text:
\section{Introduction}

Graphene, a single sheet of pure carbon atoms, has been the subject of intense focus and research for the last few years due to its unique and amazing properties that could make it more suitable for future electronic devices and possibly replace silicon-based semiconductors in electronics \cite{1,2}. Graphene nanoribbons, in particular, are of interest because they exhibit a conduction bandgap that arises due to size confinement and edge effects \cite{3}-\cite{11}. From the electronic applications point of view, graphene-based materials with gap are very desirable. This lead to substantial theoretical and experimental efforts to generate and control the energy gap in graphene based devices. One approach is based on quantum confinement as in quantum dots and nanoribbons, where it was shown that the energy gap value increases with decreasing nanoribbon width \cite{12}.

Theoretical studies have suggested that graphene nanoribbons could have interesting magneto-electronic properties, with predicted very large magnetoresistance \cite{4,13}. Experimental observation of a significant enhancement in the conductance of a graphene nanoribbon field-effect transistor by a perpendicular magnetic field has been reported recently \cite{14}. They have observed an extraordinarily large tunable magnetoresistance in graphene nanoribbon--FET devices and an increase in conductance by a factor of over 10,000 was demonstrated at $1.6 K$. This magnetoresistance can be readily tuned by the gate voltage and source-drain bias, with enhancement reaching maxima near the edges of the conduction bandgap. These experimental findings clearly demonstrate that the graphene nanoribbons exhibit interesting magneto-transport properties, with the possibility of opening up exciting opportunities in magnetic sensing and a new generation of magneto-electronic devices.

On the other hand, more efforts have been employed to understand the scattering behavior of fermions
in graphene. In particular we cite \cite{peeters} where
the transmission through magnetic barriers in graphene-based nanostructures. Several particular
cases were considered: a magnetic step, single and double barriers, and $\del$-function barriers. A separate class of
magnetic-barrier structures are those with inhomogeneous magnetic-field profiles, such that the average magnetic
field vanishes, which can be realized by nanostructured ferromagnetic stripes placed on top of the
graphene layer. Quantum bound states that are localized near or in the barrier are predicted for a magnetic step
and some structures with finite-width barriers but none for $\del$-function barriers. When a bound state is localized
close to the barrier edge, it has a nonzero velocity parallel to this edge. The transmission depends strongly on
the direction of the incident electron or hole wave vector and gives the possibility to construct a direction dependent wave vector filter. In general, the resonant structure of the transmission is significantly more
pronounced for (Dirac) electrons with linear spectrum than for the usual electrons with a parabolic spectrum.

Motivated by different results on the scattering behavior, we study
fermions in graphene nanoribbon subject to a sharply localized magnetic field.
Indeed, we show that the solution space of the present system is the union of the two solution subspaces
governed by two different kinetic balance equations. These two solution subspaces are not identical and their union constitutes the whole
space of solution of our problem. To resolve the issue of which energy domain is selected by each
kinetic balance relation, we perform a unitary transformation on the fundamental Dirac
equation. Such a transformation does not affect the energy spectrum or the physics of the problem.
We choose a rotation by $\pi/4$ about the $y$-axis, $U = e^{i\frac{\pi}{4}\si_2}$. After
matching the eigenspinors  at the boundary conditions, we evaluate the reflection and transmission
amplitudes in terms of the energy and magnetic field. A detailed study of their coefficients is
presented as well.

Subsequently, we consider a magnetic field normal to the graphene sheet of a bell shape, i.e. $\vec B(x)= \hat z B_0\sech^2(\mu x)$
where $B_0$ is the strength of the field and $\mu^{-1}$ stands for its range. We show that the solution
space of the corresponding Hamiltonian splits into three regions depending on the sign of $kB_0$ and
the energy range, with $k$ wave vector along the $y$-axis. Using the corresponding current density, we evaluate the
reflection and transmission coefficients, which reduce to those obtained in section 3 for $\mu=1000$. Finally, we treat
the case of a double step pseudoscalar potential and also double Gaussian type magnetic field.

Our manuscript is organized as follows. We present our theoretical model by setting the general form of potential
in section 2.  As a first illustration of potential type, we consider $\delta$-type magnetic field in section 3.
After getting the energy spectrum solutions, we study the scattering problem by evaluating explicitly
the reflection and transmission coefficients and underline their physical properties. Because of $\delta$-type magnetic field
is a limit case of a general form, we study Dirac fermions in a Gaussian magnetic field, in section 4.
These studies suggested to deal with an integrating case that is Dirac fermions in a double $\delta$-type magnetic field
in section 5 and the corresponding double Gaussian type magnetic field is considered in appendix. We conclude our work in the final section.

\section{Theoretical model}

In graphene, the low energy linear electronic band dispersion near the Dirac points gave rise to charge carriers (electrons or holes) that propagate as if they were massless fermions with speeds of the order of $10^6 m/s$ rather than the speed of light $3\times10^8 m/s$. Hence, charge carriers in this system should be described by the massless Dirac equation rather than the usual Schrodinger equation. However, we should stress that such a continuum approximation remains valid up to wave vectors of the order of the inverse lattice spacing. Under this approximation we can describe our charge carriers by a gauge invariant Dirac Hamiltonian in $2+1$ space-time dimensions with minimal coupling to the three-vector potential $A_{\mu } =(A_{0} ,\vec{A})$ $=(V,A_{x} ,A_{y} )$ as follows
\begin{equation} \label{GrindEQ1}
H=m\gamma _{0} +V+\gamma _{0} \vec{\gamma }\cdot (i\vec{\nabla }+\vec{A})
\end{equation}
where $\gamma _{0} =\sigma _{3} $, $\vec{\gamma }=(\gamma _{x} ,\gamma _{y} )=i(\sigma _{1} ,\sigma _{2} )$ and $\left\{\sigma _{i} \right\}_{i=1}^{3} $ are the 2$\times$2 Pauli matrices. Adopting the conventional relativistic units $\hbar =c=1$, we obtain \cite{15}
\begin{equation} \label{GrindEQ2}
H=\left(\begin{array}{cc} {m+V} & {-\frac{\partial }{\partial x} +i\frac{\partial }{\partial y} +iA_{x} +A_{y} } \\
{\frac{\partial }{\partial x} +i\frac{\partial }{\partial y} -iA_{x} +A_{y} } & {-m+V}
\end{array}\right).
\end{equation}

As we claimed before, for a system made of graphene the charge carriers are massless ${m} = 0$ and  moving with the Fermi velocity $v_{\sf F}$
(about $10^6 m/s$). Moreover, we specialize to a physical configuration corresponding to a single graphene sheet in a magnetic field with vector potential
$\vec{A}=\hat{y} W(x)$. Thus, the associated stationary Dirac equation becomes
\begin{equation} \label{GrindEQ3}
\left(\begin{array}{cc} {-\varepsilon } & {-\frac{\partial }{\partial x} +{\rm i}\frac{\partial }{\partial y} +W} \\ {\frac{\partial }{\partial x} +{\rm i}\frac{\partial }{\partial y} +W} & {-\varepsilon } \end{array}\right)\left(\begin{array}{c} {\mathop{\psi ^{+} }\limits^{} } \\ {} \\ {\mathop{\psi ^{-} }\limits_{} } \end{array}\right)=0.
\end{equation}
We can separate variables and write
\beq
\psi ^{\pm } (x,y)=\varphi ^{\pm } (x)\chi (y)
\eeq
 where $\chi (y)=e^{-{\rm i}{\kern 1pt} ky} $ and \textit{k} is a real parameter that stands for the wave number of the excitations along the \textit{y}-axis. The resulting reduced equation is given by
\begin{equation} \label{GrindEQ4}
\left(\begin{array}{cc} {-\varepsilon } & {-\frac{d}{dx} +W+k} \\ {\frac{d}{dx} +W+k} & {-\varepsilon } \end{array}\right)\left(\begin{array}{c} {\varphi ^{+} } \\ {} \\ {\varphi ^{-} } \end{array}\right)=0.
\end{equation}
In the present representation $W$ plays the role of a pseudoscalar potential coupling. The above equation is equivalent to the following set of equations
\begin{eqnarray}
&&\varphi ^{\mp } =\frac{1}{\varepsilon } \left(\pm \frac{d}{dx} +W+k\right)\varphi ^{\pm }\label{GrindEQ5}\\
&&\left[-\frac{d^{2} }{dx^{2} } +W^{2} \mp \frac{dW}{dx} +2kW+k^{2} -\varepsilon ^{2} \right]\varphi ^{\pm } =0.\label{GrindEQ6}
\end{eqnarray}
The structure of the Schr\"odinger-like equation (\ref{GrindEQ6}) has the features associated with supersymmetric quantum mechanics
(SSQM) \cite{16}. The two potential partners in SSQM are ${\rm {\mathcal V}}^{2} \pm {\rm {\mathcal V}}'$, where ${\rm {\mathcal V}}$
is the superpotential
 and in our case we have ${\rm {\mathcal V}}=W+k$. The relativistic extension of SSQM exhibited in some models that are governed by the Dirac theory is due to the fact that the associated Dirac Hamiltonian is an element of the 4-dimensional superalgebra $U(1/1)$, which is a $Z_{2} $ graded extension of $SO(2,1)$ Lie algebra \cite{17}. It is interesting to note that the corresponding massive (1+1) Dirac equation
\begin{equation} \label{GrindEQ7}
\left(\begin{array}{cc} {m-\varepsilon } & {-\frac{d}{dx} +W} \\ {\frac{d}{dx} +W} & {-m-\varepsilon } \end{array}\right)\left(\begin{array}{c} {\varphi ^{+} } \\ {} \\ {\varphi ^{-} } \end{array}\right)=0
\end{equation}
results in the following Schr\"odinger-like equation
\begin{equation} \label{GrindEQ8}
\left[-\frac{d^{2} }{dx^{2} } +W^{2} \mp \frac{dW}{dx} +m^{2} -\varepsilon ^{2} \right]\varphi ^{\pm } =0
\end{equation}
which has the same structure associated with SSQM as in (\ref{GrindEQ6}) with
the mapping $W\to W+k$. Therefore, the solution of the two problems are similar with $k$ playing the role of the mass $m$. We have encountered this phenomenon before, where space reduction (due to compactification or symmetry) transforms  the 2D massless problem into an effective 1D massive problem \cite{18}. Note that the complete solution space of the Dirac equation (\ref{GrindEQ4}) is the union of the two solution subspaces of equations (\ref{GrindEQ5}) and (\ref{GrindEQ6})
with the top and bottom signs, respectively. Below, we identify the energy regions associated with each subspace.

\section{Dirac Fermions in a $\delta$-type magnetic field}

Here we consider the zero range and infinite strength limit where
the magnetic field takes the form $\vec{B}(x)=\hat{z} B_{0} \delta ({x\mathord{\left/ {\vphantom {x a}} \right. \kern-\nulldelimiterspace} a} )$, with \textit{a} is a length scale parameter. The main advantage of this configuration  is that it is amenable to analytical treatment
and interesting results. Thus,
the single-step pseudoscalar potential is given by
\beq
W(x)=a B_{0} \Theta ({x\mathord{\left/ {\vphantom {x a}} \right. \kern-\nulldelimiterspace} a} )
\eeq
 where $\Theta (x)$ being the Heaviside step function, such as
\begin{equation} \label{GrindEQ9}
\Theta (x)=\left\{\begin{array}{cc} {1}, & \qquad {x>0} \\ {0}, & \qquad {x<0} \end{array}\right.
\end{equation}
Figure 1 shows the schematics of a laboratory set-up where a coil of a rectangular cross section with very narrow width will result in the necessary current sheet that should produce a magnetic field approximating that of our problem. The graphene ribbon is the strip that penetrates the coil along the \textit{x}-axis in the figure:

\begin{center}
  \includegraphics[width=4in]{figure2}
\end{center}
{\sf{Fig. 1:} \sf{Schematic of a set-up where a coil of a rectangular cross section with very narrow width produces a magnetic field approximating that of our problem.}}\\

