text:
\section{INTRODUCTION}

The algebra of quaternions \cite{hamilton} can be used to describe
the scalar invariants and some conservation laws in the
gravitational field \cite{newton}. The algebra of octonions
\cite{cayley} can be used to demonstrate the scalar invariants in
the case for electromagnetic field \cite{maxwell} and gravitational
field, including conservation of mass \cite{lavoisier} and
conservation of energy \cite{lorentz}. The results are only dealt
with quaternion operator, but octonion operator. In the octonion
space, the operator should be extended from the quaternion operator
to the octonion operator.

Making use of the octonion operator, the gravitational field
demonstrated by the octonion operator will generate an adjoint
field. The source of adjoint field includes the adjoint mass and
adjoint linear momentum. In general, the adjoint mass and its
movement can not be observed by usual experiments. However, when the
adjoint mass is combined with the ordinary mass to become one sort
of particles, their movements will be accompanied by some mechanical
effects. Moreover, this kind of adjoint mass may influence the
distribution of electric charge.

With the invariant property of octonions, we find that the adjoint
mass and field strength have the influence on conservation laws in
the gravitational field, under the octonion coordinate
transformation.

\section{Octonion transformation}

In the quaternion space for the gravitational field, the basis
vector is $\mathbb{E}_g$ = ($1$, $\emph{\textbf{i}}_1$,
$\emph{\textbf{i}}_2$, $\emph{\textbf{i}}_3$), and radius vector is
$\mathbb{R}_g$ = ($r_0$, $r_1$, $r_2$, $r_3$), with velocity
$\mathbb{V}_g$ = ($v_0$, $v_1$, $v_2$, $v_3$). For the
electromagnetic field, the basis vector is $\mathbb{E}_e$ =
($\emph{\textbf{I}}_0$, $\emph{\textbf{I}}_1$,
$\emph{\textbf{I}}_2$, $\emph{\textbf{I}}_3$), the radius vector is
$\mathbb{R}_e$ = ($R_0$, $R_1$, $R_2$, $R_3$), and the velocity is
$\mathbb{V}_e$ = ($V_0$, $V_1$, $V_2$, $V_3$).

The $\mathbb{E}_e$ is independent of the $\mathbb{E}_g$, with
$\mathbb{E}_e$ = $\mathbb{E}_g$ $\circ$ $\emph{\textbf{I}}_0$. The
basis vectors $\mathbb{E}_g$ and $\mathbb{E}_e$ can be combined
together to become the basis vector $\mathbb{E}$ of the octonion
space.
\begin{eqnarray}
\mathbb{E} = \mathbb{E}_g + \mathbb{E}_e = (1, \emph{\textbf{i}}_1,
\emph{\textbf{i}}_2, \emph{\textbf{i}}_3, \emph{\textbf{I}}_0,
\emph{\textbf{I}}_1, \emph{\textbf{I}}_2, \emph{\textbf{I}}_3)
\end{eqnarray}

In the octonion space, the radius vector $\mathbb{R}$ is
\begin{eqnarray}
\mathbb{R} = \Sigma ( r_i \emph{\textbf{i}}_i ) + \Sigma ( R_i
\emph{\textbf{I}}_i)
\end{eqnarray}
and the velocity $\mathbb{V}$  is
\begin{eqnarray}
\mathbb{V} = \Sigma ( v_i \emph{\textbf{i}}_i ) + \Sigma ( V_i
\emph{\textbf{I}}_i)
\end{eqnarray}
where, $r_0 = v_0 t$; $v_0$ is the speed of light, $t$ denotes the
time; $R_0 = V_0 T$; $V_0$ is the speed of light-like, $T$ denotes a
time-like physical quantity; the $\circ$ denotes the octonion
multiplication. $i = 0, 1, 2, 3$, $j = 1, 2, 3$,
$\emph{\textbf{i}}_0 = 1$.

We may consider directly the quaternion space as the two-dimensional
complex space, and the octonion space as the four-dimensional
complex space.

In some special cases, the adjoint mass is combined with the
ordinary mass to become a sort of special particle. Therefore we can
measure its various characteristics, and have following relation
equation.
\begin{eqnarray}
R_i \emph{\textbf{I}}_i = r_i \emph{\textbf{i}}_i \circ
\emph{\textbf{I}}_0~;~ V_i \emph{\textbf{I}}_i = v_i
\emph{\textbf{i}}_i \circ \emph{\textbf{I}}_0~.
\end{eqnarray}

The octonion quantity $\mathbb{D} (d_0, d_1, d_2, d_3, D_0, D_1,
D_2, D_3 )$ is defined as follows.
\begin{eqnarray}
\mathbb{D} = d_0 + \Sigma (d_j \emph{\textbf{i}}_j) + \Sigma (D_i
\emph{\textbf{I}}_i)
\end{eqnarray}
where, $d_i$ and $D_i$ are all real.

When the coordinate system is transformed into the other, the
physical quantity $\mathbb{D}$ will be transformed into the new
octonion $\mathbb{D}' (d'_0 , d'_1 , d'_2 , d'_3 , D'_0 , D'_1 ,
D'_2 , D'_3 )$ .
\begin{equation}
\mathbb{D}' = \mathbb{K}^* \circ \mathbb{D} \circ \mathbb{K}
\end{equation}
where, $\mathbb{K}$ is the octonion, and $\mathbb{K}^* \circ
\mathbb{K} = 1$; $*$ denotes the conjugate of octonion; $\circ$ is
the octonion multiplication.

The octonion $\mathbb{D}$ satisfies the following equations.
\begin{eqnarray}
d_0 = d'_0
\end{eqnarray}

In the above equation, the scalar part $d_0$ is preserved during the
octonion coordinates are transforming. Some scalar invariants of
electromagnetic field will be obtained from this characteristics of
the octonion.

\begin{table}[t]
\caption{\label{tab:table1}The octonion multiplication table.}
\begin{ruledtabular}
\begin{tabular}{ccccccccc}
$ $ & $1$ & $\emph{\textbf{i}}_1$  & $\emph{\textbf{i}}_2$ &
$\emph{\textbf{i}}_3$  & $\emph{\textbf{I}}_0$  &
$\emph{\textbf{I}}_1$
& $\emph{\textbf{I}}_2$  & $\emph{\textbf{I}}_3$  \\
\hline $1$ & $1$ & $\emph{\textbf{i}}_1$  & $\emph{\textbf{i}}_2$ &
$\emph{\textbf{i}}_3$  & $\emph{\textbf{I}}_0$  &
$\emph{\textbf{I}}_1$
& $\emph{\textbf{I}}_2$  & $\emph{\textbf{I}}_3$  \\
$\emph{\textbf{i}}_1$ & $\emph{\textbf{i}}_1$ & $-1$ &
$\emph{\textbf{i}}_3$  & $-\emph{\textbf{i}}_2$ &
$\emph{\textbf{I}}_1$
& $-\emph{\textbf{I}}_0$ & $-\emph{\textbf{I}}_3$ & $\emph{\textbf{I}}_2$  \\
$\emph{\textbf{i}}_2$ & $\emph{\textbf{i}}_2$ &
$-\emph{\textbf{i}}_3$ & $-1$ & $\emph{\textbf{i}}_1$  &
$\emph{\textbf{I}}_2$  & $\emph{\textbf{I}}_3$
& $-\emph{\textbf{I}}_0$ & $-\emph{\textbf{I}}_1$ \\
$\emph{\textbf{i}}_3$ & $\emph{\textbf{i}}_3$ &
$\emph{\textbf{i}}_2$ & $-\emph{\textbf{i}}_1$ & $-1$ &
$\emph{\textbf{I}}_3$  & $-\emph{\textbf{I}}_2$
& $\emph{\textbf{I}}_1$  & $-\emph{\textbf{I}}_0$ \\
\hline $\emph{\textbf{I}}_0$ & $\emph{\textbf{I}}_0$ &
$-\emph{\textbf{I}}_1$ & $-\emph{\textbf{I}}_2$ &
$-\emph{\textbf{I}}_3$ & $-1$ & $\emph{\textbf{i}}_1$
& $\emph{\textbf{i}}_2$  & $\emph{\textbf{i}}_3$  \\
$\emph{\textbf{I}}_1$ & $\emph{\textbf{I}}_1$ &
$\emph{\textbf{I}}_0$ & $-\emph{\textbf{I}}_3$ &
$\emph{\textbf{I}}_2$  & $-\emph{\textbf{i}}_1$
& $-1$ & $-\emph{\textbf{i}}_3$ & $\emph{\textbf{i}}_2$  \\
$\emph{\textbf{I}}_2$ & $\emph{\textbf{I}}_2$ &
$\emph{\textbf{I}}_3$ & $\emph{\textbf{I}}_0$  &
$-\emph{\textbf{I}}_1$ & $-\emph{\textbf{i}}_2$
& $\emph{\textbf{i}}_3$  & $-1$ & $-\emph{\textbf{i}}_1$ \\
$\emph{\textbf{I}}_3$ & $\emph{\textbf{I}}_3$ &
$-\emph{\textbf{I}}_2$ & $\emph{\textbf{I}}_1$  &
$\emph{\textbf{I}}_0$  & $-\emph{\textbf{i}}_3$
& $-\emph{\textbf{i}}_2$ & $\emph{\textbf{i}}_1$  & $-1$ \\
\end{tabular}
\end{ruledtabular}
\end{table}

\section{Gravitational field}

The gravitational field and its adjoint field both can be
demonstrated by the quaternions, although they are quite different
from each other indeed.

\subsection{Invariants in gravitational field}

\subsubsection{Potential and strength}

The gravitational field potential is
\begin{eqnarray}
\mathbb{A}_g = \Sigma (a_i \emph{\textbf{i}}_i)~.
\end{eqnarray}

The strength $\mathbb{B}_g = \Sigma (b_{gi} \emph{\textbf{i}}_i) +
\Sigma (B_{gi} \emph{\textbf{I}}_i)$ consists of the gravitational
strength $\mathbb{B}_{gg}$ and adjoint field strength
$\mathbb{B}_{ge}$.
\begin{eqnarray}
\mathbb{B}_g = \lozenge \circ \mathbb{A}_g = \mathbb{B}_{gg} +
\mathbb{B}_{ge}
\end{eqnarray}
where, $\mathbb{B}_{gg} = \Sigma (b_{gi} \emph{\textbf{i}}_i)$,
$\mathbb{B}_{ge} = \Sigma (B_{gi} \emph{\textbf{I}}_i)$; $b_{gi}$
and $B_{gi}$ are all real; $ \lozenge = \Sigma \emph{\textbf{i}}_i (
\partial/\partial r_i) + \Sigma \emph{\textbf{I}}_i (
\partial/\partial R_i)$; $\partial_i =
\partial/\partial r_i$.

