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%===================================================================================
\chapter{Mathematical Considerations}\label{s:math}
%===================================================================================

% What does CVODE do?
%--------------------
{\cvode} solves ODE initial value problems (IVPs) in real $N$-space, which we
write in the abstract form
\begin{equation}\label{e:ivp}
  \dot{y} = f(t,y) \, ,\quad y(t_0) = y_0 \, ,
\end{equation}
where $y \in \mbox{\bf R}^N$.
Here we use $\dot{y}$ to denote $dy/dt$.  While we use $t$ to denote
the independent variable, and usually this is time, it certainly need
not be.  {\cvode} solves both stiff and nonstiff systems.  Roughly
speaking, stiffness is characterized by the presence of at least one
rapidly damped mode, whose time constant is small compared to the time
scale of the solution itself.

%------------------------
\section{IVP solution}\label{ss:ivp_sol}
%------------------------

% Linear multistep methods
%-------------------------
The methods used in {\cvode} are variable-order, variable-step multistep
methods, based on formulas of the form
\begin{equation}\label{e:lmm}
 \sum_{i = 0}^{K_1} \alpha_{n,i} y^{n-i} +
     h_n \sum_{i = 0}^{K_2} \beta_{n,i} {\dot{y}}^{n-i} = 0 \, .
\end{equation}
Here the $y^n$ are computed approximations to $y(t_n)$, and
$h_n = t_n - t_{n-1}$ is the step size.  The user of {\cvode} must choose
appropriately one of two multistep methods.  For nonstiff problems,
{\cvode} includes the Adams-Moulton formulas \index{Adams method},
characterized by $K_1 = 1$
and $K_2 = q$ above, where the order $q$ varies between $1$ and $12$.
For stiff problems, {\cvode} includes the Backward Differentiation
Formulas (BDFs)  \index{BDF method}
in so-called fixed-leading coefficient form, given by
$K_1 = q$ and $K_2 = 0$, with order $q$ varying between $1$ and $5$.
The coefficients are uniquely determined by the method type, its
order, the recent history of the step sizes, and the normalization
$\alpha_{n,0} = -1$.  See \cite{ByHi:75} and \cite{JaSD:80}.

% Nonlinear system
%-----------------
\index{nonlinear system!definition|(}
For either choice of formula, the nonlinear system
\begin{equation}\label{e:nonlinear}
  G(y^n) \equiv y^n - h_n \beta_{n,0} f(t_n,y^n) - a_n = 0 \, ,
\end{equation}
where $a_n\equiv\sum_{i>0}(\alpha_{n,i}y^{n-i}+h_n\beta_{n,i} {\dot{y}}^{n-i})$,
must be solved (approximately) at each integration step.  For this, {\cvode}
offers the choice of either {\em functional iteration}, suitable only
for nonstiff systems, and various versions of {\em Newton iteration}.
Functional iteration, given by
\[ y^{n(m+1)} = h_n \beta_{n,0} f(t_n,y^{n(m)}) + a_n \, , \]
involves evaluations of $f$ only.  In contrast, Newton iteration requires
the solution of linear systems
\begin{equation}\label{e:Newton}
  M [y^{n(m+1)} - y^{n(m)}] = -G(y^{n(m)}) \, ,
\end{equation}
in which
\begin{equation}\label{e:Newtonmat}
  M \approx I - \gamma J \, ,
  \quad J = \partial f / \partial y \, ,
  \quad \mbox{and} \quad
  \gamma = h_n \beta_{n,0} \, .
\end{equation}
The initial guess for the iteration is a predicted value $y^{n(0)}$
computed explicitly from the available history data.
\index{nonlinear system!definition|)}

For the solution of the linear systems within the Newton corrections,
{\cvode} provides several choices, including the option of an user-supplied
linear solver module. The linear solver modules distributed with {\sundials}
are organized in three families, a {\em direct} family comprising direct linear
solvers for dense or banded matrices, a {\em sparse} family comprising
direct linear solvers for matrices stored in compressed-sparse-column
format, and a {\em spils} family comprising
scaled preconditioned iterative (Krylov) linear solvers.
%%
In addition, {\cvode} also provides a linear solver module which only uses
a diagonal approximation of the Jacobian matrix.
%%
The methods offered through these modules are as follows:
\begin{itemize}
\item dense direct solvers, using either an internal implementation or
  a Blas/Lapack implementation (serial or threaded vector modules only),
\item band direct solvers, using either an internal implementation or
  a Blas/Lapack implementation (serial or threaded vector modules only),
\item sparse direct solvers, using either the KLU sparse solver
  library \cite{KLU_site}, or the PThreads-enabled SuperLU\_MT sparse
  solver library \cite{SuperLUMT_site} (serial or threaded vector modules only),
\item a diagonal approximate Jacobian solver,
\item {\spgmr}, a scaled preconditioned GMRES (Generalized Minimal Residual method)
  solver without restarts,
\item {\spbcg}, a scaled preconditioned Bi-CGStab (Bi-Conjugate Gradient Stable
  method) solver, or
\item {\sptfqmr}, a scaled preconditioned TFQMR (Transpose-Free Quasi-Minimal
  Residual method) solver.
\end{itemize}
For large stiff systems, where direct methods are not feasible, the
combination of a BDF integrator and any of the preconditioned Krylov
methods ({\spgmr}, {\spbcg}, or {\sptfqmr}) yields a powerful tool
because it combines established methods for stiff integration,
nonlinear iteration, and Krylov (linear) iteration with a
problem-specific treatment of the dominant source of stiffness, in the
form of the user-supplied preconditioner matrix \cite{BrHi:89}.
%%
Note that the direct linear solvers (dense, band and sparse) can only be
used with the serial and threaded vector representations.

% WRMS Norm
%----------
\index{weighted root-mean-square norm|(}
In the process of controlling errors at various levels, {\cvode} uses a
weighted root-mean-square norm, denoted $\|\cdot\|_{\mbox{\scriptsize WRMS}}$,
for all error-like quantities.  The multiplicative weights used are
based on the current solution and on the relative and absolute
tolerances input by the user, namely
\index{tolerances}
\begin{equation}\label{e:errwt}
 W_i = 1 / [\mbox{\sc rtol} \cdot |y_i| + \mbox{\sc atol}_i ] \, .
\end{equation}
Because $1/W_i$ represents a tolerance in the component $y_i$, a vector
whose norm is 1 is regarded as ``small.''  For brevity, we will
usually drop the subscript WRMS on norms in what follows.
\index{weighted root-mean-square norm|)}

% Newton iteration
%-----------------
\index{nonlinear system!Newton iteration|(}
In the cases of a direct solver (dense, band, sparse, or diagonal), the
iteration is a Modified Newton iteration, in that the iteration matrix
$M$ is fixed throughout the nonlinear iterations.  However, for any of
the Krylov methods, it is an Inexact Newton iteration, in which $M$ is
applied in a matrix-free manner, with matrix-vector products $Jv$
obtained by either difference quotients or a user-supplied routine.
The matrix $M$ (direct cases) or preconditioner matrix $P$ (Krylov
cases) is updated as infrequently as possible to balance the high costs
of matrix operations against other costs.  Specifically, this matrix
update occurs when:
\begin{itemize}
\item starting the problem,
\item more than 20 steps have been taken since the last update,
\item the value $\bar{\gamma}$ of $\gamma$ at the last update
satisfies $|\gamma/\bar{\gamma} - 1| > 0.3$,
\item a non-fatal convergence failure just occurred, or
\item an error test failure just occurred.
\end{itemize}
When forced by a convergence failure, an update of $M$ or $P$ may or
may not involve a reevaluation of $J$ (in $M$) or of Jacobian data
(in $P$), depending on whether Jacobian error was the likely cause of
the failure.  More generally, the decision is made to reevaluate $J$
(or instruct the user to reevaluate Jacobian data in $P$) when:
\begin{itemize}
\item starting the problem,
\item more than 50 steps have been taken since the last evaluation,
\item a convergence failure occurred with an outdated matrix, and
the value $\bar{\gamma}$ of $\gamma$ at the last update
satisfies $|\gamma/\bar{\gamma} - 1| < 0.2$, or
\item a convergence failure occurred that forced a step size reduction.
\end{itemize}
\index{nonlinear system!Newton iteration|)}

% Newton convergence test
%------------------------
\index{nonlinear system!Newton convergence test|(}
The stopping test for the Newton iteration is related to the
subsequent local error test, with the goal of keeping the nonlinear
iteration errors from interfering with local error control.  As
described below, the final computed value $y^{n(m)}$ will have to
satisfy a local error test $\|y^{n(m)} - y^{n(0)}\| \leq \epsilon$.
Letting $y^n$ denote the exact solution of (\ref{e:nonlinear}), we want
to ensure that the iteration error $y^n - y^{n(m)}$ is small relative
to $\epsilon$, specifically that it is less than $0.1 \epsilon$.
(The safety factor $0.1$ can be changed by the user.)  For this, we
also estimate the linear convergence rate constant $R$ as follows.
We initialize $R$ to 1, and reset $R = 1$ when $M$ or $P$ is updated.
After computing a correction $\delta_m = y^{n(m)}-y^{n(m-1)}$, we
update $R$ if $m > 1$ as
\begin{equation*}
  R \leftarrow \max\{0.3R , \|\delta_m\| / \|\delta_{m-1}\| \} \, .
\end{equation*}
Now we use the estimate
\begin{equation*}
  \| y^n - y^{n(m)} \| \approx \| y^{n(m+1)} - y^{n(m)} \|
  \approx R \| y^{n(m)} - y^{n(m-1)} \|  =  R \|\delta_m \| \, .
\end{equation*}
Therefore the convergence (stopping) test is
\begin{equation*}
  R \|\delta_m \| < 0.1 \epsilon \, .
\end{equation*}
We allow at most 3 iterations (but this limit can be changed by the
user).  We also declare the iteration diverged if any $\|\delta_m\| /
\|\delta_{m-1}\| > 2$ with $m > 1$. If convergence fails with $J$ or
$P$ current, we are forced to reduce the step size, and we replace
$h_n$ by $h_n/4$.  The integration is halted after a preset number
of convergence failures; the default value of this limit is 10,
but this can be changed by the user.
\index{nonlinear system!Newton convergence test|)}

When a Krylov method is used to solve the linear system, its errors must also be
controlled, and this also involves the local error test constant.  The
linear iteration error in the solution vector $\delta_m$ is
approximated by the preconditioned residual vector.  Thus to ensure
(or attempt to ensure) that the linear iteration errors do not
interfere with the nonlinear error and local integration error
controls, we require that the norm of the preconditioned residual
be less than $0.05 \cdot (0.1 \epsilon)$.

