text:
Social Licence: Complicity in the Age of Extraction
Mar 15, 2012 • 11:28 am
This article, by Kevin Smith of Platform and Clayton Thomas Muller of the Indigenous Environmental Network first appeared in the Winter 2011/12 issue of Fuse Magazine in Canada.
At first glance, there might not seem to be an obvious common ground between indigenous activists in Canada, performance artists in the UK and climate activists in both countries. However, the international controversy over Canada's tar sands industry in northern Alberta has galvanised individuals from all these communities into new cooperative relationships opposing the developments. Over the last few years, environmental groups and artists have influenced each other's practices, resulting in innovative, cross-platform public interventions
While traditional environmental NGOs have lobbied government officials and targeted the oil companies that are involved on both sides of the Atlantic, people in the UK cultural sector have recently started to interrogate their particular complicity in enabling oil companies to commit environmental and human rights abuses in other parts of the world. This article describes collaborative projects by arts-activist organisation Platform, indigenous rights group the Indigenous Environmental Network (IEN) and performance interventionists Liberate Tate designed to problematize the involvement of oil companies in gallery spaces, and to challenge the role of arts institutions in diverting attention from the devastation that their primary sponsors are carrying out in other parts of the world.
In London (UK), an overwhelming majority of cultural institutions have acquired sponsorship from a major oil company, predominantly BP or Shell. For more than 20 years, BP has been the main sponsor of the Tate museums. The relationship between the cultural behemoth and the corporation has been so close that the ex-CEO of BP, Lord John Browne, has sat on the Tate Board of Trustees since 2007. In December 2011, BP announced a £10 million sponsorship deal spread over 5 years between Tate, the British Museum, the Royal Opera House and the National Portrait Gallery.
An oil corporation such as BP combines the business models of an engineering company and a bank. It constantly faces the practical challenges of extracting, transporting and processing oil and gas, shifting the geology of distant lands to the cars and turbines of its customers. Like all engineering problems, these challenges are approached in the belief that ultimately they can be solved. The point of solving them is to make money, profit on invested capital.
The construction of an offshore oil platform is one of the most expensive projects on earth. Usually it can only offer a high return on capital if oil production if maintained over two or three decades. The maintenance of this production is often threatened by social and political shifts in the countries of extraction. Any such threat to production — or the perception that that threat might exist — can immediately undermine the profitability of a corporation. BP's share value was almost halved by the Deepwater Horizon disaster in the Gulf of Mexico, not because of the potential costs of the oil spill clean up, but because investors were concerned that the company's future prospects in the United States were being undermined by the collapse of support in Washington DC and in the media.
To guard against any such threat to the company's value, BP works constantly to engineer its social license to operate — a term widely used in business and government circles that usually applies to the process of engendering support for a company's activities in the communities who live close to their factories, oil wells, and so on. This term can shed light on how corporations construct public support far from the places of extraction or manufacture — for example how BP builds support in London. The construction of the social licence to operate is what links gallery-goers in London to the devastation of boreal forests and indigenous communities in Canada through tar sands extraction.
In the summer of 2009, four First Nations activists associated with the IEN, including co-author, Clayton Thomas-Muller, came to London to take part in the Camp for Climate Action. This annual protest camp had an enormous impact on climate change discourse in the UK, and the First Nations visitors engaged activists on the devastation being caused by tar sands extraction. It was at this Climate Camp that members of Liberate Tate and Platform first met the indigenous community representatives. At that stage, BP had not fully committed to entering into the tar sands market, but in December 2010, it committed a £1.6 billion investment in the Sunrise Project. Located in northern Alberta, the project could be producing 200,000 barrels of oil a day in the space of a few years. Sunrise will use so-called SAG-D (Steam Assisted Gravity Drainage) extraction methods, in which water is super-heated into steam with vast amounts of natural gas, then injected deep into the earth to "melt" the oil from the sand and clay.
The entire tar sands infrastructure in Canada has been the subject of extensive criticism for clear-cutting boreal forests, polluting waterways and some indigenous communities that live downstream of the polluted waterways are experiencing higher that expected rates of rare cancers. According to a report by the Alberta Health Services released in 2009, in Fort Chipewyan, a remote community 300km north of Fort McMurray often described as the ground zero of tar sands extraction, 51 cancers developed in 47 people between 1995 and 2006, almost a third more than would have been statistically predicted. [1]
Extracting oil from tar sands is far more polluting and destructive to the climate than light sweet crude oil, which comes naturally out of the ground in liquid form. Tar sands are only 10% oil mixed with 90% sand, clay and corrosive agents such as quartz and other minerals, heavy metals and volatile organic compounds (VOCs). The extra energy involved in super-heating the bituminous substance to create a usable, transportable makes it a far more carbon intensive fuel source than light sweet crude. The size of these oil reserves (the greatest in the world outside of Saudi Arabia), combined with this increased carbon intensity, has lead NASA Scientist and climate advocate James Hansen to state that if the development of the tar sands continues, then it is "essentially game over" for the climate. [2]
Since the initial visit of the IEN activists to the UK, action on tar sands has been a regular feature of the political scene. The initial targets in these collaborations were the UK oil companies that were involved in the industry and the UK banks that were involved in financing other tar sands companies, but this has now widened to include those galleries and museums that are complicit in allowing oil companies to divert attention away from their destructive activities.
Activist groups such as Art Not Oil have been protesting against the involvement of oil companies in UK galleries since 2004. The issue gained a new level of prominence in 2010 in the wake of the Gulf of Mexico Disaster. Just weeks after the oil rig blow-out that caused 11 deaths and devastated vast stretches of US coastline, the annual Tate Summer Party was celebrating 20 years of BP sponsorship. Platform coordinated a letter in the Guardian newspaper signed by over 160 people in the cultural sector calling on Tate to end its relationship with BP and distributed literature about oil sponsorship of the arts to party goers entering Tate Britain where the party was taking place. [3] Meanwhile, recently formed art-activist group Liberate Tate performed Licence to Spill, with 11 performers dressed in black with their faces covered in veils pouring gallons of an oil-like substance over the entrance steps of the gallery. This was a symbolic act designed to create maximum disruption to the 'celebrations' and draw attention back from the canapés and champagne to the horrors of the Gulf of Mexico. Inside the party, two elegantly dressed ladies going by the names of Toni [Hayward] and Bobbi [Dudley], released another oil spill from beneath their bouffant dresses, a "relatively tiny one, compared to the size of the gallery," echoing the comments of then-BP CEO Tony Heyward in describing the size of the oil spill relative to the Gulf of Mexico. [4]
In the following year, more evocative, and often headline-grabbing, performance interventions took place in gallery spaces. Sunflower (September 2010) took place in Tate Modern's iconic Turbine Hall, with 30 performers forming a circle before stepping on tubes of black oil paint, monographed with BP's green and yellow sunflower logo. The prescient performance was later echoed by Ai Wei Wei's Sunflower Seeds (2010) installation that saw millions of handcrafted porcelain seeds deposited in the same location. On the anniversary of the Gulf of Mexico disaster, Liberate Tate did a durational intervention, Human Cost (April 2011), in the exhibition Single Form at Tate Britain. In the performance, a naked figure lay on the ground and was covered with another oil-like substance, an image of which appeared on the front page of the Financial Times the next day.
While BP's criminal negligence in causing the Gulf of Mexico disaster was one of the re-invigorating factors behind the Liberate Tate performances and campaign, BP's involvement in tar sands extraction in particular has subsequently become one of the main foci. In April 2011, Clayton Thomas Muller and Jasmine Thomas, a member of the Frog clan from Saik'uz, spoke outside Tate Modern about the art world complicity in the destruction of indigenous communities during a protest by climate action group Rising Tide. In July, Liberate Tate and UK Tar Sands Network invited performance artists Reverend Billy and the Church of the Earthalujah to perform an exorcism of BP in the Tate Turbine Hall, accompanied by a 12-piece gospel choir singing about the evils of tar sands extraction. In March 2012, Platform, Art Not Oil and Liberate Tate, working with content contributed by Indigenous Environmental Network are launching the Tate a Tate Audio Tour, [4] a site-specific sound work in three pieces that enables listeners to tour Tate Modern, Tate Britain and the boat journey between the two institutions while listening to the voices of impacted communities, artists and oil campaigners.
Of course, all the activities around sponsorship are occurring at a time when the arts are facing massive cuts in public funding, as part of the austerity measures being carried out by the coalition government. Many feel that now is not the time for the art world to start getting choosy about where the money comes from, with Guardian art critic Jonathan Jones going as far to assert that museums should take "money from Satan himself" if it means they can "stay strong and stay free." [5]
However it is precisely because of the decrease in public funding that a debate about the ethics of particular corporate sponsors is more relevant than ever. Rather than pitting the need for ethical discussion against the need to secure funding, we must ground this debate in a respect for the value of the arts to society, and the importance of access. State support commits arts institutions to remaining open to all, ensuring that everyone has the possibility to connect with a vivid and changing cultural history, and valuing what the arts can bring to people's lives and experience.
Raoul Martinez, a portrait painter whose work has been exhibited as part of the BP Portrait Award at the National Portrait Gallery for the past two years' running, has written that:
Unless we're willing to accept the sponsorship of the pornography industry or arms manufacturers, we clearly believe a line must be drawn somewhere. So the issue is not whether we draw a line, but where we draw it. In the case of BP, I believe there is a strong case for placing them on the wrong side of that line… If society decides it genuinely values institutions like the National Portrait Gallery and Tate Modern, it can provide money to support them. [6]
The call to end oil sponsorship of the arts is not without precedent. Sponsorship shifts have occurred on numerous occasions according to changing social norms and contexts. A few decades ago, many of the same cultural institutions were receiving tobacco money – the creativity of art provided a great decoy to the devastating consequences of cancer – yet now tobacco logos are absent from the cultural sphere. Smoking is simply not socially acceptable anymore. The major cultural shift over tobacco sponsorship is now widely applauded as an appropriate response, and was in part due to the push given by anti-smoking campaign groups. Yet despite widespread public concern about the dramatic threat of climate change and the ongoing violation of the rights of Indigenous Peoples in Canada, oil money is still found greasing the wheels of so many of our cultural institutions. The idea that it is therefore normal to continue to burn fossil fuels subtly seeps into our imaginations, fixing the image of a certain kind of culture, a certain kind of destructive behaviour. This cultural acceptance of oil is diminishing, and at some point it will more dramatically wane.
Breaking the sponsorship link between Tate and BP will not alone prevent the devastating tar sands projects being inflicted across the Northern wildernesses of Canada. By creating and informing a public debate that questions the legitimacy of these companies in being associated with respectable and cherished cultural institutions, we can strengthen attempts to hold them accountable in other political and financial spheres. This is an essential step in ending the stranglehold that the companies have on the corridors of power – a major obstacle that we face in the transition to a low carbon society. The shift away from oil takes place in many municipal sites as well as in our personal daily experience. From the infrastructure of transport, to the shareholdings of pension funds, from where the food we eat is grown, to divorcing fossil fuel industry interests apart from the seats of governmental power. For a fair and just transition to a post-oil era, we see the creativity and collaborative practices of artists as essential to the process, and cultural institutions as a key space to nurture that evolution.
[1] 'Fort Chip cancer rates higher than expected: report', CBC News, 6 Feb 2009. See http://www.cbc.ca/news/health/story/2009/02/06/edm-fort-chip-cancer.html
[2] James Hansen slams Keystone XL Canada-U.S. Pipeline: "Exploitation of tar sands would make it implausible to stabilize climate and avoid disastrous global climate impacts"', Climate Progress, % June 2011. See: http://thinkprogress.org/romm/2011/06/05/236978/james-hansen-keystone-pipeline-tar-sands-climate/
[3] Licence to Spill, Platform, June 2010, www.platformlondon.org/carbonweb/documents/licencetospill.pdf
[4] Tim Webb, "BP boss admits job on the line over Gulf oil spill," The Guardian (14 May 2010).[5] see www.tateatate.org for more info and a sound clip.
[5] 'Tate is right to take BP's money', Guardian Blog, 29 June 2010. See: http://www.guardian.co.uk/culture/jonathanjonesblog/2010/jun/29/tate-bp-sponsorship.
[6] Interview with the authors, August 2011.
Places: Canada, UK
Players: BP, Tate
Issues: Corporate Sponsorship of the Arts