In the above equation, we choose the following gauge conditions to
simplify succeeding calculation.
\begin{eqnarray}
&& \partial a_0 / \partial r_0 - \Sigma (\partial a_j /
\partial r_j) = 0 \nonumber\\
&& \partial a_0 / \partial R_0 + \Sigma (\partial a_j /
\partial R_j) = 0 \nonumber
\end{eqnarray}

The gravitational strength $\mathbb{B}_{gg}$ in Eq.(9) includes two
parts, $\textbf{g}_g = ( g_{g01} , g_{g02} , g_{g03} ) $ and
$\textbf{b}_g = ( g_{g23} , g_{g31} , g_{g12} )$,
\begin{eqnarray}
\textbf{g}_g/v_0 = && \emph{\textbf{i}}_1 ( \partial_0 a_1 +
\partial_1 a_0 ) + \emph{\textbf{i}}_2 ( \partial_0 a_2 + \partial_2
a_0 )
\nonumber\\
&& + \emph{\textbf{i}}_3 ( \partial_0 a_3 + \partial_3 a_0 )
\\
\textbf{b}_g = && \emph{\textbf{i}}_1 ( \partial_2 a_3 -
\partial_3 a_2 ) + \emph{\textbf{i}}_2 ( \partial_3 a_1 - \partial_1
a_3 )
\nonumber\\
&& + \emph{\textbf{i}}_3 ( \partial_1 a_2 - \partial_2 a_1 )
\end{eqnarray}
while the adjoint field strength $\mathbb{B}_{ge}$ involves two
parts, $\textbf{E}_g = ( B_{g01} , B_{g02} , B_{g03} ) $ and
$\textbf{B}_g = ( B_{g23} , B_{g31} , B_{g12} )$ .
\begin{eqnarray}
\textbf{E}_g/v_0 = && \emph{\textbf{I}}_1 ( \partial_1 a_0 -
\partial_0 a_1 ) + \emph{\textbf{I}}_2 ( \partial_2 a_0 - \partial_0 a_2 )
\nonumber\\
&& + \emph{\textbf{I}}_3 ( \partial_3 a_0 - \partial_0 a_3 )
\\
\textbf{B}_g = && \emph{\textbf{I}}_1 ( \partial_3 a_2 -
\partial_2 a_3 ) + \emph{\textbf{I}}_2 ( \partial_1 a_3 - \partial_3
a_1 )
\nonumber\\
&& + \emph{\textbf{I}}_3 ( \partial_2 a_1 - \partial_1 a_2 )
\end{eqnarray}

The linear momentum density $\mathbb{S}_{gg} = m \mathbb{V}_g $ is
the source of gravitational field, and its adjoint linear momentum
density $\mathbb{S}_{ge} = \bar{m} \mathbb{V}_g \circ
\emph{\textbf{I}}_0$ is that of adjoint field. They combine together
to become the field source $\mathbb{S}_g$ .
\begin{eqnarray}
\mu \mathbb{S}_g && = - ( \mathbb{B}_g/v_0 + \lozenge)^* \circ
\mathbb{B}_g
\nonumber\\
&& = \mu_{gg} \mathbb{S}_{gg} + \mu_{ge} \mathbb{S}_{ge} -
\mathbb{B}_g^* \circ \mathbb{B}_g/v_0
\end{eqnarray}
where, $\bar{m}$ is the adjoint mass density; $\mu_{gg}$ and
$\mu_{ge}$ are the coefficients; $*$ denotes the conjugate of
octonion.

The $\mathbb{B}_g^* \circ \mathbb{B}_g/(2\mu_{gg})$ is the field
energy density.
\begin{eqnarray}
\mathbb{B}_g^* \circ \mathbb{B}_g/ \mu_{gg} = ( \mathbb{B}_{gg}^*
\circ \mathbb{B}_{gg} + \mathbb{B}_{ge}^* \circ \mathbb{B}_{ge} ) /
\mu_{gg}
\end{eqnarray}

The above means that the adjoint field energy makes a contribution
to the gravitational mass.

\subsubsection{Conservation of mass}

In the gravitational field and its adjoint field, the linear
momentum density $\mathbb{P} = \mu \mathbb{S}_g / \mu_{gg}$ is
written as
\begin{eqnarray}
\mathbb{P} = \widehat{m} v_0 + \Sigma (m v_j \emph{\textbf{i}}_j ) +
\Sigma ( M_g V_i \emph{\textbf{i}}_i \circ \emph{\textbf{I}}_0 )
\end{eqnarray}
where, $\widehat{m} = m - (\mathbb{B}_g^* \circ \mathbb{B}_g /
\mu_{gg} )/v_0^2 $ ; $M_g = \bar{m} \mu_{ge}/\mu_{gg}$ . $p_0 =
\widehat{m} v_0$, $p_j = m v_j $; $P_i = M_g V_i $.

The above means that the gravitational mass density $\widehat{m}$ is
changed with either the gravitational strength or the adjoint field
strength in the gravitational field and its adjoint field.

From Eq.(6), we have one linear momentum density, $\mathbb{P}'
(p'_0, p'_1, p'_2, p'_3, P'_0, P'_1, P'_2, P'_3)$, when the octonion
coordinate system is rotated. And we obtain the invariant equation
from Eqs.(7) and (16).
\begin{eqnarray}
\widehat{m} v_0 = \widehat{m}' v'_0
\end{eqnarray}

Under Eqs.(3), (7), and (17), we find the gravitational mass density
$\widehat{m}$ remains unchanged.
\begin{eqnarray}
\widehat{m} = \widehat{m}'
\end{eqnarray}

The above means that if we choose the definitions of velocity and
linear momentum, the inertial mass density and gravitational mass
density will keep unchanged respectively, under the coordinate
transformation in Eq.(6) in the gravitational field and its adjoint
field.

\subsubsection{Mass continuity equation}

In the gravitational field and its adjoint field, the applied force
density $\mathbb{F} = \Sigma (f_i \emph{\textbf{i}}_i ) + \Sigma
(F_i \emph{\textbf{I}}_i )$ is defined from the linear momentum
density $\mathbb{P}$ in Eq.(16).
\begin{eqnarray}
\mathbb{F} = v_0 (\mathbb{B}_g/v_0 + \lozenge )^* \circ \mathbb{P}
\end{eqnarray}
where, the scalar $f_0 = v_0 \Sigma (\partial p_i / \partial r_i) +
v_0 \Sigma ( \partial P_i / \partial R_i ) + \Sigma ( b_{gj} p_j +
B_{gj} P_j ) $.

When the coordinate system rotates, we have the new force density
$\mathbb{F}' (f'_0, f'_1, f'_2, f'_3, F'_0, F'_1, F'_2, F'_3)$.

By Eq.(7), we have
\begin{eqnarray}
f_0 = f'_0
\end{eqnarray}

When $f'_0 = 0$ in the above, we have the conservation of mass in
the case for coexistence of the gravitational field and its adjoint
field.
\begin{eqnarray}
\Sigma \left\{ \partial (p_i + P_i )/
\partial r_i \right\} + \Sigma ( b_{gj} p_j + B_{gj} P_j ) / v_0 = 0
\end{eqnarray}

If the $b_{gi} = B_{gi} = 0$, the above will be reduced to the
following equation.
\begin{eqnarray}
\partial (m + M_g )/ \partial t + \Sigma \left\{ \partial (p_j + P_j )/
\partial r_j \right\} = 0
\end{eqnarray}
further, if there is not adjoint field, we have
\begin{eqnarray}
\partial m / \partial t + \Sigma (\partial p_j / \partial r_j) = 0
\end{eqnarray}

The above states that the adjoint field strength, adjoint mass, and
gravitational strength have a tiny influence on the conservation of
mass in the gravitational field and its adjoint field, although the
$\Sigma ( b_{gj} p_j + B_{gj} P_j ) / v_0$ and $\Sigma ( \partial
P_i / \partial r_i )$ both are usually very tiny when the fields are
weak. In case of we choose the definitions of the applied force and
velocity in the gravitational field and adjoint field, the
conservation of mass will be the invariant under the octonion
transformation in Eq.(6).

\subsubsection{Conservation of spin}

The angular momentum density $\mathbb{L} = \Sigma (l_i
\emph{\textbf{i}}_i ) + \Sigma (L_i \emph{\textbf{I}}_i )$ is
defined from the radius vector $\mathbb{R}$, physical quantity
$\mathbb{X}$, and linear momentum density $\mathbb{P}$ in the
octonion space.
\begin{eqnarray}
\mathbb{L} = (\mathbb{R} + k_{rx} \mathbb{X}) \circ \mathbb{P}
\end{eqnarray}
where, $l_0$ is considered as the spin angular momentum density in
the gravitational field and adjoint field; $l_0 = (r_0 + k_{rx} x_0
) p_0 - \Sigma \left\{ (r_j + k_{rx} x_j ) p_j \right\} - \Sigma
\left\{ (R_i + k_{rx} X_i ) P_i \right\}$; $k_{rx}$ is the
coefficient.

When the octonion coordinate system rotates, we have the new angular
momentum density $\mathbb{L}' = \Sigma ( l'_i \emph{\textbf{i}}'_i +
L'_i \emph{\textbf{I}}'_i )$. Under the octonion coordinate
transformation, the spin density remains unchanged from Eq.(7).
\begin{eqnarray}
l_0 = l'_0
\end{eqnarray}

The above means the adjoint field, space, time, and strength have an
influence on orbital angular momentum and spin angular momentum. The
spin angular momentum density $l_0$ will change with time in the
gravitational field and adjoint field, although $l_0$ is one
invariant under the octonion transformation.

\begin{table}[b]
\caption{\label{tab:table1}The definitions and the mechanics
invariants of the gravitational field with its adjoint field in the
octonion space.}
\begin{ruledtabular}
\begin{tabular}{lll}
$definition$    &    $invariant $    &    $ meaning $                            \\
\hline
$\mathbb{R}$    &    $r_0 = r'_0 $   &    $Galilean~invariant$                   \\
$\mathbb{V}$    &    $v_0 = v'_0$    &    $invariable~speed~of~light$            \\
$\mathbb{A}$    &    $a_0 = a'_0$    &    $invariable~scalar~potential$          \\
$\mathbb{B}$    &    $b_0 = b'_0$    &    $invariable~gauge$                     \\
$\mathbb{P}$    &    $p_0 = p'_0$    &    $invariable~mass~density$              \\
$\mathbb{F}$    &    $f_0 = f'_0$    &    $conservation~of~mass$                 \\
$\mathbb{L}$    &    $l_0 = l'_0$    &    $invariable~spin~density$              \\
$\mathbb{W}$    &    $w_0 = w'_0$    &    $invariable~energy~density$            \\
$\mathbb{N}$    &    $n_0 = n'_0$    &    $conservation~of~energy$               \\
\end{tabular}
\end{ruledtabular}
\end{table}

\subsubsection{Conservation of energy}

The total energy density $\mathbb{W} = \Sigma (w_i
\emph{\textbf{i}}_i ) + \Sigma (W_i \emph{\textbf{I}}_i )$ is
defined from the angular momentum density $\mathbb{L}$.
\begin{eqnarray}
\mathbb{W} = v_0 ( \mathbb{B}_g/v_0 + \lozenge) \circ \mathbb{L}
\end{eqnarray}
where, the scalar part $w_0 = v_0 \partial l_0 / \partial r_0 - v_0
\Sigma (\partial l_j / \partial r_j) - v_0 \Sigma ( \partial L_i /
\partial R_i ) - \Sigma ( b_{gj} l_j + B_{gj} L_j ) $.

When the coordinate system rotates, we have the new energy density
$\mathbb{W}' = \Sigma ( w'_i \emph{\textbf{i}}'_i + W'_i
\emph{\textbf{I}}'_i )$. Under the octonion transformation, the
scalar part of total energy density is the energy density and
remains unchanged by Eq.(7).
\begin{eqnarray}
w_0 = w'_0
\end{eqnarray}

In some special cases, the right side is equal to zero. We obtain
the conservation of spin angular momentum.
\begin{eqnarray}
&& \partial l_0 / \partial r_0 - \Sigma (\partial l_j / \partial
r_j)
\nonumber\\
&& - \Sigma (\partial L_i / \partial r_i) - \Sigma ( b_{gj} l_j +
B_{gj} L_j ) / v_0 = 0
\end{eqnarray}

If the last term is neglected, the above is reduced to
\begin{eqnarray}
\partial l_0 / \partial r_0 - \Sigma (\partial l_j / \partial r_j)
- \Sigma ( \partial L_i /
\partial r_i ) = 0
\end{eqnarray}
further, if there is not adjoint field, we have
\begin{eqnarray}
\partial l_0 / \partial r_0 - \Sigma (\partial l_j / \partial
r_j) = 0
\end{eqnarray}

The above means the energy density $w_0$ is variable in the case for
coexistence of the gravitational field and adjoint field, because
the adjoint mass, velocity, and strength have the influence on the
angular momentum density. While the scalar $w_0$ is the invariant
under the octonion transformation from Eqs.(7) and (25).

\subsubsection{Conservation of power}

In the gravitational field with adjoint field, the external power
density $\mathbb{N}$  can be defined from the total energy density
$\mathbb{W}$ in Eq.(26).
\begin{eqnarray}
\mathbb{N} = v_0 ( \mathbb{B}_g/v_0 + \lozenge)^* \circ \mathbb{W}
\end{eqnarray}
where, the external power density $\mathbb{N}$ includes the power
density in the gravitational field and adjoint field.

The external power density can be rewritten as follows.
\begin{eqnarray}
\mathbb{N} = n_0 + \Sigma (n_j \emph{\textbf{i}}_j ) + \Sigma (N_i
\emph{\textbf{I}}_i )
\end{eqnarray}
where, the scalar $n_0 = v_0 \Sigma (\partial w_i / \partial r_i) +
v_0 \Sigma ( \partial W_i / \partial R_i ) + \Sigma ( b_{gj} w_j +
B_{gj} W_j ) $.

