text:
\section{Introduction}

Three-dimensional (3D) topological insulators are characterized by their gapless surface states and bulk gap as a consequence of time-reversal symmetry and band inversion induced by a strong spin-orbit coupling \cite{Hasan2010,Qi2011,Ando2013}. As a result of such a strong interaction, the magnetic heterostructures composed of topological materials have received significant attention for both their possible technological applications and the potential to promote our fundamental understanding of the underlying physics \cite{Han-PRL2017,Wang-NatComm2017,Yasuda-PRL2017}. Moreover, the spin–momentum locking in the surface states of the topological insulators is able to induce a non-equilibrium spin accumulation which can be electrically detected by measuring the hysteresis loops of the in-plane resistance of the magnetic tunnel junctions \cite{Li-NanoTec2014,Dankert-Nano-2015,Liu-Richardella-2015}.

On the other hand, gate voltages and external magnetic fields can cause many interesting effects in propagating behaviour of Dirac fermions by inducing electric and/or magnetic barriers on the surface of topological insulators \cite{Zhang-Wang-2012,Vali-Dideban-2016,Wang2012,Zhang-Zhai-2010,Song2014}. The electronic transport properties of a ferromagnet/normal/ferromagnet junction on the surface of a topological insulator showed that the conductance oscillates with the width of normal segment and gate voltage, like a spin field-effect transistor \cite{Zhang-Wang-2012}. Based on a transfer-matrix method, a theoretical investigation on the transport properties of Dirac electrons on the surface of 3D topological insulators under the modulation of electromagnetic superlattices has shown an imbalance between the number of transport channels for parallel and antiparallel magnetic configurations \cite{Wang2012,Zhang-Zhai-2010}. Moreover, the electric and magnetic barriers can reveal electron beam collimating property \cite{Wang2012}. Transport properties of electrons through a step junction, quantum wells and quantum superlattices on the surface of topological insulators have also suggested a clear oscillating behaviour in terms of incident angle of electrons, similar to those seen in Fabry–Perot interference in optics \cite{Song2014}. Chiba \textit{et al.}, \cite{Chiba-Takahashi-2017} modelled magnetic-proximity-induced magnetoresistance in disordered topological/ferromagnetic insulator bilayers by means of Kubo and Boltzmann theories. It was shown that for in-plane magnetizations the magnetoresistance ratio vanishes, while for out-of-plane magnetizations an energy gap opens up at the Dirac point which causes a large magnetoresistance value. Indeed, the interface between a ferromagnet and a topological insulator is considered as a spin source and accordingly, the spin-orbit coupling can enhance the magnitude of both charge and spin currents in the system \cite{Burkov-Hawthorn-2010,Ando-Hamasaki-2014}.

At low energies, the Fermi surface of the topological surface states is a circle and the electronic states near the Dirac point can be well described by the Dirac equation. As the Fermi energy increases, however, the shape of the constant-energy contour may change from a circle to a hexagon and then to a snowflake with sharp tips along the six  $\Gamma$-M directions. This phenomenon which is known as the hexagonal warping effect \cite{Fu2009,Nomura2014} and causes significant modifications in both DC conductivity \cite{Wang-Yu-2011} and optical conductivity \cite{Li-Carbotte-2013}, first observed in a Bi$_{2}$Te$_{3}$ sample \cite{Chen2009}. Angle-resolved-photoemission spectroscopy experiments have demonstrated that Bi$_{2}$Te$_{3}$ has a single Dirac cone on its surface \cite{Chen2009}. In addition to the in-plane spin polarization, the warping effect leads to an out-of-plane spin component which is carried by the surface states.

Transport properties of topological insulators with warped surface states have recently been studied \cite{An2012,Li2013,Fu-Zhang-2014,Siu-Jalil-2014,Yu-Ma-2017,Akzyanov2018}. For instance, the scattering properties of a straight step defect on the surface of Bi$_{2}$Te$_{3}$ revealed a strong dependence on the direction in which the defect extends \cite{An2012}. At high energies where the warping effect is large, several critical momenta on the constant-energy contour are found, so that an incident wave with one of these momenta can be totally reflected or perfectly transmitted. There is always a finite reflection if the incident electron direction is not perfectly normal \cite{An2012}. Here, we would like to emphasize that not all the surface states of topological insulators exhibit the hexagonal warping effects. The size of the energy band gap and the crystal symmetry of topological insulators are crucial in their hexagonal warping strength of surface band dispersions \cite{Fu2009,Chen2009}.

In this paper, we examine the influence of double-magnetized and double-gated regions on transport properties of Dirac fermions on the surface of a 3D topological insulator with hexagonal warping effect. We find that the resonant states and the electric conductance are strongly modulated by the gate voltage, incident energy and the exchange field strength. When the in-plane magnetizations are aligned in the growth direction, the time reversal symmetry is not broken and the conductance profile remains gapless for all electron energies. Although the conductance of double-well structure is nearly higher than that of the double-barrier structure, the magnetoresistance ratio versus the separation distance between the two magnetized regions exhibits pronounced oscillations due to the resonant tunnelling states.

This paper is organized as follows: In Sec. II, we introduce our model and formalism for electron scattering from the double-gated and magnetized structure in the presence of hexagonal warping effect. By tuning our system parameters, numerical results and discussions for transmission properties, conductance spectra, and magnetoresistance ratios of incident electrons are presented in Sec. III. A brief conclusion is given in Sec. IV.
 \begin{figure}[hbt!]
\centerline{\includegraphics[width=0.95\linewidth]{Fig1.eps}}
\caption{(a) Schematic view of a 3D topological insulator, modulated by double gate voltage and magnetization effect on its surface.
Panels (b), (c), and (d) show the Dirac cone of fermions on the surface of a 3D topological insulator in the presence proximity effect with magnetization orientation along the $z$, $x$, and $y$ axis, respectively. Panels (e), (f), and (g) show the constant-energy contours corresponding to Dirac cones (b), (c) and (d), respectively, at incident energy $E=400$\,meV. The black dots in (e)-(g) represent the Dirac point, while the green and blue solid lines are associated with $\Delta=0$, and $\Delta=70$\,meV, respectively. }
\label{F1}
\end{figure}

\section{Model and formalism}
We consider the 3D topological insulator $\mathrm{Bi}_{2}\mathrm{Te}_{3}$ which demonstrates strong warping effects and a Dirac cone on its surface. The interaction between bulk states and the surface states in such a structure can be ignored by tuning the Fermi level on only the surface states via appropriate doping \cite{Chen2009}. Therefore, we only focus on the topological surface states as one of the most important features of the topological insulators. We have applied gate voltages and magnetic proximity effects in two regions, called modulated regions of width $W$, separated by a distance $d$, as shown in Fig. 1(a). The effective Hamiltonian of the surface states in units of $\hbar=1$ and in the absence of particle-hole asymmetry can be given by \cite{An2012}:
\begin{equation}\label{eq1}
\hat{H}=\upsilon_{F}(k_{x}\sigma_{y}-k_{y}\sigma_{x})+\lambda(k_{x}^{3}-3k_{x}k_{y}^{2})\sigma_{z}+V(x) \ ,
\end{equation}
with
\begin{eqnarray}\label{eq11}
V(x)=(U_g&+&\Delta\mathrm{\bf{m}}\cdot\boldsymbol{\sigma})[\Theta(x)\Theta(W-x)\nonumber\\
&+&\Theta(x-d-W)\Theta(d+2W-x)]\ ,
\end{eqnarray}
where $\upsilon_{F}$ is the Fermi velocity, $\lambda$ is the warping parameter, and $\boldsymbol{\sigma}=(\sigma_{x},\sigma_{y},\sigma_{z})$ are Pauli matrices. $k_x=k\cos\beta$ and $k_y=k\sin\beta$ are the in-plane momentum components in which $\beta$ is the incident angle of electrons at $x=0$.
The first term in Eq. (\ref{eq1}) describes the helical Dirac fermions on the surface of the topological insulator (see Fig. 1a),
while the second term represents the hexagonal warping effect. $V(x)$ denotes the effects of gate voltage $U_g$ and magnetic proximity of
a ferromagnetic insulator with magnetization direction ${\bf m}=(\sin\theta\cos\varphi,\sin\theta\sin\varphi,\cos\theta)$ in the regions $0\le x\le W$ and
$d+W\le x\le d+2W$. Here,  $\theta$ is the polar angle with respect to the $z$-axis and $\varphi$ is the azimuthal angle measured from the $x$-axis. Also, $\Theta(x)$ is the step function and $\Delta$ is the proximity-induced exchange energy. Note that the gate voltage may act as a potential barrier $(U_g>0)$ or a quantum well $(U_g<0)$ for incident electrons with energy $E$.

