text:
\section{Introduction}

	Relativistic jets are collimated plasma outflows arising under intense accretion of matter onto a central object in different types of active galaxy nuclei (AGN) \cite{doi:10.1146/annurev-astro-081817-051948}, as well as in closed binary stellar systems under accretion of matter from a companion onto a relativistic object. The pioneer works \cite{1977MNRAS.179..433B},\cite{1982MNRAS.199..883B} describe conditions for the occurrence of axisymmetric jet emissions. The most powerful emissions of the matter in space are seen in AGN and supernova explosions (SNE). The SNE are occurred during the simultaneous short intense release of matter, in which the energy of accelerated protons by the shock wave can reach $10^{15}$ eV \cite{2004Natur.432...75A}. The acceleration of protons in AGN on the contrary is characterized by relative stationary and continuity, as well as achievement of large energy up to $10^{20} $ eV and above \cite{2020MNRAS.492.4884I}.

	High energy protons are the most essential component of cosmic rays \cite{Ginzburg:1961}. They arise in large matter and energy release processes. Observations of protons and high energy nuclei, $E > 3\cdot 10^{18}$ eV, of extragalactic origin, are traditionally carried by broad air shower detectors. The observed energies approach the so-called Greisen-Zatsepin-Kuzmin (GZK) cutoff \cite{1966PhRvL..16..748G}. However the identification of the sources of ultrahigh energy particles, due to deviations of charged particles by an intergalactic magnetic field, is not possible. It is only clear that high energies are associated with high energy release objects such as AGN and related with them relativistic emissions. Also observations by the Cherenkov telescopes such as HESS, VERITAS, etc. observed the energy of incoming photons above the threshold of 100 TeV \cite{2016Natur.531..476H}. This makes it possible to estimate the real energy of protons, $E > 10^{16}$ eV.

	The recent discovery of neutrino radiation from blazars by the IceCube project \cite{2019BAAS...51c.431O} proves the possibility of an electron neutrinos production mechanism due to high-energy protons collisions:
\begin{equation}\label{neutrino}
	p+p = p+n + e^{+} + \nu_e. \nonumber
\end{equation}
	Such collisions can occur not only in the region of the base of the jet, but also throughout its volume, which can explain the origin of neutrinos in blazars during collisions of high-energy protons propagating along the jet. This increases the probability of proton-proton collisions. In this case the proton energy spectrum can take values from $ 10^{15} $ eV to the maximum of $10^{19} - 10^{21}$ eV, which coincides with the threshold energy values of the registered neutrinos on IceCube \cite{2020ApJ...894..101P}.

	In recent decades, great progress has been made in the study of relativistic jets using the general relativity general relativistic magnetohydrodynamic (GRMHD) modeling method  \cite{2016A&A...586A..38M}. The relativistic particle-in-cell (RPIC) method \cite{2007Ap&SS.307..319N} is also widely developed, which also allows taking into account the features of the above-mentioned GRMHD approximation. However, to understand the physics of the charged particles acceleration in an electromagnetic field to high energies, the magnetohydrodynamic (MHD) approximation is clearly not sufficient \cite{2020MNRAS.492.4884I}. In the present paper we are taking into account the fact that the proton cyclotron radii become so large during the acceleration, which leads to violation of the MHD approximation conditions, namely, the magnetization of particles. It becomes necessary to apply a kinetic approach, i.e. the calculation of individual particle trajectories. In our previous work \cite{2009Ap&SS.321...57I}, \cite{2020MNRAS.492.4884I} this approach was used for the study of proton acceleration in the magnetosphere of the central object, a black hole.

	The structure of jet's electromagnetic fields is described in the Sec. \ref{section2}. The motion equations and their solution are presented in the Sec. \ref{section3}. Application for the obtained analytical solutions for different AGN systems is made in the Sec. \ref{section4}. Discussion of the results and their interpretation in the context of physical parameters of AGN is presented in the Sec. \ref{section5}.

\section{Electromagnetic field structure}\label{section2}

    To calculate the motion of charged particles we need to define the jet magnetic and electric fields structure. We consider of stationary or quasistationary structure of the jet. This means that the characteristic time of changing the jet parameters significantly exceeds the motion time of the plasma flow and individual particles in the jet, which is obviously fulfilled. We will also consider the jet to be quasicylindrical, i.e., all values do not depend on the azimuthal angle $\phi$. This does not mean that the jet radius $R_J$ is constant over the entire jet length $L$. Due to the collimation of the stream, $d R_J/dz<<1$, the dependence of parameters and values on the $z$ coordinate along the flow propagation is much weaker than on the cylindrical radius $\rho$. Thus, locally, at each level $z$, the jet parameters depend only on the radius $\rho$. This means that there is no radial magnetic field $B_\rho$ due to the condition of the finiteness of the field at the jet axis $\rho=0$, $B_\rho=0$. Similarly, the radial velocity of the plasma flow is zero, $u_\rho=0$. As a result, the magnetic field has two components $B_\phi$ and $B_z$. The magnetic field lines are helices, $z=\rho (B_z (\rho)/B_\phi(\rho))\phi$, with the step $h=2\pi\rho B_z/B_\phi $ varying with of the radius $\rho$.

    The jet is formed at a sufficiently large distance from the black hole magnetosphere, $r\simeq 10^2 \, r_L$. The value of $r_L$ is the so-called radius of the light cylinder, $r_L\simeq c/\Omega^H$, where $\Omega^H$ is the frequency of rotation of the black hole. The poloidal magnetic field of the black hole's magnetosphere is close to the radial field (split-monopole), which depends only on the distance $r$. The plasma flow is collimated at the base of the jet and the poloidal magnetic field of the jet $B_z$ is formed from the magnetic field of the magnetosphere. Therefore, in a good approximation, the field $B_z=B_0\simeq const(\rho)$ can be considered homogeneous. The field value decreases with moving up from the base of the jet when it expands due to the conservation of the magnetic flux. As for the toroidal magnetic field in the jet, $B_\phi$, it should vanish at the axis $\rho=0$ and at the boundary of the jet, $\rho=R_J$. The jet carries a longitudinal electric current flowing in one direction in the central region and in the opposite direction in the outer region. The total electric current flowing in the jet has zero value. In addition, the derivative of the toroidal magnetic field over the radius $dB_\phi (\rho)/d\rho$ must become zero at the jet boundary $\rho=R_J$. This is because the density of the longitudinal electric current $j_z\propto \rho^{-1}d(\rho B_\phi)/d\rho $ must also vanish at the jet boundary. Thus, the simplest configuration of a toroidal field has the form
 \begin{equation}\label{bphi}
    B_\phi =\alpha B_0\frac{\rho}{R_J}\left(1-\frac{\rho}{R_J}\right)^2.
\end{equation}
    Here the value of $\alpha$ is proportional to the amplitude of the toroidal magnetic field. The maximum of longitudinal electric current $I(\rho)=2\pi\int_0^\rho j_z \rho' d\rho'=c\rho B_\phi(\rho)/2$ is achieved when $\rho=R_J/2$. Therefore, the longitudinal electric current $I$ flowing through the jet is equal to
\begin{equation}\label{i}
    I=\frac{1}{32}|\alpha| c R_J B_0.
\end{equation}
   Here the question arises about continuity of the electric current $I$ when the jet moves away from its base on the distance $z$. Since electric currents flow in different directions in the central and peripheral regions, there is a possibility of partial reconnection of the current, i. e. its decreasing at large distances $z$. Charged plasma particles move along the magnetic field, i.e. along spiral magnetic lines lying on magnetic surfaces that have a fixed value of the radial coordinate $\rho$. Thus, in the collisionless approximation, there is no transverse electric current, $j_{\perp} =0$. However, electrons, namely they carry an electric current, experience collisions with protons and move in a radial direction. It seems that $j_{\perp}= \sigma_{\perp} E_\rho$, where the value of $\sigma_{\perp}$ is the transverse conductivity of the plasma, across the magnetic field. For a magnetized plasma, the transverse conductivity is much less than the longitudinal one, $\sigma_{\perp}<<\sigma_{\parallel}$. Ohm's law in the form ${\bf j}={\hat \sigma}{\bf E}$ takes place in the coordinate frame where the plasma is at rest. The radial electric field $E_\rho$ in the magnetic field $B_z$ causes the plasma to rotate with an angular velocity $ \Omega^F$. If we are in the frame  rotating with angular velocity $ \Omega^F$, the radial electric field disappears, $E'_\rho=0$. In this case, to find the transverse current $j_\perp$, we use the generalized Ohm's law \cite{gurnett_bhattacharjee_2005}
\begin{eqnarray}\label{ohm}
    {\bf j}=\sigma_\parallel\left\{\left[{\bf E}-\frac{1}{c}[{\bf uB}]\right]+\frac{1}{enc}[{\bf jB}] +\frac{1}{en}\nabla P_e\right\}.
\end{eqnarray}
    Here the quantity $ P_e $ is the electron pressure. Generalized Ohm's law is derived for a plasma in which motion of electrons and ions is considered separately. As a result, we have
$$
    j_\perp = \frac{\sigma_\perp}{e}\frac{1}{n}\frac{\partial(nT_e)}{\partial\rho}\simeq \frac{\sigma_\perp}{eR_J}T_e.
$$
    The total transverse electric current, $I_\perp = 2\pi R_J L j_\perp$, is equal to
$$
    \frac{I_\perp}{I}=\frac{\omega_p^2}{\omega_c^2}\frac{T_e}{m_e c^2} \frac{1}{\omega_c\tau_e}\frac{L}{R_J}.
$$
    It is taken into account that $\sigma_\parallel=ne^2\tau_e/m_e$, $\sigma_\perp=\sigma_\parallel/(\omega_c\tau_e)^2$. The value of $\tau_e$ is the electron relaxation time, i.e. the time between collisions of electrons with protons, $\omega_p$ and $\omega_c$ are the plasma and cyclotron frequencies of electrons, accordingly. For characteristic quantities $n\simeq 10^2 \, cm^{-3}$, $B\simeq 10^{-2} \, G$, $T_e\simeq 10^5 \, eV$ and $\Lambda\simeq 20$ we have $\omega_c\tau_e\simeq 10^{15}$, $\omega_p/\omega_c\simeq 3$. We obtain the result
$$
    \frac{I_\perp}{I}\simeq 10^{-15}\frac{L}{R_J}.
$$
    Thus, practically there is no reconnection of the electric current $I$ in the jet.

    The radial electric field $E_\rho$, as well as the toroidal magnetic field, must vanish at the jet boundary $\rho=R_J$. The derivative, $d (\rho B (\rho))/d\rho$ at $\rho=R_J$, which is proportional to the electric charge density $\rho_e$ is equal to zero also. Thus,
\begin{equation}\label{e}
    E_\rho=\beta B_0\frac{\rho}{R_J}\left(1-\frac{\rho}{R_J}\right)^2.
\end{equation}
    The total potential difference $U$ between the jet axis $\rho=0$ and the periphery $\rho=R_J$ is equal to
\begin{equation}\label{u}
    U=\frac{1}{12}|\beta| R_J B_0.
\end{equation}
    This is the voltage created by a rotating black hole in the presence of a poloidal magnetic field in its magnetosphere, $B_p$, $ U = B_p r_g^2 \Omega^H / 2c $ \cite{1984ENG}, \cite{1986USA}. The values of $r_g$ and $ \Omega^H$ are the gravitational radius and the angular rotation frequency of the black hole, respectively. Thus, the dimensionless quantities $ \alpha$ and $\beta$ are proportional to the amplitudes of the toroidal magnetic field and the radial electric field in the jet, respectively. They are proportional to the electric current $I$ (\ref{i}) in the jet and the voltage $U$ (\ref{u}), respectively, as well as the power of the jet $L_j=UI$.

    The jet plasma can be considered as ideal with good accuracy,
\begin{equation}\label{f}
    {\bf E}=-\frac{1}{c} {\bf u}\times{\bf B}.
\end{equation}
 From (\ref{f}) it follows that
$$
    u_\phi=u_z\frac{B_\phi}{B_z} - c\frac{E_\rho}{B_z}.
$$
    The first term reflects the fact that the plasma moves along a spiral magnetic field. The second term is the plasma drift in crossed electromagnetic fields $E_\rho,\, B_z$. This motion can be considered as the rotation of magnetic field lines together with the plasma with the angular velocity of $ \Omega^F= - cE_\rho/ \rho B_z= - c\beta(1 - \rho/R_J)^2/R_J$. Thus, the angular velocity of rotation of the jet is constant in the inner regions and tends to zero when approach the boundary. It should be noted that for relativistic motion, $u_z\simeq c$, the ratio of the fields $B_\phi/B_z$ and $E_\rho/B_z$ can be larger than 1, since the plasma motion along the spiral magnetic field and the drift can compensate for each other.