% Jacobian DQ approximations
%---------------------------
With the direct dense and band methods, the Jacobian may be supplied
by a user routine, or approximated by difference quotients,
at the user's option.  In the latter case, we use the usual
approximation
\[ J_{ij} = [f_i(t,y+\sigma_j e_j) - f_i(t,y)]/\sigma_j \, . \]
The increments $\sigma_j$ are given by
\[ \sigma_j = \max\left\{\sqrt{U} \; |y_j| , \sigma_0 / W_j \right\} \, , \]
where $U$ is the unit roundoff, $\sigma_0$ is a dimensionless value,
and $W_j$ is the error weight defined in (\ref{e:errwt}).  In the dense
case, this scheme requires $N$ evaluations of $f$, one for each column
of $J$.  In the band case, the columns of $J$ are computed in groups,
by the Curtis-Powell-Reid algorithm, with the number of $f$ evaluations
equal to the bandwidth.

We note that with the sparse direct solvers, the Jacobian {\em must}
be supplied by a user routine in compressed-sparse-column format.

In the case of a Krylov method, preconditioning may be used on the left, on the
right, or both, with user-supplied routines for the preconditioning
setup and solve operations, and optionally also for the required
matrix-vector products $Jv$.  If a routine for $Jv$ is not supplied,
these products are computed as
\begin{equation}\label{jacobv}
Jv = [f(t,y+\sigma v) - f(t,y)]/\sigma \, .
\end{equation}
The increment $\sigma$ is $1/\|v\|$, so that $\sigma v$ has norm 1.

% Error test
%-----------
\index{error control!step size selection|(}
A critical part of {\cvode} --- making it an ODE ``solver'' rather than
just an ODE method, is its control of local error.  At every step, the
local error is estimated and required to satisfy tolerance conditions,
and the step is redone with reduced step size whenever that error test
fails.  As with any linear multistep method, the local truncation
error LTE, at order $q$ and step size $h$, satisfies an asymptotic
relation
\[ \mbox{LTE} = C h^{q+1} y^{(q+1)} + O(h^{q+2}) \]
for some constant $C$, under mild assumptions on the step sizes.
A similar relation holds for the error in the predictor $y^{n(0)}$.
These are combined to get a relation
\[ \mbox{LTE} = C' [y^n - y^{n(0)}] + O(h^{q+2}) \, . \]
The local error test is simply $\|\mbox{LTE}\| \leq 1$.  Using the above,
it is performed on the predictor-corrector difference
$\Delta_n \equiv y^{n(m)} - y^{n(0)}$ (with $y^{n(m)}$ the final
iterate computed), and takes the form
\[ \|\Delta_n\| \leq \epsilon \equiv 1/|C'| \, . \]
If this test passes, the step is considered successful.  If it fails,
the step is rejected and a new step size $h'$ is computed based on the
asymptotic behavior of the local error, namely by the equation
\[ (h'/h)^{q+1} \|\Delta_n\| = \epsilon/6 \, . \]
Here 1/6 is a safety factor.  A new attempt at the step is made,
and the error test repeated.  If it fails three times, the order $q$
is reset to 1 (if $q > 1$), or the step is restarted from scratch (if
$q = 1$).  The ratio $h'/h$ is limited above to 0.2 after two error test
failures, and limited below to 0.1 after three.  After seven failures,
{\cvode} returns to the user with a give-up message.
\index{error control!step size selection|)}

% Step/order control
%-------------------
\index{error control!order selection|(}
In addition to adjusting the step size to meet the local error test,
{\cvode} periodically adjusts the order, with the goal of maximizing the
step size.  The integration starts out at order 1 and varies the order
dynamically after that.  The basic idea is to pick the order $q$ for
which a polynomial of order $q$ best fits the discrete data involved
in the multistep method.  However, if either a convergence failure or
an error test failure occurred on the step just completed, no change
in step size or order is done.  At the current order $q$, selecting a
new step size is done exactly as when the error test fails, giving a
tentative step size ratio
\[ h'/h = (\epsilon / 6 \|\Delta_n\| )^{1/(q+1)} \equiv \eta_q \, . \]
We consider changing order only after taking $q+1$ steps at order $q$,
and then we consider only orders $q' = q - 1$ (if $q > 1$) or
$q' = q + 1$ (if $q < 5$).  The local truncation error at order $q'$
is estimated using the history data.  Then a tentative step size ratio
is computed on the basis that this error, LTE$(q')$, behaves
asymptotically as $h^{q'+1}$.  With safety factors of 1/6 and
1/10 respectively, these ratios are:
\[ h'/h = [1 / 6 \|\mbox{LTE}(q-1)\| ]^{1/q} \equiv \eta_{q-1} \]
and
\[ h'/h = [1 / 10 \|\mbox{LTE}(q+1)\| ]^{1/(q+2)} \equiv \eta_{q+1} \, . \]
The new order and step size are then set according to
\[ \eta = \max\{\eta_{q-1},\eta_q,\eta_{q+1}\} ~,~~ h' = \eta h \, , \]
with $q'$ set to the index achieving the above maximum.
However, if we find that $\eta < 1.5$, we do not bother with the
change.  Also, $h'/h$ is always limited to 10, except on the first
step, when it is limited to $10^4$.
\index{error control!order selection|)}

The various algorithmic features of {\cvode} described above, as
inherited from the solvers {\vode} and {\vodpk}, are documented in
\cite{BBH:89,Byr:92,Hin:00}.  They are also summarized in
\cite{HBGLSSW:05}.

% Output modes
%-------------
\index{output mode}
Normally, {\cvode} takes steps until a user-defined output value
$t = t_{\mbox{\scriptsize out}}$ is overtaken, and then it computes
$y(t_{\mbox{\scriptsize out}})$ by interpolation.  However, a
``one step'' mode option is available, where control returns to the
calling program after each step.  There are also options to force
{\cvode} not to integrate past a given stopping point
$t = t_{\mbox{\scriptsize stop}}$.

%------------------------
\section{Preconditioning}\label{s:preconditioning}
%------------------------
\index{preconditioning!advice on|(}
When using a Newton method to solve the nonlinear system (\ref{e:nonlinear}),
{\cvode} makes repeated use of a linear solver to solve linear systems of the form
$M x = - r$, where $x$ is a correction vector and $r$ is a residual vector.
If this linear system solve is done with one of the scaled preconditioned iterative
linear solvers, these solvers are rarely successful if used without preconditioning;
it is generally necessary to precondition the system in order to obtain acceptable efficiency.
A system $A x = b$ can be preconditioned on the left, as $(P^{-1}A) x = P^{-1} b$;
on the right, as $(A P^{-1}) P x = b$; or on both sides, as
$(P_L^{-1} A P_R^{-1}) P_R x = P_L^{-1}b$.  The Krylov method is then
applied to a system with the matrix $P^{-1}A$, or $AP^{-1}$, or
$P_L^{-1} A P_R^{-1}$, instead of $A$.  In order to improve the
convergence of the Krylov iteration, the preconditioner matrix $P$, or
the product $P_L P_R$ in the last case, should in some sense
approximate the system matrix $A$.  Yet at the same time, in order to
be cost-effective, the matrix $P$, or matrices $P_L$ and $P_R$, should
be reasonably efficient to evaluate and solve.  Finding a good point
in this tradeoff between rapid convergence and low cost can be very
difficult.  Good choices are often problem-dependent (for example, see
\cite{BrHi:89} for an extensive study of preconditioners for
reaction-transport systems).

The {\cvode} solver allow for preconditioning either
side, or on both sides, although we know of no situation where
preconditioning on both sides is clearly superior to
preconditioning on one side only (with the product $P_L P_R$).
Moreover, for a given preconditioner matrix, the merits of left vs. right
preconditioning are unclear in general, and the user should experiment
with both choices.  Performance will differ because the inverse of the
left preconditioner is included in the linear system residual whose
norm is being tested in the Krylov algorithm.  As a rule, however, if
the preconditioner is the product of two matrices, we recommend that
preconditioning be done either on the left only or the right only,
rather than using one factor on each side.