The energy dispersion of the topological surface states in the presence of a gate voltage and magnetic proximity effects can be obtained by:
\begin{equation}\label{eq2}
E({\bf k})=U_g+s\epsilon({\bf k})\ ,
\end{equation}
with
\begin{equation}\label{eq3}
 \epsilon({\bf k})=\sqrt{[{{\lambda}({k_{x}}^{3}-3k_{x}{{k_{y}}^2})+
\Delta\cos\theta}]^2+A}\, ,
\end{equation}
where $s={\pm 1}$ correspond to the upper and lower surface bands, respectively,
and $A=(\Delta\sin\theta\cos\varphi-\upsilon_{F}k_{y})^2+(\Delta\sin\theta\sin\varphi+\upsilon_{F}k_{x})^2$. We shall assume the Fermi level lies in the upper band $(s=+1)$.

Using $({k_{x}}^{3}-3{{k_{y}}^2}k_{x})=k^{3}\cos3\beta$, we can rewrite Eq. (\ref{eq3}) as
\begin{equation}\label{eq4}
\epsilon({\bf k})=\sqrt{\upsilon_{F}^2k^{2}+\Delta^{2}\sin^{2}{\theta}-B+C}\, ,
\end{equation}
where  $B=2\upsilon_{F}k\Delta\sin\theta\sin(\beta-\varphi)$ and $C=({\lambda}k^{3}\cos3\beta+\Delta\cos\theta)^2$.
If we ignore the warping effect and rewrite Eq. (\ref{eq4}) as a second-order equation in
terms of $k$, the condition of having real values for $k$ is obtained as
\begin{equation}\label{eq5}
 |E-U_g|\geq\Delta\sqrt{\sin^{2}\theta\cos^{2}(\beta-\varphi)+\cos^{2}\theta}.
 \end{equation}

In this case, when the magnetization direction is perpendicular to the surface of topological insulator ($\theta=\phi=0$), the largest energy gap, $2\Delta$, opens up at the Dirac point. This gap opening which suppresses the longitudinal conductivity can cause a large magnetoresistance ratio \cite{Chiba-Takahashi-2017}. For other magnetization directions, however, the energy gap is determined by $|2\Delta\cos\theta|$. In other words, the minimum value of the square root in Eq. (\ref{eq5}) can be obtained when $\cos(\beta-\phi)=0$. Therefore, in the case of in-plain magnetization ($\theta=\pi/2$), the energy dispersion becomes gapless.

In the presence of hexagonal warping effect, however, we find that the Fermi contour deforms into a snowflake shape. Moreover, the magnetic proximity effect can shift the Dirac cone and open up a gap in the band structure. In Figs. 1(b)-(d) we have shown the energy dispersion of the surface states when the magnetization is along the $z$, $x$, and $y$ axis, respectively. When the magnetization is fixed along the $z$ axis, the change in the Fermi contour is very small (see Fig. 1(e)), whereas the energy contour is modulated and shifted for the magnetization along $x$ and $y$ axes [see panels (f) and (g) in Fig. 1]. It is clear that in the case of magnetization along the $y$ axis, an energy gap which is much smaller than that with the magnetization along the $z$ axis opens up at the Dirac point. Nevertheless, since the gap width of 11 meV [panel (d) in Fig. 1] is much smaller than the thermal energy of 26 meV at room temperature, such a band gap does not considerably affect device performance.

Now we turn to electron transport through our main structure shown in Fig. 1(a). We consider an electron with momentum ${\bf q}=(q_{x},q_{y})$ and energy $E>0$ incident from left on the interface of normal/modulated regions at $x_1=0$. The energy and $y$-component of the momentum are conserved in the scattering process.
In the normal regions $(\Delta=0, U_g=0)$, the equation $E(q_{x},q_{y})=E_{F}$ in terms of $q_x$ is a sextic algebraic equation with six solutions.
If the energy is above the critical value $E_{c}\approx 377$ meV, the six roots are all real numbers, otherwise two roots are real and the rest are complex \cite{An2012}. In the modulated regions, however, the six roots are obtained from the equation $E(k_{x},k_{y})=E_{F}$ in terms of $k_x$.

By solving Eq. (\ref{eq1}), the corresponding eigenstates in the modulated regions can be written as:
\begin{equation}\label{eq7}
u({\bf k}_{m},{\bf r})=\sqrt{\frac{|\varphi_{1m}|^2}{|\varphi_{1m}|^2+|\varphi_{2m}|^2}}
\left(\begin{array}{cc}
1 \\  \frac{\varphi_{2m}}{\varphi_{1m}}
\end{array}\right)e^{ik_{x,m}x}e^{ik_{y}y}\ ,
\end{equation}
with
\begin{equation}\label{eq8}
\varphi_{1m}(k_{x,m},k_{y})=\Delta\cos\theta+\epsilon({\bf k})+\lambda k_{x,m}(k_{x,m}^{2}-3k_{y}^{2})\, ,
\end{equation}
\begin{equation}
\varphi_{2m}(k_{x,m},k_{y})=\Delta\sin\theta\,e^{i\phi} - \upsilon_{F}(k_{y}-ik_{x,m})\, ,
\end{equation}
where $m=1-6$. Moreover, the electron eigenstates $u_{m}({\bf q},{\bf r})$  in the normal regions follow similarly from Eq. (\ref{eq7}).
As a result, for an incident electron with given energy $E_{F}$, the wave functions of the scattering states in all regions can be written as
\begin{align}
\psi_{1}({\bf r})&=u(q_{x}^{i},q_{y})+\sum_{m=1}^{3} r_{m}u(q_{x,m}^{r},q_{y})~~~~x\le 0\ ,\\
\psi_{2}({\bf r})&=\sum_{m=1}^{6} s_{m}u(k_{x,m},k_{y})~~~~~~0\le x\le W \ ,
\end{align}
\begin{multline}
\psi_{3}({\bf r})=\sum_{m=1}^{3} f_{m}u(q_{x,m}^{r},q_{y})+\sum_{m=1}^{3} g_{m}u(q_{x,m}^{t},q_{y}) \\
W\le x\le d+W \ ,
\end{multline}
\begin{align}
\psi_{4}({\bf r})&=\sum_{m=1}^{6} h_{m}u(k_{x,m},k_{y})~~~~d+W\le x\le d+2W\, ,\\
\psi_{5}({\bf r})&=\sum_{m=1}^{3} t_{m}u(q_{x,m}^{t},q_{y})~~~~x\ge d+2W\, ,
\end{align}

Here $u(q_{x}^{i},q_{y})$ is the incident eigenstate, $g_{m}$ and $t_{m}$ are the transmission amplitudes with eigenstates $u(q_{x,m}^{t},q_{y})$ in the central and right normal regions, respectively, $r_{m}$ and $f_{m}$ are the reflection amplitudes associated with the eigenstates $u(q_{x,m}^{r},q_{y})$ in the left and central normal regions, while
 $s_{m}$ and $h_{m}$ are the scattering amplitudes in the modulated regions.

