy Chou produced three of them himself. He also launched an international digital film festival the same year, Festival des Nouveaux Cinémas (www.nouveaucine.com), the fifth anniversary of which was just recently celebrated. He has worked from January 2007 to December 2008 at Studio 37, Orange France Telecom's branch for movie production.
In 2007 he directed his first professional short film, Davy Chou's first film, and his second short film Expired, shot during his first trip in Cambodia, was selected at International Film Festival Entrevues de Belfort 2008.
In 2008, the short film Girls of fire, on which he was production manager, was selected at the International Critics' Week at the Cannes Film Festival.
He has developed a filmmaking workshop in Phnom Penh, and is now preparing an exhibition and a documentary film about the golden era of Cambodian films in the 60s and the 70s, as his grandfather, Van Chann, was one of the greatest producers in that time in Cambodia.


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Home » Newpages Blog » Eclipse – Fall 2005
Eclipse – Fall 2005
Boasting 10-15% student work per issue, Eclipse, published by Glendale Community College, is the only nationally distributed literary journal that continues to publish students alongside authors of international prominence. Boasting 10-15% student work per issue, Eclipse, published by Glendale Community College, is the only nationally distributed literary journal that continues to publish students alongside authors of international prominence. As any freelancer or writing student knows, having your work published alongside Walter Cummins or Rick Moody is a reassuring nod to the quality of your work, but for readers unconcerned with such things, rest assured: student work is indistinguishable from that of the pros; the only sign of who's who are the contributors notes. At 201 pages, this issue, wrapped in a simple, matted cover, contains 11 short stories and 70 poems. The fiction all runs short, bitingly concise, ranging from urban to rural, voice-driven to traditional. Two highlights: Richard Lange's "My Inheritance," about kid whose desire for normalcy goes up in flames in the chaparral of his hippie family's California home; George Rabasa's "Feast," a rollicking character-driven glimpse at the way a book-obsessed, Marx-loving, transient cross-dresser's mental illness has disrupted his family and ruined Thanksgiving dinner. Packed with imaginative details, there's enough family drama in Rabasa's story to fill a novel, and its strangeness alone makes Eclipse worth tracking down. The poetry stands out as well: from the fun pop culture take of Ryan G. Van Cleave's "Five Failed Movie Projects Starring Britney Spears" to the emotional refinement of students Katherine Tedrow and Cynthie Cuno. Clint McCown's poem, "Boring Sunset West of Fort Stockton, After a Storm," is a snare of evocative description and pinprick emotion: "Back home, where truth nails its joke / to both sides of the door, / the hardest thing to throw away / is the garbage can. / Ideals are ladders built to fall from, / and every crack in the pavement / sprouts fire ants and weeds." Student versus professional, community college versus university, Eclipse proves that the only thing that matters for a reader is the work.
Magazine Stand :: Months To Years – Winter 2023
New Book :: In the War Zone of the Heart
New Book :: Black Women Writers at Work
New Book :: Taking the F Train


We are blessed to have a small house and some land near our family. It's an older home and has needed quite a bit of work. There is still much to be done, but the basement is our first big project (if you don't count replacing the HVAC system that died at Thanksgiving). This past week I spent much time up to my elbows in paint. Luckily my little guy got to spend a lot of time with his grandparents. Otherwise he would have also been up to his elbows and knees and probably every other little body part in paint as well.
I'm constantly amazed at how productive I can be now when left alone. I marvel at the quantity of time I was obviously wasting before he came in to our lives and shook things up.
The first order of business with any job around the house is getting the supplies. I could've headed to either of the large chain hardware stores to buy what I needed, but I kept it local. I instead headed to a locally owned building supply to get my paint and a little advice about brushes. I also ran into an old friend that has worked there for decades! That doesn't happen often in the other options. I'm a huge fan of locally owned hardware stores. They often have the best stuff. More on my love of hardware stores another time.