To study the scattering behavior in the present problem, we first determine the plane wave solutions associated with both regions, $\pm x>0$. The two components of the wavefunction satisfying equations (\ref{GrindEQ5}) and  (\ref{GrindEQ6}) with the top sign are
given by
\bqr
\varphi ^{-} =\frac{1}{\varepsilon } \left(-\frac{d}{dx} +\omega _{\pm } \right)\varphi ^{+}           \lb{5p}\\
\left[-\frac{d^{2} }{dx^{2} } +\omega _{\pm }^{2} -\varepsilon ^{2} \right]\varphi ^{+} =0         \lb{6p}
\eqr
with $\omega _{+} =aB_{0} +k$ and $\omega _{-} =k$. It is easy to show that the solution of these equations
reads
\begin{equation} \label{GrindEQ10}
\varphi (x)=A\left(\begin{array}{c} {1} \\ {\alpha _{\pm } } \end{array}\right)e^{\kappa _{\pm } x} +B\left(\begin{array}{c} {1} \\ {\beta _{\pm } } \end{array}\right)e^{-\kappa _{\pm } x}
\end{equation}
  where the parameters read as
  \beq
  \kappa _{\pm } =\sqrt{\omega _{\pm }^{2} -\varepsilon ^{2} }, \qquad \alpha _{\pm } ={\left(\omega _{\pm } -\kappa _{\pm } \right)\mathord{\left/ {\vphantom {\left(\omega _{\pm } -\kappa _{\pm } \right) \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }, \qquad \beta _{\pm } ={\left(\omega _{\pm } +\kappa _{\pm } \right)\mathord{\left/ {\vphantom {\left(\omega _{\pm } +\kappa _{\pm } \right) \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }.
  \eeq
  On the other hand, considering the lower sign in equations (\ref{GrindEQ5}) and  (\ref{GrindEQ6}) for $\pm x>0$ we obtain
\bqr
 \varphi ^{+} =\frac{1}{\varepsilon } \left(+\frac{d}{dx} +\omega _{\pm } \right)\varphi ^{-}           \lb{GrindEQ5pp}\\
\left[-\frac{d^{2} }{dx^{2} } +\omega _{\pm }^{2} -\varepsilon ^{2} \right]\varphi ^{-} =0        \lb{GrindEQ6pp}
\eqr
which can be solved to give
\begin{equation} \label{GrindEQ101}
\varphi (x)=A\left(\begin{array}{c} {\beta _{\pm } } \\ {1} \end{array}\right)e^{\kappa _{\pm } x} +B\left(\begin{array}{c} {\alpha _{\pm } } \\ {1} \end{array}\right)e^{-\kappa _{\pm } x}.
\end{equation}
In summary, the oscillatory solutions (for both cases and for $\pm x>0$) are obtained for all $\left|\varepsilon \right|>\left|\omega _{\pm }\right| $ while evanescent wave solutions will result if $\left|\varepsilon \right|<\left|\omega _{\pm }\right| $. Thus the quantity $\left|\omega _{\pm }\right|$ plays the role of an effective mass with different asymptotic values at $\pm x>0$. That is, our massless problem is equivalent to a space dependent massive problem whose effective mass depends on both the sign and strength of the localized magnetic field and the value of component of the wave number along the $y$-direction.

We need to reassert that the total solution space of the problem is the union of the two solution subspaces (\ref{GrindEQ5}) and (\ref{GrindEQ6}). These two solution subspaces are not identical and their union constitutes the whole space of solution of our problem. To resolve the issue of which energy domain is selected by which kinetic balance relation (\ref{5p}) or (\ref{GrindEQ5pp}), we perform a unitary transformation on the fundamental Dirac equation (\ref{GrindEQ4}). Such a transformation does not affect the energy spectrum or the physics of the problem. We choose a rotation by ${\pi \mathord{\left/ {\vphantom {\pi  4}} \right. \kern-\nulldelimiterspace} 4} $ about the $y$-axis, $U=e^{i{\textstyle\frac{\pi }{4}} \sigma _{2} } $. Thus, the transformed Hamiltonian and wavefunction
read
\begin{eqnarray} \label{GrindEQ12}
\tilde{H}&=&UHU^{\dag } =-i\sigma _{2} \frac{d}{dx} +(W+k)\sigma _{3}\\
  \tilde{\varphi }&=&U\varphi \nonumber
\end{eqnarray}
 then (\ref{GrindEQ4}) becomes
\begin{equation} \label{GrindEQ13}
\left(\tilde{H}-\varepsilon {\mathbb I}\right)\tilde{\varphi }=\left[-i\sigma _{2} \frac{d}{dx} +(W+k)\sigma _{3} -\varepsilon {\mathbb I}\right]\tilde{\varphi }
\end{equation}
 leading to the following new kinetic balance relation
\begin{equation} \label{GrindEQ14}
\tilde{\varphi }^{\mp } =\frac{\mp 1}{\varepsilon \pm (W+k)} \frac{d}{dx} \tilde{\varphi }^{\pm }
\end{equation}
which is not valid for
\beq
\varepsilon =\mp \left(aB_0+k\right)=\mp \om_+.
\eeq
Thus, in the case when $aB_0$ is a positive constant, this relation with the top/bottom sign corresponds to the positive/negative energy subspace\footnote{ If $k$ is taken negative in equation (4), then equation (14) with the top/bottom sign corresponds to negative/positive energy subspace if W+k becomes negative.}. Now, since equation (\ref{GrindEQ13}) results from a unitary transformations of (\ref{5p}) and (\ref{GrindEQ5pp}), then the same applies to those equations as well. That is, equations (\ref{5p}) and  (\ref{GrindEQ5pp}) are valid for positive and negative energy, respectively. Figure 2 shows the potential configuration of the problem. Dark/light grey areas correspond to negative/positive energy continuum where the solution is oscillatory of the form $e^{\pm i\kappa x} $. The white areas correspond to bound states where the solutions are exponentials, $e^{\pm \kappa x} $. In the subsequent developments, we will only be considering scattering solutions with a normalized incident beam from left. Thus, the relativistic energy must be $\varepsilon >\left|k\right|$ and the solution space is built only from the positive energy solutions (\ref{GrindEQ10}).

\begin{center}
  \includegraphics[width=2.8in]{figg}
\end{center}
{\sf{Fig. 2:}  \sf{The potential configuration of the problem. Dark/light grey areas correspond to negative/positive energy continuum. The white areas correspond to bound states where the solutions are exponentials.}}\\

The total solution space splits into two regions depending on the energy range as follows. For $k<\varepsilon <\omega _{+} $, scattering with total reflection will take place. It should be noted that there is no Klein tunneling in this problem due to the absence of vector interaction. With a normalized incident flux from left, the solution of equation (\ref{GrindEQ4}) is obtained from (\ref{GrindEQ10}) as
\bqr
\varphi (x)=\left\{\begin{array}{cc} {\left(_{\alpha }^{\, 1} \right)e^{i\kappa x} +R\left(_{\alpha ^{*} }^{\, \, 1} \right)e^{-i\kappa x} }, & \qquad {x<0} \\ {A\left(_{\beta _{+} }^{\, \, 1} \right)e^{-\kappa _{+} x} }, & \qquad {x>0} \end{array}\right.
\eqr
where $\kappa =\left|\kappa _{-} \right|=\sqrt{\varepsilon ^{2} -k^{2} } $ and $\alpha ={(k-i\kappa )/\varepsilon }$.
Continuity of the wavefunction at \textit{x} = 0 gives the reflection amplitude
\begin{equation}\lb{RRT}
R=-\frac{\beta _{+} -\alpha }{\beta _{+} -\alpha ^{*} } =-\frac{aB_{0} +\kappa _{+} +i\kappa}{aB_{0} +\kappa _{+} -i\kappa}
\end{equation}
and the normalization parameter $A=1+R$. It is clear that we have complete reflection in this case since $\left|R\right|=1$. It is also worth mentioning that the probability density in the positive $x$-direction is given by
\beq
\rho (x) = |A|^2 e^{-2 |\kappa _{+ }| x}(1+|\beta _{+ }|^2)\lb{ro}
\eeq
which shows that the penetration depth, $\lambda$, of the Fermion into the barrier region defined by
\beq
\lambda = \frac{1}{2|\kappa _{+ }|^2}=\frac{1}{2\sqrt{(aB_0+k)^2-\epsilon^2}}
\eeq
decreases very rapidly with increase in the magnetic field strength. This result indicates the possibility to confine the fermions in any region between two
$\del$-like magnetic fields generated by a symmetric double step pseudoscalar potential, this situation will be treated in section 5.

Now, let us move on to analyze the scattering situation when $\varepsilon >\omega _{+} $ so that partial reflection will take place. Again, with a normalized incident wave from left, the solution of  (\ref{GrindEQ4}) is obtained from (\ref{GrindEQ10}) as
\bqr
\varphi (x)=\left\{\begin{array}{cc} {\left(_{\alpha }^{\, 1} \right)e^{i\kappa x} +R\left(_{\alpha ^{*} }^{\, \, 1} \right)e^{-i\kappa x} }, & \qquad {x<0} \\ {T\left(_{\beta }^{\, 1} \right)e^{i\gamma x} }, & \qquad {x>0} \end{array}\right.
\eqr
where $\gamma =\left|\kappa _{+} \right|=\sqrt{\varepsilon ^{2} -\omega _{+}^{2} } $ and $\beta ={\left(\omega _{+} -i\gamma \right)\mathord{\left/ {\vphantom {\left(\omega _{+} -i\gamma \right) \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon } $. Again matching the spinor wavefunctions
 at \textit{x} = 0 gives the reflection and transmission amplitudes
\beq
R=-\frac{\alpha -\beta }{\alpha ^{*} -\beta }, \qquad T=\frac{{2i\kappa \mathord{\left/ {\vphantom {2i\kappa  \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon } }{\alpha ^{*} -\beta } \lb{rtt}.
\eeq
One can verify the flux conservation relation
\beq
\left|R\right|^{2} +\left|{\gamma \mathord{\left/ {\vphantom {\gamma  \kappa }} \right. \kern-\nulldelimiterspace} \kappa } \right|\left|T\right|^{2} =1.
\eeq
Figure 3 is a plot of the reflection and transmission coefficients as a function of the
energy for several values of the magnetic field strength $B_{0} $.\\

\begin{center}
  \includegraphics[width=4in]{conservation}
 \end{center}
  {\sf{Fig. 3:  \sf{Reflection and transmission amplitudes as a function of energy for $B_{0}=0.5, 1.0, 2.0, 3.0, 5.0$ in units of $a^{-2}$ (left to right curves) and $k=0.5$. We defined $\mathbf{\mathrm{T}}(\varepsilon)=T(\varepsilon)\sqrt{\gamma/\kappa}$.}}}\\

\noindent It is also worthwhile to study the transmission coefficient as a function of the magnetic field strength $B_{0} $. For this purpose we can write explicitly $|T|$, in this regime, as follows
\beq
|T| = 2\sqrt{\frac{\va^2 -k^2} {(aB_0)^2 + \left( \sqrt{\va^2 -k^2} +\sqrt{\va^2 - (aB_0+k)^2}\right)^2}}
\eeq
which shows clearly that the transmission is unity at $B_0=0$ and reduces to zero for strong field.
Figure 4 shows the behavior of the transmission and reflection coefficients as a function of the applied magnetic field. We would like to note that the transmission vanishes for energies below the critical energy value of $\varepsilon^{\ast}=B_{0}+k$, as shown in figure 3. A similar remark can be made regarding figure 4.

\begin{center}
  \includegraphics[width=3.5in]{TRfunctionB0}
 \end{center}
{\sf{Fig. 4:  {Reflection and transmission amplitudes as a function of strength of the field for $\varepsilon=3, 4, 8$ in units of $a^{-2}$ (left to right curves) and $k=2$.}}}

\section{Dirac fermions in a Gaussian magnetic field}

We consider a magnetic field normal to the graphene sheet of a bell shape. Specifically,
we take $\vec{B}(x)=\hat{z}B_{0}\sech^{2}(\mu x)$ (Fig. 5)~\cite{kuru,milpas}, where $B_{0} $ is the strength of the field and $\mu ^{-1} $ stands for its range. The corresponding vector potential (Fig. 5) is
\beq
\vec{A}(x)=\hat{y}W(x)= \hat{y} \left(B_{0} /\mu \right)\ \tanh (\mu x)
\eeq
 which  turns equation (\ref{GrindEQ6}) into
\begin{equation}
 \left[-\frac{d^{2} }{dx^{2} } \mp B_{0} \left(1-\tanh^{2} \mu x\right) +\left(\frac{B_{0} }{\mu } \tanh \mu x+k\right)^{2}-\varepsilon ^{2} \right]\varphi ^{\pm } =0.   \lb{A1}
\end{equation}
Note that as $x\to \pm \infty $, this equation reduces to a simple form
\beq
\left(-\frac{d^{2} }{dx^{2} } +\omega _{\pm }^{2} -\varepsilon ^{2} \right)\varphi ^{\pm } =0
\eeq
 where $\omega _{\pm } =k\pm B_{0} /\mu $. This equation is similar to that of a massive 1D problem with asymptotic masses $m=\left|\omega _{\pm } \right|$ at $x\to \pm \infty $. The solution space of  (\ref{A1}) splits into three regions depending on the sign of $kB_{0} $ and the energy range. If $kB_{0} >0$, then $\left|\omega _{-} \right|<\left|\omega _{+} \right|$
 and these energy regions can be defined as follows
\begin{itemize}
     \item  $\left|\varepsilon \right|<\left|\omega _{-} \right|$: Bound states with the boundary condition $\mathop{\lim }\limits_{x\to \pm \infty } \varphi (x)=0$.

