text:
\section{Introduction}
{The evolution of accretion discs  is determined by the outward transport of angular momentum, which induces infall of matter toward the orbital center. It is generally assumed that the accretion rate depends on an effective viscosity (Shakura \& Sunyaev 1973).  In  magnetized discs this mechanism is triggered by a linear axisymmetric destabilization, the magnetorotational instability, which occurs when a weak poloidal magnetic field is coupled to rotation (Balbus \& Hawley 1991).}\\
In hydrodynamic Keplerian discs, instead, the presence of an efficient outward transport of angular momentum is still an open question. In this context there is no linear axisymmetric mechanism of growth, since Kepler rotation is stable according to Rayleigh criterion.\\
A possibility is given by the bypass scenario (Ioannou \& Kakouris 2001, Chagelishvili et al. 2003), where arbitrarily  large amplifications of perturbations can occur due to the leading-trailing evolution of shearwise wavenumbers. These growths occur independently of the presence of a linear instability drive. This linear mechanism and non-linear interactions, providing a positive feedback loop, could trigger a subcritical transition into turbulence. However, Lesur \& Longaretti (2005) showed that, while subcritical transition to turbulence indeed occurs in non-stratified discs, values of the Shakura-Sunyaev $\alpha$ parameter (Shakura \& Sunyaev 1973) are much too low to give rise to an efficient  turbulent transport.

If radial stratification is taken into account radial entropy gradients can drive non-linear subcritical baroclinic destabilization leading to positive angular momentum transport  (Klahr \& Bodenheimer 2003, Lesur \& Papaloizou 2010) and formation of vortices.\\
However, discs are in general radially and vertically stratified and the angular velocity is a function of both radial and vertical coordinates (Kippenhahm \& Thomas 1982, Urpin 1984). Vertical velocity shear drives an axisymmetric instability (Goldreich \& Schubert 1967; Urpin 2003) which can result in positive transport of angular momentum in the non-linear regime (Arlt \& Urpin 2004). The linear destabilization mechanism was derived by means of a local dispersion relation in the full cylindrical geometry. Instability occurs when $k_r\gg k_z$. \\
In a recent study Nelson, Gressel \& Umurhan (2012) found that in non-axisymmetric non-linear simulations outward transport can occur with $\alpha\sim10^{-4}$.

Vertical convection is another possible path to turbulence. Ryu \& Goodman (1992) showed, by means of a linear analysis, that an unstable vertical stratification is not favourable for accretion; angular momentum transport occurs, but inward. Stone \& Balbus (1996) extended the analysis to non-linear regimes with analogous results. {Departures from this picture are however possible as shown by Lesur \& Ogilvie (2010), in the strongly non-linear regime of high Rayleigh number, and by Volponi (2010), for linear non-axisymmetric Boussinesq perturbations in discs with radial and vertical stratification.}