I was also trying to find a couple unusual things from the pharmacy. The big box stores had let me down. My first thought was to head to one of the big national pharmacies. I realized I was right at a small local pharmacy owned by another friend. I figured it was at least with a shot. He had exactly what I was looking for – both items. One was in a version I didn't even know I could find. It was perfect and I was still keeping my money local.
So far, I was 2 for 2.
My tummy was beckoning for food at this point. It's amazing the dining options that will open up to you when there isn't a 3 year old to consider. I headed across town to a little spot I've wanted to try. It was under new ownership, and I was probably a little underdressed for the whole place, but it was wonderful. As I waited for my food, I enjoyed the quiet, did a little people watching and caught up on Twitter. I paid for lunch, keeping my money local, and headed off for a little walk.
One of the last tweets was from a yarn shop just down the street. Since there was no 3 year old in tow it was safe to go in. I was thanked by the owner for recognizing that this was indeed not a place for a 3 year old. I know we all love our children, but you still need to be respectful of others and their property. I bought a lovely book mentioned in the tweet and was on my way – again keeping the money local.
It was a wonderful start to the day. According to The 3/50 Project, $68 of every $100 spent at locally owned, independent store returns back to the community as compared to $43 if I'd shopped in a national chain. So while I got everything I needed and wanted in one town, I also helped it out at the same time.
At the end of the day I was 4 for 4, batting 1.000. That's pretty good; ask any baseball fan.


THE THEORY OF ECONOMIC VALUE by Michael Huemer 1. Basic Assumptions of Economics People want things, and they tend to act in such a way as to get the things they want,... Thus, Scholars began to try to introduce economic value added ideas into DuPont analysis. Tully (1993) claimed Tully (1993) claimed that EVA is the actual approach to create value, and establishes three ways to increase EVA.
that are based on different versions of economic value added, while Pearson (1998) compared the explanatory power of EVA to that of Refined Economic Value Added (REVA) for share returns on the mining sector of the JSE.
He shows that economic value is to be distinguished from any notion of the aggregate value or life value of some good or service, which is why luxury goods unnecessary for life can be so much more valued than bread and water.
Contrary to classic financial performance indicators, the EVA (Economic Value Added) is a type of economic performance indicator that provided good parameters on which high management and investors can base to learn about the evolution of the economic value in the organization.


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About Last Night: Grizz Punch Their Ticket
by Spike Friedman
In case you were busy remembering the 96, here are the top five stories you missed in sports on Monday:
In beautiful sunsets:
The Memphis Grizzlies punched the final ticket into the NBA playoffs with a 97-91 win over the Phoenix Suns. Things got a little testy during the postgame handshake, however, when Grizzlies head coach David Joerger told Suns head coach Jeff Hornacek, "Fitting this would happen on the night of a lunar eclipse." The normally mild-mannered Hornacek then flew into a rage, spitting back, "Lunar eclipses are the moon getting blocked out. Not the sun, Joerger." Joerger then shrugged Hornacek off, saying, "Whatever, man." But Hornacek remained furious, yelling back, "No! Not whatever, man. The only thing more important to me than basketball is that people understand basic scientific concepts. So you get back here and tell me what it is when the sun is blocked out, you bastard! Say solar eclipse to my damn face." A deeply confused Joerger then retreated to his team's locker room. Rumor has it that after the teams changed, Hornacek was waiting by Joerger's car with a DVD boxed set of Cosmos and a strongly worded note about the role of coaches as educators.
In surprising heroes:
John Jaso hit a ninth-inning blast to give the A's a 3-2 win over the Angels, while Dan Uggla hit two late home runs to power the Atlanta Braves past the Philadelphia Phillies by a 9-6 margin. Meanwhile, the Angels and Phillies just found their next ideal free-agent target: home run hero Dan Uggla.