text:
package com.sensirion.smartgadget.view.history.graph.plot_formatter;

import android.content.Context;
import android.graphics.Color;
import android.support.annotation.NonNull;

import com.androidplot.Plot;
import com.androidplot.ui.XLayoutStyle;
import com.androidplot.ui.YLayoutStyle;
import com.androidplot.xy.BoundaryMode;
import com.androidplot.xy.XYPlot;
import com.androidplot.xy.XYStepMode;
import com.sensirion.smartgadget.R;

import java.text.Format;

public abstract class LinearPlotFormatter {

    public static void formatPlot(@NonNull final Context context, @NonNull final XYPlot plot, final String domainLabel, final String rangeLabel, final Format xAxisFormat, final Format yAxisFormat) {
        configurePlotLookAndFeel(plot);
        setPlotPadding(context, plot);
        preparePlotGrid(context, plot);
        setPlotMargins(context, plot);
        configurePlotTitle(context, plot);
        preparePlotRange(context, plot, rangeLabel, yAxisFormat);
        preparePlotDomain(context, plot, domainLabel, xAxisFormat);
    }

    private static void configurePlotLookAndFeel(@NonNull final XYPlot plot) {
        plot.setMarkupEnabled(false);
        plot.setBorderStyle(Plot.BorderStyle.NONE, null, null);
        plot.getLayoutManager().remove(plot.getLegendWidget());
    }

    private static void configurePlotTitle(@NonNull final Context context, @NonNull final XYPlot plot) {
        plot.getTitleWidget().getLabelPaint().setTextSize(context.getResources().getDimensionPixelSize(R.dimen.history_fragment_axis_text_size));
    }

    private static void setPlotMargins(@NonNull final Context context, @NonNull final XYPlot plot) {
        final int marginLeft = context.getResources().getInteger(R.integer.history_fragment_margin_left_graph);
        plot.getGraphWidget().setMarginLeft(marginLeft);
    }

    private static void setPlotPadding(@NonNull final Context context, @NonNull final XYPlot plot) {
        final int leftPadding = context.getResources().getInteger(R.integer.history_fragment_plot_left_padding);
        final int topPadding = context.getResources().getInteger(R.integer.history_fragment_plot_top_padding);
        final int rightPadding = context.getResources().getInteger(R.integer.history_fragment_plot_right_padding);
        final int bottomPadding = context.getResources().getInteger(R.integer.history_fragment_plot_bottom_padding);

        plot.getGraphWidget().setPadding(leftPadding, topPadding, rightPadding, bottomPadding);
    }

    private static void preparePlotGrid(@NonNull final Context context, @NonNull final XYPlot plot) {
        plot.getGraphWidget().getBackgroundPaint().setColor(Color.WHITE);
        plot.getGraphWidget().getGridBackgroundPaint().setColor(Color.WHITE);
        plot.getGraphWidget().getGridBackgroundPaint().setColor(Color.WHITE);
        plot.getGraphWidget().getRangeLabelPaint().setColor(context.getResources().getColor(R.color.font_dark));
        plot.getGraphWidget().getRangeLabelPaint().setTextSize(context.getResources().getDimensionPixelSize(R.dimen.history_fragment_axis_text_size));
        plot.getGraphWidget().getDomainLabelPaint().setColor(context.getResources().getColor(R.color.font_dark));
        plot.getGraphWidget().getDomainLabelPaint().setTextSize(context.getResources().getDimensionPixelSize(R.dimen.history_fragment_axis_text_size));
        plot.getGraphWidget().getDomainOriginLinePaint().setColor(Color.TRANSPARENT);
        plot.getGraphWidget().getRangeOriginLabelPaint().setTextSize(context.getResources().getDimensionPixelSize(R.dimen.history_fragment_axis_text_size));
        plot.getGraphWidget().getRangeOriginLabelPaint().setColor(context.getResources().getColor(R.color.font_dark));
        plot.getGraphWidget().getDomainGridLinePaint().setColor(Color.TRANSPARENT);
    }

    private static void preparePlotRange(@NonNull final Context context, @NonNull final XYPlot plot, final String rangeLabel, final Format yAxisFormat) {
        plot.getRangeLabelWidget().getLabelPaint().setColor(context.getResources().getColor(R.color.font_dark));
        plot.getRangeLabelWidget().getLabelPaint().setTextSize(context.getResources().getDimensionPixelSize(R.dimen.history_fragment_axis_text_size));
        plot.getRangeLabelWidget().setText(rangeLabel);
        plot.setRangeBoundaries(0, 100, BoundaryMode.FIXED);
        plot.setRangeValueFormat(yAxisFormat);
        plot.setRangeStep(XYStepMode.SUBDIVIDE, context.getResources().getInteger(R.integer.history_graph_view_num_default_range_labels));
    }

    private static void preparePlotDomain(@NonNull final Context context, @NonNull final XYPlot plot, final String domainLabel, final Format xAxisFormat) {
        plot.getDomainLabelWidget().getLabelPaint().setColor(context.getResources().getColor(R.color.font_dark));
        plot.getDomainLabelWidget().getLabelPaint().setTextSize(context.getResources().getDimensionPixelSize(R.dimen.history_fragment_axis_text_size));
        plot.setDomainValueFormat(xAxisFormat);
        final float domainLabelWidth = plot.getDomainLabelWidget().getLabelPaint().measureText(domainLabel);
        plot.getDomainLabelWidget().setText(domainLabel);
        plot.getDomainLabelWidget().position(-domainLabelWidth / 2, XLayoutStyle.ABSOLUTE_FROM_CENTER, 20, YLayoutStyle.ABSOLUTE_FROM_BOTTOM);
        plot.setDomainStep(XYStepMode.SUBDIVIDE, context.getResources().getInteger(R.integer.history_graph_view_default_num_domain_labels));
    }
}

redpajama_set_name: RedPajamaGithub


This year i'm lucky enough to have pancake day the day after my birthday! So basically this whole week is going to be full of food...not much different from the norm but hey...any excuse!
The weekend just gone has been full of scrummy foods, and i've really been feeling the american theme (more to come on that later in the week),so decided to stick to it and make Buttermilk pancakes with crispy bacon and maple syrup.
Start by mixing the flour, salt and bicarb in a bowl.
Add the egg, buttermilk, melted butter and give it a good mix.
The batter is quite a thick one, but don't be put off by this. Heat a frying pan and grease lightly (I used a little bit of butter for the first pancake but didn't add any more for the second and third, my pan is a very good non stick brand).
Add as much batter to the pan as you like, depending on the size you want. Make sure you place it in the centre and then use the back of the spoon or ladle to move the batter around to make the desired shape.
You will know when its time to flip when little pockets open up on the top, like little air bubbles.
Americans like their pancakes with Bacon, I went for Oscar Mayer as its "American style" bacon and it crisps up nicely.
They also smother their pancakes in maple syrup, but I just went for a little drizzle as I find it a little to sweet.
Theres lots more to come this week on the blog, including my weekend in london, a restaurant review and last but by no means least....BEYONCÉ!


text:
\section{Introduction}
The teleparallel equivalent of general relativity (TEGR) is a
consistent geometrical framework for the dynamics of the gravitational
field. The theory is formulated in terms of tetrad fields. It is known
that these fields are necessary for establishing the interaction
of Dirac spinor fields with the gravitational field, as well as for
the description of reference frames in spacetime. In the general case,
i.e., if no boundary conditions are imposed on the field quantities,
the TEGR is invariant under global SO(3,1) frame transformations.
Therefore six degrees of freedom of the tetrad field (with respect to
the metric tensor) cannot be removed by gauge transformations as in
the Einstein-Cartan theory, for instance, which exhibits local SO(3,1)
symmetry. On the other hand, the reference frame is characterized by
the six components of the acceleration tensor \cite{Maluf1}, which
characterizes the inertial properties of the frame. It follows
that in the TEGR the tetrad field determines both the reference frame
and the gravitational field.

The field equations of the theory (Euler-Lagrange and first class
constraint equations) are interpreted as equations that define the
energy, momentum and angular momentum of the gravitational field. The
interpretation of a constraint equation as an energy equation for a
physical system is not a specific feature of the TEGR. It takes place,
for instance, in the consideration of Jacobi's action \cite{Lanczos,HG}
for a parametrized nonrelativistic particle. In order to understand
this feature, let us consider a particle of mass $m$ described in the
configuration space with generalized coordinates $q^i$,
$i=1,2,3$. The particle is subject to the potential $V(q)$ and has
constant energy $E$. Denoting $\dot{q}^i=dq^i/dt$, where $t$ is a
monotonically increasing parameter between the (fixed) initial and end
points of the path, the Jacobi action integral for this particle can
be written as \cite{BY1}

$$I=\int_{t_1}^{t_2} dt
\sqrt{m g_{ij}(q) \dot{q}^i \dot{q}^j}
\sqrt{2\lbrack E-V(q)\rbrack}\,.$$

\noindent The action is extemized by varying the configuration space
path and requiring $\delta q(t_1)=\delta q(t_2)=0$. We may simplify
the integrand by writing $dt \sqrt{m g_{ij}\dot{q}^i \dot{q}^j}=
\sqrt{m g_{ij} dq^i dq^j}$, which shows that the action is invariant
under reparametrizations of the time parameter $t$.
Thus in Jacobi's formulation of the action principle it is
the energy $E$ of the particle that is fixed, not its initial and
final instants of time. In view of the time reparametrization of the
action integral, the Hamiltonian constructed out of the Lagrangian
above vanishes identically, which is a known feature of
reparametrization invariant theories.
If we denote $p_i$ as the momenta conjugate to $q^i$, we find
$p_i=g_{ij} \dot{q}^j\sqrt{2(E-V)/\dot{q}^2}$ (where
$\dot{q}^2=g_{kl}\dot{q}^k\dot{q}^l$), which leads to the
constraint

$$C(q,p)\equiv {1\over 2}g^{ij}p_i p_j + V(q)-E\approx 0$$

\noindent The equation of motion obtained from the action integral
has to be supplemented by the constraint equation $C=0$, in order to
be equivalent with Newton's equation of motion with fixed energy $E$
\cite{BY1}. Therefore we see that the constraint equation defines
the energy of the particle. This is the feature that takes place in
the TEGR: the definitions of the energy-momentum and angular momentum
of the gravitational field emerge from the constraint equations of the
theory \cite{Maluf2,Maluf3}. These definitions are viable as long as
they yield consistent values in the consideration of well understood
gravitational field configurations.