For fixed value of Fermi energy $E_F$ and $q_y$, the solution of $E(q_{x},q_{y})=E_{F}$ is dependent on whether $E_F<E_c$ or $E_F>E_c$. Therefore, there are two types of solutions. The first type which corresponds to $E_F<E_c$ consists of two real roots and four complex ones. Therefore, since the incident wave vector $q^i$ must be a real number, the conditions for the reflected wave vector $q^r$ and the transmitted wave vector $q^t$ can be chosen as $q^{i}_x=q^{t}_{x,1}=-q^{r}_{x,1}$ (real roots) and $q^{t}_{x,2(3)}=-q^{r}_{x,2(3)}$ (imaginary roots) \cite{An2012}. For the second type of solutions corresponding to $E_F>E_c$, all the roots are real numbers (three positive roots and three negative roots with the same absolute values) so that, two of them are hole-like propagating waves $(q_x\upsilon_{x}({\bf q})<0)$ and the other roots are electron-like waves $(q_x\upsilon_{x}({\bf q})>0)$. Considering the fact that the incident wave vector must be real, the wave vectors can be chosen as $q^{i}_x=q^{t}_{x,1}=-q^{r}_{x,1}$, $q^{t}_{x,2(3)}=-q^{r}_{x,2(3)}$, $q^{t}_{x,1(2)}>0$,  $q^{t}_{x,3}<0$, $\upsilon_ {x}(q^{t}_{x,m},q_{y})>0$ \cite{An2012}. Here, $\upsilon_{x}(q)=\frac{\partial E}{\partial q_{x}}$ is the electron group velocity along the $x$ axis.

Since the Hamiltonian Eq. (\ref{eq1}) is a third-order partial differential equation with respect to $k_{x}$, to determine the reflection and transmission amplitudes, the following boundary conditions should be satisfied:
\begin{equation}\label{eq10}
\begin{array}{ccc}
\psi_{n}({\bf r})\mid_{r=(x_{n},y)} = \psi_{n+1}({\bf r})\mid_{r=(x_{n},y)} \, , \\\\
\partial_{x} \psi_{n}({\bf r})\mid_{r=(x_{n},y)} = \partial_{x}\psi_{n+1}({\bf r})\mid_{r=(x_{n},y)} \, ,  \\\\
\partial_{x}^{2}\psi_{n}({\bf r})\mid_{r=(x_{n},y)} = \partial_{x}^{2}\psi_{n+1}({\bf r})\mid_{r=(x_{n},y)} \, ,
\end{array}
\end{equation}
with $n$=1-4. Using the above boundary conditions and the transfer matrix method which connects the incident wave to the
transmitted wave \cite{Saffar2003,Saffar2005,Li2013},  all the reflection and transmission amplitudes can be determined.
\begin{figure}
\centerline{\includegraphics[scale=0.58]{Fig2.eps}}
\caption{Transmission probability $T$ as a function of the incident angle $\beta$ with magnetization angles (a) $\theta=\varphi=0$, and
 (b) $\theta=\pi/2, \phi=0$ at different energies $E=200$ meV (red), $E=300$ meV (blue), and  $E=400$ meV (green).
The other parameters are  $U_{g}=300$ meV, $\Delta=30$\,meV and $d=W=4$\,nm. }
\label{F2}
\end{figure}

\begin{figure}
\centerline{\includegraphics[scale=0.54]{Fig3.eps}}
\caption{Transmission probability $T$ as a function of the incident angle $\beta$ with $E=U_{g}=350$ meV, $\Delta=50$ meV and $\theta=\varphi=\pi/4$ for  (a) $d=3$ nm and (b) $W=3$ nm.}
\label{F3}
\end{figure}

For the first type of solution, the total transmission coefficient of electrons with energy $E$ and incident angle $\beta=\arctan(\frac{q_{y}}{q_{x}})$ is given by $T(E,\beta)=|t_1|^2$, whereas for the second type of solution, the total transmission coefficient is calculated by $T(E,\beta)=\sum_{i=1}^3|t_i|^2$. Moreover, using the continuity equation $\nabla\cdot\mathbf{J}+\frac{\partial\rho}{\partial t}=0$, the charge current density $\mathbf{J}$ of an electron with charge $e$ can be expressed by the following components:
\begin{equation}\label{jx}
J_x=ev_F(\psi_l^\dagger\sigma_y\psi_l) + 3e\lambda k^2\cos 2\beta(\psi_l^\dagger\sigma_z\psi_l)\ ,
\end{equation}
\begin{equation}
J_y=-ev_F(\psi_l^\dagger\sigma_x\psi_l) - 3e\lambda k^2\sin 2\beta(\psi_l^\dagger\sigma_z\psi_l)\ ,
\end{equation}
where $\rho$ is the charge density and $k$ is the magnitude of wave vector in region $l (\equiv1-5)$. Therefore, assuming that the system has a large width in the $y$ direction given by $L_y$, the net current going from left to right is given by
\begin{equation}
I=\frac{L_y}{2\pi^2}\int_0^\infty\int_{-\pi/2}^{\pi/2} J_x [f_1(\epsilon_\mathbf{k})-f_5(\epsilon_\mathbf{k})]kdkd\beta\  ,
\end{equation}
where $f_l(\epsilon)$ is the Fermi function in region $l$. Considering Eq. (\ref{jx}) for region 5 and the difference of Fermi functions at low temperature and a small bias voltage, the differential conductance $G$ of electrons at Fermi energy can be obtained by
\begin{equation}\label{G}
G=g_0\int_{-\pi/2}^{\pi/2} T(E_F,\beta)F(k_F(\beta),\beta) d\beta\  ,
\end{equation}
with
\begin{equation}
F(k_F,\beta)=\frac{[2Bv_F^2k_F^{2}\cos\beta+3\lambda k_F^3(B^2-v_F^2k_F^2)\cos 2\beta]v_{F}}{E_{F}(B^2+v_F^2k_F^2)[\frac{dE(k,\beta)}{dk}]|_{k_F(\beta)}}\  ,
\end{equation}
\begin{equation}
B=\lambda k_F^3\cos 3\beta+\sqrt{v_F^2k_F^2+\lambda^2 k_F^6\cos^2 3\beta}\  ,
\end{equation}
\begin{equation}
k_F=\sqrt{[\sqrt{\frac{\kappa_{2}^3}{27}+\frac{\kappa_{1}^2}{4}}+\frac{\kappa_{1}}{2}]^{1/3} - [\sqrt{\frac{\kappa_{2}^3}{27}+\frac{\kappa_{1}^2}{4}}-\frac{\kappa_{1}}{2}]^{1/3}}\  ,
\end{equation}
where $k_F\equiv k_F(E_F,\beta)$ is the Fermi wave vector of incident electrons, $\kappa_{1}=\frac{E^2_F}{\lambda^2\cos^2 3\beta}$,
$\kappa_{2}=\frac{v_F^2}{\lambda^2\cos^2 3\beta}$, and $g_0=\frac{e^2E_FL_y}{2\pi^2v_F}$ is the unit of conductance with $\hbar=1$.

Note that, we expect the maximum value of conductance to be $2g_0$ due to the integral over $\beta\in [-\frac{\pi}{2},\frac{\pi}{2}]$. Such an interval for angle of incidence is especially necessary when the mirror symmetry in the constant-energy contour is broken in the presence of an external  magnetic field (see Fig. 1(f)).

\section{Results and discussion}
We now use the above method to obtain the numerical results of electronic transport through the double modulated structure presented in Fig. 1(a). We choose $\upsilon_{F}=2.55$ eV\,$\mathrm{\AA}$ and $\lambda=250$ eV\,$\mathrm{\AA^3}$ which produce the Fermi surface of $\mathrm{Bi}_{2}\mathrm{Te}_{3}$ in good agreement with experiments \cite{Chen2009}. The electron scattering in our system is governed by the exchange field strength $\Delta$, applied gate voltage $U_g$, the width of gate regions $W$, the separation distance $d$ and the magnetic alignments of the two modulated regions.