    The selected electromagnetic fields in the form of (\ref{bphi}, \ref{e}) are the simplest, satisfying the necessary requirements. They are characterized by a minimum number of parameters, $\alpha$ and $\beta$. They determine the important physical parameters of the jet: the electric current $I$ carried by the outflow and the voltage $U$ generated by the central machine. In fact, on the periphery of the jet near the boundary, $\rho\simeq R_J$, additional electromagnetic fields occur. They are not so significant in magnitudes and appear when the internal solution is matched with the external environment. In the case of an external matter in the form of a gas with a finite pressure, the structure of fields near the jet boundary is presented in the paper \cite{10.1093/mnras/stx2204}. For the vacuum boundary the solution is described in \cite{10.1093/mnrasl/sly017}. For our problem of accelerating protons to high energies, $ E \simeq R_J B_z$, the influence of boundary fields can be ignored.

\section{Proton acceleration}\label{section3}

    Motion of particles with the mass $ m $ and the charge $ q $ in an electromagnetic field is described by the equations
\begin{eqnarray}\label{lorenz}
    &&\frac{d{\bf p}}{dt}=q\left({\bf E}+\frac{1}{c}\left[{\bf v,B}\right]\right),  \nonumber \\
    &&\frac{d{\bf r }}{dt}=\frac{{\bf p}}{m\gamma}, \\
    &&\gamma^2=1+\frac{p^2}{m^2 c^2}. \nonumber
\end{eqnarray}
    Here $ {\bf r} $ and $ {\bf p} $ are coordinates and momentum of a charged particle, $ \gamma $  is its Lorentz factor. Let introduce the dimensionless time, coordinates and variables
\begin{equation}\label{dimensionless}
    t'=\frac{c}{R_J} t, \,  \rho'=\frac{\rho}{R_J}, \, z'=\frac{z}{R_J}, \, {\bf p'}=\frac{c}{\omega_c R_J}\frac{{\bf p}}{mc},
    \, \gamma' = \frac{c}{\omega_c R_J} \gamma.
\end{equation}
    The value of $\omega_c$ is the nonrelativistic frequency of rotation of a particle in the magnetic field $ B_0 $, $ \omega_c = qB_0 / mc $. The relation $c/\omega_c$ is the cyclotron radius of a nonrelativistic particle. It is significantly smaller than the jet radius $R_J,\, c/ \omega_c R_J<<1$. Omitting the primes, we move to the equations of particle motion in the fields $B_z=B_0,\, B_\phi, \, E_\rho$ (\ref{bphi}, \ref{e}).
\begin{eqnarray}\label{move}
    &&\frac{dp_\rho}{dt} = \frac{p_\phi^2}{\rho \gamma} + \frac{p_\phi}{\gamma} - \alpha \frac{p_z  \rho (1 - \rho)^2}{\gamma} + \beta\rho (1 - \rho)^2 , \nonumber \\
    &&\frac{dp_\phi}{dt}=-\frac{p_\rho p_\phi}{\rho \gamma} - \frac{p_\rho}{\gamma}, \nonumber \\
    &&\frac{dp_z}{dt}=\alpha\frac{p_\rho  \rho (1 - \rho)^2}{\gamma}, \nonumber \\
    &&\frac{d\rho}{dt}=\frac{p_\rho}{\gamma}, \\
    &&\frac{d\phi}{dt}=\frac{p_\theta}{\rho \gamma}, \nonumber \\
    &&\frac{dz}{dt}=\frac{p_z}{\gamma}.  \nonumber
\end{eqnarray}
     The first terms in the right-hand sides of the first and second equations are inertial forces. The system of equations of motion (\ref{move}) has two integrals of motion: energy $ {\cal E} = const $ and angular momentum $ {\cal L} = const $
\begin{eqnarray}\label{conserve}
    &&{\cal E}=\gamma - \beta \psi(\rho), \nonumber \\
    &&{\cal L}=\rho p_\phi+\frac{1}{2}\rho^2.
\end{eqnarray}
    Here the value of $\psi(\rho)$ is the \textquotedblleft potential\textquotedblright\, of the radial electric field, $d\psi/d\rho=\rho(1-\rho)^2$,
\begin{equation}\label{psi}
    \psi(\rho)=\frac{1}{2}\rho^2\left(1-\frac{4}{3}\rho+\frac{1}{2}\rho^2\right).
\end{equation}
    We are interested in the acceleration of protons in a jet to high energies much higher than the energy of particles escaping from the black hole magnetosphere. We previously showed that protons accelerated in the magnetosphere gain energy corresponding only to the part of the potential $U$ passed by particles, $  \gamma_i=(eU/m_p c^2)^{2/3}$  \cite{2020MNRAS.492.4884I}. For the initial Lorentz factors in variables (\ref{dimensionless}), we have $\gamma'_i = \beta(eU/m_p c^2)^{-1/3}/12 << \beta/12$. The value of $ \beta/12$ is the maximum Lorentz factor of particles $\gamma_{m}$ that have passed the total potential difference $U$, $\gamma_{m}=\beta\psi (\rho=1)=\beta/12$. Similarly, due to the conservation of angular momentum (\ref{conserve}) for particles accelerated from small values of $\rho$, we have
$$
    p_\phi=-\frac{1}{2}\rho.
$$
    Next, from the third equation of the system (\ref{move}) we get
$$
    p_z=\frac{\alpha}{\beta}\gamma.
$$
    From the ratio $\gamma^2=p^2+(c/ \omega_c R_J)^2$, $c/\omega_c R_J<<1$, it follows that the acceleration of particles in a jet is possible only under the condition $|\beta|>|\alpha|$, i.e. under the condition of a sufficiently strong electric field compared to a toroidal magnetic field. For dimensional quantities we have $U>8 I/3c$. Otherwise, the particles leaving the black hole magnetosphere with energies $\gamma_i = (eU/m_p c^2)^{2/3}$ do not propagate in the radial direction, but move along the jet axis (see Fig. \ref{fig3}). The toroidal magnetic field does not allow them to move far from the axis. Note, that if you enter the jet resistance ${\cal R}=U/I$, the acceleration condition means ${\cal R}>8/3c$. It is known \cite{1986USA}, that if the central machine is fully matched with the neighboring chain, its resistance ${\cal R}$ must be equal to the resistance of the black hole horizon ${\cal R}^H=4\pi/c$. Thus, the acceleration condition obtained corresponds to the proximity to the matching condition.

    Knowing the momentum components $p_\phi$ and $p_z$, we find the radial momentum of the particle
\begin{eqnarray}
    p_\rho^2=\left(1-\frac{\alpha^2}{\beta^2}\right)\gamma^2-\frac{\rho^2}{4}= \nonumber  \\
    \frac{\rho^2}{4}\left[(\beta^2-\alpha^2)\left(1-\frac{4}{3}\rho+\frac{1}{2}\rho^2\right)^2\rho^2 -1\right].
\end{eqnarray}
     We see that the radial motion of the particle occurs between the reflection points, $\rho_{1,2}, \, \rho_1<\rho<\rho_2$,
\begin{equation}
    \frac{2\psi(\rho_{1,2})}{\rho_{1,2}}=\rho_{1,2}\left(1-\frac{4}{3}\rho_{1,2}+\frac{1}{2}\rho_{1,2}^2\right)=
    (\beta^2-\alpha^2)^{-1/2}.
\end{equation}
    The third root of the equation $2\psi(\rho)/\rho=(\beta^2-\alpha^2)^{-1/2}$ lies to the right of the jet boundary $\rho=1$, $\rho_3>1$ (see Fig. \ref{fig1}). However, the roots $\rho_1$ and $\rho_2$ exist only if the line $(\beta^2-\alpha^2)^{-1/2} = const $ lies below the maximum of the curve $2\psi(\rho)/\rho$. The maximum is at $\rho=\rho_{1 m}=(8-10^{1/2})/9$. Second extreme point $\rho_{2 m}=(8+10^{1/2})/9$ is located outside of the jet. Thus, acceleration inside the jet, i.e. reaching of particles of the Lorentz factor exceeding the acceleration level in the magnetosphere, $\gamma>\gamma_i$, occurs only under the condition $\beta^2-\alpha^2>\rho_{1 m}^2/4\psi^2(\rho_{1 m})=a_1^2=19$. Acceleration takes place not only under the condition $|\beta|>|\alpha|$, but under more hard condition, $\beta^2-\alpha^2>19$.

\begin{figure}
    \includegraphics[width=\columnwidth]{fig1.eps}
        \caption{The reflection points of the radial motion of particles, $p_\rho=0$, $\rho_1, \, \rho_2$, and $\rho_3$. The point $\rho_3>1$ is outside the jet. For $  \beta^2-\alpha^2>a_2^2=36$, the point $\rho_2$ is also outside the jet, $\rho_2>1$, and the particle freely escapes the jet. The points $\rho_{1 m}$ and $\rho_{2 m}$ are extremes of the function $2\psi (\rho)/\rho$, $\rho_{1 m}=(8-10^{1/2})/9<1, \, \rho_{2 m}>1$. At $ \beta^2-\alpha^2<a_1^2\simeq 19$ there are no reflection points inside the jet at all, and particle acceleration does not occur inside the jet.}
    \label{fig1}
\end{figure}

    When the difference $\beta^2-\alpha^2$ further increases, the reflection point $\rho_{2}$ crosses the jet boundary, $\rho_{2}>1$. This means that the proton moving from the jet inner regions, crossing the jet periphery and leaves outside with receiving the maximum possible energy $eU$, $\gamma_m = |\beta|\psi (\rho_1)=|\beta|/12=eU/m_p c^2$. This case exists under the condition $(\beta^2-\alpha^2)^{-1/2}<2\psi(\rho=1)=1/6$, or $\beta^2-\alpha^2>a_2^2=36$. The trajectory of such untrapped particle is shown in Fig. \ref{fig3}.

    In the parameter range $a_1^2< \beta^2-\alpha^2 <a_2^2$ the particle is captured inside the jet. It oscillates between the points $\rho_1$ and $\rho_2$, changing its Lorentz factor, $12\psi(\rho_1)<\gamma/\gamma_{m}<12\psi(\rho_2)$. This region of parameters is shown in Fig. \ref{fig2} as the dashed area. The trajectory of trapped particles is shown in Fig. \ref{fig3}. Let us sum up the results: \\
    (1) $\beta^2-\alpha^2>a_2^2 =36$ \textendash \, protons are untrapped, they receive the maximum energy $\gamma=\gamma_m$, \\
    (2) $19=a_1^2<\beta^2-\alpha^2<a_2^2=36$ \textendash \, protons are trapped inside the jet, their energy oscillates around the value of $\gamma=0.74\gamma_m$, \\
    (3) $\beta^2-\alpha^2<a_1^2=19$ \textendash \, protons are not accelerated in the jet, $\gamma=\gamma_m^{2/3}$, their trajectories are pressed toward the jet axis.
\begin{figure}
    \includegraphics[width=\columnwidth]{fig2.eps}
        \caption{Lorentz factors of protons in the jet depending on the parameter $\beta^2-\alpha^2$. At $\beta^2-\alpha^2>a_2^2=36$, the particles escape the jet and acquire the maximum energy $eU=m_p c^2\gamma_m,\, \gamma_m=\beta/12$. At $19=a_1^2< \beta^2-\alpha^2<a_2^2=36 $ the particles are trapped in the jet, their energies oscillate around the value of the Lorentz factor of $\gamma=0.74\gamma_m$. This region is shown as the dashed area. At $ \beta^2-\alpha^2<a_1^2=19$, the particles are not accelerated in the jet and their energy remains equal to the energy of protons escaping the black hole magnetosphere, $\gamma=\gamma_m^{2/3}<<\gamma_m$.}
 \label{fig2}
\end{figure}

\begin{figure}
    \includegraphics[width=\columnwidth]{fig3.eps}
        \caption{Particle trajectories on the plane $(\rho,\, z)$. The figure shows three types of particle trajectories: untrapped, trapped and nonaccelerated. }
    \label{fig3}
\end{figure}

   Shown in Fig. \ref{fig3} the trajectories of accelerated protons in the jet electromagnetic fields are somewhat idealized. Actually, the magnetic field in the jet to some extent is turbulent, i.e. ${\bf B}={\bf B}_r+\delta{\bf B}$. The regular magnetic ${\bf B}_r$ is the poloidal $B_z$ and the toroidal $B_\phi$ fields described above. The disturbed magnetic field is $ \delta{\bf B}$. It is characterized by the amplitude $ \delta B$ and by the size or correlation length $l$. We will consider $l<<R_J$. The deviation $ \delta v$ of an accelerated particle, moving with the speed of light $c$, by the field $\delta B$ is equal to $\delta v= l\Omega_c(\delta B/B)$. The value of $ \Omega_c=eB/c m_p\gamma$ is the cyclotron frequency of the particle. Its cyclotron radius $c/ \Omega_c$ is of the order of the jet radius $R_J$. The particle is scattered on the angle $ \delta\alpha\simeq \delta v/c$. Thus, the diffusion coefficient of the particle over angle is equal to $D_\alpha=\delta\alpha^2 c/l=(lc/R_J^2) (\delta B/B)^2$. On the length $z$, which is of the order of the oscillation length of a trapped particle $z\simeq R_J$ (see the Fig. \ref{fig3}), the deviation of $\alpha$ from the ideal trajectory is small, $\alpha=(D_\alpha R_J/c)^{1/2}=(l/R_J)^{1/2}(\delta B/B)<<1$.