In top draft picks:
Stanford star Chiney Ogwumike went first overall in the WNBA draft to the Connecticut Sun. The pick marks the first time a Stanford alum has moved to Connecticut directly out of college for any reason other than working at a hedge fund in Greenwich.
In unretirements:
Twenty-two-time Olympic medalist Michael Phelps has officially unretired, and will reenter the pool in advance of a potential attempt to make the 2016 U.S. Olympic squad. When asked why he unretired, Phelps explained, "Wrangler Jeans is thinking about branching out into comfortable, relaxed-fit swimwear, and it pretty much only has the one move in its marketing playbook."
In surprising villains:
Barry Trotz was unceremoniously dispatched by the Nashville Predators, ending his reign as the longest-tenured head coach in the NHL. When asked if he was worried his team would descend into a pit of chaos after the Trotz firing, Predators general manger David Poile replied, "No, chaos is not a pit. Chaos is a ladder. Only the ladder is real. The climb is all there is." When asked who that meant he was favoring to replace Trotz, Poile said, "It's gotta be Danny, right?" When asked if he was referring to Daenerys Stormborn, Mother of Dragons, Breaker of Chains, Khaleesi of the Great Grass Sea and rightful heir to the Iron Throne, Poile said, "No. What? I meant [Penguins head coach] Dan Bylsma. The Khaleesi is a fictional character. Come on."
Filed Under: About Last Night, NBA, WNBA, NHL
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Exams at Sobeys Stadium
Where is Sobeys Stadium?
Sobeys Stadium, formerly the Aviva Centre and the Rexall Centre, is labelled as item 8 on our Keele Campus map. Exams are written in the Centre of Excellence, which is the large covered building behind Sobeys Stadium.
How is writing at Sobeys Stadium different from writing at other locations?
The primary difference is that you will be writing in a large building with hundreds of other students. There may also be several different exams being conducted at the same time.
Are there shuttle services?
Yes. Transportation Services offers regular shuttle services between the Commons and Sobeys Stadium during exam periods. You can also access GoSafe to walk you back to your parking spot during their operating hours. Information about the shuttle and GoSafe will be posted on the exam search page closer to the start of the exam period.
What time should I arrive?
You are allowed into the building no earlier than 20 minutes before the start of the exam period. If you arrive earlier, there is a sheltered waiting area at Sobeys Stadium, which open 8 a.m. to 10:30 p.m. Monday to Saturday and from 1 p.m. to 10:30 p.m. on Sundays. The waiting area is indoors and there is access to washrooms which you may care to use before starting your exam. To access the waiting area, just follow the signage at the Stadium.
What is allowed in the exam centre?
Once you are seated, announcements will be made by the invigilators about what is and is not allowed for your particular exam; you should also get this information from your instructors before-hand. Note that cell phones must be turned off for the duration of the exam. If your cell phone rings or you are found to be using it during the exam, it will be confiscated.
What about after the exam?
If you finish early, please gather all your belongings and leave as quietly as possible. If you need to wait for a ride or for your classmates to finish, feel free to return to the sheltered waiting area at Sobeys Stadium and wait there. The sheltered are is open until 10:30pm and will have a security guard on site. You are encouraged to wait for a ride or classmates in the secured waiting area.


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A small French Canadian village in the time of coronavirus
How Irish immigrant history is helping to shape one man in the Laurentians understanding of coronavirus.
Don McMahon
An aerial view of Laurentians in Canada, just north of Montreal. Getty Images
How Irish immigrant history is helping to shape one man in the Laurentians understanding of coronavirus
I live in a small French-Canadian community nestled in the Laurentians north of Montréal. There is a tiny percentage of the population, including myself, who can claim ancestors and family from Ireland or Scotland, and a few from Brittany.
Read More: Bringing Celtic culture to my French Canadian community through Irish music
When I talk to my friends here, who are now mostly under self-imposed isolation, out of fear or prudence due to the Covid-19 virus, our discussions often turn to what each of us is doing to pass the time, hibernating in our artificial caves. All St.Patrick's Day festivities were canceled and any public gatherings including Sunday Mass and celebrations are now prohibited.