In Figs. 2(a) and (b), we have depicted the variation of transmission probability with incident angle of electrons through the structure, when ${\bf m}$ in both modulated regions is aligned along the $z$- and $x$-directions, respectively. As can be seen, the the system is fully transparent ($T=1$) at some incident angles, whereas the normally incident electrons are not perfectly transmitted due to the induced magnetic field. Indeed, the perfect transmission found for normally incident Dirac fermions is shifted from normal incidence ($\beta=0$) to an off-normal angle ($\beta\neq 0$) when the  magnetic fields align along the $x$-direction (see Fig. 2(b)) \cite{Katsnelson2006,Li2015}. Such an effect, however, does not occur for the case of ${\bf m}$ in the $z$-direction, as a result of broken time-reversal symmetry. Note that time reversal symmetry on the surface of each modulated region is dependent on the magnetization orientation in that region. Therefore, the time reversal symmetry remains broken as long as the magnetization orientations in both modulated regions are not fully aligned in the $x$-direction.
\begin{figure}
\centerline{\includegraphics[scale=0.55]{Fig4.eps}}
\caption{Calculated conductance as a function of gate voltage $U_{g}$ (a) at different values of $\Delta$ but fixed $E=$\,200 meV and (b) various incident energies $E$ but fixed $\Delta=50$\, meV. The other parameters are $\theta=\phi=\pi/4$ and $W=d=5$\,nm.}
\label{F4}
\end{figure}

The number of tunnelling resonances increases with increasing the incident electron energy and that the incident angles at which the resonances occur are considerably energy dependent. When $\bf m$ aligns along the $z$-direction the transmission profile is symmetric about $\beta=0$ while, this symmetry is broken for the case of $\bf m$ in the $x$-direction. This effect is fully associated with the broken mirror symmetry in the constant-energy contour around $\Gamma$-K direction as shown in Fig. 1(f). For the special case of $E=U_{g}=300$\,meV with $\bf m$ in the $z$-direction a strong suppression in the transmission probability of normally incident electrons happens compared to the transmission panels in the case of $E\neq{U_{g}}$. Due to the gap opening in energy dispersion and the influence of warping effect (see Fig. 1(b)), this behaviour is in contrast to p-n-p graphene junctions, where the transmission is nonzero and perfect ($T=1$) only at normal incidence \cite{Li2015}.
\begin{figure}
\centerline{\includegraphics[scale=0.68]{Fig5.eps}}
\caption{Calculated conductance as a function of incident energy $E$ with $U_{g}=200$\,meV, $\Delta=50$\,meV
for parallel magnetization directions at (a) $\theta=\varphi=0$, and (b) $\theta=\pi/2$, $\phi=0$. The insets represent the conductance vs incident energy in the presence and absence of warping effect with $U_{g}=100$\,meV and $d=W=5$ nm.}
\label{F5}
\end{figure}

In Figs. 3(a) and 3(b), we show our analysis of the transmission probability for $\theta=\phi=\frac{\pi}{4}$
with different $W$ values but fixed separation distance $d$ and with different $d$ values but fixed $W$, respectively.
It can be seen that with decreasing $W$, the transmission lobes become progressively wider and that the $T(E,\beta)$ profile approaches the maximum value around normal incidence, confirming the role of proximity effect in suppression of transmission for normal incident electrons.
Moreover, as the spatial separation $d$ between the two modulated regions is increased the transmission probability spans over a wider angular range.
For a fixed magnetization direction, the transmission probabilities are equally shifted from the normal incidence, regardless of the values of $W$ and $d$, as shown in Fig. \ref{F3}.
\begin{figure}[h]
\centerline{\includegraphics[scale=0.55]{Fig6.eps}}
\caption{Calculated conductance as a function of incident energy $E$ with $\Delta=40$\,meV and $d=W=4$\,nm,
when the magnetization orientations align along the (a) $z$- and (b) $x$-axes.}
\label{F6}
\end{figure}

To investigate the effect of double gate voltage on transmitted electrons, we have depicted in Fig. 4(a) the conductance versus gate voltage for fixed parallel magnetization directions with $\theta=\phi=\frac{\pi}{4}$ at different exchange energies $\Delta$. In such a magnetic direction an energy gap opens up around the Dirac point as a result of nonzero $\bf m$ component in $z$-direction. We see that the conductance decreases with increasing the exchange field and hence the band gap (Fig. 4(a)). For instance, in the case of $\Delta=60$ meV, we found an energy gap of 86.4\,meV around the Dirac point and the conductance reaches a minimum and nearly constant value in the interval $180<U_g<250$\,meV around the gate value at which $U_g=E=200$\,meV. As $U_{g}$ increases, $G$ decreases for all $\Delta$ values until the Dirac point approaches the incident energy at which the coherent tunnelling governs the mechanism of charge transport. Then the conductance gradually increases with gate voltage to almost 1$g_0$ and exhibits distinct resonant peaks. The magnetic proximity effect reduces the conductance in the system, while the behaviour of $G$ remains nearly unchanged with gate voltage. Such a behaviour has also been seen in p-n-p graphene heterojunctions under the influence of external magnetic field \cite{Li2015}.
Moreover, Fig. 4(b) shows the conductance as a function of gate voltage at different incident energies $E$. At $U_{g}<E$, the conductance has larger values for higher energies and its minimum value is shifted along the voltage axis as the energy is increased. The position and the hight of resonant peaks are dependent on $\Delta$ and $E$ values.
\begin{figure}
\centerline{\includegraphics[scale=0.55]{Fig7.eps}}
\caption{Calculated magnetoresistance ratio as a function of incident energy $E$ with $\Delta=40$\,meV and $d=W=4$\,nm.
The magnetization orientations align along the (a) $z$- and (b) $x$-axes.}
\label{F7}
\end{figure}

Energy dependence of the conductance at different $d$ and $W$ values with parallel magnetizations in the $z$- and $x$-direction is shown in Figs. 5(a) and (b), respectively. In the conductance spectra, one can see several resonant peaks whose positions are shifted by changing $d$ and $W$, simultaneously, regardless of the orientation of magnetizations. When the magnetizations align along the $z$-direction ($\theta=0, \phi=0$) the conductance around $E=U_g$ approaches to zero and a gap opens up in the conductance spectra as $d$ and $W$ are increased. This is a typical signature of broken time-reversal symmetry as a result of the normal component of $\bf m$ in the modulated regions. In contrast, the conductance spectra do not exhibit any gap opening when the magnetizations align in the $x$-direction ($\theta=\pi/2, \phi=0$). The conductance in the minimum case is greater than $0.2g_{0}$, indicating that due to the time reversal symmetry, the system is conductive for all surface electron energies, i.e.,  $E\leq U_{g}$ and  $E> U_{g}$.  This result clearly suggests that magnetization directions can control the electron charge transport on the surface of double-gated topological insulators. In addition, to examine the influence of warping effect on the electronic transport, we have depicted in the insets of Fig. 5 the conductance vs incident energy in the presence and absence of warping term (see Eq. (\ref{eq1})).  At low energies, the conductance is not affected by the warping strength, as expected from Fig. 1(b) and (c). At high energies relative to the Dirac point, however, the warping effect considerably enhances the conductance due to more transport channels resulting from the snowflake shape of the constant-energy contour.

\begin{figure}[h]
\centerline{\includegraphics[scale=0.55]{Fig8.eps}}
\caption{Calculated magnetoresistance ratio as a function of distance between the two magnetized regions at $E=150$\, meV with $\Delta=40$\,meV and $W=4$\,nm.
The magnetization orientations align along the (a) $z$- and (b) $x$-axes.}
\label{F8}
\end{figure}

