text:
\section{Introduction}

A stellar system responds to a disturbance by both phase-mixing, an
incoherent response, and by collective excitation of discrete modes, a
coherent response.  Since galaxy and star cluster models must be
stable to be useful, {\it growing} modes\footnote{For our purposes, a
mode is a well-defined pattern with a possibly complex frequency,
$\omega$.  If $\mathop{\it Im}\nolimits(\omega)>0$, the initial equilibrium is unstable and
the mode initially grows exponentially.  If $\mathop{\it Im}\nolimits(\omega)\le0$, the
equilibrium is stable and the modes are oscillatory or damped.} have
been studied extensively both analytically in the form of stability
criteria and using n-body simulation (see Binney \& Tremaine 1987,
hereafter BT, for a review\nocite{BiTr:87}).  The most well-known of
these is the bar-forming mode which significantly reorganizes its host
galaxy.  In general, {\it damped} modes will also be excited by a
disturbance and transport momentum globally but their amplitude decays
with time.  If the decay time is short, these modes will not be
perceptible. However, if a mode is weakly damped, it may persist for
many dynamical times, even though the system is stable.  For example,
a galaxy ``fly-by'' could excite such a mode which might persist long
after the encounter even if the system is not strictly unstable.
Several authors, in particular Miller and Smith (Miller 1992, Miller
\& Smith 1993\nocite{Mill:92,MiSm:93}), have observed oscillatory
modes in simulations.  Mathur (1990\nocite{Math:90}) formally
demonstrated the existence of oscillating solutions in both
one-dimensional and spherical systems.  In this paper, we explore the
existence and implication of weakly damped modes in spherical stellar
systems.

The existence of damped modes is not in question.  Collective damping
in a homogeneous plasma, {\it Landau damping}, is well-known.  The
simultaneous solution of the Vlasov equation and the Poisson equation
yield a dielectric response function which describes the reaction of
the plasma to an imposed disturbance.  Even in the presence of no
external disturbance, a stochastic space-charge field may give rise to
spontaneous density fluctuations resulting in Landau modes.  The zeros
of the dielectric function are the conditions for collective
solutions.  This use of the response function is sometimes known as
the {\it dispersion relation} (e.g.  Ichimaru 1973\nocite{Ichi:73})
since the it determines the frequency-wavelength relation for
electromagnetic waves in a medium.\footnote{The analogy does not carry
over the stellar dynamical problem but the term {\it dispersion
relation} is still used.} The relationship between the full modal
spectrum and the initial value for the homogeneous plasma has been
discussed by van Kampen (1955\nocite{vanK:55}) and the same physical
principles apply here.

Damped modes are difficult to study in arbitrary stellar systems for
two reasons.  First, the dispersion relation is analytically
intractable in nearly all but the homogeneous cases.  Second, although
one can study damped modes in simulations, one must be able to
discriminate the mode from numerical artifacts.  In this paper, I will
develop a numerical procedure for evaluating the dispersion relation
for spherical stellar systems and locating damped modes (\S2).  Armed
with a prediction for the shape and frequency of a damped mode, we may
initialize and efficiently search for it in n-body simulations.
Spherical models are considered because of the theoretical simplicity,
because they represent a wide variety of astrophysical scenarios and
to relate to the large body of literature on spherical stellar
systems.  In \S3, the technique is applied to King models of varying
concentration.  King models are known to be stable, for example, by
Antonov's criterion (Antonov 1962, see also
BT\nocite{Anto:62,BiTr:87}).  Nonetheless, we will see that these
models all have {\it very} weakly damped $l=m=1$ modes, with damping
times longer than $\sim20$ half-mass crossing times.  This is contrary
to the widely expressed belief that a disturbance in a stable system
will phase mix in several crossing times.  As a check, we realize the
$l=m=1$ mode and follow its evolution in a set of n-body simulations.
The results of the simulation (\S4) show that the expected mode
persists with no obvious decay.  The paper concludes with a discussion
of astronomical applications (\S5).

\section{Method}

For collisionless systems, the dispersion relation describes the
solution to an initial value problem as the result of a Laplace
transform; each component has time-dependence of the form
$\exp(-i\omega t)$, where the frequency $\omega$ may be complex.
Although the dispersion relation for infinite homogeneous stellar
systems has been derived (Ikeuchi et al. 1974,
BT\nocite{IkNT:74,BiTr:87}), most stellar systems are finite and
inhomogeneous. In a stellar sphere in particular, orbits are
quasiperiodic and the repetitive effect of a disturbance at the same
point in an orbit's phase can have a large effect (resonance).
Periodicity may be introduced in a homogeneous medium by carving out a
cube and connecting opposite faces; topologically, this is a 3-torus.
The resulting so-called periodic cube has been used by several authors
(Barnes et al. 1986, Weinberg 1993\nocite{BaGH:86,Wein:93a}) to take
the quasiperiodicity into account without sacrificing the theoretical
simplicity of spatial homogeneity and will be used below as an
example.

Inhomogeneous models of galaxies and clusters are considerably more
difficult to treat analytically because the collisionless Boltzmann
and Poisson equations are separable in different bases.  By Jean's
theorem, the solution to the collisionless Boltzmann equation may be
written conveniently in terms of its integrals of motion.  In the
spherical case, these are energy and angular momentum or radial and
angular actions.  Since the unperturbed Hamiltonian is then
independent of associated angle-like coordinate variables, a linear
perturbation to this equilibrium may be written as a Fourier series in
the coordinate angles.  The Poisson equation is naturally expanded in
a different basis: spherical hamonics.  However, by expanding the
self-consistent gravitational potential in an harmonic series which
satisfies the Poisson equation by construction, the simultaneous
linearized solution to the whole system may be reduced to a matrix
equation.  In particular, let $a_j, b_j$ be two sets of expansion
coefficients.  Then the response $b_j$ to a perturbation $a_j$ is
given by $b_i=M_{ij}(\omega)a_j$ where $M_{ij}$ is the response matrix
and describes the dynamical response of the stellar sphere to that
part of perturbation with time-dependence $\exp(-i\omega t)$.  A
self-consistent response has $a_j=b_j$ (cf.  Appendix B).
This formalism, sometimes called the matrix method, has had varied
applications beginning with Kalnajs (1977\nocite{Kaln:77}) who was
interested in the modes of stellar disks.  Polyachenko and Shukhman
(1981\nocite{PoSh:81}) first adapted the method to the study a
spherical system (see also Fridman and Polyachenko 1984,
Appendix\nocite{FrPo:84b}) and the method was later employed by both
Palmer and Papaloizou (1987\nocite{PaPa:87}) in the study of the
radial orbit instability and by Bertin and Pegoraro
(1989\nocite{BePe:89}) to study the instability of a family of models
proposed by Bertin and Stiavelli (1984\nocite{BeSt:84}).  Weinberg
(1989\nocite{Wein:89}) used the matrix formulation to study the
response of a spherical galaxy to an encounter with a dwarf companion
and Saha (1991\nocite{Saha:91}) and Weinberg (1991\nocite{Wein:91a},
hereafter Paper I) investigated the stability of anisotropic galaxian
models.  Using this approach, the dispersion relation is the condition
that the self-consistent response have a non-trivial solution:
$\det[\delta_{ij}-M_{ij}(\omega)]=0$.  The general dispersion relation
can be calculated for a spherical model with an arbitrary phase-space
distribution function, although only isotropic distributions will be
discussed here.

\begin{figure}[e]
\caption{\label{fig:dispcube} Contours in magnitude of the
analytically-generated dispersion relation for the stellar cube.}
\end{figure}

\begin{figure}[e]
\caption{\label{fig:dispcrat} Same as in Fig. \protect{\ref{fig:dispcube}}
but for the numerically-generated dispersion relation for the stellar
cube.}
\end{figure}

\subsection{Analytic continuation of the dispersion relation}

Just as in the case of the plasma dispersion relation, the derivation
in Paper I explicitly shows that the dispersion relation as written
(see Appendix
B)
is only valid in the upper-half $\omega$ plane.  Causality in the
initial value problem demands that various integrands be analytically
continued to the lower-half plane.  This is readily done in the plasma
case (cf.  Ichimaru 1973\nocite{Ichi:73}) where the natural
coordinates for both the Boltzmann and Poisson equations are
cartesian.  This is problematic in the case of the sphere, whose
dispersion relation is given by equations (\ref{sphmatrix}),
(\ref{potrans}), and (\ref{sphdisp}).  Since equation
(\ref{sphmatrix}) contains the term $1/[\omega-{\bf
n}\cdot{\bf\Omega}({\bf I})]$, explicit analytic continuation requires
analytic continuation of orbital frequencies and actions.  To sidestep
this daunting task, I propose to evaluate the dispersion relation in
the upper-half plane and perform the analytic continuation numerically
by approximating it by a function which may be easily continued.
Given that poles are expected because of the form of equation
(\ref{sphmatrix}), rational functions are a natural choice.

Before applying this to cases of interest, we would like some
assurance that this procedure for analytic continuation will work
reliably.  To do this, I evaluated the dispersion relation for the
periodic cube (eq. \ref{dispcube}), both analytically and numerically.
The simple form of the velocity integrals in equation (\ref{delcube})
allow explicit analytic continuation.  Analytically generated contours
for the fundamental harmonic in the dispersion relation, $|{\cal
D}_{1,0,0}(\omega)|$, are shown in Figure \ref{fig:dispcube}.  The
zeros are at the centers of the concentric contours and the location
of the zeros indicate the type of growth; if the zeros are in the
lower (upper) half-plane, disturbances are damped (growing).  The
model depicted is stable.  The most weakly damped mode has
$\mathop{\it Re}\nolimits(\omega)=0$ and and therefore damps in situ.  The other modes both
damp and propagate with group velocity $\mathop{\it Re}\nolimits(\omega)$.  As the stellar
velocity dispersion is decreased, the solution with $\mathop{\it Re}\nolimits(\omega)=0$
moves toward the real axis from below and will become the Jeans
instability for sufficiently small velocity dispersion.  Modes in
spherical systems, discussed below, have spatial distributions
proportional to spherical harmonics and $\mathop{\it Re}\nolimits(\omega)$ indicates a
pattern speed rather than a group velocity.