Typical preconditioners used with {\cvode} are based on approximations
to the system Jacobian, $J = \partial f / \partial y$.  Since the
Newton iteration matrix involved is $M = I - \gamma J$, any
approximation $\bar{J}$ to $J$ yields a matrix that is of potential
use as a preconditioner, namely $P = I - \gamma \bar{J}$.  Because the
Krylov iteration occurs within a Newton iteration and further also
within a time integration, and since each of these iterations has its
own test for convergence, the preconditioner may use a very crude
approximation, as long as it captures the dominant numerical
feature(s) of the system.  We have found that the combination of a
preconditioner with the Newton-Krylov iteration, using even a fairly
poor approximation to the Jacobian, can be surprisingly superior to
using the same matrix without Krylov acceleration (i.e., a modified
Newton iteration), as well as to using the Newton-Krylov method with
no preconditioning.  \index{preconditioning!advice on|)}

%------------------------
\section{BDF stability limit detection}\label{s:bdf_stab}
%------------------------

\index{Stability limit detection}
{\cvode} includes an algorithm, {\stald} (STAbility Limit Detection),
which provides protection against potentially unstable behavior of the
BDF multistep integration methods is certain situations, as described below.

When the BDF option is selected, {\cvode} uses Backward Differentiation
Formula methods of orders 1 to 5.  At order 1 or 2, the BDF
method is A-stable, meaning that for any complex constant $\lambda$ in
the open left half-plane, the method is unconditionally stable (for
any step size) for the standard scalar model problem $\dot{y} = \lambda y$.
For an ODE system, this means that, roughly speaking, as long as all
modes in the system are stable, the method is also stable for any
choice of step size, at least in the sense of a local linear stability
analysis.

At orders 3 to 5, the BDF methods are not A-stable, although they are
{\em stiffly stable}. In each case, in order for the method to be stable
at step size $h$ on the scalar model problem, the product $h\lambda$ must
lie in a {\em region of absolute stability}.
That region excludes a portion of the left half-plane that is concentrated
near the imaginary axis.  The size of that region of instability grows as the order
increases from 3 to 5.  What this means is that, when running BDF at
any of these orders, if an eigenvalue $\lambda$ of the system lies close
enough to the imaginary axis, the step sizes $h$ for which the method is
stable are limited (at least according to the linear stability theory)
to a set that prevents $h\lambda$ from leaving the stability region.
The meaning of {\em close enough} depends on the order.
At order 3, the unstable region is much narrower than at order 5,
so the potential for unstable behavior grows with order.

System eigenvalues that are likely to run into this instability are
ones that correspond to weakly damped oscillations.  A pure undamped
oscillation corresponds to an eigenvalue on the imaginary axis.
Problems with modes of that kind call for different considerations,
since the oscillation generally must be followed by the solver, and
this requires step sizes ($h \sim 1/\nu$, where $\nu$ is the frequency)
that are stable for BDF anyway.  But for a weakly damped oscillatory mode,
the oscillation in the solution is eventually damped to the noise level,
and at that time it is important that the solver not be restricted to step
sizes on the order of $1/\nu$.  It is in this situation that the new option may
be of great value.

In terms of partial differential equations, the typical problems for
which the stability limit detection option is appropriate are
ODE systems resulting from semi-discretized PDEs (i.e., PDEs discretized
in space) with advection and diffusion, but with advection dominating
over diffusion.
Diffusion alone produces pure decay modes, while advection tends to
produce undamped oscillatory modes.  A mix of the two with advection
dominant will have weakly damped oscillatory modes.

The {\stald} algorithm attempts to detect, in a direct
manner, the presence of a stability region boundary that is limiting
the step sizes in the presence of a weakly damped oscillation \cite{Hin:92}.
The algorithm supplements (but differs greatly from) the existing
algorithms in {\cvode} for choosing step size and order based on
estimated local truncation errors.  It works directly
with history data that is readily available in {\cvode}.  If it concludes
that the step size is in fact stability-limited, it dictates a
reduction in the method order, regardless of the outcome of the
error-based algorithm.  The {\stald} algorithm has been tested in
combination with the {\vode} solver on linear advection-dominated
advection-diffusion problems \cite{Hin:95}, where it works well.  The
implementation in {\cvode} has been successfully tested on linear
and nonlinear advection-diffusion problems, among others.

This stability limit detection option adds some overhead computational
cost to the {\cvode} solution.  (In timing tests, these overhead costs
have ranged from 2\% to 7\% of the total, depending on the size and
complexity of the problem, with lower relative costs for larger
problems.)  Therefore, it should be activated only when there is
reasonable expectation of modes in the user's system for which it is
appropriate.  In particular, if a {\cvode} solution with this option
turned off appears to take an inordinately large number of steps at
orders 3-5 for no apparent reason in terms of the solution time scale,
then there is a good chance that step sizes are being limited by
stability, and that turning on the option will improve the efficiency
of the solution.

%------------------------
\section{Rootfinding}\label{ss:rootfinding}
%------------------------

\index{Rootfinding}
The {\cvode} solver has been augmented to include a rootfinding
feature.  This means that, while integrating the Initial Value Problem
(\ref{e:ivp}), {\cvode} can also find the roots of a set of user-defined
functions $g_i(t,y)$ that depend on $t$ and the solution vector
$y = y(t)$.  The number of these root functions is arbitrary, and if
more than one $g_i$ is found to have a root in any given interval, the
various root locations are found and reported in the order that they
occur on the $t$ axis, in the direction of integration.

Generally, this rootfinding feature finds only roots of odd
multiplicity, corresponding to changes in sign of $g_i(t,y(t))$,
denoted $g_i(t)$ for short.  If a user root function has a root of
even multiplicity (no sign change), it will probably be missed by
{\cvode}.  If such a root is desired, the user should reformulate the
root function so that it changes sign at the desired root.

The basic scheme used is to check for sign changes of any $g_i(t)$ over
each time step taken, and then (when a sign change is found) to home
in on the root (or roots) with a modified secant method \cite{HeSh:80}.
In addition, each time $g$ is computed, {\cvode} checks to see if
$g_i(t) = 0$ exactly, and if so it reports this as a root.  However,
if an exact zero of any $g_i$ is found at a point $t$, {\cvode}
computes $g$ at $t + \delta$ for a small increment $\delta$, slightly
further in the direction of integration, and if any $g_i(t + \delta)=0$
also, {\cvode} stops and reports an error.  This way, each time
{\cvode} takes a time step, it is guaranteed that the values of all
$g_i$ are nonzero at some past value of $t$, beyond which a search for
roots is to be done.

At any given time in the course of the time-stepping, after suitable
checking and adjusting has been done, {\cvode} has an interval
$(t_{lo},t_{hi}]$ in which roots of the $g_i(t)$ are to be sought, such
that $t_{hi}$ is further ahead in the direction of integration, and
all $g_i(t_{lo}) \neq 0$.  The endpoint $t_{hi}$ is either $t_n$,
the end of the time step last taken, or the next requested output time
$t_{\mbox{\scriptsize out}}$ if this comes sooner.  The endpoint
$t_{lo}$ is either $t_{n-1}$, or the last output time
$t_{\mbox{\scriptsize out}}$ (if this occurred within the last
step), or the last root location (if a root was just located within
this step), possibly adjusted slightly toward $t_n$ if an exact zero
was found.  The algorithm checks $g$ at $t_{hi}$ for zeros and for
sign changes in $(t_{lo},t_{hi})$.  If no sign changes are found, then
either a root is reported (if some $g_i(t_{hi}) = 0$) or we proceed to
the next time interval (starting at $t_{hi}$).  If one or more sign
changes were found, then a loop is entered to locate the root to
within a rather tight tolerance, given by
\[ \tau = 100 * U * (|t_n| + |h|)~~~ (U = \mbox{unit roundoff}) ~. \]
Whenever sign changes are seen in two or more root functions, the one
deemed most likely to have its root occur first is the one with the
largest value of $|g_i(t_{hi})|/|g_i(t_{hi}) - g_i(t_{lo})|$,
corresponding to the closest to $t_{lo}$ of the secant method values.
At each pass through the loop, a new value $t_{mid}$ is set, strictly
within the search interval, and the values of $g_i(t_{mid})$ are
checked.  Then either $t_{lo}$ or $t_{hi}$ is reset to $t_{mid}$
according to which subinterval is found to have the sign change.  If
there is none in $(t_{lo},t_{mid})$ but some $g_i(t_{mid}) = 0$, then
that root is reported.  The loop continues until
$|t_{hi}-t_{lo}| < \tau$, and then the reported root location is
$t_{hi}$.

In the loop to locate the root of $g_i(t)$, the formula for $t_{mid}$
is
\[ t_{mid} = t_{hi} - (t_{hi} - t_{lo})
             g_i(t_{hi}) / [g_i(t_{hi}) - \alpha g_i(t_{lo})] ~, \]
where $\alpha$ a weight parameter.  On the first two passes through
the loop, $\alpha$ is set to $1$, making $t_{mid}$ the secant method
value.  Thereafter, $\alpha$ is reset according to the side of the
subinterval (low vs high, i.e. toward $t_{lo}$ vs toward $t_{hi}$)
in which the sign change was found in the previous two passes.  If the
two sides were opposite, $\alpha$ is set to 1.  If the two sides were
the same, $\alpha$ is halved (if on the low side) or doubled (if on
the high side).  The value of $t_{mid}$ is closer to $t_{lo}$ when
$\alpha < 1$ and closer to $t_{hi}$ when $\alpha > 1$.  If the above
value of $t_{mid}$ is within $\tau/2$ of $t_{lo}$ or $t_{hi}$, it is
adjusted inward, such that its fractional distance from the endpoint
(relative to the interval size) is between .1 and .5 (.5 being the
midpoint), and the actual distance from the endpoint is at least
$\tau/2$.

redpajama_set_name: RedPajamaGithub


text:
Oxneria ussuriensis is a species of corticolous, crustose lichen in the family Teloschistaceae. It is found in a single location in the Russian Far East.