When the coordinate system rotates, we have the new external power
density $\mathbb{N}' = \Sigma ( n'_i \emph{\textbf{i}}'_i + N'_i
\emph{\textbf{I}}'_i )$. Under the octonion coordinate
transformation, the scalar part of external power density is the
power density and remains unchanged by Eq.(7).
\begin{eqnarray}
n_0 = n'_0
\end{eqnarray}

In a special case, the right side is equal to zero. And then, we
obtain the conservation of energy.
\begin{eqnarray}
\Sigma \left\{ \partial (w_i + W_i )/
\partial r_i \right\} + \Sigma ( b_{gj} w_j + B_{gj} W_j ) / v_0 = 0
\end{eqnarray}

If the last term is neglected, the above is reduced to
\begin{eqnarray}
\Sigma ( \partial w_i / \partial r_i ) + \Sigma ( \partial W_i /
\partial r_i ) = 0
\end{eqnarray}
further, if the last term is equal to zero, we have
\begin{eqnarray}
\Sigma ( \partial w_i / \partial r_i ) = 0
\end{eqnarray}

The above means that the power density $n_0$ will be variable in the
case for coexistence of the gravitational field and its adjoint
field, although the $n_0$ is the scalar invariant under the octonion
transformation. And the adjoint mass, strength, and torque density
etc. have a few influence on the energy continuity equation in the
gravitational field and the adjoint field.

\subsection{Invariants in gravitational adjoint field}

\subsubsection{Conservation of adjoint mass}

In the adjoint field, a new physical quantity $\mathbb{P}_g =
\mathbb{P} \circ \emph{\textbf{I}}_0^* $ can be defined from
Eq.(16).
\begin{eqnarray}
\mathbb{P}_g = M_g V_0 + \Sigma (M_g V_j \emph{\textbf{i}}_j ) -
\left\{ \widehat{m} v_0 \emph{\textbf{I}}_0 + \Sigma (m v_j
\emph{\textbf{I}}_j ) \right\}
\end{eqnarray}

By Eq.(6), we have the linear momentum density, $\mathbb{P}'_g =
\Sigma ( P'_i \emph{\textbf{i}}'_i - p'_i \emph{\textbf{I}}'_i )$,
when the octonion coordinate system is rotated. Under the octonion
coordinate transformation, the scalar part of $\mathbb{P}_g$ remains
unchanged.
\begin{eqnarray}
M_g V_0 = M'_g V'_0
\end{eqnarray}

With Eqs.(3), (7), and the above, we obtain the conservation of
adjoint mass as follows. And $M_g$ is the scalar invariant, which is
in direct proportion to the adjoint mass density $\bar{m}$ .
\begin{eqnarray}
M_g = M'_g
\end{eqnarray}

The above means that if we emphasize the definitions of velocity and
linear momentum, the adjoint mass density will remain the same,
under the coordinate transformation in the adjoint field and
gravitational field.

\subsubsection{Continuity equation of adjoint mass }

In the octonion space, a new physical quantity $\mathbb{F}_g =
\mathbb{F} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(19).
\begin{eqnarray}
\mathbb{F}_g = F_0 + \Sigma (F_j \emph{\textbf{i}}_j ) - \Sigma (f_i
\emph{\textbf{I}}_i )
\end{eqnarray}
where, the scalar $F_0 = v_0 \Sigma ( \partial P_i / \partial r_i )
- v_0 \Sigma ( \partial p_i / \partial R_i ) + \Sigma ( b_{gj} P_j -
B_{gj} p_j ) $.

When the coordinate system rotates, we have the octonion applied
force density $\mathbb{F}'_g = \Sigma ( F'_i \emph{\textbf{i}}'_i -
f'_i \emph{\textbf{I}}'_i )$. Under the coordinate transformation,
the scalar part of $\mathbb{F}_g$ remains unchanged.
\begin{eqnarray}
F_0 = F'_0
\end{eqnarray}

When the right side is equal to zero in the above, we have the
continuity equation of adjoint mass in the case for coexistence of
the adjoint field and gravitational field.
\begin{eqnarray}
\Sigma \left\{ \partial ( P_i - p_i ) / \partial r_i \right\} +
\Sigma ( b_{gj} P_j - B_{gj} p_j ) / v_0 = 0
\end{eqnarray}

If the last term is neglected, the above is reduced to
\begin{eqnarray}
\Sigma ( \partial P_i / \partial r_i ) - \Sigma ( \partial p_i /
\partial r_i ) = 0
\end{eqnarray}
further, if the last term is equal to zero, we have
\begin{eqnarray}
\Sigma ( \partial P_i / \partial r_i ) = 0
\end{eqnarray}

The above states that the gravitational strength and adjoint
strength have an influence on continuity equation of adjoint mass,
although $\Sigma ( b_{gj} P_j -  B_{gj} p_j ) / v_0$ is usually very
tiny when field are weak. The continuity equation of adjoint mass is
the invariant under the octonion coordinate transformation.

Comparing Eq.(20) with Eq.(41), we find that the mass continuity
equation Eq.(21) and continuity equation of adjoint mass Eq.(42)
can't be effective at the same time. That means that some invariants
will not be effective simultaneously in the gravitational field and
adjoint field.

\subsubsection{Conservation of adjoint spin}

In the octonion space, a new physical quantity $\mathbb{L}_g =
\mathbb{L} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(24).
\begin{eqnarray}
\mathbb{L}_g = L_0 + \Sigma (L_j \emph{\textbf{i}}_j ) - \Sigma (l_i
\emph{\textbf{I}}_i )
\end{eqnarray}
where, $L_0 = (r_0 + k_{rx} x_0 ) P_0 - \Sigma \left\{(r_j + k_{rx}
x_j ) P_j \right\} + \Sigma \left\{(R_i + k_{rx} X_i ) p_i \right\}
$ .

When the octonion coordinate system rotates, we have the angular
momentum density $\mathbb{L}'_g = \Sigma ( L'_i \emph{\textbf{i}}'_i
- l'_i \emph{\textbf{I}}'_i )$ from Eq.(6). Under the coordinate
transformation, the scalar part of $\mathbb{L}_g$ deduces the
conservation of adjoint spin.
\begin{eqnarray}
L_0 = L'_0
\end{eqnarray}

The above means that the adjoint spin density $L_0$ is an invariant
in the case for coexistence of the gravitational field and its
adjoint field, under the octonion coordinate transformation.

\subsubsection{Conservation of adjoint energy}

In the octonion space, a new physical quantity $\mathbb{W}_g =
\mathbb{W} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(26).
\begin{eqnarray}
\mathbb{W}_g = W_0 + \Sigma (W_j \emph{\textbf{i}}_j ) - \Sigma (w_i
\emph{\textbf{I}}_i)
\end{eqnarray}
where, the scalar part $W_0 = v_0 \partial L_0 / \partial r_0 - v_0
\Sigma ( \partial L_j / \partial r_j ) + v_0 \Sigma ( \partial l_i /
\partial R_i ) - \Sigma ( b_{gj} L_j - B_{gj} l_j ) $.

When the octonion coordinate system rotates, we have the energy
density $\mathbb{W}'_g = \Sigma ( W'_i \emph{\textbf{i}}'_i - w'_i
\emph{\textbf{I}}'_i )$ from Eq.(6). Under the coordinate
transformation, the scalar part of $\mathbb{W}_g$ remains unchanged.
And then, we can obtain the conservation of adjoint energy.
\begin{eqnarray}
W_0 = W'_0
\end{eqnarray}

When the right side is equal to zero in the above, we have the
continuity equation of adjoint spin in the case for coexistence of
the adjoint field and gravitational field.
\begin{eqnarray}
&& \partial L_0 / \partial r_0 - \Sigma ( \partial L_j /
\partial r_j )
\nonumber\\
&& + \Sigma ( \partial l_i / \partial r_i ) - \Sigma ( b_{gj} L_j -
B_{gj} l_j ) / v_0 = 0
\end{eqnarray}

If the last term is neglected, the above is reduced to
\begin{eqnarray}
\partial L_0 / \partial r_0 - \Sigma ( \partial L_j / \partial r_j )
+ \Sigma ( \partial l_i / \partial r_i ) = 0
\end{eqnarray}
further, if the last term is equal to zero, we have
\begin{eqnarray}
\partial L_0 / \partial r_0 - \Sigma ( \partial L_j / \partial r_j ) = 0
\end{eqnarray}

The above means that the adjoint energy density $W_0$ is an
invariant in the case for coexistence of gravitational field and its
adjoint field, under the octonion coordinate transformation.

\begin{table}[t]
\caption{\label{tab:table1}The definitions and adjoint invariants of
physical quantities in the gravitational field with its adjoint
field in the octonion space.}
\begin{ruledtabular}
\begin{tabular}{llll}
$ definition $                           & $ invariant$       &    $conservation$                         \\
\hline
$\mathbb{R}\circ\emph{\textbf{I}}_0^*$   & $R_0 = R'_0$       &    $invariable~scalar$                    \\
$\mathbb{V}\circ\emph{\textbf{I}}_0^*$   & $V_0 = V'_0$       &    $invariable~speed~of~light-like$       \\
$\mathbb{X}\circ\emph{\textbf{I}}_0^*$   & $X_0 = X'_0$       &    $invariable~scalar$                    \\
$\mathbb{A}\circ\emph{\textbf{I}}_0^*$   & $A_0 = A'_0$       &    $invariable~adjoint~scalar~potential$  \\
$\mathbb{B}\circ\emph{\textbf{I}}_0^*$   & $B_0 = B'_0$       &    $invariable~adjoint~field~gauge$       \\
$\mathbb{P}\circ\emph{\textbf{I}}_0^*$   & $P_0 = P'_0$       &    $conservation~of~adjoint~mass$         \\
$\mathbb{F}\circ\emph{\textbf{I}}_0^*$   & $F_0 = F'_0$       &    $continuity~equation~of~adjoint~mass~$ \\
$\mathbb{L}\circ\emph{\textbf{I}}_0^*$   & $L_0 = L'_0$       &    $conservation~of~adjoint~spin$         \\
$\mathbb{W}\circ\emph{\textbf{I}}_0^*$   & $W_0 = W'_0$       &    $conservation~of~adjoint~energy$       \\
$\mathbb{N}\circ\emph{\textbf{I}}_0^*$   & $N_0 = N'_0$       &    $conservation~of~adjoint~power$        \\
\end{tabular}
\end{ruledtabular}
\end{table}

\subsubsection{Conservation of adjoint power}

In the octonion space, a new physical quantity $\mathbb{N}_g =
\mathbb{N} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(31).
\begin{eqnarray}
\mathbb{N}_g = N_0 + \Sigma (N_j \emph{\textbf{i}}_j ) - \Sigma (n_i
\emph{\textbf{I}}_i)
\end{eqnarray}
where, the scalar $N_0 = v_0 \Sigma ( \partial W_i / \partial r_i )
- v_0 \Sigma ( \partial w_i / \partial R_i ) + \Sigma ( b_{gj} W_j -
B_{gj} w_j ) $.

When the octonion coordinate system rotates, we have the adjoint
power density $\mathbb{N}'_g = \Sigma ( N'_i \emph{\textbf{i}}'_i -
n'_i \emph{\textbf{I}}'_i )$ from Eq.(6). Under the coordinate
transformation, the scalar part of $\mathbb{N}_g$ remains unchanged
by the above. And then we obtain the conservation of adjoint power
as follows.
\begin{eqnarray}
N_0 = N'_0
\end{eqnarray}

When the right side is equal to zero in the above, we have the
continuity equation of adjoint energy in the case for coexistence of
the adjoint field and gravitational field.
\begin{eqnarray}
\Sigma \left\{ \partial ( W_i - w_i ) / \partial r_i \right\} +
\Sigma ( b_{gj} W_j - B_{gj} w_j ) / v_0 = 0
\end{eqnarray}

If the last term is neglected, the above is reduced to
\begin{eqnarray}
\Sigma ( \partial W_i / \partial r_i ) - \Sigma ( \partial w_i /
\partial r_i ) = 0
\end{eqnarray}
further, if the last term is equal to zero, we have
\begin{eqnarray}
\Sigma ( \partial W_i / \partial r_i ) = 0
\end{eqnarray}

The above means the adjoint power density $N_0$ is the invariant in
the case for coexistence of the gravitational field and adjoint
field, under the octonion coordinate transformation.