The evaluation of the expression for the gravitational energy-momentum
in the TEGR is not difficult because it reduces to a surface integral
in the three-dimensional spacelike hypersurface.
However, the gravitational angular momentum is given by a volume
integral, and we did not succeed in reducing the latter to a surface
integral in the general case. Surprisingly, we find that in the
framework of static observers the expression for the gravitational
angular momentum due to the most general rotating source reduces to a
simple surface integral. This feature
not only allows the evaluation of the expression in an easy way, but
it also points out which is the necessary fall-off of the components
of the metric tensor that yields a finite value for the total
angular momentum. We find that if the metric tensor obeys
asymptotically flat boundary conditions, the total gravitational
angular momentum will be finite provided the metric components
fall off as $1/r$ or faster in the limit $r \rightarrow \infty$. This
result agrees with the detailed analysis of Beig and \'O Murchadha
\cite{BM} and of Szabados \cite{Sza}, who investigated the Poincar\'e
structure of asymptotically flat spacetimes.

In this paper we analyze in detail the gravitational angular
momentum of a pulsar model that describes a rotating neutron star. If
$J$ represents the angular momentum of the source, we find that the
gravitational angular momentum is given by $2J/3$. According to our
analysis this result seems to be general: if $J$ is the angular
momentum of an arbitrary rotating source, the gravitational
angular momentum is given by $2J/3$.
The constraint equation that defines the gravitational angular
momentum is not related to the energy-momentum tensor. Thus we
interpret the angular momentum discussed here as the angular momentum
of the field, not of the source.

In the Newtonian description of classical
mechanics the angular momentum of the source is frame dependent. This
feature also holds in relativistic mechanics. If the angular momentum
of the source in general is frame dependent, in principle one cannot
exclude the possibility that the angular momentum of the field is
frame dependent as well.
Differently from other definitions of gravitational angular momentum
that are formulated in terms of surface integrals at spacelike
infinity and depend only on the asymptotic behaviour of the
metric tensor, the definition considered here naturally depends
on the frame, as it is invariant under global
(rather than local) SO(3,1) transformations of the tetrad field.
In the present framework,
observers that are in rotational motion around the rotating source
measure the gravitational angular momentum differently from
static observers. These observers also measure
the angular momentum of the source differently from stationary
observers (in Newtonian mechanics the angular
momentum of the source in the frame of observers that
rotate at the same angular frequency vanishes). We will show that
the concept of the present definition of gravitational angular
momentum is closely related to the dragging of inertial frames.

In section 2 we present a summary of the formulation of the TEGR.
In section 3 we address the gravitational angular momentum of a
rotating neutron star, and then of an arbitrary gravitational field
configuration. In section 4 we argue that the dependence of the
gravitational angular momentum on the frame is a natural feature of
the present formalism. Observers whose angular velocity around the
rotating source is the same as the dragging velocity do not measure
dragging effects (the dragging velocity, for instance)
as do static observers. We show that for such
observers the gravitational angular momentum vanishes.
Finally, in section 5 we present the final remarks.

Notation: space-time indices $\mu, \nu, ...$ and SO(3,1)
indices $a, b, ...$ run from 0 to 3. Latin indices from the middle
of the alphabet $(i,j,k)$ run from 1 to 3. Time and space indices are
indicated according to
$\mu=0,i,\;\;a=(0),(i)$. The tetrad field is denoted by $e^a\,_\mu$,
and the torsion tensor reads
$T_{a\mu\nu}=\partial_\mu e_{a\nu}-\partial_\nu e_{a\mu}$.
($T_{a\mu\nu}$ is related
via $T_{a\mu\nu}=e_{a \lambda} T^\lambda\,_{\mu\nu}$ to the torsion
tensor of Cartan's connection
$\Gamma^\lambda_{\mu\nu}=e^{a\lambda}\partial_\mu e_{a\nu}$).
The flat, Minkowski space-time metric tensor raises and lowers
tetrad indices and is fixed by
$\eta_{ab}=e_{a\mu} e_{b\nu}g^{\mu\nu}= (-+++)$. The determinant of
the tetrad field is represented by $e=\det(e^a\,_\mu)$.\par
\bigskip

\section{The Hamiltonian form of the TEGR}

The equivalence of the TEGR with Einstein's general relativity may be
understood by means of an identity between the scalar curvature
$R(e)$ constructed out of the tetrad field and a combination of
quadratic terms of the torsion tensor (see, for example,
ref. \cite{Maluf4}),

\begin{equation}
eR(e)\equiv -e({1\over 4}T^{abc}T_{abc}+{1\over 2}T^{abc}T_{bac}-T^aT_a)
+2\partial_\mu(eT^\mu)\,.
\label{1}
\end{equation}

The Lagrangian density of the TEGR in empty spacetime is given by
the combination of the quadratic terms on the right hand side of
eq. (1),

\begin{eqnarray}
L&=& -k e({1\over 4}T^{abc}T_{abc}+{1\over 2}T^{abc}T_{bac}-
T^aT_a) \nonumber \\
&\equiv& -ke\Sigma^{abc}T_{abc}\,,
\label{2}
\end{eqnarray}
where $k=c^3/16\pi G$, $T_a=T^b\,_{ba}$,
$T_{abc}=e_b\,^\mu e_c\,^\nu T_{a\mu\nu}$ and

\begin{equation}
\Sigma^{abc}={1\over 4} (T^{abc}+T^{bac}-T^{cab})
+{1\over 2}( \eta^{ac}T^b-\eta^{ab}T^c)\;.
\label{3}
\end{equation}
The field equations derived from eq. (2) are
equivalent to Einstein's equations.

The Hamiltonian formulation of the theory has been investigated
in detail in ref. \cite{Maluf5}. The Hamiltonian density $H$ may be
obtained from $L$ by rewriting it as $L=p\dot{q}-H$, and expressing
$H$ in terms of the canonical variables. There is no time derivative
of $e_{a0}$, and therefore this field quantity arises as a
Lagrange multiplier. The momenta canonically conjugated to $e_{ak}$
is denoted by $\Pi^{ak}$. In the configuration space we have

\begin{equation}
\Pi^{ai}=-4ke\Sigma^{a0i}\,.
\label{4}
\end{equation}
We find that $H$ may indeed be expressed
in terms of $e_{ak}$, $\Pi^{ak}$ and Lagrange multipliers. In ref.
\cite{Maluf3} we have redefined some Lagrange multipliers and
constraints in order to arrive at simpler form of $H$. Except for
a surface term it reads

\begin{equation}
H=e_{a0}C^a+{1\over 2}\lambda_{ab}\Gamma^{ab}\,,
\label{5}
\end{equation}
where $e_{a0}$ and $\lambda_{ab}=-\lambda_{ba}$
are Lagrange multipliers, and $C^a$ and $\Gamma^{ab}$ are
first class constraints. After solving one set of Hamilton's
field equations we may identify $\lambda_{ik}=1/2(T_{i0k}-T_{k0i})$
and $\lambda_{0k}=T_{00k}$. The quantities $\lambda_{ik}$ and
$\lambda_{0k}$ are components of
$\lambda_{\mu\nu}=e^a\,_\mu e^b\,_\nu \lambda_{ab}$.
For further details see refs. \cite{Maluf3,Maluf5}.

The constraint $C^a$ may be written in the form
$C^a=-\partial_i\Pi^{ai}+h^a$, where $h^a$ is an intricate
expression of the field quantities. We note that
$-\partial_i\Pi^{ai}$ is the only total divergence of the momenta
$\Pi^{ai}$ that arises in the expression of $C^a$. The integral form
of the equation $C^a=0$ motivates the definition of the gravitational
energy-momentum $P^a$ \cite{Maluf2},

\begin{equation}
P^a=-\int_V d^3x\,\partial_i \Pi^{ai}\,,
\label{6}
\end{equation}
where $V$ is an arbitrary volume of the three-dimensional space.
The emergence of
a nontrivial total divergence is a feature of theories with torsion.
Metric theories of gravity do not share this feature. The
integration of this total divergence yields a surface integral. If we
consider the $a=(0)$ component of eq. (6) and adopt asymptotic
boundary conditions for the tetrad field we find \cite{Maluf2} that
the resulting
expression is precisely the surface integral at infinity that
defines the ADM energy \cite{ADM}. This fact is a strong indication
(but no proof) that eq. (6) does indeed represent the gravitational
energy-momentum.

The constraint $\Gamma^{ab}$ is defined by \cite{Maluf3,Maluf5}

\begin{equation}
\Gamma^{ab}=M^{ab}+4ke(\Sigma^{a0b}-\Sigma^{b0a})\,,
\label{7}
\end{equation}
where $M^{ab}=e^a\,_\mu e^b\,_\nu M^{\mu\nu}=-M^{ba}$, and
$M^{\mu\nu}$ is given by

\begin{eqnarray}
M^{ik}&=&2\Pi^{\lbrack ik \rbrack}=e_a\,^i \Pi^{ak}-
e_a\,^k \Pi^{ai}\,, \\
M^{0k}&=&\Pi^{0k}=e_a\,^0 \Pi^{ak}\,.
\label{8,9}
\end{eqnarray}

Similar to the definition of $P^a$, the integral form of
the constraint equation $\Gamma^{ab}=0$ motivates the definition
of the space-time angular momentum. The equation $\Gamma^{ab}=0$
implies

\begin{equation}
M^{ab}=-4ke(\Sigma^{a0b}-\Sigma^{b0a})\,.
\label{10}
\end{equation}
Therefore we define \cite{Maluf3}

\begin{equation}
L^{ab}=-\int_V d^3x\; e^a\,_\mu e^b\,_\nu M^{\mu\nu}\,,
\label{11}
\end{equation}
as the 4-angular momentum of the gravitational field. This
definition differs by a sign from the definition presented in
ref. \cite{Maluf3}.

The evaluation of definitions (6) and (11) are carried out in the
configuration space, by means of eqs. (4) and (10), respectively.
However, if we consider (6) and (11) in the phase space of the
theory, with the right hand side of the latter equations given in
terms of the momenta $\Pi^{ai}$ (with the help of eqs. (8) and (9)),
we find that $P^a$ and $L^{ab}$ constitute a representation of the
Poincar\'{e} group. By working out the Poisson brackets between
$P^a$ and $L^{ab}$ in the full phase space of the theory we find
\cite{Maluf3}

\begin{eqnarray}
\lbrace P^a , P^b \rbrace &=& 0\,, \nonumber \\
\lbrace P^a , L^{bc} \rbrace &=& \eta^{ab} P^c -\eta^{ac} P^b
\,, \nonumber \\
\lbrace L^{ab}, L^{cd} \rbrace &=&
\eta^{ac}L^{bd} +\eta^{bd}L^{ac} -\eta^{ad}L^{bc}-\eta^{bc}L^{ad}
\,.
\label{12}
\end{eqnarray}
The Poincar\'{e} algebra of $P^a$
and $L^{ab}$ confirms the consistency of the definitions. We recall
that the evaluation of $P^a$ and $L^{ab}$ is carried out in an
arbitrary  volume $V$ of the three-dimensional space.

Two important
points must be noted. First, the Poincar\'e
algebra above is rigorously verified irrespective of the
specification of any surface term (surface integral) on the boundary
of $V$. Thus it is not necessary to impose boundary conditions to
obtain (12). Second, the procedure for obtaining (12) is {\it exactly
the same} procedure for obtaining the algebra of constraints of a
theory in Hamiltonian form (as in ref. \cite{Maluf5}, for instance).
Therefore the validity of the constraint algebra and of eq. (12) are
on equal footing.