I then evaluated ${\cal D}_{1,0,0}(\omega)$ at 20 points for
$-40<\mathop{\it Re}\nolimits(\omega)<40$ for each of $\mathop{\it Im}\nolimits(\omega)=0, 0.5, 1.0$ and found
the corresponding rational function fit (cf. Appendix \ref{app:rat}).
Contours of the approximating rational function are shown in Figure
\ref{fig:dispcrat}.  Comparing Figures
\ref{fig:dispcube} and \ref{fig:dispcrat} we see that the least
damped modes are determined accurately.  I checked the robustness of
the method to the choice of evaluations by varying the number and
placement of points included in the rational function fit.  The three
most weakly damped modes are accurately determined even if any two of
the ``rows'' of constant $\mathop{\it Im}\nolimits(\omega)$ are eliminated.  The most
weakly damped mode remains accurately determined even for 10 points
along the real $\omega$-axis from $-40<\mathop{\it Re}\nolimits(\omega)<40$.  The behavior
of ${\cal D}_{1,0,0}$ near the real axis is dominated by the true
weakly damped modes, allowing zeros to appear at
$\mathop{\it Im}\nolimits(\omega)\approx-28$ in Figure \ref{fig:dispcrat}.  This is an
expected and generic feature; zeros on the lower-half plane will
only be well-approximated by the rational function if they affect the
${\cal D}$ on the upper-half plane.  In general, we can not expect
accurate determination of all features on the lower half-plane from a
finite grid and, in particular, the upper half-plane will place little
constraint on the rational function extrapolation on the lower
half-plane if more weakly damped modes at similar values of
$\mathop{\it Re}\nolimits(\omega)$ exist.

\subsection{Application to the dispersion relation for stellar spheres}

In the next section, we investigate the low-order damped modes for
isotropic King models with dimensionless central potential
$W_0\equiv(E_t-E_o)/\sigma^2=3, 5, 6, 7$ and concentration
$c\equiv\log_{10}(r_t/r_c)=0.67, 1.0, 1.3, 1.5$ respectively where
$r_c$ and $r_t$ are the core and tidal radii (see King
1966 and BT for more
details\nocite{King:66,BiTr:87}).  Linear perturbation theory allows
each harmonic order, $\propto Y_{lm}$, to be considered separately.
However, because the sphere has no symmetry axis, all terms $m$ are
degenerate for a given $l$.  In realizing specific modes below, we
will choose $l=m$.  Units are chosen so that $M=G=1$ and the total
gravitational potential $W=-1/4$.  In most cases, we use a grid in the
upper-half $\omega$-plane with $\mathop{\it Im}\nolimits(\omega)=0.01, 0.05, 0.1$ and 10 to
40 evenly spaced points in $-1<\mathop{\it Re}\nolimits(\omega)<1$.  In some cases the
domain is extended to $-5<\mathop{\it Re}\nolimits(\omega)<5$ to check for ``fast'' pattern
speeds but none were found in any cases explored here.  The
evaluations of ${\cal D}(\omega)$ (cf. eq. \ref{sphdisp}) are fit to a
rational function and zeros in the lower-half plane are noted.  The
robustness of the zeros to the input grid is checked by successively
truncating the grid in $|\mathop{\it Re}\nolimits(\omega)|$, halving the resolution of the
grid and leaving out ``rows'' in $\mathop{\it Im}\nolimits(\omega)$.  In all cases, the
existence of the zeros and general topology of the function did not
change although the position of particular zeros varied by as much as
$10\%$ in a few cases.

The elements of the response matrix $M_{ij}(\omega)$ (cf. eq.
\ref{sphmatrix}) require a two-dimensional integral and a
two-dimensional sum in $l_1$ and $l_2$.  The sum is only two
dimensional since $M_{ij}(\omega)$ is independent of $l_3=m$ given
$l$.  The sum in $l_1$ must be truncated at a chosen value,
$l_{1,max}$ and the sum in $l_2$ has $|l_2|<l$.  Twenty point grids
for the integral evaluation using rational functions were found to be
adequate; large numbers of grid points ($\ga40$) cause significant
truncation error (see App. D).  The rational function technique gives
surprisingly good results with a small number of integrand
evaluations.  Standard lower order integration techniques (e.g.
Simpson's rule) ultimately give better results but only after an order
of magnitude more evaluations.  The value of $l_{1,max}$ was
successively increased to obtain convergence.  The appropriate value
of $l_{1,max}$ depends on $l$; $l_{1,max}$ was chosen to be 6 and 10
for $l=1$ and 2, respectively.  Finally the order of the $n\times n$
matrix $M_{ij}$ was varied to obtain convergence in ${\cal
D}(\omega)$.  The required order increases with $\mathop{\it Re}\nolimits(\omega)$; $n=30$
gave adequate convergence for $|\mathop{\it Re}\nolimits(\omega)|\la1$.  The resulting
error in ${\cal D}(\omega)$ is estimated to be ${\cal O}(10^{-2})$.

\def\sround#1{\hbox to1.6cm{\hfil#1\hfil}}
\def\ssround#1{\hbox to2.5cm{\hfil#1\hfil}}

\begin{table}[t]
\caption{Model parameters and modal frequencies}
\begin{tabular}{ccccccl}
\multicolumn{2}{c}{Model}	& Order
			& \multicolumn{2}{c}{Frequency} & Shift & Example\\[.2ex]
King $W_0$ & $c$	& \sround{$l$}
			& \sround{$\mathop{\it Re}\nolimits(\omega)$}
			& \sround{$\mathop{\it Im}\nolimits(\omega)$}
			& \sround{$r_{shift}/r_c\epsilon$}
			& Cluster name \\
\tableline
3	&0.67	&\sround{1} &\sround{0.010} & \sround{$-0.0016$}
&\sround{0.41}	& NGC 6496	\\
	&	& 2	& 0.10	& $-0.076$	\\
5	&1.0	& 1	& 0.034	& $-0.0011$	& 0.40	& NGC 288 \\
	&	& 2	& 0.0	& $-0.11$	\\
6	&1.26	& 1	& 0.042	& $-0.0065$	& 0.42	& $\omega$ Cen \\
7	&1.5	& 1	& 0.064	& $-0.025$	& 0.54	& M13 \\
	&	& 2	& 0.0	& $-0.20$	\\
\end{tabular}
\end{table}

\section{Properties of damped modes}

This section describes the application of the methods from \S2 in
determining the damped modes of King models with $W_0=3,5,6,7$.  The
complex frequencies of the most weakly damped modes are shown in Table
1.  To summarize, one finds the $l=1$ modes are {\it very} weakly
damped for all $W_0$ studied with the damping proportional to
concentration.  The existence of such modes imply that low-order
excitations of stable galaxies and clusters may persist for many
crossing times and scaled to physical units, perhaps as long as the
age of the galaxy itself.  Very weakly damped $l=2$ modes were found
for the $W_0=3,5$ cases and the same mode is relatively more strongly
damped for $W_0=7$.  No weakly-damped $l=3$ modes were found. A
detailed discussion of these trends and an examination of the modal
shape is given below.

\begin{figure}[e]
\caption{\label{fig:modeloc} Shows the location of the damped $l=1$
modes for $W_0=3,5,6,7$ King models (labeled by $W_0$).  The estimated
precision is indicated by the errorbar at the upper left.}
\end{figure}

\begin{figure}[e]
\caption{\label{fig:mode_w05_1} Contours of the density perturbation
for the $l=m=1$ mode for the $W_0=5$ model on the $x$--$y$ plane.
Only the inner region of the model is shown; the tidal radius is
$r_t=8.72$.  Overdensity (underdensity) is shown as a solid (dashed)
line.}
\end{figure}

\begin{figure}[e]
\caption{\label{fig:comp_w05_1} Effect of the density perturbation
shown in Fig.
\protect{\ref{fig:mode_w05_1}} on the background model.  The peak
perturbation is 30\% of the background.  Note the shift of the central
density peak.  The core radius is at 0.81 in these units.  The dotted
contours show the unperturbed background at the same levels.}
\end{figure}

\begin{figure}[e]
\caption{\label{fig:ek_mode} Absolute value of the phase-space
perturbation for the $l=m=1$ mode for the $W_0=5$ model as a function
of energy $E$ and $\kappa^2=(J/J_{max})^2$.}
\end{figure}

\begin{figure}[e]
\caption{\label{fig:mode_w05_2} Contours of the density perturbation
for the $l=m=2$ mode in the $W_0=5$ model on the $x$--$y$ plane.}
\caption{\label{fig:comp_w05_2} Effect of the density perturbation
shown in Fig. \protect{\ref{fig:mode_w05_2}} on the background model.
The peak perturbation is 30\% of the background.}
\end{figure}

\subsection{Frequencies of lowest order modes} \label{sec:lowest}

For comparison, Figure \ref{fig:modeloc} plots the zeros of the
dispersion relation for $l=1$ damped modes in $W_0=3,5,6$ and $7$
King models.  For example, the $l=1$ harmonic for the $W_0=5$ King
model has a {\it very} weakly-damped mode at $\omega=(\pm0.034,
-0.0011)$.  The $\omega$-plane was searched for
$-1\le\mathop{\it Re}\nolimits(\omega),\mathop{\it Im}\nolimits(\omega)\le1$ and no other modes were
indicated.  Changes in the input grid of ${\cal D}(\omega)$ change the
location of $\mathop{\it Im}\nolimits(\omega)$ for the modes by ${\cal O}(10^{-3})$.  The
errorbar in upper left corner of Figure \ref{fig:modeloc} gives the
estimated precision in $\omega$.  Both the $W_0=3$ and $5$ have nearly
zero damping within the resolution of the technique; the value
$\mathop{\it Im}\nolimits(\omega)=0$ can not be ruled out for these cases.  The analogous
modes for the $W_0=6,7$ models are clearly damped but still only
weakly.