In the present study we will concentrate on the vertical shear and vertical convective instabilities. Precisely, first, we will extend the linear analysis of the vertical shear instability to non-axisymmetric perturbations. Results will be derived by solving the shearing sheet equations in the presence of vertical velocity shear (Knobloch \& Spruit 1986) and in the short wavelength regime. We will show that, while non-axisymmetric perturbations eventually decay, they experience transient exponential growths which are indistinguishable from a {genuine} instability.\\
Second, we will study the interaction between {the vertical shear and convective instabilities}. This is the central part of the present study. We will show that the presence of vertical shear changes the direction of the vertical convection induced angular momentum transport from inward to outward depending on the sign of the product of vertical and radial wavenumbers (i.e. positive for $A_z>0$ or negative for $A_z<0$, where $A_z$ is the local vertical shear). Thermal diffusion has a stabilizing influence on the convective instability, specially for short wavelengths.
\section{Equations and equilibrium}
In the shearing sheet approximation, the equations governing the dynamics of a 3-dimensional disc are
\begin{equation}
\partial_{t}{\cal D}+\nabla \cdot{\cal D \Vvec}=0,
\label{eq1.1}
\end{equation}
\begin{equation}
\partial_{t}{\Vvec}+\Vvec\cdot\nabla{\Vvec}=-\frac{\nabla{P}}{\cal D}-2{\Omegavec}\times{\Vvec}+2q{\Omega}^2 x \hat{{\xvec}}-{\Omega}^2 z \hat{{\zvec}},
\label{eq1.2}
\end{equation}
\begin{equation}
\partial_{t}{(\ln{S})}+\Vvec\cdot\nabla{(\ln{S})}=0,
\label{eq1.3}
\end{equation}
where $\cal D$ and $P$ are density and pressure, $\Vvec$ is the fluid velocity, $S=P{\cal D}^{-\gamma}$ is a measure of the fluid entropy, $\gamma$ is the adiabatic index, $\Omega$ is the local rotation frequency and $q$ is the shear parameter ($q=1.5$ for Keplerian rotation). The term $-2{\Omegavec}\times{\Vvec}$ is the Coriolis term, $2q{\Omega}^2 x \hat{{\xvec}}$ is the tidal expansion of the effective potential and $-{\Omega}^2 z \hat{{\zvec}}$ is the vertical gravitational acceleration. The equations are expressed in terms of the pseudo-Cartesian coordinates $x=r-r_0$, $y=r_0(\phi-{\phi}_0)$ and $z$  ($r_0$ and ${\phi}_0$ are reference radius and angle).\\
The above equations are more manageable than the full equations in cylindrical geometry due to the neglect of curvature effects. The simplification holds if the length scale of radial gradients $L\ll r$, where $r$ is the cylindrical radial coordinate (Knobloch \& Spruit 1986).\\
We consider fully stratified (i.e. radially and vertically) baroclinic discs. $P_{\rm e}(x,z)$ and ${\rho}_{\rm e}(x,z)$ are respectively the equilibrium pressure and density. Equilibrium in general requires the angular velocity to be $x$ and $z$ dependent. \\
The equilibrium velocity field is then given by
\begin{equation}
[-q\Omega x+\frac{\partial_{x}P_{\rm e}(x,0)}{2 \Omega {\rho}_{\rm e}(x,0)}+a_V z^2]\hat{\yvec},
\label{eq1.4}
\end{equation}
which is obtained from the expansion of the angular velocity profile about the midplane as given in Kley \& Lin (1992) (see as well Urpin 1984), in the limit $L/r\ll 1$. The dimensional coefficient $a_V$ can be derived from equation (A23) of Kley \& Lin (1992).\\
The $z$ dependence gives rise to vertical shear at the origin of the axisymmetric vertical shear instability. Notice that at the midplane the vertical shear goes to zero, so the instability drive is present away from it. This is the most interesting region for the present analysis. Away from the midplane we can approximate the last $z$-quadratic term, $a_V z^2$,  in~(\ref{eq1.4}) with a linear one, $\bar{A}_z z$. Therefore in the following our reference equilibrium flow will be
\begin{equation}
{\Vvec}_{\rm e}(x, z)=[-q\Omega x+\frac{\partial_{x}P_{\rm e}(x,0)}{2 \Omega {\rho}_{\rm e}(x,0)}+\bar{A}_z z]\hat{\yvec},
\label{eq1.6}
\end{equation}
bearing in mind that our conclusions will not hold at the midplane.
The second term on the RHS of the above equation will be dealt with as in  Johnson \& Gammie (2005) by considering the background flow as giving an effective shear rate
\begin{equation}
\tilde{q}(x){\Omega}=-\frac{d{V}_{\rm e}(x)}{dx},
\label{eq1.7}
\end{equation}
that varies with $x$.\\
Vertical equilibrium gives
\begin{equation}
\frac{\partial_{z}{P_{\rm e}}}{\rho_{\rm e}}=-\Omega^2 z \equiv -g_z.
\label{eq1.8}
\end{equation}
By defining $1/{L_P}_z={\partial_{z}P_{\rm e}}/{\gamma P_{\rm e}}$ we obtain from~(\ref{eq1.8})
\begin{equation}
g_z=-\frac{{c_s}^2}{{L_P}_z},
\label{eq1.10}
\end{equation}
where ${c_s}^2=\gamma P_{\rm e} /\rho_{\rm e}$.
\section{Linear perturbations}
We decompose the physical variables in equilibrium and perturbation parts
\begin{equation}
{\Vvec}={\Vvec}_{\rm e}+{\vvec}', \hspace{0.7cm} {\cal D}={\rho}_{\rm e}+{\rho}', \hspace{0.7cm} P= P_{\rm e} + P',
\label{eq1.11a}
\end{equation}
and consider the linearized equations.
Localized on the $x$ and $z$ dependent flow (see Johnson \& Gammie 2005) and on the $x$ and $z$  dependent density and pressure backgrounds, we consider short wavelength Eulerian perturbations of the type
\begin{equation}
{\delta}'(t,x,y,z)=\hat{{\delta}'}(t)e^{i\int \tilde{K}_x(t,x)dx+iK_yy+i\tilde{K}_z(t)z},
\label{eq1.11}
\end{equation}
where
\begin{equation}
\tilde{K}_x(t,x)={K_x}+\tilde{q}(x)\Omega K_y t,  \hspace{0.2cm} \tilde{K}_z(t)={K_z}-\bar{A}_z K_y t.
\label{eq1.12}
\end{equation}
Notice that due to  the presence of vertical shear the vertical wavenumber as well evolves with time. The $x$ dependence in $\tilde{q}(x)$ is very weak and in the rest of the paper we will consider the effective shear parameter constant and  very close to its Keplerian value.\\
As previously stated to be consistent with the neglect of the curvature terms we consider a background with radial and vertical  length scales $L\ll r$ and $H\ll r$. The short wavelength perturbations are such that $\tilde{K}_x L \gg 1$ and $\tilde{K}_z H \gg 1$. \\
With equation~(\ref{eq1.11}) the evolution of linearized perturbations is given by
\begin{equation}
\partial_{t}\frac{\hat{\rho'}}{\rho_{\rm e}}+\frac{\hat{v'_x}}{{L_{\rho}}_x}+\frac{\hat{v'_z}}{{L_{\rho}}_z}+i\tilde{K}_x\hat{v'_x}+iK_y\hat{v'_y}+i\tilde{K}_z\hat{v'_z}=0,
\label{eq1.13}
\end{equation}
\begin{equation}
\partial_{t}\hat{v'_x}= 2\Omega \hat{v'_y}-i\tilde{K}_x \frac{\hat{P'}}{{\rho}_{\rm e}}+\frac{c_s^2}{{L_P}_x}\frac{\hat{\rho'}}{{\rho}_{\rm e}},
\label{eq1.14}
\end{equation}
\begin{equation}
\partial_{t}\hat{v'_y}=-(2-\tilde{q})\Omega \hat{v'_x}-\bar{A}_z\hat{v'_z}-i{K_y}\frac{\hat{P'}}{{\rho}_{\rm e}},
\label{eq1.15}
\end{equation}
\begin{equation}
\partial_{t}\hat{v'_z}=-i\tilde{K}_z\frac{\hat{P'}}{{\rho}_{\rm e}}-\frac{\hat{\rho'}}{{\rho}_{\rm e}}g_z,
\label{eq1.16}
\end{equation}
\begin{equation}
\partial_{t}\frac{\hat{P'}}{\rho_{\rm e}}-c_s^2\partial_{t}\frac{\hat{\rho'}}{\rho_{\rm e}}+c_s^2\frac{\hat{v'_x}}{{L_S}_x}+c_s^2\frac{\hat{v'_z}}{{L_S}_z}=0.
\label{eq1.16a}
\end{equation}
The radial and vertical length scales for pressure, density and entropy are defined by
\begin{equation}
\frac{1}{{L_P}_x}\equiv\frac{\partial_{x}P_{\rm e}}{\gamma P_{\rm e}}=\frac{1}{{L_{\rho}}_x}+\frac{1}{{L_S}_x}\equiv\frac{\partial_{x}{\rho}_{\rm e}}{ {\rho}_{\rm e}}+\frac{\partial_{x}S_{\rm e}}{\gamma S_{\rm e}},
\label{eq1.18}
\end{equation}
\begin{equation}
\frac{1}{{L_P}_z}\equiv\frac{\partial_{z}P_{\rm e}}{\gamma P_{\rm e}}=\frac{1}{{L_{\rho}}_z}+\frac{1}{{L_S}_z}\equiv\frac{\partial_{z}{\rho}_{\rm e}}{ {\rho}_{\rm e}}+\frac{\partial_{z}S_{\rm e}}{\gamma S_{\rm e}}.
\label{eq1.19}
\end{equation}
In the Boussinesq approximation equations~(\ref{eq1.13}) and~(\ref{eq1.16a}) become
\begin{equation}
\tilde{K}_x\hat{v'_x}+K_y\hat{v'_y}+\tilde{K}_z \hat{v'_z}=0,
\label{eq1.13a}
\end{equation}
\begin{equation}
\partial_{t}\frac{\hat{\rho'}}{\rho_{\rm e}}=\frac{\hat{v'_x}}{{L_S}_x}+\frac{\hat{v'_z}}{{L_S}_z},
\label{eq1.16b}
\end{equation}
Equations~(\ref{eq1.14})-(\ref{eq1.16}),~(\ref{eq1.13a}) and~(\ref{eq1.16b}) are equations (59)-(63) of Knobloch \& Spruit (1986) expressed in terms of the short wavelength shearing modes~(\ref{eq1.11}). The only difference is given by the presence of the radial stratification term in~(\ref{eq1.14}). We will see in the following, however, that it has essentially no influence on the perturbations evolution.\\
Now by deriving with respect to time the incompressibility condition~(\ref{eq1.13a}) and then, in the equation obtained, expressing $\partial_{t}\hat{v'_x}$, $\partial_{t}\hat{v'_y}$ and $\partial_{t}\hat{v'_z}$ with equations~(\ref{eq1.14}),~(\ref{eq1.15}) and~(\ref{eq1.16}),
we can express $\hat{P'}$ in terms of $\hat{\rho'}$, $\hat{v'_x}$, $\hat{v'_y}$ and $\hat{v'_z}$
\begin{eqnarray}
i\frac{\hat{P'}}{{\rho}_{\rm e}}=\frac{1}{\tilde{K}^2}[(\tilde{K}_x\frac{c_s^2}{{L_P}_x}-g_z \tilde{K}_z)\frac{\hat{\rho'}}{\rho_{\rm e}}+ \nonumber \\ 2(\tilde{q}-1)\Omega k_y \hat{v'_x} + 2\Omega \tilde{K}_x \hat{v'_y}-2 \bar{A}_z K_y \hat{v'_z}],
\label{eq1.20}
\end{eqnarray}
where ${\tilde{K}^2}={\tilde{K}_x^2}+K_y^2+\tilde{K}_z^2$. By means of equation~(\ref{eq1.20}) we obtain the system
\begin{eqnarray}
\partial_{t}\hat{v'_x}= - 2(\tilde{q}-1)\Omega\frac{ K_y \tilde{K}_x }{{\tilde{K}^2}}\hat{v'_x} + 2\Omega  (1-\frac{{\tilde{K}_x^2}}{{\tilde{K}^2}})\hat{v'_y} + \nonumber \\ 2\bar{A}_z\frac{ \tilde{K}_x  K_y}{{\tilde{K}^2}}\hat{v'_z}+\frac{c_s^2}{{L_P}_x}(1-\frac{{\tilde{K}_x^2}}{{\tilde{K}^2}}) \frac{\hat{\rho'}}{{\rho}_{\rm e}}+g_z\frac{ \tilde{K}_z \tilde{K}_x }{{\tilde{K}^2}} \frac{\hat{\rho'}}{{\rho}_{\rm e}},
\label{eq1.21}
\end{eqnarray}
\begin{eqnarray}
\partial_{t}\hat{v'_y}=\Omega [\tilde{q}-2-2(\tilde{q}-1)\frac{K_y^2}{{\tilde{K}^2}}]\hat{v'_x}- 2\Omega\frac{ K_y \tilde{K}_x}{{\tilde{K}^2}}\hat{v'_y}+ \nonumber \\ 2\bar{A}_z\frac{K_y^2}{{\tilde{K}^2}}\hat{v'_z}-\bar{A}_z\hat{v'_z}-\frac{K_y}{{\tilde{K}^2}}(\tilde{K}_x\frac{c_s^2}{{L_P}_x}-g_z \tilde{K}_z)\frac{\hat{\rho'}}{{\rho}_{\rm e}},
\label{eq1.22}
\end{eqnarray}
\begin{eqnarray}
\partial_{t}\hat{v'_z}= - 2(\tilde{q}-1)\Omega\frac{ K_y \tilde{K}_z }{{\tilde{K}^2}}\hat{v'_x} - 2\Omega  \frac{{\tilde{K}_x\tilde{K}_z}}{{\tilde{K}^2}}\hat{v'_y} + \nonumber \\2\bar{A}_z\frac{ K_y \tilde{K}_z }{{\tilde{K}^2}}\hat{v'_z}-g_z(1-\frac{{\tilde{K}_z^2}}{{\tilde{K}^2}}) \frac{\hat{\rho'}}{{\rho}_{\rm e}}-\frac{c_s^2}{{L_P}_x}\frac{ \tilde{K}_z \tilde{K}_x }{{\tilde{K}^2}} \frac{\hat{\rho'}}{{\rho}_{\rm e}},
\label{eq1.23}
\end{eqnarray}
\begin{equation}
\partial_{t}\frac{\hat{\rho'}}{\rho_{\rm e}}=\frac{\hat{v'_x}}{{L_S}_x}+\frac{\hat{v'_z}}{{L_S}_z}.
\label{eq1.24}
\end{equation}
Normalizing time with ${\Omega}^{-1}$, velocities with ${L_S}_z \Omega$ and density with $\rho_{\rm e}$  we obtain for the evolution of the non-dimensional variables $v_x$, $v_y$, $v_z$, $\rho$ the system
\begin{eqnarray}
\partial_{t}{v_x}= - 2(\tilde{q}-1)\frac{ k_y \tilde{k}_x }{{\tilde{k}^2}}{v_x} + 2 (1-\frac{{\tilde{k}_x^2}}{{\tilde{k}^2}}){v_y} +\nonumber \\  2{A_z}\frac{  \tilde{k}_x k_y }{{\tilde{k}^2}}{v_z}+ \frac{{L_S}_x}{{L_S}_z}Ri_x(\frac{{\tilde{k}_x^2}}{{\tilde{k}^2}}-1) {{\rho}}+Ri_z\frac{ \tilde{k}_z \tilde{k}_x }{{\tilde{k}^2}} {{\rho}},
\label{eq1.25}
\end{eqnarray}
\begin{eqnarray}
\partial_{t}{v_y}= [\tilde{q}-2-2(\tilde{q}-1)\frac{k_y^2}{{\tilde{k}^2}}]{v_x}- 2\frac{ k_y \tilde{k}_x}{{\tilde{k}^2}}{v_y}+\nonumber \\  2{A_z}\frac{k_y^2}{{\tilde{k}^2}}{v_z}-{A_z}{v_z}+ \frac{k_y}{{\tilde{k}^2}}(\tilde{k}_x\frac{{L_S}_x}{{L_S}_z}Ri_x+Ri_z \tilde{k}_z){{\rho}},
\label{eq1.26}
\end{eqnarray}
\begin{eqnarray}
\partial_{t}{v_z}= - 2(\tilde{q}-1)\frac{ k_y \tilde{k}_z }{{\tilde{k}^2}}{v_x} - 2  \frac{{\tilde{k}_x\tilde{k}_z}}{{\tilde{k}^2}}{v_y} + \nonumber \\  2{A_z}\frac{ k_y \tilde{k}_z }{{\tilde{k}^2}}{v_z}+ Ri_z(\frac{{\tilde{k}_z^2}}{{\tilde{k}^2}}-1) {{\rho}}+\frac{{L_S}_x}{{L_S}_z}Ri_x\frac{ \tilde{k}_z \tilde{k}_x }{{\tilde{k}^2}} {{\rho}},
\label{eq1.27}
\end{eqnarray}
\begin{eqnarray}
\partial_{t}{{\rho}}=\frac{{L_S}_z}{{L_S}_x}v_x+{v_z},
\label{eq1.28}
\end{eqnarray}
where $(k_x,{k}_y,k_z)\equiv{{L_S}_z}(K_x,{K}_y,K_z)$, $\tilde{k}_x\equiv{{L_S}_z}\tilde{K}_x$, $\tilde{k}_z\equiv{{L_S}_z}\tilde{K}_z$ and ${{\tilde{k}^2}}\equiv{{L_{S_z}^2}}{{\tilde{K}^2}}$. We introduced, as well, $A_z\equiv\frac{\bar{A}_z}{\Omega}$ and the Richardson numbers
\begin{equation}
Ri_x\equiv\frac{N_x^2}{{\Omega}^2}, \hspace{2cm} Ri_z\equiv\frac{N_z^2}{{\Omega}^2}.
\label{eq1.29}
\end{equation}
$N_x$ and $N_z$ are the Brunt-V\"{a}is\"{a}l\"{a} frequencies
\begin{equation}
N_x^2\equiv-\frac{c_s^2}{{L_S}_x{L_P}_x},  \hspace{0.5cm} N_z^2\equiv\frac{g_z}{{L_S}_z}=-\frac{c_s^2}{{L_S}_z{L_P}_z}.
\label{eq1.30}
\end{equation}
We notice that the above equations are scale invariant in the sense that results pertaining to wavenumbers $k_x$, $k_y$ and $k_z$ hold as well for wavenumbers $\beta k_x$, $\beta k_y$ and $\beta k_z$, where $\beta$ is a real number. This symmetry is broken if we introduce the effect of thermal diffusivity in the system above.\\
\section{Axisymmetry}
For axisymmetric perturbations (i.e. $k_y=0$) equations~(\ref{eq1.25})-(\ref{eq1.28}) become
\begin{equation}
\partial_{t}{v_x}=  2 \frac{{{k}_z^2}}{{{k}^2}}{v_y} - \frac{{L_S}_x}{{L_S}_z}Ri_x\frac{{{k}_z^2}}{{{k}^2}}{{\rho}}+Ri_z\frac{ k_z {k}_x }{{{k}^2}} {{\rho}},
\label{eq1.31}
\end{equation}
\begin{equation}
\partial_{t}{v_y}= (\tilde{q}-2){v_x}-{A_z}{v_z},
\label{eq1.32}
\end{equation}
\begin{equation}
\partial_{t}{v_z}= - 2  \frac{{{k}_x{k}_z}}{{{k}^2}}{v_y} -Ri_z\frac{{{k}_x^2}}{{{k}^2}} {{\rho}}+\frac{{L_S}_x}{{L_S}_z}Ri_x\frac{ {k}_z {k}_x }{{{k}^2}} {{\rho}},
\label{eq1.33}
\end{equation}
\begin{equation}
\partial_{t}{{\rho}}=\frac{{L_S}_z}{{L_S}_x}v_x+{v_z}.
\label{eq1.34}
\end{equation}
In the above equations there are no time dependent coefficients and therefore we can assume an exponential form of the type $e^{st}$ for the velocity and density perturbation fields. Neglecting radial stratification the dispersion relation reads
\begin{equation}
s^2+\frac{2(2-\tilde{q})k_z^2}{k^2}+\frac{Ri_z k_x^2}{k^2}-\frac{2k_x k_z A_z}{k^2}=0.
\label{eq1.35}
\end{equation}
This is the shearing sheet equivalent of equation (9) in Urpin (2003) in the case of zero diffusivity. For finite $Ri_z$ the vertical shear term is dominated either by the epycyclic frequency term or by the $Ri_z$ term.
In the case of weak vertical stratification (i.e. $Ri_z\ll1$) and for $\tilde{q}=3/2$ the maximum growth rate of the instability occurs for
\begin{equation}
\frac{k_x}{k_z}=\frac{\frac{1}{A_z}\pm\sqrt{\frac{1}{A_z^2}+4}}{2},
\label{eq1.36}
\end{equation}
which is the same as equation (34) of Urpin (2003) since $\frac{1}{A_z^2}\gg4$ and $\bar{A}_z=r\partial_{z}\Omega$.
The growth rate is given by
\begin{equation}
s_{\rm max}=\sqrt{\frac{2\sqrt{{1}+4{A_z^2}}}{4+\frac{1}{A_z^2}+\frac{1}{A_z}\sqrt{\frac{1}{A_z^2}+4}}} .
\label{eq1.37}
\end{equation}
For $A_z^2\ll 1$, a condition to be expected in astrophysical discs, we have therefore $s_{\rm max}\approx \vert A_z \vert$.\\
Next we consider the opposite limit by neglecting the vertical stratification. In this case the dispersion relation becomes
\begin{equation}
s^2+\frac{k_z^2}{k^2}[2(2-\tilde{q})+Ri_x]-\frac{2k_x k_z}{k^2}{A_z}=0.
\label{eq1.35A}
\end{equation}
Being radial stratification typically weak, stability is not influenced.\\
When both radial and vertical gradients are present the dispersion relation reads
\begin{eqnarray}
s^2+\frac{k_z^2}{k^2}[2(2-\tilde{q})+Ri_x]-\frac{k_x k_z}{k^2}(2{A_z}+ \nonumber\\ \frac{{L_S}_x}{{L_S}_z}Ri_x+\frac{{L_S}_z}{{L_S}_x}Ri_z)+\frac{Ri_z k_x^2}{k^2}=0.
\label{eq1.35B}
\end{eqnarray}
In this case additional destabilization is possible in principle due to the term $\Sigma=\frac{{L_S}_x}{{L_S}_z}Ri_x+\frac{{L_S}_z}{{L_S}_x}Ri_z$. However its effect will be dominated either by the stabilizing effect of the epicyclic frequency (for $k_z\geqslant k_x$) or by the last term on the LHS of~(\ref{eq1.35B}) (for $k_x\gg k_z$).
We notice that for a barotropic equilibrium ($A_z=0$) we have $\Sigma=\pm2\sqrt{Ri_x Ri_z}$ and $Ri_x$, $Ri_z$ are bound to have the same sign (Volponi 2010) and
\begin{equation}
s^2=-\frac{{k_z^2}2(2-\tilde{q})+(k_z\sqrt{Ri_x }\pm k_x\sqrt{Ri_z})^2}{k^2}
\end{equation}
In the presence of diffusion the only modification of the evolution equations occurs in~(\ref{eq1.16b}), which becomes
\begin{equation}
\partial_{t}\frac{\hat{\rho'}}{\rho_{\rm e}}=\frac{\hat{v'_x}}{{L_S}_x}+\frac{\hat{v'_z}}{{L_S}_z}-\chi {\tilde{K}^2}\frac{\hat{\rho'}}{\rho_{\rm e}},
\label{eq1.43}
\end{equation}
where $\chi$ is the thermal diffusion coefficient.\\
Once  normalized the above equation reads
\begin{equation}
\partial_{t}{{\rho}}=\frac{{L_S}_z}{{L_S}_x}v_x+{v_z}-{\tilde{k}^2}\frac{1}{Pe}{{\rho}},
\label{eq1.44}
\end{equation}
where $Pe=\frac{{{L_S^2}_z}\Omega}{\chi}$ is the Peclet number.\\
The axisymmetric dispersion relation then  becomes
\begin{eqnarray}
s^3+k^2 Pe^{-1}s^2+s\bigg[\frac{k_z^2}{k^2}[2(2-\tilde{q})+Ri_x]- \nonumber \\  \frac{k_x k_z}{k^2}(2{A_z}+\frac{{L_S}_x}{{L_S}_z}Ri_x+  \frac{{L_S}_z}{{L_S}_x}Ri_z)+\frac{Ri_z k_x^2}{k^2}\bigg]+  \nonumber \\  Pe^{-1}[2k_z^2(2-\tilde{q})-{2k_x k_z}{A_z}]=0.
\label{eq1.35C}
\end{eqnarray}
The above equation is completely equivalent to the dispersion relation (7) in Urpin (2003)  when neglecting the effect of viscosity and the same instability conditions derived in his paper follow. We briefly sum up his results. By casting equation~(\ref{eq1.35C}) in the form
\begin{equation}
s^3+a_2s^2+a_1s+a_0=0,
\label{eq1.35D}
\end{equation}
where
\begin{eqnarray}
a_2=k^2 Pe^{-1}, \nonumber \\ a_1=\bigg[\frac{k_z^2}{k^2}[2(2-\tilde{q})+Ri_x]-\frac{k_x k_z}{k^2}(2{A_z}+\nonumber \\  \frac{{L_S}_x}{{L_S}_z}Ri_x+\frac{{L_S}_z}{{L_S}_x}Ri_z)+\frac{Ri_z k_x^2}{k^2}\bigg], \nonumber\\
a_0=Pe^{-1}[2k_z^2(2-\tilde{q})-{2k_x k_z}{A_z}],
\label{eq1.35E}
\end{eqnarray}
instability conditions read (see Urpin 2003 and references therein)
\begin{equation}
a_0<0, \hspace{1cm} a_1 a_2<a_0, \hspace{1cm} a_2<0.
\label{eq1.35F}
\end{equation}
The first of the inequalities above (equation (17) in Urpin 2003),
\begin{equation}
Pe^{-1}[2k_z^2(2-\tilde{q})-{2k_x k_z}{A_z}]<0,
\end{equation}
shows that the presence of thermal diffusion relaxes the instability condition with respect to the ideal case. \\
The second inequality (equation (14) in Urpin 2003) reads
\begin{equation}
\bigg[\frac{k_z^2}{k^2}Ri_x-\frac{k_x k_z}{k^2}(\frac{{L_S}_x}{{L_S}_z}Ri_x+\frac{{L_S}_z}{{L_S}_x}Ri_z)+\frac{Ri_z k_x^2}{k^2}\bigg]<0
\end{equation}
and it is a statement about the convective stability of the disk (vertical shear does not appear in it).