\section{Electromagnetic field}

Making use of the octonion operator, the electromagnetic field
demonstrated by the octonion operator will also generate an adjoint
field. The source of adjoint field includes the adjoint charge and
adjoint electric current. Similarly, the adjoint charge and its
movement can not be observed by usual experiments. However, when the
adjoint charge is combined with the ordinary charge to become the
charged particles, their movements will be accompanied by some
mechanical or electric effects. And this kind of adjoint charge may
be considered as one kind of candidate for dark matter
\cite{zwicky}.

The electromagnetic field and its adjoint field both can be
demonstrated by the quaternions also, although they are quite
different from each other indeed.

With the invariant property of octonions, we find that the adjoint
charge, adjoint mass, velocity curl, and field strength have the
influence on some conservation laws in the electromagnetic field,
under the octonion coordinate transformation.

In some cases, the adjoint charge is combined with the ordinary
charge to become one sort of particle. Further, the ordinary mass
$m$, adjoint mass $\bar{m}$, ordinary charge $q$, and adjoint charge
$\bar{q}$ can be combined together to become another sort of
particle. Therefore we can measure their various characteristics,
and have following relation.
\begin{eqnarray}
R_i \emph{\textbf{I}}_i = r_i \emph{\textbf{i}}_i \circ
\emph{\textbf{I}}_0~;~ V_i \emph{\textbf{I}}_i = v_i
\emph{\textbf{i}}_i \circ \emph{\textbf{I}}_0~.
\nonumber
\end{eqnarray}

\subsection{Invariants in electromagnetic field}

\subsubsection{Potential and strength}

The electromagnetic field potential is
\begin{eqnarray}
\mathbb{A}_e = \Sigma (A_i \emph{\textbf{I}}_i)~.
\end{eqnarray}

The electromagnetic potential are combined with the gravitational
potential to become the field potential $\mathbb{A} = \mathbb{A}_g +
k_a \mathbb{A}_e $, with $k_a$ being the coefficient.

The field strength $\mathbb{B} = \Sigma (b_i \emph{\textbf{i}}_i) +
\Sigma (B_i \emph{\textbf{I}}_i)$ consists of the gravitational
strength $\mathbb{B}_g$ and the electromagnetic strength
$\mathbb{B}_e$ , with $k_b$ being the coefficient.
\begin{eqnarray}
\mathbb{B} = \lozenge \circ \mathbb{A} = \mathbb{B}_g + k_b
\mathbb{B}_e
\end{eqnarray}

The strength $\mathbb{B}_e = \Sigma (b_{ei} \emph{\textbf{i}}_i) +
\Sigma (B_{ei} \emph{\textbf{I}}_i)$ consists of the electromagnetic
strength $\mathbb{B}_{eg}$ and adjoint strength $\mathbb{B}_{ee}$ .
\begin{eqnarray}
\mathbb{B}_e = \lozenge \circ \mathbb{A}_e = \mathbb{B}_{eg} +
\mathbb{B}_{ee}
\end{eqnarray}
where, $\mathbb{B}_{ee} = \Sigma (b_{ei} \emph{\textbf{i}}_i)$,
$\mathbb{B}_{eg} = \Sigma (B_{ei} \emph{\textbf{I}}_i)$; $b_{ei}$
and $B_{ei}$ are all real.

In the above equation, we choose the following gauge conditions to
simplify succeeding calculation.
\begin{eqnarray}
&& \partial A_0 / \partial r_0 - \Sigma (\partial A_j /
\partial r_j) = 0 \nonumber\\
&& \partial A_0 / \partial R_0 + \Sigma (\partial A_j /
\partial R_j) = 0 \nonumber
\end{eqnarray}

The adjoint field strength $\mathbb{B}_{ee}$ in Eq.(59) includes two
parts, $\textbf{g}_e = ( g_{e01} , g_{e02} , g_{e03} ) $ and
$\textbf{b}_e = ( g_{e23} , g_{e31} , g_{e12} )$,
\begin{eqnarray}
\textbf{g}_e/v_0 = && \emph{\textbf{i}}_1 ( \partial_0 A_1 -
\partial_1 A_0 ) + \emph{\textbf{i}}_2 ( \partial_0 A_2 - \partial_2
A_0 )
\nonumber\\
&& + \emph{\textbf{i}}_3 ( \partial_0 A_3 - \partial_3 A_0 )
\\
\textbf{b}_e = && \emph{\textbf{i}}_1 ( \partial_3 A_2 -
\partial_2 A_3 ) + \emph{\textbf{i}}_2 ( \partial_1 A_3 - \partial_3
A_1 )
\nonumber\\
&& + \emph{\textbf{i}}_3 ( \partial_2 A_1 - \partial_1 A_2 )
\end{eqnarray}
simultaneously, the electromagnetic field strength $\mathbb{B}_{eg}$
involves two components, $\textbf{E}_e = ( B_{e01} , B_{e02} ,
B_{e03} ) $ and $\textbf{B}_e = ( B_{e23} , B_{e31} , B_{e12} )$ .
\begin{eqnarray}
\textbf{E}_e/v_0 = && \emph{\textbf{I}}_1 ( \partial_0 A_1 +
\partial_1 A_0 ) + \emph{\textbf{I}}_2 ( \partial_0 A_2 + \partial_2
A_0 )
\nonumber\\
&& + \emph{\textbf{I}}_3 ( \partial_0 A_3 + \partial_3 A_0 )
\\
\textbf{B}_e = && \emph{\textbf{I}}_1 ( \partial_3 A_2 -
\partial_2 A_3 ) + \emph{\textbf{I}}_2 ( \partial_1 A_3 - \partial_3
A_1 )
\nonumber\\
&& + \emph{\textbf{I}}_3 ( \partial_2 A_1 - \partial_1 A_2 )
\end{eqnarray}

The electric current density $\mathbb{S}_{eg} = q \mathbb{V}_g \circ
\emph{\textbf{I}}_0$ is the source of electromagnetic field, and its
adjoint electric current density $\mathbb{S}_{ee} = \bar{q}
\mathbb{V}_g $ is that of adjoint field. They combine together to
become the field source $\mathbb{S}_e$ .

In the octonion space, the electromagnetic source $\mathbb{S}_e$ can
be combined with gravitational source $\mathbb{S}_g$ to become the
source $\mathbb{S}$ .
\begin{eqnarray}
\mu \mathbb{S} = && - ( \mathbb{B}/v_0 + \lozenge)^* \circ
\mathbb{B}
\nonumber\\
= && \mu_{gg} \mathbb{S}_{gg} + \mu_{ge} \mathbb{S}_{ge}  -
\mathbb{B}^* \circ \mathbb{B}/v_0
\nonumber\\
&& + k_b (\mu_{ee} \mathbb{S}_{ee} + \mu_{eg} \mathbb{S}_{eg})
\end{eqnarray}
where, $k_b^2 = \mu_{gg} /\mu_{eg}$; $\mu_{gg}$, $\mu_{ge}$,
$\mu_{ee}$, and $\mu_{eg}$ are the coefficients.

The $\mathbb{B}^* \circ \mathbb{B}/(2\mu_{gg})$ is the field energy
density.
\begin{eqnarray}
\mathbb{B}^* \circ \mathbb{B}/ \mu_{gg} = \mathbb{B}_g^* \circ
\mathbb{B}_g / \mu_{gg} + \mathbb{B}_e^* \circ \mathbb{B}_e /
\mu_{eg}
\end{eqnarray}

The above means that the electromagnetic field and its adjoint field
make a contribution to the gravitational mass also in the octonion
space.

\subsubsection{Conservation of mass}

In the electromagnetic field, gravitational field and their adjoint
fields, the linear momentum density $\mathbb{P} = \mu \mathbb{S} /
\mu_{gg}$ is written as
\begin{eqnarray}
\mathbb{P} = && \widehat{m} v_0 + \Sigma (m v_j \emph{\textbf{i}}_j
) + \Sigma ( M_g V_i \emph{\textbf{i}}_i \circ \emph{\textbf{I}}_0 )
\nonumber\\
&& + \Sigma ( M_q V_i \emph{\textbf{i}}_i \circ \emph{\textbf{I}}_0
) + \Sigma ( M_e v_i \emph{\textbf{i}}_i )
\end{eqnarray}
where, $\widehat{m} = m - (\mathbb{B}^* \circ \mathbb{B} / \mu_{gg}
)/v_0^2 $ ; $M_q = q k_b \mu_{eg}/\mu_{gg}$ ; $M_e = \bar{q} k_b
\mu_{ee}/\mu_{gg}$ .

The above means that the gravitational mass density $\widehat{m}$ is
changed with all four kinds of field strengthes in the
electromagnetic field, gravitational field, and their two kinds of
adjoint fields.

From Eq.(6), we have one linear momentum density, $\mathbb{P}'
(p'_0, p'_1, p'_2, p'_3, P'_0, P'_1, P'_2, P'_3)$, when the octonion
coordinate system is rotated. And we obtain the invariant equation
from Eqs.(7) and (66).
\begin{eqnarray}
(\widehat{m} + M_e ) v_0 = (\widehat{m}' + M'_e) v'_0
\end{eqnarray}

Under Eqs.(3), (7), and (67), we find the gravitational mass density
$(\widehat{m} + M_e)$ remains unchanged.
\begin{eqnarray}
\widehat{m} + M_e = \widehat{m}' + M'_e
\end{eqnarray}

The above means that if we choose the definitions of velocity and
linear momentum, the inertial mass density $(m + M_e)$ and
gravitational mass density $(\widehat{m} + M_e)$ will keep unchanged
respectively, under the octonion coordinate transformation in Eq.(6)
in the electromagnetic field, gravitational field, and their adjoint
fields.

\subsubsection{Mass continuity equation}

In the electromagnetic field, gravitational field, and their adjoint
fields, the applied force density $\mathbb{F} = \Sigma (f_i
\emph{\textbf{i}}_i ) + \Sigma (F_i \emph{\textbf{I}}_i )$ is
defined from the linear momentum density $\mathbb{P} = \Sigma (p_i
\emph{\textbf{i}}_i ) + \Sigma (P_i \emph{\textbf{I}}_i )$ in
Eq.(66).
\begin{eqnarray}
\mathbb{F} = v_0 (\mathbb{B}/v_0 + \lozenge )^* \circ \mathbb{P}
\end{eqnarray}
where, the scalar $f_0 = v_0 \Sigma (\partial p_i / \partial r_i) +
v_0 \Sigma ( \partial P_i / \partial R_i ) + \Sigma ( b_{gj} p_j +
B_{gj} P_j + k_b b_{ej} p_j + k_b B_{ej} P_j ) $.

When the coordinate system rotates, we have the new force density
$\mathbb{F}' (f'_0, f'_1, f'_2, f'_3, F'_0, F'_1, F'_2, F'_3)$.

By Eq.(7), we have
\begin{eqnarray}
f_0 = f'_0
\end{eqnarray}

When $f'_0 = 0$ in the above, we have the conservation of mass in
the case for coexistence of the electromagnetic field, gravitational
field, and their adjoint fields.
\begin{eqnarray}
&& \Sigma \left\{ \partial (p_i + P_i )/ \partial r_i \right\}  +
\Sigma ( b_{gj} p_j + B_{gj} P_j ) / v_0
\nonumber\\
&& + \Sigma k_b ( b_{ej} p_j + B_{ej} P_j ) / v_0 = 0
\end{eqnarray}

If the $b_{gi} = B_{gi} = b_{ei} = B_{ei} = 0$, the above will be
reduced to the following equation.
\begin{eqnarray}
\Sigma ( \partial p_j / \partial r_j ) + \Sigma ( \partial P_j /
\partial r_j ) = 0
\end{eqnarray}
further, if the last term can be neglected, we have
\begin{eqnarray}
\Sigma (\partial p_i / \partial r_i) = 0
\end{eqnarray}

In case of we choose the definitions of applied force and velocity
in the electromagnetic field, gravitational field, and their adjoint
fields, the conservation of mass will be the invariant under the
octonion transformation in Eq.(6). The above states also that four
kinds of field strengthes, adjoint mass, and adjoint charge have a
tiny influence on conservation of mass, although the impact is
usually very small when the fields are weak.