     \item  $\left|\omega _{-} \right|<\left|\varepsilon \right|<\left|\omega _{+} \right|$: Scattering with total reflection to the negative \textit{x}-axis (note that there is no Klein tunneling in this problem due to the absence of vector interaction). The boundary conditions in this case are: $\mathop{\lim }\limits_{x\to +\infty } \varphi (x)=0$, $\mathop{\lim }\limits_{x\to -\infty } \varphi (x)=e^{{\rm i}{\kern 1pt} \kappa _{-} x} \left(_{\rho _{-} }^{{\kern 1pt} {\kern 1pt} {\kern 1pt} 1} \right)+{\rm {\mathcal R}}e^{-{\rm i}{\kern 1pt} \kappa _{-} x} \left(_{\rho _{-}^{*} }^{{\kern 1pt} {\kern 1pt} 1} \right)$, where $\kappa _{\pm } =\sqrt{\varepsilon ^{2} -\omega _{\pm }^{2} } $, $\rho _{\pm } =\frac{1}{\varepsilon } \left(\omega _{\pm } -{\rm i}{\kern 1pt} \kappa _{\pm } \right)$ and the reflection amplitude is such that $\left|{\rm {\mathcal R}}\right|=1$.

     \item  $\left|\varepsilon \right|>\left|\omega _{+} \right|$: Scattering solutions occur with the boundary conditions: $\mathop{\lim }\limits_{x\to +\infty } \varphi (x)=$ ${\rm {\mathcal T}}e^{{\rm i}{\kern 1pt} \kappa _{+} x} \left(_{\rho _{+} }^{{\kern 1pt} {\kern 1pt} {\kern 1pt} 1} \right)$, $\mathop{\lim }\limits_{x\to -\infty } \varphi (x)=e^{{\rm i}{\kern 1pt} \kappa _{-} x} \left(_{\rho _{-} }^{{\kern 1pt} {\kern 1pt} {\kern 1pt} 1} \right)+{\rm {\mathcal R}}e^{-{\rm i}{\kern 1pt} \kappa _{-} x} \left(_{\rho _{-}^{*} }^{{\kern 1pt} {\kern 1pt} 1} \right)$, where is
         ${\rm {\mathcal T}}$ the transmission amplitude such that $\left|{\rm {\mathcal R}}\right|^{2} +\left|\rho _{+} /\rho _{-} \right|\left|{\rm {\mathcal T}}\right|^{2} =1$. However, if $kB_{0} <0$, then $\left|\omega _{-} \right|>\left|\omega _{+} \right|$ and the above subspaces should be interchanged with $\omega _{+} \leftrightarrow \omega _{-} $ and $x\to -x$.\\
\end{itemize}

\begin{center}
 \includegraphics[width=2in]{Potenial2}
  \includegraphics[width=2in]{Potenial}
  \includegraphics[width=2in]{Poteniall}
  \end{center}
{\sf Fig. 5}:  {\sf{Hyperbolic tangent pseudoscalar potential profile along with the associated magnetic field for the strength $B_{0}=2$.}}\\

 To be more specific, let us  consider the scattering problem in the negative $x$ regions, $x<0$. Making the change of variable $z=-e^{2\mu x}$, equation (\ref{A1}) becomes
\begin{equation}
 \left[4 k^{2} z \frac{d}{dz}\left(z\frac{d}{dz}\right)\mp B_{0} \frac{4 z}{(1-z)^{2}} -\left(-\frac{B_{0} }{\mu } \frac{1+z}{1-z}+k\right)^{2}+\varepsilon ^{2} \right]\varphi ^{\pm} =0.\lb{AA}
\end{equation}
Now, we  solve (\ref{AA}) for $\varphi ^{+}$ and then deduce $\varphi ^{-}$ using (\ref{GrindEQ5}).
The general solution of (\ref{AA}) can be expressed in terms of the hypergeometric functions~\cite{hf} as follows
\begin{eqnarray}
\varphi ^{+} &=&A z^{h'} (1-z)^{\lambda} {F}\left(h'-\nu+\lambda,h'+\nu+\lambda,1+2h;z\right)\nonumber\\
 &+&B z^{-h'} (1-z)^{\lambda}
{F}\left(-h'-\nu+\lambda,-h'+\nu+\lambda,1-2h';z\right)\lb{so}
\end{eqnarray}
where we have set
$h'=\frac{\sqrt{\omega_{-}^{2}-\varepsilon^{2}}}{2k}$, $\nu=\frac{\sqrt{\omega_{+}^{2}-\varepsilon^{2}}}{2k}$ and $\lambda=\frac{1}{2}-\frac{\sqrt{k^{2}+4B_{0}+4(\frac{B_{0}}{\mu}})^{2}}{2k}$. To study the scattering problem we need to investigate the
asymptotic behavior of (\ref{so}) when $x\rightarrow-\infty$, which corresponds to $z\rightarrow 0$. Using
 the asymptotic behavior of the hypergeometric functions we obtain for $\varphi ^{+}$
\begin{equation}
\mathop{\lim }\limits_{x\to - \infty }\varphi ^{+}=A e^{ik_{-} x}+B e^{-ik_{-} x} \lb{s}
\end{equation}
with $k_{-}=2i\mu \left|h'\right|$. From $(\ref{GrindEQ5})$ the other component, $\varphi ^{-}$, is  given by
\begin{equation}
\varphi ^{-} =\frac{1}{\varepsilon } \left(\frac{d}{dx} +\frac{B_{0}}{\mu}+k\right)\varphi ^{+} .\lb{f}
\end{equation}
Substituting equation $(\ref{s})$ in $(\ref{f})$ gives the asymptotic behavior of $\varphi ^{-}$
\begin{equation}
\mathop{\lim }\limits_{x\to - \infty }\varphi ^{-}=A \eta_{+} e^{ik_{-} x}+B \eta_{-} e^{-ik_{-} x} \lb{}
\end{equation}
where $\eta_{\pm}=\frac{\omega_{+}\pm 2\mu h'}{\varepsilon}$.

Next, we consider the solution of equation $(\ref{A1})$ for $x>0$. The analysis of the solution can be simplified by making the substitution $z=-e^{-2\mu x}$. Equation $(\ref{A1})$ becomes
\begin{equation}
 \left[4 k^{2} z \frac{d}{dz}\left(z\frac{d}{dz}\right)\mp B_{0} \frac{4 z}{(1-z)^{2}} -\left(\frac{B_{0} }{\mu } \frac{1+z}{1-z}+k\right)^{2}+\varepsilon ^{2} \right]\varphi ^{\pm} =0.\lb{Ab}
\end{equation}
The general solution to the above is
\begin{eqnarray}
\varphi ^{+} &=& C z^{h} (1-z)^{\lambda} {F}\left(h-\nu+\lambda,h+\nu+\lambda,1+2h;z\right)\nonumber\\
&+& D z^{-h} (1-z)^{\lambda}
{F} \left(-h-\nu+\lambda,-h+\nu+\lambda,1-2h;z\right)\lb{}
\end{eqnarray}
where
$h=\frac{\sqrt{\omega_{+}^{2}-\varepsilon^{2}}}{2k}$, $\nu=\frac{\sqrt{\omega_{-}^{2}-\varepsilon^{2}}}{2k}$ and $\lambda=\frac{1}{2}-\frac{\sqrt{k^{2}+4B_{0}+4(\frac{B_{0}}{\mu}})^{2}}{2k}$.

Also as $x\rightarrow-\infty$, $z\rightarrow 0$. Therefore in order to have a plane wave traveling to the right as $x\rightarrow \infty$, we require that $\left|\varepsilon \right|>\left|\omega _{+} \right|$ and $C=0$ so that as $x\rightarrow\infty$ we have
\begin{equation}
\varphi ^{+} =D z^{-h} (1-z)^{\lambda} {F} \left(-h-\nu+\lambda,-h+\nu+\lambda,1-2h;z\right)\lb{}
\end{equation}
and the limit
\begin{equation}
\mathop{\lim }\limits_{x\to + \infty }\varphi ^{+}=D e^{ik_{+} x} \lb{ss}
\end{equation}
with $k_{+}=2i\mu  \left|h\right|$. The other component is
\begin{equation}
\mathop{\lim }\limits_{x\to + \infty }\varphi ^{-}=D \beta e^{ik_{+} h x} \lb{sss}
\end{equation}
where $\beta=\frac{2\mu h+\omega_{+}}{\varepsilon}$.

For one-dimensional scattering problems, the particles in the beam are in plane wave states with definite momentum.
Given the wave functions relevant to incident, reflected and transmitted beams, one may calculate the corresponding
current densities~\cite{DH}. The reflection and transmission coefficients are defined to be the ratio of the reflected current
density $j^{\sf re}$ to the incident current density $j^{\sf in}$ and transmitted current density $j^{\sf tr}$ to the incident current
density, respectively, leading to
\begin{equation}\label{RT}
R=\frac{\left|j^{\sf re}\right|}{\left|j^{\sf in}\right|}=
\frac{\left|\eta_{-}-\eta_{-}^{\ast}\right|}{\left|\eta_{+}-\eta_{+}^{\ast}\right|}\left|r\right|^{2},\\ \qquad
T=\frac{\left|j^{\sf tr}\right|}{\left|j^{\sf in}\right|}=
\frac{\left|\beta-\beta^{\ast}\right|}{\left|\eta_{+}-\eta_{+}^{\ast}\right|}\left|r\right|^{2}
\end{equation}
where the conservation law $R+T=1$ is obeyed.\\
\begin{center}
  \includegraphics[width=2.5in]{plot}
   \includegraphics[width=2.5in]{plott}\\
{\sf Fig. 6}:  \sf{Transmission as a function of energy with $k=1$,  $B_{0} = 2$ and (a) $\mu=3$, (b) $\mu=1000$.}
\end{center}

\noindent We notice that for the Hyperbolic tangent magnetic field  (figure 5), figure 6 show clearly that for the value of $\mu=1000$ we obtain the same result for the transmission and reflection coefficients as those generated in section 3 for a single step pseudoscalar potential.

We can also characterize the transmission amplitude by giving the
corresponding phase shifts $\delta$. Indeed, in the case of $\left|\omega _{-} \right|<\left|\varepsilon \right|<\left|\omega _{+} \right|$
one obtains
\begin{equation}\label{psh}
t=\left|t\right|e^{i\delta}.
\end{equation}
The calculations lead to the scattering phase shift in the form
\beq
\delta=\arctan\left(\frac{h}{h''}\right), \qquad h''=\frac{\sqrt{\varepsilon^{2}-\omega_{-}^{2}}}{2k}.
\eeq
A complementary information about the phase shift can be obtained by studying the trajectories in the complex
transmission amplitude plane where full reflections will appear whenever these trajectories pass through the origin.

\section{Dirac fermions in a double $\delta$-type magnetic field }

Motivated by the above analysis, let us investigate the scattering of Dirac fermions in a double $\delta$-type magnetic field. This can be described by
the double-step pseudoscalar potential
\beq \lb{double}
W(x)=B_1\left[1-\Theta(x+a)\right]+B_2\Theta(x-a)
\eeq
presented in figure 7  with $a$ defined to be positive real number.
This pseudoscalar double step potential generates a magnetic field $B = B_1 \delta(x+a) + B_2 \delta(x-a)$, $B_1$ and $B_2$ are the strengths of the  $\delta$-type magnetic fields
at $x = -a$ and $x = +a$, respectively.\\
\begin{center}
  \includegraphics[width=3in]{double}\\
{\sf Fig. 7}:  \sf{Double-step pseudoscalar potential.}
\end{center}

Using (\ref{double}), we show that the general solutions of the Dirac equation (\ref{GrindEQ6}) for the case of $\left|\varepsilon \right|>\left|\omega _{+} \right|$ can be written as
\begin{eqnarray}\label{41}
\begin{array}{l}
\ \ \ \ {\varphi (x<-a)=\left\{\begin{array}{cc} {A_-}e^{{\rm i}\, \kappa _{-} x} \left(_{\alpha _{-} }^{1} \right)+B_-e^{-{\rm i}\, \kappa _{-} x} \left(_{\alpha _{-}^{*} }^{1} \right), & \qquad \qquad \qquad \varepsilon <\omega _{+}  \\
A_+e^{{\rm i}\, \kappa _{-} x} \left(_{1}^{\alpha _{-}^{*} } \right)+{B_+}e^{-{\rm i}\, \kappa _{-} x} \left(_{\; 1}^{\, \alpha _{-} } \right), &
\qquad \qquad \qquad \ \   \varepsilon >-\omega _{+}
\end{array}\right. } \\
\ \ \ \ {\varphi (\left|x\right|<a)=\left\{\begin{array}{cc} {C_-}e^{{\rm i}\, k _{2} x} \left(_{\gamma _{+} }^{1} \right)+D_-e^{-{\rm i}\, k _{2} x} \left(_{\gamma _{+}^{*} }^{1} \right), & \qquad \qquad\qquad \ \   \varepsilon <\omega _{+}  \\
{C_+}e^{{\rm i}\, k _{2} x} \left(_{1}^{\gamma _{+}^* } \right)+{D_+}e^{-{\rm i}\, k _{2} x} \left(_{1}^{\gamma _{+} } \right), &
 \qquad\qquad\qquad \ \  \ \ \  \varepsilon >-\omega _{+}  \end{array}\right.}  \\
 \ \ \ \ \ \ {\varphi (x>a)=\left\{\begin{array}{cc} {E_-}e^{{\rm i}\, \kappa _{+} x} \left(_{\beta _{+} }^{1} \right)+F_-e^{-{\rm i}\, \kappa _{+} x} \left(_{\beta _{+}^{*} }^{1} \right), & \qquad \qquad\qquad \  \varepsilon <\omega _{+}  \\
 {E_+}e^{{\rm i}\, \kappa _{+} x} \left(_{1}^{\beta _{+}^* } \right)+{F_+}e^{-{\rm i}\, \kappa _{+} x} \left(_{1}^{\beta _{+} } \right), &
 \qquad\qquad\qquad \ \ \ \varepsilon >-\omega _{+}  \end{array}\right.}  \end{array}
 \end{eqnarray}
where

 $\gamma _{+}=(ik_{2}-k)/\varepsilon$,  $\kappa_\pm=\sqrt{\varepsilon^2-\omega _{\pm}^2}$, $k_2=\sqrt{\varepsilon^2-k^2}$, $\omega _{+}=B_{2}+k$ and $\omega _{-}=B_{1}+k$. These wavefunctions will be used to study the scattering and the bound states for the present case.