To end this section we present the evolution of axisymmetric perturbations for a convectively unstable vertical stratification. In Fig.~\ref{axifig:1} we set  $k_x/k_z=10$, which pertains to the maximal vertical shear growth rate for $A_z=0.1$, $Ri_z=-0.2$ and $Pe=10^7$.
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig1.eps}

	\end{center}
	\caption{Evolution of velocities and normalized $xy$-Reynolds stress (i.e. $W_{xy}\equiv(v_x v_y)/ v^2$, where $v^2=v_x^2+v_y^2+v_z^2$) for $Pe=10^7$, $Ri_z=-0.2$, $Ri_x=0.01$, ${L_S}_z/{L_S}_x=0.223$, $A_z=0.1$ and $k_x=500$, $k_z=50$, $k_y=0$.}
\label{axifig:1}
\end{figure}
We notice that the growth rate is the convective one ($\sqrt{-Ri_z}$), but differently from conventional understanding $W_{xy} \equiv (v_x v_y)/ v^2>0$, where $v^2=v_x^2+v_y^2+v_z^2$. To ascertain the origin of the positive sign of $W_{xy}$  we set $A_z=0$. As can be seen in Fig.~\ref{axifig:2}, this results in $W_{xy}<0$.\\
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig2.eps}

	\end{center}
	\caption{Same as previous figure but with $A_z=0$.}
\label{axifig:2}
\end{figure}
We can therefore conclude that, when the vertical convective growth rate is larger than the vertical shear one, the ensuing instability is of mixed type in the sense that the growth rate is given by convection whereas the sign of $W_{xy}$ is determined by vertical shear. \\
Linear inviscid axisymmetric perturbations cannot transport angular momentum in hydrodynamic discs (Ruden, Papaloizou \& Lin 1988), however we will see in the next section that for non-axisymmetric perturbations, which induce transport, the same type of behaviour described above holds. \\
We determined as well the effect of thermal diffusion on the growth rate $s$. In Table~\ref{tab:1} we report the dependence of $s$ on $Pe$. We notice that $s$ is drastically reduced down to $s\sim A_z$. Further decreasing of $Pe$ does not have effect on $s$.
\begin{table}
\caption {Dependence of mixed (convective + vertical shear) axisymmetric growth rate on Peclet number (relative to the case in Fig. 1)}
\label{tab:1}
\begin{center}
    \begin{tabular}{ | l | p{0.7cm} | p{0.7cm} | p{0.7cm} | p{0.7cm} | p{0.7cm} | p{0.7cm} |}
    \hline
    $Pe$ &  $\infty$ &  $10^7$ & $10^6$  & $10^5$ & $10^4$ & $10^3$\\ \hline
    $s$ & $0.44$ & $0.44$ & $0.35$ & $0.14$ & $0.1$ & $0.1$\\ \hline
    \end{tabular}
\end{center}
\end{table}
\section{Non-axisymmetry}
\subsection{Case 1: only vertical shear drive}
We consider here the evolution of ideal non-axisymmetric perturbations in the presence of a convectively stable vertical stratification.\\
With a reference stratification of $Ri_z=0.1$, $Ri_x=0.01$ and a realistic $A_z$, perturbations always decay for any value of the wavenumbers. In this case the vertical shear destabilizing drive is never able to overcome the stabilizing influence of stratification and epicyclic frequency. \\
If we allow for weaker stratification the vertical shear can drive huge transient growths in the perturbations.\\
Fixing $A_z$ to a positive value, the interval of growth is connected to $\tilde{k}_x$ and $\tilde{k}_z$ having the same sign. We can see this in Fig.~\ref{fig:1} for the case $\tilde{k}_x>0$ and $\tilde{k}_z>0$, where we set the $k_x/k_z$ ratio to the value pertaining to the maximal axisymmetric growth rate $A_z$. By increasing $k_y$ clearly the interval of growth is shortened  and therefore the largest amplification reached diminishes. We stress that the transients are indistinguishable from a full-fledged instability. The growths are in fact exponential with growth rate close to $A_z$. Varying the ratio $k_x/k_z$, as well, causes a decrease in the maximum amplification reached. \\
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig3.eps}

	\end{center}
	\caption{Evolution of velocities and normalized $xy$-Reynolds stress in the case of very weak stratification for $A_z=0.1$ and $k_x=1000$, $k_z=100$, $k_y=1$.}
\label{fig:1}
\end{figure}
In the case $A_z<0$  growths occurs when $\tilde{k}_x$ and $\tilde{k}_z$ have opposite signs. \\
We notice as well that during the phase of growth, radial transport is always positive. \\
As stated before eventually all perturbations decay. Heuristically this can be shown neglecting the stratification in equations~(\ref{eq1.25})-(\ref{eq1.28}). By using the incompressibility condition~(\ref{eq1.13a}) we obtain for the $x$ and $y$ velocity components the evolution equations
\begin{eqnarray}
\partial_{t}{v_x}= - 2(\tilde{q}-1+{A_z}\frac{\tilde{k}_x }{{\tilde{k}_z}})\frac{ k_y \tilde{k}_x }{{\tilde{k}^2}}{v_x} + \nonumber \\ 2 (1-\frac{{\tilde{k}_x^2}}{{\tilde{k}^2}}-{A_z}\frac{ k_y^2 \tilde{k}_x }{{\tilde{k}^2}\tilde{k}_z}){v_y} ,
\label{eq1.38}
\end{eqnarray}
\begin{eqnarray}
\partial_{t}{v_y}= [\tilde{q}-2-2(\tilde{q}-1)\frac{k_y^2}{{\tilde{k}^2}}-2{A_z}\frac{k_y^2 \tilde{k}_x }{{ \tilde{k}^2 \tilde{k}_z }}+\nonumber \\ {A_z}\frac{ \tilde{k}_x }{{ \tilde{k}_z }}]{v_x}+({A_z}\frac{k_y}{{ \tilde{k}_z}}- 2\frac{ k_y \tilde{k}_x}{{\tilde{k}^2}}-2{A_z}\frac{k_y^3}{{\tilde{k}^2 \tilde{k}_z}}){v_y},
\label{eq1.39}
\end{eqnarray}
which in the limit $t\longrightarrow\infty$ become
\begin{equation}
\partial_{t}{v_x}=  2\frac{A_z^2}{q^2+A_z^2}{v_y} ,
\label{eq1.40}
\end{equation}
\begin{equation}
\partial_{t}{v_y}= -2{v_x}.
\label{eq1.41}
\end{equation}
These can be reduced to the equation
\begin{equation}
\partial_{t}^2{v_x}=  -4\frac{A_z^2}{q^2+A_z^2}{v_x} ,
\label{eq1.42}
\end{equation}
which implies stability.