Definitions (6) and (11) are invariant under (i) general coordinate
transformations of the three-dimensional space, (ii) time
reparametrizations, and (iii) global SO(3,1) transformations. The
non-invariance of these definitions under the local SO(3,1) group
reflects the frame dependence of the definitions. We have argued
\cite{Maluf1,Maluf3,GRG} that this dependence is a natural feature
of the gravitational energy-momentum defined by eq. (6).
In the TEGR each set of tetrad
fields is interpreted as a reference frame in spacetime. The
tetrad frame is adapted to observers whose four-velocity $u^\mu$ in
spacetime is identified with $e_{(0)}\,^\mu$, namely,
$e_{(0)}\,^\mu=u^\mu$, and is characterized by the acceleration
tensor $\phi_{ab}$ defined by \cite{Maluf1}

\begin{equation}
\phi_{ab}={1\over 2} \lbrack T_{(0)ab}+T_{a(0)b}-T_{b(0)a}
\rbrack\,.
\label{13}
\end{equation}
The tensor $\phi_{ab}$ characterizes the inertial properties of the
frame. It is clearly not invariant under the local SO(3,1) group. It
provides the values of the inertial accelerations that are necessary
to maintain the frame in a given orientation and inertial state, in
the gravitational field configuration defined by $g_{\mu\nu}$.

\section{The gravitational angular momentum of rotating sources}

\subsection{A simple model for rotating neutron stars}

The starting point of the present analysis is the analytic pulsar
model described in ref. \cite{AJ1}, which is taken to represent a
rotating neutron star. The model represents a star that
is approximately rigidly rotating.
In the latter reference the authors argue that although the stellar
rotation rate is a function of radius, it can be made arbitrarily
close to rigid rotation. For our purposes the model is important
because it is simple and singularity free, and allows to carry out
integration over the whole three-dimensional space. It is represented
by the metric tensor

\begin{equation}
ds^2=-\alpha^2dt^2+\beta^2dr^2+r^2d\theta^2+r^2\sin^2\theta
(d\phi-\Omega dt)^2\,.
\label{14}
\end{equation}

We denote by $R$ the stellar radius. For $r \le R$ we have

\begin{eqnarray}
\alpha&=&{1\over 2}\lbrack 3(1-8\pi\rho R^2/3)^{1/2}-
(1-8\pi\rho r^2/3)^{1/2}\rbrack \,, \nonumber \\
\beta^2&=&(1-8\pi\rho r^2/3)^{-1}\,, \nonumber \\
\Omega&=&\Omega(0)\lbrack 1- b(r/R)^2-b\tau (r/R)^4\rbrack \,,
\label{15}
\end{eqnarray}
and for $r \ge R$,

\begin{eqnarray}
\alpha^2&=& \lbrack 1-2m(R)/r \rbrack\,, \nonumber \\
\beta^2&=& \lbrack 1-2m(R)/r \rbrack^{-1}\,, \nonumber \\
\Omega&=&{{2J}\over r^3}={{2GJ_s}\over c^3r^3} \,,
\label{16}
\end{eqnarray}
where $\Omega$ is the angular velocity of inertial frames along the
rotation axis and $J_s$ represents the angular momentum of the star;
$\rho$ is the uniform density and $m(r)=4\pi\rho r^3/3$. The
quantity $b$ is defined by $b=3/(5+7\tau)$, where $\tau$ is a free
parameter. The case $\tau=0$ yields completely rigid rotation in the
Newtonian limit. For further details, see ref. \cite{AJ1}.

The evaluation of definition (11) is conceptually simple. It
requires the calculation of the tensors $T_{\lambda\mu\nu}$ and
$\Sigma^{\lambda\mu\nu}$. We only need to determine the tetrad field
adapted to a particular class of observers. We choose to work with
the tetrad field adapted to stationary observers. Such observers have
the velocity field $u^{\lambda}=(u^0,0,0,0)$.
Therefore we identify $e_{(0)}\,^\mu=u^\mu $ and require

\begin{equation}
e_{(0)}\,^i=0\,.
\label{17}
\end{equation}
Moreover we choose the $e_{(3)}\,^\mu$ component to coincide
asymptotically ($r\rightarrow \infty$) with the unit vector
$\hat{\bf z}$ along the $z$ axis, namely,

\begin{equation}
e_{(3)}\,^\mu (t,x,y,z)
\cong (0,0,0,1)\,.
\label{18}
\end{equation}
These two conditions were imposed
on the set of tetrad fields for the Kerr spacetime, discussed in
ref. \cite{Maluf1}. They do not fix the tetrad field completely
because of the axial symmetry of the spacetime. The orientations of
the $x$ and $y$ directions are arbitrary, except that the latter are
orthogonal.

The requirement of
the conditions above on $e_{a\mu}$ constructed out of (14) yields

\begin{equation}
e_{a\mu}(t,r,\theta,\phi)=\pmatrix{-A&0&0&-C\cr
0&B \,\sin\theta \cos\phi&
r \cos\theta \cos\phi & -D\, r \sin\theta \sin\phi\cr
0& B\, \sin\theta \sin\phi&
r \cos\theta \sin\phi &  D\, r \sin\theta \cos\phi\cr
0& B\, \cos\theta & -r\sin\theta&0}\,,
\label{19}
\end{equation}
with the following definitions,

\begin{eqnarray}
A(r,\theta)&=& (-g_{00})^{1/2}\,, \nonumber \\
B(r)&=&(g_{11})^{1/2}\,, \nonumber \\
C(r,\theta)&=&-{{g_{03}}\over{(-g_{00})^{1/2}}}\,, \nonumber \\
D(r,\theta)
&=&\biggl( {{-\delta} \over {g_{00}g_{33}}}
\biggr)^{1/2}\,, \nonumber \\
\delta&=& g_{03}g_{03}-g_{00}g_{33}\,.
\label{20}
\end{eqnarray}

The gravitational angular momentum density along the $z$ direction
is given by $M^{(1)(2)}$. Taking into account the definition of
$\Sigma^{abc}$ in (10) we find

\begin{equation}
M^{(1)(2)}=-2ke\,e^{(1)}\,_\mu e^{(2)}\,_\nu
\lbrack T^{0\mu\nu}-g^{0\mu}T^\nu+g^{0\nu}T^\mu \rbrack\,.
\label{21}
\end{equation}
The determinant $e$ reads
$e=r(g_{11}\,\delta)^{1/2}$. We recall that
$T^\mu=T^\lambda\,_\lambda\,^\mu$. The following relations are valid
for the metric tensor in spherical coordinates for the spacetime of
an arbitrary rotating source,

\begin{eqnarray}
g^{00}&=&- {g_{33} \over {\delta}}\,, \nonumber \\
g^{03}&=&{g_{03} \over {\delta}}\,, \nonumber \\
g^{33}&=& - {g_{00} \over {\delta}}\,.
\label{22}
\end{eqnarray}

In view of (19) we have

\begin{eqnarray}
e^{(1)}\,_1 e^{(2)}\,_2- e^{(1)}\,_2 e^{(2)}\,_1&=&0 \,,\nonumber \\
e^{(1)}\,_1 e^{(2)}\,_3- e^{(1)}\,_3 e^{(2)}\,_1&=&
BD\,r\sin^2\theta \,, \nonumber \\
e^{(1)}\,_2 e^{(2)}\,_3- e^{(1)}\,_3 e^{(2)}\,_2&=&
D\,r^2\sin\theta\,\cos\theta\,,
\label{23}
\end{eqnarray}
and $M^{(1)(2)}$ is first simplified as

\begin{eqnarray}
M^{(1)(2)}&=& -2ke\,BD\,r \sin^2\theta
(T^{013}+g^{03}T^1) \nonumber \\
{}&{}&-2ke\,D\,r^2\sin\theta \cos\theta
(T^{023}+g^{03}T^2) \nonumber \\
&=& -2ke\,BD\,r \sin^2\theta
\lbrack g^{11}(g^{00}g^{33}-g^{03}g^{03})T_{013} \nonumber \\
&{}&- g^{03}g^{11}g^{22}T_{212}\rbrack \nonumber \\
&{}&-2ke\,D\,r^2\sin\theta \cos\theta
\lbrack g^{22}(g^{00}g^{33}-g^{03}g^{03})T_{023} \nonumber \\
&{}&+
g^{03}g^{11}g^{22}T_{112}\rbrack \,.
\label{24}
\end{eqnarray}

The necessary torsion tensor components are

\begin{eqnarray}
T_{013}&=&-A\partial_1 C\,,\nonumber \\
T_{023}&=&-A\partial_2 C\,,\nonumber \\
T_{112}&=& 0 \,, \nonumber \\
T_{212}&=&r(1-B) \,,
\label{25}
\end{eqnarray}
where $\partial_1=\partial_r$ and $\partial_2=\partial_\theta$.
Considering $g^{00}g^{33}-g^{03}g^{03}=-1/\delta$ we find that
eq. (24) is written as

\begin{eqnarray}
M^{(1)(2)}&=&-2ke(BDr\sin^2\theta)\biggl[
{g^{11}\over \delta} A \partial_1 C-g^{03}g^{11}g^{22}\,r(1-B)
\biggr] \nonumber \\
&{}&-2ke(Dr^2\sin\theta\cos\theta)\biggl[{g^{22}\over \delta}
A\partial_2 C \biggr]\,.
\label{26}
\end{eqnarray}

After substitution of eq. (20) into (26) we obtain

\begin{eqnarray}
M^{(1)(2)}&=&2kr\sin\theta\;\partial_1 \biggl[
{g_{03} \over {(-g_{00})^{1/2}}}\biggr]
+2k\sin\theta \biggl[{g_{03} \over (-g_{00})^{1/2}}\biggr]
\biggl[1-(g_{11})^{1/2}\biggr] \nonumber \\
&{}&+2k \cos\theta \;(g_{11})^{1/2}\;\partial_2
\biggl[ {g_{03} \over {(-g_{00}^{1/2})}} \biggr]\,,
\label{27}
\end{eqnarray}
which leads to the final form of $M^{(1)(2)}$,

\begin{equation}
M^{(1)(2)}=2k\,{\partial \over {\partial r}}
\biggl[ {{r\,\sin\theta\,g_{03}}\over (-g_{00})^{1/2}}
\biggr]+2k\,{\partial \over {\partial \theta}}
\biggl[ {{\cos\theta\,(g_{11})^{1/2}\,g_{03}}\over (-g_{00})^{1/2}}
\biggr]\,.
\label{28}
\end{equation}

From eq. (14) we have $g_{03}=-\Omega(r)\,r^2\,\sin^2\theta$.
Taking into account definitions (15) and (16) we find

\begin{eqnarray}
\int_0^\infty dr\,
{\partial \over {\partial r}}
\biggl[ {{r\,\sin\theta\,g_{03}}\over (-g_{00})^{1/2}}
\biggr]&=&-2J\sin^3\theta \nonumber \\
\int_0^\pi d\theta\,{\partial \over {\partial \theta}}
\biggl[ {{\cos\theta\,(g_{11})^{1/2}\,g_{03}}\over (-g_{00})^{1/2}}
\biggr]&=&0 \,.
\label{29}
\end{eqnarray}

Therefore we have

\begin{eqnarray}
L^{(1)(2)}&=&-\int d^3x M^{(1)(2)} \nonumber \\
&=&-2k\int_0^{2\pi}d\phi \int_0^\pi
d\theta(-2J\sin^3\theta)\nonumber \\
&=&{{32\pi}\over 3}k\,J\,.
\label{30}
\end{eqnarray}
Considering that $k=c^3/(16\pi G)$ and $J=(G/c^3)J_s$, where $J_s$
is the angular momentum of the star, we finally obtain

\begin{equation}
L^{(1)(2)}={2\over 3} J_s\,.
\label{31}
\end{equation}
The evaluation of $L^{(1)(2)}$ is easy because $M^{(1)(2)}$ can be
expressed as a total divergence, and eventually $L^{(1)(2)}$ is given
by a surface integral. We see that the expression of $L^{(1)(2)}$ is
finite provided $-g_{00}\cong 1+O(1/r)$ and $g_{03}\cong O(1/r)$ at
spacelike infinity.