The $l=2$ modes exhibit a similar trend: the rate of damping increases
with concentration.  For the $W_0=5,7$ cases, the pattern speed is
zero but it is nonzero for the lowest concentration model.

Grids for the $l=3$ harmonic were constructed for models $W_0=3, 5, 7$
but no weakly damped modes with $|\mathop{\it Re}\nolimits(\omega)|\la0.3$ and
$\mathop{\it Im}\nolimits(\omega)\ga-0.3$ were found, suggesting that the $l=3$
disturbances are moderately to strongly damped.

\newpage

\subsection{Shape of lowest order modes} \label{sec:shape}

The $l=1$ weakly-damped mode for the $W_0=5$ King model discussed in
\S\ref{sec:lowest} is shown in Figure \ref{fig:mode_w05_1}.  The
procedure for finding the eigenfunction is discussed in Appendix
\ref{app:eigfct}  The peak of the disturbance occurs at $\sim75\%$ of
the core radius of the background model.  The half-mass radius is
$r_{1/2}\approx1.6$.  At larger radii, the density contours remain
concentric.  However, the shape of an $m=1$ mode depends on the
expansion center; therefore one would observe this mode as a coherent
$m=1$ shift at large galactocentric radius by fixing the expansion
center on the density center.

The $l=1$ mode manifests itself as a shift of the central density.
The shift is given by the linear relation
$r_{shift}/r_c\approx0.4\epsilon$, where $\epsilon$ is the ratio of
perturbed density at peak relative to background and
$\epsilon\la0.3$ to have positive density everywhere.  As an example,
the solid contours in Figure
\ref{fig:comp_w05_1} show the combined background and perturbation
with the near maximum amplitude of 30\% at peak.  The dotted contours
show the unperturbed model at the same levels for comparison.  The
shifted center revolves about the original center at angular frequency
$\mathop{\it Re}\nolimits(\omega)$.  The center-of-mass shift for other concentrations is
given in Table 1.  The value $r_{shift}/r_c\epsilon$ is similar for
all concentrations.

The magnitude of the perturbed phase-space distribution averaged over
angles is shown in Figure \ref{fig:ek_mode}.  The energies of
perturbed orbits are small but do not include the most bound particles
and the peak toward large $\kappa^2$ at constant $E$ indicates that
the perturbed orbits tend to be more circular on average.

The $l=m=2$ mode (Fig. \ref{fig:mode_w05_2}) appears as a bar which
peaks at a fraction of the core radius, at roughly the same radial
scale as the $l=1$ mode.  Figure \ref{fig:comp_w05_2} shows the mode
at 30\% amplitude combined with the $W_0=5$ King model background
density.  Since $\mathop{\it Re}\nolimits(\omega)=0$, the pattern will have a fixed
orientation and the bar distortion will decay with time.  The phase
space perturbation is similar in extent to that shown in Figure
\ref{fig:ek_mode} but with a larger contribution of eccentric orbits.

\section{Simulation}

Although the dispersion relation indicates the existence of a weakly
damped $l=1$ mode, can such a mode be excited at significant amplitude?

In partial answer, we may attempt to realize the mode in an n-body
simulation.  Success would also serve as an independent check of the
linearized solution.  Unfortunately, such a simulation is fraught with
serious systematic problems.  First, most simulation schemes do not
explicitly conserve momentum.  Since an $l=1$ perturbation shifts the
density center, numerical artifacts may not be distinguishable from
the mode itself.  To minimize possible artifacts, we use a
direct-summation force calculation which {\it does} conserve
momentum.  Second, minimization of two-body relaxation requires
softening at, roughly, the mean interparticle spacing.  However, the
feature we wish to resolve is only a factor of a few larger than this
scale for $\sim10000$ bodies.  Therefore the softening itself is
likely to change the dispersion relation and this will require that
the dependence on softening be investigated.  Third, even with
softening, relaxation significantly changes the background on a
shorter timescale than the predicted damping, suggesting that
relaxation in the simulation may affect the mode.  Finally, although
these difficulties could be addressed with larger $n$, the $n^2$ FLOP
scaling of the direct summation scheme practically limited the
simulations to $n=10000$.\footnote{Computations were performed on a
Sun Microsystems Sparc 10/41 workstation which required
$3.4\times10^2$ CPU seconds per step.}

\begin{figure}[e]
\caption{\label{fig:virial} The virial quantity $-2T/W$
(top panel) and the run of gravitational potential energy (bottom
panel) shown as a function of time.}
\end{figure}

\begin{figure}[e]
\caption{\label{fig:pos_ang} Position angle as a function of time
for the $l=m=1$ component in the n-body simulation described in \S4.
Three radial wavefunctions (orders $n=8,9,10$) are shown separately
(solid lines) along with the theoretical prediction from \S3 (dashed
line).}
\end{figure}

Because the mode is computed in action-angle variables, the perturbed
n-body phase space is easiest to realize in these variables.  The
details are described in Appendix
\ref{app:nbody} The mode described in
\S3.2
is realized with a peak level of 20\% of background.  The softening is
chosen to be the mean interparticle spacing at the half-mass radius.
Because of both the imposed perturbation and modification of the
interparticle force by softening, the initial conditions are not in
equilibrium.  The system appears to settle at $t=25$
as indicated by a constant value of $-2T/W\sim1$ (cf. Fig.
\ref{fig:virial}).  For comparsion, the radial crossing time at the
half-mass ($\approx1.6$) is roughly 4 time units.  The $-2T/W$
profile looks similar for initial conditions without an initial
perturbation, suggesting that softening causes the poor initial
equilibrium state.

The evolution of the introduced mode may be diagnosed using the same
harmonic decomposition used to evaluate the dispersion relation
(Appendix
B).
The original expansion center is preserved in the center-of-mass frame
since the direct force scheme explicitly conserves momentum.  The
azimuthal phase of the $l=m=1$ distortion for several of the
higher-order radial wavefunctions are shown in Figure
\ref{fig:pos_ang}.  The low-order radial terms are less sensitive to
the mode which has a scale length of $\sim1/10$ the system radius.
The real part of the eigenfrequency is the pattern speed for an $m=1$
distortion.  The dashed line indicates the slope predicted by
$\mathop{\it Re}\nolimits(\omega)$.  The agreement is quite good.  However, the evolution
due to relaxation removes sensitivity to changes in amplitude of the
mode which is predicted to have a longer timescale.

The amplitude of a disturbance may be computed from the total
gravitational potential energy in the disturbance.  From Appendix
B,
it follows that this energy for a particular harmonic is $W_{lm} =
-2\pi G\sum_{j=1}^{n_{max}} |a_j^{lm}|^2$ where $a_j^{lm}$ are the
expansion coefficients.  For the current simulation, the energy per
order $l$, $W_l\equiv\sum_m W_{1m}$, converges with increasing radial
wavenumber $n_{max}$ at fixed time, confirming that the disturbance is
global.  In addition, $W_1$ is roughly constant over the course the
simulation.  More precisely, $W_1$ does appear to grow slightly with
time but this can not be distinguished from the effects of relaxation
which causes the central potential to deepen.  An additional
simulation with a $7\%$ rather than $20\%$ amplitude perturbation
exhibited similar behavior, both in phase and amplitude.

To understand the effects of softening, simulations with softening
length of both half and double the half-mass interparticle spacing
were performed with the same initial conditions.  The same general
trends were seen: the introduced $l=1$ mode persisted with the
expected pattern speed.

However, in all three runs, there were ``bursts'' of the $l=2$ mode,
which might be expected given its long damping time (cf.  Table 1).
The $l=2$ power was larger for smaller softening, possibly suggesting
that either or both relaxation and softening are changing the modal
structure.  In addition, for $t\ga30$, relaxation causes the central
potential to deepen and at the same time, the relative contribution of
the $l=2$ disturbance grows and appears to saturate without damping,
roughly at the level of the initial $l=1$ perturbation.  For the case
with $7\%$ perturbation intially, the $l=1$ mode continues at the
predicted pattern for $t\ga30$ even though the $l=2$ distortion is
evident.  For the $20\%$ case, the growth of the $l=2$ distortion
appears to significantly change the $l=1$ mode.  The importance of
these effects (especially the possible implication for bar growth)
remains to be investigated.

Finally, a set of simulations with no perturbation {\it a priori} were
used to check the significance of the observed disturbance by
comparing the gravitational potential energy in $l=1$ mode.  The
stochastically excited $l=1$ components contained $\la3\%$ of the
energy in the introduced mode described above.  Nevertheless, it is
worth noting that a coherent pattern was seen in these control runs
with the expected pattern speed even though the peak density contrast
was only $1\%$ to $3\%$.