Taxonomy

The lichen was formally described as a new species in 2014 by lichenologists Sergey Kondratyuk, Soon-Ok Oh, and Jae-Seoun Hur. The type specimen was collected by the first author from a park in Kraskino (in the Khasansky District of Primorsky Krai), where he found it growing on a Populus tree. The species epithet refers to the type locality.

Description
Oxneria ussuriensis has a deep orange to orange-yellow rosette-like thallus that has a diameter of . The individual lobes comprising the thallus are 1.5–2 mm long, and have a width that ranges from 0.3–0.7 mm in the narrowest parts to 1 mm in the widest parts. The terminal parts of the lobes sometimes branch out to form secondary lobes or lobules. The underside of the lobes are covered with bluish-greyish soredia. Individual soredia are irregularly elongated and have a diameter from 20 to 50 μm; sometimes soredia aggregate into larger structures (consoredia) that are irregularly rounded with a diameter of 60–70 μm.

The apothecia made by Oxneria ussuriensis are lecanorine in form with a diameter of 0.6–1.7 mm and a bright orange disc that is either flat or somewhat concave. Ascospores have a narrow ellipsoidal shape and dimensions of 9–23 by 5.5–10 μm.

Xanthomendoza huculica, found in Ukraine, is somewhat similar in appearance and morphology to Oxneria ussuriensis, but X. huculica has a larger thallus (up to 3 cm wide) made of larger lobes (2.5–7 mm long and 0.3–0.7 mm wide), and its spores have a smaller length range (10–17 μm) and are thinner (5–7 μm).

Habitat and distribution
Oxneria ussuriensis grows on the bark of roadside or parkland trees. It is only known from the type collection in the Russian Far East. Associated lichen species include Caloplaca ussuriensis, Candelaria concolor, Hyperphyscia adglutinosa, Phaeophyscia adiastola, Physconia detersa, and species from the genera Arthothelium, Lecanora, Phaeophyscia, Melaspilea, and Rinodina.

References

Teloschistales
Lichen species
Lichens described in 2014
Lichens of the Russian Far East
Taxa named by Sergey Kondratyuk

redpajama_set_name: RedPajamaWikipedia


Navigating the Complexities of a Medical Crisis Away from Home!
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Be passionate about our company, our customers, and our industry.
Employ enthusiastic people who do whatever it takes.
Be ethical in our business dealings.
Provide the best value to our customers.
Answer our phones, return calls and correspondence, and thank people in writing.
Negotiate hard - but fair.
Recognize employees for what they get done - not what they do.
Improve our community and environment.


text:
An entire Yorkshire village is on sale for £20 million
Complete with a mansion, 43 houses, and a pub
If you're a multi-millionaire, sinking £20 million into a property in London will get you either a luxury flat or a house in one of Britain's capital's most sought after areas.
However, if you're looking further afield, £20 million will buy you an entire Yorkshire village.
As of April 4, estate agency Cundalls is selling West Heslerton — a Yorkshire village that comes complete with a 21-bedroom mansion, 43 houses, and over 2,000 acres of surrounding countryside. The village comes with its own sports pavilion and playing fields, too.
Tom Watson, a director of Cundalls estate agency, told the Yorkshire Post that "it would be perfect for somebody wanting to build up and leave a legacy. The estate has been very much untouched in the past 50 years and is now a blank canvas ready to be shaped for the next generation." He added that expects a huge amount of interest from developers and investors. Take a look inside the incredible and quaint Yorkshire village that is up for sale.
West Herslerton was owned by Eve Dawnay who inherited the village from her father following his death in 1964. The village has been owned by her family for 150 years.
She died in 2010 at the age of 84 but didn't leave the village to a single heir.
Instead she left the Yorkshire village, near Malton, to a number of beneficiaries who are looking to sell it off via Cundalls.
The village has 43 houses — all of which, according to Watson who spoke to the Yorkshire Post, were rented out at low prices.
"[Dawnay] was very kind and the property rents are, and have always been, very low. This has helped keep a village community with a mixed group of ages and there are obviously a lot of people hoping that somebody with a similar benevolent nature will come along to take over the estate," said Watson.
The village also comes with over 2,000 acres of surrounding countryside.
It is made up of 2,116 acres of agricultural land, including 112 acres of woodland. Watson told the Yorkshire Post that the total annual rental and agricultural subsidy income is around £388,000.
West Heslerton even has its own sports pavilion, playing fields and its own football, cricket, and bowling teams.
It even has its own petrol station / garage.
One of the beneficiaries, Dawnay's younger sister Verena Elliott, told the Yorkshire Post: "It's not the prettiest of villages. It wouldn't go on the front of a chocolate box but my great grandfather, grandfather and father loved it."
"We all loved it and it would be very hard to find a village with more loyal and lovely people living in it. There is a real sense of community, which is hard to find these days. There are generations of families who have lived in the estate houses. In fact, there was a time when nobody ever seemed to move away," added Elliott, who now lives in London.
Elliott said that while her family appreciates the loyalty of the villagers, "times have changed, especially when it comes to farming, and it will be lovely to see new life breathed into the estate."
The centre-point to the village is the 21-bedroom West Heslerton Hall. However, Cundalls said that it is in need of renovation as Dawnay hadn't lived in the hall for three decades.
Watson said that it is possible for a buyer to further expand and develop the land — into potentially more houses — without "spoiling the character of the village."
Basically, if you buy the village, you'll be able to make a lot of money off rent and expand your income by building more houses on it.
"It is a once in a lifetime opportunity. I just hope we can find the perfect buyer," said Watson.

redpajama_set_name: RedPajamaCommonCrawl


Hayden Christensen and Ian McDiarmid reunited at SWCC today!
It's very dangerous, putting them together.
This.. is getting out of hand?
Hand problem, we can solve that.
I don't think the boy can handle it. I don't trust him.
"I need your help, son."
I'm appointing you to be my personal representative on the Jedi Council.
Put the gold with the D of two together, very dangerous.
Do you want Order 66? Because that's how you get Order 66.
If you what you told me is true, you will have gained my trust.
Hayden has aged great. Hope he's in IX somehow.
I'm hoping we get a Force Ghost Council with at least Luke, Obi Wan, Yoda, and Anakin. Qui Gonn and Mace Windu would also be welcome additions.
That's when he gets mad and seeks out Palpatine's Force ghost. Cue Episode X: Revenge of Revenge of the Sith.
I can't wait to see Force Ghost Death Star. Luke will have to blow it up again with his Force Ghost X-Wing.
Mace and Qui-Gon wouldn't make sense though. Mace never learned how and Qui-Gon was only able to retain his consciousness without a ghost form.