The expressions for $L^{(1)(3)}$ and $L^{(2)(3)}$
vanish because $e^{(1)}\,_i e^{(3)}\,_j- e^{(1)}\,_j e^{(3)}\,_i$
and $e^{(2)}\,_i e^{(3)}\,_j- e^{(2)}\,_j e^{(3)}\,_i$ contain the
functions $\sin\phi$ or $\,\cos\phi$, and the integration of these
functions from $0$ to $2\pi$ vanishes. We note that the quantities
above arise in the expressions of $M^{(1)(3)}$ and $M^{(2)(3)}$,
respectively, exactly like
$e^{(1)}\,_i e^{(2)}\,_j- e^{(1)}\,_j e^{(2)}\,_i$ does in eq. (21).

For the same reason above, we conclude that the
center-of-mass moments $L^{(0)(1)}$ and $L^{(0)(2)}$ vanish. The
only component that does not vanish on account of integrals like
$\int_0^{2\pi} d\phi\, \sin\phi=\int_0^{2\pi} d\phi\, \cos\phi=0$
is $L^{(0)(3)}$. From definition (10) we obtain

\begin{eqnarray}
M^{(0)(3)}&=&-2ke\lbrack e^{(0)}\,_0 e^{(3)}\,_1
(T^{001}-g^{00}T^1)\nonumber \\
&{}&+e^{(0)}\,_0 e^{(3)}\,_2
(T^{002}-g^{00}T^2)\nonumber \\
&{}&-e^{(0)}\,_3 e^{(3)}\,_1 (T^{013}-g^{03}T^1)\nonumber \\
&{}&-e^{(0)}\,_3 e^{(3)}\,_2 (T^{023}-g^{03}T^2)\rbrack\,.
\label{32}
\end{eqnarray}
After a long calculation and
several simplifications we arrive at

\begin{equation}
M^{(0)(3)}=2k\lbrack
\partial_1(D\,r^2\sin\theta\,\cos\theta)-
\partial_2(BD\,r\sin^2\theta)\rbrack \,.
\label{33}
\end{equation}
Since $D$ is a function of $\sin^2\theta$ we conclude that

\begin{equation}
\int_0^\pi d\theta\, \partial_1(D\,r^2\sin\theta\,\cos\theta)=
\int_0^\pi d\theta\, \partial_2(BD\,r\,\sin^2\theta)=0\,,
\label{34}
\end{equation}
and therefore $L^{(0)(3)}=0$. Thus the only nonvanishing component
of $L^{ab}$ is given by eq. (31).

\subsection{An arbitrary rotating source with axial symmetry}

The most general form of the metric tensor that describes the
spacetime generated by an arbitrary stationary
rotating source with axial
symmetry is represented by the line element
(see section 6.4 of ref. \cite{NKG})

\begin{equation}
ds^2=g_{00}dt^2+g_{11}dr^2+g_{22}d\theta^2+g_{33}d\phi^2
+2g_{03}d\phi\, dt\,,
\label{35}
\end{equation}
where {\it all} metric components depend on $r$ and $\theta$:
$g_{\mu\nu}=g_{\mu\nu}(r,\theta)$.
Denoting by $g$ the determinant of the metric tensor, we have
$\sqrt{-g}=\lbrack g_{11}g_{22}
(g_{03}g_{03}-g_{00}g_{33})\rbrack^{1/2}$. The inverse metric
components $g^{00}$, $g^{03}$ and $g^{33}$ are given by
eq. (22). Here we also have the quantity $\delta$ defined by
$\delta=g_{03}g_{03}-g_{00}g_{33}$.

The tetrad field adapted to stationary observers in spacetime (i.e.,
that satisfies conditions (17) and (18)) is written as

\begin{equation}
e_{a\mu}(t,r,\theta,\phi)=\pmatrix{-A&0&0&-C\cr
0&\sqrt{g_{11}} \,\sin\theta \cos\phi&
\sqrt{g_{22}} \cos\theta \cos\phi & -D\, r \sin\theta \sin\phi\cr
0& \sqrt{g_{11}}\, \sin\theta \sin\phi&
\sqrt{g_{22}} \cos\theta \sin\phi &  D\, r \sin\theta \cos\phi\cr
0& \sqrt{g_{11}}\, \cos\theta & -\sqrt{g_{22}}\sin\theta&0}\,.
\label{36}
\end{equation}
The functions $A, C$ and $D$ are quite similar to the corresponding
quantities in eq. (20),

\begin{eqnarray}
A(r,\theta)&=& (-g_{00})^{1/2}\,, \nonumber \\
C(r,\theta)&=&-{{g_{03}}\over{(-g_{00})^{1/2}}}\,, \nonumber \\
D(r,\theta)
&=&\biggl[ {{-\delta} \over {(r^2\sin^2\theta) g_{00}}}
\biggr]^{1/2} \,.
\label{37}
\end{eqnarray}
The same remarks about the fixation of the tetrad field given by (19)
hold in the present case.

The evaluation of $M^{ab}$ is carried out exactly as in the previous
subsection, and for this reason we will not present the details of
the calculations. The expression below for $M^{(1)(2)}$ does not
immediately arise as a total divergence. A number of simple
manipulations has
to be made in order to obtain its final form. We find that the two
nonvanishing components of $M^{ab}$ are

\begin{equation}
M^{(1)(2)}= 2k\biggl[
\partial_1\biggl(
{{g_{03}\sqrt{g_{22}}\,\sin\theta}\over \sqrt{-g_{00}}}\biggr)+
\partial_2 \biggl(
{{g_{03}\sqrt{g_{11}}\,\cos\theta}\over \sqrt{-g_{00}}}\biggr)
\biggr]\,,
\label{38}
\end{equation}
and

\begin{eqnarray}
M^{(0)(3)}&=& 2k\biggl[
\partial_1
\biggl(
{{\delta^{1/2}\sqrt{g_{22}}\,\cos\theta}
\over {\sqrt{-g_{00}} }}
\biggr)
-\partial_2
\biggl(
{{
\delta^{1/2}\sqrt{g_{11}}\,\sin\theta
}\over {
\sqrt{-g_{00}}
}}
\biggr) \biggr]\,.
\label{39}
\end{eqnarray}
It is not difficult to verify that if we reduce the metric
components to the values of eq. (14) we arrive at eqs. (28)
and (33).

In order to calculate the total gravitational angular momentum we
transform definition (11) into a surface integral such that the
surface of integration $S$, determined by the condition $r=$
constant, is located at spacelike infinity. Therefore we have

\begin{eqnarray}
L^{(1)(2)}
=-\int d^3x\,M^{(1)(2)}= -2k
\oint_{S\rightarrow \infty}\,d\theta d\phi
\biggl(
{{g_{03}\sqrt{g_{22}}\,\sin\theta}\over \sqrt{-g_{00}}}\biggr)\,,
\label{40}
\end{eqnarray}
assuming that the components of the metric tensor are regular at
the origin, and that $g_{03}=0$ for $r=0$.

At this point we may evaluate whether for a given spacetime metric
tensor the total gravitational angular momentum is finite, vanishes
or diverges. If $g_{\mu\nu}$ is given in spherical coordinates and
if the following asymptotic behaviour is verified,

\begin{eqnarray}
g_{03}& \cong & O(1/r)+\cdots \nonumber \\
g_{22}& \cong & r^2 + O(r)+ \cdots \nonumber \\
-g_{00}& \cong & 1 + O(1/r) + \cdots\,,
\label{41}
\end{eqnarray}
expression (40) will be finite. This result agrees with the analysis
of Beig and \'O Murchadha \cite{BM} and of Szabados \cite{Sza}.

The quantity $M^{(0)(3)}$ is interpreted as the gravitational center
of mass moment. It vanished for the model described by (14) because
the latter is spherically symmetric in the limit
$\Omega \rightarrow \infty$, and a nonvanishing $\Omega(r)$ given by
(15) and (16) does not alter the gravitational center of mass along
the $z$ axis. The model determined by (36) is arbitrary in the sense
that the metric tensor depends on $\theta$. In view of the axial
symmetry of the model, it is natural that the gravitational center of
mass vanishes along the $x$ and $y$ directions. Because of the
$\theta$ dependence of the metric tensor, (39) does not vanish
a priori.

Finaly we mention that the angular momentum of the Kerr spacetime
will be addressed elsewhere. In the spacetime of a rotating black
hole there exists the ergosphere, and inside the ergosphere it is not
possible to define stationary reference frames. The tetrad field
determined by conditions (17) and (18) and that yields the Kerr
spacetime is not (mathematically) defined inside the ergosphere.

\section{The frame dependence of the gravitational angular momentum}

Definition (11) for the gravitational angular momentum is not
invariant under local Lorentz transformations, and therefore it is
frame dependent. In this section we will discuss a physical
aspect of this feature. Before addressing this issue, let us
consider the frame dependence of the gravitational energy-momentum.
For this purpose we consider a black hole of mass $m$ and an
observer that is very distant from the black hole. The black hole
will appear to this observer as a particle of mass $m$, with energy
$mc^2$ ($m$ is the
rest mass of the black hole, i.e., the mass of the black hole
in the frame where the black hole is at rest).
If, however, the black hole is
moving at velocity $v$ with respect to the observer, then its total
gravitational energy will be $\gamma m c^2$, where
$\gamma=(1-v^2/c^2)^{-1/2}$. This example is a consequence of
the special theory of relativity, and demonstrates the
frame dependence of the gravitational energy-momentum. We note that
the frame dependence is not restricted to observers at spacelike
infinity. It holds for observers located
everywhere in the three-dimensional space.