 The continuity of the wavefunction at $x=\pm a$ gives the reflection amplitudes $r_\mp=B_{\mp}/A_{\mp}$ and the transmission amplitudes $t_\mp=E_{\mp}/A_{\mp}$ for the negative (top sign) and positive (bottom sign) energy solutions. More precisely, we find
\begin{eqnarray}
 t_{\mp}&=&\frac{4e^{-ia(-2k_{2}+\kappa_-+\kappa_+)}\kappa_-k_{2}}{e^{4iak_{2}}(\kappa_- -k_{2}\mp iB_{1})(k_{2}-\kappa_+ \mp iB_{2})
 +(\kappa_- +k_{2}\mp iB_{1})(k_{2}+\kappa_+ \pm iB_{2})}\label{tt}\\
r_{\mp}&=&\frac{e^{-2ia\kappa_-}\left[e^{4iak_{2}}(\kappa_- +k_{2}\mp iB_{1})(k_{2}-\kappa_+ \mp iB_{2})+(\kappa_- -k_{2}
\pm iB_{1})(k_{2}+\kappa_+ \pm iB_{2})\right]}{e^{4iak_{2}}(\kappa_- -k_{2}\mp iB_{1})(k_{2}-\kappa_+ \mp iB_{2})
 +(\kappa_- +k_{2}\mp iB_{1})(k_{2}+\kappa_+ \pm iB_{2})}.\label{rr}
\end{eqnarray}
The result of the passage to the limits, $B_{1}\rightarrow 0$ ($k_{2}\rightarrow\kappa_-$) and $a\rightarrow0$, in  (\ref{tt}) and (\ref{rr}) coincides with the transmission and reflection amplitudes in (\ref{rtt}) of the Dirac particle scattered by a pseudoscalar single step potential.  If we take the limit $a \rightarrow 0$ in the above equations we get, by replacing $\omega_+$ and $\omega_-$ by $\omega_+ = B_2-k$ and $\omega_- = B_1-k$, respectively, and $B_0$ by $B_1-B_2$, the transmission and reflection amplitude for the Dirac particle scattered by a double-step pseudoscalar potential    $W(x)$ (\ref{double}).
For the special case $B_2 = -B_1=0.002$ the transmission and reflection coefficients coincide with those obtained in the case of scattering of Dirac fermions by a single step pseudoscalar potential plotted in figure 6 (b).

Given the wavefunctions associated with the incident, reflected and transmitted beams, one may calculate
the corresponding current densities according to~\cite{DH}. Figure 8 illustrate the configuration of the solution
space of our problem. Dark/light grey areas correspond to negative/positive energy continuum where we have
evanescent or transmitted waves (EWs/TWs). The white areas correspond to the bound states (BS).
The reflection and transmission coefficients for the positive and negative energy solutions are
\begin{equation}\label{wx}
{R_{\mp}}=\left|r_{\mp}\right|^{2}, \qquad
{T_{\mp}}=\frac{\Re(\kappa_+)}{\Re(\kappa_-)}\left|t_{\mp}\right|^{2}.
\end{equation}
which obey the conservation relation
\beq
 \left|r_{\mp}\right|^{2} + \frac{\Re(\kappa_+)}{\Re(\kappa_-)}\left|t_{\mp}\right|^{2}=1.
\eeq
 Figures 9 and 10 show more clearly that, for the confinement by a double-step pseudoscalar potential, the EWs, TWs and BS always appear for the energy that $\left|\omega _{-} \right|<\left|\varepsilon \right|<\left|\omega _{+} \right|$ , $\left|\varepsilon \right|>\left|\omega _{+} \right|$ and $\left|\varepsilon \right|<\left|\omega _{-} \right|$, respectively. In figures 9 (a), (b) and 10 (b) the transmission resonances appear for $B_1$ and $B_2\neq0$. From figure 10 (a) one readily notice that, for the value of $B_2=0$, the double-step pseudoscalar potential reduces to a one step with $W(x)=B_1(1-\Theta(x))$. We can easily find the EWs, TWs and BS for this later representation by replacement the $\omega_+$ and $\omega_-$ by $\omega_+=k$ and $\omega_-=B_1-k$ respectively.
\begin{center}
  \includegraphics[width=2.6in]{confinement}
\end{center}
{\sf Fig. 8}:  {\sf{The potential configuration associated with the double step pseudoscalar potential. Dark/light grey areas correspond to negative/positive energy continuum. The white areas correspond to bound states where the solutions are exponentials.}}\\

\begin{center}
  \includegraphics[width=2.6in]{confinement2}
  \includegraphics[width=2.6in]{confinement3}
  \end{center}
{\sf Fig. 9}:  {\sf{Reflection and transmission coefficients as a function of energy for $B_{2}=-B_1=0.5, 2.0, 3.0, 5.0$ (left to right curves) with $k=1$. (a) for $a=1$ and (b) for $a=2$.}}\\

\begin{center}
  \includegraphics[width=2.6in]{confinement4}
  \includegraphics[width=2.6in]{confinement5}
  \end{center}
{\sf Fig. 10}:  {\sf{The transmission coefficient as a function of energy for $a=2$ and $k=1$. (a) for the Dirac particle scattered by a pseudo-scalar one step potential when $B_2=0$ and $B_{1}=-0.5, -2.0, -3.0, -5.0$ (left to right curves). (b) for our the case of $B_2=B_1=-0.5, -2.0, -3.0, -5.0$.}}\\

We wish to study the bound states of a double-step pseudoscalar potential for the case $\left|\varepsilon \right|<\left|\omega _{-} \right|$ and for $B_1=B_2$. From equation (\ref{41}) we must have $A_{-}=F_{-}=0$ in order to obtain normalizable wavefunction in the region $\left|x \right|>a/2$. We now have the full solution, given our assumption of particles incident from the left
\begin{eqnarray}\label{}
\varphi=
\left\{
  \begin{array}{ll}
    {B_-e^{{\rm }\, \kappa _{-} x} \left(_{\alpha _{-}}^{1} \right),
\qquad \qquad \qquad  \qquad \qquad  x<-a }, \\
    {{C_-}e^{{\rm i}\, k _{2} x} \left(_{\gamma _{+} }^{1} \right)+D_-e^{-{\rm i}\, k _{2} x} \left(_{\gamma _{+}^{*} }^{1} \right),
\qquad \ \ \left|x\right|<a }, \\
    {{E_-}e^{-{\rm }\, \kappa _{+} x} \left(_{\alpha _{-} }^{1} \right),
\qquad \qquad \qquad  \qquad \qquad   x>a }.
  \end{array}
\right.
\end{eqnarray}
This means that the solutions separate into even parity and odd parity states. We could have guessed this from the potential.
The even states $(C_-=D_-, B_-=E_-)$ have the (quantization) constraint on the energy that
\begin{equation}\label{cd}
\sqrt{1-\upsilon^{2}-\frac{ak}{\varepsilon}\upsilon}+\upsilon+\frac{ak}{\varepsilon}=\tan(\varepsilon)
\end{equation}
and the odd states $(C_-=-D_-, B_-=-E_-)$ have the constraint
\begin{equation}\label{dc}
\sqrt{1-\upsilon^{2}-\frac{ak}{\varepsilon}\upsilon}+\upsilon+\frac{ak}{\varepsilon}=-\cot(\varepsilon)
\end{equation}
where we have used $\upsilon=\frac{Ba}{2\varepsilon}$. These are transcendental equations, so we will solve them graphically. The plot in figure 11 shows the left hand side of the transcendental equation along with the tangent for even parity states and minus cotangent for odd parity states, respectively. The intersection of these curves gives the bound states. From  this figure we see that there are two bound states for even parity solution and two for odd parity solutions. The wider and deeper the step, the more bound states become available.
\begin{center}
  \includegraphics[width=3.5in]{BS}
\end{center}
{\sf Fig. 11}:  {\sf{The double-step pseudoscalar potential bound states for $k=1$ and $a=1$. The solid line represents $\tan(\varepsilon)$ and the dashed line represents $-\cot(\varepsilon)$. The dotted lines represent the left-hand side of equations (\ref{cd}) and (\ref{dc}).}}

\section{Conclusion}

We considered Dirac
fermions in graphene nanoribbon subject to a sharply localized magnetic field.
After setting the theoretical model we obtained the energy spectrum solutions
for a sharply localized $\delta$-type magnetic field. After matching the wavefunction at the point
$x=0$, the reflection and transmission amplitudes are derived in the standard way.
 A study of the transmission coefficient as a function
of the strength of field $B_0$ was done, the transmission is unity
for $B_0=0$ and reduces sharply for strong field.

The general case of a bell shape magnetic field normal to the graphene sheet, namely $\vec B(x)= \hat z B_0\sech^2(\mu x)$
was studied, $B_0$ being the strength of the field and $\mu^{-1}$ stands for its range. It was shown that the solution
space of the corresponding Hamiltonian splits into three regions depending on the sign of $kB_0$ and
the energy range, $k$ is the wave vector along the $y$-axis. To obtain the reflection and transmission coefficients
we used the current density, our results reduce to those obtained for $\delta$-type magnetic field
for large values of $\mu$, here we took $\mu=1000$. Moreover, the phase shift that characterizes the transmission amplitude is given in terms of the energy and magnetic field.

Subsequently, we considered the case of an asymmetric double step pseudoscalar potential of the form
$W(x)=B_1\left[1-\Theta(x+a)\right]+B_2\Theta(x-a)$. After obtaining the general solution of the Dirac equation,
we matched the wavefunction at the point $\pm a$ to obtain the reflection and transmissions amplitudes
for the negative and positive energy solutions. Different field configuration were considered
but the interesting situation obtains when  $B_2=-B_1= 0.002$ which enables us to recover
 the reflection and transmission
coefficients for scattering of Dirac fermions by a double step pseudoscalar potential. Moreover,
for the present potential we studied  the corresponding bound states using a graphical solution
of the transcendental equations. We reached the conclusion that there are at most two bound states for even
parity and two for old parity solutions.

Finally a double Gaussian type magnetic field was considered in appendix A where a second order
differential equation for spinor components was solved. The corresponding general solution was given in terms of
the HeunG functions. The asymptotic behavior as $x\rightarrow \pm \infty$ of these wavefunctions were studied and enable us to extract the corresponding reflection and transmission coefficients.

\section*{Acknowledgments}

The generous support provided by the Saudi Center for Theoretical Physics (SCTP)
is highly appreciated by all Authors. AJ and A.E. acknowledge partial support by King Faisal University and KACST, respectively. We also acknowledge the support of KFUPM under the theoretical physics research group project RG1108-1-2.