The spin of topological surface states which lies in-plane is locked at right angles to the electron momentum, so that electrons in $\bf k$ and $-\bf k$ states carry opposite spins and possess opposite group velocities. Moreover, in the presence of hexagonal warping effect, an in-plane magnetic field not only deforms the constant-energy contour, but also shifts the Dirac point, as shown in Figs. 1(f) and (g) by a black dot. Therefore, the currents of electrons with opposite spin directions can no longer compensate each other, and hence, a spin-polarized current can be produced \cite{Li-NanoTec2014,Dankert-Nano-2015}. This property can be used to examine the magnetoresistance effect in our double-gated and magnetized structure. To do this, the electric conductance should be calculated in the two cases of parallel (Pa) and antiparallel (APa) magnetization directions. In Figs. 6(a) and (b), we have depicted the conductance versus energy, for both Pa and APa magnetization orientations along $z$- and $x$-axes, respectively. Also, we have shown the effect of positive and negative gate voltages on the conductance values for the two magnetization orientations. A positive (negative) gate voltage in the surface of topological insulator induces a double quantum barrier (well) structure and hence, the resonant states play the main role in the process of electron transport. For magnetizations in the $x$-direction, the conductance exhibits more oscillatory behaviour and the overlap between conductance values in the Pa and APa magnetizations is negligible compared to that for magnetizations in the $z$-direction, regardless of the sign of $U_g$.  The structure with quantum wells is more conductive than the structure with quantum barriers due to the electron tunnelling process, except for low energy electrons. Furthermore, due to the quantum interference of propagating waves in the region between the two magnetized segments, the conductance oscillations in the APa configuration are $180^{\circ}$ out-of-phase with respect to those in the Pa magnetic configuration, regardless of the sign of gate voltage. This indicates that one can obtain a large magnetoresistance effect in these double-modulated devices.

The magnetoresistance ratio is defined as
\begin{equation}
\mathrm{MR}=\frac{G_{Pa}-G_{APa}}{G_{Pa}}\times 100\%\,
\end{equation}
where $G_{Pa}$ and $G_{APa}$ are the conductances in the parallel and antiparallel magnetization orientations, respectively.

In Figs. 7(a) and (b), we plot the magnetoresistance versus energy, when magnetization aligns along the $z$- and $x$-axes, respectively. We can see that MR exhibits an oscillatory behaviour due to the existence of resonant states in both double-barrier and double-well structures. In the case of magnetization in the $z$-axis, MR value can reach $\sim$ -170\% for the structure with double quantum barrier, whereas it reaches $\sim$ +60\% for double quantum well structure. On the other hand, when magnetization aligns along $x$-axis, MR oscillation decreases and the values are mostly positive. A positive magnetoresistance ratio which indicates a low resistance in the parallel magnetic configuration is of key importance for spintronic applications. For high energy electrons, MR approaches zero and the difference in the MR values in a double-barrier or double-well structure becomes negligible due to the suppression of conductance oscillations at high energies, as shown in Fig. 6.

Figure 8 shows the MR as a function of separation $d$ between the two magnetized regions. The MR exhibits large oscillations with distance $d$ in double-barrier structures, whereas the change in the magnetoresistance is very small in double-well structures. When $\bf m$ directions align along the $z$-axis, the MR finds positive and negative values by varying the separation distance. On the contrary, MR is fully positive and exceeds +50\%, when $\bf m$ orientations align in the $x$-direction. Note that MR is a function of energy as discussed in Fig. 7, nevertheless the nature of oscillations versus the separation distance between the two magnetized regions is independent of energy and it comes from spin-momentum locking of surface states. The MR oscillations closely resemble Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions between two impurity magnetic moments placed on the surface of a topological insulator and predict that the surface electronic states mediate such a RKKY interaction among the magnetic modulated regions \cite{Garate-Franz,Biswas-Balatsky}. It is worth mentioning that although magnetic impurities on the surface of topological insulators break time reversal symmetry by inducing a band gap in the energy dispersion, time reversal breaking does not form in a system consisting of magnetic modulated regions with magnetization directions along the $x$-axis.

\section{conclusions}
In summary, we have theoretically investigated the effects of double gate voltage and magnetism on Dirac fermions on the surface of a topological insulator.
Our findings demonstrate that the conductance decreases with increasing the exchange field and that the resonant states are not strongly affected by changing the magnetization orientation. The hexagonal warping effect increases the conductance at high energies when the constant-energy contour forms a snowflake shape. For magnetization direction along $x$-axis, time reversal symmetry is not broken and the system remains conductive for all surface electron energies.
Although the double-well structure is more conductive than the double-barrier structure, the MR oscillations corresponding to a positive gate voltage are more significant than those in the case of negative gate voltages. The MR is an oscillatory function in terms of energy and the separation distance between the two magnetized regions.
Our results suggest that the charge transport and MR effect on the surface of double-gated topological insulators can be effectively controlled by tuning the double gate voltage and magnetism.

redpajama_set_name: RedPajamaArXiv


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SPARTAN PERFORMANCE CROSSFIT SUFFOLK
15 minutes to practice or work up to a heavy Hi-Hang Clean (no hip, just knee extension).
-then-
12 minute AMRAP of:
10 KB Clean & Jerk (left) 24/16kg
15 KBS 24/16kg
10 KB Clean & Jerk (right) 24/16kg
15 KB Hi-Pulls 24/16kg
Notes: The KB should touch the floor between every rep of Clean and Jerks, and every Hi-Pull.
9 Reasons To Olympic Lift For A Better Physique "Doing cleans teaches the body to move weight fast. This leads to increases in force production, and more force production means more type II fibers being recruited. More type II fiber recruitment equals bigger, stronger, denser, and fuller muscle bellies. This is a classic rich-get-richer scenario."—Daniel Brown, For TNation.com
What Runners Can Learn From Cheetahs "Up to a speed of about 40 miles per hour, there's very little difference," Dr. Wilson says. "But what happens after that," when the cheetah finds another gear and accelerates to 65 miles per hour, "is something we'd like to understand. We believe it can help us to better understand the determinants and limits of speed itself."—Alan H. Wilson, a professor at the Royal Veterinary College at the University of London

redpajama_set_name: RedPajamaCommonCrawl


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Join us in conversation with Shivani Siroya, CEO and Founder of Tala (formerly InVenture) and her investor, Anu Duggal of Female Founders Fund, to learn about how Tala is building world class technology to revolutionize financial services in emerging markets.
Founded in 2011, Tala launched in Kenya as a mobile app aggregating customer data to determine a credit score and offer loans. Since then, Tala has gone on to expand across Africa and Asia and is one of the fastest growing fintech companies in the world.
Shivani founded Tala (InVenture) after witnessing firsthand the tremendous gaps in financial access in emerging markets. Prior to founding Tala, Shivani held a variety of positions in global health, microfinance, and investment banking, including with the United Nations Population Fund, Health Net, Citigroup and UBS. Shivani is a 2016 Aspen Institute Finance Leader Fellow, 2016 WEF Young Global Leader, 2015 Senior TED Fellow and 2013 Ashoka Fellow. She is also on the board of Stellar.org. She holds a M.P.H from Columbia University and a B.A. from Wesleyan University.
Rise New York is part of a global community of the world's brightest thinkers and doers, from startups to industry leaders, working together to create the future of financial services. We listen, nurture and oxygenate through our international network of Rise spaces, and connect, co-create, and scale innovation, in partnership with Barclays. Rise New York also houses a beautiful co-working space in the heart of Manhattan, a world-class events Theatre, and is home to the U.S. cohort of the Barclays Accelerator, powered by Techstars.


text:
Speaking the Language of Data Visualization
CSU Bolsters Continuity Plan with Infrastructure Management Software
The California State University system this week said it's deployed Planet IRM enterprise software on 10 of its 23 campuses as part of an effort to bolster its business continuity efforts in a "massive system-wide upgrade of its network infrastructure."
CSU's upgrade includes, among other things, new fiber, routing and switching equipment, and WAN access support. The Planet IRM ("Infrastructure Relationship Management") software, from Planet Associates, helps track the quipment, cable connections, maps, and other information in a relational database for data viz, analysis, and management.
"Ideally, we wanted a solution for our infrastructure upgrade that not only allows more accurate assessment of technologies needed for various installations but one designed to help the university system rebuild more easily should it ever face damage to a facility in the future," said Charlotte Ferguson, CSU systems analyst, in a statement released this week. "When it comes time to rebuild after a system disruption, or if someone inadvertently cuts a line, we should know instantly what it will take to get the campus back up and running. This is an important part of our business continuity plan."
Campuses and facilities that have been equipped with the Planet IRM sytem include Chico, Dominguez Hills, East Bay, Los Angeles, Monterey Bay, Northridge, Pomona, San Jose, San Luis Obispo, and San Marcos, as well as the chancellor's office, located in Long Beach.
CSU will add Planet IRM on three more campuses this year, including Bakersfield, Fullerton, and San Francisco. The system serves a total of about 450,000 students in California and employs about 46,000 faculty and staff.