   Let us now express the dimensionless parameters $ \beta$ and $\alpha$ (\ref{u}, \ref{i}) in terms of the potential $U$ and the electric current $I$. The potential can be fairly reliably estimated from the mass of the central black hole, its angular frequency of rotation and the magnitude of the poloidal magnetic field near the horizon. The value of the electric current  is not directly estimated. However, knowing the luminosity of the jet, $L_j$, can be put $I=L_j/U$. As a result, the conditions for the existence of different regimes of proton acceleration inside the jet look like: \\
   (1) regime of the maximum proton acceleration, $E=eU$. Acceleration in the jet in this case occurs in the region near the base of the jet, $z\simeq R_J$,
\begin{eqnarray}\label{r1}
    U>B_z R_J\left\{\frac{1}{2}\left(\frac{a_2}{12}\right)^2+\left[\frac{1}{4}\left(\frac{a_2}{12}\right)^4+ \right.\right.\nonumber \\
    \left.\left. \left(\frac{8}{3}\right)^2\frac{1}{(B_z R_J)^4}\left(\frac{L_J}{c}\right)^2\right]^{1/2}\right\}^{1/2}.
\end{eqnarray}
    Here the value of $a_2$ is, $a_2=6$. \\
    (2) protons are trapped inside the jet. Moving along the jet, they oscillate in a radial direction, periodically accelerating and decelerating. The value of the energy around which particles oscillate is $E=0.74 eU$ (see Fig. \ref{fig2}). The value of the potential $U$ in this regime satisfies the following conditions:
\begin{eqnarray}\label{r2}
    U<B_z R_J\left\{\frac{1}{2}\left(\frac{a_2}{12}\right)^2+\left[\frac{1}{4}\left(\frac{a_2}{12}\right)^4+ \right.\right.\nonumber \\
    \left.\left. \left(\frac{8}{3}\right)^2\frac{1}{(B_z R_J)^4}\left(\frac{L_J}{c}\right)^2\right]^{1/2}\right\}^{1/2}, \, a_2^2=36; \nonumber \\
    U>B_z R_J\left\{\frac{1}{2}\left(\frac{a_1}{12}\right)^2+\left[\frac{1}{4}\left(\frac{a_1}{12}\right)^4+ \right.\right.\nonumber \\
    \left.\left. \left(\frac{8}{3}\right)^2\frac{1}{(B_z R_J)^4}\left(\frac{L_J}{c}\right)^2\right]^{1/2}\right\}^{1/2}, \, a_1^2=19.
\end{eqnarray}
    (3) there is no acceleration of protons in the jet. They move in the axial region along the jet. Their energy corresponds to the energy of particles accelerated in the black hole magnetosphere, $E=m_pc^2 (eU/m_pc^2)^{2/3}<<eU$.
For this regime,
\begin{eqnarray}\label{r3}
    U<B_z R_J\left\{\frac{1}{2}\left(\frac{a_1}{12}\right)^2+\left[\frac{1}{4}\left(\frac{a_1}{12}\right)^4+ \right.\right.\nonumber \\
    \left.\left. \left(\frac{8}{3}\right)^2\frac{1}{(B_z R_J)^4}\left(\frac{L_J}{c}\right)^2\right]^{1/2}\right\}^{1/2}, \, a_1^2=19.
\end{eqnarray}

\section{Jets}\label{section4}

    In order to determine the proton acceleration regime in the real AGN object it is first necessary to calculate the values of the voltage $U$ generated by the central machine and transmitted along the magnetic field lines into the jet. Here it should be noted that the voltage $U$ is actually transmitted to the jet without loss and does not change there. The voltage drop $\Delta U$ along the jet length $L$ is determined by Ohm's law, $\Delta U=j_{\parallel}L/\sigma_{\parallel}=IL/R_J^2\sigma_{\parallel}=UL/R_J^2{\cal R}\sigma_{\parallel}$. The conductivity of a plasma along the magnetic field is
$$
    \sigma_{\parallel}=\frac{(T_e/1 eV)^{3/2}}{4 \pi m_e^{1/2}e^2\Lambda}.
$$
Setting the characteristic value of the electron temperature, $T_e\simeq 10^5 \, eV$, we get $\sigma_{\parallel}\simeq 10^{20} \, s^{-1}$. Thus,
$$
    \frac{\Delta U}{U}=\frac{1}{4\pi^2}\frac{L}{R_J}\frac{{\cal R}^{H}}{{\cal R}}\frac{c}{R_J\sigma_{\parallel}}\simeq 10^{-29}\frac{L}{R_J},
$$
     and the voltage $U$ is also the potential difference between the jet axis and its radius. The derived estimate corresponds to the result obtained in \cite{refId0}: the ohmic resistance of the jet is very small, ${\cal R}_{ohm}\simeq 10^{-10} {\cal R}^{H}$.

    So the voltage $U$ is also the potential difference between the jet axis and its radius. The generated voltage is
\begin{equation}\label{uH}
    U = B_p r_g^2 \Omega^H / 2c.
\end{equation}
    It is taken into account that the angular velocity of rotation of magnetic field lines in the magnetosphere, $\Omega^F$, is half the angular velocity of rotation of the black hole $\Omega^H$, $\Omega^F\simeq \Omega^H/2 $ \cite{1977MNRAS.179..433B}. The angular velocity of the black hole rotation is proportional to the angular moment of the black hole rotation, $J=j(M^2 G/c)$, where $j$ is the specific angular momentum of the black hole, $j<1$,
\begin{equation}\label{omegH}
    \Omega^H=\frac{2c}{r_g}\frac{j}{1+(1-j^2)^{1/2}}.
\end{equation}
    The value of $ r_g $ is the gravitational radius of a black hole of the mass $ M $,
\begin{equation}\label{rg}
    r_g=\frac{2GM}{c^2} = 3 \cdot 10^5 \frac{M}{ M_\odot} \, cm = 3 \cdot 10^{14} M_9 \, cm.
\end{equation}
    The value of $ M_9 $ denotes the mass represented in units $ 10^9 M_\odot $. Accordingly, $\Omega^H=2\cdot 10^{-4} M_9^{-1}j/[1+(1-j^2)^{1/2}] \, s^{-1}$. If we also measure the strength of the poloidal magnetic field in the vicinity of the black hole horizon in the characteristic values $10^4$ G, $B_p=10^4 B_4$ G, then the voltage $U$ is equal to
\begin{equation}\label{ud}
    U=3\cdot 10^{18}M_9 B_4\frac{j}{1+(1-j^2)^{1/2}} \, cgs.
\end{equation}
    The mass $M_9$, the magnetic field $B_4$, the specific angular momentum $j$ and the calculated voltage $U$ (\ref{ud}) for AGN are shown in Table \ref{tab1}.

\begin{table}
		\caption{AGN parameters. \\
			\\
			$\ce{^{(1)}}$\cite{2019ApJ...886...37D},
			$\ce{^{(2)}}$\cite{2020MNRAS.495.3576K},
			$\ce{^{(3)}}$\cite{2009MNRAS.400...26O},
			$\ce{^{(4)}}$\cite{2015ApJ...805..179B},
			$\ce{^{(5)}}$\cite{2017ApJ...834...65A},
			$\ce{^{(6)}}$\cite{2014ApJ...789..143P},
			$\ce{^{(7)}}$\cite{Nakahara_2018},
			$\ce{^{(8)}}$\cite{2018NatAs...2..472G},
			$\ce{^{(9)}}$\cite{2018Galax...6...15A},
			$\ce{^{(10)}}$\cite{2008PASA...25..167G},
			$\ce{^{(11)}}$\cite{2017MNRAS.472..788G},
			$\ce{^{(12)}}$\cite{2009ApJ...696L..32D},
			$\ce{^{(13)}}$\cite{2019ApJ...879...75H},
			$\ce{^{(14)}}$ \cite{2006MNRAS.370..399B},
			$\ce{^{(15)}}$ \cite{1999ASTRO...11032F},
			$\ce{^{(16)}}$ Estimated based on the data from \cite{Jones_2000}, \\
			$\ce{^{(17)}}$ The Kerr parameter taken equal to $\simeq 1.00$ \\}

		\begin{tabular}{lcccr}
			\hline
			Object      &         j          &       $M_9$           & $B_4$                 &       U            \\
			&                    & $[10^9 M_{\odot}]$     & $[10^4 G]$            &      [cgs]         \\
			\hline
			OQ 530      & $\ce{^{(17)}}1.00$ & $\ce{^{(3)}}0.55$     & $\ce{^{(3)}}0.08$     & $1.2 \cdot 10^{17}$ \\

			S5 2007+77  & $\ce{^{(17)}}1.00$ & $\ce{^{(3)}}0.4$      & $\ce{^{(3)}}0.14$     & $1.7 \cdot 10^{17}$ \\

			S4 0954+65  & $\ce{^{(17)}}1.00$ & $\ce{^{(3)}}0.23$     & $\ce{^{(3)}}0.4$      & $2.8 \cdot 10^{17}$ \\

			NGC 1275    & $\ce{^{(1)}}1.00$  & $\ce{^{(8)}}2.0$      & $\ce{^{(2)}}1.05$     & $6.3 \cdot 10^{18}$ \\

			NGC 4261    & $\ce{^{(1)}}1.00$  & $\ce{^{(7)}}0.49$     & $\ce{^{(16)}}0.32$    & $4.7 \cdot 10^{17}$ \\

			NGC 4486    & $\ce{^{(4)}}0.66$  & $\ce{^{(4)}}6.6$      & $\ce{^{(1)}}0.07$     & $5.2 \cdot 10^{17}$ \\

			3C 371      & $\ce{^{(1)}}1.00$  & $\ce{^{(2)}}8.51$     & $\ce{^{(16)}}0.23$    & $5.9 \cdot 10^{18}$ \\

			3C 405      & $\ce{^{(12)}}0.78$ & $\ce{^{(10)}}2.5$     & $\ce{^{(12)}}1.2$     & $4.3 \cdot 10^{18}$ \\

			NGC 6251    & $\ce{^{(1)}}1.00$  & $\ce{^{(2)}}8.78$     & $\ce{^{(1)}}0.5$      & $1.3 \cdot 10^{19}$ \\

			3C 120      & $\ce{^{(1)}}1.00$  & $\ce{^{(1)}}8.13$     & $\ce{^{(1)}}0.74$     & $1.8 \cdot 10^{19}$ \\

			BL Lac      & $\ce{^{(1)}}1.00$  & $\ce{^{(3)}}8.23$     & $\ce{^{(3)}}1.7$      & $4.2 \cdot 10^{19}$ \\

			3C 273      & $\ce{^{(17)}}1.00$ & $\ce{^{(9)}}6.59$     & $\ce{^{(16)}}0.91$    & $1.8 \cdot 10^{19}$ \\

			3C 390.3    & $\ce{^{(17)}}1.00$ & $\ce{^{(1)}}8.83$     & $\ce{^{(1)}}1.66$     & $4.4 \cdot 10^{19}$ \\