\section*{Appendix A: Dirac fermions in a double Gaussian type magnetic field}

We consider a magnetic field normal to the graphene sheet and of a Gaussian shape. Specifically, we take
$\vec{B}(x)=\hat{z}\left[B_1 \sech^{2}\left[\mu(x+a)\right] + B_2 \sech^{2}\left[\mu(x-a)\right]\right] $
(Fig. 12), with $B_{1}$ and $B_2$ are the strengths of the field. The corresponding vector potential (Fig. 12) is
\begin{equation}
 \vec {A}(x)=\hat{y}\left[\frac{B_1}{\mu}\left[\tanh \left[\mu(x+a)\right]-1\right]+ \frac{B_2}{\mu}
 \left[\tanh \left[\mu(x-a)\right]+1\right]\right].
 \tag{A1} \lb{pot}
\end{equation}
We note that the double delta magnetic field considered in  section 5 is obtained in the limit $\mu \gg 1$ in the present more general model.

By using the same change of variable as in section 4 for $\pm x>0$, equation (\ref{GrindEQ6}) can write in the following form
\beq
\left[4 \mu^{2} z \frac{d}{dz}\left(z\frac{d}{dz}\right) \mp
 \left({\frac {4B_{{1}}qz}{ \left( qz-1 \right) ^{2}}}+{\frac {
4B_{{2}}qz}{ \left( z-q \right) ^{2}}}\right)- \left( {\frac {2B_{{1}}}{\mu\,
 \left( qz-1 \right) }}+{\frac {2B_{{2}}z}{\mu\, \left( z-q \right) }}+
k \right) ^{2}+{\varepsilon}^{2} \right]\varphi ^{\pm } =0. \tag{A2}   \lb{qqqq}
\eeq
for $x<0$ with $q=e^{2a}$.\\

\begin{center}
  \includegraphics[width=1.6in]{A1}
  \includegraphics[width=1.6in]{A2}
  \includegraphics[width=1.6in]{A3}
  \includegraphics[width=1.6in]{A4}\\
  \includegraphics[width=1.6in]{Y1}
  \includegraphics[width=1.6in]{Y2}
  \includegraphics[width=1.6in]{Y3}
  \includegraphics[width=1.6in]{Y4}
  \end{center}
{\sf Fig. 12}:  {\sf{The pseudoscalar potential $W(x)$ and the associated double Gaussian type magnetic field $B(x)$ (\ref{pot}) for $\mu=1.5$ and $a=3$.}}\\

The general solution of (\ref{qqqq}) can be expressed in terms of the HeunG function~\cite{hf} as follows
\begin{align}
\varphi ^{+} &=A z^{l_{+}} (q-z)^{n_{+}}(-1+qz)^{m_{+}} {\mbox{HeunG}}
\left(p,b_{+},\alpha_{+},\beta_{+},\gamma_{+},\delta_{+};\frac{z}{q}\right) \tag{A3}\lb{os}\\
 &+B z^{-l_{+}} (q-z)^{n_{+}}(-1+qz)^{m_{+}}
{\mbox{HeunG}}\left(p,b_{1_{+}},\alpha_{1_{+}},\beta_{+},2-\gamma_{+},\delta_{+};\frac{z}{q}\right).\nonumber
\end{align}
where we have set
\begin{eqnarray}
&& l_{\pm} =(\gamma_{\pm}-1)/2, \qquad n_{\pm}=- \delta_{\pm}/2, \qquad m_{\pm}= \left(1+\frac{S_{4\pm}}{S_{3\pm}}\right)/2,\qquad p={q}^{-2}\nonumber\\
&&  \alpha_{\pm} = \left(S_{2\pm}+S_{3\pm}\right) {\mu}^{-2}/2
,\qquad \alpha_{1\pm} = \left( -4B_{{2(1)}}+2{\mu}^{2}-S_{2\pm}+S_{3\pm}\right) {\mu}^{-2}/2,\nonumber\\
&&  \gamma_{\pm} =1 +  \mu^{-2} \sqrt {{\mu}^{2}{k}^{2}-{\mu}^{2}{\epsilon}^{2}\mp 4\,B_{{1(2)}}k\mu+{4B_{{1(2)}}}^{2}}
,\qquad \delta_{\pm}=- 2\mu^{-2}B_{2(1)} \nonumber\\
&& \beta_{\pm} =
\left[S_{2\pm} S_{3\pm}+ {\mu}^{4}+ \left( -{
\epsilon}^{2}+{k}^{2}-4\,B_{{1(2)}} \right) {\mu}^{2}\pm 4\,B_{{2(1)}}k\mu\pm{4B_{
{2}}}^{2}\mp{4B_{{1}}}^{2} \right] {\frac {\mu^{-2}}{2S_{3\pm}}} \nonumber \\
 && b_{\pm} =\mp1/2 \Bigg[  \Big[  \left( \mp{\mu}^{2}{q}^{2}\pm 2B_{{2(1)}} \right) (1-\gamma_{\pm}){\mu}^{2}
\mp{\mu}^{4}{q}^{2}\mp 2B_{{1(2)}}{q}^{2}{\mu}^{2}+k \left( 2B_{{1(2)}}{q}^{2}+2B_{
{2(1)}} \right) \mu \nonumber\\
  && \mp {2B_{{1(2)}}}^{2}{q}^{2}\mp 4B_{{1}}B_{{2}} \Big] \mu\,
S_{3\pm}\mp
 \left( S_{1\pm}+ \left( 2B_{{1(2)}}+{\mu}^{2}
  \right) ^{2}\mu \right) {\mu}^{2} \gamma_{\pm} {q}^{2}\Bigg]{\frac {{\mu}^{-5}{q}^{-2}}{S_{3\pm}}}\nonumber\\
 && b_{1\pm} = \mp 1/2 \Bigg[ \mu \Big]  \left( \pm{\mu}^{2}{q}^{2}\mp 2B_{{2(1)}}
 \right) (1-\gamma_{\pm}){\mu}^{2}\mp{\mu}^{4}{q}^{2}\mp 2B_{{1(2)}}{q}^{2}{\mu}^{2}+k \left( 2B
_{{1(2)}}{q}^{2}+2B_{{2(1)}} \right) \mu \nonumber\\
 && \mp{2B_{{1(2)}}}^{2}{q}^{2}\mp 4B_{{1}}B_{{2}} \Big] S_{3\pm}-
( 2-\gamma_{\pm} )  \left( S_{1\pm}+ \left( 2B_{{1(2)}}+{\mu}^{2} \right) ^{2}\mu \right) {\mu}^{2}{q}^{2}\Bigg]
\frac {{\mu}^{-5}{q}^{-2}}{S_{3\pm}}\nonumber
\end{eqnarray}
with
\begin{eqnarray}
S_{1\pm}&=&\sqrt { \left( 2B_{{1(2)}}+{\mu}^{2} \right) ^{2}
 \left[  \left( k+\epsilon \right) \mu\pm 2B_{{2(1)}} \right] {\mu}^{2}
 \left[  \left( k-\epsilon \right) \mu\pm 2B_{{2(1)}} \right] }\nonumber \\
 S_{2\pm} &=& -2B_{{2(1)}}+{\mu}^{2} \gamma_{+(-)} \nonumber \\
S_{3\pm} &=& \sqrt {{2\,S_{1\pm}+{\mu}^{4}+ \left( -{\epsilon}^{2}+4\,B_
{1(2)}+{k}^{2} \right) {\mu}^{2}\pm 4\,k{\mu}B_{2(1)}+4B_{2(1)}
^{2}+4B_{1}^{2}}} \nonumber \\
S_{4\pm} &=&\left( 2B_{{1}}+
{\mu}^{2} \right)  \left( {\mu}^{2}\gamma_{\pm}+2B_{{1}} \right)\nonumber.
\end{eqnarray}
\noindent The asymptotic behavior of (\ref{os}) when $x\rightarrow-\infty$  corresponds to $z\rightarrow 0$ and gives for $\varphi ^{+}$ and $\varphi ^{-}$
\begin{align}
\mathop{\lim }\limits_{x\to - \infty }\varphi ^{+} &= A e^{ik_{-} x}+B e^{-ik_{-} x}\nonumber\\
\qquad \mathop{\lim }\limits_{x\to - \infty }\varphi ^{-} &= A \rho_{+} e^{ik_{-} x}+B \rho_{-} e^{-ik_{-} x}\tag{A4}\lb{sss}
\end{align}
with
\beq
k_{-}=i\mu \sqrt{\left|\omega_{-}^{2}-\varepsilon^{2}\right|}, \qquad
\rho_{\pm}=\frac{\omega_{+}\pm ik_-}{\varepsilon}, \qquad
\omega_{+}=k+\frac{2B_2}{\mu}, \qquad \omega_{-}=k-\frac{2B_1}{\mu}\nonumber.
\eeq

 In the region when $x>0$ the analogous equation to (\ref{GrindEQ6}) reads
\beq
\left[4 \mu^{2} z \frac{d}{dz}\left(z\frac{d}{dz}\right) \mp
 \left({\frac {4B_{{1}}qz}{ \left( q-z \right) ^{2}}}+{\frac {
4B_{{2}}qz}{ \left( 1-qz \right) ^{2}}}\right)- \left( {\frac {2B_{{1}}z}{\mu\,
 \left( q-z \right) }}+{\frac {2B_{{2}}}{\mu\, \left( 1-qz \right) }}+
k \right) ^{2}+{\varepsilon}^{2} \right]\varphi ^{\pm } =0.\tag{A5}   \lb{qg}
\eeq
The solution of (\ref{qg}) can be expressed in terms of the HeunG function as follows
\begin{align}
\varphi ^{+} &=C z^{l_{-}} (q-z)^{n_{-}}(-1+qz)^{m_{-}} {\mbox{HeunG}}\left(p,b_{-},\alpha_{-},\beta_{-},\gamma_{-},\delta_{-};\frac{z}{q}\right)\tag{A6}\lb{oDs}\\
 &+D z^{-l_{-}} (q-z)^{n_{-}}(-1+qz)^{m_{-}}
{\mbox{HeunG}}\left(p,b_{1_{-}},\alpha_{1_{-}},\beta_{-},2-\gamma_{-},\delta_{-};\frac{z}{q}\right)\nonumber
\end{align}
where the wavefunction parameters have been defined previously. The
asymptotic behavior of (\ref{oDs}) when $x\rightarrow +\infty$, which corresponds to $z\rightarrow 0$ gives for $\varphi ^{+}$ and $\varphi ^{-}$
asymptotic behavior of (\ref{os}) when $x\rightarrow-\infty$  corresponds to $z\rightarrow 0$ and gives for $\varphi ^{+}$ and $\varphi ^{-}$
\begin{align}
\mathop{\lim }\limits_{x\to + \infty }\varphi ^{+} &=C e^{-ik_{+} x}+D e^{ik_{+} x}\nonumber\\
\qquad \mathop{\lim }\limits_{x\to + \infty }\varphi ^{-} &=C \rho e^{-ik_{+} x}+D \rho e^{ik_{+} x}\tag{A7}\lb{ssss}
\end{align}
with $k_{+}=i\mu \sqrt{\left|\omega_{+}^{2}-\varepsilon^{2}\right|}$ and $\rho=\frac{\omega_{+}+ ik_+}{\varepsilon}$. The reflection and transmission coefficients for the positive and negative energy solutions are given by equation (\ref{wx}). With the reflection and the transmission amplitudes are given by $r=\frac{\rho_{2}-\rho}{\rho-\rho_1}$ and $t=\frac{\rho_2-\rho_1}{\rho-\rho_1}$. Figure 13 show transmission for the Dirac particle scattered by the pseudo-scalar potential (\ref{pot}), we can see from figures 13 (a) and (d) that, the EWs, TWs and BS constantly
appear from the energy $\left|\omega_-\right|<\left|\varepsilon\right|<\left|\omega_+\right|$, $\left|\varepsilon\right|>\left|\omega_+\right|$ and $\left|\varepsilon\right|<\left|\omega_-\right|$, respectively. In this later case the pseudo-scalar potential (\ref{pot}) behaves like a potential in well. In figures 13 (b) and (c) the pseudo-scalar potential (\ref{pot}) behaves like a potential barrier. We also notice the vanishing of the energy range for the EWs  but the TWs and BS appear for the energy $\left|\varepsilon\right|>\left|\omega_-\right|$ and $\left|\varepsilon\right|<\left|\omega_-\right|$, respectively. The position of energy range for EWs, TWs and BS is affected by the value of the parameter $\mu$.\\
\begin{center}
  \includegraphics[width=1.6in]{a}
  \includegraphics[width=1.6in]{b}
  \includegraphics[width=1.6in]{c}
  \includegraphics[width=1.6in]{d}
\end{center}
{\sf Fig. 13}:  {\sf{The transmission coefficient as a function of energy. (a) $2B_1=2B_{2}=0.5, 2.0, 3.0, 5.0$ (left to right curves). (b) $2B_1=2B_2=-0.5, -2.0, -3.0, -5.0$. (c) $2B_1=-2.0$ and $2B_2=-3.0, -6.0$. (d) $2B_1=-0.5$ and $2B_2=1.0, 2.0, 3.0, 5.0$. With $a=1$, $k=1$ and $\mu=1$. Note that, for the case $B_1=-B_2$, we have total transmission.}}

redpajama_set_name: RedPajamaArXiv


text:
require "graphql/schema/build_from_definition/resolve_map/default_resolve"

module GraphQL
  class Schema
    module BuildFromDefinition
      # Wrap a user-provided hash of resolution behavior for easy access at runtime.
      #
      # Coerce scalar values by:
      # - Checking for a function in the map like `{ Date: { coerce_input: ->(val, ctx) { ... }, coerce_result: ->(val, ctx) { ... } } }`
      # - Falling back to a passthrough
      #
      # Interface/union resolution can be provided as a `resolve_type:` key.
      #
      # @api private
      class ResolveMap
        module NullScalarCoerce
          def self.call(val, _ctx)
            val
          end
        end

        def initialize(user_resolve_hash)
          @resolve_hash = Hash.new do |h, k|
            # For each type name, provide a new hash if one wasn't given:
            h[k] = Hash.new do |h2, k2|
              if k2 == "coerce_input" || k2 == "coerce_result"
                # This isn't an object field, it's a scalar coerce function.
                # Use a passthrough
                NullScalarCoerce
              else
                # For each field, provide a resolver that will
                # make runtime checks & replace itself
                h2[k2] = DefaultResolve.new(h2, k2)
              end
            end
          end
          @user_resolve_hash = user_resolve_hash
          # User-provided resolve functions take priority over the default:
          @user_resolve_hash.each do |type_name, fields|
            type_name_s = type_name.to_s
            case fields
            when Hash
              fields.each do |field_name, resolve_fn|
                @resolve_hash[type_name_s][field_name.to_s] = resolve_fn
              end
            when Proc
              # for example, "resolve_type"
              @resolve_hash[type_name_s] = fields
            else
              raise ArgumentError, "Unexpected resolve hash value for #{type_name.inspect}: #{fields.inspect} (#{fields.class})"
            end
          end