All are invited to takebrpart in the Run4Elise 5K and 1-Mile Fun Run on April 8 at DragonbrStadium. Elise Cerami was a passionate 13-year-old competitive swimmer whobrpassed away during warm-ups at a club practice last summer. Run4Elise is abrdivision of the SWIM4Elise Foundation, a registered nonprofit organization thatbrpromotes water safety through swimming scholarships. On race day, $10,000 in scholarships will be awarded. North Texas swimmers from 6th through 12th grade (including Dragon swimmers who are on NTN, LAC or other USA Swimming clubs) are eligible for swim camp and college scholarships.
Group registration is $25 (four or more participants) and $30 for single participants in the 1-Mile Fun Run or 5K. Click here to register.
The event kicks off with scholarship awards at 8 a.m., followed by the 1-mile Fun Run at 8:15 and the 5K at 8:45. Each participant will receive a finisher's medal, and awards will be given in the 5K to the overall top male and female, along with the first, second and third male/female by age group.
Katie Meili, 2016 U.S.brOlympic team swimmer and two-time Olympic medalist in both gold and bronze,brwill be the special guest at the event. Gather your family and friends andbrcreate a team to run in memory of Elise—the team deadline is March 17. Plaquesbrwill be awarded to the two teams with the most registered participants.
Visit Swim4Elise.com tobrlearn more and click here to make a donation to the Elise Cerami Memorial Scholarship.


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Q: Setting Login page as default page in asp.net mvc 5 i want this url "http://localhost:45678/" to bring me to my Login.cshtml that has a AccountController that contains
public ActionResult Login()
{
    return this.View();
}

This is how i do it in RoutesConfig.cs
public static void RegisterRoutes(RouteCollection routes)
    {
        routes.IgnoreRoute("{resource}.axd/{*pathInfo}");
        routes.MapMvcAttributeRoutes();

        routes.MapRoute(
            name: "Default",
            url: "{controller}/{action}/{id}",
            defaults: new { controller = "AccountController", action = "Login", id = UrlParameter.Optional }
        );
    }

However, it is giving me a "Server Error in '/' Application." "The resource cannot be found.". what is the right way to do it?

A: Your controller name is wrong. instead calling AccountController, you need to call Account.
public static void RegisterRoutes(RouteCollection routes)
    {
        routes.IgnoreRoute("{resource}.axd/{*pathInfo}");
        routes.MapMvcAttributeRoutes();

        routes.MapRoute(
            name: "Default",
            url: "{controller}/{action}/{id}",
            defaults: new { controller = "Account", action = "Login", id = UrlParameter.Optional }
        );
    }

A: Try this
public ActionResult Login()
{
  return View();
}

Make sure you have login page in the views section > Account

A: Add authorization attribute to all the controllers where you need to be logged in.
then u create a redirect in your login logic.