The dependence of the gravitational angular momentum on the frame is
an intrinsic feature of definition (11). In order to understand some
consequences of this
feature, we will investigate a special set of tetrad fields. Let us
consider the frame for the spacetime of the rotating neutron star that
satisfies Schwinger's time gauge condition,

\begin{equation}
e_{(i)}\,^0=0\,.
\label{42}
\end{equation}
It reads

\begin{equation}
e_{a\mu}=\pmatrix{-\alpha&0&0&0\cr
\Omega r\,\sin\theta\,\sin\phi&\beta\,\sin\theta\,\cos\phi&
r\,\cos\theta\,\cos\phi&-r\,\sin\theta\,\sin\phi\cr
-\Omega r\,\sin\theta\,\cos\phi&\beta\,\sin\theta\,\sin\phi&
r\,\cos\theta\,\sin\phi&r\,\sin\theta\,\cos\phi\cr
0&\beta\,\cos\theta&-r\,\sin\theta&0}\,,
\label{43}
\end{equation}
where $\alpha$, $\beta$ and $\Omega$ are the quantities defined in
(14-16). This frame is adapted to the field of observers whose
velocity $e_{(0)}\,^\mu$ is given by

\begin{equation}
e_{(0)}\,^\mu(t,r,\theta,\phi)=
{1\over \alpha}(1,0,0,\Omega(r)\,)\,.
\label{44}
\end{equation}
$\Omega(r)$ is the dragging velocity of inertial frames that rotate
under the action of the neutron star.
The expression above for $e_{(0)}\,^\mu$ describes the velocity
field of observers in circular motion around the star.
It turns out that the angular momentum of the gravitational
field calculated out of (43) vanishes:
$L^{(1)(2)}=0$. It is not difficult to arrive at this result. Out of
eq. (43) we find

\begin{eqnarray}
T_{013}&=& -(1-\beta)\Omega r\sin^2\theta \,, \nonumber \\
T_{212}&=& (1-\beta)r \,, \nonumber \\
T_{313}&=& (1-\beta)r\sin^2\theta \,.
\label{45}
\end{eqnarray}
Working out and simplifying the expression for $M^{(1)(2)}$ we obtain

\begin{eqnarray}
M^{(1)(2)}&=& -2ke\biggl[
(e^{(1)}\,_0e^{(2)}\,_1-e^{(1)}\,_1e^{(2)}\,_0)g^{11}[(g^{00}g^{33}
-g^{03}g^{03})T_{313}\nonumber \\
&{}&+g^{00}g^{22}T_{212}] \nonumber \\
&{}&+(e^{(1)}\,_1e^{(2)}\,_3-e^{(1)}\,_3e^{(2)}\,_1)g^{11}
[(g^{00}g^{33}-g^{03}g^{03})T_{013}\nonumber \\
&{}&-g^{03}g^{22}T_{212}]
\biggr]
\,. \label{46}
\end{eqnarray}
Taking into account

\begin{eqnarray}
(g^{00}g^{33}-g^{03}g^{03})T_{313}+g^{00}g^{22}T_{212}
&=& -\frac{2}{\delta}\,T_{212}\sin^2\theta  \,, \nonumber \\
(g^{00}g^{33}-g^{03}g^{03})T_{013}-g^{03}g^{22}T_{212}
&=&\frac{2}{\delta}\,\Omega\,
T_{212}\sin^2\theta  \,,
\label{47}
\end{eqnarray}
and also that

\begin{eqnarray}
e^{(1)}\,_0e^{(2)}\,_1-e^{(1)}\,_1e^{(2)}\,_0
&=&  \Omega \beta r\sin^2\theta \,, \nonumber \\
e^{(1)}\,_1e^{(2)}\,_3-e^{(1)}\,_3e^{(2)}\,_1
&=&\beta r\sin^2\theta  \,,
\label{48}
\end{eqnarray}
we find that $M^{(1)(2)}=0$. The other components also vanish. We
note that observers with four-velocity given by (44) are
known in the literature as ZAMOs (zero angular momentum observers)
(see Ref. \cite{Schutz}, section 11.3). These observers follow
trajectories with constant radial coordinate $r$ and with angular
velocity given by the dragging velocity of inertial frames.

The result above shows that
observers that are in rotational motion around the rotating source
measure the gravitational angular momentum differently from
static observers. An explanation for this result must take into
account the angular momentum of the source, which is different for
observers at rest and for those that rotate around the source.
In the Newtonian limit of the theory the angular momentum of the
source in the frame of observers that rotate at the same angular
frequency vanishes. We know that this feature holds for a rigid body
in Newtonian mechanics, where the angular momentum depends not only
on the frame, but also on the origin of the frame.

We conclude that definition (11) for the angular momentum of
the field is a measure of the dragging of inertial frames.
Observers whose angular velocity around the rotating
source is the same as the dragging velocity $\Omega(r)$ do not
measure the dragging velocity itself (and possibly other dragging
effects), and therefore for these observers the
gravitational angular momentum vanishes.

Because of the frame dependence, the interpretation of definition
(11) is different from the standard interpretation of the
gravitational angular momentum \cite{BM,Sza} based on the idea of
conserved field quantities. The latter are obtained by means of
surface integrals at spacelike infinity. In our opinion these are
just two different interpretations that do not seem to be in
conflict.

\section{Conclusions}

The major reason for considering the present definition of
gravitational angular momentum is that it satisfies the Poincar\'e
algebra. In the framework of the TEGR the energy-momentum and
angular momemtum of the gravitational field are defined by suitably
interpreting the constraint equations of the theory, not by means of
boundary integrals of the Hamiltonian. Definitions (6) and (11) are
evaluated in the configuration space of the theory.

The definition for the gravitational angular momentum investigated
here yields consistent results in the consideration of
a rotating neutron star.
In the context of isolated rotating sources, we observe that
the angular momentum of the gravitational field is related to the
dragging velocity of inertial frames $\Omega(r)$.
By inspecting eqs. (28) and
(38) we see that the angular momentum density depends on $g_{03}$,
and typically we have $g_{03}\cong -\Omega(r) r^2\sin^2\theta$,
at least at great distances from the source. Therefore the
angular momentum of the spacetime is a closely related to the
dragging of inertial frames.

One main result of the paper
is eq. (40), which gives the gravitational angular momentum
generated by an isolated rotating source. Equation
(40) allows to verify precisely which is the asymptotic behaviour of
the metric tensor that leads to a finite value for the angular
momentum in the frame of stationary observers. In the consideration
of a rotating neutron star, we found that if $J$ is the angular
momentum of the star, the angular momentum of the gravitational field
is $2J/3$, in the limit of rigid rotation.
So far we do not have an explanation as to why the angular
momentum of the field is $2J/3$ (and not $J$).
This issue will be addressed in the
future. However, to our knowledge there is no physical requirement
for the two angular momenta, of the field and of the source, to be
the same.

\bigskip
\noindent {\bf Acknowledgement}\par
\noindent This work was supported in part by CNPQ.

redpajama_set_name: RedPajamaArXiv


Claudia and Augusto Florez-Cavassa, our partners in Peru, recently spent one year in the UK to train as community leaders. On their return to Peru they set out to find out what their community needed and consider what they could offer. Having trained as facilitators to deliver the Crossroads Personal Development Course, they decided to run the first Crossroads course in Peru in June.
The course itself challenges people to change negative views of life, by giving them the tools to approach their dreams and goals, their purpose. It teaches them that life can be difficult sometimes, but it doesn't end there.


Pentek ® Big Blue Filter Housings by Pentair offer the versatility to meet all of your large-capacity filtration needs, including high-flow and heavy-sediment applications. The extra large housing allows for greater cartridge capacity, reducing the number of vessels required for high flow-rate applications. The High-Flow Polypropylene (HFPP) cap is available with 3/4" inlet and outlet ports. The 1-1/2" internal port allows a greater volume of liquid to pass through the HFPP cap more rapidly.
Big Blue Housings are compatible with a broad range of chemicals and have a pressure relief button to assist with cartridge changes. They accept a wide variety of 4-1/2" diameter cartridges.


text:
FCC Sets Stage for Supplemental Changes to the Federal Telecom Pole Attachment Rate Formula
By Jim Tomlinson and John Seiver
Today, the FCC Wireline Competition Bureau released a Public Notice seeking to refresh the record on a Petition for Reconsideration filed by the National Cable & Telecommunications Association (NCTA), COMPTEL, and tw telecom in June 2011 seeking to change certain aspects of the FCC's new telecommunications pole attachment rate formula to make the telecommunications and cable pole attachment rates equivalent even when the number of attaching entities differ from the Commission's presumptions. Without changes to the formula, the telecommunications rate could significantly exceed the cable rate, thwarting the Commission's effort to align the two federal pole attachment rates.
In April 2011, the FCC voted to amend the federal telecommunications rate formula for pole attachments in an effort to equalize pole attachment fees for cable and telecom attachers. However, the rates were equalized only when the presumptions of five and three attaching entities were applied in urban and rural areas, respectively. The NCTA/COMPTEL/tw telecom Petition in June 2011 requested that the Commission clarify or expand the telecom rate formula to "provide the corresponding cost adjustments scaled to other entity counts" because the telecommunications rate could exceed the cable rate by as much as 70 percent if the number of attaching entities used was less than the presumptions. No action had been taken on the Petition although parties filed comments supporting and opposing the Petition.
As detailed in our March 2015 Advisory, the Commission recognized the possibility that its recent reclassification of broadband Internet access as a telecommunications service in the Open Internet Order could open the door for pole owners to impose higher telecommunications pole attachment fees, typically by rebutting the attaching entity presumptions, and the FCC even cautioned utilities against taking such action. Remarks by FCC Chairman Thomas Wheeler in a speech delivered today at NCTA-INTX in Chicago, however, suggest that the Commission may be inclined to revisit the changes it made in 2011 and again revise the telecom rate formula to achieve rate parity. Chairman Wheeler stated:
I intend to ensure that you do not confront excessive rates for pole attachments.
Today the Wireline Competition Bureau is issuing a short public notice calling for comment on the pending NCTA and COMPTEL petition for reconsideration seeking to clarify the Commission's intent from its 2011 reforms to level-set the cable and telecommunications rates for pole attachments.
Once the record is refreshed, my expectation is that a recommendation will be made to the full Commission to take any action it can to further align cable and telecommunication rates.
Comments will be due 21 days after publication of the Public Notice in the Federal Register, which has not yet occurred, and reply comments will be due 10 days thereafter.

redpajama_set_name: RedPajamaCommonCrawl


text:
Nigeria In Urgent Need Of Demilitarization As Army Treats 500 Human Rights Violation Cases
Chief of Civil Military Affairs in the Nigerian Army, Maj. Gen. Markus Kangye, said his department has received and treated more than 500 complaints of human rights violations since 2016. This is a tip of the iceberg, but, however, it underscores the urgent need to end the decades old militarization of the country.
Lt. Gen. Kangye who disclosed this during the first quarter Civil Military Cooperation (CIMIC) media chat on Tuesday in Abuja, added that appropriate sanctions were applied where necessary.
The general said the formation of the Civil-Military Legal Desk (CMLD) in February 2016 to address alleged human rights violations by troops during internal security and counter terrorism and counter insurgency operations was a milestone.
General Kangye said the desk is a cell under this department that receives and facilitates investigations of alleged human rights violations against military personnel and recommends appropriate sanctions.
He added that the desk was established at the various divisions to address similar issues in their respective areas of responsibility, adding that plans were being made to establish same at unit level.
Gen. Kangye stated that all the complaints received were investigated, adding that some of the complaints were found credible while some were not.
"This underscores the premium the COAS places on human rights issues.
"In order to drive this policy, 24-hour call centre, with designated short code, 193, was established on May 30, 2017 to receive emergency calls.
"Since inception, the desk has received over 500 complaints which were treated and appropriate sanctions applied where necessary.
"Thus, available statistics show that there has been a drastic reduction in litigation cases involving Nigerian army personnel in recent times.
"This could be attributed to the constant sensitisation workshops to human rights conducted across the divisions and formations coupled with the impact of the desk's sanctions on offenders," he said.
He said the media chat was organised in line with army's drive toward keeping the media informed of its CIMIC and Civil-Military Relations (CMR) activities.
He said it was a means of eliminating rumours as well as providing accurate and timely information in line with international best practices.
According to him, the forum presents an avenue for the department to engage with various media practitioners for a better understanding.
He said it was with a view to charting a mutually benefitting relationship to improve media reportage and the non-kinetic lines of army operations.
He said it reinforced the COAS' vision of having "a Professional Nigerian Army Ready to Accomplish Assigned Missions within a Joint Environment in Defence of Nigeria".
Brig.-Gen. Ojogbane Adegbe, the Director, Psychological Operations, Department of Civil Military Affairs, said the combination of kinetic and non-kinetic operations in addressing security challenges was in line with international best practices.
Adegbe said the department had achieved milestone in the non-kinetic approach through various intervention programmes for communities in places where there were military operations across the country.
He said that the department had constructed or renovated a number of classrooms and hospitals in different communities toward winning the hearts and minds of the civil populace.
Adegbe added that social media seminars were being organised for social media influencers and bloggers across the country to counter fake news and wrong narratives about military operations in public space.
He said that cyberspace dimension was added to warfare operations adding that there was need to play active in secondary cyberspace.
According to him, the conduct of the seminar has so far created unique and valuable platform for army to interact with social media practitioners and influencers in support of its operations.
A former army spokesperson, retired Brig.-Gen. Sani Usman, said there was need for constructive engagement between the military and the media to ensure cordial relationship.
Usman, who delivered a paper titled "Media Operations in Contemporary Warfare: Operation Hadin Kai in perspective", said the military needed the media to succeed in its operations.
He also urged military spokespersons to be proactive in their media engagements to avoid giving room for speculations adding that information was an essential requirement of journalism profession.
He said that military spokespersons should know that timely, accurate and valid information were what the media required to function effectively.
He also urged newsmen to also strive to do their job without jeopardising military operations as reporting a planned operation could jeopardise such operation.
"So the suspicion against the media is not out of place because they tend to report sensationally and unprofessionally.
"Of course, there are several instances where the media usually are also guilty by jeopardising the military operations, compromising national security and even the lives of troops and citizens," he said.
Usman, however, urged the military and the media to work together as partners in progress toward tackling the security challenges bedeviling the country.
Categories: National Security, Nigeria
Tagged as: Atlantic Post National Security, Civil Military Affairs, Demilitarization, featured, Human Rights Violations, Markus Kangye, The Nigerian Army
BREAKING: Umanah Umanah, Infamous Ponzi Scheme Operator Jailed 20 Years in Uyo
2023: Stick To Constitutional Mandate, Avoid Politicking, Army Chief Orders Troops