			3C 454.3    & $\ce{^{(17)}}1.00$ & $\ce{^{(11)}}2.3$     & $\ce{^{(16)}}0.39$    & $2.7 \cdot 10^{18}$ \\

			1H 0323+342 & $\ce{^{(6)}}0.96$  & $\ce{^{(9)}}0.73$     & $\ce{^{(16)}}1.43$    & $2.4 \cdot 10^{18}$ \\
			\hline
			SS433       & $\ce{^{(14)}}1.00$ & $\ce{^{(14)}}10^{-8}$ & $\ce{^{(15)}}10^{8}$ & $3.0 \cdot 10^{18}$ \\
			\hline \\
		\end{tabular}
		\label{tab1}
	\end{table}

    For the same objects the Table \ref{tab2} shows the luminosity values $L_j$. We also calculated the value of $(L_j/c)^{1/2}$, which is necessary to determine the acceleration regime (see formulas (\ref{r1}, \ref{r2}, \ref{r3})). It is interesting to note that the values of $U$ and $(L_j/c)^{1/2}$ are values of the same order. This follows from the fact that the jet resistance,
$$
    {\cal R}=U^2/L_j = \frac{1}{c}\left[\frac{U}{(L_j/c)^{1/2}}\right]^2,
$$
    is really close to the resistance of the black hole horizon ${\cal R}^H = 4\pi/c$. Another necessary parameter is the value of $B_z R_J$. Here $R_J$ is the radius of the jet at its base in the region where the parabolic and conical profiles intersect. Their values are obtained from observations and are shown in the Table \ref{tab2}. As for the value of the longitudinal magnetic field $B_z$ at the base of the jet, there are no reliable observations data of this value now. A simple estimate following from conservation of the flux of the poloidal magnetic field, $B_z=B_p (r_g/R_J)^2$, gives too low magnetic field at the base of the jet, which becomes even more insignificant when removed from the base. So, for example, in the galaxy M87 (NGC 4486) the resulting value of the field $B_z \simeq 10^{-4}$ G at the base of the jet in the region of intersection of the parabolic and conical profiles contradicts observations and the numerical modeling gives the result of the order of $\simeq 100 r_g$, $B_z\simeq 1$ G \cite{2019MNRAS.486.2873C}, \cite{Kino_2014}. The conservation of magnetic flux implies the existence of well organized magnetic surfaces with magnetic field lines embedded inside them. GRMHD numerical simulations do not show laminar fluid flow from the magnetosphere to the region where the jet is formed. The magnetic field is also highly turbulent.

    To estimate the value of $B_z$, we will based on the fact that the field is frozen into the well conducting relativistic plasma. It is captured in the magnetosphere and transferred to the jet. The equation of state of a relativistic gas is $PV^{4/3}=const$, where $P$ is the gas pressure, $V$ is its volume. The plasma pressure and magnetic field in the magnetosphere are in the equipartition, $P\simeq B_p^2/8\pi$. On the other hand,  for the radial equilibrium $B_z^2/8\pi\simeq P$ in the jet. The volume of a gas near the black hole, $V\simeq r_g^3$, goes to $V\simeq r_g R_J^2$. Thus, eventually we get
\begin{equation}\label{bzp}
     B_{z} = B_p \left (\frac{r_g}{R_J}\right)^{4/3}.
\end{equation}
    Such dependence, the power 4/3, just lies between the power 2 for a pure poloidal field and the power 1 for a pure toroidal field. The resulting magnetic fields are on average equal to $B_z \simeq 10^{-2}$ G.

    Based on the values $R_j$ and $B_z$, we get the value of the product $B_z R_j$ presented in the Table \ref{tab2}. Note that the value of $B_z R_j$, which plays an auxiliary role in our work, can be interpreted as the maximum energy of particles accelerated in the presence of a magnetic field $B_z$. According to the Hillas's criterion, \cite{1984ARA&A..22..425H}, the cyclotron radius of a particle with such energy is compared with the size of the system. In our case this is the jet radius $R_j$. It is important that using the formula (\ref{bzp}) for estimation of the magnetic field $B_z$ significantly approaches the value of $B_z R_J$ to $U$, as it should be.

    We also set the value of the potential $U_2$ (\ref{r1}),
\begin{eqnarray}
    U_2=B_z R_J\left\{\frac{1}{2}\left(\frac{a_2}{12}\right)^2+\left[\frac{1}{4}\left(\frac{a_2}{12}\right)^4+ \right.\right.\nonumber \\
    \left.\left. \left(\frac{8}{3}\right)^2\frac{1}{(B_z R_J)^4}\left(\frac{L_J}{c}\right)^2\right]^{1/2}\right\}^{1/2} , \, a_2=6,
\end{eqnarray}
    separating the regime of untrapped trajectories from trapped trajectories. For $U>U_2$ trajectories are untrapped, for $U<U_2$  trajectories are trapped. However, if values $U$ and $U_2$ are not very different due to some uncertainty of the presented data, we cannot clearly determine the acceleration regime, whether it is untrapped or trapped.

    The value of energy in different acceleration regimes is given by the potential $U$ calculated by the formula (\ref{ud}) and presented for each object in the Tables \ref{tab1} and \ref{tab2}: \ \
    for a proton accelerated in the untrapped regime the energy is defined as,
\begin{equation}\label{poteni1}
    E_{max}[eV] = 300 \cdot U[cgs];
\end{equation}
    for a proton in trapped regime the average energy is,
\begin{equation}\label{poteni2}
    E_{max}[eV] = 0.74 \cdot 300 \cdot U [cgs];
\end{equation}
    and finally, the proton energy in the regime of motion without acceleration is,
\begin{equation}
    E_i [eV] = 0.94 GeV \cdot \left(\frac{U[eV]}{0.94 GeV}\right)^{2/3}.
\end{equation}
    Energies in all acceleration regimes are shown in the Table \ref{tab2}.

    The exact value of the boundary potential $U_2$ between untrapped mode and trapped mode is somewhat uncertain. This is due to the fact that energy and the potential are determined by a large number of parameters including only observable ones such as the radius of the jet $R_j$. Their total error does not allow us to clearly find the border between trapped and untrapped regimes if the values $U$ and $U_2$ are of the same order. If $U > U_2$, but they are of the same order, the regime in the Table \ref{tab2} is denoted as \textquotedblleft untrapped/trapped,\textquotedblright\, otherwise the regime is denoted as \textquotedblleft trapped/untrapped.\textquotedblright\, In these two special cases the particle energy is calculated using the formula (\ref{poteni1}). In all cases of untrapped particles the regime is designated as \textquotedblleft untrapped\textquotedblright\, and the energy is calculated  using the formula (\ref{poteni2}), accordingly.

\clearpage
	\begin{table}
		\caption{Jet parameters and acceleration regimes in the AGNs. \\
			\\
			$\ce{^{(1)}}$The jet radius taken from Mojave catalogue, \\
			$\ce{^{(2)}}$\cite{2020MNRAS.495.3576K},
			$\ce{^{(3)}}$\cite{Nakahara_2018},
			$\ce{^{(4)}}$\cite{2018Galax...6...15A},
			$\ce{^{(5)}}$\cite{2017ApJ...834...65A},
			$\ce{^{(6)}}$ \cite{2006MNRAS.370..399B},
			$\ce{^{(7)}}$\cite{2009MNRAS.400...26O},
			$\ce{^{(8)}}$\cite{2018NatAs...2..472G},
			$\ce{^{(9)}}$\cite{2019ApJ...886...37D},
			$\ce{^{(10)}}$\cite{2018Galax...6...15A},
			$\ce{^{(11)}}$\cite{2009ApJ...696L..32D},
			$\ce{^{(12)}}$\cite{2019ApJ...879...75H},
			$\ce{^{(13)}}$\cite{2017MNRAS.472..788G},
			$\ce{^{(14)}}$ \cite{2006MNRAS.370..399B},
			$\ce{^{(15)}}$ \cite{1999MNRAS.304..271D},
			$\ce{^{(16)}}$ \cite{2003A&A...400..477T},\\
			$\ce{^{(17)}}$ BLL - BL Lac, S2 - seyfert 2nd. type, L2 - LINER, FR1 fan.ray. 1st type, N - narrow line, HPQ - highly polarized quasar, G - radiogalaxy, MQ - microquasar
		}
		\begin{tabular}{lcccccccccr}
			\hline
			Object      & $\ce{^{(17)}}Type$ & $R_j$  & $\log_{10}(L_j)$ & $(L_j/c)^{1/2}$ & $B_z R_j$  &    $U$    &   $U_2$   & $E_{max}$ & $E_i $ & regime \\
			&                    & [cm]   & [erg/s]          &  [cgs]          &    [cgs]  &    [cgs]   &   [cgs]   &  [eV]     &     [eV]    &         \\
			\hline
			OQ 530      & BLL & $\ce{^{(16)}}6.0 \cdot 10^{18}$ & $\ce{^{(7)}}45.23$ & $2.4 \cdot 10^{17}$ & $3.7 \cdot 10^{15}$ & $1.2 \cdot 10^{17}$ & $3.9 \cdot 10^{17}$ & $3.6 \cdot 10^{19}$ & $2.4 \cdot 10^{14}$ & trapped/untrapped \\

			S5 2007+77  & BLL & $\ce{^{(1)}}6.0 \cdot 10^{18}$ & $\ce{^{(7)}}45.50$ & $3.3 \cdot 10^{17}$ & $4.5 \cdot 10^{15}$ & $1.7 \cdot 10^{17}$ & $5.3 \cdot 10^{17}$ & $5.1 \cdot 10^{19}$ & $3.0 \cdot 10^{14}$ & trapped/untrapped  \\

			S4 0954+ 5  & BLL & $\ce{^{(1)}}6.0 \cdot 10^{18}$ & $\ce{^{(7)}}46.04$ & $6.1 \cdot 10^{17}$ & $6.1 \cdot 10^{15}$ & $2.8 \cdot 10^{17}$ & $9.9 \cdot 10^{17}$ & $8.4 \cdot 10^{19}$ & $4.2 \cdot 10^{14}$ & trapped/untrapped \\

			NGC 1275    & S2  & $\ce{^{(2)}}3.5 \cdot 10^{17}$ & $\ce{^{(8)}}46.75$ & $1.4 \cdot 10^{18}$ & $7.4 \cdot 10^{17}$ & $6.3 \cdot 10^{18}$ & $2.2 \cdot 10^{18}$ & $1.9 \cdot 10^{21}$ & $3.3 \cdot 10^{15}$ & untrapped/trapped \\

			NGC 4261    & FR1 & $\ce{^{(3)}}1.5 \cdot 10^{18}$ & $\ce{^{(9)}}44.06$ & $6.2 \cdot 10^{16}$ & $2.1 \cdot 10^{16}$ & $4.7 \cdot 10^{17}$ & $1.0 \cdot 10^{17}$ & $1.4 \cdot 10^{20}$ & $5.9 \cdot 10^{14}$ & untrapped/trapped \\

			NGC 4486    & L2  & $\ce{^{(2)}}3.7 \cdot 10^{18}$ & $\ce{^{(9)}}44.47$ & $9.9 \cdot 10^{16}$ & $1.1 \cdot 10^{17}$ & $5.2 \cdot 10^{17}$ & $1.6 \cdot 10^{17}$ & $1.6 \cdot 10^{20}$ & $6.4 \cdot 10^{14}$ & untrapped/trapped \\

			3C 371      & BLL & $\ce{^{(2)}}7.7 \cdot 10^{17}$ & $\ce{^{(10)}}44.41$ & $9.3 \cdot 10^{16}$ & $8.6 \cdot 10^{17}$ & $5.9 \cdot 10^{18}$ & $1.5 \cdot 10^{17}$ & $1.3 \cdot 10^{21}$ & $3.2 \cdot 10^{15}$ & untrapped \\

			3C 405      & S2  & $\ce{^{(15)}}6.0 \cdot 10^{17}$ & $\ce{^{(11)}}45.67$ & $4.0 \cdot 10^{17}$ & $4.4 \cdot 10^{17}$ & $4.3 \cdot 10^{18}$ & $6.5 \cdot 10^{17}$ & $9.6 \cdot 10^{20}$ & $2.6 \cdot 10^{15}$ & untrapped \\