\subsubsection{Conservation of spin}

The angular momentum density $\mathbb{L} = \Sigma (l_i
\emph{\textbf{i}}_i ) + \Sigma (L_i \emph{\textbf{I}}_i )$ is
defined from the radius vector $\mathbb{R}$, physical quantity
$\mathbb{X}$, and linear momentum density $\mathbb{P}$ in the
octonion space.
\begin{eqnarray}
\mathbb{L} = (\mathbb{R} + k_{rx} \mathbb{X}) \circ \mathbb{P}
\end{eqnarray}
where, $l_0$ is considered as the spin angular momentum density in
the gravitational field and adjoint field; $l_0 = (r_0 + k_{rx} x_0
) p_0 - \Sigma \left\{ (r_j + k_{rx} x_j ) p_j \right\} - \Sigma
\left\{ (R_i + k_{rx} X_i ) P_i \right\}$; $k_{rx}$ is the
coefficient.

When the octonion coordinate system rotates, we have the new angular
momentum density $\mathbb{L}' = \Sigma ( l'_i \emph{\textbf{i}}'_i +
L'_i \emph{\textbf{I}}'_i )$. Under the octonion coordinate
transformation, the spin density remains unchanged from Eq.(7).
\begin{eqnarray}
l_0 = l'_0
\end{eqnarray}

The above means that the space, time, adjoint fields,
electromagnetic field, and gravitational field have small influence
on orbital angular momentum and spin angular momentum. The spin
angular momentum density $l_0$ will change with time, although $l_0$
is an invariant under the octonion transformation.

\begin{table}[b]
\caption{\label{tab:table1}The definitions and the mechanics
invariants of electromagnetic field and gravitational field with
their adjoint fields in the octonion space.}
\begin{ruledtabular}
\begin{tabular}{lll}
$definition$    &    $invariant $    &    $ meaning $                            \\
\hline
$\mathbb{R}$    &    $r_0 = r'_0 $   &    $Galilean~invariant$                   \\
$\mathbb{V}$    &    $v_0 = v'_0$    &    $invariable~speed~of~light$            \\
$\mathbb{A}$    &    $a_0 = a'_0$    &    $invariable~scalar~potential$          \\
$\mathbb{B}$    &    $b_0 = b'_0$    &    $invariable~gauge$                     \\
$\mathbb{P}$    &    $p_0 = p'_0$    &    $invariable~mass~density$              \\
$\mathbb{F}$    &    $f_0 = f'_0$    &    $conservation~of~mass$                 \\
$\mathbb{L}$    &    $l_0 = l'_0$    &    $invariable~spin~density$              \\
$\mathbb{W}$    &    $w_0 = w'_0$    &    $invariable~energy~density$            \\
$\mathbb{N}$    &    $n_0 = n'_0$    &    $conservation~of~energy$               \\
\end{tabular}
\end{ruledtabular}
\end{table}

\subsubsection{Conservation of energy}

The total energy density $\mathbb{W} = \Sigma (w_i
\emph{\textbf{i}}_i ) + \Sigma (W_i \emph{\textbf{I}}_i )$ is
defined from the angular momentum density $\mathbb{L}$.
\begin{eqnarray}
\mathbb{W} = v_0 ( \mathbb{B}/v_0 + \lozenge) \circ \mathbb{L}
\end{eqnarray}
where, the scalar part $w_0 = v_0 \partial l_0 / \partial r_0 - v_0
\Sigma (\partial l_j / \partial r_j) - v_0 \Sigma ( \partial L_i /
\partial R_i ) - \Sigma ( b_{gj} l_j + B_{gj} L_j + k_b b_{ej} l_j +
k_b B_{ej} L_j ) $.

When the coordinate system rotates, we have the new energy density
$\mathbb{W}' = \Sigma ( w'_i \emph{\textbf{i}}'_i + W'_i
\emph{\textbf{I}}'_i )$. Under the octonion transformation, the
scalar part of total energy density is the energy density and
remains unchanged by Eq.(7).
\begin{eqnarray}
w_0 = w'_0
\end{eqnarray}

In some special cases, the right side is equal to zero. We obtain
the conservation of spin angular momentum.
\begin{eqnarray}
&& - \Sigma ( b_{gj} l_j + B_{gj} L_j + k_b b_{ej} l_j + k_b B_{ej}
L_j ) / v_0
\nonumber\\
&& + \partial l_0 / \partial r_0 - \Sigma (\partial l_j /
\partial r_j) - \Sigma ( \partial L_i /
\partial r_i ) = 0
\end{eqnarray}

If the first term is zero, the above is reduced to
\begin{eqnarray}
\partial l_0 / \partial r_0 - \Sigma (\partial l_j /
\partial r_j) - \Sigma ( \partial L_i /
\partial r_i ) = 0
\end{eqnarray}
further, if last term is zero, we have
\begin{eqnarray}
\partial l_0 / \partial r_0 - \Sigma (\partial l_j /
\partial r_j) = 0
\end{eqnarray}

The above means the energy density $w_0$ is variable with time in
the case for coexistence of the electromagnetic field, gravitational
field, and their adjoint fields, because the adjoint mass, adjoint
charge, velocity, and strength have the influence on the angular
momentum density. While the scalar $w_0$ is the invariant under the
octonion transformation from Eq.(7).

\subsubsection{Conservation of power}

In the electromagnetic field and gravitational field with their
adjoint fields, the external power density $\mathbb{N}= \Sigma (n_i
\emph{\textbf{i}}_i ) + \Sigma (N_i \emph{\textbf{I}}_i )$ can be
defined from the total energy density $\mathbb{W}$ .
\begin{eqnarray}
\mathbb{N} = v_0 ( \mathbb{B}/v_0 + \lozenge)^* \circ \mathbb{W}
\end{eqnarray}
where, the scalar $n_0 = v_0 \Sigma (\partial w_i / \partial r_i) +
v_0 \Sigma ( \partial W_i / \partial R_i ) + \Sigma ( b_{gj} w_j +
B_{gj} W_j + k_b b_{ej} w_j + k_b B_{ej} W_j ) $.

When the coordinate system rotates, we have the new external power
density $\mathbb{N}' = \Sigma ( n'_i \emph{\textbf{i}}'_i + N'_i
\emph{\textbf{I}}'_i )$. Under the octonion coordinate
transformation, the scalar part of external power density is the
power density and remains unchanged by Eq.(7).
\begin{eqnarray}
n_0 = n'_0
\end{eqnarray}

In a special case, the right side is equal to zero. And then, we
obtain the conservation of energy.
\begin{eqnarray}
&& \Sigma \left\{ \partial (w_i + W_i )/
\partial r_i \right\} + \Sigma ( b_{gj} w_j + B_{gj} W_j ) / v_0
\nonumber\\
&& + \Sigma k_b ( b_{ej} w_j + B_{ej} W_j ) / v_0 = 0
\end{eqnarray}

If last two term are zeros, the above is reduced to
\begin{eqnarray}
\Sigma ( \partial w_i / \partial r_i ) + \Sigma ( \partial W_i /
\partial r_i ) = 0
\end{eqnarray}
further, if last term is equal to zero, we have
\begin{eqnarray}
\Sigma ( \partial w_i / \partial r_i ) = 0
\end{eqnarray}

The above means that the power density $n_0$ will be variable in the
case for coexistence of the electromagnetic field, gravitational
field, and their adjoint fields, although the $n_0$ is the invariant
under the octonion transformation. And the adjoint mass, adjoint
charge, field strength, and torque density etc. have a few influence
on the energy continuity equation in the octonion space.

\subsection{Invariants in electromagnetic adjoint field}

\subsubsection{Conservation of charge}

In the adjoint field, a new physical quantity $\mathbb{P}_q =
\mathbb{P} \circ \emph{\textbf{I}}_0^* $ can be defined from
Eq.(66).
\begin{eqnarray}
\mathbb{P}_q = P_0 + \Sigma (P_j \emph{\textbf{i}}_j ) - \left\{ p_0
\emph{\textbf{I}}_0 + \Sigma (p_j \emph{\textbf{I}}_j ) \right\}
\end{eqnarray}
where, $P_0 = (M_g + M_q ) V_i$ .

By Eq.(6), we have the linear momentum density, $\mathbb{P}'_q =
\Sigma ( P'_i \emph{\textbf{i}}'_i - p'_i \emph{\textbf{I}}'_i )$,
when the octonion coordinate system is rotated. Under the octonion
coordinate transformation, the scalar part of $\mathbb{P}_q$ remains
unchanged.
\begin{eqnarray}
(M_g + M_q ) V_0 = (M'_g + M'_q ) V'_0
\end{eqnarray}

By means of Eqs.(3), (7), and the above, we obtain the conservation
of charge as follows. And $(M_g + M_q )$ is a scalar invariant,
which is a function of the adjoint mass density $\bar{m}$ and
ordinary charge $q$ .
\begin{eqnarray}
M_g + M_q = M'_g + M'_q
\end{eqnarray}

The above means if we emphasize definitions of velocity and linear
momentum, the charge density $(M_g + M_q )$ will remain the same,
under the coordinate transformation in the electromagnetic field,
gravitational field, and their adjoint fields.

\subsubsection{Charge continuity equation}

In the octonion space, a new physical quantity $\mathbb{F}_q =
\mathbb{F} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(69).
\begin{eqnarray}
\mathbb{F}_q = F_0 + \Sigma (F_j \emph{\textbf{i}}_j ) - \Sigma (f_i
\emph{\textbf{I}}_i )
\end{eqnarray}
where, the scalar $F_0 = v_0 \Sigma ( \partial P_i / \partial r_i )
- v_0 \Sigma ( \partial p_i / \partial R_i ) + \Sigma ( b_{gj} P_j -
B_{gj} p_j + k_b b_{ej} P_j - k_b B_{ej} p_j ) $.

When the octonion coordinate system rotates, we have the applied
force density $\mathbb{F}'_q = \Sigma ( F'_i \emph{\textbf{i}}'_i -
f'_i \emph{\textbf{I}}'_i )$. Under the coordinate transformation,
the scalar part of $\mathbb{F}_q$ remains unchanged.
\begin{eqnarray}
F_0 = F'_0
\end{eqnarray}

When the right side is equal to zero, we have the charge continuity
equation in the case for coexistence of the gravitational field,
electromagnetic field, and adjoint fields.
\begin{eqnarray}
&& \Sigma \left\{ \partial ( P_i - p_i ) / \partial r_i \right\} +
\Sigma ( b_{gj} P_j - B_{gj} p_j ) / v_0
\nonumber\\
&& + \Sigma k_b ( b_{ej} P_j - B_{ej} p_j ) = 0
\end{eqnarray}

If last two terms are zeros, the above is reduced to
\begin{eqnarray}
\Sigma ( \partial P_i / \partial r_i ) - \Sigma ( \partial p_i /
\partial r_i ) = 0
\end{eqnarray}
further, if the last term is equal to zero, we have
\begin{eqnarray}
\Sigma ( \partial P_i / \partial r_i ) = 0
\end{eqnarray}

The above states that the electromagnetic strength, gravitational
strength, and adjoint field strengthes have an effect on the charge
continuity equation, although the impact is usually very tiny when
fields are weak. And the charge continuity equation is an invariant
under the octonion coordinate transformation.

\subsubsection{Conservation of spin magnetic moment}

In the octonion space, a new physical quantity $\mathbb{L}_q =
\mathbb{L} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(74).
\begin{eqnarray}
\mathbb{L}_q = L_0 + \Sigma (L_j \emph{\textbf{i}}_j ) - \Sigma (l_i
\emph{\textbf{I}}_i )
\end{eqnarray}
where, $L_0 = (r_0 + k_{rx} x_0 ) P_0 - \Sigma \left\{(r_j + k_{rx}
x_j ) P_j \right\} + \Sigma \left\{(R_i + k_{rx} X_i ) p_i \right\}
$ .

When the octonion coordinate system rotates, we have the angular
momentum density $\mathbb{L}'_q = \Sigma ( L'_i \emph{\textbf{i}}'_i
- l'_i \emph{\textbf{I}}'_i )$ from Eq.(6). Under the octonion
coordinate transformation, the scalar part of $\mathbb{L}_q$ deduces
the conservation of spin magnetic moment.
\begin{eqnarray}
L_0 = L'_0
\end{eqnarray}

The above states the spin magnetic moment density $L_0$ is an
invariant in the case for coexistence of the electromagnetic field,
gravitational field and their adjoint fields, under the octonion
coordinate transformation.