\section{Discussion and Summary}

The numerical evaluation of the dispersion relation for King models
predicts the existence of low-order weakly damped modes.  In
particular, the $l=1$ ($m=1$) mode is {\it very} weakly damped with
small pattern speed over a range of central concentrations.  Similar
results might be expected for other spherical systems.

This mode causes the density center to shift and rotate about the
original center.  Using the linear theory, the shift is given by the
linear relation $r/r_c\approx0.4\epsilon$, where $\epsilon$ is the
ratio of perturbed density at peak relative to the background and must
be $\la30\%$ of background at peak.  This mode has been realized and
observed in a simulation of a $W_0=5$ King model.  A strong excitation
of this mode results in a shift of the density center of roughly
$10\%$ of the core radius as predicted and such levels were maintained
for the duration of the simulation.  However, intrinsic limitations
and features such as softening and relaxation modify the evolution of
and limit temporal sensitivity to weakly damped modes.  This, in part,
explains both the reason they were not discovered by n-body simulation
and the general belief that excitations of stable equilibria vanish in
several crossing times.

Because the low-order damped modes are simple, they should result from
general perturbations.  For example, the differential acceleration due
to a passing galaxy may cause a significant $m=1$ perturbation which
might mix quickly {\it except} for the weakly damped modes.  A
companion on an eccentric orbit may have similar effects.  The induced
distortion due to a companion on circular orbit will be dominated by
the quadrupole ($l=2$) moment; the dipole force is canceled by the
barycentric motion (Weinberg 1989\nocite{Wein:89}).

In the halo of a halo-dominated galaxy, such a mode could result in
the appearance of an $m=1$ distortion or position-shift of the
luminous disk.  Baldwin, Lynden-Bell and Sancisi
(1980\nocite{BLBS:80}) have pointed out that a number of nearby
galaxies have lopsided HI distributions relative to their optical
centers and that a large fraction of spiral galaxies show this
effect.  Damped modes may be partly responsible for the ubiquity of
such offsets, especially in the more moderate cases.  Using the
$W_0=5$ model as an example, the excitation of a $10\%$ perturbation
in a halo with core radius of $15{\rm\,kpc}$ by, say, a companion or
``fly-by'' would result a central density offset of $\sim600\,\hbox{pc}$ which
would persist long after the encounter.  In the bulge or spheroid of a
disk galaxy, the mode would shift the density center from the
kinematic center as determined, say, by the large-scale HI rotation
curve.  Using the same example, for a bulge--spheroid with a $1{\rm\,kpc}$
core radius with $\epsilon=0.01,0.1$ the offset would be
$\sim4,40\,\hbox{pc}$.  In addition, since the mode is slowly varying, one
might expect a massive central black hole, $M\ga10^6{\rm\,M_\odot}$ to remain
within the potential well of the shifted density center since the
equipartition radius would be $r_c m_\ast/M_{bh}$ for mean stellar
mass, $m_\ast$.

Similarly, a time-dependent external force or {\it gravitational
shock} differentially accelerates globular clusters, possibily
exciting weakly-damped modes.  Clusters on eccentric orbits will
suffer gravitational shocking due to the halo and bulge and all
clusters with mean galactocentric radii within $20{\rm\,kpc}$ will suffer
shocking due to the disk.  In addition, there are relaxation-driven
internal momentum sources such as binary recoil which could in
principle produce an $m=1$ disturbance (Makino \& Sugimoto
1987\nocite{MaSu:87}).  Either way, an offset core may change the
subsequent dynamical evolution by decreasing the thermal contact of
the core and the population of eccentric halo orbits.  This may also
have implications for gravothermal oscillation.  In addition, we may
have to reexamine the intepretation of off-centered compact objects if
any of the $m=1$ excitations keep the density central offset, on
average, from the geometric center.  On the other hand, the physical
picture is further complicated by two-body relaxation whicy may lead
to more rapid damping of these modes.  Also, the largest relative
central density shifts and damping times occur for the lowest
concentrations where we expect rates of relaxation and subsequent
production of exotic objects to be low.  Additional work will be
necessary to understand these competing trends and the extent to which
these modes may be excited in globular clusters.

\acknowledgments
I thank Susan Kleinmann and David van Blerkom for comments on the
manuscript and Dave Chernoff and Ira Wasserman for discussion.  This
work was supported in part by NASA grant NAGW-2224.

\def\astroncite#1#2{#1, #2}

redpajama_set_name: RedPajamaArXiv


TR Equipment Products are well estabilished and utilized within burn units and rehabilitation treatment facilities for wound debridement. Water can have a cooling effect on burns, or a warming effect on stiff joints or sore muscles.
Safeguard against bacterial growth inside and outside the bath.
Bariatric Shower trolley, Atlas Jr.


text:
Cheltenham Festival Races
Cheltenham Festival History
The National Hunt Chase, or National Hunt Chase Challenge Cup, to give the race its full title, is run over 4 miles on the Old Course at Cheltenham, where it is currently scheduled as the penultimate race on the opening day of the Cheltenham Festival in March each year. The National Hunt Chase is open to novice steeplechasers, that is, horses that have yet to win a race over fences at the start of the current season, aged five years and upwards, and restricted to amateur riders.
The race became part of the Cheltenham Festival programme in 1911 and has been run more often than any other event in that sphere; it is also the longest race run at the Festival. The National Hunt Chase was upgraded to Listed status prior to the 2014 running and, following a resurgence in popularity, upgraded to Grade 2 status prior to the 2017 running.
Since World War II, no jockey has won the National Hunt Chase more than twice, although Jonjo O'Neill is far and away the most successful trainer in recent years. The Master of Jackdaws Castle has saddled Front Line (1995), Rith Dubh (2002), Sudden Shock (2003), Native Emperor (2004), Butler's Cabin (2007), Minella Rocco (2016) for a total of six wins.
The Arkle Challenge Trophy
St. James's Place Foxhunter Chase Challenge Cup
Triumph Hurdle
Fred Winter Juvenile Novices' Handicap Hurdle
David Nicholson Mares' Hurdle
Festival Trophy Handicap Chase
Novices' Handicap Chase
Neptune Investment Management Novices' Hurdle
Coral Cup
Dawn Run Mares' Novices' Hurdle
The Fulke Walwyn Kim Muir Challenge Cup
Vincent O'Brien County Handicap Hurdle
Martin Pipe Conditional Jockeys' Handicap Hurdle
Johnny Henderson Grand Annual Chase
Stayer's Cup (World Hurdle)
Racing Blog
Cheltenham Betting Blog
Cheltenham New Year's Day Fixture Cancelled Due to Waterlogging
Cheltenham Festival 2021 - Ones to Watch

redpajama_set_name: RedPajamaCommonCrawl


Karen now incorporates all her conventional and complementary knowledge and skills that facilitate a holistic approach to caring and supporting people and horses.
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Maureen Bradshaw is a Toronto based artist. Her work is primarily oil on canvas. She layers lively brush strokes over a loose sketch of the animal, painting with a spontaneous energy that allows surprises of bright background colours to peer through. With a lengthy career as a creative director in the graphics business in downtown Toronto, additional training in fashion illustration at the Ontario College of Art and Design, and a love for the outdoors, she explores the individual animal's personality in each painting.


text:
Soft Skull Press
Jill Talbot
JILL TALBOT is the author of Loaded: Women and Addiction, the co-editor of The Art of Friction: Where (Non) Fictions Come Together, and the editor of Metawritings: Toward a Theory of Nonfiction. One of her essays was named a Notable Essay in Best American Essays 2014 and her work has appeared in journals such as Brevity, DIAGRAM, Ecotone, The Paris Review Daily, The Pinch, The Rumpus, and Under the Sun.
The Way We Weren't
by Jill Talbot
To say that Jill Talbot steps into the controversial borderlands between fiction and non fiction with The Way We Weren't is a vast understatement. It is more like she plunges into them off the fifty-meter springboard, doing three somersaults and a half gainer on the way down. This gut wrenching tale of abandonment (though it is never perfect clear who was the abandoner, who the abandonee) makes us ask giant, soul-bending questions, like 'Does anyone ever know anyone?' and 'Are we always the creators of our own misery?' A brave story of one woman's fight to survive, most of all, her own proclivities. — Pam Houston, author of Contents May Have Shifted
The Soft Skull
Feed your bookshelves
Soft Skull
1140 Broadway, Suite 704
contact@softskull.com
Download Soft Skull's Winter-Sping 2019 catalogue
Your book will arrive via USPS in 5-10 business days.
Learn more about new releases, events, promos and more cool stuff!
Not in the US? Contact us for international order.
Place my order
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Which ships to