redpajama_set_name: RedPajamaStackExchange


text:
Home » Price Range » From $1M and Above » How Much Does It Cost to Open Sweet Frog Franchise?
How Much Does It Cost to Open Sweet Frog Franchise?
Do you want to open an ice cream business by buying Sweet Frog franchise? If YES, here is how much it cost to open a Sweet Frog franchise successfully. If you are looking towards opening a Sweet Frog Franchise, it will be nice for you to have a of what the company represents before going ahead to enquire about opening their franchise.
Sweet Frog started operations in 2009 and they began selling franchise in 2012. They have their corporate headquarters at Scottsdale, Arizona and presently they have an estimated 330 franchise units in operation.
MTY Franchising USA, Inc. is the franchisor of Sweet Frog. The franchisor sells franchises for retail shops that offer and sell soft-serve yogurt and other authorized products and services and that use a self-service format which allows customers to create individualized yogurt-based desserts. The shops do business under the mark "Sweet Frog."
Here are areas where you are expected to spend money and the cost associated with it;
Financial Investment Required to Open a Sweet Frog Franchise
1. Initial Franchise Fee: $30,000
2. Purchase of Merchandise, Furniture, and Promotional Items: $16,000 to $21,000
3. Royalty Fee: 5% of Net Sales
4. Marketing Assessment: Up to 3% of Net Sales
5. Advertising and Promotional Material
6. Website Review and Hosting Fee:
7. Additional Training or Training Additional, Successor, or Replacement Personnel:
8. Alternative Product or Supplier Inspection and Testing
9. Audit Fee:
10. Costs and Attorneys' Fees
11. Costs for Correction of Deficiencies:
Please note that when you sign the Franchise Agreement, you will pay Sweet Frog an initial franchise fee in the amount of $30,000, which may be reduced as follows:
1 Shop: $30,000
2 to 5 Shops: $25,000
6 or more Shops: $15,000
Please note that Sweet Frog currently offers qualified veterans a financial incentive for newly developed franchised sweet Frog Shops. If you are a qualified veteran (as specified by Sweet Frog), sweet Frog will reduce the initial franchise fee by 20%.
Prior to opening the Shop, you must acquire from the franchisor a start up package ("Start Up Package"), which includes the items noted in the Manual (i.e., logoed merchandise, tables and chairs, interior signage, decor items, and costumes).
The estimated cost for the standard Start Up Package for Franchised Shops ranges from $16,000 to $21,000. Please note that The franchisor or its affiliate may charge an average margin of 50% on the items in the Start Up Package to cover administrative and warehousing costs.
Due Date: On or before each Wednesday for the preceding week (Sunday through Saturday). Please note that you must pay the royalty fee by electronic funds transfer. So also, Sweet Frog may modify the weekly period and the due date for the royalty fee and the Net Sales reports, and publish any modifications in the Manual.
To be divided among the System Marketing Fund and Local Advertising (or a Cooperative). Currently, your total Marketing Assessment will be 2.5% of Net Sales as follows: 1.5% for System Marketing Fund and 1% for Local Advertising
Due Date: System Marketing Fund – same as royalty fee; Cooperative – as required by the Cooperative; Local Store Marketing – these amounts are not paid to Sweet Frog, payments for local advertising are due when billed.
Sweet Frog will not increase the Marketing Assessment by more than 1/2% in any 12-month period. It may increase the System Marketing Fund to 2% in the next 12-month period. It can change the allocation of the Marketing Assessment at any time.
Sweet Frog has the right, in its sole discretion, to establish regional Cooperatives in the geographic area that covers your Shop to which you will be required to contribute. Please note that Sweet Frog will have one vote for each Shop operated by it or its Affiliates in the geographic area covered by a regional Cooperative.
Reasonable fee, which currently will not exceed $1,000 for each set of materials and the Due Date for this is as invoiced. Please note that Sweet Frog may provide you promotional and advertising materials that it develops.
Reasonable fee per Website review and per year for hosting services. Currently, no charge. The Due Date for this fee is As invoiced. Please note that Sweet Frog may charge you a fee for developing, reviewing, and approving your Website and/or for hosting the Website.
Reasonable fee, which is currently $1,000 per training session and the Due Date for this fee is Before training. Please note that Sweet Frog does not charge a fee for two management personnel to attend the management training program. For any additional, successor, or replacement personnel or any additional training programs, Sweet Frog may charge you a reasonable fee.
Cost of inspection and of the test (including Sweet Frog's administrative expenses), which currently will not exceed $2,000 for each new supplier or product. Due Date: Before Sweet Frog approves the supplier, as invoiced.
Please note that If you wish to use any item or service that Sweet Frog has not yet evaluated or if you wish to purchase or lease any such item from a supplier that Sweet Frog has not yet approved, you must submit a written request for approval to Sweet Frog.
Sweet Frog may require you to submit information, specifications, and samples to it to enable it to determine whether the item complies with its standards and specifications and that the supplier meets its criteria. Sweet Frog may send its representatives to inspect the supplier's facilities or require you to have samples from the supplier delivered to Sweet Frog or to an independent laboratory designated by Sweet Frog for testing.
All costs and expenses Sweet Frog incurs, which currently will not exceed $5,000 and the Due Date for this fee is as invoiced. Please note that these costs and expenses include reasonable accounting and attorneys' fees and costs. Payable if an examination or audit discloses you have understated any amount owed to Sweet Frog by 2% or more.
Sweet Frog's costs and expenses and the Due Date for this fee is as incurred. Please note that if Sweet Frog prevails in a judicial or arbitration proceeding regarding enforcement of the terms of any agreement, you must pay Sweet Frog's attorneys' fees and costs.
Reasonable fee for Sweet Frog's expenses in taking corrective action (including costs of re-inspection), which currently will not exceed $1,500 per violation. The Due Date for this cost is Upon demand.
Please note that Sweet Frog may conduct inspections of the Shop and you must promptly correct any deficiencies. If you fail to correct such deficiencies, Sweet Frog may correct the deficiencies and charge you a reasonable fee for its expenses.
Customer Satisfaction Programs: All costs related to the Shop for these programs, which currently include up to $100 per visit for secret shoppers. The Due Date for this is Upon demand.
Please note that you must participate in programs initiated to verify customer satisfaction and/or your compliance with all operational and other aspects of the System, including (but not limited to) secret shoppers.
Enforcement Costs and Expenses: Any and all costs and expenses incurred by Sweet Frog in enforcing the terms of the Franchise Agreement. Sweet Frog can collect these costs and expenses upon your default without filing an action against you. The Due Date for this is on demand.
Please note that these costs and expenses include, but are not limited to, costs and commissions due a collection agency, reasonable attorneys' fees (including attorneys' fees for in-house counsel employed by Sweet Frog or its affiliates and any attorneys' fees incurred by it in bankruptcy proceedings), costs incurred in creating or replicating reports demonstrating Net Sales of the Shop, court costs, expert witnesses' fees, discovery costs, and reasonable attorneys' fees and costs on appeal, together with interest charges.
Indemnification: Varies according to loss and the Due Date for this is on demand.
Please note that you must indemnify Sweet Frog when certain of your actions or omissions result in loss to it.
Interim Management After Termination: Reasonable fee for management services, which is currently $5,000 per month and the Due Date for this is as agreed.
Please note that if Sweet Frog gives you notice that you are in default, then it may assume management of the Shop.
Interest: Lesser of 5% per year or the maximum lawful rate and the Due Date for this is on demand.
Please note that Sweet Frog may charge interest on all overdue amounts.
Intranet Fee: A reasonable amount based on Sweet Frog's actual cost to support your usage (which will not exceed $700 annually). The Due Date is as invoiced.
Please note that although Sweet Frog does not currently do so, it may charge you a reasonable fee per month per Shop for using its Intranet.
Insurance Fee: Cost of insurance, plus Sweet Frog's reasonable expenses incurred in obtaining the insurance on your behalf. The Due Date for this is on demand.
Please note that if you fail to maintain the required insurance, Sweet Frog may (but need not) obtain it for you.
Liquidated Damages: For early termination of Franchise Agreement, a lump sum equal to the royalty fee percentage multiplied by the weekly average of your Net Sales for the 52-week period preceding the effective date of termination multiplied by the lesser of (i) 104 weeks (2 years); or (ii) the number of weeks remaining in the term. The Due Date for this is at termination, on demand.
Merchandise for Resale, Equipment, Decor Items: Reasonable cost, which currently ranges from $3,000 to $10,000 and the Due Date for this is as invoiced.
Please note that this cost will vary significantly based upon customer demand for these items.
So also, Sweet Frog will develop and make available to you certain merchandise using its Marks, such as hats, t-shirts, toys, and other System memorabilia, and/or certain equipment, decor items, or other products and services.
On-site Additional or Remedial Training: Then-current per diem fee, plus expenses incurred by Sweet Frog's representatives. Currently, the per diem is $250. The Due Date for this is before training.
Please note that if Sweet Frog determines additional or remedial training is required at your Shop, you will pay the per diem fee plus Sweet Frog's expenses. Sweet Frog's expenses include the costs of travel, lodging, and meals.
Renewal Fee: 50% of Sweet Frog's then-current initial franchise fee not including any discounts or reductions. The Due Date is prior to Sweet Frog's execution of renewal documents.
Relocation: The greater of (i) $5,000, or (ii) Sweet Frog's costs and expenses connected with the relocation and the Due Date this is on demand, if required.
Please note that you may not relocate the Shop without Sweet Frog's express prior written consent.
In limited circumstances, you may request Sweet Frog's consent to relocate the Shop to another location in the Protected Area. If Sweet Frog grants you the right to relocate the Shop, you must comply with such reasonable site selection and construction procedures as Sweet Frog may require.
Sweet Frog may condition its approval upon the payment of an agreed minimum royalty to it during the period in which the Shop is not in operation.
Securities Offering Fee: Sweet Frog's reasonable costs and expenses (including legal and accounting fees and costs) associated with reviewing the offering materials. The Due Date for this fee is upon demand. Currently, the cost for this review will not exceed $2,500.
Please note that Sweet Frog limits its review to the manner in which the offering materials treat your and Sweet Frog's relationship and the use of Sweet Frog's Marks (if any).
Software or Systems Modifications: Reasonable fee for any software or systems modifications enhancements made for Sweet Frog that it or its affiliates license to you and the Due Date for this is on demand.
Please note that you must purchase and use certain software programs and related computer systems that Sweet Frog requires.
Taxes: You must reimburse Sweet Frog for any taxes imposed on it by reason of furnishing products, intangible property (including the trademarks), or services to you and the Due Date for this is within 30 days after your receipt of an invoice from Sweet Frog.
Transfer Fee: Greater of (i) $5,000 or (ii) Sweet Frog's costs and expenses connected with transfer and the Due Date for this fee is on request for Sweet Frog's consent to transfer.
Please note that Sweet Frog's costs and expenses include legal and accounting fees and costs.
If transfer is to a legal entity controlled by the same interest holders for convenience of ownership, the transfer fee is reduced to the greater of $500 or reimbursement of Sweet Frog's out-of-pocket costs and expenses (including legal and accounting fees and costs).
Non-Cash Payment System Reimbursement: Amounts specified in Sweet Frog's gift card program and the Due Date for this fee is as invoiced.
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Home > Reviews > Post
Secret Harmonies
A Darker Shade of Magic (Shades of Magic, volume 1)
A Darker Shade of Magic is the first volume in V. E. Schwab's Shades of Magic series.
Kell is an Antari, one of two known world-walkers, able to travel between the four known alternate Londons, White, Red, Gray, and forbidden Black. His is a gift rare enough to make him a treasured possession of Red London's Royal Family.
Officially, Kell uses his gift to serve as an ambassador between the three Londons — White, Red, and Gray — that are still in limited contact with each other. On his own time Kell likes to collect souvenirs. That's forbidden. But moving minor trinkets from one world to another seems a harmless hobby.
Years earlier, the inhabitants of Black London lost control of their magic. Magic gained control, first of the mages and then of the world entire. The three other Londons could do nothing to save Black London. All they could do is seal the gates between the worlds, limiting contact to those with the world-walking gift, people like Red London's Kell.
Persuaded to transfer a package from one world to another, Kell learns too late that the package contains a relic of Black London. Possession of the relic makes Kell a target. There is a conspiracy that spans worlds and the people behind it will stop at nothing to regain the relic.
Cross-dressing thief Lila Bard has no idea that that magic exists or that there are more Londons than the drab one in whose slums she dwells. To her, Kell is just another mark, someone whose pocket she can pick without consequence. She's half right; she can pick Kell's pocket … but there are consequences. Now Kell is hunting Lila, desperate to get the artifact back.
So are the people who were stalking Kell.
~oOo~
This is an oddly constrained world. Partly due to the fact that Kell is never given the chance to wander far from London in any world. It also seems as though only London matters in each world. This is too bad for White London, whose dwindling magical supply means the city is eternally covered in snow and dying. But the Dane twins who rule White London seem to have take Johnson's
"Why, Sir, you find no man, at all intellectual, who is willing to leave London. No, Sir, when a man is tired of London, he is tired of life; for there is in London all that life can afford."
to heart, except replace "at all intellectual" with "a power-mad mage". And "all that life can afford" with "everything two power-mad mages can force weaker people to hand over." The same thing, really.
This tight focus does have the downside that when matters head south, it's pretty easy to work out who has to be at fault; the cast of characters is smaller than the cast of a country estate cozy. For example, if it seems like a world walker is up to shenanigans and there are only two known world walkers, and one of them can be ruled out because he's the protagonist, it's not as if there's a long list of suspects left. Although I suppose "known" is an important qualifier.
But then there's one-eyed Lila, who lives outside the worlds of courtly power that define Kell's life. As soon as she appears, what should have been a straight-forward scheme to reshape the world goes off the rails. She's not playing the same game as the Dane Twins (White London's rulers) or Kell himself. What she lacks in magical power, she replaces with ruthless focus on her goals.
This is an enjoyable, readable standalone. It is also clearly scene-setting for further instalments in the series. There's the matter of Lila's glass eye. A hint that she might be a world-walker too, one whose tell — an eye turned black by the magic that enables world-walking — was hidden by misfortune. I guess I'll find out in the next volume.
A Darker Shade of Magic is available here (Amazon) and here (Chapters-Indigo).
Robert Carnegie
Does the London of Earth Prime appear and what is the date there? (Earth Prime is the planet where these fictions are published. This one, probably.)
And actually, are we talking about London in England or...? Perhaps it's a story like the "Silo" series, except that after conventional civilisation collapses, only towns around the world called London exist, due to... whimsy, I suppose it'd be.
"Rivers of London" has magic and a protagonist who complains hilariously if the plot ever requires him to go outside the city, but doesn't do parallel worlds, much. (The author' afterword sometimes points out landmarks in the story that don't exactly exist on Earth Prime, and some that do, asking that they're treated with respect... more than in the story, usually.)
Jim Butcher's Harry Dresden does urban magic and parallel worlds with e.g. fairies, but the nearest I've seen him get to our Metropolis is Edinburgh.
Then there's - https://en.wikipedia.org/wiki/Undone_(radio_series) In which initially "Undone" is rather a Lewis Carroll looking-glass version of "London", and the main plot is to find and return "Undone" people and artifacts that hv strayed across. But then it gets impossibly complicated with lots more alternate Londons. Earth Prime's is briefly glimpsed.