\subsubsection{Conservation of energy-like}

In the octonion space, a new physical quantity $\mathbb{W}_q =
\mathbb{W} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(76).
\begin{eqnarray}
\mathbb{W}_q = W_0 + \Sigma (W_j \emph{\textbf{i}}_j ) - \Sigma (w_i
\emph{\textbf{I}}_i)
\end{eqnarray}
where, the scalar part $W_0 = v_0 \partial L_0 / \partial r_0 - v_0
\Sigma ( \partial L_j / \partial r_j ) + v_0 \Sigma (
\partial l_i / \partial R_i ) - \Sigma ( b_{gj} L_j - B_{gj} l_j +
k_b b_{ej} L_j - k_b B_{ej} l_j ) $.

When the octonion coordinate system rotates, we have the energy
density $\mathbb{W}'_q = \Sigma ( W'_i \emph{\textbf{i}}'_i - w'_i
\emph{\textbf{I}}'_i )$ from Eq.(6). Under the coordinate
transformation, the scalar part of $\mathbb{W}_q$ remains unchanged.
Therefore, we can obtain the conservation of energy-like.
\begin{eqnarray}
W_0 = W'_0
\end{eqnarray}

When the right side is equal to zero in the above, we have the
continuity equation of spin magnetic moment in the case for
coexistence of the electromagnetic field, gravitational field and
their adjoint fields.
\begin{eqnarray}
&& - \Sigma ( b_{gj} L_j - B_{gj} l_j + k_b b_{ej} L_j - k_b B_{ej}
l_j ) / v_0
\nonumber\\
&& + \partial L_0 / \partial r_0 - \Sigma ( \partial L_j /
\partial r_j ) + \Sigma ( \partial l_i / \partial r_i ) = 0
\end{eqnarray}

If the first term is zero, the above is reduced to
\begin{eqnarray}
\partial L_0 / \partial r_0 - \Sigma ( \partial L_j /
\partial r_j ) + \Sigma ( \partial l_i / \partial r_i ) = 0
\end{eqnarray}
further, if the last term is equal to zero, we have
\begin{eqnarray}
\partial L_0 / \partial r_0 - \Sigma ( \partial L_j /
\partial r_j ) = 0
\end{eqnarray}

The above means that the energy-like density $W_0$ is an invariant
in the case for coexistence of the electromagnetic field,
gravitational field and their adjoint fields, under the octonion
coordinate transformation.

\begin{table}[t]
\caption{\label{tab:table1}The definitions and their adjoint
invariants of the physical quantities in the electromagnetic field,
gravitational field with their adjoint fields.}
\begin{ruledtabular}
\begin{tabular}{llll}
$ definition $                           & $ invariant$       &    $conservation$                      \\
\hline
$\mathbb{R}\circ\emph{\textbf{I}}_0^*$   & $R_0 = R'_0$       &    $invariable~scalar$                 \\
$\mathbb{V}\circ\emph{\textbf{I}}_0^*$   & $V_0 = V'_0$       &    $invariable~speed~of~light-like$    \\
$\mathbb{X}\circ\emph{\textbf{I}}_0^*$   & $X_0 = X'_0$       &    $invariable~scalar$                 \\
$\mathbb{A}\circ\emph{\textbf{I}}_0^*$   & $A_0 = A'_0$       &    $electric~scalar~potential$         \\
$\mathbb{B}\circ\emph{\textbf{I}}_0^*$   & $B_0 = B'_0$       &    $electromagnetic~gauge$             \\
$\mathbb{P}\circ\emph{\textbf{I}}_0^*$   & $P_0 = P'_0$       &    $conservation~of~charge$            \\
$\mathbb{F}\circ\emph{\textbf{I}}_0^*$   & $F_0 = F'_0$       &    $charge~continuity~equation$        \\
$\mathbb{L}\circ\emph{\textbf{I}}_0^*$   & $L_0 = L'_0$       &    $spin~magnetic~moment$              \\
$\mathbb{W}\circ\emph{\textbf{I}}_0^*$   & $W_0 = W'_0$       &    $conservation~of~energy-like$       \\
$\mathbb{N}\circ\emph{\textbf{I}}_0^*$   & $N_0 = N'_0$       &    $conservation~of~power-like$        \\
\end{tabular}
\end{ruledtabular}
\end{table}

\subsubsection{Conservation of power-like}

In the octonion space, a new physical quantity $\mathbb{N}_q =
\mathbb{N} \circ \emph{\textbf{I}}_0^*$ can be defined from Eq.(81).
\begin{eqnarray}
\mathbb{N}_q = N_0 + \Sigma (N_j \emph{\textbf{i}}_j ) - \Sigma (n_i
\emph{\textbf{I}}_i)
\end{eqnarray}
where, the scalar $N_0 = v_0 \Sigma ( \partial W_i / \partial r_i )
- v_0 \Sigma ( \partial w_i / \partial R_i ) + \Sigma ( b_{gj} W_j -
B_{gj} w_j + k_b b_{ej} W_j - k_b B_{ej} w_j ) $.

When the octonion coordinate system rotates, we have the power-like
density $\mathbb{N}'_q = \Sigma ( N'_i \emph{\textbf{i}}'_i - n'_i
\emph{\textbf{I}}'_i )$ from Eq.(6). Under the coordinate
transformation, the scalar part of $\mathbb{N}_q$ remains unchanged
by the above. And then we obtain the conservation of power-like as
follows.
\begin{eqnarray}
N_0 = N'_0
\end{eqnarray}

When the right side is equal to zero in the above, we have the
continuity equation of energy-like in the case for coexistence of
the electromagnetic field, gravitational field and their adjoint
fields.
\begin{eqnarray}
&& \Sigma \left\{ \partial ( W_i - w_i ) / \partial r_i \right\} +
\Sigma ( b_{gj} W_j - B_{gj} w_j ) / v_0
\nonumber\\
&& + \Sigma k_b ( b_{ej} W_j - B_{ej} w_j ) / v_0 = 0
\end{eqnarray}

If last two terms are zeros, the above is reduced to
\begin{eqnarray}
\Sigma ( \partial W_i / \partial r_i ) - \Sigma ( \partial w_i /
\partial r_i ) = 0
\end{eqnarray}
further, if the last term is equal to zero, we have
\begin{eqnarray}
\Sigma ( \partial W_i / \partial r_i ) = 0
\end{eqnarray}

The above means that the power-like density $N_0$ is one scalar
invariant in the case for coexistence of the electromagnetic field,
gravitational field and their adjoint fields, under the octonion
coordinate transformation.

\section{CONCLUSIONS}

In the octonion space, the gravitational field described by the
octonion operator will generate one adjoint field. Similarly, the
electromagnetic field will be accompanied by its adjoint field.
These two sorts of adjoint fields will impact the scalar invariants
and conservation laws in the electromagnetic field and gravitational
field.

In the gravitational field with its gravitational adjoint field, the
gravitational mass density is changed with the gravitational
strength and adjoint field strength. And the mass continuity
equation will be changed with the field strength, velocity, and
adjoint mass. From the definitions of the angular momentum and
velocity, the spin density, energy density, and power density will
be variable for the influence of the adjoint field potential and
adjoint field strength. While the spin continuity equation and
energy continuity equation will be changed with the impact of the
velocity and adjoint field strength etc.

The gravitational mass density will be variable in the case for
coexistence of the gravitational field and electromagnetic field
with their adjoint fields. The gravitational mass density is changed
with the gravitational strength, electromagnetic strength,
gravitational adjoint field, and electromagnetic adjoint field. And
the mass continuity equation will be changed with the
electromagnetic field strength, velocity, and adjoint charge. The
spin density, energy density, and power density all will be variable
for the influence of the electromagnetic adjoint field, adjoint
field strength, and adjoint charge. Meanwhile the spin continuity
equation and energy continuity equation will be changed with the
impact of the adjoint charge and electromagnetic adjoint field
strength etc.

In the gravitational field and electromagnetic field with their
adjoint fields, there exist some electric invariants, which are
associated with ordinary charge and adjoint mass. These electric
invariants will be variable for the influence of the field potential
and field strength. And some conservation laws and scalar invariants
can not be effective simultaneously.

It should be noted that the study for some scalar invariants of
electromagnetic and gravitational adjoint fields examined only one
simple case with very weak field strength and low velocity in the
gravitational field and electromagnetic field with their adjoint
fields. Despite its preliminary character, this study can clearly
indicate the field strength and adjoint fields of the gravitational
field and electromagnetic field have the limited influence on the
scalar invariants. For the future studies, the related investigation
will concentrate on only the predictions of scalar invariants in the
strong adjoint field strength with high velocity in gravitational
field and electromagnetic field with their adjoint fields.

\begin{acknowledgments}
This project was supported partially by the National Natural Science
Foundation of China under grant number 60677039, Science \&
Technology Department of Fujian Province of China under grant number
2005HZ1020 and 2006H0092, and Xiamen Science \& Technology Bureau
of China under grant number 3502Z20055011.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
The effect of dosage on the efficiency o...
The effect of dosage on the efficiency of LLLT in new bone formation at the expanded suture in rats
ALTAN A. B. , Bicakci A. A. , Avunduk M. C. , Esen H.
LASERS IN MEDICAL SCIENCE, cilt.30, ss.255-262, 2015 (SCI İndekslerine Giren Dergi)
Dergi Adı: LASERS IN MEDICAL SCIENCE
The aim of this study was to investigate the effect that dosage has on the efficiency of low-level laser therapy (LLLT) in bone formation in a rat study model. Twenty-eight rats were divided into four groups as only expansion (OE), expansion + low dose (0.15 J) (LD), expansion + medium dose (0.65 J) (MD), and expansion + high dose (198 J) (HD) laser therapy groups. The midpalatal suture was expanded during 5 days. Afterwards, irradiations were started and performed with an 820 nm, continuous wave, Ga-Al-As diode laser (Doris, CTL-1106MX, Warsaw, Poland). At the end of experiment, the premaxillae of the animals were dissected. The sections were transferred into PC environment and analyzed by using Image Analysis program. Number of osteoblasts, osteoclasts, fibroblasts, vessels, transforming growth factor beta (TGF-beta) expression, and new bone formation were evaluated with this program. Amount of expansion did not show any difference among the groups. All parameters except the number of osteoclasts were increased in all lased groups while that parameter was significantly decreased. Vessels, TGF-beta expression, and new bone formation were mostly increased in LD group followed by HD group. Among the lased groups, a significant difference was observed only for the amount of new bone formation, which was between the LD and the MD groups. On the other hand, the difference in this parameter was insignificant between OE and MD groups. Low-level laser therapy with both 5 and 6,300 J/cm(2) doses was found to be significantly effective, while the 20 J/cm(2) dose did not show a significant effect in increasing new bone formation. This finding reveals that the efficiency of the therapy is affected by the dosage.

redpajama_set_name: RedPajamaCommonCrawl


Script is desgined to combine the following tools into one interface.
The initial purpose was to create gears/cogs by modeling one tooth at a time. This allows for a more efficient uv texture map. The modeler can build one tooth of the gear, unwrap it then easily bend, duplicate and combine the teeth into on object while maintaining the efficient map.
In order for the script to work properly an object must be selected prior to launch. It's original intent is that this object be a tooth or piece of a gear that has been modeled and aligned to a particular axis in the scene so that it can be duplicated and rotated around an axis.