text:
A nation of snitches
More than 85% of fraud allegations made by the public over the last five years were false, according to figures obtained by the Observer.
A freedom of information request to the Department for Work and Pensions discloses that between 2010 and 2015 the government closed 1,041,219 alleged cases of benefit fraud put forward by the public. Insufficient or no evidence of fraud was discovered in 887,468 of these. In 2015 alone, of the 153,038 cases closed by the DWP's Fraud and Error Service, 132,772 led to no action.
Explains how the Stasi got away with it, doesn't it?
previousOn the rugby
nextQuestions in the Observer we can answer
41 thoughts on "A nation of snitches"
JuliaM February 28, 2016 at 10:15 am
Well, hold up there! 'Insufficient or no evidence..' How many in each category?
And 'led to no action' doesn't mean that the accusation was false, only that the useless CPS declined to do the legwork.
Or at least, that's what we are always told about rape stats by the feminists…
Steve February 28, 2016 at 10:39 am
What JuliaM said.
Remember how the police and social work departments found "insufficient evidence" (or similar weasel excuses) in Rotherham and other towns for ten years.
Of course, we are still a nation of snitches. You wouldn't be human if you didn't secretly hate your neighbours and long for the day when you can bludgeon open their skulls with their own femur and feast on the raw, pulsing, meaty goodness within.
Hence those "This is a Neighbourhood Watch Area" stickers.
Edward Lud February 28, 2016 at 11:00 am
I think it's still mostly local authorities and the DWP, not the CPS, who bring these prosecutions. Pendantic point, distinction without a difference, I accept.
Sam Jones February 28, 2016 at 11:11 am
In all probability many of these complaints are made against people successfully playing the system e.g. single parents with children by different fathers, working part time for minimum wage, and getting large amounts in tax credits, child benefit and housing benefit, thus enjoying a very comfortable lifestyle for minimum effort. Entirely legal, but the volume of complaints indicates it it not very popular.
tolkein February 28, 2016 at 11:26 am
So, at least 15% of cases are justified.
ukliberty February 28, 2016 at 11:41 am
In all probability many of these complaints are made against people successfully playing the system …
Or the complainants don't know what they are talking about.
Rob February 28, 2016 at 11:41 am
Twitter should have told us what sort of country we are. You can whip a censorious mob on that in under ten minutes.
Or they are acting out of malice.
Martin Davies February 28, 2016 at 12:24 pm
Having worked in the civil service and had thousands of fraud complaints its usually envy or revenge.
Mr X who is missing both legs is reported as being able to go jogging every evening? Mrs Y who is able to have a free car and go on holiday 4 times a year? Severe problems a medical report confirmed.
Mrs Z who reports her ex husband is hiding his money as he has much more income than that from his self employment.
Have had hundreds of fraud letters where it was literally just 3 or 4 lines relating to seeing them shopping twice a week. Lots of disabled go shopping twice a week. Might be all they can manage that day but gets them out.
Mr Ecks February 28, 2016 at 1:05 pm
It is moot if the few shining examples of the human spirit outweigh a mass of shite .
With varying degrees of gutless custard making up the numbers.
Theophrastus February 28, 2016 at 2:45 pm
IanB will be along soon to say that cannibalism like incest is objectionable only because of Puritanism. Or something.
Henry Marsh February 28, 2016 at 3:12 pm
I agree with Martin Davies. The quality of the reports submitted by the public are very poor. I've seen in previous work men ( for it is usually them ) reporting child benefit fraud because they are still paying maintenance to their ex for a young person who has dropped out of education, with no name of the last college attended.
We want evidence – a college administrator, an employer, a friend who can corroborate, something you can work with, but many of them don't give you a bone.
So the report gets filed but not acted on.
Ian B February 28, 2016 at 4:43 pm
I am along to ignore Theophrastus and his silly straw men, to say that this is typical of the nasty curtain twitchers that infest this country. Who tend to also fall on the Puritan side of things. But they normally call themselves "conservative" and have endless discussions with people like themselves about how the only people who should be allowed to live are people like themselves.
My general point being that Britain really needs to revive that fine old British virtue of people minding their own fucking business.
John Galt February 28, 2016 at 4:56 pm
Cannibalism like incest is objectionable only because of Puritanism. There you go.
In other news vast numbers of hard working families object to having to get up at sparrows fart and go out to work when he's the same age as Arthur across the road who has been on the pan crack for the past 7-years with a bullshit medical condition (agoraphobia, lardyarseis or similar), hence writing letters to the people whose wages they are paying complaining about Arthur's terminal boneidleness.
whatcha gonna do?
Put posters up around the neighbourhood saying "Snitches get stitches"?
Please feel free to ignore the widening gulf between "fit for work" and "somebody wants to employ them". Now due to get even worse thanks to the Tories and their insane jacking up of the minimum wage.
Fit to do £6.00/hr of work, no jobs allowed below £6.70, and no jobs anyway because there's always a younger, fitter migrant to do it instead.
"…the nasty curtain twitchers that infest this country. Who tend to also fall on the Puritan side of things…Britain really needs to revive that fine old British virtue of people minding their own fucking business."
When the welfare state – you know, that product of the period 1945-79, which you prefer to 1980 onwards – stops subsidising the feckless and idle (and their breeding) at the expense of the prudent and hard-working, people will be more inclined to mind their own business. Reduce the financial incentive for snitching and you'll get much less curtain-twitching and snitching.
But it is their business, because it is their local and national taxes picked from their pockets by a thieving government that pays for these layabouts.
If we have to chose a side then I'm on the side of the fucked off majority rather than the feckless minority. I'm not saying what they are doing is right, but what other alternative do they have?
Certainly no elected official will care unless the target of their accusations are "protected" (gypsies, Muslims, etc.) in which case the police will be knocking on their door to investigate a charges of incitement to racial hatred or some such bollocks.
Fine Theo, let's have a free market then.
The period since 1980- not I hasten to add what Thatcher intended- has ended up as a massive job creation scheme for the "upper middle class" who, contrary to being the backbone of Britain as they once were now refers to an enormous, parasitic carbuncle living on government funding. The economy is in a catastrophic state. The old working class now virtually have to lie on their back with their legs open to get a job at Aldi.
Look, I don't agree with the post-war dispensation. But most everyone seems to agree that at least people felt more free then, that their country was their own and there was some kind of future for us. My parents married in the 1950s, bought their own bungalow, had decent jobs, raised two children and moved up to semi-detached, all on a very ordinary income.
Look at the place now. The country is an authortarian, terrified shithole. We can't predicate an entire economy on escalating property prices and flooding the country with bomb-wielding immigrants (however cheap their labour) forever.
I cannot comprehend how a self-described conservative can look at this disastrous clusterfark and think it's an improvement. And before you say it, yes I do remember the Winter Of Discontent.
This is why the State stays as it is. It makes us all hate each other and blame each other, instead of them.
We have had systemic unemployment for decades, and it's not due to people not wanting to work. The Residuum are a small minority. Don't fall into the SMFS/Theo trap of thinking there are only two classes of people, the good middle class and the oxygen thieves.
Martin Davies February 28, 2016 at 7:13 pm
There still exist those who believe in classifying by class.
There are also those of us, usually younger, who could not care about class and will not classify someone by class.
john square February 28, 2016 at 8:32 pm
@ Martin D
There's also those folk who don't take any notice of class nowadays as it's bunk: I know lower class folk who work like stink and are rich and clever. Ditto for many of the posh. The cleverest person I ever met was lower middle class and terrifyingly well socialised and sharp. I also know very upper class folks who can mingle with anyone and get the best out of them in social or work circumstances. And the converse.
Me? People think I'm posh because I talk well, and are surprised to find I'm state schooled and from lowly brummie stock. It's not the facts of class that cause problems in the UK: it's the British fascination with it. It means nothing, and for every Prince Phillip, there's a Marquis of Bath; every Alan Sugar a Richard Branson and every Danny Dyer a Lawrence Fox.
Who are the upper middle class that constitute this enormous parasitic carbuncle?
Examples, please. With numbers, preferably.
An "authoritarian, terrified shithole"?
You sound like Laurie Penny on a bad day. Have you thought of leaving, if it's so bad?
And what is "systemic unemployment"? We live in an opportunity-rich society. It isn't the government's role to provide work for anyone. And the British working class has a poor work ethic, tends not to value education and has been failed by progressive schooling. The result is that employers prefer numerate and literate immigrants.
The majority of both the House of Commons and the Lords.
Cameron, Osbourn, Clegg and Miliband being perfect examples of the type.
Some 1500 people do not constitute an "enormous parasitic carbuncle". And not that many of them are upper middle class either.
They do when you remember they are backed up by the legislative force of this land and many millions of administrators, civil servants, NHS managers, consultants, etc.
All of which is eating 40% of our GDP. I would describe that as quite an "enormous parasitic carbuncle". All controlled to a greater or lesser extent from the parasites in Whitehall and Westminster.
Sure you could argue that some of that 40% of GDP goes towards meaningful stuff, but I would argue that much of it is wasted or given to folks like Camila Batmanghelidjh who use it on their own fiefdoms and personal benefit rather than public good.
Jim February 28, 2016 at 9:49 pm
Its not the Tories who got us here. As I recall, the country was fairly OK in the 90s, until that shyster Blair got elected, and proceeded to fuck the country royally up the arse.
Yes, the current lot haven't managed to do anything to reverse all that, but to be honest no-one can in the current situation, as the entire State sector is rotten to the core, infested with SJW types and their ilk, who would violently resist any elected governments attempts to reform public administration. Short of a sort of military coup I can't see any elected government, however nominally right wing, managing to turn back the clock now.
Ian B February 28, 2016 at 10:13 pm
John Galt,
Yes, that's who I meant.
John Galt February 28, 2016 at 10:22 pm
Apologies Ian.
Didn't mean to speak on your behalf.
Just annoyed and suffering from insomnia here in Penang.
Apology? I was thanking you! 🙂
So Much For Subtlety February 29, 2016 at 12:03 am
Theophrastus – "IanB will be along soon to say that cannibalism like incest is objectionable only because of Puritanism. Or something."
Damn straight. I will fight for my inalienable right to eat my niece.
And there isn't much of a non-Christian argument why I shouldn't be allowed to either.
And for the record, the Stasi relied on recruiting informers. They took neighbours who denounced each other too but the Soviet approach involved recruiting people to spy on each other.
The Gestapo on the other hand relied on denunciation. Partly because they were so small. There weren't that many of them anywhere in Germany. They were also usually professional policemen rather than Nazis.
Allegedly the Gestapo tried to bring order to France. They provided special facilities for the French to denounce each other. The story goes the system collapsed because so many French people used it to settle personal scores with neighbours and employers that the Gestapo could not cope.
And if you want to find a middle class parasite, can I recommend the school teacher who called the police because a boy looked at UKIP's website?
Ian B February 29, 2016 at 12:23 am
SMFS-
That is one example. The point I am trying to make being that the old "backbone" middle class has been shoved aside by the people now calling themselves middle class, who are basically the "state-sponsored" class. And who are empowered by the (new) moral system, as with that teacher.
I keep banging on about this because (it seems to me) many conservatives (in particular) characterise the "Left" as immoralists, or amoralists, when in fact they are driven by an intense moral fervour (which I characterise as you know as resurgent puritanism).
Nowadays you have to read illicit literature like UKIP websites behind the bike sheds. Then go back into the classroom for proper education in the correct method of anal sex.
Ian B – "The point I am trying to make being that the old "backbone" middle class has been shoved aside by the people now calling themselves middle class, who are basically the "state-sponsored" class. And who are empowered by the (new) moral system, as with that teacher."
I am not disagreeing with you. When the State takes 40% of GDP, they are going to spend a large proportion of that on civil servants and NGOs and the like. That means they need to greatly expand the number of useless courses like sociology to provide enough paper pushers for the state.
These people are not middle class in the traditional sense. They are simply paid like the middle class. They are actually our equivalent of the Soviet functionary and just as supine to the powers-that-be.
In America this is even more obvious because virtually the entire Black middle class is made up of policemen, teachers, people who work in the DMV and so on. It is a pseudo-middle class because it does not involve any of the values that actually make someone middle class and so the children of this fantasy middle class often fall into the underclass.
The oddity is why you are making this argument. Don't you usually claim there is nothing wrong with welfare for the poor and it does not change their values? Why would welfare for the middle class?
Theophrastus February 29, 2016 at 7:45 am
JG and IanB
The claim was that there is an enormous parasitic carbuncle of upper middle class people. When pressed, all you can do to identify these people is to refer to the 40% of gdp spent by the state and to members of the Houses of Parliament. But, as SMFS points out, most state employees are not truly middle class, never mind upper middle class. So the initial claim is class prejudice and bunk.
Indeed. But she (?) is most probably semi-educated, indoctrinated at a teacher training college, and certainly not upper middle class.
So Much For Subtlety February 29, 2016 at 9:34 am
Theophrastus – "But, as SMFS points out, most state employees are not truly middle class, never mind upper middle class. So the initial claim is class prejudice and bunk."
That depends on how you define Upper Middle Class. I prefer values. Some people would prefer income. Someone like Mary Warnock is famous for the fatuousness of her opinions. She has never held a proper job. She has been supported by the State her entire life. But a very well rewarded life it has been.
Theophrastus – "Indeed. But she (?) is most probably semi-educated, indoctrinated at a teacher training college, and certainly not upper middle class."
A head master. People who can earn £60-100,000 a year are fairly upper middle class.
Theophrastus February 29, 2016 at 10:13 am
SMFS
£60-£100k — my plumber's income — doesn't make anyone upper middle class, and there are plenty of vulgar brutes on much more than that.
And headteachers are generally not what they were.
Someone on £100,000 a year just qualifies for the top 1%.
As I have said, I prefer values. Because a plumber may earn that and still not be middle class much less upper middle class. But there is a raft of parasitic scum who do earn that sort of money.
Pingback: Animal farm – O Insurgente
Mr Ecks on Weird complaint
Mr Ecks on No, this would work nicely
Pat on Weird complaint