text:
Beauty Diplomacy
Embodying an Emerging Nation
Oluwakemi M. Balogun
SERIES: Globalization in Everyday Life
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Sociology / Race, Class, and Gender
Sociology / Global Issues, Economy, and Work
Even as beauty pageants have been critiqued as misogynistic and dated cultural vestiges of the past in the US and elsewhere, the pageant industry is growing in popularity across the Global South, and Nigeria is one of the countries at the forefront of this trend. In a country with over 1,000 reported pageants, these events are more than superficial forms of entertainment. Beauty Diplomacy takes us inside the world of Nigerian beauty contests to see how they are transformed into contested vehicles for promoting complex ideas about gender and power, ethnicity and belonging, and a rapidly changing articulation of Nigerian nationhood. Drawing on four case studies of beauty pageants, this book examines how Nigeria's changing position in the global political economy and existing cultural tensions inform varied forms of embodied nationalism, where contestants are expected to integrate recognizable elements of Nigerian cultural identity while also conveying a narrative of a newly-emerging, globally-relevant Nigeria. Oluwakemi M. Balogun critically examines Nigerian pageants in the context of major transitions within the nation-state, using these events as a lens through which to understand Nigerian national identity and international relations.
Oluwakemi M. Balogun is Assistant Professor of Women's, Gender, and Sexuality Studies and Sociology at the University of Oregon.
"With vivid description and sharp analysis, Beauty Diplomacy reveals the layers upon layers of complexity that surround the Nigerian beauty pageant industry. Seen through the eyes of contestants, producers, and anti-pageant protesters, the pageants are the object of contradictory desires, ambitions and fears. This highly engaging study shows how pageants have become the focal point for debates about the meaning of the nation, global political campaigns, and more."
—Maxine Leeds Craig, author of Sorry I Don't Dance: Why Men Refuse to Move
"It's one thing to describe beauty practices and place them in historical context. It's quite another, bigger challenge to show how these practices embody disputes over national identity, culture, and economic development. Combining deep knowledge of Nigerian society with rich, painstaking field research, Dr. Balogun's book is the best I've read on the intersection of postcolonial nationalism, globalization, and bodies."
—Erynn Masi de Casanova, University of Cincinnati, and co-editor of Bodies without Borders and Global Beauty, Local Bodies
"In Beauty Diplomacy, Balogun argues that beauty pageants are not benign; rather, they are arenas in which young women are trained, transformed, and deployed as beauty diplomats—forging ties among Nigerian businessmen and politicians, embodying nationalism, and serving as cultural ambassadors tasked with repairing the nation's reputation on the global stage. This clearly written and conceptually innovative book is a significant achievement."
—Sanyu A. Mojola, author of Love, Money, and HIV: Becoming a Modern African Woman in the Age of AIDS
Chapter 1 Excerpt
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text:
Peter Lichtenthal, (ou Pietro Lichtenthal), né le  à Preßburg (actuel Bratislava), mort le  à Milan) est un musicien, médecin, musicologue, compositeur et arrangeur autrichien.

Biographie
Il a passé la plus grande partie de sa vie à Milan, et était un proche de la famille Mozart, et en particulier Karl Thomas Mozart (1784-1858), fils de Wolfgang Amadeus Mozart.

Grâce à ses recherches sur la musicothérapie, il acquiert une renommée internationale.

Œuvre

Lichtenthal a réalisé des transcriptions d'œuvres de Mozart pour quintette à cordes, notamment
 Sinfonie Nr. 40 (g-moll), KV 550
 Sinfonie Nr. 41 (C-dur, "Jupiter"), KV 551
 Requiem, KV 626

Publications
 1807 : Der musikalische Arzt, oder Abhandlung von dem Einflusse der Musik auf den Körper, und von ihrer Anwendung in gewissen Krankheiten: nebst einigen Winken, zur Anhörung einer guten Musik, Wien
 1834 : Manuale bibliografico del viaggiatore in Italia: concernente località, storia, arti, scienze, antiquaria e commercio, Milano
 1839 : Dictionnaire de musique, traduit et augmenté par Dominique Mondo, Paris, Troupenas.

Notes et références

Liens externes

Naissance en mai 1778
Naissance à Bratislava
Musicien autrichien
Musicologue autrichien
Décès en août 1853
Décès à Milan
Décès à 73 ans

redpajama_set_name: RedPajamaWikipedia


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