WOW! I thought I would get a good overview of the Bible, but didn't expect more. I was wrong! Each day the Lord revealed things I'd never noticed (or at least never understood) previously! Reading the Bible this way showed me context like I never imagined. This has been such a powerful experience for me! It has deepened my relationship with God! I am so thrilled that I made this commitment and that the Lord gave me the grace to see it through! I would HIGHLY recommend this to anyone (and I do!). Kelly supported me in this daily. I really enjoyed discussing things that caught my attention with him. I think it has deepened our communication. We did this as our church's women's summer study in 2010… and doing it with these women has been wonderful! Being able to discuss things we didn't understand or things that were significant to us was great! Doing it as a group also helped encourage us and helped us have the stamina to make it through.
This was an unexpected blessing! Thank you Lord! I was just planning to do this 90 day Bible reading with the ladies of our church and God just drew me and created a hunger to read His Word and share time with Him! I was compelled to stay in the Word and in so doing gained a much better vision of our great God and His awesome plan to redeem His creation. Thank you Lord!
I had read the Bible through a few times before but on the "through the Bible in 1 year schedule" I really enjoyed reading the Bible through in 90 days. At first it was hard to find a time (45 min-1hr) a day to do it but once I found a time that would work for me I stuck with it and made it a priority every day. It was part of my day and the couple of times that I didn't read my day felt incomplete. The hardest parts for me to read were Leviticus-Deut. and then the books in the Old Testament that were prophecy-it was hard to keep straight if what the going to happen was in the near future or far future! I enjoyed Genesis, Esther, Ruth and Hebrews the best. Reading the Bible in 90 days helped me to tie the stories, events and people together-to see the whole picture.
I am DONE ! ! Happy to have done it – kinda sad, also, because I want to read more. Hard to believe I did this in 90 days! Thank you for the opportunity! More later…..
How could anyone read God's word for 90 days straight, complete the entire bible and not be changed? This has been a great experience and soooo worthwhile. I really connected the Old Testament to the New Testament in a whole new way-Putting the events and people in a whole new understanding.
I feel energized to seek God's wisdom and look at my life and the world through the words of the bible.
Reading the bible in 90 days has given me a new and improved joy in God and the hope that he promises. Thank you Jesus. Do it! You will be blessed!
I am so thankful that I followed through with the nudge to read the Bible in 90 days. I didn't think I could do it but God is so faithful in helping. If you think God could not love you for the person you think you are and for the things you have done, reading threw the bible 90 days has helped me see even more how loving and merciful He is and it's still beyond my human understanding and I am so thankful to Him for that. God is good!
I finished my reading yesterday morning – I got it done in 90 days!!! I've already started back in Genesis 1:1 again. I intend on going back through again at 6 pages a day and finishing in 6 months. Now that the discipline has been developed I know I can do it and am so encouraged! Thanks so much, Suzanne. I' tried many times before and never managed to stick with it. I've been a committed Christian for over 20 years and always felt guilty that I could never get the entire Bible read. This has been a major encouragement and hurdle for my spiritual life and walk with the Lord.


text:
Santa Clara's New Council Districts All in a Day's Work for Registrar of Voters
Carolyn Schuk Posted on POSTED 05:00 PM, August 8, 2018
This November, the Santa Clara County Registrar of Voters will run 13 congressional elections, 12 state elections, 17 municipal elections, 67 school community college board elections and 20 special district elections. That's hundreds of different ballot permutations. Multiplied by five different languages, that's more than one thousand unique ballots and voting guides.
It's all in a day's work for Santa Clara County Registrar of Voters (ROV) Shannon Bushey (pronounced boo-shay) and her expert team.
Incorporating Santa Clara's new City Council districts is nothing out of the ordinary for Bushey and her team. "We have made new districts before," she said. While allowing that the schedule was short, "It was a condensed time frame, but this isn't new for us. We're used to working six, seven days a week for months at a time."
"We regularly get notices of new properties," she continued. "Entering and confirming district information — that happens regularly."
The ROV will be doing the same thing on a huge scale after the 2020 census data is compiled. "It's the same process," said Bushey, "connecting addresses to new congressional, state assembly and senate districts."
The City met a very tight deadline for providing district maps and parcel and address information, and Bushey's office is now at work. "We delivered the maps to the City on Saturday [July 28] and the City approved them the same day and returned them Sunday [July 29]," Bushey said. "I was proud that our first submission of new boundary maps were approved by the City."
After the geographic information system (GIS) data is mapped, every residential address and parcel number is connected with a voting precinct. Then individual street segments are assigned to districts and the ROV team identifies any voting precincts that need to be changed.
Finally the information goes into the voter database — the Election Information Management System — where the precise details of what will be on every individual voter's ballot and their preferences, such as permanent vote-by-mail, are stored. It's this system that will generate all of the different ballots and election booklets.
"Every step of the process is checked and double-checked for accuracy," said Bushey.
Checking and rechecking is part of the ROV's routine for getting ready for the November election. Before elections the office verifies the logic and accuracy on ballot counting machines.
After the election there are numerous state-mandated audits — called the 30-day Canvass of the Vote — including reconciling election materials returned by poll workers, validating voter signatures, reviewing spoiled and provisional ballots and making a manual count of 1 percent of the precincts.
The ROV brings on hundreds of temporary employees at election time, thousands of poll workers, as well as hundreds of volunteers for election night — which officially begins at 5 a.m. Tuesday and ends Wednesday night for ROV staff.
Bushey wants people to know that the ROV is hiring and accepting volunteer applications right now.
"Poll workers do a tremendous service for their community and for democracy," she said. "There is a sense of accomplishment that comes from providing such a vital function in the election process."
If you're interested in being a poll worker, call 408-299-POLL. Anyone interested in being an election night volunteer should call 408-918-9169. For more information, visit www.sccgov.org/sites/rov.
More : Bay Area News, elections, Mission City, Official Santa Clara News, registrar of voters, Santa Clara, Santa Clara news, Santa Clara WEEKLY, Silicon Valley News, Silicon Valley Voice
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Civil Grand Jury Says VTA Board Needs New Leadership: City Council Sets Sights on Ad Hoc Committee to Study Solutions
Author David AlexanderPosted on August 21, 2019
Recommendations in a Santa Clara County Civil Grand Jury report calling for major overhauls to the Valley Transit Authority (VTA) Board will require "further...
A Budget Tale of Three Bay Area Cities
Author Carolyn SchukPosted on August 17, 2011
We know how severe our operating budget problems have been in Santa Clara. But how are neighboring cities faring? Using Sunnyvale and Palo Alto...
County Cannot Reopen Personal Care Services, State Denies Reopening Plans
Author Alissa SorotenPosted on July 6, 2020 July 6, 2020
Last week, Santa Clara County asked the State to review their request for a county variance that would allow for a new health order....


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When we walk alongside other believers, we become part of something bigger than ourselves - we belong to a people.


For most of the outfits of fashion week, I first uploaded the pics onto social media and then slowly started updating them here except for this one. This one is brand new and actually one of my favourites. I like it because I think I look really different to my usual self.


For the past decade, the Federal Reserve has maintained historically low interest rates. A great deal of the economic growth that the United States has experienced can be attributed to this. The phenomenon of the "boom and bust" cycle is nothing new to the US, with an abundance of alternating phases of economic growth and decline. Historically, "booms" have come from geo-political events like World War II, or domestic policy enactments such as the Employment Act of 1946 under the Truman Administration or the Stimulus Spending Bill under the Kennedy Administration. All of these examples helped to propel the United States away from times of sluggish growth. "Busts" have often resulted from similar but converse events. Industrial growth during World War II dwindled following post-war demobilization, and wage-price controls such as those adopted under the Nixon Administration put a damper on improving employment rates. Above all else however, busts can be attributed to the Federal Reserve raising interest rates. Following the 2008 financial crisis, the interest rate cycle was halted and the American Recovery and Reinvestment Act, instituted by the Obama Administration, has since allowed interest rates to hover around zero percent. After close to ten years of economic expansion and growth, and with the national unemployment at 4.1%, inflationary rhetoric is back to being front and center on Capitol Hill. This partially explains the recent volatility in the stock market. Much of the anxiety revolves around household consumption and the rise in prices of goods and services, apart from food and gasoline. As it becomes evident that the prolonged period of exceedingly low inflation could be coming to an end, the role of the Federal Reserve becomes once again important for a restoration of confidence in the economy. With imminent interest rate hikes on the horizon, the looming threat of inflation is set to impact not only the success of President Trump's Stimulus package, but more importantly the trajectory of the economy as a whole.
Moral impairments and subsequent impeachment aside, Bill Clinton's achievement as the first Democratic President to win re-election since Franklin D. Roosevelt must be acknowledged. Much of his success and popularity was largely due the prolonged period of economic growth throughout his time in office. The focal points of Clinton's economic policies included deficit reduction, tax-hikes, and welfare reform. He famously quipped that "[the government will] give you opportunity, but you have to take responsibility", signaling his position on the welfare system that yielded waves of inefficiency. This was the beginning of what would arguably become his greatest achievement in office. On the aggregate, the Clinton Administration created over 21 million jobs, brought unemployment down to 4.0%, transformed the budget deficit into a surplus, and lowered the poverty rate. Although President Clinton's time in office will be forever associated with an aura of despondency, the economic prosperity that was enjoyed across the country is testament to his economic efforts.
George W. Bush's time in office was preceded by the technology bubble, which famously wreaked havoc on the equity markets when venture capital-funded internet-based companies collapsed with little notice. The economy and a geo-political situation that President Bush inherited would be the driving factors that impacted the country's economic growth prospects during his administration. Unlike his predecessors, President Bush dealt with two economic recessions, the latter of which leaving a more substantial impact than the Great Depression. While the recession in 2001 was caused by a rise in unemployment, the administration's efforts to successfully combat it was heavily impaired by the 9/11 Terrorist Attacks. The 2008 Financial Crisis was a bi-product of both the Bankruptcy Prevention Act of 2005 and the Subprime Mortgage Crisis. Much of the damage came from a period of excessive regulatory flexibility that the Bush Administration introduced, however, the 9/11 Terrorist Attacks also played a significant role in exacerbating the economic peril. The evolution of foreign policy under President Bush, and the subsequent $850 Billion that was spent to manage and handle the resulting conflicts abroad significantly contributed to the aggregate increase to the national debt.
President Obama's honeymoon phase didn't last long, given his inheritance of the biggest Financial Crisis in United States History. To his credit, President Obama made swift and sweeping policy enactments. Although the direction that these policy implementations would take the economy was considered a bit of a leap of faith, it eventually resulted in a positive outcome. The American Recovery and Reinvestment Act was an economic stimulus bill that reinvested close to $800 billion back in to the economy. As GDP growth became positive after multiple contractionary quarters for the first time since The Great Depression, businesses focused on adjusting to new production and supply levels to meet rising demand for consumer goods and services. The Obama Administration was also responsible for a hefty $850 Billion tax cut which added to President Bush's stimulus package, increased unemployment benefits, and gave corporations tax cuts and credits for infrastructure projects and advancements in research. The appointment of Janet Yellen ushered in, and held steady, the lowest interest rates that the United States had seen in 200 years. While President Obama is extensively criticized for his sizeable additions to the national debt, his decisions were necessary as a means to bring the economy out of immediate turmoil, and were responsible for almost a decade of robust growth.
The Federal Reserve has kept interest rates at historically low levels over the past decade as a way to supplement low inflation. However, newly appointed Chair of the Fed Jerome Powell, is faced with a new predicament. The last several years have increased concerns about the likelihood of looming accelerated inflation, and the role of the Federal Reserve will be to enact measures that tighten monetary policy. While an interest rate hike at the March 20-21 Policy meeting seems imminent as a result of wide-ranging increases in household costs, the question of whether the Fed should allow inflation to rise above 2% (considering the extended period of time where inflation was well below 2%) is resulting in a heated discussion on Capitol Hill.
Much of the rhetoric coming out of the White House regarding the budget proposal, stimulus package, and overall vision for the economy is largely revolving around the notion that the economy must see growth before inflation, and interest rates, result in disruption. The Trump Budget Proposal indicates an opportunity to cut the federal budget deficit by close to $3 Trillion over the next ten years, contingent on several speculative assumptions. Many of the provisions associated with tax reform itself indicate that the needle on the budget deficit could be pushed even further. While in theory the Republican economic agenda, which is positioned around driving long term economic growth through tax cuts for business and infrastructure-spending, might have an opportunity to tackle national debt, higher interest rates could be counter-productive to all of President Trump's fiscal stimulus.
The interest rate cycle, inflationary trends, and the financial industry in general are far from an exact science. Projections involve the use of several qualitative trends that are modeled based on socio-economic and geo-political concerns. This results in cognitive judgement biases, irrespective of political affiliation. At a time where the United States is once again confronted with volatility amid multiple foreign policy concerns, domestic capital and consumer market trends are not the only factors that affect the way both the Fed and the White House view the trajectory of the economy. Much of President Trump's new budget proposal is based on the brazen assumption of 3% economic growth, which deviates quite substantially from both Wall Street and Capitol Hill forecasts. When an interest hike does indeed occur, it could result in a considerable adjustment to the long-term budget and limited productivity from the stimulus package.
Retrospectively, there is much to applaud and appreciate with respect to economic growth over the last few years. The Trump Administration is in a much more favorable position to implement long-lasting, wide-ranging economic policy initiatives, but the rate of success will be largely dependent on the administration's ability to adequately predict and react to changes in the long-term. As the unemployment rate drops and the labor force moves toward full employment, and as prices associated with household consumption increase, the very stark reality of an economic "bust" lies ahead if the government does not tread carefully. Both the Federal Reserve and the White House will be in the spotlight as timing, direction, and uniformity become be vital components for developing a strategy to ensure stable long-term growth potential without derailing accelerated growth in the interim.