text:
Bossier may refer to:

 Bossier City, Louisiana
 Bossier Parish, Louisiana
 Pierre Bossier, French explorer for whom Bossier City and Parish are named


There are many ways to celebrate Earth Day. Some people ride their bicycle to work, plant a tree in their community, or simply learn more about the environment. There are also a wide variety of ways to become more green around the house, which can significantly boost your home's value.
Redfin recently released a list of the greenest neighborhoods in the nation based on homes for sale that mentioned green features. These features include solar panels, low-flow faucets, dual-pane windows, energy-efficient appliances, environmental ratings, and green home-building projects like "Built Green" in Colorado or "Green Built" in Washington. Overall, the median sale price of homes with green features was $47,600 higher than homes without green features. The majority of green homes are not new construction, but are on average six years newer than non-green homes.
Let's take a look at the 10 neighborhoods with the largest number of green homes, according to Redfin.


large historical storyboards of the past 150 years. Heritage tours, a Victorian tea party and fashion show, music, food, historical children's games and so much more will round out this memorable weekend.
We have a wonderful Canadian story to tell about our community and its people and our many volunteers are motivated by this momentous occasion to tell it.
each passing year. With the investment for 2017, there is a return that should be self-sustaining and continuing for years into the future.


Go anywhere with extra tough Australian Built Camper Trailers. Johnno's Camper Trailers provide a range of on-road and off-road camper trailer for sale.
Specifically created for the Australian market, these camper trailers are built from lightweight durable materials to perfectly suit the Australian environment.
The campers are tested in rough conditions in northern Australia to ensure that the trailer will suit even the most demanding situations.


text:
Fifty Shades of Grey author to attend Curragh races this Sunday
Fifty Shades of Grey author…
EL James, the author of 50 Shades of Grey, has accepted an invitation from the Curragh Racecourse to attend the races this Sunday 26th August to present the trophy to the winning owner of the inaugural Irish Field Grey Horse Handicap, the first time a race has been run in Ireland exclusively for grey horses.
Fifty Shades of Grey has been number 1 for 18 consecutive weeks in Ireland and the series of books has been number 1 ,2 ,3 for the last 13 weeks. It is now the UK's biggest selling book since records began outselling the Harry Potter series. Time Magazine included British born James in its annual list of "The 100 Most Influential People in the World" this year.
Evan Arkwright, Commercial Manager of the Curragh Racecourse, commented, "We are delighted that EL James has accepted our invitation to attend the races this Sunday. Grey horses always seem to capture the imagination of the public in a way that few other horses can and with the hope that the race will boost our attendance and provide a real spectacle for the public to enjoy."
The Fegentri World Championship race for international lady riders supported by Tipperary Crystal is another highlight on the day with Lisa O'Neill representing Ireland in the contest which will also feature riders from Germany, Britain, Italy, Sweden, Norway, Netherlands, Austria, Switzerland, Turkey and Spain
The Group 2 Galileo Futurity Stakes is expected to feature top 2 year olds Mars and Dawn Approach. while other races include the Group 3 Lanwades Stud Stakes and Group 3 bettor.com Flying Five Stakes. Racing also takes place on Saturday 25th August featuring the Irish Cambridgeshire and Gain Horse Feeds Irish St Leger Trial Stakes, while the Wuhan Goodwill Cup will promote the association between horse racing in Ireland with China.
Admission €15, U25s and Seniors €8, U16s Free
Free car parking, trains to Kildare Town with free shuttle to racecourse, Dublin Coach also provide service (see dublincoach.ie)
PreviousPrevious post:First Cornerstone supplemented for Galileo Futurity StakesNextNext post:Moyglare Stud Stakes attracts three supplementary entries


Experienced by Adrienne & Damian.
A gorgeous couple approached us with a passion to see and explore Botswana in depth. Wanting to avoid busy areas and tourist traps, we focussed our efforts on a slower paced itinerary to allow the couple the opportunity to completely immerse themselves in the wilderness and experience the rhythm of daily life in the bush.
The regions we focused on were selected based on great wildlife at the time of year guests wanted to travel and exceptional properties with talented guides and tracker teams on each vehicle for big wildlife viewing.
Linyanti Reserve, Kwando River and the Okavango Delta were explored for 3 nights each, flying in between before heading south to cosmopolitan Cape Town to wash of the safari dust, dine at internationally renowned restaurants and savour the world class wines.
We had a great trip and it meet all of our expectations! We were really happy with our guides and accommodation was very good.
It was quite hot in Botswana and there was no fan in one of the camps, so you just had to find a shady spot, breeze and cold drink. The VIP service on arrival from Maun to then transfer to Cape Town was excellent and helped ease any worries about missing flights! Thanks again for everything Encompass Africa.