For sake of completeness, we considered as well the case of stable weak vertical and unstable strong radial stratifications. The vertical shear growth rate is only slightly enhanced.
\subsection{Case 2: combined effect of vertical shear and vertical unstable convection drives}
We examine here the evolution of ideal perturbations in the presence of an unstable vertical stratification. This is the central part of this study, because the interaction of vertical shear and convective drives results in evolutions which are determined by the relative strength of the vertical shear growth rate ($s_{\rm vs} \sim \vert A_z \vert$) and the vertical convective growth rate ($s_{\rm c}\sim\sqrt{-Ri_z}$). For $s_{\rm vs}>s_{\rm c}$ we observed the same type of behaviour described in Case 1 - large exponential amplifications with growth rate $s_{\rm vs}$  occur with asymptotic stabilization. For $s_{\rm c}>s_{\rm vs}$ the system is asymptotically unstable with growth rate $s_{\rm c}$. For $s_{\rm vs} \sim s_{\rm c}$ a variety of mixed evolutions is possible: these include transient growths, exponential instability and algebraic instability.\\
In the following we will concentrate on the case $s_{\rm c}>s_{\rm vs}$, for which the system is asymptotically unstable. Similarly to what we found in the axisymmetric case, the main difference with a purely convective instability is given by the sign of the angular momentum transport, which is positive exactly in the same time intervals in which transient growth occured in Case 1. In other words for $A_z>0(<0)$ positive transport occurs when $\tilde{k}_x\tilde{k}_z>0(<0)$.\\
This is shown in Figs.~\ref{fig:2} and~\ref{fig:3} where we fixed $k_x/k_z\sim10$ pertaining to maximal axisymmetric vertical shear growth rate for $A_z=0.1$ ($s_{\rm vs}\sim 0.1$), and chose $Ri_z=-0.2$. As can be seen, the growth rate is given by $s_{\rm c}\sim \sqrt{-Ri_z}$ and transport is positive in the regimes described above. This is important because, in the absence of vertical shear, convection has the tendency to transport angular momentum inward rather than outward (Ryu \& Goodman 1992). To see this we switched off the vertical drive (i.e. $A_z=0$) and found that this results in negative transport (Fig.~\ref{fig:4}).\\
We stress that this mechanism occurs for any value of the vertical shear growth rate, however small.\\
We noticed as well that when $s_{\rm c}>s_{\rm vs}$, but their values are close, the growth rate of the mixed instability, $s_{\rm mix}$, is enhanced of a fraction of $s_{\rm c}$. For example, in the case $k_x/k_z\sim3$, $A_z=0.4$ (i.e. $s_{\rm vs} \sim 0.4$), $Ri_z=-0.2$ (i.e. $s_{\rm c} \sim 0.45$) and $k_y=0.1$  we obtained $s_{\rm mix} \sim 0.55$.
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig4.eps}

	\end{center}
	\caption{Evolution of velocities and normalized $xy$-Reynolds stress (up to $t=400$)  for $Ri_z=-0.2$, $Ri_x=0.01$, ${L_S}_z/{L_S}_x=0.223$, $A_z=0.1$ and $k_x=500$, $k_z=50$, $k_y=1$.}
\label{fig:2}
\end{figure}
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig5.eps}
	\end{center}
	\caption{Same as previous picture up to $t=800$.}
\label{fig:3}
\end{figure}
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig6.eps}
	\end{center}
	\caption{Evolution of velocities and normalized $xy$-Reynolds stress (up to $t=400$) for $Ri_z=-0.2$, $Ri_x=0.01$, ${L_S}_z/{L_S}_x=0.223$, $A_z=0$ and $k_x=500$, $k_z=50$, $k_y=1$.}
\label{fig:4}
\end{figure}
\subsection{Case 3: presence of thermal diffusion}
Two are the main differences with respect to the ideal case. \\
The first regards the vertical shear instability and consists in the fact, predicted by the axisymmetric theory (Urpin 2003), that the condition for instability is relaxed. Indeed for non-axisymmetric perturbations as well, we noticed that the presence of a stable vertical stratification does not have influence on growth, which occurs for any value of $Ri_z$. In this case also, instability transforms into a transient amplification with growth rate close to the axisymmetric one, as shown in Fig.~\ref{fig:5}. Again growth is connected to the signs of $\tilde{k}_x$ and $\tilde{k}_z$ exactly in the same way discussed in Case 1.\\
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig7.eps}
	\end{center}
	\caption{Evolution of velocities and normalized $xy$-Reynolds stress for $Pe=10^5$, $Ri_z=0.1$, $Ri_x=0.01$, ${L_S}_z/{L_S}_x=0.316$, $A_z=0.1$ and $k_x=1000$, $k_z=100$, $k_y=1$.}
\label{fig:5}
\end{figure}
The second difference consists in the fact that, as for the axisymmetric case, thermal diffusion has a stabilizing effect on the convective instability. This can be seen in Fig.~\ref{fig:6}, where we considered $Ri_z=-0.2$, $A_z=0.1$, $k_x=500$, $k_y=1$, $k_z=50$, with $Pe=10^5$. Convective growth is suppressed and the growth rate in the amplification phase is the one pertaining to the vertical shear destabilization.
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig8.eps}
	\end{center}
	\caption{Evolution of velocities and normalized $xy$-Reynolds stress for $Pe=10^5$, $Ri_z=-0.2$, $Ri_x=0.01$, ${L_S}_z/{L_S}_x=0.223$, $A_z=0.1$ and $k_x=500$, $k_z=50$, $k_y=1$.}
\label{fig:6}
\end{figure}
We can however increase the growth rate toward the one pertaining to a convective instability in two ways. The first is by increasing the Peclet number as done in Fig.~\ref{fig:7}, where parameters have the same values as in Fig.~\ref{fig:6} but with $Pe=10^6$.
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig9.eps}
	\end{center}
	\caption{Evolution of velocities and normalized $xy$-Reynolds stress for $Pe=10^6$, $Ri_z=-0.2$, $Ri_x=0.01$, ${L_S}_z/{L_S}_x=0.223$, $A_z=0.1$ and $k_x=500$, $k_z=50$, $k_y=1$.}
\label{fig:7}
\end{figure}
The second is by increasing the wavelength of the perturbations as done in Fig.~\ref{fig:8} which is the same as Fig.~\ref{fig:6} except that now $k_x=100$, $k_z=10$, $k_y=0.2$. It can be seen that the growth rate is strongly enhanced. We caution however that here we are reaching a borderline regime for our short wavelength theory.\\
\begin{figure}
\epsfxsize=3.0in
\epsfysize=2.0in
	\begin{center}
		\includegraphics[scale=1]{cfig10.eps}
	\end{center}
	\caption{Evolution of velocity and normalized $xy$-Reynolds stress for $Pe=10^5$, $Ri_z=-0.2$, $Ri_x=0.01$, ${L_S}_z/{L_S}_x=0.223$, $A_z=0.1$ and $k_x=100$, $k_z=10$, $k_y=0.2$.}
\label{fig:8}
\end{figure}
We can sum up the effects of thermal diffusivity as follows. Diffusivity acts as a stabilization mechanism for convection and not for the vertical shear instability. By decreasing the Peclet number the growth rate decreases until  the vertical shear instability growth rate is reached. There the diffusion induced stabilization stops.
On the other side if we keep $Pe$ fixed and decrease wavenumbers, the growth rate increases toward the convective instability value ($\sim\sqrt{-Ri_z}$). Therefore we can conclude that the stabilizing effect of thermal diffusion affects convection for short wavelengths.
\section{Summary}
We presented the evolution of non-axisymmetric perturbations in discs whose rotation profile is $x$ and $z$ dependent. In the shearing sheet limit and moving to a reference frame corotating with the background flow the presence of vertical shear induces the evolution of the vertical wavenumber $\tilde{k}_z$.  We considered short wavelength perturbations.

Perturbations are always stabilized asymptotically; however, huge exponential growths can occur which are virtually indistinguishable from a full-fledged instability. The condition for the occurrence of such amplifications is $\tilde{k}_x\tilde{k}_z>0$ for $A_z>0$ and $\tilde{k}_x\tilde{k}_z<0$ for $A_z<0$. We summarized this in Table~\ref{tab:2}.\\
We examine more in detail this condition. Let's consider $A_z>0$, $k_x>0$ and $k_z>0$. In this case $\tilde{k}_x$ is always positive, $\tilde{k}_z$ instead evolves from positive to negative values. Therefore we observe the transient exponential phase of growth when $k_z-A_z k_y t>0$ (i.e. for $t<\frac{k_z}{A_z k_y}\equiv t_g)$. We stress that this is different from the usual transient growth paradigm (Chagelishvili et al. 2003) since here the growth is exponential and the physical origin is the vertical shear drive. Similar type of exponential transient growths were described by Balbus \& Hawley (1992) in the context of the non-axisymmetric magnetorotational instability, Korycansky (1992) in hydrodynamic convection and Volponi, Yoshida \& Tatsuno (2000) in the stabilization of plasmas kink modes. In all these studies, though, the flow was just radially sheared. \\
For $t\sim t_g$ our short wavelength approximation breaks down since $\tilde{k}_z\longrightarrow 0$; however, huge amplification values are reached at times $t$ well before $t_g$, when $\tilde{K}_z\gg H$.\\
The growth rate is close to the axisymmetric growth rate. The transport is positive in the phase of growth. As for the axisymmetric theory the most easily destabilizable modes occur in the non-adiabatic case of finite thermal diffusivity. In the ideal case the presence of a stable vertical stratification prevents the occurrence of growth. Growth is possible only for small values of the vertical Richardson number.

This first set of results extends the axisymmetric theory to non-axisymmetric perturbations, providing as well a linear local mechanism to explain the non-axisymmetric non-linear results in Nelson et al. (2012). The linear non-axisymmetric mechanism is essentially the axisymmetric one which is still active for short to intermediate times.
\begin{table}
\caption {Vertical Shear (Ideal, $Ri_z\ll1$, or Non ideal)}
\label{tab:2}
\begin{center}
    \begin{tabular}{ | l | p{2.5cm} | p{2.5cm} | }
    \hline
     &  $A_z>0$ & $A_z<0$  \\ \hline
    $\tilde{k}_x\tilde{k}_z>0$ & Transient \hspace{-0.3cm}
Exp. Growth ($W_{xy}>0$) & Decay  \\ \hline
    $\tilde{k}_x\tilde{k}_z<0$ & Decay & Transient Exp. Growth ($W_{xy}>0$)\\ \hline
    \end{tabular}
\end{center}
\end{table}
\begin{table}
\caption {Vertical Shear and Convection (Ideal, $s_{\rm c}>s_{\rm vs}$)}
\label{tab:3}
\begin{center}
    \begin{tabular}{ | l | p{1.5cm} | p{1.5cm} | p{1.5cm} | }
    \hline
     &  $A_z>0$ & $A_z<0$  & $A_z=0$\\ \hline
    $\tilde{k}_x\tilde{k}_z>0$ & Instability ($W_{xy}>0$)& Instability ($W_{xy}<0$)& Instability ($W_{xy}<0$)\\ \hline
    $\tilde{k}_x\tilde{k}_z<0$ & Instability ($W_{xy}<0$) & Instability ($W_{xy}>0$) & Instability ($W_{xy}<0$) \\ \hline
    \end{tabular}
\end{center}
\end{table}

We considered as well the concomitant action of the vertical shear and vertical convective instabilities. The asymptotic behaviour depends on the relative strength of $s_{\rm vs}$ and $s_{\rm c}$.\\
For $s_{\rm vs}>s_{\rm c}$ we observed the same type of behaviour described above - large growths occur with asymptotic stabilization. When $s_{\rm c}>s_{\rm vs}$ the system is asymptotically unstable. For $s_{\rm vs} \sim s_{\rm c}$ a variety of mixed evolutions is possible.\\
The most interesting feature for the present study is connected with the sign of the angular momentum transport. In fact we observed that in the phase in which the vertical shear driven transients growths occur (i.e. $\tilde{k}_x\tilde{k}_z>0$ for $A_z>0$ and $\tilde{k}_x\tilde{k}_z<0$ for $A_z<0$) transport is always positive, even in the case $s_{\rm c}>s_{\rm vs}$. When the vertical shear drive is switched off (i.e. $A_z=0$), the convective transport turns negative. Table~\ref{tab:3} summarizes these results.\\
We conclude that, for $s_{\rm c}>s_{\rm vs}$, the interaction of vertical shear growths and convective instability results in a destabilization whose strength (i.e. growth rate) is governed mainly by convection and whose transport by vertical shear. This mechanism holds for any value of $s_{\rm vs}(<s_{\rm c})$, however small. Again in the case $s_{\rm c}>s_{\rm vs}$, but when their values are close, the growth rate of the mixed instability is increased of a fraction of $s_{\rm c}$ with respect to $s_{\rm c}$.

Thermal diffusion has a stabilizing influence on the convective instability. This is specially strong for short wavelengths. Instead it has no influence on the vertical shear growth rate. In the case $s_{\rm c}>s_{\rm vs}$, by decreasing the Peclet number, we observed the transition from convection to vertical shear dominated evolution. By increasing the Peclet number or decreasing the wavenumbers huge growths occur. The regime of very long wavelengths is outside the scope of the present theory.\\
We can say that whereas non-axisymmetricity stabilizes the axisymmetric vertical shear instability asymptotically for $t\longrightarrow \infty$ (not for intermediate times though) but has weak influence on the convective one, non-adiabaticity stabilizes the convective instability but has no influence on the vertical shear growth rate.