This is the discussion related to the wiki page	SCP-3510.
Second time entering a contest woot!
Thanks to MaliceAforethought, Captain Kirby, TheGreatSea, BananaRepublic, Modern_Erasmus for reading and critting this draft! Special thanks to Tanhony and Decibelles for coming up with the task force names.
Note to self: about the lampshading you mentioned, would adding a sentence to the description about how the mimicking is basically creating the anomaly in a more controlled state help?
That was really interesting! Footnote four seems out of place, though. Like, placed incorrectly.
I was thinking about placing it after the mention of the cadavers, though I was worried about it taking away from the twist about the MTF still being alive. Once the contest is over I may switch it around though.
The Foundation basically becoming SCP-3510-B as a means of containing SCP-3510 has a certain irony to it that I personally enjoy enough to upvote.
So…you're saying I do not recognize the bodies in the water?
Based on how SCP-3510-A instances said variations on them "filling a gap in the world that had to be filled" when interrogated for motivations, researchers slowly developed the current containment procedures for SCP-3510.
This sentence was clunky to read. I had to go over it a few times to catch the meaning. Maybe flip the sentence around, like "Current containment procedures have been developed after an instance was found, in an interview, to reveal that the replacing of persons of interest is the process of 'filling a gap in the world that had to be filled'."or something of the like.
Wait a second… is this the Jewish conspiracy? Does that mean InfoWars is a Foundation front? Requesting Word of God on the matter.
Addendum: I am not arguing that the Jewish conspiracy is real. In fact, I believe that there are entries on this site that have more of a basis in objective reality than the Jewish conspiracy.
I just love fiction that re-contextualizes the real world and it's history. In fact, the only parts of Harry Potter I found paletteable (sc?) were the bits where they went back to important parts of London history and gave the story about what was *actually* happening. You know, Jack the Ripper was actually a Death Eater rampage intended to wipe out the mudbloods, the London Fires were actually a duel between professional rivals that got hilariously out of hand and resulted in the current government's rules for dueling, etc.
It has nothing to do with that. It's simply a take on generic New World Order type conspiracy theories.
after drinking a cup of water containing high quantities of hydrochloric acid.
Upvoted for making me laugh.
Reading this, I was immediately reminded of two SCPs - SCP-1659 and SCP-2390. A simple crosslink could be added to reference both of these SCPs.
Description: SCP-3510 is an unknown anomaly that can affect subjects in positions of major governmental or economic control. Affected subjects (hereafter referred at as SCP-3510-A instances) will believe that they are a member of "New Providence," (SCP-3510-B) a global organization claimed to exert control over all national governments and large corporations.
Description: Description: SCP-3510 is an unknown anomaly that can affect subjects in positions of major governmental or economic control. Affected subjects1 (hereafter referred at as SCP-3510-A instances) will believe that they are a member of "New Providence," (SCP-3510-B) a global organization claimed to exert control over all national governments and large corporations.
If anyone has any other ideas, feel free to suggest them below.
1. No subjects have been known to be affected by both SCP-3510 and either SCP-1659 or SCP-2390.
My only suggestion would be to shift that to the second sentence of the description, right after "Affected subjects," only out of personal preference for keeping references outside of the opening line of the description. Other than that these are solid crosslinks.


In 2005, when Pastor Doug, Paul's son, visited the mission field in India, he brought back the request of the Christians there for more radios. Inexpensive AM radios cost $5, and D batteries are another dollar. For $6 a leader in a village receives a radio which can be used to gather the people together to worship and hear the Word of God. Up to 50 people gather to hear the program. These are the nucleus of a rural church in the countries where The Word Today is broadcast.
The distribution of the radios exponentially multiplies the effectiveness of The Word Today. In India alone millions could hear the Good News of Jesus if only several thousands of radios were distributed! With God's blessing over time radio distribution will number in the tens of thousands across the world!


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Eddie Robinson, the subject of Tuesday's post, was at Game Six that night; Fox showed him during its telecast.
As far as I know, Robinson wasn't involved in the pregame activities (Dennis Martinez, another member of the 1990s Indians, threw out the ceremonial first pitch). But he is, obviously, not persona non grata with the organization.
Baseball America's J.J. Cooper compiled an extensive list of minor league pitchers who hit 100 mph in the past season. Two Twins are on that list: Pat Light, who was acquired from Boston for Fernando Abad and finished the season pitching (poorly) on the big league club; and Fernando Romero, a 21-year-old starting pitcher who split 2016 between low A Cedar Rapids and high A Fort Myers. It was his first season back from Tommy John surgery, and one would have to say it was a success: 90.1 innings, 1.89 ERA combined.
I wasn't impressed at all in September by Light. Romero is a genuine prospect, but years away from the majors.
There are 62 names on Cooper's list. and he expects more names to be added as people around the game see the list and say, hey, so-and-so hit 100.
There are other high velocity arms in the Twins system. Nick Burdi is one, but he barely pitched after spring training (three innings for Double A Chattanooga). There are several others who I'm a little surprised didn't hit triple digits at least once.
One game left to the 2016 season. May it be a good one tonight.
Labels: Eddie Robinson, Fernando Romero, Pat Light
All or nothing, and it's nothing
Hunter, Cuddyer, Hawkins in the the front office
Narrative stats versus evaluative stats
From the Handbook: Joe Mauer's baserunning
The meaning of Jason Castro
A defense first signing
From the Handbook: Tyler Duffey's pitches
Turnover among the catchers
Plouffe, there he goes
From the Handbook: Oswaldo Arcia, pinch non-hitter
From the Handbook: Team defense
From the Handbook: Molitor's managing
On keeping Neil Allen
The Rangers stadium vote
BA's Top Ten Twins prospects
The coaching staff: Bruno and Butch
Non-players in charge
Today it begins
A big celebration
A No. 2 is hired
On to the offseason
The complications of history and honor


How do I select variables for an analysis?
Can variables be selected for analyses by highlighting them in the spreadsheet?
How do I select a subset of cases (observations) to be included in an analysis?
How are case selection conditions stored and saved?
Can I select random subsets of data?
What is the quickest way to review basic descriptive statistics for a variable?
What is the quickest way to review a sorted list of all unique values of a variable?
What are statistics of block data?
Can matrix data be used for input instead of raw data?


Shipping cost is €33.50 as package with tracking.
If the total price is above €20.00, the shipping cost is €30.00 as package with tracking.
If the total price is above €40.00, the shipping cost is €26.00 as package with tracking.


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Channels & Networks
Animation Studios
Movie Time at the Metropol! - "Demons" Review
Sam Shepards
Hi, I'm Sam, I love movies. My main interest is science fiction and zombie movies. Pessimistic and survival films I also enjoy a lot.
A beautiful girl feels persecuted by a strange presence while riding the Berlin subway. When she gets off at a deserted station, she watches a strange masked man who seems to be chasing her.
Paranoia. Chaotic and random synths by Claudio Simonetti that already sounded outdated in 1987. The girl, named Cheryl (Natasha Hovey) believes to have escaped only to be surprised by the strange masked man, who is now in front of her.
The masked man, whose scars are very convincing, just raises his hand and gives her a flyer/free entry to a screening in an old theater that has just been reopened: The Metropol.
Cheryl then completely abandons her survival instinct (that were right all along!) and invites her best friend Kathy (Paola Cozzo) to the theater, without even knowing what film they are going to project.
In the Metropol, the atmosphere is convincingly mysterious. The usher and usheress are silent and enigmatic. There are demon masks, katanas and motorcycles decorating the place.
The audience is diverse. There is a pimp extracted from the 70s, accompanied by two loud and chaotic prostitutes, which he mistreats. An elderly married couple argues at every single thing. A blind man decides to attend the screening (??) and asks his beautiful partner to describe to him what's happening on the screen.
But the woman prefers to have a makeout session with a stranger while her poor blind partner screams for an explanation. Cheryl and Kathy are greeted by George (Urban Barberini) and Ken (Karl Zinny), who have obvious intentions to have sex.
The movie starts. It's a horror story based on a group of young characters who decide to desecrate the tomb of Nostradamus. When they open it, what they find is a weird book and a demon mask identical to the one that adorned the foyer of the theater.
When putting on the mask, one of the characters ends up with a cut on the cheek. The wound would get rapidly worst. The poor bastard would end up becoming a bloodthirsty demon.
Back on the movie theater, one of the prostitutes, who cut her face while jokingly putting on one of the decoration masks, will also end up becoming a demon, unleashing hell and general panic.
Metropol exits are sealed. The audience of the screening must seek to survive at any cost.
Demons seems to be a very sarcastic parody about the demonization of the arts (yeah, subtlety is not Demons' cup of tea), taking as a starting point the conservative point of view that accuses violence in the cinema as a corrupter of minds and behaviors. That script written by Lamberto Bava, Franco Ferrini, Dardano Sacchetti and the master Dario Argento, seemed to have much more depth than what it shows.
The idea of a deceived audience, lured to a screening where demons will be literally invoked on the screen to attack them, kill them and turn them into new demons, seems to make clear that satire about the "bad influence" of movie violence.
Demons doesn't make its intentions very clear but does more than enough to stir up the debate. And besides, it's a fucking blast. That is a total success in my book.
Demons has a punk aesthetic that at times remind us of The Return of the Living Dead. Of course, Demons is not openly a comedy and the aesthetics displayed is not so cartoonish. Demons wants to be taken seriously most of the time so that its, supposedly, unintentional humor works.
Television as the Devil - "Demons 2" Review
Lamberto Bava's "Demons" (1985)
By Keith Abt
"[REC]" - Zombie Movie Review
The 69 Best Zombie Movies Ever Made - A Deadly Countdown
'Evil Dead 2' Review: Bloody Looney Tunes
'Black Sheep' - Zombie Movie Review
The Best 80s Zombie Movies
'Cargo' Movie Review
"[REC] 4: Apocalypse" Review
2020 Netflix Halloween Countdown: "Demonic"
By Movie Beasts
'Slither' (2006) - Zombie Movie Review
Hereditary Movie Review - The Inherited Demons of the Family
By Vikas Yadav
Cronenberg's Tragic Love Story - "The Fly" Review
'Dead Snow 2: Red Vs. Dead' Film Review
"Evil Dead II" Review – Continuity Is My Deadite


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meghan kline tuls

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Everyone is Watching
Author(s): Megan Bradbury
Location(s): New York City (NYC)
Era(s): Various
'Beautiful, kaleidoscopic . . . everyone should be watching Megan Bradbury from now on' Eimear McBride, Baileys Prize-winning author of A Girl Is a Half-formed Thing
New York: A city that inspires. A city that draws people in. A city where everyone is watching, waiting to see what will happen next.
1967. Robert Mapplethorpe knows he is an artist. From his childhood home in Queens he yearns for the heat and excitement of the city, the press of other people's bodies. He wants to be watched, he wants to be known.
1891. Walt Whitman has already found fame, and has settled into his own sort of old age. Still childlike, still passionate, he travels with his friend and biographer Bucke to the city he has always adored, the scene of his greatest triumphs and rejections.
1922. Robert Moses is a man with a vision. Standing on the edge of Long Island he knows what it could become. Walking down a street in Brooklyn he sees its future. He is the man who will build modern New York.
2013. Edmund White is back in New York. It's the city of his youth, of his life and loves. He remembers days of lazy pleasure, nights of ecstasy and euphoria. But years have gone by since then.
Everyone is Watching is a novel about the men and women who have defined New York. Through the lives and perspectives of these great creators, artists and thinkers, and through other iconic works of art that capture its essence, New York itself solidifies. Complex, rich, sordid, tantalizing, it is constantly changing and evolving. Both intimate and epic in its sweep, Everyone is Watching is a love letter to New York and its people – past, present and future.
Happy and You Know It
Isabelle in the Afternoon
Lead Review
An unusual writing style. But it brilliantly captures the feel of New York through fiction, so many different voices, an absolute MUST if you are heading out to the city, it will reveal the...
Lead Review plus chatting to the author
Author: tripfiction
Snapshots of the life and people in the metropolis spanning a century and a half. This is a very unusually constructed book, a classic of short story pieces. The oftentimes brief chapters chart the lives of selected New Yorkers...


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