text:
Post Position
Nick Montfort
Putting the WTF Back into YouTube
What … exactly … is … the … deal?
Another attack — NOT
An analyst assesses Alphabetical Africa and another authorial account about antithesis and absence.
Luis Bury does not pull punches in reviewing Doug Nufer's Negativeland and Walter Abish's Alphabetical Africa in ebr.
Bill Gates at MIT
Bill Gates spoke at MIT's Kresge Auditorium today as the chairman of the Bill and Melinda Gates Foundation, advocating for the brightest minds to work on the most important problems of the world – such as reducing childhood deaths through health, sanitation, and development programs. The talk was part of a tour that also includes Stanford, Berkeley, the University of Chicago, and Harvard. There were only a few seats free in Kresge. Among other things, Gates suggested separating the accreditation function of higher education to allow for non-place-based learning. He softened the blow by praising MIT's Open Courseware and listing several of the OCW courses that he himself had taken.
Since I didn't see Richard Stallman in line, I didn't stay for all of the Q&A.
There wasn't a torrent of new information in Gates's talk, but it was fascinating to hear in relation to Gates's 1976 "An Open Letter to Hobbyists." There are actually some similarities in tone: In both the letter and the talk, Gates expressed dismay at the current system not working very well. But in the letter, he declares that computer hobbyists should stop stealing software, says that people who have been re-selling his product without authorization should be kicked out of the club, and invites members to write him and pay up. This, he hopes, will advance him toward his dream, in which he can "hire ten programmers and deluge the hobby market with good software." Today, he's the world's wealthiest man, actively seeking more effective ways to benefit society by giving his money away.
On the one hand, one wonders if we might have done just as well if we had kept our money in the first place.
On the other hand, Gates becoming a full-time philanthropist and speaking to our technical institute here from that perspective makes for quite a development. It reminds me that his rival and fellow college drop-out, Steve Jobs, got his start selling blue boxes with Steve Wozniak to allow his customers in the Berkeley dorms to resist the man and make free long-distance calls. Now, Jobs, the man, has a worldwide telephony empire of his own via the iPhone and its thought-crushing App Store.
It's too bad you can't tell who the good guys are going to be – say, by looking for a "don't be evil" button.
Two Profs on Boing Boing
Two of my friends and fellow investigators of digital media have recently been featured on Boing Boing:
"Reducing the World's Suck with Henry Jenkins" is an article that deals with Henry's perspectives on fandom and the still-prevalent myths of videogame violence and addiction.
"Chimerical Avatars and Other Identity Experiments from Prof. Fox Harrell" details Fox's ongoing work on better representing identity in videogames and other computing systems.
The article on Fox Harrell was reblogged on Kotaku, too: "Making Avatars That Aren't White Dudes Is Hard." While the title is catchy, I have to point out that Fox's work is about richer and more multidimensional ways of representing oneself digitally, beyond the one idea of skin color or race. So, we should anticipate that this work is likely to benefit "whitey" as well – and anyone who wants more than a Monopoly token as an in-game or online representation.
Video of the Get Lamp PAX Panel
Jason Scott, the filmmaker behind the soon-to-be-released interactive fiction documentary, has posted video of the Get Lamp panel at PAX-East. He's also put up an MP3 with just the audio. The panelists are Dave Lebling, Don Woods, Brian Moriarty, Andrew Plotkin, your very own Nick Montfort, Steve Meretzky, and Jason Scott.
H. Edward Roberts, Inventor of the Personal Computer
The inventor of the MITS Altair 8800, the inexpensive kit computer that is widely considered to be the first personal computer, has died at age 68.
Rilke and Prejudice and Robots
In Robot Rilke, you can find the selected poems of Rainer Maria Rilke translated by robots. "With a special biographical introduction cut-and-pasted from Wikipedia."
If you love it, you may want to sing Robot Love, I Love You. (Video by Ignatz Topolino, audio by Echelon and Jane Dowe, a.k.a. Oh Astro.)
Today's CMS Masters Presentations
Today we heard final thesis presentations from the 2010 masters students in MIT's Comparative Media Studies Program.
I've taught in CMS, which has an undergraduate and masters program, since I came to MIT three years ago. It's a diverse program that has included digital media research and has brought contemporary computational work, among other types of media production and reception, into juxtaposition and under consideration. Here are the titles of this semester's masters presentations:
M. Flourish Klink: "Laugh Out Loud in Real Life: Twilight, Women's Humor, and Fan Identity"
Sheila Seles: "Audience Research for Fun and Profit: Rediscovering the value of television audiences"
Florence Gallez: "Open Park Online News Production: A Proposal for a Code of Ethics for Collaborative Journalism in the Digital Age"
Audubon Dougherty: "New Medium, New Practice: Civic production in live-streaming mobile video"
Nick Seaver: "A Brief History of Re-performance"
Madeleine Elish: "The Evolution of the Companion Species: Creating Realms of Possibility for the Personal Computer"
Jason Begy "Interpreting Abstract Games: The Metaphorical Potential of Formal Game Elements"
Elliot Pinkus: "The Physicality of Floating Numbers"
Hillary Kolos: "Not in it just to win it: Inclusive gaming in an MIT dorm"
Michelle Moon Lee: "Designing Game Ethics: A Pervasive Game Adaptation of The Count of Monte Cristo"
I'm not advising any CMS masters students this year, but this program does allow for research into my area of interest (computational art and media) and should accommodate more research in these areas in the future. (The program has had some great thesis on computational media in the past, too: Brett Camper's work on the Game Boy Advance homebrew programming community is an example.) In 2010-2011, because the program is in transition to new co-directors, we won't have any graduate students around, but we will be running admissions for a class of masters students that will join us in 2011. If you're interested in working with me or my colleagues here at MIT on a masters degree, let me know.
Two to Read on ebr
That's electronic book review, which does indeed host electronic reviews of good old books, but also offers up scholarly articles on digital literature, as it has been doing for a while. Two recent articles, in particular, are not to be missed by those interested e-lit.
First, Daniel Punday's piece on how computer games could break the homogeneity of e-books, in which he describes the uniformity implicit in the e-book concept, in the idea of a modular library, and the disappointing implications of such restricted formats for digital, bookish innovation. Punday is more optimistic than I am about the possibility that gaming might lead us out of e-book thralldom, but whether or not he's right about this potential solution, he points out an important and overlooked aspect of the e-book situation that we need to attend to – at least, for instance, by being willing to build e-books as individual iPhone apps when we want to do more than the standard formats can accomodate.
And, Maire-Laure Ryan's discussion of how digital art engages with dysfunctionality extends the conversation beyond the playful forms of programming that Michael Mateas and I have discussed to broadly consider political, ludic, programmatic, and even inadvertent types of digital malfunctioning, or breakdown – or should we call it "dysfunctionality"? (Thank goodness that my creative work wasn't cited in the section about that last category of brokenness, although I'll admit that it could have been…) Ryan argues that the digital medium has proven better at producing anti-books than books (or, I suppose, e-books) and that creative dysfunction helps to make us "aware of the codes and processes (technological, linguistic, cultural and cognitive) that regulate our social and mental life."
PAX Blurb
This weekend was a great time, both at the official PAX-East, where we saw the premiere of Get Lamp, and in the alternate but connected universe of the People's Republic of Interactive Fiction Hospitality Suite, where Andrew Plotkin's organizational acumen and contributions allowed us to hear panels, write and play Speed IF games, and snack and converse. The 2010 IF Summit at PAX-East was a great success. There and at the main expo, I got to speak with people from the contemporary IF community and many old-school IF luminaries from Infocom and before – and even got to be on a panel with several of them.
Dave Lebling, Don Woods, Brian Moriarty, Andrew Plotkin, Nick Montfort, Steve Meretzky, Jason Scott (standing, in absurd outfit). It is April Fool's Day. Am I Photoshopped into this panel? Photo CC by Eric Havir.
And, I got to play on the proto-Ms. Pac Man board – the one Crazy Otto board that is known to still exist.
After PAX, I hosted a great reading of interactive fiction by Emily Short (who read from Alabaster) and Jeremy Freese (Violet), with interacting done by Kevin Jackson-Mead and Jenni Poladni. The event was at MIT (as with all Purple Blurb presentations), had standing room only, and prompted a great deal of good conversation afterwards.
There is much more that could be said, and many more PAX-East IF people that I could mention – a few of those, beyond the PR-IF regulars, are: Sam Kabo Ashwell, Liza Daly, Brendan Desilets, Stephen Granade, Juhana Leinonen, Jacqueline Lott, Jesse McGrew, Carl Muckenhoupt, Aaron Reed, Dan Schmidt, Robb Sherwin, Dan Shiovitz, Emily Short, and Rob Wheeler. (My apologies to those whose names I'm overlooking or don't have on hand.) Some of these are locals I rarely see; others are people I have known for years, had numerous extensive discussions with, and in one case, collaborated with, and yet PAX-East was my first chance to meet them in person.
Based on last weekend and last Monday, the outlook for IF is extremely bright: We can share games and discuss important questions about IF in person as well as online, we have plenty of ideas that we're making progress on but can certainly discuss further, and we have a documentary film coming on DVD that will please IF diehards and help to introduce students and other sympathetic viewers to the pleasures of the text adventure.
Post Position is Nick Montfort's blog about interactive narrative, imaginative and poetic writing (often digital), the material history of computational media, video and computer games, et cetera.
Please Discuss:
Ma?y Format on A Web Reply to the Post-Web Generation
Text-Savvy AI Is Here to Write Fiction – iTech – Blog: iOS • Android • Windows • Mac • Game • Technology on Nano-NaNoGenMo or #NNNGM
Nick Montfort on Nano-NaNoGenMo or #NNNGM
Nick Montfort on Computer-Generated Books
Stephen Pentecost on Computer-Generated Books
Months Past:


text:
Story of Chief Consolidated Operations in Tintic
The following article is excerpted from the article "Story of Chief Consolidated Operations in Tintic", in the August 8, 1916 issue of the Eureka Reporter
Iron Ore, one of the mining publications of the great copper district of Michigan, in its issue of August 2nd, 1918, has a most interesting front page story of the Tintic mining operations of Walter Fitch, whose keen foresight and splendid business ability gave our district its largest mining enterprise.
How the Chief Was Born
The idea of the enterprise was started by a trip made over the mountain to Eureka, Utah by J. R. Finley and Walter Fitch in 1906, this following the time when Mr. Fitch had given up his mining affairs in the Michigan iron and copper districts to take a look through the great west. They had made an inspection of the Mammoth and Grand Central mines laying in the southern part of the district, and concluded to walk back following the lime beds on their strike to the north. These lime beds Finlay recognized as of the same character as those enclosing the ore in those mines. These beds were followed over to the north slope of the mountain until on that side they were lost to view by the covering of rhyolite. The eruptive at this point presents its thin edge, gradually growing thicker until in the gorge where Eureka City is, it is estimated it has a thickness of approximately six or seven hundred feet. The Chief shaft occupies a position about midway between the large mountain and the town and there this rhyolite is about three hundred feet thick. The complete covering of lime stone measures in that section accounts for the failure of the prospectors and miners of the ore possibilities there and led to its being dubbed Poverty Flat.
There Was Small Shaft That Was Abandoned
The shaft referred to was at the time Mr. Fitch and Finlay made their trip of inquiry about eight hundred feet deep and was owned by a company known as the Little Chief. This company had been operating twelve years and had the distinction of having levied 43 assessments and of finding no ore. Mr. Fitch and Finlay wanted to go into the mine and were told this was against the rules.
Mr. Fitch finally decided that the opportunity was just as good as he had expressed himself concerning it, and he went in and carried out the plan, finding the ore zone, and ore in it of commercial grade and quantity.
The Good Results
The Chief Consolidated Company was then organized, and on February 16, 1909 took over all the property of the Little Chief. Since that time the company has mined 352,000 tons of ore which has yielded mineral as follows:
Gold 45,000 Ounces
Silver 8,250,000 Pounds
Lead 53,800,000
Copper 362,000
Zinc 2,200,000
In addition to the foregoing, several tons of manganese has been produced. For the sale of these products the company received $5,600,000, and has expended for opening the mine equipping it, making better than nineteen miles of workings: mining the ore, enlarging and sinking the shaft to the eighteen hundred level, enlarging the stations, putting in a pumping system, together with pump stations and reservoirs, and all the electric appliance connected with the pumps, also for exploring for ore in the different parts of the district, and the unsuccessful trying out of one mine outside of the district – the total of these cost about $3,000,000. There have been expended in acquiring new mineral lands about $1,000,000. The additions give the company an ownership of about 5,000 acres as against about 50 acres with which it started business. There has been paid out in dividends $1,124,342.12 and there are still on hand $300,000 in cash and $420,000 in liberty bonds.
Changed Views of Many Mining Men
The developments of Chief Consolidated have brought about a great change with respect to this particular mining camp or district whose early glories failed so fast because developments were not properly directed. Now that new ore zones have been found at greater depth and at considerable distances from former openings mining men have been attracted but find the best located claims are now all in the ownership of the Chief through the enterprise and far-sightedness of its management.
Are Wise Financially
The directors believe in the protection of infant industries, that good old Republican doctrine that has always worked out so well for those who practiced it. They therefore propose to maintain a liberal treasury, and have regularly set aside from the earnings of the company a liberal allowance each year, and this reserve has now reached a figure not far from the amount of its capital liability. This they deem necessary to insure proper protection to the enterprise, possibly to insure or to help maintain regularity of the dividend disbursements, to meet the contingencies resulting from the irregularity of its ore depositions, and the contained values, to meet the increasing exactions of war, and to prepare for the extending working capital demands of an expanding business.
Securing These Fine Results
A considerable part of these quite satisfactory results are said by those who are familiar with to be largely attributable to the concentrated efforts of the Fitch family, which was not only contented to leave Salt Lake City and live in Eureka, but has confined itself, with slight exception, exclusively to this particular enterprise. In doing this it has commandeered all outside necessary technical skill to help the work along and this included expert mechanical, electrical, metallurgical, geological and accounting men. The geology of the district has been intensively studied and plotted all the time, and for the last four years has had Mr. G W Crane, a special geologist, devoting his undivided attention to that special department.
To the sons of Mr. Fitch credit is given for having had direct charge of the work and of building up the fine organization now possessed. They opened the mine and established it as it is today. Cecil Fitch has always been the superintendent, taking that place on his graduation from the Michigan College of Mines at Houghton, Michigan. His brother Walter graduated a little later and worked as his assistant for six and a half years, and then went into the business of doing mine development work, having a couple of hundred expert shaft and drill men, and is conducting operations in three states.