text:
Pat Rothfuss XVII: Games, Bets, and Minecraft
By Ser Scot A Ellison,
December 3, 2021 in Literature
Ser Scot A Ellison
My children's daddy and Social Justice Warrior!
So, I saw this this morning. It's the first time in a Decade he's been willing to release information or portions of the third book. Is this him giving up and throwing what he's got at the world, or, is this a sign he's getting close and might actually have a book close to finished?
This is a link to the current fundraising total:
https://fundraise.worldbuilders.org/fundraiser/3614242
Proudfeet
I don't think it tells us anything about his progress. It could be chapters cut from WMF or it could be something recent.
As to why he's doing it, maybe it is just an attempt to boost his charity, or he was being being trash talked and turned to the only thing he knows that he has an advantage over his twitch followers so that he can feel smug again.
The book will be officially announced if/when it's done. That's the appropriate amount of attention his progress on the book deserves at this point. I'm not going to be bothered with crumbs or teases. Either it is ready or it isn't. It's not worth speculating over.
19 minutes ago, Proudfeet said:
Hold on. The prologue can't be left overs from the other books. We have those prologues already.
I'd much rather have the book… but… this isn't a bad sign… is it?
4 minutes ago, Ser Scot A Ellison said:
I mean, the prologue is just him chatting with Chronicler, with minor glimpses of what's happening in the present. Say, NoTW or WMF was cut into half. Would it be so out of place to repurpose one of those scenes as a prologue?
Anyway, my point is, he has no credit left. Reading signs is a waste of time. It is either an official announcement or nothing.
Kyll.Ing.
I would have been hyped for this if not for the third option. It is a much lower-hanging fruit than the other two, so to speak. It is the opt-out option for Doors of Stone content, allowing him to pick something down from his shelf instead of opening the locked cabinet, as it were. I think I picked up this series in 2014, and the seven years of bad news have jaded me a bit. Some say The Doors of Stone barely exists as a rough draft of ideas that haven't been touched for years, and this news wouldn't do much to quell those fears.
It's like a cryptozoologist offering "I will show definite proof of the existence of Bigfoot, or a living, breathing unicorn, or pictures from my summer holiday last year!" The existence of option three suggests the two others weren't ever realistically considered anyway.
That being said, it's a pretty good thing to raise so much money for charity, so it's not all doom and gloom. He's almost up to $150,000 already.
Larry of the Lake
the laer in winter
Location:Hudson Valley
21 minutes ago, Kyll.Ing. said:
The way it's written it sounds like he's doing all three items if the threshold is met. Beyond that, not holding my breathe.
Edited December 3, 2021 by 1066 Larry
16 minutes ago, 1066 Larry said:
Ahh, curse my gloomy jaded-ness clouding my vision. I swear I only read: "If the goals are met, I will do one of three things".
Okay, this suddenly got a lot more exciting.
Larry of the Lake and Ser Scot A Ellison
Entirely possible he's only got the prologue and first chapter done. This ain't a series I'm really expecting to be finished.
Starkess
It that's all he's written it would be odd to release it. It's likely to change in big ways during editing and revision.
26 minutes ago, Ser Scot A Ellison said:
why would it be weird if that's all he has? there would also be nothing to stop him from further edits and revisions.
Nothing. Just my impression that you don't (usually) want to release a really unfinished product or part of a product to the world…
1 minute ago, Ser Scot A Ellison said:
Obviously you're not a procrastinator by nature. I eek my way through life by throwing half baked ideas and jobs and payments at people to keep the wolves at bay. I can relate to Rothfuss.
Rhom, Myrddin and Ser Scot A Ellison
Ninefingers
5 hours ago, Ser Scot A Ellison said:
Not a bad sign to be sure, but I'd pump the brakes on just how good it is.
Rothfuss has a "tricky" relationship with his stretch goals. Several in the past never got delivered, and then there's the "Book 3 Q&A" from a couple years back where he refused to talk about, y'know, book 3. (This is not 100% true. Book 3 was mentioned. But it was swamped out by refusals to answer questions due to spoilers and talk about other things.)
Edit: Here's a link to what was said in the Book 3 Q&A. The fanbase was mostly furious with the lack of questions and answers on the stated topic.
Edited December 3, 2021 by Ninefingers
jurble
The No-Horned Brother
eegads, i saw this as well today
but as someone on reddit pointed out, this likely doesn't mean anything with regards to his work on DoS in general - he had an 'alpha' manuscript ready almost immediately after the last book, which he sent out to his beta (alpha?) readers - and the reddit commenter notes that it's likely within that alpha manuscript were at least a few bits he was satisfied with keeping. that is to say, anything he releases could easily be among the few 'finished' parts he had ready a decade ago
also why is the forum blue now?
44 minutes ago, jurble said:
The forum isn't blue for me.
El Kabong
Hmm, I always thought the whole alpha/beta readers manuscript thing was debunked as fake a long time ago. Even so, aren't some of the chapters only one page? I wouldn't put that past him at this point.
Oh and if it's blue you probably have to mess with your settings. The board upgrade reset stuff.
Garlan the Gallant
I'm sure he's at the point where he'll read the three pages he has to stay relevant.
Say what you want about the quality of Sanderson's books compared to Rothfuss, Lynch or GRRM but he is very forthright with his readers about the progress of his work. My point is that it's possible to offer legitimate insight into where you are with your book, even if the answer is roughly 2% done.
At this point, after so much effort spent to NOT answer that question in the slightest makes me think this is not a sign he has been putting pen to paper. It's more about raising money for his charity and staying relevant.
1 minute ago, Garlan the Gallant said:
If chef efficiently makes mac and cheese… it's still just mac and cheese. Rothfuss, Martin, and Lynch are making much better than mac and cheese.
Babblebauble


One that can haunt us from day through the night.
It's one that will actually hide in our head.
If not spider, nor ghost, nor spooky banshee?
And we know it's not even a colony of bats.
No, it's not any of those scary things at all.
In fact it's quite scarier, though so thin and small.
It's the thing in your pockets, your purse, your bank.
Have an idea yet, or still drawing a blank?
Okay, my friend, I will give it to you straight.
Otherwise the poem won't end at this rate.
This big scary thing I've been going on about?
It's money, my friend. Money and all its clout.
And all the good things we've been promised from above!


text:
Tag: Evidence Act 119 – Dumb Witnesses
Pritilata Majumder Vs Krishnapada Majumder on 23 Apr 2021
Posted on May 13, 2021 by ShadesOfKnife
Based on Apex Court decision here, Single Judge of High Court of Tripura held that the evidence of a dumb witness is a competent witness as per section 119 of Evidence Act.
[14] Evidently the petitioner was produced in court and an expert trained in sign language was also engaged by the court to interpret her evidence. As observed by the court, since the petitioner did not understand sign language she could not communicate her evidence to the interpreter and as a result the interpreter could not interpret her evidence to court. However, the petitioner was able to communicate to the court by her signs and gestures that everything of her life was known to her mother.
[15] In this emerged situation, mother [PW-2] of the petitioner is the best witness on her side. She had intimate knowledge of the signs and gestures and meaning of all expressions of her daughter who was brought up by her since her birth. None on earth other than her could better understand her daughter. The mother categorically stated at the trial that marriage of her daughter with the respondent was solemnized in a temple at Kumarghat and after marriage a daughter was born to her and thereafter the respondent left the area. Her evidence was supported by PW-3, a 70 years old man, unrelated to the petitioner who had no reason to tell lie. Moreover, the husband managed to escape. He never appeared either at the trial court or before this Court to discharge his burden. It was not unknown to him that legal proceedings were initiated by his wife against him because he was arrested in one of the cases instituted by his petitioner wife.
[16] A bare perusal of section 119 of the Evidence Act would show that a deaf and dumb witness who is unable to speak may give his evidence in any other manner intelligible to the court. It may be by writing or by signs in open court. It is evident that the mother [PW-2] and her petitioner daughter [PW-1] came to the court on the same day for giving deposition in the case. It also appears from the record that the petitioner was a literate person. She was able to read and write. Therefore, in case of any doubt, the court could have asked her to communicate her words in writing. The court could have also cleared its doubts from the mother of the petitioner by putting the questions to her in exercise of its power under section 165 of the Evidence Act. Without taking recourse to such means, the Family Court rejected the petition declining to grant maintenance allowance to the petitioner and her daughter which is unacceptable.
Posted in High Court of Tripura Judgment or Order or Notification | Tagged 1-Judge Bench Decision CrPC 125 - Order for Maintenance of Wives Children and Parents Dwarika Prasad Satpathy Vs Bidyut Prava Dixit and Anr Evidence Act 119 - Dumb Witnesses Pritilata Majumder Vs Krishnapada Majumder | Leave a comment


First, this work is probably the most helpful thing I've ever read on the "sacramentality" of the world. I've been mildly obsessed lately with how "heaven" intersects with "earth," with how we may articulate the relationship between the world above and the world below in a way that is not dualistic. According to Schmemann (it is always perilous to paraphrase something as brilliant as his work), religion emphasizes the world above (heaven) as escape from the world below (earth), and tries to replicate the life of the world above by living apart from the world below; secularism by contrast emphasizes the world below and ignores the world above. Both of these, he says, are outgrowths of the fall of man, which was (and is) "noneucharistic life in a noneucharistic world" (page 18). God intended all created things to be "sacramental" to man, in the sense that man was to "respond to God's blessing with his blessing" (page 15). It was precisely man's refusal to use the world in this sacramental way – it was his insistence on eating and drinking the blessing of God apart from God, and without thanksgiving to God – that was the essence of man's fall. It was in this "noneucharistic" partaking of the world that heaven and earth were rent asunder – heaven is now pursued by religion, earth by secularism, while both agree that "this world" is no longer the sphere of "life in God." The world, by both religion and secularism, has been secularized.
It is in the Eucharist, and in the liturgy of the church as a whole, says Schmemann, that this "life in God," abandoned by Adam but restored in Christ the Last Adam, is enacted once again; and it is out of the liturgy of the church that she goes forth into the world on a mission to "live in God" once again. Her life in the world is an extension of her liturgy, one might say: she receives all of life, in Christ, as God's blessing, blesses Him in all of life, and in this life disciples the nations.
Second, even before reading Schmemann, I had been thinking about the distinctive "atmosphere" generated by "eucharistic living"; and I found Schmemann deeply confirming at every turn. It is amazing how cold and harsh is the "climate" of so much life among the religious. Where is "the joy of the Lord" and its strength? Where is serving Him "with joyfulness and gladness of heart, because of the abundance of all things" (Deut 28:47)? Where is the light and laughter, the delight in fire and food, in oil and wine, in His daily benefits in the land of the living? Why the suspicion of created things that nourish our bodies and gladden our hearts? Why do we "secularize" these things, distancing ourselves from them as much as possible so as to concentrate on "holy" things with deadly seriousness? Can we possibly expect our children to be excited about such a life, or to have any idea how to connect it with the "real world" they must live in every day?
I will go back to this work again and again. But my deepest desire is to live in this way, to live a heavenly life firmly embodied in this wonderful created world.