          # Check the normalized hash, not the user input:
          if @resolve_hash.key?("resolve_type")
            define_singleton_method :resolve_type do |type, obj, ctx|
              @resolve_hash.fetch("resolve_type").call(type, obj, ctx)
            end
          end
        end

        def call(type, field, obj, args, ctx)
          resolver = @resolve_hash[type.graphql_name][field.graphql_name]
          resolver.call(obj, args, ctx)
        end

        def coerce_input(type, value, ctx)
          @resolve_hash[type.graphql_name]["coerce_input"].call(value, ctx)
        end

        def coerce_result(type, value, ctx)
          @resolve_hash[type.graphql_name]["coerce_result"].call(value, ctx)
        end
      end
    end
  end
end

redpajama_set_name: RedPajamaGithub


The Race to Beat POTS will take place in the scenic Anson B. Nixon Park in Kennett Square, PA. All proceeds from the event will benefit Dysautonomia International. The race will be chip timed by 2L Race Services and is sanctioned by USATF. The race course features a combination of paved, gravel, boardwalk, and trails that span throughout the park. Only the 1 Mile is wheelchair accessible. There are no major hills and the course narrows in a few places. Along the way you will get picturesque views including a lake and streams. Two water stations will be provided along the course and drinks will be provided before and after the race.
The cost to register for the 5K or 1 mile is $30. Register by May 18th to be guaranteed a T-shirt and a goody bag. Raffle tickets will be available for purchase at the event for $1 each, so bring some extra cash to enter for our great prizes! Children under 6 are welcome and are free. Please register early!
Ample parking available at the park at the main entrance off of N Walnut Rd. Additional parking is available in town at the parking garage for free.
The race will begin at 10 am. Bibs will be available for pickup starting at 8:30 am as well as on-site registration. The bib pick-up and same day registration will be next to the stage. Please arrive early in order to receive your bib and T-Shirt. Same day registration will start at 8 am. Refreshments will be provided after the race.
All proceeds will benefit Dysautonomia International. If you can't make the race, feel free to make a fundraising team or participate by running a 5K at home . Click the Donate link below to get started!
Awards will be given to the top 2 males and females in the following age groups: 13 & under, 14-19, 20-39, 40-59, and 60 & up.


Here's a video that I chanced upon where an octopus was being attacked by a school of Leather Jackets.
I felt strange as to why the predator was the prey this time and even more baffled why this octopus was so passive and hardly retaliating. Old age perhaps?
Anyway, the moral of the story is in life is don't be too kuai lan because karma will be served to you one day and you will be whacked big time.
The other thought that was going through my mind was "Wow.... the octopus flesh is so white and juicy! Yummy!"


A castle that is constantly rearranging itself, and a young royal family sworn to protect it. Celie, Rolf, and their beloved Castle Glower are back in this exciting sequel to Tuesdays at the Castle.
When her brother Rolf dares her to catch magical Castle Glower creating a new room, Princess Celie takes the challenge. No one knows the Castle better than she does. But as usual, the Castle has ideas of its own. Celie finds the new room first, and inside it is hidden a giant egg. It looks like the Castle wants Celie to care for the egg and whatever creature it hatches, but Celie hadn't bargained for a pet. And caring for this one will prove to be especially tricky once Celie and her siblings realize what else the Castle is hiding . . .
Jessica Day George's magical series is a classic in the making—and not to be missed.


text:
Last edited by Zulrajas
6 edition of Goldie"s inheritance found in the catalog.
Goldie"s inheritance
a story of the siege of Atlanta
by Louisa M. Whitney
Published 1903 by Free Press Association in Burlington, Vt .
Atlanta Campaign, 1864 -- Fiction,
Sieges -- Fiction,
Georgia -- History -- Civil War, 1861-1865 -- Fiction
Statement by Louisa M. Whitney.
Contributions Free Press Association (Burlington, Vt.)
LC Classifications PZ3.W6146 G
Pagination 263, [1] p. (last p. blank) ;
Books for Kids: 1. Thank You, Omu, by Oge Mora 2. Midnight Sun, by Stephenie Meyer 3. You Matter, by Christian Robinson 4. Stamped by Jason Reynolds and Ibram X. Kendi 5. Miss Rumphius, by Barbara Cooney 6. Zen Shorts, by Jon Muth 7. Little Dreamers, by Vashti Harrison 8. Kamala and Maya's Big Idea, by Meena Harris, with illustrations by Ana Ramirez Gonzalez. Discover Book Depository's huge selection of Whitney Bailey books online. Free delivery worldwide on over 20 million titles. We use cookies to give you the best possible experience. Goldie's Inheritance. Louisa Maretta Bailey Whitney. 31 Jan Hardback. US$ Add to basket. Goldie's Inheritance. Louisa Maretta Bailey Whitney. 23 Feb.
Ally Hilfiger is a socialite, TV producer, and author. Due to her struggle with Lyme disease as a child, she wrote a couple of books about her experience. One of her books is titled: 'Bite Me: How Lyme Disease Stole My Childhood.' The source of her wealth comes mainly from the Tommy Hilfiger -a significant fashion brand fortune. 9. Carly Simon. Nightingale Point - Ebook written by Luan Goldie. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Nightingale Point.
In one of the mini-adventures in the book, "A Fistful of Karma", the PC's must defeat a cruel tyrant who oppresses the people of a mining town. Dragon magazine #71 (back when it wasn't just Dungeons & Dragons) had a Boot Hill module called "The Taming of Brimstone", in which the player characters had to clean up the eponymous town. The Paperback of the Diary of a Lawyer by Goldie Millan at Barnes & Noble. FREE Shipping on $35 or more! Due to COVID, orders may be delayed. Thank you for your patience. Coupons & Deals Book Annex Buy 1, Get 1 50% Off: Books for All Ages Bestsellers 30% .
Determination of longitudinal aerodynamic derivatives using flight data from an icing research aircraft
Kai-lans super tea party
Review of the law of succession
Blood for a Butcher and Other Septic Stories
The Council of Chalcedon and the Armenian Church
An episode of Jewish romanticism
House ownership in portugal: communication to the XVIIth Congress of the International Union of Apartment House Owners, Copenhagen, 1962.
Human rights brought home
FSL FORUM... U.S. DEPARTMENT OF COMMERCE... JANUARY 1995.
Forgive us our trespasses
Sacred names, saints, martyrs and church officials in the Greek inscriptions and papyri pertaining to the Christian church of Palestine
Yahweh or the Highway
The metaphysics of being of St. Thomas Aquinas in a historical perspective
When Tears Fall Short
Egyptian sculptures
Directory of African-American students and teachers in all Smyth County schools
Frauds, hoaxes, and swindles
Familiar lessons on food and nutrition : intended to serve as a handbook to the Food Department of the Parkes Museum of Hygiene, and to form one of the proposed sequels to the course of elementary lectures, entitled, Science made easy. Pt. 1
stage.
The Divine Comedy of Dante
Goldie"s inheritance by Louisa M. Whitney Download PDF EPUB FB2
Goldie's Inheritance: A Story Of The Siege Of Atlanta () [Whitney, Louisa Maretta] on *FREE* shipping on qualifying offers. Goldie's Inheritance: A Story Of 5/5(1). Goldie's Inheritance: A Story of the Siege of Goldies inheritance book by Louisa Maretta Bailey Whitney (Author) out Goldies inheritance book 5 stars 1 rating.
ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The digit and digit formats both work.5/5(1).
Get this from a library. Goldie's inheritance: a story of the siege of Atlanta. [Louisa M Whitney; Free Press Association (Burlington, Vt.); Cairns Collection of American Women Writers.].
Get this from a library. Goldie's inheritance: a story of the siege of Atlanta. [Louisa M Whitney; Free Press Association (Burlington, Vt.)].
First Edition. Hardcover. 8vo. pages. Tan cloth hardcover with black lettered title and illustration on front cover and black title on spine.
Plain brown paper dust jacket. Addeddate Foldoutcount 0 Identifier GoldiesInheritance Identifier-ark ark://t4pk3x Ocr ABBYY FineReader Openlibrary OLM.
Inheritance: A Memoir of Genealogy, Paternity, and Love by Dani Shapiro is a Knopf publication. A poignant journey to self-rediscovery.
The home DNA kit is so popular right now. I know many people who have purchased one and mostly it was a fun and fascinating exercise/5(K). The Inheritance of Goodness: the Early Books.
Goldie Morgentaler. Pages The Inheritance of Goodness: David Copperfield and Pip. Goldie Morgentaler. Pages Illegitimacy and Villainy: the Negative Aspects of Heredity. Goldie Morgentaler. Pages The Public Face of Heredity.
Inheritance Book 4 of the Inheritance Cycle By Christopher Paolini A Review by Eric Allen After his early success, Christopher Paolini set to the final book of his trilogy.
Unfortunately, for everyone involved, the outline he'd written for the third book wasn't going to fit in a. Welcome to the AP Biology Lecture Notes page.
Here will files of all the lectures from class. They are in a condensed format which has six slides to a page. Directed by Colin Higgins. With Goldie Hawn, Chevy Chase, Burgess Meredith, Rachel Roberts.
A shy San Francisco librarian and a bumbling cop fall in love as they solve a crime involving albinos, dwarves, and the Catholic Church. Goldie's Inheritance A Story of the Siege of Atlanta.
David A. Hamilton Americana Books ABAA. P.O. Box Stone Mountain, GA (JavaScript must be enabled to view this email address) () Specializing in History, Travel & Exploration, General Stock, Ephemera.
Directed by Jay Sandrich. With Goldie Hawn, Chevy Chase, Charles Grodin, Robert Guillaume. Wrongfully accused of a bank robbery, a writer seeks the help of his ex-wife, who is now married to the soon-to-be D.A. of California. Golda Meir (born Golda Mabovitch; May 3, – December 8, ) was an Israeli teacher, kibbutznik, stateswoman, politician and the fourth Prime Minister of Israel.
Born in Kiev, Russian Empire, she emigrated to the United States as a child with her family inand was educated there, becoming a marrying, she and her husband emigrated to then Palestine insettling.
The play ' Inheritance ' revolves around a conflict between the African natives and the white settlers over the inheritance of land, its resources and leadership.
> The British invasion in African is motivated bythe desire to tap resources from Africathroughtheir colonial rule under the guise of. The Inheritors is a work of prehistoric fiction and the second novel, published inby the British author William Golding, best known for Lord of the Flies. It concerns the extinction of one of the last remaining tribes of Neanderthals at the hands of the more sophisticated Homo sapiens.
In Louisa M. Whitney's "Goldie's Inheritance: A Story of the Siege of Atlanta" was published. The Goldie of Whitney's novel was based on her own sister, Cyrena Bailey Stone (), who. Alexander Technique Teachers' Portal. Introducing Miss Goldies; Learning to Teach Online; Calendar; Workshops; Booklet.
A Milwaukee Inheritance, a novel by David Milofsky; Strong Towns: A Bottom-Up Revolution to Rebuild American Prosperity, by Charles L. Marohn, Jr. Plagued by Fire: The Dreams and Furies of Frank Lloyd Wright, by Paul Hendrickson; Call Me Zebra, a novel by Azareen Van der Vlieet Oloomi; How to Stop Time, a novel by Matt Haig.
Willie Lynch Letter, Miseducation Of The Negro, The Isis Papers, Nutricide, Save The Cat, The Screenplay Bible, How To Hustle and Win, Rap, Race, and Revolution, Knowledge of Self, Behold A Pale Horse, The Bluest Eye, Nervous by Zane, Shame On It All by Z.
Inheritance Cycle has 34 entries in the series. The Fork, the Witch, and the Inheritance Cycle (Series) Christopher Paolini Author ().Great deals on Literature & Fiction Hardcover Antiquarian & Collectible Books. Get cozy and expand your home library with a large online selection of books .Goldie Hawn's life is an ongoing tableau of stories, and she has a born knack for telling them.
In this candid and insightful book, Goldie invites us to join her in a look back at the people, places, and events that have touched her. It is the spiritual journey of a heart in search of enlightenment.
niarbylbaycafe.com - Goldies inheritance book © 2020