One of the areas many people ask me about is what I like to do for entertainment. Inevitably, I bring up the vast plethora of Celtic music and dance, stories, histories and documentaries, television, films, and interviews that are now freely available on the internet. Many are interested in the music and dance which I happily provide links for, some want to know more about Ireland and its history and some, with a more morbid bent, want to delve deeper into the Famine stories and visuals.
There is a certain love-hate relationship with the Irish and Scots Canadians who lived and still live in Montréal and a few areas of the Laurentians. We still have towns named after Irish, British or Scottish places, such as Gore, Grenville, Brownsburg-Chatham, and Doncaster. The French Canadians were very generous and accepting of the Famine victims emigrating to Montréal and the thousands of orphans who were left alone after their parents perished during the crossing or shortly after arriving at Gros-Iles. Many were adopted by French Canadian families who preserved these children's' family names and raised them as Catholics. We now have many French-Canadian families named Ryan, O'Neil, Arthur, Murray, Chisholm, McCallum, etc. It is estimated that up to 5.5% of Québec have some family connection to Celtic ancestors, based on surveys done as recently as 2006.
Read More: The Irish Famine ghosts linger still on Grosse Isle
When people ask me about the Irish experience of plagues, I usually mention that the Irish have, like many insular peoples, experienced epidemics but that, in particular, the Gros Isles immigrants suffered through major typhus and cholera outbreaks and that about 5000 people died between 1846 and1849 out of approximately 100,000, most of whom arrived during the ¨black year¨ of 1847. The Celts are no strangers to devastating national events either natural or imposed by foreign power.
One of the unexpected but welcome aspects of this pandemic is that it brings isolated people closer together despite cultural and language differences. The other is that spirituality (NOT religion) is beginning to take a front seat in many people's lives. People are questioning their values and especially those who choose to ignore public health warnings or hoard stocks that may be needed by the elderly. There is a growing sense of prioritizing how we live our daily lives, how we seem to be obsessed with material pursuits and how important our families are.
I recently read on the internet two articles by parents who were ¨forced¨ to deal with their kids, confined to home, because of school closures. Both finished by saying that after 1 hour trying to entertain and teach their kids, they supported the idea that teachers and school support staff should be paid a million dollars a year!
What we are seeing is a paradigm shift in social and ethical consciousness about others and ourselves. Watching places like Italy, Spain, Iran, and the US battle through this pandemic with thousands dying, especially the older generation, and the frailty of our current health care systems, but also the extraordinary dedication and self-sacrifice of our health care workers, has awoken a profound sense of our shared humanity, our profound community strengths, and our potential to work together to protect ourselves and the most vulnerable in every community. My sincerest prayers for everyone going through these trying times is that the road will always rise to meet you and the wind be always at your back!
Read More: Black Rock - the world's oldest Irish Famine memorial in Montreal
This article was submitted to the IrishCentral contributors network by a member of the global Irish community. To become an IrishCentral contributor click here.
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Resize the window to its minimum. The buttons at the bottom are now cut off/hidden.
Might have to do with hrev49481.
A somewhat similar problem can be seen in E-mail preflet.
Also in Network preflet FTP, SSH, and Telnet server views seem affected.
Text in CodyCam's preview window is not visible anymore.
MediaPlayer's settings window became taller.
Text in Installer's main window is cut off now.
Devices window layout is all wrong now.
Unfortunately, that didn't fix it.
For this issue, a new ticket was opened by idefix (including a screenshot that illustrates this problem), see #12314.
Is this not the same as ticket #7560? In both cases the bottom row of buttons are cut off.
No, this issue is related to hrev49481.
Text in CodyCam's preview window is fixed in hrev50653 (however, it's not centered).


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