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U bent hier:Home»Automotive»Infineon chief executive Wijburg: European 'localisation' unfortunate but understandable
Infineon top executive Rutger Wijburg on the decision of the Siemens and Philips boards at the time to spin off their semiconductor manufacturing operations. No, I wouldn't call that an error of judgement. The zeitgeist was different. And the current geopolitical tensions did not exist.' Photo: Infineon
Infineon chief executive Wijburg: European 'localisation' unfortunate but understandable
Door John van Ginkel op 3 oktober 2021 Automotive, Autonomous technology, China, co-development, Continuous Manufacturing, Duitsland, Durfkapitaal, Economie, ecosystemen, elektrificeren, Elektronica industrie, Europese industrie, Europese Unie, Factory of the future, Financiering, GELEVERD/GEÏNVESTEERD, Grondstoffen, high precision, hightech systemen, industrialisatie/maakbaarheid, Industrie 4.0, Industriebeleid, Industriële automatisering, Innovatie, Internationaal, Internet of Things, Ketencollectiviteit, leverbetrouwbaarheid/levertijden, local4local, Logistiek, maakindustrie, Machinebouw, Medische Industrie, menselijk kapitaal, monitoring en kwaliteit, multidiciplinair, Ondernemerschap, Overheidsbeleid, Procesinnovatie, Productie, Productiviteit, Regio Zuid, semiconductor industrie, technology partner, Transitie, waardeketens, Zero Hour Defect Rate
Over the past decades, chips have become increasingly fast and energy-efficient, and the technology to produce them has become more complex as a result. The players in the semicon chain are all specialists, world leaders in one or two steps in that value chain. A global chain in which the work is done where the conditions are best. A balanced status quo that, however, now suddenly cannot stand the test of politics. An interview with Infineon chief executive Rutger Wijburg about the 'exciting time' ahead, in which competencies will be redistributed. 'A global war for talent is about to erupt.'
'It would be unwise to opt out'
'Chips? We can buy them. Developing and producing semiconductors is too cyclical an activity and distracts us too much from our core business. So we'd better forget about them.' In short, that must have been the reasoning of the boards of Philips and Siemens when they decided to dispose of their semiconductor divisions at the beginning of this century. These continued independently as NXP and Infineon respectively. In the years since, it has become clear that ICs play a role everywhere in the economy, just as oil (still) does. Chips have proved to be far from cyclical. They are now indispensable in every economic sector and play a crucial role in solving the major challenges facing humanity. Chips are found in every electronic product, are indispensable in electric cars and wind turbines and crucial for the Industry 4.0 that can only be brought about with innovations such as edge computing and artificial intelligence. Nevertheless, Rutger Wijburg does not want to call the decision of the Philips and Siemens boards an 'error of judgement'.
Semicon career
HybridPACK, drive power module voor elektric cars Infineon.
Wijburg is by no means a random person to be asked for his opinion on this matter, as his CV demonstrates. He started his career at Philips Semiconductors in Nijmegen and stayed there until 2011 when it had already been NXP for quite some time. From there he made the move to the GlobalFoundries office in Dresden, East Germany. There he turned the former plant of American AMD, an Integrated Device Manufacturer (IDM) where both IC development and manufacturing are done, into a foundry dedicated entirely to producing chips for customers who develop them themselves. In 2018 he moved to Infineon Technologies, formerly part of Siemens AG. Not coincidentally, it is also located in Dresden, currently the world's fifth largest semiconductor ecosystem, which also includes Bosch Semiconductor Manufacturing and the Fraunhofer Institute, ahead of Eindhoven/Leuven in sixth place. Since last January, Wijburg has held the position of executive vice president, global front-end manager at Infineon's Munich head office.
Different zeitgeist
He starts the interview via Webex with a sigh of relief saying 'that he is able at last to have a conversation in Dutch' and apologises in advance for any Germanisms and Anglicisms he may use. The discussion then quickly turns to the decision by the Siemens and Philips boards to hive off their semiconductor manufacturing operations. 'No, I wouldn't call that an error of judgement. After all, it is impossible to anticipate all technological and market developments. And the zeitgeist was different. The current geopolitical tensions, particularly between China and the US, did not exist. So these types of decisions were made.' Decisions that have helped to create all kinds of specialised companies, but well integrated in a global semiconductor industry. 'In which sub-operations were carried out where the best resources were available at the lowest price.'
European key positions
The availability of talent allowed ASML to grow into a machine builder without which the enormous efficiency gains of the semicon – within 30 years from thousands to billions of transistors per square millimetre of IC – would not have been possible. Some of the talent comes from Imec a little further away in Leuven, which has developed into the leading research institute in the field of IC manufacturing processes.
After the fall of the Wall, the necessary EU funds allowed Infineon Dresden to grow into the world's largest plant for the development and production of discrete devices and power ICs for the efficient conversion of electricity. Essential technology for electric mobility and wind and solar power and hence for combating climate change. Infineon, together with NXP, also has a key position in the development and production of chips needed for edge computing, essential for managing the massive data flows that Industry 4.0 will bring. So says Wijburg about some of Europe's key positions in the global semiconductor chain.
Top 4 ecosystems
But Asia and the US have them too. It is not without reason that the top 4 largest semiconductor ecosystems are located outside the Old World. Number one today is in Taiwan with TSMC being by far the largest foundry in the world, for ICs for almost every application, including the most advanced in the 5 nanometre range. By 2023, the company hopes to be producing even 2 nm chips. A company with a turnover of 38.3 billion euros (2020) that has mastered the extremely delicate production process, consisting of 700 to 1,000 different steps, that results in finished 300 millimetre wafers after two to three months. The US, with companies such as LAM Research and Applied Materials, has machine builders in house that control other – not much less crucial – process steps. And with big tech companies such as Amazon, Apple, Microsoft and Google, the Americans have by far the most important data processors/cloud service providers, in this case those applying semiconductor technology.
Political problem
At first glance, it looks like a fairly even distribution of the various necessary semiconductor competences across the three continents that has worked well for a long time and forms the basis of the enormous innovation that the sector has undertaken. For geopolitical reasons, however, this distribution is no longer sufficiently balanced. Intel has long been the leading chip manufacturer, capable of producing the most advanced chips. TSMC has taken over that position, and in the past year it has suddenly become a political issue. The same applies to the 'only 8 percent' of chip production that takes place on European soil. This has everything to do with the rapidly growing power of China, which is rivalling the US. And that, even in the view of non-politician Wijburg, makes the economies of Europe and the US vulnerable. 'Because what if China decides to seize their "renegade province" of Taiwan? This is why Intel wants to expand its production capacity, in the US but also in Europe. Why TSMC has a major foundry planned in the US and – along with Sony and Toyota – in Japan. Why GlobalFoundries is expanding its production facilities in Germany and the United States. And why we are also expanding our capacity', says Wijburg. Infineon has always kept wafer production (front end) in Europe, has recently expanded it in Dresden, and is commissioning a completely new plant this fall in Villach, Austria.
Infineon Rutger Wijburg Foto's: Infineon
Inefficiencies
ASML's Peter Wennink has since publicly 'fully committed' himself to the European Commission's desire to step up chip production in Europe, but said during a webinar at the digital Hannover Messe in April that he was still not in favour of semicon supply chains per continent. 'The process from chip design to a chip built into a mobile phone requires more than a thousand steps that cross about 60 national borders. The chip builders in South Korea, Taiwan and the US need our technology for this. And we their business. You should not look for European technological sovereignty, but for mutual technological dependence.' Rutger Wijburg thinks this is a 'good idea of Peter'. 'Because localisation – local4local – is bound to cause inefficiencies in semicon. And you certainly won't be able to build everything locally.'
War for talent
An ASML-per-continent seems almost out of the question. But the material development that takes place at Imec also cannot easily be copied. The ecosystems mentioned, such as those in Eindhoven/Leuven and Dresden, with their power to innovate, do not allow themselves to be duplicated, says Wijburg. But when it comes to manufacturing, that is a different story, even for Infineon. The company undertakes the more fundamental technology development in Europe, the development of products and systems for the market largely takes place in the US and Europe, but the innovation of packaging technology (which connects chips with the surrounding technology) is entrusted to Asian branches of the group. 'We want to retain that division, but I realise that a global war for talent is about to erupt.'
Lees Link magazine digitaal of vraag een exemplaar op: mireille.vanginkel@linkmagazine.nl'
Exciting time
'The world should not be surprised that China is trying to build its own ASML. Huawei and SMIC are definitely suffering from the US special export control of critical technologies and/or tools to China. So China will try to localise all the technology needed for chip production in China. The Americans are also localising, for example by inviting TSMC to build a large new plant in Arizona. Companies such as ASML and Imec ensure that Europe holds important keys. And Europe also has localisation plans. After all, Europe now produces only 8% of the chips for market of critical applications, while we hold 20% of that worldwide market. So the goal is to design and produce 20 percent of the chips in Europe again.'
Infineon is going to contribute to this. 'We are building additional production capacity in Europe. To avoid dependence. To supply markets such as European automotive, medical technology and industrial automation. The apparent need for semicon development and production to localise is unfortunate, but it is understandable for reasons of power politics. And it would be unwise to opt out. Infineon is a European company then and will remain so. Culturally speaking, Europe is now the closest.'
'It's an exciting time. I haven't experienced this in my thirty years in semicon,' he says, looking cheerfully into the webcam.
5 nanometre Amazon AMD Apple Applied Materials Asia ASML Automotive Bosch Semiconductor Manufacturing China chip production chips critical technologies ecosystems energy-efficient foundry fundamental technology geopolitical global semiconductor industry Globalfoundries Google Huawei ic's Imec industrial automation innovate Intel Lam Research machine builder manufacturing material development medical technology Microsoft NXP Packaging Technology Peter Wennink philips production capacity production process Rutger Wijburg semicon development semicon supply chains semiconductor ecosystems semiconductor manufacturing semiconductor technolog siemens SMIC South Korea Taiwan transistors TSMC US value chain wafer production war for talent
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