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There has been a lot of recent discussions and questions about reputation, content and delivery of email. I started to answer some of them, and then realized there weren't any basic reference documents I could refer to when explaining the interaction. So I decided to write some.
This post is about IP address reputation with some background on why IPs are so important and why ISPs focus so heavily on the sending IP.
ISPs built reputation around IP addresses because it was one bit of data that malicious senders / spammers couldn't forge. The connecting IP is a fundamental part of the network transaction and if you forge an IP then SMTP can't work. Because that was the reliable data they had to work with, that's what they used. Even now, when there are other kinds of data, the IP address is still the first thing the receiving MTA sees.
IP reputation can best be summed up as "past performance is an indicator of future results." In other words if recipients responded well to mail from an IP address in the past, then they're likely to respond well to new mail from that IP address.
How many "known bad" email addresses (spamtraps) is this IP attempting to deliver to?
Does this IP stop mailing addresses after receiving a "user unknown" message?
That is by no means an exhaustive list of what ISPs measure. If they can measure it they've tried. If the measurement helps them separate spam mail from not-spam mail then they're using it.
IP reputation is often measured over multiple time periods. ISPs can look at a 1 day, 7 day, 30 day and 90 day reputation. A good analogy is stock prices. Prices can be very volatile in the short term, but more consistent over the long term. A single bad day, where one or more reputation measurements go bad, may affect delivery that day or the next day but won't damage an overall good reputation. Likewise, a few days of improved mail may not be sufficient to counter months of poor reputation.
Brief changes (for good or bad) don't necessarily ruin delivery over the long term.
While I understand and sympathize with the rationales and justifications used to make decisions based on the reputation of IP addresses, this strategy is fundamentally doomed. With IPv6, the vast amount of address space and the ease by which miscreants can change addresses means attempts to use IPv6 addresses as keys in a reputation database are going to get a bit complicated. What's the point of blocking an IP address if the bad guy can trivially source their spam from 2^64 (or 2^96 or more) -1 alternatives? Worse, with the likely inevitable deployment of large scale/carrier grade NAT, entire universes of users are going to be represented by a single IPv4 address. It is unlikely that a service that relies upon IP reputation is going to have a happy experience blocking a single IPv4 address when blocking that address is going to block thousands (or more) innocent users/sites/etc.
IP(v4) address reputation was a valuable tool, but that tool's usefulness is rapidly drawing to a close. Continued use of that tool past its sell-by date is a recipe for unhappy users and a broken Internet. Folks who currently use IP reputation really need to find alternatives to determining the legitimacy of traffic sources.
There's a lot of rhetoric in your comment (the second paragraph in particular), but not a lot of reasoning to back it up. Concentrating on the reasoning alone, I see two points: the vastness of the IPv6 address space, and IPv4 address sharing as a consequence of NAT.
On the first point, yes, it will be ineffective to blacklist individual IPv6 addresses in the face of an opponent with control over his client IP addresses. This makes it unlikely that anyone will try to represent reputation at such a fine-grained level. Instead, the probable approach will be some form of address aggregation, with a reputation assigned to that range of addresses. This already happens with IPv4 anyhow: if numerous addresses in a range exhibit bad behaviour, it's often simplest to describe the whole surrounding address range as disreputable.
The second point, of NAT, is even less of an issue. It has been out there in the wild for some time now, and if it's creating headaches for IP reputation measurement, I haven't heard about it. Your primary concern in this area seems to be the issue of collateral damage — the blocking of "innocent users/sites/etc" along with the bad actors. Again, this is not a new issue. The defining moments in that saga happened in 1998, when Paul Vixie's RBL decided to list the likes of netcom.com and msn.com for being too spam-friendly. The collateral damage was significant at the time, but there was a long-term benefit: network owners have been taught that they can not simply deny all responsibility for the actions of their users — and nobody is too big to block. I believe the Internet today would be a worse place if not for this piece of history.
In short, if ISPs want the reputation of their NAT IP ranges to be positive, it's up to them to enforce the appropriate terms of service on their users. If address-sharing like this makes the job harder, and makes the potential collateral damage worse in the case of a bad reputation, then guess what: that's the network owner's problem, not everyone else's problem.
Reputation, as a concept, is only going to get more important, not less. The changing identity landscape of IPv6 will have its impact, so be sure, but unless you fix human nature, or eliminate all the bad actors from the network, public-facing services can be made much more robust with the appropriate use of reputation information than without.
Given that most tunneled v6 providers are glad to give you very "large sounding" v6 CIDRs - all of them on a tunnel mapped to your 1U pizzabox colo with a single v4 address .. why should reputation providers restrict themselves to blocking /128 at a time?
And v4 is going to be there almost forever at least for email.
Folks who are relying on IP reputation are basing decisions about whether to (for example) accept email or block access to websites based on past traffic emanating from that IP address (or block of IP addresses if you prefer). In a world where addressing is relatively stable and usually maps one-to-one, this makes sense. I believe we are rapidly leaving that world.
In the case of IPv6, the (presumably) increasing ease in which one may obtain IPv6 addresses will probably mean it'll be straightforward to get a block, use it, discard it, and get another. Are folks relying on IP reputation going to block address blocks they see for the first time? I hope not. As for blocking aggregates, how much of a prefix will get blocked? A /64? /56? /48? /32? How big do you think these block lists will get before they become unmanageable? Then there is http://www.circleid.com/posts/why_dns_blacklists_dont_work_for_ipv6_networks/.
With respect to IPv4, no longer will single organizations be behind an IPv4 address, rather it'll be a number of (likely dynamically changing) unrelated organizations who happen to map into the same NAT'd address(es). If a customer of a CGN-deploying major ISP (and I suspect it'll be major ISPs that deploy CGN due to cost) happens to have a machine zombified and subsequently sends out spam, the IP address that spam will be coming from will the the same one shared by (dozens,hundreds,thousands) of other unrelated organizations. Will reputation services block the entire major ISP? And yes, I can assure you that this is indeed a problem today any place multiple sites get aggregated into a single address. For example, in multi-site web hosting, the various "cloud"-based services, and shared addressing virtualized server farms.
And then there is the issue of IPv4 address reuse. Even today with relatively low IPv4 address churn, folks getting 'previously loved' IPv4 address blocks are often faced with trying to get their blocks removed from various blacklists that the previous owners of the blocks happened to have gotten themselves on. In the future, as address blocks get "transferred" more frequently, this problem is probably going to get (much) worse.
At some point, I figure folks who are relying on IP reputation as a means of blocking are going to get weary of innocent folks calling them up and yelling at them. I agree reputation as a concept is going to get more important, but basing that reputation on the likely increasingly ephemeral nature of the then current mapping of IP address to traffic generation seems to be a losing proposition.
In the case of IPv6, the (presumably) increasing ease in which one may obtain IPv6 addresses will probably mean it'll be straightforward to get a block, use it, discard it, and get another.
It would be unwise to increase the ease with which one may obtain an address block for this very reason. There must be appropriate and reasonable barriers to obtaining additional address blocks, just so that miscreants don't treat it like a cookie jar into which they may dip their hands as they please. Even the IPv6 address space can be exhausted if you treat it as a consumable (rather than durable) resource.
The general problem of reputation laundering through identity change is also a reason why "no reputation" must be distinguished from "good reputation" and "bad reputation".
As for blocking aggregates, how much of a prefix will get blocked?
Suresh has voiced an opinion on this, above. I expect that it will relate to the size of the allocation and the type of network owner. Experience will be necessary to determine what is effective.
As for the article by John Levine to which you provide a link, yes, existing practices in relation to IPv4 don't map straightforwardly into the larger IPv6 space. There is nothing to suggest that this problem is insoluble, however: the article mentions several avenues of research, and I'm sure it's not an exhaustive list. Rumours of the death of DNSBLs have been greatly exaggerated, although it may be time to stop using DNS, as such. DNS was never the ideal protocol, just an adequate and extremely convenient hack.
If a customer of a CGN-deploying major ISP (and I suspect it'll be major ISPs that deploy CGN due to cost) happens to have a machine zombified and subsequently sends out spam, the IP address that spam will be coming from will the the same one shared by (dozens,hundreds,thousands) of other unrelated organizations. Will reputation services block the entire major ISP?
Whatever address range is used by the NAT will attract a deservedly poor reputation. This may result in the address range being blocked outright, or merely downgraded in various ways. Yes, this is happening even as we speak. It's a poor idea to set up SMTP clients behind a NAT range for this reason (among others). SMTP servers require a static IP address; SMTP clients don't, but it's advisable unless you are a miscreant deliberately trying to work around the effects of a bad reputation.
We don't need NAT to experience this problem: if customers use their ISP's mail servers for outgoing mail, then they share the reputation of those mail servers. This is why it's important for ISPs to be pro-active about acceptable use, including unwitting violations like zombies. This also goes for cloud services and similar arrangements: the service providers must manage the behaviour of their users, or the reputation of the service provider will suffer, and their future customers will be unhappy customers. As I said before, that's the network owner's problem, not everyone else's problem.
And then there is the issue of IPv4 address reuse.
Yes, it's important to investigate the reputation of any address block one might acquire. The same applies for domain names, which might be similarly tarnished by previous owners. Address reuse should be considerably less of an issue under IPv6, though, shouldn't it? So the rise of IPv6 is not all bad news for reputation.
At some point, I figure folks who are relying on IP reputation as a means of blocking are going to get weary of innocent folks calling them up and yelling at them.
No, we've already been down this path. The smart ESPs listen to their customers, not the people sending mail to their customers. So long as the customers are happy, it's all good. The mail senders can be politely instructed to fix the problem at their end, no matter how indignantly they yell. If the customers are complaining about false positives, then there may be a need to do something, but even the customers tend to get the picture when given the option to turn filtering off. Reputation-based filtering doesn't need to be perfect — it just needs to be better when it's turned on than turned off.
There are a couple of lingering issues that I feel are implied by your comments, which need to be addressed explicitly. First, you seem to imply or assume that "reputation is forever"; second, you seem to imply or assume that "bad reputation means outright blocking". Both of these may be true for the simplest approach to the problem: dumping address ranges into a local firewall or "deny service" list. This does happen, but not usually in large scale operations. Reputation service providers (e.g. DNSBLs) treat reputation as a dynamic thing: if an address range cleans up its act, its reputation improves. Similarly, outright blocking is just one possible response to a bad reputation, and not always the best one. There's a lot to be said for accepting delivery of disreputable mail to a "spam" folder.
I do not subscribe to your prophecies of doom.
It would be unwise to increase the ease with which one may obtain an address block for this very reason.
Given that most tunneled v6 providers are glad to give you very "large sounding" v6 CIDRs - all of them on a tunnel mapped to your 1U pizzabox colo with a single v4 address.
I'm not sure this supports your point regarding not increasing the ease by which one can obtain IPv6 addresses.
It's a poor idea to set up SMTP clients behind a NAT range for this reason (among others).
This implies you have a choice. In a world where IPv4 addresses are either unavailable or are available only at high cost, I'm guessing choices will be limited. It seems likely you will see a proliferation of services (SMTP included) residing behind CGN/LSN. The obvious alternatives, such as relying on "cloud" based services, are undoubtedly going to proliferate, but I seem to recall a non-trivial amount of spam (etc) originating from those services today and I'm unsure how effective reputation services are against Google, AWS, etc. Maybe this will improve in the future.
I believe that reputation services that base decisions on increasingly ephemeral data such as the IP address from which badness originates are likely to cause more and more non-trivial collateral damage over time. It may be that you are correct and people will ignore the damage and continue to use such services (I have some skepticism since communication between two parties tends to require both parties are able to hear each other), but I would argue that this does not bode well for the reliability of Internet services or for the Internet's model of providing those services.
These are hardly the sort of IPs you would expect to connect directly to your MX to deliver mail inbound to you. Outbound mail on the other hand - yes, certainly - but I can't think of any ISP dumb enough to use a DNSBL to blindly filter their outbound mail stream.
So I would put it to you that the IP address of a real mailserver is just not likely to be ephemeral, whereas dhcpv6 connected devices - sure.
And I would also put it to you that real mailservers, emitting real SMTP traffic, are going to be a vanishingly small fraction of the larger v6 IP space, compared to whatever other IP capable devices that get v6 connectivity.
No filtering provider relies 100% on IP reputation. But it is an extremely important data point for them. And I just don't see v6 suddenly deprecating IP reputation at all.
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ACCL » Ahlers, John P.
Mr. Ahlers is a founding member of the firm, his practice has focused on the resolution of construction disputes since 1983. John's experience spans from small private construction to complex engineering, building, heavy construction and insurance matters. He represents owners, general contractors, subcontractors, suppliers, architects, engineers, and construction industry trade associations. John has handled a large number of jury and non-jury trials, as well as arbitrations and mediations involving a wide variety of construction related disputes. Mr. Ahlers has argued cases before all three Divisions of the Washington State Court of Appeals, before the Washington Supreme Court, the Alaska Supreme Court, and before the Federal Circuit, Ninth Circuit and Tenth Circuit Courts of Appeal.
U.S. Court of Appeals for the Federal Circ.