			NGC 6251    & S2  & $\ce{^{(2)}}4.9 \cdot 10^{17}$ & $\ce{^{(9)}}45.30$ & $2.6 \cdot 10^{17}$ & $2.3 \cdot 10^{18}$ & $1.3 \cdot 10^{19}$ & $4.3 \cdot 10^{17}$ & $2.9 \cdot 10^{21}$ & $5.5 \cdot 10^{15}$ & untrapped \\

			3C 120      & S1 & $\ce{^{(2)}}9.2 \cdot 10^{17}$  & $\ce{^{(9)}}45.54$ & $3.4 \cdot 10^{17}$ & $2.5 \cdot 10^{18}$ & $1.8 \cdot 10^{19}$ & $5.6 \cdot 10^{17}$ & $4.0 \cdot 10^{21}$ & $6.7 \cdot 10^{15}$ & untrapped \\

			BL Lac      & BLL & $\ce{^{(2)}}2.9 \cdot 10^{18}$ & $\ce{^{(7)}}45.90$ & $5.2 \cdot 10^{17}$ & $3.9 \cdot 10^{18}$ & $4.2 \cdot 10^{19}$ & $8.4 \cdot 10^{17}$ & $9.3 \cdot 10^{21}$ & $1.2 \cdot 10^{16}$ & untrapped \\

			3C 273      & BLL & $\ce{^{(4)}}7.0 \cdot 10^{17}$ & $\ce{^{(12)}}47.60$ & $1.8 \cdot 10^{18}$ & $2.5 \cdot 10^{18}$ & $1.8 \cdot 10^{19}$ & $6.0 \cdot 10^{18}$ & $5.4 \cdot 10^{21}$ & $6.7 \cdot 10^{15}$ & untrapped \\

			3C 390.3    & G   & $\ce{^{(5)}}3.2 \cdot 10^{18}$ & $\ce{^{(9)}}45.42$  & $3.0 \cdot 10^{17}$ & $4.1 \cdot 10^{18}$ & $4.4 \cdot 10^{19}$ & $4.9 \cdot 10^{17}$ & $9.8 \cdot 10^{21}$ & $1.2 \cdot 10^{16}$ & untrapped \\

			3C 454.3    & HPQ & $\ce{^{(1)}}6.0 \cdot 10^{18}$ & $\ce{^{(13)}}47.20$ & $2.3 \cdot 10^{18}$ & $1.3 \cdot 10^{17}$ & $2.7 \cdot 10^{18}$ & $3.8 \cdot 10^{18}$ & $8.1 \cdot 10^{20}$ & $1.9 \cdot 10^{15}$ & trapped/untrapped \\

			1H 0323+342 & N   & $\ce{^{(2)}}3.6 \cdot 10^{18}$ & $\ce{^{(10)}}45.82$ & $4.7 \cdot 10^{17}$ & $1.2 \cdot 10^{17}$ & $2.4 \cdot 10^{18}$ & $7.7 \cdot 10^{17}$ & $5.2 \cdot 10^{20}$ & $1.7 \cdot 10^{15}$ & untrapped \\
			\hline
			SS433       & MQ & $\ce{^{(6)}}1.2 \cdot 10^{11}$ & $\ce{^{(14)}}39.00$  & $1.8 \cdot 10^{14}$ & $8.6 \cdot 10^{16}$ & $3.0 \cdot 10^{18}$ & $3.1 \cdot 10^{14}$ & $6.7 \cdot 10^{20}$ & $2.0 \cdot 10^{15}$ & untrapped \\
			\hline
		\end{tabular}
		\label{tab2}
	\end{table}
	\clearpage

\section{Discussion}\label{section5}

    We have considered the acceleration of protons depending on the parameters characterizing the structure of the jet. This is primarily the amplitude of the toroidal magnetic field $B_\phi$ compared to the longitudinal magnetic field $B_z$. If the longitudinal field drawn out from the magnetosphere of a black hole by the jet outflow, from the almost radial poloidal field (split-monopole), can be considered homogeneous with good accuracy, not depending on the radial coordinate $\rho$, then the toroidal field must necessarily vanished at the jet axis, $\rho=0$, and on its periphery, $\rho=R_J$. The simplest, one-parameter relationship has the form, $B_\phi=\alpha B_z(\rho/R_J) (1-\rho/R_J)^2$. Thus, the parameter $\alpha$ determines the amplitude of the electric current $I$ flowing along the jet in one direction near the axis region and in the opposite direction at the peripheral region, $|\alpha|=32 I/cR_J B_z$ (\ref{i}). The second important value is the radial electric field $E_\rho$. It must also vanish at the jet axis and at its periphery, $E_\rho=\beta B_z(\rho/R_J) (1-\rho/R_J)^2$. The parameter $\beta$ defines the value of the potential difference $U$ between the jet axis and its periphery, $|\beta|=12 U/R_J B_z$ (\ref{u}). The voltage $U$ is created by a central machine, a rotating black hole. Depending on the values of the parameters $\alpha$ and $\beta$, the motion of protons is divided into three groups: untrapped, trapped and not accelerated. At $ \beta^2-\alpha^2>36$ particles, preaccelerated in the magnetosphere, getting the base of the jet at small radii, $ \rho/R_J<<1$, crossing the entire jet in the radial direction with receiving the maximum possible energy, $E=eU$. We call them untrapped. The jet magnetic field does not trap them. At $19< \beta^2-\alpha^2<36$ protons are captured in the radial direction moving in the direction of the jet axis and oscillating in the radial direction (see Fig. \ref{fig3}). The energy of the particles also oscillates around the value of $0.74 eU$. At $ \beta^2-\alpha^2<19$ protons are captured near the jet axis and are not accelerate in the jet, retaining their original energy, $E_i=m_p c^2(eU/m_p c^2)^{2/3}<< eU$, obtained in the magnetosphere of the central black hole.

    Untrapped particles accelerated to high energies, $E_{max} \simeq 10^{20} - 10^{21}$ eV (see Table \ref{tab2}), escape the jet at $z\simeq R_J$. Thus, the bases of jets are the sources of these protons. Trapped protons, achieved the average energy $0.74E_{max}$, can move along the jet for considerable distances. The fact is that in the definition of the values $ \alpha$ and $\beta$, in addition to the constant values $I, U, L_j$, the value of $B_z R_J$ is included, which changes with the distance from the base of the jet $z$. Due to the conservation of the magnetic field flux, $B_z R_J^2=const (z)$, the value of $B_z R_J$ decreases with distance from the base when the jet expands, $B_z R_J=B_z R_J|_{z=0} R_J(z=0)/R_J$. Therefore, if initially ($z=0$) the jet parameters are in the region of the trapped particle motion, $\beta^2-\alpha^2<36$, then when particles are removed from the base for a sufficiently large distance,  particles become untrapped and leave the jet with the maximum energy $E_{max}$. This circumstance is very important when considering the interaction of high-energy protons accelerated in a jet with jet plasma particles. Particularly it is important for the production of secondary high-energy particles including gamma radiation and neutrinos.

    For comparison of proton acceleration processes in massive AGN with their less energetic counterpart, microquasars (MQ) in binary systems with a stellar mass of black hole, the object SS 433 is considered as an example. Substituting the parameters of the MQ (see Table \ref{tab1}) into the calculation procedure for AGN, you can see that the potential of $U$ significantly exceeds the value of $U_2$, which indicates the unambiguous untrapped regime.

\section{Acknowledgments}
    This work was supported by Russian Foundation for Fundamental Research, grant No. 20-02-00469.

redpajama_set_name: RedPajamaArXiv


A colleague at the Meadowlands Commission has been bugging us for a "sunny" photo for him to use as a screensaver. Today was finally sunny enough to help the poor guy out.
We hope he likes the photo.
We are seeing some changes in bird activity in the Meadowlands — lots more Red-winged Blackbirds, for example, and far fewer Rough-legged Hawks (above).
In the DeKorte impoundments, we saw the usual raft of Canvasbacks, many Mallards, several Buffleheads, a few Black Ducks and some Northern Pintails.


text:
Trine Dahl
NHH
NHH Executive
Professor Trine Dahl
Trine.Dahl@nhh.no
+47 55 95 93 40 / +47 958 35 347
Professional and Intercultural Communication
Language and Communication Science communication English professional communication Academic writing Climate change discourse.
Biography and CV Selected publications Teaching Dissemination
Biography and CV
Trine Dahl has been working at NHH since 1985, first as Assistant Professor, then Associate Professor, and since 2008 as full Professor of English. She holds a doctorate in English linguistics from the University of Bergen.
Trine Dahl's research belongs within pragmatics and discourse studies. Her main projects in recent years (all financed by the Research Council of Norway) have been in cooperation with research colleagues at the University of Bergen: KIAP- Cultural identity in academic prose, studying writing styles in economics, linguistics and medicine in three different languages (2002-2006); two interdisciplinary projects investigating climate change discourse: LINGCLIM –Linguistic representations of climate change discourse and their individual and collective interpretations (2013-2016), and CLIMLIFE–Living with climate change: motivation and action for lifestyle change (2020–2023). Her work has appeared in journals such as Applied Linguistics, Corporate Communications: An International Journal, Journal of Pragmatics, Text & Talk, and Written Communication. Her teaching portfolio at the bachelor level comprises courses on English for business; at the master level, strategic & political communication, and communication skills for business; and at the PhD level, academic writing for research purposes.
Trine Dahl has been an expert member of several accreditation and assessment committees on higher education programmes involving professional language and communication.
Areas of expertise (Norwegian):
Akademisk skriving, Fagkommunikasjon
Dahl, Trine; Fløttum, Kjersti Climate change as a corporate strategy issue: A discourse analysis of three climate reports from the energy sector Corporate Communications. An International Journal Volume 24 (3); page 499 - 514; 2019
Dahl, Trine; Fløttum, Kjersti Verbal–visual harmony or dissonance? A news values analysis of multimodal news texts on climate change Discourse, Context & Media Volume 20; page 124 - 131; 2017
Dahl, Trine Contested science in the media: linguistic traces of news writers' framing activity Written Communication: an international quarterly of research, theory, and application Volume 32 (1); page 39 - 65; 2015
Dahl, Trine; Fløttum, Kjersti A linguistic framework for studying voices and positions in the climate debate Text & Talk Volume 34 (4); page 401 - 420; 2014
Fløttum, Kjersti; Dahl, Trine Different contexts, different "stories"? A linguistic comparison of two development reports on climate change Language & Communication Volume 32 (1); page 14 - 23; 2012
Dahl, Trine Contributing to the academic conversation: A study of new knowledge claims in economics and linguistics Journal of Pragmatics Volume 40 (7); page 1184 - 1201; 2008
Fløttum, Kjersti; Dahl, Trine; Kinn, Torodd Academic voices : across languages and disciplines John Benjamins Publishing Company; 2006
More publications in Cristin
Business institutions, business communication, academic writing, intercultural communication
Media's power over science
21 October 2015 Language and Communication
According to NHH Professor Trine Dahl, the media shape the public's views about controversial scientific issues through the language they use to frame these issues.