This second set of results instead points at a new possible path to explain outward angular momentum transport in astrophysical discs: interaction of vertical shear and convective instabilities.
\section*{Acknowledgements}
The author would like to express his gratitude to Prof. Zensho Yoshida for his suggestions, advice  and continuous support and to Prof. Ryoji Matsumoto for the many discussions and encouragement. He would also like to acknowledge very stimulating conversations with Prof. Alexander Tevzadze.


Precious Memories of Prairie War Heroes is an anthology of Saskatchewan War Veterans that examines their exploits, both in Canada and overseas. It documents their lives both during and after their time in Canada's Armed Forces.
It is our desire that these stories be handed down to the next generation as a legacy to the freedom won. The price paid by these veterans was extensive and therefore should be remembered and honoured. This book reflects the personal history of many of your parents, grandparents, and great-grandparents. Always remember the role Saskatchewan and Alberta veterans played in making our lives better. They may not have been your family, but they were someone's, and as such were loved. Their contributions to our society should be cherished.
Fern Haight, President of the Saskatchewan Seniors Mechanism at time of writing, utilized her broad network to locate stories about Saskatchewan World War II veterans who served overseas. She obtained many interesting anecdotes from survivors and/or their families, not only about their war experiences, but also about their lives, both before and after, the war. While speaking to veterans, Fern would often receive references to other people who also had stories to share. Thus grew the collection of Saskatchewan war veteran stories.
Staff at the Saskatchewan Seniors Mechanism compiled the collection of stories about Alberta World War II veterans who served overseas. While funds prohibited travel to Alberta from Regina to personally interview these war heroes, we did take every opportunity to locate transcripts of personal interviews done with Alberta veterans. From these one can glean the true personality of the person whose stories we told.
Our publication is divided into two sections: Veterans of Saskatchewan and Veterans of Alberta. There is a photo of provincial war memorials at the front of each section. At the end of a section, you will find an extensive list of the names of veterans from that province who served overseas during World War II. We attempted to offer a wide spectrum of war experiences, including land, sea and air in almost all war theatres. We also tried to include the experiences of both men and women to offer as many perspectives as possible.
While this book is serious in nature, we have tried as well to incorporate a humorous, or light-hearted, side to better portray real-life situations encountered by those who served overseas. Veterans saw and experienced horrific things - things that no human being should ever see or experience. However, most did not lose their human spirit, finding opportunities to joke and appreciate one another in a time when relationships with people were "all-important." No one knew when he or she might see their friend, or acquaintance, again. It magnified how important these people were in their lives, and when they were together, they relished every moment. They also had the love of those back home to keep them going. It is our wish that this book be read in this light.


text:
NEXT WEEK: The Ukraine War: Agriculture Edition
Russia's abundance of flat, cool-temperate land doesn't provide much in terms of defensible geography. But it is good for growing grain, particularly wheat. Russia's place in global grain markets is also a great example of technology helping a country overcome geographic limitations. Moscow was not blessed with a country boasting an American or German level of navigable riverways, nor are its prime grain producing regions particularly close to any of its ports.
Enter rail.
The below graphic is an excerpt from my upcoming fourth book, The End of the World is Just the Beginning: Mapping the Collapse of Civilization. We can see that as Russia was able to install more railways, grain production and exports exploded by the mid-to-late 19th century. And the Russians have never really looked back. (Russian agricultural technology has not really advanced much since the introduction of rail cars and mechanical tractors and harvesters, but I digress…)
Now we are gearing up for the release of our newest project – The End of the World is Just the Beginning: Mapping the Collapse of Globalization. The new book breaks down the future shape of various economic sectors in a post-globalized world: finance, manufacturing, agriculture.
Consider the above map. Every country that is not green or blue is a food importer. Keeping the global population alive requires global peace and global sRussia is often derided as a gas station masquerading as a country. As I have noted before, this is an oversimplification that belies the significant role Moscow plays in global agricultural markets. Russia and its wheat belt neighbors, particularly Ukraine, are significant agricultural exporters of grains and seed oils. But Russia is also leading global exporter of fertilizers and fertilizer components. Not only do Russian fertilizer exports help support agricultural production in Brazil, China, India and Europe, but they help provide necessary supply in a globalized market that is increasingly seeing farmers' input costs rise.
The breaking of trade relationships, spasms in energy pricing, and most certainly the Ukraine War will limit sharply what is possible in the world of agriculture, and do so more quickly than I have ever feared. Join us March 11 for a seminar on the impact of the Ukraine War on global agriculture. We'll dive deep into the product and input disruptions that will shape our world this year, and deep into the future.
REGISTER FOR THE UKRAINE WAR: AGRICULTURE EDITION
Can't make it to the live webinar? No problem! All paid registrants will be sent a link to access the recording of the webinar and Q&A session, as well as a copy of presentation materials, after the live webinar concludes.
PRE-ORDER PETER'S NEW BOOK
NEXT WEEK: The Ukraine War: Agriculture Edition2022-03-032022-03-03https://zeihan.com/wp-content/uploads/2022/04/zeihan-logo-white-2022.pngZeihan on Geopoliticshttps://zeihan.com/wp-content/uploads/2022/03/wheat-2.jpg200px200px
TOMORROW: The Ukraine War: Energy EditionRussia, Ukraine
TODAY: The Ukraine War: Energy EditionRussia, Ukraine

redpajama_set_name: RedPajamaCommonCrawl


text:
Film, Video 2022 National Book Festival: Time to Meet Her Majesty the Queen of Kindergarten! with Derrick Barnes and Vanessa Brantley-Newton
2022 National Book Festival: Time to Meet Her Majesty the Queen of Kindergarten! with Derrick Barnes and Vanessa Brantley-Newton
The best way to greet the start of a new school year is with confidence - and a tiara! Companion to "The King of Kindergarten," "The Queen of Kindergarten," tells the story of MJ, a young Black girl, on her first day of kindergarten, where her tiara reminds her of all the good things she brings to the classroom.
2022 National Book Festival: Please Read Me a Story (10)
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Barnes, Derrick
Please Read Me a Story
Best of the Fest 2022: Please Read Me a Story
2022 National Book Festival | Events at the Library of Congress
National Book Festival: Time to Meet Her Majesty the Queen of Kindergarten! with Derrick Barnes and Vanessa Brantley-Newton . 2022. Video. https://www.loc.gov/item/webcast-10635/.
(2022) National Book Festival: Time to Meet Her Majesty the Queen of Kindergarten! with Derrick Barnes and Vanessa Brantley-Newton . [Video] Retrieved from the Library of Congress, https://www.loc.gov/item/webcast-10635/.
National Book Festival: Time to Meet Her Majesty the Queen of Kindergarten! with Derrick Barnes and Vanessa Brantley-Newton . 2022. Video. Retrieved from the Library of Congress, <www.loc.gov/item/webcast-10635/>.
2022 National Book Festival: 75 Years of Reading "Goodnight Moon" with Mac Barnett Can you believe it? It has been 75 years since the publication of Margaret Wise Brown's beloved children's book "Goodnight Moon!" Mac Barnett, author of "The Important Thing about Margaret Wise Brown,"...
Contributor: Smith, Clay - Barnett, Mac
2022 National Book Festival: Literature to Life Presents a Performance from Richard Wright's "Black Boy" Watch a performance of Richard Wright's "Black Boy," presented by Literature to Life. Your favorite book comes to life before your eyes: one person telling the story, performing all of the characters,...
Contributor: Literature to Life
2022 National Book Festival: Literature to Life Presents a Performance from Junot Díaz's "The Brief Wondrous ... Watch a performance of Junot Díaz's "The Brief Wondrous Life of Oscar Wao," presented by Literature to Life. Your favorite book comes to life before your eyes: one person telling the story,...
2022 National Book Festival: Literature to Life Presents a Performance from James Baldwin's "If Beale Street ... Watch a performance of James Baldwin's "If Beale Street Could Talk," presented by Literature to Life. Your favorite book comes to life before your eyes: one person telling the story, performing all...
Ruby Bridges Talks About Her New Picture Book! Ruby Bridges was just six years old when she made history as the first Black student to integrate an elementary school in the South. In "I Am Ruby Bridges External," she tells...
Contributor: Pinkney, Andrea Davis - Bridges, Ruby
Authors | 2022 National Book Festival | Events at the Library of Congress Check out more than 100 of the nation's best authors, poets and illustrators, who will discuss their work and answer your questions at your National Book Festival.
Contact Us | 2022 National Book Festival | Events at the Library of Congress Author Information Potential participating authors, illustrators and poets must be nominated by their respective publishers. Preferred candidates are usually popular, nationally known authors, illustrators and poets who have won book awards at...
Festival Information | 2022 National Book Festival | Events at the Library of Congress The 22nd annual Library of Congress National Book Festival will be held at the Walter E. Washington Convention Center in Washington, D.C., on Saturday, Sept. 3, from 9 a.m. to 8 p.m....
Frequently Asked Questions | Festival Information | 2022 National Book Festival | Events at the Library ... The 22nd annual Library of Congress National Book Festival will be held at the Walter E. Washington Convention Center in Washington, D.C., on Saturday, Sept. 3, from 9 a.m. to 8 p.m....
Accessibility | Frequently Asked Questions | Festival Information | 2022 National Book Festival | Events at ... Information on accessibility resources available at the Festival, including ASL interpreters and Braille maps and programs.