hd00:16Looped seamless footage for your event, concert, title, presentation, site, DVD, music videos, video art, holiday show, party, etc… Also useful for motion designers, editors and VJ s for led screens.
hd00:11Vj Background Pink Motion With Fractal Background. Abstract background for use with music videos. Disco spectrum lights concert spot bulb. Seamless loop.


text:
#ifndef PCL_SAMPLE_CONSENSUS_MODEL_NORMALSPHERE_H_
#define PCL_SAMPLE_CONSENSUS_MODEL_NORMALSPHERE_H_

#include <pcl/sample_consensus/sac_model.h>
#include <pcl/sample_consensus/sac_model_sphere.h>
#include <pcl/sample_consensus/model_types.h>
#include <pcl/common/common.h>

namespace pcl
{
  /** \brief @b SampleConsensusModelNormalSphere defines a model for 3D sphere
    * segmentation using additional surface normal constraints. Basically this
    * means that checking for inliers will not only involve a "distance to
    * model" criterion, but also an additional "maximum angular deviation"
    * between the sphere's normal and the inlier points normals.
    *
    * The model coefficients are defined as:
    *

    *
a : the X coordinate of the plane's normal (normalized)
    *
b : the Y coordinate of the plane's normal (normalized)
    *
c : the Z coordinate of the plane's normal (normalized)
    *
d : radius of the sphere
    *

    *
    * \author Stefan Schrandt
    * \ingroup sample_consensus
    */
  template <typename PointT, typename PointNT>
  class SampleConsensusModelNormalSphere : public SampleConsensusModelSphere<PointT>, public SampleConsensusModelFromNormals<PointT, PointNT>
  {
    public:
      using SampleConsensusModel<PointT>::model_name_;
      using SampleConsensusModel<PointT>::input_;
      using SampleConsensusModel<PointT>::indices_;
      using SampleConsensusModel<PointT>::radius_min_;
      using SampleConsensusModel<PointT>::radius_max_;
      using SampleConsensusModelFromNormals<PointT, PointNT>::normals_;
      using SampleConsensusModelFromNormals<PointT, PointNT>::normal_distance_weight_;
      using SampleConsensusModel<PointT>::error_sqr_dists_;

      typedef typename SampleConsensusModel<PointT>::PointCloud PointCloud;
      typedef typename SampleConsensusModel<PointT>::PointCloudPtr PointCloudPtr;
      typedef typename SampleConsensusModel<PointT>::PointCloudConstPtr PointCloudConstPtr;

      typedef typename SampleConsensusModelFromNormals<PointT, PointNT>::PointCloudNPtr PointCloudNPtr;
      typedef typename SampleConsensusModelFromNormals<PointT, PointNT>::PointCloudNConstPtr PointCloudNConstPtr;

      typedef boost::shared_ptr<SampleConsensusModelNormalSphere> Ptr;

      /** \brief Constructor for base SampleConsensusModelNormalSphere.
        * \param[in] cloud the input point cloud dataset
        * \param[in] random if true set the random seed to the current time, else set to 12345 (default: false)
        */
      SampleConsensusModelNormalSphere (const PointCloudConstPtr &cloud,
                                        bool random = false)
        : SampleConsensusModelSphere<PointT> (cloud, random)
        , SampleConsensusModelFromNormals<PointT, PointNT> ()
      {
        model_name_ = "SampleConsensusModelNormalSphere";
      }

      /** \brief Constructor for base SampleConsensusModelNormalSphere.
        * \param[in] cloud the input point cloud dataset
        * \param[in] indices a vector of point indices to be used from \a cloud
        * \param[in] random if true set the random seed to the current time, else set to 12345 (default: false)
        */
      SampleConsensusModelNormalSphere (const PointCloudConstPtr &cloud,
                                        const std::vector<int> &indices,
                                        bool random = false)
        : SampleConsensusModelSphere<PointT> (cloud, indices, random)
        , SampleConsensusModelFromNormals<PointT, PointNT> ()
      {
        model_name_ = "SampleConsensusModelNormalSphere";
      }

      /** \brief Empty destructor */
      virtual ~SampleConsensusModelNormalSphere () {}

      /** \brief Select all the points which respect the given model coefficients as inliers.
        * \param[in] model_coefficients the coefficients of a sphere model that we need to compute distances to
        * \param[in] threshold a maximum admissible distance threshold for determining the inliers from the outliers
        * \param[out] inliers the resultant model inliers
        */
      void
      selectWithinDistance (const Eigen::VectorXf &model_coefficients,
                            const double threshold,
                            std::vector<int> &inliers);

      /** \brief Count all the points which respect the given model coefficients as inliers.
        * \param[in] model_coefficients the coefficients of a model that we need to compute distances to
        * \param[in] threshold maximum admissible distance threshold for determining the inliers from the outliers
        * \return the resultant number of inliers
        */
      virtual int
      countWithinDistance (const Eigen::VectorXf &model_coefficients,
                           const double threshold);

      /** \brief Compute all distances from the cloud data to a given sphere model.
        * \param[in] model_coefficients the coefficients of a sphere model that we need to compute distances to
        * \param[out] distances the resultant estimated distances
        */
      void
      getDistancesToModel (const Eigen::VectorXf &model_coefficients,
                           std::vector<double> &distances);

      /** \brief Return an unique id for this model (SACMODEL_NORMAL_SPHERE). */
      inline pcl::SacModel
      getModelType () const { return (SACMODEL_NORMAL_SPHERE); }

    	EIGEN_MAKE_ALIGNED_OPERATOR_NEW

    protected:
      /** \brief Check whether a model is valid given the user constraints.
        * \param[in] model_coefficients the set of model coefficients
        */
      bool
      isModelValid (const Eigen::VectorXf &model_coefficients);

  };
}

#ifdef PCL_NO_PRECOMPILE
#include <pcl/sample_consensus/impl/sac_model_normal_sphere.hpp>
#endif

#endif  //#ifndef PCL_SAMPLE_CONSENSUS_MODEL_NORMALSPHERE_H_


Keep your digital strategy project in New York on a tight rein!
Searching for a collaborator in the neighborhood of New York for your next communication operation? Do not lose lots of hours and call us. Since digital marketing companies will be a huge support for your digital strategy building or your linkbuilding operations.
digital marketing companies in New York.
A large inventory of services is provided by digital marketing companies, for example digital strategy building and digital strategy formations. Thus don't hold off anymore and call those firms through our site, and you will manage to commence your activity directly.
To be successful in, for example, a campaign in digital strategy formations or in digital strategy building, is cooperating with a expert company in digital strategy of capital importance. And your company surely fathoms that there is a flood of expert companies like that in the world. So keep things simple and email Sortlist.
digital marketing companies in New York have a lot of genius, so your firm can be sure that they will convey huge benefits to your task. They will have a immense positive imprint on your business. This is one more reason to collaborate with our company.
Why work with a digital marketing company in New York?
We also can mention an advantage with the popular dictum: time is money! Why waste time on an task that your business doesn't fully understand. Keep focused on your core business and do not take a chance with the creation of an activity that your enterprise doesn't master.
No more annoyance and neverending investigating for the perfect digital marketing company, Sortlist is the ideal solution. Deliver Sortlist your assignment immediately, and our team will guide your company in finding the perfect agency.