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Lenovo Launches New 2015 IdeaPads and Miix 700 Surface Rival
Travis Pope
To kick off the fall and holiday shopping season Windows device maker Lenovo is back with a new line-up of IdeaPad notebooks and a Miix Tablet that's absolutely going to catch the eye of shoppers. The IdeaPad 100S, IdeaPad 300S, IdeaPad 300 and IdeaPad 500 each have advantages different kinds of buyers will love. The new Lenovo Miix 700 is a straight Surface Pro 3 killer.
Lenovo revealed the new winter Windows 10 ready IdeaPad lineup and the Miix 700 this morning. With the Surface Pro 3 being a highly successful form factor for Microsoft, it's the Miix 700 that's garnering the most attention. Both devices are made for users ready to embrace the 2-in-1 lifestyle.
The Lenovo Miix 700 is a gold 12-inch tablet with the internals of a notebook PC. Inside there is a new 6th generation Intel Core M7 processor, Intel HD graphics, a 5 megapixel camera, 5 megapixel rear-facing camera and up to 9 hours of battery life. Miix 700 users can get a better view of their display by flipping out the embedded kickstand built into the rear of the device. Display options are limited to a 12-inch FHD+ display with a resolution of 2160 x 1440 pixels. Users can add up to 256GB of storage.
Lenovo goes farther than Microsoft is willing to with its professional tablet that can double as notebook PC. Standard, a 5 megapixel rear-facing camera with flash sits in for the optional Intel RealSense camera. Connectivity options include Bluetooth 4.0, and wireless 802.11 AC, the latest in internet standards. RealSense cameras allow Windows 10 devices to unlock for users on site. The Lenovo Miix 700 also includes a MicroSIM card slot and support for LTE mobile broadband. There's a USB 3.0 and a USB 2.0 port for connecting extra accessories. By comparison, the Surface Pro 3 only has a single port. The Miix 700 swaps the mini DisplayPort in the Surface Pro 3 for a micro HDMI Port. Lenovo says that it'll have versions with less powerful processors too.
The Lenovo Miix 700 kickstand is on a rotating hinge so that users can get the best viewing angle possible. For $699 Lenovo plans to include a case with the built-in mechanical keyboard. Color options will also include black.
Windows 2-in-1s are great for people looking to slim down the amount of devices they carry everyday. That market is growing, but many just want a great PC at a great price. That's where the new Lenovo IdeaPad 500, IdeaPad 300, IdeaPad 500S, IdeaPad 300S, IdeaPad 100S.
The IdeaPad 100S has two configurations. The first features an 11.6-inch 1366×768 display with an Intel Atom processor and 2 USB 2.0 ports for $189. There's also a 14-inch IdeaPad 100S for $259 with a 1366 x 768 14-inch display, Intel Celeron Processor, 1 USB 3.0 port, 1 USB 2.0 port and Bluetooth 4.0. Both can be configured with at least 32GB of RAM. They each get 8 hours of battery life running Microsoft's Windows 10 operating system.
IdeaPad 100S 11" in Blue.
Lenovo has the IdeaPad 300S for people who need more power and more storage. Windows 10 comes installed in machine already. Options include up to an Intel Core i7 processor, up to 8GB of memory, as much as 256GB of SSD storage, discrete Nvidia GeForce 940M graphics card. The machine has a single USB 3.0 port, a USB 2.0 port, a single HDMI port, a media card reader and 801.11AC wireless network technology. Options include a 14-inch 1920 x 1080p display. Lenovo says the IdeaPad 300s will go on sale for $479. Lenovo has a plain IdeaPad 300 machine coming for those who need integrated Radeon graphics, more display sizes, and more options where storage and RAM for running programs is concerned for $399.
Lenovo IdeaPad 300S in Black.
Finally, there are two configurations of the IdeaPad 500 for holiday shoppers: one with an AMD processor and another with an Intel processor. Both have 14-inch display and 15-inch display options. Both come with Windows 10, up to 6th generation Intel Core i7 processor, up to an 8GB RAM and up to a speedy 1TB SSD.
The IdeaPad 500s 13-inch in red.
The IdeaPad 500 is one of the few PCs that have optional backlit keys and optical disc drive. A single USB 2.0, USB 3.0 port, HDMI port and VGA cable complete the experience. Lenovo says users can opt to add an Intel RealSense 3D camera to the 15-inch 1080p model that costs $849. The 14-inch 1080p model starts at $499.
All told, it's a pretty strong line-up from Lenovo, with machines built for every kind of user running Windows. Adding options for Intel RealSense camera is smart bit of future proofing too, since Windows 10 uses the camera to power its Windows Hello security feature.
All of these machines will launch this holiday season to entice shoppers ahead of Christmas.
Related Topics:IdeaPad 100SIdeaPad 300IdeaPad 300sIdeaPad 500SLenovo