redpajama_set_name: RedPajamaCommonCrawl


Coffee Caffeine: How Much in your Cup?
Coffee is a complex mixture of chemical components of the coffee bean. Some of these components are partially destroyed by the roasting process; however, many of these components are not. Caffeine is one of the components that is not affected by the roasting process. With the addition of hot water, the caffeine is extracted from the coffee bean. Caffeine was discovered in coffee in 1820. Caffeine is an alkaloid that acts as a mild stimulant.
It increases the blood pressure, stimulates the central nervous system and the action of the heart and lungs, and promotes urine formation. It also acts as a diuretic and delays fatigue. Caffeine does have some positive side effects. It has been found to help treat migraines since it helps constrict the dilated blood vessels, therefore reducing the pain. It also has been documented to increase the potency of aspirin and to slightly relieve the affects of asthma attacks. It has been suggested that caffeine has been linked to possible cancers and birth defects.
However, this has not been confirmed and there are no bans or warnings that have been issued by the US Food and Drug Administration (US FDA). The amount of caffeine found in the coffee beans varies. On average, a regular cup of coffee contains approximately 90 to 150 mg of caffeine.
Coffee brewed in a drip coffee maker has about 115 to 175 mg of caffeine while other coffee makers may brew coffee with about 80 to 135 mg. Typically, espresso has about as much caffeine as a regular cup of coffee. On average, a standard espresso cup would have about 100 mg of caffeine. However, the serving size for espresso is much smaller. The actual content of caffeine per milliliter in an espresso is much higher than in a regular brew. Also, caffeine is assimilated quicker when ingested in a concentrated dosage such as an espresso cup.
The amount of caffeine found in coffee blends will also vary. The following are examples of the caffeine content for different coffee blends: -Brazilian Bourbons: contains 1.20% caffeine -Columbia Excelso: contains 1.34% caffeine -Columbia Supremo: contains 1.
34% caffeine -French Roast: contains 1.22% caffeine -Costa Rican Tarrazu: contains 1.35% caffeine -Vienna Roast: contains 1.27% caffeine -Decafs: contains 0.02% caffeine People hypersensitive to the caffeine found in coffee may decide to drink decaffeinated coffee.
This way, they can still enjoy the great coffee taste, yet avoid the caffeine. Coffee can be "decaffeinated" by treating the green beans with solvents called chlorinated hydrocarbons. Once the solvents are removed, the beans are then roasted by ordinary procedures. Most people become accustomed to decaffeinated coffee and do not have to worry about the effects of caffeine.


NOTE: Research Report 3 is an optional assignment that will allow you to replace a lower grade on one of the first two research assignments (or replace a missing research assignment).
ASSIGNMENT: Global inequality is thought to be getting worse today, and in many ways the concentration of wealth is troubling. But in this assignment we will use data to examine over 200 years of history along three critical datapoints: income, life expectancy, and babies per woman. You may be surprised by what you find!
Work on the printouts while you analyze the data/watch the video on your computer. When you have completed the worksheets and writing assignments, bring them to class and turn them in on Wednesday, May 1.
As you saw in research assignment 1, the U.S. Census produces data on many aspects of American life, including employment and crime. This assignment asks you to do some more detailed data mining of the U.S. Census "Statistical Abstracts of the U.S., 2012", a compilation of statistics that tells us about trends in various activities and behaviors of people in the United States. Also useful in studying formal American negative deviance (crime) is the "Bureau of Justice Statistics." Following the instructions provided in the links below, you will complete the data mining, fill in the tables for each part and then, in three separate writing reflections discuss how the data fits the hypotheses which you are testing.
You need only turn in one of the Research Report Sheet formats.
Due on or before Monday, April 1 by 2pm.
The U.S. Census is a sociological project identifying the demographic characteristics (population, age, ethnicity, income, education, government, business, etc.) for people across the United States. Information can be analyzed in many different ways, including by local address.
an example of role conflict or role strain that you experienced while living there.
Discuss these terms in relation to what you learn from the census information you are studying. Use the additional tables that are linked under each descriptive area for more detail. Here is an example of what a "C" report might vaguely resemble (go further than the example if you want to achieve maximum points). The report should be around 500 words and have a heading with your name, date and class/professor's name.
Due Monday, February 18 in class.
GRADING RUBRIC: The rubric is what I use to grade everyone's reports to reduce subjectivity in the grading process. It is based on the assignment instructions and the degree to which you communicate your knowledge of the topics effectively.
4 points: Social Institution -- was this described effectively as an abstract representation of social organization?
4 points: Status Set -- did you describe your positions within the social groups you belong to?
4 points: Role Behavior -- did you use active verbs to describe the behavior of the roles you play?
4 points: Ascribed and Achieved Status -- did you provide meaningful and correct examples of these social traits?
4 points: Role Conflict and/or Strain -- did you provide meaningful and correct examples of these social problems?
Grammar: 1 point redution for problematic grammar.
Bold: 1 point reduction if you did not follow instructions and put key terms in bold.


Ducted 13,500 BTU AC, Auto ignition Furnace, Systems Monitor Panel, Power Converter With Charger, LED 12 Volt Interior Lighting, Fold out aluminum steps, Mounted 32″ LCD TV Digital, AM/FM/CD/DVD w/ Remote, MP3 Player Hook-Up, Slide-out U-dinette/sleeper, Sofa/sleeper with leg recliners & work tables/Murphy Bed, Over-under rear twin beds, Auto Gas/Electric Refrigerator, Three Burner High Output Gas Range, Microwave, Tub Surround, Bathroom Skylight, 110 DSI Gas/Electric water heater, Foot Flush Toilet.
Fully Laminated Aluminum Framing, R-7 Side Wall, R-12 Floor and R-14 Ceiling Radius Roofs w/ Interior Vaulted Ceilings, Vinyl Composite Roofing Membrane, TV Antenna w/ Cable & Satellite Hook-Up, Laminated Fiberglass Sidewalls, Electric Slide-Out, Decorative Frame Skirting, Entrance / Screen Door, Grab Handle, Radius Corner Frameless Windows, Radius front with automotive style windshield, Safety Glass, Large Dinette Picture Window, Outside Speakers, Outside Shower, Two-30 Lb Gas Bottles with Molded Bottle Cover, Surface Coated Steel I-Beam Frame, Power hitch jack, Stabilizer Jacks, Torsion Axle/Rubber-Ryde Suspension, Easy Lube Axles, Outside Speakers, Carbon Monoxide Detector, Fantastic Fan with Vent Cover, Heated Mattress, Wood look floor, Raised Refrigerator Panels, Power Awning With Adjustable Rain Dump & LED light, Outside Gas Grill and Worktable, Aluminum Wheels, Spare Tire Carrier & Cover.
Exterior graphics package, Power jack & stabilizers, heated mattress, water purifier, Maxxair vent fan.


Gold is currently testing the intermediate support of its medium term bearish channel at 1,530 and is expected to rebound. However, a break through this level will trigger a decline to the lower limit – 1,512.
Technical indicators do not provide clear signals but evolving in oversell zone supporting the assumption of a pull back. Bollinger bands are much discarded due to strong recent increase. The situation is expected to stabilize in the nearest future.
According to previous events the market will provide a bullish opportunity at the level of 1,530 with 1,545 and 1,550 seen as first objectives. A break through 1,527 will alter this scenario.


text:
Mieczysław Zygmunt Lipert (ur. 1900 w Łokaczach, zm. 1968 w Warszawie) – hutnik szkła, przewodniczący Prezydium Warszawskiej Wojewódzkiej Rady Narodowej (1948-1953), przewodniczący Prezydium Wojewódzkiej Rady Narodowej w Bydgoszczy (1953-1954), działacz polityczny.

Życiorys
Urodził się 24 grudnia 1900 r. w miejscowości Łokacze w powiecie horochowskim na Wołyniu. Był synem Stanisława, hutnika szkła i Stanisławy z Sikilskich. Uczęszczał do szkoły powszechnej w Hulewiczach, powiecie włodzimierskim, gdzie zamieszkali jego rodzice. Po zajęciu tej miejscowości przez wojsko austriackie w 1914 r., został wzięty do obozu wojskowego i przez trzy lata był tam woźnicą.

Od jesieni 1917 r. należał do Polskiej Organizacji Wojskowej w Lubelskiem. W końcu 1918 r. czynnie uczestniczył w rozbrajaniu Niemców i Austriaków, po czym wstąpił do Milicji Ludowej i służył w niej jako podoficer. W kwietniu 1919 r. znalazł sic w nowo utworzonym batalionie milicyjnym z którym udał się do Pińska, gdzie batalion ten brał udział w pogromie Żydów. Wkrótce batalion został rozwiązany, a należących do niego milicjantów rozbrojono, przejściowo aresztowano i wcielono do wojska. Lipert został przydzielony do 34 pułku piechoty, a następnie do szpitala polowego nr 203.

Działalność zawodowa i polityczna do 1939 r.
W marcu 1922 r. rozpoczął pracę w hucie szkła w Lubartowie. Następnie pracował kolejno w hutach szkła w: Wołominie (1925–1926), Legionowie (1926–1928), Kostopolu (1928–1929) i hucie Widok Radomiu (1929–1930). Od 1935 do stycznia 1939 r. pracował jako mistrz w Hucie Szkła Vitrum w Wołominie.

Od 1924 do 1938 r. należał do nielegalnej Komunistycznej Partii Polski, od 1926 był sekretarzem komórki KPP w wołomińskiej hucie oraz sekretarzem Zarządu Oddziałowego Związku Zawodowego Pracowników Przemysłu Szklarskiego w Wołominie. Za uczestnictwo w strajku generalnym szklarzy został zwolniony z pracy. Podczas pracy w Radomiu nawiązał kontakty partyjne i został wybrany sekretarzem Komitetu Dzielnicowego i członkiem egzekutywy Komitetu Okręgowego w Kielcach. W latach 1930-1935 był funkcjonariuszem tej partii w Warszawie, z ramienia Okręgu Warszawa-Podmiejska pełnił funkcję instruktora. Z powodu działalności w tej partii był w 1937 r. sądzony w Radomiu i skazany na 3 lata więzienia w zawieszeniu na 5 lat.

Okupacja hitlerowska
Po najeździe Niemiec na Polskę ewakuował się na wschód i 23 września 1939 r. znalazł się w Kostopolu, zajętym przez wojska sowieckie. Tam otrzymał pełnomocnictwo do nacjonalizowania zakładów pracy, m.in. tamtejszej huty szkła. Został jej wicedyrektorem oraz dyrektorem technicznym. Na tym stanowisku przetrwał do wybuchu wojny niemiecko-sowieckiej w czerwcu 1941 r. W hucie zarządzanej przez Niemców był palaczem na urządzeniach gazowych. W 1943 r. przeniesiono go do Huty Szkła w Wołominie. Organizował tam Polską Partię Robotniczą, Gwardię Ludową i Armię Ludową oraz prowadził działalność sabotażową. W końcu 1943 r. był współorganizatorem konspiracyjnej Miejskiej Rady Narodowej w Wołominie, a następnie warszawskiej Wojewódzkiej Rady Narodowej.

Działalność zawodowa i polityczna po II wojnie światowej
Od 1944 r. pracował w aparacie partyjnym PPR. W Komitecie Wojewódzkim PPR w Mińsku Mazowieckim pełnił kolejno funkcje: kierownika Wydziału Przemysłu, Wydziału Administracyjno-Samorządowego oraz kierownika Wydziału Personalnego. 3 maja 1945 został posłem do Krajowej Rady Narodowej. Od czerwca do grudnia 1945 r. był członkiem Centralnej Komisji Rewizyjnej KC PPR. Od grudnia 1948 r. należał do nowo utworzonej Polskiej Zjednoczonej Partii Robotniczej.