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Questions from the Samaritan Pentateuch
Q: What do we know about the Samaritan variant of Judaism?
A: The Samaritan version of Judaism had three differences from Judaism in Galilee and Judah
1. Place of worship: The Samaritans insisted the temple was to be at Mt. Gerizim in Samaria, not Jerusalem
2. Missing books: Like the Sadducees, they accepted only the First five books of the Old Testament (the Pentateuch), and not any others (which generally spoke highly of Jerusalem)
3. Changes to the Pentateuch: The Samaritan Pentateuch had a number of changes, which scholars today generally agree were corruptions by the Samaritans.
There were very few differences other than those three. But because of those differences, Jews looked down on Samaritans and vice versa.
Q: What do we know about the Samaritan Pentateuch?
A: The Samaritans made their own copy of the Torah in the second century B.C., though the earliest surviving Samaritan copies are from the Middle Ages. The Dead Sea Scrolls Today p.125-126. The Encyclopedia of the Dead Sea Scrolls vol.1 p.277 says "the Samaritan Pentateuch tends to expand the text by frequently inserting parallel material from other places in the Pentateuch."
The Samaritan Pentateuch compares very closely with the Massoretic text and Dead Sea scrolls, except for some obvious changes (Mt. Gerizim instead of Jerusalem, etc.) All of the Samaritan Pentateuch manuscripts are Medieval though. Some of them are Codex Add. 1846 (1100 A.D.), Codex B (1345/1356 A.D.), Manuscript E (1219 A.D.), and the Abisha' Scroll (12th -13th century). See The Meaning of the Dead Sea Scrolls p.93-95 for more info.
Among the Dead Sea Scrolls, one manuscript from Qumran cave 4 is Exodus from the Samaritan Pentateuch. According to The Anchor Bible Dictionary vol.5 p.934-939, here are the differences, from least important to most significant.
The grammar of the Samaritan Hebrew was a little different
Copyist errors are frequent in the manuscripts of the Samaritan Pentateuch.
Phrase Smoothing was done for some of the most archaic and difficult Hebrew phrases were replaced with phrases easier to understand for Samaritans. Some prepositions, nouns, subject, and appositives were added to the Samaritan text, to clarify the meaning, not unlike a Bible paraphrase today.
Altering objectionable passages was done. For example,
Worshipping God on Mt Gerizim instead of Mt. Ebal is the most famous one. (Dt 27:4)
The word "Elohim", from which one might infer a plurality of gods, is changed to the singular form in Genesis 20:13; 31:53; 35:7; Exodus 22:8.
Consolidation: In the Samaritan Pentateuch many passages in Deuteronomy are added right before or after the corresponding passage in Numbers, or in one case Exodus.
Dt 1:6-8 is added right before Num 10:11
Dt 1:20-23 is added right before Num 14:41
Dt 2:2-6 is added right after Num 20:13b
Dt 2:9 is added right after Num 21:11
Dt 2:17-19 is added right after Num 21:12
Dt 2:24-29,31 is added right after Num 21:20
Dt 3:24-28 is added right after Num 20:13.
Dt 2:8 and 10:6-7 are based on Num 20:17-18 and Num 33:31-38a.
Dt 11:29-30 and 27:2b-3a,407 after Ex 20:17, and telling the Israelites to build the temple on Mt. Gerizim.
Dt 27:2-7 is after Dt 5:21.
Q: What are manuscript variations between the Massoretic text and other versions vs. the Samaritan Pentateuch?
A: Here are some of them. The verse references in bold are where we are uncertain of the correct reading. The ones not in bold are almost certainly where the Samaritan Pentateuch is incorrect. There are many other variants not listed here where the Samaritan Pentateuch is almost certainly incorrect too.
Gen 4:8 "Abel" vs. "Abel, Let us go out to the field" (Samaritan Pentateuch, Septuagint, Neophyti I targum, Syriac, compare Vulgate)
The genealogical tables in Genesis 5 and 11:10-26 are a little different in the Samaritan Pentateuch (The Anchor Bible Dictionary vol.5)
Gen 10:4 "Dodanim" vs. "Rodanim" (some Hebrew, Samaritan Pentateuch, Septuagint)
Gen 22:19 "Ram behind [him]" (most Massoretic texts) vs. "Ram" (some Massoretic texts, Samaritan Pentateuch, Septuagint, Syriac)
Gen 30:36 absent vs. "that an angel appeared to Jacob in a dream revealing his portion in Laban's herds" (Samaritan Pentateuch)
Gen 31:49 "Mizpah" vs. "pillar witnesses" (Septuagint) vs. "the pillar of Mizpah" (Samaritan Pentateuch)
Gen 36:3 "Basemath" (Massoretic texts, Septuagint) vs. "Mahalath" (Samaritan Pentateuch) (The Expositor's Bible Commentary p.195)
Gen 36:16 "Korah/Core" (Massoretic texts and Septuagint) vs. (absent) (Samaritan Pentateuch, 1 Chronicles 1:36)
Gen 36:39 "Hadar" (most Massoretic texts) vs. "Barad" (Septuagint) vs. "Hadad" (some Massoretic texts, Samaritan Pentateuch, Syriac)
Gen 37:36 "Medanites" vs. "Midianites" (Septuagint, Samaritan Pentateuch, Vulgate, Syriac)
Gen 41:48 "food of the seven years which were in the land" vs. "food of the seven years, in which was the plenty in the land " (Septuagint, Samaritan Pentateuch)
Gen 46:13 "Puah" vs. "Phua" (Septuagint) vs. "Puvah" (Samaritan Pentateuch, Syriac, 1 Chronicles 7:1)
Gen 46:13 "Iob" vs. "Jashub" (some Septuagint, Samaritan Pentateuch)
Gen 46:16 "Ziphion" vs. "Zephon" (Septuagint, Samaritan Pentateuch, Numbers 26:15)
Gen 47:21 "he removed them to the cities" vs. "he made slaves of them" (Septuagint, Samaritan Pentateuch)
Gen 49:7 "their anger is cursed" vs. "their anger is beautiful" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Gen 50:23 "upon the knees of Joseph vs. "in the days of Joseph" (4 letters) (The Anchor Bible Dictionary vol.5)
Ex 1:22 "born" vs. "born to Hebrews" (Samaritan Pentateuch, Septuagint, and Targums)
Ex 4:22 "my first-born son" vs. "My own people" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Ex 12:16 "all work" vs. "any kind of servile work" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Ex 12:40 "children of Israel lived in Egypt" (Massoretic) vs. "children of Israel lived in Egypt and Canaan" in (Septuagint) vs. "children of Israel and their fathers lived in Egypt and Canaan" (Samaritan Pentateuch). Josephus writing about 93-94 A.D. in Antiquities of the Jews 2.15.2 also says they were in Egypt 215 years which is consistent with the Samaritan Pentateuch and the Septuagint. Josephus said it was 430 years after Abraham came into Canaan. See Pharaohs and Kings : A Biblical Quest p.330-331 for more info. The Anchor Bible Dictionary vol.5 says, "in the land of Canaan".
Ex 15:8 "breath from your nostrils" vs. "breath from you" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Ex 20:17 is immediately followed by Dt 11:29-30 and 27:2b-3a,407, telling the Israelites to build the temple on Mt. Gerizim in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Ex 20:24 "in the placed where I have caused my name" vs. "in every place where I will cause my name" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Ex 22:8 "Elohim" to "El" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Lev 11:13-19, vulture" (21 birds) vs. absent (20 birds) Septuagint, Samaritan Pentateuch
Lev 26:31 "your sanctuary" vs. "your sanctuaries" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Num 2:14 the name "Reuel" vs. "Deuel" in the Samaritan Pentateuch, Vulgate, and many Massoretic manuscripts. The Hebrew letters for "r" and "d" are very similar, and this is similar to "Rodanim vs. Dodanim in Genesis 10:4. The Expositor's Bible Commentary vol.2 p.715 says that Deuel is probably the superior reading.
Num 3:12 "I have taken the Levites … instead of every firstborn" (Massoretic text and 4Q23 vs. "I have taken the Levites … they will be the ones redeemed instead of every firstborn" (Samaritan Pentateuch
Num 3:39 "and Aaron" with special dots over the word (many Massoretic texts) vs. "and Aaron" (Septuagint) vs. absent in numerous Hebrew manuscripts, Syriac, and the Samaritan Pentateuch. Scribes would do this to express doubt about the verse. The Expositor's Bible Commentary vol.2 p.728 says, "The presence of these dots over a questionable word the scribes were loath to drop shows the level of care and concern for the minutia of the text by the Jewish scholars through the ages."
Num 4:3 "from 30 years old" (Massoretic text, 4Q23, Samaritan Pentateuch) vs. "from 25 years old) (Septuagint)
Num 9:3 "in the evening" (Massoretic text, Samaritan Pentateuch, Septuagint) vs. "in the day" (4Q23)
Num 10:11 is immediately preceded by Dt 1:6-8 in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Num 14:41 is immediately preceded by Dt 1:20-23 in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Num 20:13 is immediately followed by Dt 3:24-28 in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Num 20:13b is immediately followed by Dt 2:2-6 in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Num 21:11 is immediately followed by Dt 2:9 in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Num 21:20 is immediately followed by Dt 2:24-29,31 in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Num 22:20; 23:4,5,16 "God" vs. "an angel of God" Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Num 24:17 (uncertain) vs. "the skulls" in the Samaritan Pentateuch
Num 26:17 "Arod" vs. "Arodi" in the Samaritan Pentateuch and the Syriac
Num 26:23 "through Puvah/Puwah/Puwwah, the Punite" (many Hebrew manuscripts) vs. "through "Pu'ah, the Puite" in the Septuagint, Samaritan Pentateuch, Vulgate, and Syriac.
Num 26:39 "Shephupham" vs. "Shupham" in the Samaritan Pentateuch, Vulgate, Syriac, Septuagint, and some Massoretic manuscripts
Num 26:40 absent vs. "through Ard" in the Samaritan Pentateuch and Vulgate
Num 27:23 the Samaritan Pentateuch adds "and said to him and then adds Deuteronomy 3:21-22.) The Expositor's Bible Commentary vol.2 p.94
Num 32:29,31,33 "Gad … Reuben" 3 times ( Massoretic, 4Q23) vs. "Reuben … Gad" 3 times (Samaritan Pentateuch, Septuagint)
Num 33:8 "from before Hahiroth" vs. "Pi Hahiroth" in the Samaritan Pentateuch, Vulgate, and many Massoretic manuscripts
Dt 1:8 "The Lord" vs. "I" (Samaritan Pentateuch, Septuagint)
Dt 2:8 and 10:6-7 are based on Num 20:17-18 and Num 33:31-38a in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Dt 5:5 "word" vs. "words" (Dead Sea Scrolls, Samaritan Pentateuch, Septuagint, Syriac, Vulgate, Targum)
Dt 5:21 is immediately followed by Dt 27:2-7 in the Samaritan Pentateuch. (The Anchor Bible Dictionary vol.5 p.937)
Dt 9:24 "I have known" vs. "he has known" (Samaritan Pentateuch, Septuagint)
Dt 9:28 "Lest the land" vs. "Lest the people of the land" (Septuagint, Samaritan Pentateuch)
Dt 11:14 "I" vs. "he" (Samaritan Pentateuch, some Septuagint, Vulgate, a mezuzah quotation from the Dead Sea Scrolls)
Dt 12:5 "place where the LORD your God will choose" (Massoretic) vs. "place where the LORD has chosen" (Samaritan Pentateuch)
Dt 20:8 "lest the heart of his brothers faint" (Massoretic, Targum) vs. "lest he make his brother's heart faint" (Samaritan Pentateuch, Septuagint, Syriac, Vulgate)
Dt 25:1 "his private parts" vs. "his flesh" (Samaritan Pentateuch)
Dt 27:4 "Mount Ebal" vs. "Mount Gerizim" (Samaritan Pentateuch and Old Latin) [The Samaritans likely changed this to improve their claim that Gerizim, not Jerusalem, was the mountain where they should worship.]
Dt 28:30 changes "grabbed his private parts" (sgl) to "grabbed his flesh" (yshbn)
Dt 28:11 "cattle … ground" (Massoretic, some Septuagint, Samaritan Pentateuch) vs. "g[round, … c[attle]" (4QDeut( c ), some Septuagint)
Dt 30:9 "cattle … ground" (Massoretic) vs. "ground … cattle" (4Deut(b), Samaritan Pentateuch, Septuagint) The Dead Sea Scrolls Bible p.187
Dt 31:7 "You will go" vs. "You will bring" (Some Massoretic text, Samaritan Pentateuch, Vulgate)
Dt 32:6 "he repented" vs. "he forgave" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)
Dt 32:10 "found him" vs. "sustained him" (Samaritan Pentateuch, Septuagint)
Dt 32:15 "Jeshurun" vs. "Jacob ate his fill; Jeshurun" (Dead Sea scrolls, Samaritan Pentateuch, Septuagint)
Dt 32:43 "cleans his land his people" vs. "cleans the land for his people") Dead Sea Scrolls, Samaritan Pentateuch, Septuagint, Vulgate)
Dt 32:44 "Hoshea" (Massoretic) vs. "Joshua" (Samaritan Pentateuch, Septuagint, Syriac, Vulgate) Hosea was Joshua's name prior to Moses renaming him.
Dt 33:2 "He came from Ribebot-kodesh" vs. "with him were myriads of holy ones" (Samaritan Pentateuch, Septuagint, Syriac, Vulgate)
Dt 33:12 "will dwell securely upon him" (Massoretic) vs. "will dwell securely" (Samaritan Pentateuch) vs. "upon God" (Septuagint, Dead Sea scroll 4Q35)
Dt 34:10 "there arose not again a prophet like Moses in Israel vs. "there will not arise again" (Samaritan Pentateuch) (The Anchor Bible Dictionary vol.5)