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The association between cyclin D1 G870A polymorphism and hepatocellular carcinoma in an Egyptian population
Maha A El-Bassiounya1, Eman A Gawishb2, Enas S Eissaa1, Gehan A Tawfeeka1, Esraa T A Allam2
1 Clinical Pathology Department, Faculty of Medicine, National Liver Institute, Menoufia University, Shebeen El-Kom, Egypt
2 Clinical Pathology Department, National Liver Institute, Menoufia University, Shebeen El-Kom, Egypt
Date of Submission 28-Jun-2016
Date of Acceptance 21-Aug-2016
Esraa T A Allam
MBBCH, Menoufia, 32511
DOI: 10.4103/mmj.mmj_348_16
To study the relationship between cyclin D1 G870A polymorphism and hepatocellular carcinoma (HCC) in Egyptian patients.
Cyclin D1, encoded by the gene CCND1, is a regulatory protein in the cell cycle transition from G1 phase to S phase. A common polymorphism (G870A) in the exon 4 of CCND1 gene affects splicing of the CCND1 transcript and may cause uncontrollable cellular growth. Therefore, the CCND1 G870A polymorphism may influence an individual's susceptibility to the development of certain tumors, which may include HCC.
Patients and methods
This study was carried out on 100 participants: 60 patients with HCC and 40 healthy age-matched and sex-matched volunteers. All participants underwent full history, liver profile, α-fetoprotein, and cyclin D1 G870A polymorphism assessment, which was done by PCR-restriction fragment length polymorphism assay.
The CCND1 genotype distribution among patients with HCC was significantly different from that of healthy controls (P = 0.000). Compared with the wild-type GG genotype, both the variant AA and AA+GA genotype and the A allele were associated with risk of HCC [odds ratio (OR): 64; 95% confidence interval (CI): 6.67–614.2;P = 0.000; OR: 19.67; 95% CI: 2.4–160.94;P = 0.000; and OR: 4.03; 95% CI: 2.2–7.41;P = 0.000, respectively]. Moreover, there is no significant correlation between the different cyclin D1 genotypes and clinicopathologic features of HCC.
Our results suggest that the CCND1 G870A polymorphism is associated with an increased risk of HCC in our Egyptian population.
Keywords: cyclin D1 gene, hepatocellular carcinoma, PCR-RFLP, polymorphism
El-Bassiounya MA, Gawishb EA, Eissaa ES, Tawfeeka GA, Allam ET. The association between cyclin D1 G870A polymorphism and hepatocellular carcinoma in an Egyptian population. Menoufia Med J 2018;31:333-8
El-Bassiounya MA, Gawishb EA, Eissaa ES, Tawfeeka GA, Allam ET. The association between cyclin D1 G870A polymorphism and hepatocellular carcinoma in an Egyptian population. Menoufia Med J [serial online] 2018 [cited 2022 Jan 18];31:333-8. Available from: http://www.mmj.eg.net/text.asp?2018/31/1/333/234211
Approximately 700 000 people die of hepatocellular carcinoma (HCC) each year worldwide, making it the third leading cause of cancer death [1]. Owing to the lack of efficient approaches in clinical management, the mortality of HCC remains very high. The 5-year survival for patients with HCC has poorly improved over the past decades. As a result, more and more attention has been paid to the discovery of potential biomarkers that are of diagnostic and prognostic value for HCC [2].
The main etiology of HCC is liver cirrhosis caused by chronic hepatitis B or C, alcohol, fatty liver diseases, or less commonly, autoimmune or genetic metabolic liver diseases [3].
Cyclin D1 is a key regulatory protein in the cell cycle, playing a critical role in the transition from G1 to S phase of the cell cycle [4].
The CCND1 gene, CCND1, is located on chromosome 11q13. The gene is polymorphic with a common A/G substitution at nucleotide 870 (A870G, rs9344) in the conserved splice donor region of exon 4. The A870G has been shown to increase the frequency of alternative splicing and can lead to an increase in the half-life of the protein. The variant CCND1 corresponding to the A allele may have a longer half-life than the G allele, which may bypass the G1/Scheck point [5]. Several studies, including meta-analysis, indicated the association of CCDN1 870A genotype with a great variety of cancers such as colorectal, lung, esophageal, breast, oral, and squamous cell carcinoma of head and neck [6]. Therefore, in this study, we aimed to investigate its association with HCC risk in an Egyptian population.
The present study was conducted at Clinical Pathology Department, Faculty of Medicine, Menoufia University, during the period from March 2014 to January 2015.
This study was carried out on 100 participants: 60 patients with HCC as case group and 40 healthy age-matched and sex-matched volunteers, with no previous history of liver or malignant diseases and negative for hepatitis viral markers, as controls. Patients with HCC were excluded if they have inflammatory diseases, hematological malignancy, and cancer of any organ other than the liver. The diagnosis of HCC cases was based on the recommendations of the European Association for the Study of Liver using imaging technique (computed tomography or MRI) [7]. A written consent was obtained from each individual, and the protocol was approved by the Ethical Committee of Menoufia Faculty of Medicine.
All participants were submitted to history taking; clinical examination; Child–Pugh classification; radiological examination including abdominal ultrasound and triphasic computed tomography; and laboratory tests including CBC (Symex XT 1800; Menemeni, Thessaloniki, Greece), liver function tests (Rochintegra 400 plus; Basel, Switzerland), α-fetoprotein (Hitachi Cobas E 411; Basel, Switzerland), qualitative measurement of HCV-RNA and HBs Ag by PCR (CA, USA), and determination of CCND1 gene polymorphisms by PCR-restriction fragment length polymorphism.
DNA extraction and genotyping
Genomic DNA was isolated from ethylene diamine tetra acetic acid-preserved whole blood by standard proteinase K digestion ethanol precipitation using Thermo Scientific Gene JET Genomic DNA Purification Kit (Thermo Fisher Scientific, Massachusetts, USA).
After ethanol precipitation, the DNA was purified and dissolved in double distilled water and frozen at −20°C until use. The CCND1 G870A genotype was determined by PCR-restriction fragment length polymorphism assay. The PCR primers (Thermo scientific) were as follows: forward 5'-GTG AAG TTC ATT TCC AAT CCG C-3' and reverse 5'-GGG ACA TCA CCC TCA CTT AC-3'. PCR cycling conditions were 5 min at 95°C, followed by 35 cycles of 45 s at 94°C, 45 s at 55°C, and 45 s at 72°C, with a final elongation step at 72°C for 5 min. For restriction fragment length polymorphism, the PCR products were digested with five units ScrFI enzyme (MA 01938-2723. United States.) at 37°C and visualized by electrophoresis on 3% agarose under ultraviolet illumination. The allele types were determined as follows: a single 167 bp fragment for the AA genotype, two fragments of 22 and 145 bp for the GG genotype, and three fragments of 22, 145, and 167 bp for the AG genotype [8].
Statistical analysis of the present study was conducted with SPSS, version 17.0 (SPSS Inc., Chicago, Illinois, USA). Data were expressed into two phases: descriptive included mean, SD, and range and analytical study included χ2-test, t-test, Mann–Whitney test, Kruskal–Wallis test and Z test, Fisher's exact test, odds ratio (OR), and confidence interval (CI) test. P value more than 0.05 was considered statistically nonsignificant. P value of less than 0.05 was considered statistically significant. P value of less than 0.001 was considered statistically highly significant.
Baseline characteristics of the study patients
Baseline characteristics of the patients and controls showed no significant differences between the two groups in terms of age and sex [Table 1]. Moreover, there was a statistically significant difference between cases and controls regarding alanine aminotransferase (ALT), aspartate aminotransferase (AST), total and direct bilirubin, serum albumin, and international normalized ratio (INR) [Table 2].
Table 1: Comparison between studied patients regarding age and sex
Table 2: Descriptive statistics of the studied patients regarding laboratory investigations
CCND1 genotypes and allele distribution among study patients
The frequency distributions of the different genotypes for CCND1 polymorphism are shown in [Figure 1] and [Table 3]. There was a highly significant higher percentage of GG genotype among control group than cases group (25 vs. 1.7%, P = 0.001) and highly significant lower percentage of AA genotype among control group than cases group (12.5 vs. 53.3%, P = 0.000). Moreover, there is a highly significant lower percent of A allele among control group than cases group (75.8 vs. 43.7, P = 0.000).
Figure 1: (a) Agarose gel electrophoresis for cyclin D1 gene amplification bands correspond to ladder band size (167 bp). (b) Agarose gel electrophoresis showing PCR-restriction fragment length polymorphism analysis of cyclin D1 gene after addition of restriction enzyme: lanes (ladder) 2 and 3 (GG) band (145 and 22 bp), lanes 4–7 (AG) band (167 145 and 22 bp), and lanes 8, 9 and 10 (AA) band 167 bp.
Table 3: Comparison between cases and control regarding genotypes and alleles
CCND1 gene polymorphism and the risk for hepatocellular carcinoma
To evaluate the risk of HCC according to the CCND1 genotype using the GG genotype as the reference genotype, GA genotype significantly increased the risk of HCC by 10.08-fold (OR: 10.8; 95% CI: 1.29–90.56; P = 0.02), whereas AA genotype significantly increased the risk of HCC by 64.0-fold (OR: 64; 95% CI: 6.67–614.2; P = 0.000). Comparing A allele versus G allele, it was found that A allele significantly increased the risk of HCC by 4.03-fold compared with G allele (OR: 4.03; 95% CI: 2.2–7.41; P = 0.000) [Table 4].
Table 4: Odds ratio of genotypes and alleles between cases and control groups
CCND1 genotypes and clinic pathological features of hepatocellular carcinoma
To assess the role of CCND1 gene polymorphism in clinic pathological features of HCC cases, the distribution of clinical and laboratory parameters among CCND1 genotypes was estimated [Table 5], and there was no statistically significant difference between the different genotypes regarding clinical examination (spleen, liver, ascites, child classification, encephalopathy, and tumor size) or laboratory investigations (ALT, AST, albumin, total and direct bilirubin, INR, and α-fetoprotein).
Table 5: Clinical examination and laboratory investigation in relation to different genotypes among hepatocellular carcinoma cases
HCC is one of the 10 most commonly occurring solid cancers worldwide. The most recent data indicate that its incidence is still increasing in many countries whereas the most effective way of reducing mortality owing to HCC is prevention [9].
Liver carcinogenesis is a complex and multifactorial process, in which both environmental and genetic features interfere and contribute to malignant transformation. The identification of host factors that may play an important role in HCC development may improve our understanding of the implications of the various biological pathways involved in liver carcinogenesis; such progress may as well help refine the selection of patients who could benefit from specific preventative measures or could be given adapted screening policies. Numerous candidate gene studies have reported associations between single nucleotide polymorphism and the presence of HCC [10].
CCND1, a key regulator of cell cycle progression, plays an important role in the transition from G1 to the S phase during cell division [11],[12]. The adenine-to-guanine (A/G) substitution at nucleotide 870 (CCND1 G870A polymorphism) and excessive cyclin D1 activity are common in numerous human tumors, including breast cancer, lung cancer, head and neck cancers, gastric cancer, gynecological cancers, and blood-related cancers [13].
In this study, we investigated the association between CCND1 G870A polymorphism and the risk of HCC in Egyptian population. In the present study, the mean age of patients with HCC was 54.1 ± 6.5 years, a finding which may indicate that HCC is more commonly encountered in old ages. These results are in agreement with Luo et al. [13], who found that the mean age of patients with HCC was 54.1 ± 10.5 years. Moreover, Shaker et al. [14] found that the most frequent age category affected by HCC was between 51 and 60 year. On the contrary, higher age incidence was reported by Giakoumidakis [15], who found that HCC is more frequent in patients with age of at least 65 years.
In the present study, 83.3% of patients with HCC were males and 16.7% were females. This is in agreement with the result of the study conducted by Rizk et al. [16], who found that most patients with HCC were males. Moreover, Holah et al. [17] reported that most of patients with HCC were males.
De Lope et al. [18] suggested that this male predominance may be because of higher rates of exposure to liver carcinogens and hepatitis virus infections in men or to an estrogen-mediated inhibition of interleukin-6 production by Kupffer cells in females, leading to reduced liver injury and compensatory proliferation.
Considering cyclin D1 G870A polymorphism, our study shows statistically significant difference in distribution of the genotypes and allele frequencies between patients with HCC and healthy controls. It shows highly significant higher percentage of GG genotype among control group than cases group (25 vs. 1.7%), nonsignificant difference regarding percentage of GA genotype, and highly significant lower percent of AA genotype among control group than cases group (12.5 vs. 53.3%). Additionally, it shows highly significant higher percent of G allele among control group than cases group (56.3 vs. 24.2) and highly significant lower percent of A allele among control group than cases group (43.7 vs. 75.8).
Our results are similar to the results obtained by Akkız et al. [8], who found that the CCND1 G870A single nucleotide polymorphism is associated with an increased frequency of HCC in Turkish population. The data showed that CCND1 A allele was more frequently observed in the HCC group than control group with significant difference in the genotype frequency between the two groups (P = 0.009).
In contrast with our study, Hu et al. [19] states that the CCND1 genotype distribution among patients with HCC was not significantly different from that among healthy controls in a Chinese population (P = 0.08).
Our study also shows that GA genotype significantly increased the risk of HCC by 10.08-fold when comparing with the GG genotype (P = 0.02), whereas AA genotype significantly increase the risk of HCC by 64.0-fold when comparing with the GG genotype (P = 0.000).
Moreover, the present study show that GA+AA and GG+GA increase the risk of HCC by 19.6 and 8.0-fold, respectively.
Comparing A allele versus G allele, it was found that A allele significantly increase risk of HCC by 4.03-fold (P = 0.000), and our results are similar to the results obtained by Akkız et al. [8], who found that both AA genotype and A allele increased the risk for HCC in Turkish population.
In the meta-analysis by Zhao et al. [20], which involved leukemia and HCC, CCND1 G870A polymorphism was significantly associated with HCC risk under the recessive model (AA vs. AG+GG).
Found that the G870A genotype had no association with the susceptibility of hepatitis B virus-related HCC in the Chinese cohort study.
Hu et al. [19] stated that compared with the wild-type GG genotype, neither the variant AA genotype nor the A allele was associated with risk of HCC. However, stratification analysis by hepatitis B virus carrier status revealed that the variant genotypes containing the A allele were associated with a significantly increased risk of HCC among HBsAg-positive individuals (adjusted OR: 3.87; 95% CI: 1.12–13.30).
Studying the correlation between cyclin D1 G870A genotypes and clinical data shows that there was no statistically significant difference between the different genotypes and clinical parameters. This agrees with the results of Akkız et al. [8], and Hu et al. [20].
Moreover, there was no statistically significant difference between the different genotypes regarding laboratory investigations (ALT, AST, albumin, total and direct bilirubin, INR, and α-fetoprotein).
Our results suggest that this polymorphism may have role in liver carcinogenesis. These results may be limited by the low number of patients.
If our findings are confirmed in both larger series and other ethnic origins, genetic testing of CCND1 G870A polymorphism may be useful in detecting high-risk individuals such as hepatitis virus sero-positive patients who are at an even greater risk for HCC, and the results may encourage the higher risk population to have frequent medical examinations to detect early-stage HCC. Furthermore, the knowledge of the mechanisms involved in HCC carcinogenesis may help to identify targets for the development of chemoprevention or therapeutic strategies.
Bruix J, Reig M, Sherman M. Evidence-based diagnosis, staging, and treatment of patients with hepatocellular carcinoma. Gastroenterology 2016; 150:835–853.
Tian Q, Zhang M, Luo R, Fu J, He C, Hu G. DHX33 expression is increased in hepatocellular carcinoma and indicates poor prognosis. Biochem Biophys Res Commun 2016; 473:1163–1169.
Yim H, Suh S, Um S. Current management of hepatocellular carcinoma: an Eastern perspective. World J Gastroenterol 2015; 21:3826–3842.
Aytekin T, Aytekin A, Maralcan G, Gokalp M, Ozen D, Borazan E. A cyclin D1 (CCND1) gene polymorphism contributes to susceptibility to papillary thyroid cancer in the Turkish population. Asian Pac J Cancer Prev 2014; 15:7181–7185.
Wang W, Zhao Y, Yang J, Lin B, Gu H, Cao X. Cyclin D1 polymorphism and oral cancer: a meta-analysis. Mol Biol Rep 2012; 40:87–95.
Zeybek U, Yaylım I, Ozkan NE. Cyclin D1 gene G870A variants and primary brain tumors. Asian Pac J Cancer Prev 2013; 14:4101–4106.
EASL–EORTC Clinical Practice Guidelines. Management of hepatocellular carcinoma. Eur J Cancer 2012; 48:599–641.
Akkız H, Bayram S, Bekar A, Akgollu E, Ozdil B. Cyclin D1 G870A polymorphism is associated with an increased risk of hepatocellular carcinoma in the Turkish population: case–control study. Cancer Epidemiol 2010; 34:298–302.
Mazzanti R, Arena U, Tassi R. Hepatocellular carcinoma: Where are we? World J Exp Med 2016; 6:21–36.
Nahon P, Zucman-Rossi J. Single nucleotide polymorphisms and risk of hepatocellular carcinoma in cirrhosis. J Hepatol 2012; 57:663–674.
Wu Y, Fu H, Zhang H, Huang H, Chen M, Zhang L. Cyclin D1 (CCND1) G870A polymorphisms and cervical cancer susceptibility: a meta-analysis based on ten case–control studies. Tumor Biol 2014; 35:6913–6918.
Yang Y, Wang F, Shi C, Zou Y, Qin H. Cyclin D1 G870A polymorphism contributes to colorectal cancer susceptibility: evidence from a systematic review of 22 case–control studies. PLoS One 2012; 7:e36813.
Luo J, Zhang Z, Liu Q, Zhang W, Wang J, Yan Z. Endovascular brachytherapy combined with stent placement and TACE for treatment of HCC with main portal vein tumor thrombus. Hepatol Int 2015; 10:185–195.
Shaker MK, Abdella HM, Khalifa MO, El Dorry AK. Epidemiological characteristics of hepatocellular carcinoma in Egypt: a retrospective analysis of 1313 cases. Liver Int 2013; 33:1601–1606.
Giakoumidakis K, Nikolaos F, Ioannis E, Evangelos A, Patris Vasileios P, Hero B. Frequency and predisposing factors of hepatocellular carcinoma in a hepatology outpatient unit. Health Sci J 2015; 9:1–10.
Rizk E, Zakaria S, Abdel-Razik A, Farouk N. Soluble CD25 and Hepatocellular carcinoma. Int J Adv Res 2015; 3:658–664.
Holah NS, El-Azab DS, Aiad HA, Sweed DM. Hepatocellular carcinoma in Egypt: epidemiological and histopathological properties. Menoufia Med J 2015; 28:718–724.
De Lope C, Tremosini S, Forner A, Reig M, Bruix J. Management of HCC. J Hepatol 2012; 56:75–87.
Hu Z, Zhou Z, Xiong G, Wang Y, Lai Y, Deng L, et al. Cyclin D1 G870A polymorphism and the risk of hepatocellular carcinoma in a Chinese population. Tumor Biol 2014; 35:5607–5612.
Zhao Y, He H, Wang M, Ren X, Zhang L, Dong Y. Cyclin D1 G870A gene polymorphism and risk of leukemia and hepatocellular carcinoma: a meta-analysis. Genet Mol Res 2015; 14:5171–5180.
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
El-Bassiounya MA
Gawishb EA
Eissaa ES
Tawfeeka GA
Allam ET
cyclin D1 gene
PCR-RFLP


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Size approx 48 x 48 cm.