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I remember the time when I wanted to meet up with him to find out what he was doing with his life. He was then teaching at one of the shop houses along Jalan Pantai – possible with Yayasan Anda if I am not mistaken. I did find him and he was indeed teaching and in slippers. At home that evening I casually told my father that I had met Anwar that afternoon. My father was then Director of CID. He stopped, looked at me and said sternly "Engkau tak ada kerja lain?" Whenever my father uses "engkau" when addressing me I knew that he was not amused. And he then went on to lecture me as to why it would be in my best interest to keep away from Anwar!
Then I was away in Australia for a while and he became DPM. I was at Ampang Shopping center with my Family patiently letting my kids wander around Toy R Us. As we walked up to the counter to pay there was Anwar. We hug and he smiled that smile that light up his whole face and then he was gone again out of my life for a few more years. But always the familiarity of old classmates made for easy banter every time we meet.
Then this time he was away for a while – six years I think – as the British like to say – At her Majesty's pleasure in Sungai Buloh. I was with one of UMNO ex Ketua Bahgian who had joined Keadilan when we heard that Anwar had been released and was at home. My friend wanted to immediately head for Anwar's house in Damansara to pay his respect. Would I like to come along? He asked. I said ok. We arrived and there were people everywhere. We got into line and waited our turn. We were told that Anwar was not well – that he was sitting down and that anytime he might need to rest. One hour of waiting in line I eventually stood in front of him. He looked up from his chair, again with that smile of his, stood up and gave me a hug oblivious to what pain he must have felt –we talked for a few seconds and mindful of the others waiting to see him, I excused myself and walked on.
The last time I saw him was at a class get together in Bangsar – at Fauzi's house, a school mate of ours who was the host - a few years back. As always his arrival was greeted with good nature ribbing and for the son of one of our classmates who had not seen Anwar before – that was a real treat. We sat and talked and I could see that age had caught up with all of us – Anwar included. He looked not as robust as I though he would be- after all he has always looked good whenever he was on TV and photographed well. But sitting beside me he looked vulnerable.
Was the pressure of living constantly under public and media gaze getting to him? Was UMNO getting to him? I could not imagine what he had to go through on a daily basis in what he chose to do – POLITICS. It is one thing to be DPM where everything is laid out for you, another to be in the opposition. He constantly referred to Azizah in conversation with us and we could see that Family meant a great deal with him. As we talked I found myself thinking what more has he got to endure before his work is done. I did not envy the situation he was in.
But he had no regrets. No wanting to take his pound of flesh from those that have done him ill. A more spirited discourse came from him when we talked about Mahathir – but either he was in control of himself or that he did not think it worth his while to think to much of times gone by. The present was what mattered.
At 63 I will not run if I can walk. Stand if I can sit. Talk if I can be quiet. Anwar has chosen the path less traveled. This path requires an uncommon resolve to move relentlessly ahead no matter what. He stands in front of crowds everyday. He meets more people then he can remember everyday and all this he does with a willingness that belittle his age. He could be anywhere he wants to be in the world and be welcomed by world leaders and acquaintances. He could be in business and be rich beyond our wildest dreams. Instead he chose to serve the nation. He chose to take us to the next election because if Anwar does not do so, who will take us? I am sure sometimes in his moment of solitude he must question his capacity to physically last the distance but his commitment to our cause is great. That will see him through and he has said that Azizah has done enough while he was away.
This is a good man. As we all know he cannot sing well, neither can he dance well even if his life depended on it but he is decent man. I wish Najib and UMNO will do battle with him on a level playing field. I wish they could have enough compassion in their hearts to accept that Anwar had gone though more that a baptism of fire – a baptism that neither Najib or Muhyiddin could ever imagine or endure. But then it that would be like asking Bush to go fight Saddam one on one. No shock or awe, no overwhelming force meeting defenseless people, no doctrine of Rapid Dominance, no weapon of mass destruction on stand by just in case they are needed….none of the above. Bush would never survive.
We know that Anwar was with UMNO many years back. We do not know what he will be in the future. But this I know now. He and the other leaders in Pakatan Rakyat are the leaders we now have to lead us to the next General Election and they give us our best hope for a new beginning – without an UMNO that has already abused the trust we Malays placed in them many times over, without a corrupt PDRM, a cowered MACC, without a Government that steals from its people, without a Judiciary that does the bidding of its Political masters, without many of the injustices and unfairness that we now have. Are these not reason enough for us to give them the opportunity to do so?
Not guilty this time!:) This voice of conscience is decidedly Hussein Hamid.


The following modifications are only available to synthmorphs/robots.
Even synthmorphs can have difficulty with the cryonic temperatures found in the outer system. While almost any synthmorph can operate normally for at least an hour at these temperatures, longer exposure can cause materials to get brittle and joints to lock up, especially in an atmosphere thick enough to conduct heat away from the morph.
This cybernetic system implants nozzles in the morph's chest, back, and limbs, allowing it to maneuver in microgravity using vectored bursts of gas. It either inputs atmospheric gases through implanted intakes or draws gas from an oxygen reserve implant. This mod applies a +10 modifier to Freefall Tests.
The morph's skeleton has been laced with strengthening materials. Apply a +5 DUR and +5 SOM bonus.
The synthmorph's frame is loaded with armor that offers protection from heavy weapons for serious combat operations. This modification is bulky and noticeable; the bot frame is encased in a heavy-duty carapace. It increases the bot's built-in Armor to 16/16. The shell's mobility systems and power output are also enhanced to deal with the extra load.
Hoppers have two or more legs designed to propel the morph forward or up, much like a frog or grasshopper.
The shell uses an impeller to blast a cushion of high-pressure air off the surface below, repelling the frame off the ground (modern hovercraft do not use rubber skirts). Most hovercraft travel a meter or so above the ground, but can temporarily levitate themselves higher for short periods.
The shell is equipped with protection against collisions, extreme weather, industrial accidents, and similar wear-and-tear. Increase the bot's built-in Armor rating to 10/10.
This miniature metallic hydrogen rocket is specifically designed for low thrust. It provides an acceleration of up to 0.25 g, allowing the morph to take off and land on all moons and other small bodies in the solar system. This engine can operate for a total of one and a half hours before it requires refueling. Both the sundiver (p. 164, Sunward) and courier (p.
The shell uses principles of magnetohydrodynamics to levitate and fly, by ionizing surrounding air into plasma to create lift and momentum. The shell is also spun for stability. This system does not work in vacuum, but an underwater version uses the same mechanics for propulsion in liquid environments.
The synthmorph's frame is protected by armor designed for policing and security duties. This increases the bot's built-in Armor to 14/12.
Popular in low-grav and microgravity environments, microlights encompass several types of ultralight or lighter-than-air systems, such as powered paragliders, autogyros, balloons, aerostats, and blimps. These systems do not work in vacuum.


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text:
package com.facebook.buck.rules.macros;

/** Macro that resolves to the output location of a build rule. */
public abstract class UnconfiguredBaseLocationMacro extends UnconfiguredBuildTargetMacro {}

redpajama_set_name: RedPajamaGithub


This took way longer than I expected it to, but the first entry in my Under Cover series - Love Is A Verb - is finally here! It's a great tune by John Mayer and I highly recommend you take a listen to the original. Enjoy.


text:
FAQ: Who Were The Rulers Of The Synagogue In Mark?
1 Who were the rulers of the synagogue?
2 Who was Jairus the synagogue leader?
3 Who was Jairo in the Bible?
4 What town was Jairus from?
5 What is the meaning of Mark 5?
6 What does Talitha Cumi mean?
7 Who is the daughter of Jesus?
8 Did Jesus raise the dead?
9 Who was the first person Jesus brought back to life?
10 Where did Jesus turn the water into wine?
11 What does it mean to carry your own cross and follow Jesus?
12 What is the name of Jairus daughter in the Bible?
13 What does the name Jairus mean in the Bible?
14 Who is the father of James?
Who were the rulers of the synagogue?
The 'leader of the synagogue' (NRSV, Luke 8: 41) was an official appointed by the elders to look after the building, its contents, and its arrangements for worship.
Who was Jairus the synagogue leader?
Jairus (Greek: Ἰάειρος, Iaeiros, from the Hebrew name Yair), a patron or ruler of a Galilee synagogue, had asked Jesus to heal his 12-year-old daughter. As they were traveling to Jairus' house, a sick woman in the crowd touched Jesus' cloak and was healed of her sickness.
Who was Jairo in the Bible?
Jairo is the Spanish equivalent of Jair which is a Hebrew name meaning "he shines" Jair shows up in the Bible, in the Old Testament (Numbers) as the son of Manasseh which would make Jair the grandson of Joseph and the great-grandson of Jacob/Israel.
What town was Jairus from?
The location is the village of Nain, two miles south of Mount Tabor. This is the first of three miracles of Jesus in the canonical gospels in which he raises the dead, the other two being the raising of Jairus' daughter and of Lazarus.
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What is the meaning of Mark 5?
Mark 5 is the fifth chapter of the Gospel of Mark in the New Testament of the Christian Bible. Taken with the calming of the sea in Mark 4:35–41, there are "four striking works [which] follow each other without a break": an exorcism, a healing, and the raising of Jairus' daughter.
What does Talitha Cumi mean?
Talitha (Classical Syriac: ܛܠܝܼܬ݂ܵܐ/ܛܠܻܝܬ݂ܳܐ ṭlīṯā or ṭlīṯō) is an uncommon feminine name meaning " little girl " in Aramaic, given in reference to the Biblical story in the Gospel of Mark in which Jesus Christ was said to have resurrected a dead child with the words "Talitha cumi" or "Talitha kum" or "Talitha koum,"
Who is the daughter of Jesus?
Some wish the ceremony that celebrated the beginning of the alleged marriage of Jesus and Mary Magdalene to be viewed as a "holy wedding"; and Jesus, Mary Magdalene, and their alleged daughter, Sarah, to be viewed as a "holy family", in order to question traditional gender roles and family values.
Did Jesus raise the dead?
This is the first of three miracles of Jesus in the canonical gospels in which he raises the dead, the other two being the raising of Jairus' daughter and of Lazarus.
Who was the first person Jesus brought back to life?
The miraculous story of Lazarus being brought back to life by Jesus is known from the Gospel According to John (11:1–45). Lazarus of Bethany was the brother of Martha and Mary and lived at Bethany, near Jerusalem.
You might be interested: FAQ: Why Synagogue Are Moorish Architecture?
Where did Jesus turn the water into wine?
The transformation of water into wine at the Marriage at Cana or Wedding at Cana is the first miracle attributed to Jesus in the Gospel of John.
What does it mean to carry your own cross and follow Jesus?
Three of the Gospels mention Jesus saying, " Take up your cross and follow Me." He meant that people should follow in his ways in order to be good disciples. Then Jesus said to his disciples, "Whoever wants to be my disciple must deny themselves and take up their cross and follow me.
What is the name of Jairus daughter in the Bible?
He says " Talitha cumi ", which means "Little girl, get up."
What does the name Jairus mean in the Bible?
Meaning: God enlightens. Jairus as a boy's name is pronounced JARE-us. It is of Hebrew origin, and the meaning of Jairus is "God enlightens". Biblical: Jarius was the father of a young girl resurrected by Jesus.
Who is the father of James?
The Feeding of the 5,000 is also known as the "miracle of the five loaves and two fish"; the Gospel of John reports that Jesus used five loaves and two fish supplied by a boy to feed a multitude.
Readers ask: How Jews Dress Up For Synagogue?
How Many Synagogue In Iran?