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Buff Banded Rails are widespread across the east coast of the Australian mainland, Norfolk & Lord Howe Islands, SE Asia, NZ & New Guinea.
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Posts tagged "volcano"
Summiting Mt. St. Helens
Looking east along the crater rim of Mt. St. Helens to Mt. Adams in the distance.
Of all the volcanoes in the northern Cascades, Mt. St. Helens is by far the easiest to climb. For starters, the most common route, Monitor Ridge on the south flank, is non-technical, eliminating the need for specialized gear or advanced mountaineering skills. At just 8,366 feet, its summit elevation post-1980 eruption places it several thousand feet lower than neighbors such as Mt. Adams, Mt. Baker, and Mt. Rainier, essentially taking the ill effects of altitude out of the equation. However, at 10 miles round trip and with about 5,000 feet of elevation gain, it's still a robust day hike.
After numerous trips to the base of Mt. St. Helens over the years, reaching the summit of this active volcano has long been on my to-do list. When we moved back to Washington last summer, I knew I might finally get my chance. The Gifford Pinchot National Forest limits the number of climbers to 100 per day in the summer months, and the permits sell out quickly when they go on sale in March. Sadly, I missed the initial sale this year, leaving me to obsessively check every few days for cancellations. Eventually I got lucky and spotted two permits up for grabs in late-July. A few minutes later, they were mine.
From a distance and elevation gain standpoint, the hike up Monitor Ridge is comparable to many of Colorado's famous "Fourteeners". One major difference: on Mt. St. Helens we would be topping out at a lower elevation than one starts most Fourteener climbs at. The other big difference would be the terrain. Most Fourteeners have a fairly distinct path a good way up the mountain and are on reasonably solid rock (my dislike of exposure and falling means I haven't done any of the ones on rotten rock). On Mt. St. Helens, after a brief foray through the forest, the climb traverses a mixture of large lava boulders and a loose scree consisting of pumice and volcanic ash. This is a hike where a mask was on the suggested gear list before they were cool!
To the hike! As the National Weather Service had accurately predicted several days in advance, the morning of our climb dawned with some fairly dense fog at the Climbers Bivouac trailhead where we had camped the previous night. We hit the trail at 6:00 am, anticipating that it would take us 4-5 hours to reach the summit. The first two miles of trail climbs gently through a moist and somewhat unremarkable second growth forest. At timberline is where the route changes from a well-maintained trail to the aforementioned scree and boulder scramble. Wooden posts serve as guides for the remainder of the climb, but following them too closely didn't always make for the most sensible route. In places there is a fairly obvious path, while in others (particularly in the boulder fields), you just sort of have to find what works best. Just before arriving at timberline, we began to emerge from the clouds, revealing views of Mt. Adams to the east and the extremely conical Mt. Hood to the south that we enjoyed the rest of the day. Once above the trees, our pace slowed significantly, but before too long we were several hundred feet above the cloud deck we had been immersed in a short time earlier:
Breaking out of the trees on the Monitor Ridge route.
Heading up Mt. St. Helens with the clouds below us and Mt. Hood in the background.
Nearing the top of the boulder field on the Monitor Ridge route. Only a mile to go!
We made fairly good time through the ~2 miles of boulder fields. The final mile through a deep and loose mixture of volcanic ash and pumice was definitely the most challenging part of the hike. With masks on to prevent inhaling clouds of ash kicked up by our feet (and the wind), it was somewhat analogous to hiking up a sand dune: two steps forward, one step back, repeat. After about four hours, we were standing on the crater rim.
The first view northward into the bowels of Mt. St. Helens was stunning, and definitely one of the most dramatic viewpoints I can recall. Unlike many lesser peaks in the Cascades, or most peaks in the Rockies, where you are often surrounded by other peaks of comparable elevation, Mt. St. Helens stands alone. On this volcano, you are standing on what is, by far, the highest point for dozens of miles in any direction, with only the other volcanoes exceeding you in height. Looking down onto the crater formed by the 1980 eruption, the lava domes that are slowly rebuilding the summit, and the Crater Glacier (one of the few alpine glaciers in the world that is actually advancing) was spectacular. Cornices of hard-packed, dirty snow clung to the nearly vertical slopes of the crater walls just beneath our feet, necessitating caution as we moved our way along the rim. Gentle puffs of steam were visible on portions of the lava dome, a gentle reminder that we were standing at the summit of one of the most active volcanoes in the world. The dull roar of rock and ice fall from the crater walls was nearly constant for the hour we spent taking in the view from the summit.
Panorama from the Mt. St. Helens crater rim, looking north across the lava dome and Crater Glacier to Spirit Lake and Mt. Rainier. (Click image to enlarge)
Panorama looking south from the crater rim. Mt. Adams at left, Mt. Hood just left of center. (Click image to enlarge)
Clouds part to reveal Spirit Lake and the distant cone of Mt. Rainier, more than 4,000 feet higher that Mt. St. Helens.
While the hike up had been relatively uneventful, the journey down was definitely less pleasant. Hiking poles are a must for the descent due to the steep, loose, and rocky terrain. This is definitely one of those hikes where coming down is exponentially more difficult than going up!
Compared to our experience hiking Fourteeners in Colorado, the significantly lower elevation of this hike makes a huge difference and in my opinion dramatically lowers the overall difficultly of this route. There is a big difference between inching your way up a scree slope at 13,000′ and having to stop every few steps to take in oxygen, and doing the same at 8,000′ where breathing isn't as much of an issue. While the terrain was definitely more difficult than your average hike with similar specs, in the end we felt like the difficulty of the Monitor Ridge route was somewhat over-hyped based on some of the accounts we read in advance. We wouldn't hesitate to do it again. As far as special gear, a mask was definitely helpful for both COVID and volcanic ash purposes. Hiking poles were more or less useless on the way up, as the boulder fields often required the use of hands to navigate, but essential on the way down. Other sources recommended bringing garden gloves to protect against cuts on the sharp volcanic rocks. We bought some cheap ones and definitely found them useful. I never actually put mine on during the ascent, and made it to the summit with only one small abrasion on the back of my hand. Long pants are also a must if you don't want your lower legs ripped to shreds by the rocks.
With Mt. St. Helens checked off, next up on the to-do list is Mt. Adams, which is also a non-technical climb at the right time of year, albeit longer. We may not get to that one this summer…perhaps our goal will be to climb one Cascade volcano per year!
August 7, 2020 | Categories: Geology, Hiking, Peaks, photography, Volcanoes, Washington | Tags: Cascades, Hiking, Monitor Ridge, Mt. St. Helens, photography, volcano, volcanoes, Washington | 1 Comment
Mt. St. Helens: 40 Years Later
The volcanic cone of Mt. St. Helens rises above grassy slopes covered with scarlet paintbrush (Castilleja miniata).
This past May marked the 40th anniversary of one of the most significant natural disasters in U.S. history: the 1980 eruption of Mt. St. Helens. 2004 to 2008 brought another series of eruptions, but today Mt. St. Helens is quiet. Stratovolcanoes such as Mt. St. Helens generally provide some degree of warning (often in the form of earthquakes or surface deformation) before erupting. Given that Mt. St. Helens is one of the most closely monitored volcanoes in the U.S. (if not the world), the lack of activity in recent years has once again made the surrounding landscape a recreational destination.
The northeast side of Mt. St. Helens is just a few hours from our front door, accessed via a series of forest service roads that, while technically paved, are in such poor condition that one pines for the sweet rhythm of dirt washboards. Much of the land most directly affected by the 1980 eruption is protected as the Mt. St. Helens National Volcanic Monument, established two years after the eruption. Camping and off-trail travel is restricted across a large swath of the monument to allow scientific study of how the landscape evolves post-eruption, with minimal human disturbance. Recently, we took a short backpacking trip to the northeast flank of the mountain, where camping is allowed, but where recurring volcanic activity has still left the landscape relatively devoid of tall vegetation. The result is spectacular views of Mt. St. Helens itself and the surrounding terrain (and, it turns out, any bright comets that happen to be gracing the skies.)
This was my third visit to the area but first in about 10 years. My previous visits had been in late summer and early fall, when the only wildflowers to speak of were some hardy stalks of late-blooming fireweed. On this visit, in early July, the grassy slopes of the lower mountain were awash in what can only be described as a riot of wildflowers. Paintbrush and penstemon dominated the scene, resulting in slopes that glowed red and purple from miles away and absolutely lit up at sunset and sunrise. It was truly one of the most spectacular wildflower displays I have ever seen!
Scarlet paintbrush (Castilleja miniata) and Cardwell's penstemon (Penstemon cardwellii) frame our campsite on a barren pumice slope on the northeast flank of Mt. St. Helens.
We settled on a campsite located on a small, barren ridge of pumice and ash where we could set up for the evening without impacting the gorgeous display all around us. Shortly thereafter, a handful of mountain goats came wandering through…with a good deal less regard for the wildflowers. While this was slightly concerning at first, as mountain goats can be aggressive, they seemed to be enjoying the buffet too much to notice our presence. We watched them slowly eat their way up-slope behind our campsite for well over an hour (as we somewhat nervously heated up our cans of soup and baked beans, while hoping that they continued to find the scent of the penstemon more attractive) before they finally bedded down on a distant ridge for the evening.
A mountain goat (Oreamnos americanus) is paralyzed by indecision while looking at the wide array of tasty offerings, Mt. St. Helens National Volcanic Monument, Washington.
"The paintbrush looks tasty!"
Mountain goats, Mt. St. Helens National Volcanic Monument, Washington
A mountain goat surveys the lower, barren slopes of Mt. St. Helens.
On just a few hours of sleep, we hiked back out to our car the next morning and enjoyed some day hikes to the north of Mt. St. Helens over the next two days. This area provides the best vantage point for viewing the effects of the 1980 eruption. The blast reduced the elevation of Mt. St. Helens by over 1,000 feet, replacing the formerly sharp summit with a massive crater. Part of the crater has since been filled in by a lava dome extruded in the months following the eruption, and again during the eruptive sequence of 2004-2008. Another dramatic feature of the landscape is Spirit Lake. This once idyllic destination was directly in the path of the eruption on May 18, 1980. The massive landslide associated with the eruption filled in a large portion of the lake with debris, pushing the entire lake northward and raising the water level by about 200 feet, burying numerous buildings, camps, and, unfortunately, Mt. St. Helens Lodge owner Harry Truman, who had steadfastly ignored evacuation orders in the weeks leading up to the eruption. To this day, a massive raft of logs floats on the lake surface, the remains of trees uprooted in the 1980 eruption.
Mt. St. Helens from Bear Pass. In the foreground is Spirit Lake, covered with floating logs: the remains of trees uprooted by the 1980 eruption of Mt. St. Helens and washed into the lake.
The log raft as seen from lake level at the end of the Harmony Trail, the only legal access to the shore of Spirit Lake.
As a geologist, I find the landscape around Mt. St. Helens endlessly fascinating. Changes since my last visit 10 years ago were clearly visible in many places. Mt. St. Helens is the most active of the Cascade volcanoes and will certainly erupt again. Perhaps nowhere is it more clear that the current configuration of the Earth's surface is ultimately temporary.
July 29, 2020 | Categories: Flora, photography, Volcanoes, Washington, wildflowers, Wildlife | Tags: goats, mountain goats, Mt. St. Helens, photography, volcano, Washington, wildflowers, wildlife | 2 Comments
Views of Tahoma
Light from a nearly full moon illuminates the glaciers and icefields on the summit of Mount Rainier.
At 14,411 feet, Mount Rainier is the highest peak in Washington and in the entire Cascade Range. British naval officer Peter Rainier never even saw the mountain that now bears his name, but he had a friend that did. Clearly, it paid to have connections in the 1700s. Oddly, Rainier did fight against the Americans during the Revolutionary War, making the fact that we continue to utter his name when referring to this grand peak all the more peculiar. Mount Rainier was originally known as Tahoma or Tacoma by the Salish-speaking indigenous tribes of the Pacific Northwest. There are periodic rumblings about renaming the peak, much like the name of Alaska's Mount McKinley was officially reverted to Denali in 2015. Hopefully that will indeed happen someday…
Irrespective of name, Tahoma dominates the skyline from Seattle and much of the Puget Sound region. Tacoma and other towns to the south of Puget Sound are literally built on layers of debris deposited by gigantic lahars (volcanic mudflows) that periodically race down its flanks, filling river valleys on their way to the sea. The threat of future lahars and volcanic activity looms over those who live in its shadow. From my vantage point in the Yakima Valley of central Washington, the foothills of the Cascades obscure all but the uppermost few hundred feet of its glacier-clad summit (and which will, thankfully, block any future lahars). Obtaining a better view requires venturing into the mountains. Recently, we spent a weekend camping high on a ridge about a dozen miles to the south of the volcano's summit. Our campsite in an old clear cut provided stellar, if slightly obscured views of Tahoma's bulk.
The weather was quite variable throughout the weekend, ranging from mostly clear (but hazy) upon arrival, to partly cloudy, to overcast, to bouts of dense fog. Our view of the mountain was constantly changing. One evening I decided to capture a time-lapse of cloud movement and formation in the two hours leading up to sunset:
Sadly I did not notice the beer can stuck on top of the tree in the foreground until it was too late. Oh well. On another evening, a spectacular stack of lenticular clouds developed over the summit:
A series of stacked lenticular clouds above Mt. Rainier.
Closer view of the stacked lenticular clouds.
A nearly full moon provided sufficient light for photographing the mountain after dark:
Tahoma bathed in the light of a nearly full moon.
Not to be outdone by Tahoma, the pinnacle of High Rock just to our west also put on quite the show at sunset, with the light of the setting sun casting an amazing shadow of the peak and it's summit lookout tower on the foreground mists:
Sunset, High Rock, Gifford Pinchot National Forest, Washington
A nearly full moon rises over the forests of the Cascade Mountains.
After this trip and our stunning view of Mt. Adams a few weeks ago, our goal for the summer is now to camp in the shadow of all of Washington and northern Oregon's stratovolcanoes. Next up: Mt. St. Helens!
July 14, 2020 | Categories: Nightscapes, Peaks, photography, Volcanoes, Washington | Tags: clouds, full moon, mountains, Mt. Rainier, photography, Tahoma, volcano, Washington | 1 Comment


text:
Муратбаево () — село в Келесском районе Туркестанской области Казахстана. Входит в состав Актобинского сельского округа. Код КАТО — 515437700.