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"Pants-Only" Policy Upheld Against Free Exercise Claim in Retaliatory Termination Case
September 16, 2013 by Kara Wallis
Can a public employer require a woman to wear pants, even against her religious beliefs? In its brief opinion in Finnie v. Lee County, Mississippi, a panel of the Fifth Circuit left that question unanswered given the particular circumstances of the case.
After working for a Mississippi Sheriff's Department for years, Ms. Crystal Finnie converted to the Pentecostal religion, which she told the court, meant she could no longer wear "'clothing pertaining to a man's garments,' such as pants." But her employer, the Sheriff's Department, required pants as part of the uniform and told Ms. Finnie that she would have to "wear pants or resign."
Shortly after filing a complaint with the Equal Employment Opportunity Commission (EEOC) and requesting a transfer to a clerical position where she could wear a skirt and keep her job, Ms. Finnie was fired.
She then filed suit. She argued that the policy violated her First Amendment right to exercise her religion, "constituted unlawful gender and religious discrimination under Title VII of the Civil Rights Act of 1964, and amounted to unlawful retaliation under Title VII."
But the underlying question was whether Ms. Finnie was terminated as retaliation, and the Fifth Circuit panel held that she did not meet the burden to show she would not have been terminated "but for" her EEOC complaint. Yet the opinion does not clarify whether her dismissal based upon her religious objection to the dress code would have been actionable.
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Cover. Attribute to University Library. Photo credit: University Library
Arts & Life, Events
22 Short Scares, Three Big Winners
by Keanu Hua on December 15, 2022
Keanu Hua Author
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Courage is not the absence of fear, but rather, the ability to confront it anyway.
Over the month of October, the Long Beach State University Library hosted a spooky short story contest. A total of 22 contestants developed and submitted stories inspired by book covers.
The judges included health sciences librarian Michelle DeMars, English and comparative literature librarian Alexis Pavenick plus children and young adult librarian Cathy Outten.
Beyond just being a contest for writers to demonstrate their creativity, this was a chance to introduce the wider campus to the diverse collections within the library and promote community engagement.
As DeMarrs recalls, the contest "was also to introduce them to some of the other collections, like the mystery collection, the Masback Collection, Critics Choice, things like that."
Neither writing nor judging were easy tasks.
On the writing side, contestants had the entire library at their disposal. Whether perusing the shelves or browsing the digital catalogs, covers ranged from mysteries, children's books, nonfiction, or pre-existing horror. From there, writers then had to produce work just within the word limit, all while balancing their other obligations.
From there, writers submitted and anxiously awaited results. While frightening for writers, both DeMars and Outten found submissions delightful to read.
Outten especially appreciated "the twists at the end" and the masterful character development of many submissions, noting that she "really got to know the characters" in such a small word count.
Whether they won or not, DeMars and Outten commended students for their courage and dedication to their craft. They especially appreciate the creativity in turning seemingly harmless covers, such as a fire boat, into a good fright.
"Meahoy, memoyay? Neyoyoyminoy, ladyonmamoy!" — Let's hope Doodlebob and his pencil stay trapped in the chalk where he belongs. Photo credit: University Library
"They all had their way of conveying what they felt was a spooky story, and I think the hardest part was having to choose a winner because I really think all the students just did a really good job and I enjoyed every single one of the stories," DeMars said. "So to me the hardest part was having to apply a score to our rubric that we used."
The library plans to host additional events, engagement and outreach, with one already in action. Adorned in chalk are two pillars in the lobby, where new questions are frequently cycled in for students to respond to.
Pay Dirt by author Rita Mae Brown and cover art by Jack Unruh. Cover inspiration for "Housekeeping" by Emily Diaz. Photo credit: Jack Unruh
Emily Diaz is an English literature major, aiming to switch to English education because of her family's background in teaching. Her previous writing experience was mainly in journalism — her high school's yearbook and newspaper.
While creative writing is a new form of stress relief for her, her background has helped her find her own flow and form in creative fiction.
Diaz's story, "Housekeeping," centers on a ghostly cat guarding his home.
"I was just looking through the stacks in the school library, specifically the second floor, and I just came across the cover with a cat on it. I really like cats," Diaz said.
From there, it took off with some inspiration and help from her own three cats, whose behaviors were the basis for the cat in her story.
While Diaz isn't much of a horror fan, she was undeterred and labored over her story. "As I was revising it," she said, "I was thinking, what are some words that would have like a better image? Create a better image or what are some things that would help add to the scariness factor?"
Her desire in writing is simply for people to enjoy it.
"I'm not hoping to achieve a specific emotion or anything," Diaz said."I just kind of want someone to read it and say, 'hey, that was a good five minutes or so that I spent reading it'."
"Under Your Skin: Your Amazing Body" by author/illustrators Mick Manning and Brita Granstorm. Cover inspiration for "Deadman's Halloween" by Jaime Salazar. Photo credit: Mick Manning & Brita Granstorm
Jaime Salazar is a liberal studies major, aiming to be an elementary school teacher. While he does not have any particular inspirations, he still aims to always improve his writing with the help of his teachers and mentors.
Salazar's story, "Deadman's Halloween," tells the story of a skeleton enjoying his Halloween. In this case, the time of the year was one of his specific inspirations.
He decided to match his cover with his field by browsing the second floor of the library, which is where the education section is.
"The book cover just kind of resonated an idea within me of that, this is what I would possibly want to write about," he said. "Looking through some of the children's book covers allowed for me to feel a little bit inspired when writing the story."
During his revisions, Salazar had to carefully balance a spooky mood in his story with simplicity and the need to keep it PG, ultimately ending up with a work akin to a children's story.
Ultimately, Salazar seeks to always be improving, whether in creative works or in technical communications. He said, "I have a clear message and I just want to make that easily accessible, first of all, and then illustrate the creativity portion and the ideas that roam within my head."
"Skeleton Crew" by Stephen King, art by Don Brautigam. Cover inspiration for "Margaret's Playthings" by Brandon Shane. Photo credit: Don Brautigam
Brandon Shane, a San Diego transfer student, is a current creative writing major. His greatest inspirations are Stephen King, for his prolific and consistent success, and Sylvia Plath, for the impact of her every word, line and poem.
Shane finds that he writes largely out of instinct.
"I write in the same way as I breathe," Shane said. "It is a function which I cannot control as long as I am alive."
Shane's story was "Margaret's Plaything," inspired by a Stephen King cover and his own father's prior cancer diagnosis.
It centers on a young girl, Sarah, coping with the loss of her parents, symbolized by an evil monkey. It's a symbol of "the unintentional things left behind after loss, in the rubble of traumatic events that no one wanted to impart, but exists nonetheless as poltergeists waiting to make themselves known."
Loss and grief are complicated beasts to tackle and Shane noted that it could well have been extended into a novella. One removal included additional contexts on the two uncles, Clayton and William, and their argument over their sister's will.
Another cut consisted of the deaths of the parents and their love from beyond the grave, on which Shane remarks, "We still love those who have passed (perhaps even more), and the love of the dead still exists in the memories of the living."
In writing, Shane hopes to elicit the sense of wonder he had with stories, both as a child and today. For him, literature, read from start to finish, "holds that special essence we all thought it contained as children – where everything exists, and we are there to experience it all."
Arts and Life, books, csulb, Halloween, library, writing
Keanu Hua


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Q: Using the builtin dialog under OSX to unlock an SSH key OSX has a builtin passphrase dialog for ssh-agent, so that on the first use of a key, it'll get cached.
The problem is -- I can't find a way to spawn that dialog by just adding ssh-add. ssh-add will only prompt for a passphrase on the terminal.
Somehow, the agent checks the existence of matching .pub and private key files and uses that to know which to ask for and spawn what I assume is a builtin dialog box.
I can work around this, hilarously, by also trusting that key for logging into "localhost", and putting "ssh localhost echo -n """ into my .bashrc, but this is dumb.  If I can ssh-add and put the passphrase in on the terminal, I should also be able to use the builtin GUI.
(Why would I want to arbitarily unlock the ssh key before I log into anything, you may ask? Well, because bash-completion's ability to autocomplete things like the other side of an scp or rsync command requires an available auth mechanism -- either Kerberos or an agented/unpassworded key.)
I'm annoyed that I can't find a reference for this anywhere else.

A: I think the dialog is because it is adding the ssh key to the keychain (as well as|instead of) to the .ssh/ files.
You should be able to invoke ssh-add -K and get the same results.

redpajama_set_name: RedPajamaStackExchange


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Book Reviews Science Fiction/Fantasy Genre Book Reviews
Book Review: Toward a Secret Sky, an Alright Read
We're doing a lot better this week, now that we know for sure Jonah doesn't have a brain tumor. We have yet to get the official diagnosis of vestibular neuritis as the cause of his traumatic hospitalization a couple of weeks ago and his ongoing dizziness, but will probably get it later this week and begin his treatment. I'm confident that the treatment will be effective, as I've seen it work before, and that Jonah will completely recover. In the meantime, I've been busy catching up, working, spending time with family celebrating the 4th of July holiday, and reading. I'm reading two books (Claudia Gray's Defy the Stars audiobook, and K.B. Wager's After the Crown, which is the sequel to Behind the Throne, which I reviewed last week), and I just finished a third: Heather MacLean's Toward a Secret Sky. It was a relatively fun, imaginative read that reminded me somewhat of Cassandra Clare's City of Bones and Laine Taylor's Daughter of Smoke and Bone. But I had a hard time really getting into it.
Shortly after 17-year-old Maren Hamilton is orphaned and sent to live with grandparents she's never met in Scotland, she receives an encrypted journal from her dead mother that makes her and everyone around her a target. She finds out she's been assigned a guardian angel named Gavin, who happens to be a very handsome "teenage" boy, and struggles with her attraction toward him (and he her) while unwittingly becoming involved in a fight between demons and angels that victimizes the friends she makes at the local high school. All she wants is a normal life with parents, but the more she tries to save her friends, not fall in love with Gavin, and stay alive, the more she realizes that the parents she once had weren't who they appeared to be and that "normal" might not ever be something she can ever return to.
What I Thought
It's a fun exploration of Scottish and British culture, as seen from a teenager's perspective, with touches of Indiana Jones-like puzzle-solving. MacLean's writing is, at times, quite illustrative. Consider this description:
"The last bubbles burped over the butter's muddy grave."
Or this one, of the house of one of her rich classmates:
"Hundreds of rose bushes hugged the hedge bottoms. I marveled at the luscious fruit trees, their branches heavy with the weight of snowball-sized blossoms, and the carved marble benches, their seats held high by miniature gargoyles. In the middle, a fountain corralled life-sized granite horses swimming among arcs of shooting water."
"My first breaths in England's capital were heavy with anticipation."
The story is generally well-paced, perhaps even briskly so, with events unfolding when they should.
Heather MacLean
But ultimately, this story didn't pull me as much as other similar ones I've read (mentioned above), for various reasons. The main one is that some of the characters' actions and reactions seemed premature. Gavin reveals that he's an angel, and that he's tasked with protecting her, which makes him feel conflicted, pretty early in the tale. His and Maren's mutual attraction seems a bit rushed to me, as does Maren's willingness to risk her life for people she's barely met. Additionally, various instances of "telling" instead of "showing," pronoun slips, and out-of-the-blue or "off" details threw me out of the story a little bit.
For instance, when Maren goes to a party at her rich classmate's mansion, she says: "We learned that aside from the staff, there wasn't an adult anywhere in the building." It would have been stronger, more in-the-moment, for her to say something like: "I looked around for adults with uniforms or hawkish expressions, but saw none."
This sentence (at location 102) contains an example of a pronoun slip: "I discovered via an almost-accident that you had to pay money to unlock public restroom stalls, like a vending machine for pee." Not a big deal, but it would have been stronger, more in-Maren's-head if she'd said something like: "All of the restroom stall doors were locked, but coin slots next to each of their latches seemed to indicate that I had to pay to unlock one of them and pee."
And at location 1081, Maren talks about being in a forest just outside the angel village where Gavin lives, and a few paragraphs after, she's back in the village without having walked there.
Overall, though, I would still recommend it for young teenage girls looking for a "swoony" read.
I got a free copy of Toward a Secret Sky from NetGalley. All opinions contained herein are my own, and would be the same if I'd paid for my copy.
book review toward a secret sky, fiction books about angels, Toward a Secret Sky book review
Book Review: Sybil, a Fascinating Read, and an Update on my Crazy Life!
Six Great Escape Books and Book Deals
Book Review: The Immortalist, A Thrilling Read


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Team America to add a juniors version for developing athletes
VAIL — Following three successful years of Team America supporting senior athletes in pursuing their potential to reach for the World Cup, Junior Team America is being formed to support the next generation of Vail champions.
Junior Team America is designed to support Ski & Snowboard Club Vail athletes who have achieved a nationally or internationally recognized level of current performance and are hoping to take it up a notch.
'SUPPORT TO PURSUE THEIR GOALS'
"Junior Team America is an important initiative for Ski & Snowboard Club Vail to begin to change the paradigm in snow sports where only the most successful international athletes are funded and costs increase as athletes reach higher performance levels in their sport," said Ski & Snowboard Club Vail Executive Director Aldo Radamus. "It is critical to insure that SSCV's young athletes are supported with the programming and, where needed, the financial support to pursue their goals."
With a world class mountain, community support, facilities, coaching and academic partners Vail is uniquely positioned to provide support and opportunity for winter sports athletes, Radamus said.
The inaugural Junior Team America will include athletes Lucy Bailey, Colby Lange, Kaitlyn Harsch and Cleo Braun.
SYNC PERFORMANCE TO PARTNER
"SYNC is excited to partner with Ski & Snowboard Club Vail and the TA Foundation in support of Junior Team America," said Phil Shettig, co-president of SYNC Performance. "As a company dedicated to performance and focused on the alpine athlete, we will be providing Junior Team America with the apparel and gear they require to help them achieve their full potential. We look forward to working closely with each of the athletes, gaining valuable insight into what works and having them play an active role in new product development."
Team America Foundation founder and chairman Dan Leever said the group is pleased to add the junior athletes to their roster of supported athletes.
"Like our Senior Team America, who compete at the NorAm, Europa Cup and World Cup levels, these exceptional developing young athletes have not only achieved outstanding age group performance but also demonstrate the commitment, passion and character to fulfill their potential," Leever said.


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