W 1948 r. został wybrany na stanowisko przewodniczącego Prezydium Warszawskiej Wojewódzkiej Rady Narodowej i sprawował je do 1953 r. Za niezadowalające wyniki w pracy odwołano go w końcu 1952 r. i przeniesiono do Bydgoszczy, gdzie z dniem 1 stycznia 1953 r. został przewodniczącym Prezydium Wojewódzkiej Rady Narodowej. Już rok później, 9 lutego 1954 r. odwołano go z tego stanowiska, ponieważ "nie wykazywał dobrego zmysłu organizacyjnego; nie wpływał mobilizująco na członków Prezydium, gdyż sam był mało obowiązkowy, dużo czasu poświęcał na polowanie w czasie wolnym i służbowym".

Po odwołaniu z Bydgoszczy został zatrudniony na stanowisku p.o. dyrektora Zarządu Zaopatrzenia Robotniczego-Ministerstwa Przemysłu Chemicznego, a w końcu grudnia 1954 r. mianowano go dyrektorem tego Zarządu. Jednak po kilku miesiącach i z tego stanowiska został odwołany ponieważ: "mimo szczerych chęci nie potrafił we właściwy sposób zorganizować instruktażu i kontroli podległych oddziałów Zaopatrzenia Robotniczego". W 1957 r. przeszedł na rentę.

Zmarł 1 września 1968 r. w Warszawie. Został odznaczony m.in. Orderem Sztandarem Pracy II klasy. Pochowany na wojskowych Powązkach (kwatera D6-4-34).

Zobacz też
 Wojewodowie bydgoscy

Bibliografia
 Błażejewski Stanisław, Kutta Janusz, Romaniuk Marek: Bydgoski Słownik Biograficzny. Tom IV. Bydgoszcz 1997. , str. 67-68
 Profil na stronie Biblioteki Sejmowej
 "Warszawa Prawa Podmiejska 1942-1944, Z walk PPR, GL-AL" praca zbiorowa redakcją Benona Dymka, Wyd. MON Warszawa 1973 s. 819

Przypisy

Działacze PZPR
Funkcjonariusze Milicji Ludowej
Odznaczeni Orderem Sztandaru Pracy II klasy
Oficerowie Armii Ludowej
Oficerowie Gwardii Ludowej
Pochowani na Powązkach-Cmentarzu Wojskowym w Warszawie
Przewodniczący Prezydium Wojewódzkiej Rady Narodowej w Bydgoszczy
Przewodniczący Prezydium Wojewódzkiej Rady Narodowej w Warszawie
Działacze Komunistycznej Partii Polski
Politycy PPR
Urodzeni w 1900
Zmarli w 1968

redpajama_set_name: RedPajamaWikipedia


text:
Willoughby native stuck on highway loaned car by complete stranger to make it home for Christmas
Theresa McCluskey and her family were headed back to the Cleveland area on Saturday for Christmas when their SUV stopped on I-77 in Marietta. A total stranger stepped in and saved their holiday.
By: DaLaun Dillard
Posted at 11:06 PM, Dec 27, 2022
MARIETTA, Ohio — Theresa McCluskey is originally from Willoughby but lives in Charlotte, NC with her husband and three children, the family was headed back to Cleveland area on Saturday for the holiday when their SUV stopped on I-77 in Marietta.
"We stopped Friday night because of the bad weather, weren't sure if we were going to be able to get all the way up here with the icy roads so we drove to Marietta fine with no problems on Friday," said Theresa's husband Scott. "Then in the morning when we thought we would make it fine, we only made it a mile or two and that's when we had all these problems."
Drexel Perry just happened to be driving by on Saturday and noticed the family's SUV stopped on the side of the road.
"When I passed the car, I looked in my rear-view mirror and you could tell from the steam coming from the engine that they were overheating or having engine problems," said Perry. "My concern was how cold it was, they can't run the car or get out of the cold."
Perry nor Scott could figure out what was wrong with the truck, so Perry offered his spare jeep to this family that he just met, so they could make it to the Cleveland area in time for Christmas.
When Perry was asked why he felt so comfortable to allow a family he just met to drive away with his vehicle, he said, "I don't know, it's probably just a gut feeling that you feel about somebody."
"I asked him if he was Santa and I asked if I could give him a hug, I did, and I got emotional," said Theresa.
The McCluskey's left their SUV in Marietta with Perry and he's taking it to a shop to get fixed on Thursday. The group will then meet back up this Saturday to swap cars as the family heads back to Charlotte.
"We were so stuck that we didn't have an option, we were going to just roll the dice," said Scott.
That gut-feeling that Perry felt about the McCluskeys was a mutual feeling apparently, and it created a Christmas miracle.
"For some reason, we felt the same way, just for some reason we felt like we could trust him," said Theresa. "It was something we will never forget and taught our kids a big lesson about the act of kindness."
Watch live and local news any time:
Download the News 5 Cleveland app now for more stories from us, plus alerts on major news, the latest weather forecast, traffic information and much more. Download now on your Apple device here, and your Android device here.
You can also catch News 5 Cleveland on Roku, Apple TV, Amazon Fire TV, YouTube TV, DIRECTV NOW, Hulu Live and more. We're also on Amazon Alexa devices. Learn more about our streaming options here.


Derek Palacio is the author of the novella How to Shake the Other Man and the novel The Mortifications. With Claire Vaye Watkins, he co-directs the Mojave School, a free creative writing camp for teenagers in rural Nevada. He lives in Ann Arbor, Mich.


Mark Western is Director of the Institute for Social Science Research and a Fellow of the Academy of Social Sciences in Australia. As Institute Director Mark is responsible and accountable for all aspects of the Institute's strategy and operations. He has previously worked at the Australian National University and the University of Tasmania, and held visiting appointments at the University of Wisconsin-Madison, the University of Manchester, and the Institute of Education, London.
Mark is an International Fellow of the Centre for the Study of Poverty and Inequality at Stanford University, a Chief Investigator on the ARC Centre of Excellence for Children and Families Over the Life course and a former Chief Investigator on the ARC Centre of Excellence in Policing and Security.
Mark is also a Board Member of the Cathie Marsh Institute for Social Research at the University of Manchester. Aside from Centre of Excellence funding, Mark has held research grants and government contracts worth over $20 million.
He has edited and authored 7 books, and over 100 book chapters, journal articles and commissioned reports.
My interests in research methods are both technical and more broadly methodological. I am interested in how to improve quantitative methods like social surveys and statistical analyses to generate more valid and reliable conclusions from these kinds of data. I am also interested in how to use new computational methods like machine learning on very large social science datasets, to identify patterns, classify observations, and make better predictions. At the more methodological level, I am interested in how to design research projects and analyse data to produce useful information in real settings where we need certain kinds of good answers - for instance, knowing if a social program works in a real community that is subject to many overlapping programs, where we have too much information, but too few observations for conventional methods to work well. I am also increasingly interested in how working closely with stakeholder communities can enrich social science research and help social scientists avoid making errors, including harmful errors, that come from being too theoretical and abstract, and not sufficiently grounded in the realities they are studying.
This work focuses on how to strengthen connections between social science research and "real-world" problems in order to develop better solutions, enhance the relevance and public value of university research, and improve research quality. The key to better "solution-oriented" social science is to build strong partnerships between university researchers, government, industry, not-for-profits and civil society. I am interested in doing solution-oriented social science to address specific problems and also in researching how to do it better.
This work focuses on understanding the dimensions and causes of social and economic inequality in rich countries, and what to do about it.
This work focuses on understanding how people's opportunities for social and economic mobility are shaped by factors they don't control, such as the family they are born into and the associated advantages and disadvantages that flow from this, and factors that may be partly controllable, such as effort and motivation. I am also interested in how useful it is to talk about equal opportunities when individual success and lack of success come from a complex tangle of factors we can and cannot control, including factors we do not choose.
Social class remains one powerful way of explaining inequalities in desired rewards, and differences in certain kinds of sociopolitical behaviour and attitudes. I am interested in understanding how class "works" in countries like Australia to shape inequality, attitudes and behaviour, and whether it is becoming more or less important over time.
Mark has led or contributed to projects which have had direct impacts on policy and practice. In 2001 he led the team which produced one of the first national studies of General Practitioners' use of information technology for the Australian Department of Health. In 2005- 2006 he led a team which produced estimates of international students' non-tuition fee expenditure which were used in the Australian National Accounts to help quantify the export value of Australian education. He also led the first national study of the employment outcomes of graduates of Australian PhD training programs. More recently, he has also worked on major evaluations of government policies and programs, such as the national Paid Parental Leave Scheme, and developed evaluation frameworks for major policy initiatives such as the Health and Hospitals Fund, which supported national health infrastructure, and the Queensland Government's 10 year Domestic and Family Violence Prevention Strategy. Mark also sits on a number of Advisory and Expert Reference Groups for non-government organisations, and State and Federal Government Departments. Mark particularly enjoys working with partners in government, industry and the not-for-profit sector on problems that matter to them and have real-world relevance and impact.
Intergenerational economic mobility in contemporary Australia: Is Australia still the land of the 'fair go'?
Population Synthesis for Travel Demand Modelling in Australian cities.
Australian Social Attitudes 2: Citzenship, Work and Aspirations. Edited by David Denemark, Gabrielle Meagher, Shaun Wilson, Mark C. Western and Phillips, Timothy Sydney, NSW: UNSW Press, 2007.
Australian Social Attributes: The First Report. Edited by Shaun Wilson, Gabrielle Meagher, Rachel Gibson, David Denemark and Mark Western Western Sydney: University of New South Wales Press, 2005.
Engaged Citizens: Are Post Materialists Making a Difference?
Is there income mobility in the Philippines?
What are the housing tenure pathways of income support recipients over time?
Developments in educational and occupational mobility in Australia: are the chances of young people from low socio-economic backgrounds improving?
Is democracy needed for health systems performance assessments?
Second generation Australians and their aspirations: Do gender and ethnic background matter?
Utilization of computer technology in general practice: Does attitude matter?
Postmaterial value shift: Generational replacement or question order effect?
Postmaterialism and age: An Australian anomaly?
Postmaterialism and age: Australian anomoly or cross-national pattern?
Infrastructure for a Spatially Integrated Social Science e-Research Facility.
A Foucauldian and Quantitative Analysis of NAPLAN, the category 'Language Background Other Than English', and English as a Second Language Level.
Youth internet engagement and inequality in Australian society.


text:
SNH Report Will Help Marine Planning
Environment Politics
31 May 2011, at 1:00am
SCOTLAND, UK - Marine energy developers, regulators and advisers are set to benefit from a new report, commissioned by the Scottish Natural Heritage (SNH) and funded by Marine Scotland (MS), which presents the findings of a series of research projects carried out in Scottish waters.
The report, "An assessment of the conservation importance of species and habitats identified during a series of recent research cruises around Scotland", will help balance marine energy development and nature conservation.
SNH said that as well as the renewable energy sector, it will also help inform marine planning and licensing decisions, and the creation of Marine Protected Areas.
The study analysed imagery and data from surveys carried out at 15 locations. It identified 14 species and 17 habitats of conservation interest. Seven of the species and seven of the habitats have the added status of Priority Marine Feature'.
The report assesses the implications of renewable energy developments on some of the conservation features. This will help steer environmental impact assessment of proposed marine energy developments.
Susan Davies, SNH director of policy and advice, said the report should prove very useful to anyone with an interest in the marine renewable energy sector.
"The waters around Scotland have huge potential for marine renewable energy development. They are also internationally important for their many features of nature conservation interests," Ms Davies added.
"Our role is to help the marine energy sector to develop sustainably. We do this by providing advice and information on important marine features so these can be taken into account during development planning. The evidence in this report will be a great asset in that process."
Marine Scotland's Head of Science, Professor Colin Moffat added: "As a maritime nation Scotland is greatly influenced by the sea in terms of our climate and the habitat and species that exist in our waters. Understanding these issues through sound science is fundamental to the sustainable use of the sea. I especially welcome the ready availability of the imagery used in this assessment through Marine Scotland Interactive, which clearly illustrates the range of plants and animals that thrive throughout our coasts".


The Kano University Of Science And Technology, Wudil, Has Inaugurated Two Committee On The Recent Students Unrest That Happened In The University.
The Vice-chancellor Of Kano University Of Science And Technology, Wudil, Professor Shehu Alhaji Musa Has Inaugurated Two Committee On The Recent Students Unrest That Happened In The University As a Result of The Death Of Level 300 Biology student, Faruk Abubakar.
(2) Evaluation Headed By onetime Acting Vice Chancellor Of The University, Dr Muhammad Ibrahim Abdu Is charged With Evaluating Properties Destroyed, Extent Of Destruction, Cost Implications Etcetera.
Inaugurating The Committees,The Vice Chancellor Told The Members That They Were Appointed On Their Merit And Qualification.