Население
В 1999 году население села составляло 1611 человек (841 мужчина и 770 женщин). По данным переписи 2009 года, в селе проживали 1933 человека (1016 мужчин и 917 женщин).

Примечания

Населённые пункты Келесского района

redpajama_set_name: RedPajamaWikipedia


Your business could always use some extra support when it comes to smart software tools. The digital world is constantly evolving and you need to keep your business up to date with these trends too. Not only could you be using more online resources but you could also use many other tools to keep your information safe and secure. Now is the time to assess the business software that you are currently using and see how you can improve upon it. Whether you are operating an online business or a physical store you will always need online systems to support you. You might need a secure place to store your passwords or a certain storage plan which caters to your employees who speak other languages. Whatever your specific needs are you will be able to find the solution for it. This will not only make your business run more smoothly, but it will also enhance your overall safety and security online.
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You are in charge of the safety of your company, so always endeavour to protect it to the best of your abilities. You have the knowledge and the tools to protect yourself from all angles so you can rest at night knowing you have done everything you can to keep everything safe.
Onto more positive topics, which are going to make a huge impact on the way your business operates on a daily basis. You want to make things easy for your customers and speak their language when it comes to parting with their money. It's hugely trendy to pay for services via an app or mobile payment method. Gone are the days of cash and cheques, so make sure your business is making the most of mobile banking. You want to be able to receive money quickly and effectively too, so instantaneous payment methods like this are something you'll definitely benefit from. Rewards systems are also a huge incentive to get your target audience on board. Grab their attention and retain their loyalty using simple rewards schemes.
Mobile phones don't only have the power to send payments, but they are also the main source of connecting with your target market. Social media is an incomparable tool in today's business world. Take every opportunity when it comes to getting your business on social media platforms, such as Facebook, Instagram and Twitter. Nowadays people don't even think twice about a company if it doesn't have an impressive online presence. Make sure your online activity is enthralling and engaging, by inviting people to online discussions. Use this platform as a golden opportunity to allow your business to soar to success.
So keep tabs on your business software and never settle for second best; your business is set for success as long as you are operating a slick and smooth operation. Explore all of your options and try out new methods of working. You will soon notice what works well for you and you will be able to rely on this innovative software to keep your business running safely and effectively.
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text:
NATHAN MERTENS
Educator | Saxophonist | Performer
JAPAN COMMISSION
© 2020 Nathan Mertens.
nathancmertens@gmail.com
"Escapades" with HSO
I had an absolute blast playing "Escapades" with the Hastings Symphony Orchestra this weekend! A big thanks to John Sample on vibraphone and Dave Klein on bass for playing the whammy out of this piece. And thanks to Byron Jensen and the HSO for an all-around great conc...
Japanese Saxophone Database
After over two years of gathering, translating, and organizing the Japanese Saxophone Database is finally live! While living and studying in Tokyo, I realized how little Japanese saxophone information was available outside of Japan. So I compiled lists of Japanese saxo...
New Faculty at Hastings College
I am happy to announce that I have recently been offered and accepted a position at Hastings College! I will be a Postdoctoral Fellow in the newly established First-Year Seminar Program. Looking forward to working with Dr. Christopher Strickland, Dr. Eric Kennedy, and...
Japanese Commission Project
以下日本語
I'm very excited to be leading a commissioning consortium of six Japanese composers to each write a new work for the contemporary saxophone repertoire! The commissioned composers are from diverse backgrounds, write in a wide array of styles, and represent the next...
Blair/Mertens Duo - America Tour
Excited to be briefly headed back to the States in March for a Concerto performance with Gillian Blair at the North American Saxophone Alliance (NASA) Conference in Arkansas! We will be giving the North American premiere of Andy Scott's "Tjuonavagge." We will also be p...
Concert in Thailand
Very excited for my upcoming trip to Thailand! I'm looking forward to collaborating again with one of my former colleagues from The University of Texas, Suvida Neramit-aram, and finally playing with the great Thai saxophonist, Nitchan Pitayathorn! We are presenting a p...
Kurashiki International Saxophone Competition
At the 14th Kurashiki International Saxophone Competition the Kunitachi Saxophone Quartet won third prize in the Chamber Music Division! We performed David Maslanka's "Recitation Book" - a work that, although is quite popular in the States, was unfamiliar to many of th...
World Saxophone Congress
What a blast! I'm still on a high from the World Saxophone Congress in Zagreb! Feeling lucky to play and present with so many incredible people and groups! It was great to see old friends and make new ones from all over the world. A big congratulations to Japan for win...
England Concert Tour
It was such a pleasure to spend almost two weeks in England playing concerts in Bury, Manchester, London, and York! I performed mostly chamber music with my English friend, Gillian Blair, and her pianist, David Gibson. But, I was also able to perform with the Polaris D...
CD Recording
After a long day, the first half of our Debut CD is recorded!! We were very lucky to record in the new recording studios at The University of Salford in Manchester, England. Excited to share the following of music with you all soon!
"Aquarelle" - Andy Scott
"Right at th...


text:
package gui;

import main.Game;
import main.GridAI;
import main.AI;

/**
 * This class choose the right action for the initialization of the grid by the
 * player.
 *
 * @author CAREDDA Giuliano, DUCOBU Alexandre
 */
public class WindowInitPawn extends WindowGame {

	private static final long serialVersionUID = 1L;
	public static Game gridPane1, game = new Game(10, 1);
	public static int team = 1, nbPawn, nbPawns = 40, nbPlayer = 1;
	public static int toInit, side = 1;
	public static boolean modif = false;

	/**
	 * Main constructor of the class.
	 */
	public WindowInitPawn() {
	}

	/**
	 * Constructor of the class when a 'game' object is given.
	 *
	 * @param game
	 *            The 'game' object of the game.
	 */
	public WindowInitPawn(Game game) {
		WindowInitPawn.game = game;
		gridPane1 = new Game(10, 4, 0);
		toInit = 0;
		initGame();
	}

	/**
	 * Constructor of the class when the user loads a grid or creates an
	 * automatic grid.
	 *
	 * @param gridPane1
	 *            The panel where the loaded or automatic grid is placed.
	 *
	 * @param toInit
	 *            This value says what the 'initGame' method has to do:

	 *            if toInit = 0, the grid is complete and there's nothing to do,

	 *            if toInit = 1, the grid has to be modify,

	 *            if toInit = 2, a new grid has to be created.
	 */
	public WindowInitPawn(Game gridPane1, int toInit) {
		WindowInitPawn.gridPane1 = gridPane1;
		WindowInitPawn.toInit = toInit;
		WindowInitPawn.modif = true;
		game.setComplete(0);
		initGame();
	}

	/**
	 * This method allows the user to create or modify grid for each team of the
	 * game, and launches also the game when the grid is complete.
	 */
	public void initGame() {
		if (toInit == 2) {
			// New grid
			new InitWindow();
		} else if (toInit == 1) {
			// Modif
			if (game.getComplete() == 1) {
				int lvl = AI.getIntLevel(game.getLevel());
				game.placeTeam(new GridAI(2, lvl).getGrid(), 2);
				new WindowGame(game);
			} else if (game.getComplete() != 1) {
				new InitWindow();
			}
		} else {
			if (game.getComplete() == 2) {
				new WindowGame(game);
			} else if (game.getInitGridGame() == 0 && game.getComplete() != 1) {
				// AUTOMATICAL
				int lvl = AI.getIntLevel(game.getLevel());
				game.placeTeam(new GridAI(1, 1).getGrid(), 1);
				game.placeTeam(new GridAI(2, lvl).getGrid(), 2);
				new WindowGame(game);
			} else if (game.getComplete() == 1) {
				if (game.getInitGridGame() == 2) {
					// 1 player (BLUE)
					nbPlayer = 1;
					nbPawns = 40;
					side = 2;
					team = 2;
					new InitWindow();
				} else if (game.getInitGridGame() == 1 || game.getPlayer() == 2) {
					// 1 player (RED)
					nbPlayer = 1;
					nbPawns = game.getNbPawns();
					side = 1;
					team = 1;
					gridPane1 = Game.chosenSize(40);
					new InitWindow();
				}
			} else if (game.getInitGridGame() == 3 && game.getComplete() == 0) {
				// BLUE
				nbPlayer = 1;
				nbPawns = game.getNbPawns();
				side = 2;
				team = 2;
				new InitWindow();
			}
		}
	}
}

redpajama_set_name: RedPajamaGithub


text:
Q: How to cross compile for ARM on Ubuntu conditionally? I have written the following make file
all: writer.o

writer.o:
    gcc -Wall writer.c -o writer

clean:
    rm *.o

How do I add a functionality to this make file such that I am able to generate an application for the native build platform when GNU make variable CROSS_COMPILE is not specified on the make command line.However, when CROSS_COMPILe is set, I should generate a cross compiled output file using the compiler, aarch64-none-linux-gnu-gcc.

A: Set the CROSS_COMPILE variable itself to the compiler prefix. So for native builds:
CROSS_COMPILE =

(i.e. there's nothing, the variable is "empty").
And for cross-compilation:
CROSS_COMPILE = aarch64-none-linux-gnu-

Then set:
CC = $(CROSS_COMPILE)gcc

To complement the above, use implicit rules to build the program:
all: writer

writer: writer.o

That's all that you need.

redpajama_set_name: RedPajamaStackExchange


Strengthening the education of gratitude consciousness of poor college students is not only the need of college students' work in the new era, but also the requirement of ideological and political education throughout the whole process of education and teaching. In the precise aid-the-poor funding system, Thanksgiving Awareness Education has become an important part of the university funding system. It enables students to recognize, know, understand and repay kindness, transforms consciousness into action, and realizes the unity of cognition and behavior.
1. 李琳. 高校多元化资助体系下贫困生的感恩教育探究[J]. 天津市教科院学报, 2016(3): 33-34.
2. 王建芬, 徐晔星, 王丽丽, 吴菲. 高校贫困生感恩意识和行为现状的调查分析及对策[J]. 高校辅导员学刊, 2013, 5(4): 80-84.
3. 冯羽, 张暁文. 感恩教育与贫困生的心理健康教育[J]. 煤炭高等教育, 2015(4): 87-91.
4. 张阳. 高校资助体系下的贫困生感恩教育研究[J]. 黑龙江高教研究, 2015(2): 130-132.
5. 王婕. 青少年感恩观念培育的途径探析[J]. 中州学刊, 2015(9): 94.
6. 戴贵芬. 高校贫困生资助管理工作中的感恩教育研究[J]. 吉林工程技术师范学院学报, 2013, 29(8): 14-16.


text:
Port Angeles police determine threatening call to school a hoax
by Pierre LaBossiere
Tuesday, November 10, 2020 7:46am
PORT ANGELES — Law enforcement officers responded to several North Olympic Peninsula schools Monday morning following a phone call from a person who claimed armed kids were headed to a school.
The Port Angeles Police Department determined within an hour it was a hoax.
A call later traced to Western State Hospital in Lakewood was placed at 9:05 a.m. to Port Angeles High School claiming kids were armed with an AR-15.
The anonymous caller claimed to be a veteran and said he was following a vehicle full of kids, and "they were going to the high school to shoot it up."
School officials called the Port Angeles Police Department, which sent three officers and deputy police chief Jason Viada, according to Cpl. Clay Rife.
Meanwhile, Clallam County deputies responded to schools outside of city limits in both Joyce and Sequim because of the vagueness of the call, Rife said.
Rife said the call was traced to a pay phone Western State Hospital patients are allowed to use.
It's believed that one of the patients at the hospital has ties to the Port Angeles area, Rife said.
Once the police department determined it was a false report, officers left the school at about 9:44 a.m., he said.
Afterward, the Port Angeles School District sent an automated phone call to parents and stated the PAPD and Principal Jeff Clark responded immediately.
"PAPD found that the call originated from Western State Hospital," the message stated. "The institution identified the individual that made the prank call with the help of our local authorities. Thank you, PAPD."
Peninsula counties add new COVID-19 cases
Clallam County could extend services to social distancing center