The show takes a moment to make us care about it characters—something this Trek outing should have been doing all along.
With its two-part premiere, "The Battle of the Binary Stars" Star Trek: Discovery went 0 to 60 in a heartbeat, and the show never really took its foot off the gas. Discoverydevolved into a narrative wrecking ball, bashing through plots points and plot twists in equal measure. The show delivered great highs for adrenaline junkies, but little in the way of subtlety or true character development.
That changed with Discovery's latest episode "The War Without, The War Within." We get interactions, strategy, and nuanced performances. This welcome slowdown is probably just the calm before the Klingon storm that will be next week's season finale, but it would up being one of the best episodes of Discovery yet.
Without much time to breathe, acting captain Saru and the Discovery crew find themselves in a cosmic pickle. After overshooting their time-traveling return date by 9 months—and failing to deliver the cloaking tech they pilfered off the Klingon Ship of the Dead way back when—they find that the Klingons have won massive amounts of territory from the Federation in the meantime.
Within the show's opening few minutes, the Discovery receives a hail from Admiral Cornwell, who boards the ship and assumes command by shouting a bunch of stuff at the ship's computer. It's a bit of a backhand to Saru's character, who's more than earned the right to captain the USS Discovery. But that's the chain of command.
Burnham, Saru, and Stamets get the rundown on what they've missed: The Discovery was thought destroyed when Lorca took the ship to the Mirror Universe, but the destroyed ship was actually the ISS Discovery captained by evil Tilly. We then learn that things went from bad to worse for the Federation. No long united under a single house, the Klingons spread throughout Federation space killing anything in their path.
It's a moment we've rarely seen from the Federation, and throughout the episode, we learn just how desperate Starfleet has become after nine months on the losing side.
When Cornwell arrives on the bridge with Sarek in tow, the two quickly get an assessment of Lorca's betrayal and the Discovery's ordeal in the mirror universe thanks to a quick, no-permission-required mindmeld with Saru. Of course, there's one tiny detail still left unsaid—the Kelpian-eating psychopath Emperor Georgiou.
The Starfleet we know from other Trek shows wouldn't have much use for someone whose favorite pastime is murder, but as Discovery has made abundantly clear, this isn't the Starfleet we know. Clawing like a rabid animal backed into a corner, Cornwell and Burnham recognize the fact that in the mirror universe the Klingons are defeated, and Starfleet wants to know how.
Klingons will never stop, unless you stop them yourself.
This is a two-pronged attack. Cornwell also visits L'Rell, still locked up in Discovery's brig after a successful(?) Voq/Tyler mind extraction. Cornwell tells L'Rell that the unified Klingon race she hoped for, the empire that would blossom from a war with the Federation, has descended into chaos as the 24 Klingon houses separately savage the Alpha quadrant. She pleads with L'Rell, saying T'Kuvma was an ignorant fool for thinking the Federation wanted to homogenize and assimilate Klingon culture.
But L'Rell has bad news for Cornwell: The Klingons will never stop unless you stop them yourself. Georgiou gives similar advice, calling Klingons a cancer and saying the only way to stop a cancer is to cut out the tumor known as the Klingon homeworld Q0'nos.
A plan is born: Stamets will quickly regrow some spores (a suspiciously convenient plot point) and jump the entire Discovery ship into a cave system in the planet. Yes, inside the planet. Cornwell and Burnham seem prepared to attempt the unthinkable—they're going to give command to psycho Georgiou.
Bargaining her service for her eventual freedom, Georgiou cuts some sort of off-camera deal with Sarek and Cornwell. Whether it's to confuse the Klingons who think she's dead or because the Federation needs her bloodthirsty, victory-at-all-costs approach, the result is the same. The USS Discovery just traded one mirror universe captain for another.
"The War Within" is a welcome episode because, really for the first time, battle takes a backseat and Discovery takes some time to develop its characters.
It starts at the very beginning. Acting captain Saru meets evil Georgiou with all the emotional weight that entails. The situation isn't helped by Georgiou explaining that in her universe, Kelpians are a delicacy. Saru then speaks with Burnham, asking her to assess Ash Tyler. She asks if that's an order, and when he says it is not, she refuses.
These scenes, though not exactly Shakespearean, are showing rather than telling the audience how characters are feeling. It was a nice few minutes of character development.
Saru then comforts Tyler alone, saying the murderous actions of Voq are not Ash Tyler's actions. He places Tyler under a type of house arrest light, but says he has no desire to take away his freedom. It's a tense moment for two characters who haven't spent a ton of time interacting on screen. This consoling moment is just more evidence that Saru should remain captain, now and always.
These are the moments that Discovery needs, characters speaking with one another, sharing fears, pain, joy.
In other moments, Stamets confronts Tyler, finally giving us some indication that Culber's death is affecting the usually chipper science officer, and Tyler is welcome back into the Federation fold during a tense-but-sweet moment in the Discovery mess hall.
Finally, after speaking with Sarek for some Vulcan fatherly advice, Burnham finally works up the nerve to see Tyler. Instead of offering the audience an easy way out with any kind of closure, the conversation is angry, painful, sad, and offers no simple answers. It's the first time that really sold to me that Tyler really meant something to Burnham. I actually felt something for their relationship.
These are the moments that Discovery needs. We've now spent 14 episodes with these characters, and some of them feel like strangers, or worse, set dressing.
The episode wasn't perfect by any means. Character motivations still make no sense (Burnham, evil Georgiou is not subject to political asylum) and an entire intergalactic war is almost invisible to the audience, simply summed up in big, sweeping moments of exposition. But it lays the necessary groundwork so when Discovery does deliver eye-popping plot twists, you actually feel for Burnham, Saru, Stamets, and everyone else.
It's something the show should have been doing since its opening episode, but hey, better late than never.
The Discovery is a Crossfield-class vessel, I assume in honor or Albert Scott Crossfield, the first pilot to fly at twice the speed of sound. I dig it.
Love the NX-01 name drop. Enterprise has been getting a lot of love on this show.
I'm glad Stamets finally decided to address Culber's death somewhat this episode, but I'm still not loving how seemingly easy he's bounced back.
Starfleet thinking up its daring plan to attack Qo'nos was some great sci-fi. Love the look and feel of hashing out the exact tactics all the way through.
Being able to just quickly regrow mycelium seems like a slightly too convenient plot device to fix what felt like a devastating end to the spore drive.
I fear this was just a breather episode, connecting one action-packed episode with another action-packed finale.


A hand tied bouquet ( in water) of mixed pink flowers which will include roses. Also available as a larger bouquets, if you click the price box below. NB.NOT available to UK addresses! Select the size you require in drop down box below.


text:
Сосна или Бистрая Сосна () е река в Орловска и Липецка област на Русия, десен приток на Дон. Дължина 296 km. Площ на водосборния басейн17 400 km².

Река Сосна води началото си от Средноруското възвишение, на 240 m н.в., на 3 km западно от село Фьодоровка в Орловска област. В горното течение тече в южна посока, в средното предимно в източна, а в долното – в североизточна през източните части на Средноруското възвишение в широка и добре оформена долина. Влива се отдясно в река Дон, при нейния 1608 km, на 105 m н.в., при село село Засосенка в Липецка област. Основни притоци: леви – Фошня (52 km), Труди (89 km), Ливенка (32 km), Болшая Чернава (54 km), Ясенок (25 km), Воргол (64 km); десни – Тим (120 km), Кшен (135 km), Олим (151 km), Свишня (36 km). Има смесено подхранване с преобладаване на снежното с ясно изразено пролетно пълноводие през март и април. Среден годишен отток на 37 km от устието 74 m³/s. Замръзва през ноември или декември, в някои години през януари, а се размразява в края на март или началото на април. По бреговете на реката са разположени няколко десетки населени места, в т.ч. град Ливни и селището от градски тип Колпи в Орловска област и град Елец в Липецка област.

Вижте също
 Списък на реките в Русия (водосборен басейн на Атлантическия океан)

Източници

Външни препратки
 Государственный водный реестр России река Сосна (приток на Дон)

Реки в Орловска област
Реки в Липецка област

redpajama_set_name: RedPajamaWikipedia


However, these meanings are somewhat conceptual; one can say, or read, "unduly cheerful" or "naively optimistic" without really considering the full meaning of the idiom.
to tell you the precise colour of something?
I'm pretty sure I wouldn't!
What I mean is, with the greatest efforts to provide accurate information, the rose-tinted spectacle wearer can never truly see the actual colour without removing the spectacles.
You want everything looking pink?
That's okay by me!What I would expect though, is that ALL pink-spectacle wearers would then be responsible enough to accept that they cannot give an accurate description of coloured objects, and agree to remove their glasses as and when required.
Further though, it would not be unreasonable to expect spectacle wearers, upon realising they cannot see 'properly' with the spectacles on, to henceforth, whilst wearing them, avoid offering descriptions where colour is involved, or offering opinions on whether colours or tones match, or any aspect which would fall within the colour spectrum.
All well and good so far?
"Discerning the colour of something is insufficient grounds for risking one's life! Does knowing the true colour of things really matter?"
They may even argue that there is no distortion, and why should they prove to you, that what they see is not reality?
Whereas the individual rose-coloured spectacle wearer, may have a temporary, psychological need to believe the best of someone, to overlook another's faults, to achieve a work contract for example, the rose-tinted spectacles worn by the religious, are enforced by the religion too which they are bound!
Under threat of immortal damnation!
As an atheist, I am free to consider the mythical supernatural landscapes objectively, free from fear of reprisal, but religious doctrine often prohibits the faithful the same freedom. The moment a religious person psychologically steps away from the god figure to, freely, critically assess the concept, they have instantly committed the "worst" sin and are condemned to the hell conjured by their doctrine.
hindered by the very doctrine they promote!
Faith shackles the religious person to off-the-peg Rose-tinted spectacles, limiting their view of reality to what can be seen through their doctrine's brand of lenses.
Is any point a religious person makes valid?
I pity those trapped in the superstition soup.
Remove the spectacles friends and"Let's think about God"


text:
// @flow

import React, { Component } from 'react';
import { Link } from 'react-router'
require('./../../../public/custom.css')
import moment from 'moment'

function formatDate(date){
  if (date == null) return "-"
  return moment(date).utcOffset(8).format('M/D/YY')
}

class InspectionDetails extends Component {
  render() {
    const { inspection, toggleEdit } = this.props
    console.log('inspection details part: ',inspection)
    return (

        <button className='edit' onClick={toggleEdit} style={{float: 'right'}}>EDIT</button>

          DOB #

 {inspection.DOB}

          Address

 {inspection.address.line1}

 {inspection.address.line2}

            {inspection.address.city}, {inspection.address.state}, {inspection.address.zip}

         Client Type

 {inspection.clientType}

        Records on File

                Record Type
                Status

                Proposal
                 {formatDate(inspection.recordsOnFile.proposal)}

                Engagement Letter
                 {formatDate(inspection.recordsOnFile.engagementLetter)}

                Invoice
                 {formatDate(inspection.recordsOnFile.invoice)}

                Report Type
                TR1
                TR8

              Special Inspection
               { formatDate(inspection.reports.specialInspection.TR1)}
               { formatDate(inspection.reports.specialInspection.TR8)}

              Initial Report Copies
               { formatDate(inspection.reports.initialReportCopies.TR1)}
               { formatDate(inspection.reports.initialReportCopies.TR8)}

              Final Reports
               { formatDate(inspection.reports.finalReports.TR1)}
               { formatDate(inspection.reports.finalReports.TR8)}

        { /*  Progress Check-in Dates  */}

        Inspection Information

              Inspection Info
              Status

              Date
               { formatDate(inspection.inspectionInformation.date) }

              Inspector Name
               {inspection.inspectionInformation.inspector}

              Results
               {inspection.inspectionInformation.results}

              Report Filed
               { formatDate(inspection.inspectionInformation.reportFiled) }

              Signed-off Date
               { formatDate(inspection.inspectionInformation.signedOffDate) }

        {/* Comments  */}

    );
  }
}

export default InspectionDetails


Love that bracelet! I always get so sore when I add strength training back in after a break. Your body will adjust though! For me it depends how sore I am. If Im just a little sore I will usually do some easy runs to shake them out. Otherwise I find that yoga helps!
Yoga is a good idea. I guess I need to stretch it out!
Yea, that bracelet just made my day!
Love that bracelet. I don't do strength training - probably should. Congrats on your return to running. Good luck in your 5k. Can't wait to hear how it goes.
If I am super sore, I may give it another day of rest. Sometimes I'll do a lighter workout to flush them out. I'm typically pretty careful of when I train legs for that exact reason. Yay for 5ks!
I hope it don't take too long to shake it off!
You know me--I just push through the soreness! I always hope that the movement will loosen things up, which is usually the case.
I'm hoping to do a small run tomorrow and see how it feels.
Great job on getting everything planned! I love that bracelet! Good luck on your races!!
Thanks Tara! It's gonna be a busy month for sure!
I usually push through soreness, although not pain. Additional stretching and rolling should help reduce that quickly too. Your new bracelet was such a sweet gift. Can't wait to hear where you decided to take a vacation!
Yea, it's definitely sore an not pain. I decided to do a short run today an it was actually okay!
I do less exercises the next day if I'm sore, but if it's more than sore, I give myself a break. Mostly it's knots here and there, so I strength train as well as a lot of foam rolling.
I do need to foam roll more. Hmm, seems like I say that a lot!
Awesome that you picked out a few 5K races! I'd like to do more 5Ks but don't run races in the summer.
I love to run in the summer because I have more time to train.
The bracelet is such a sweet gesture from your sister. Since I don't do weights, I can't answer your question. But sometimes my legs are sore from cycling or skiing and I go ahead with my run cause I feel like I won't be using the exact same muscles. Good luck this weekend at the 5k! Thanks for linking with us Meranda!
Thanks Holly. It's gonna be a hot one so I don't know how it will go!
I went to see the Movie too!! I liked it, but like you said, it was a very brief version of the book. I cried more with the book... I'm a book and movie crier.
Have an awesome time on your 5K this weekend! Looking forward to the recap!
Yes! I actually cried at the book too!
I go to a trainer twice a week and more times than not I'm running on something sore. Sore = a good workout right? I do try and get my run in the morning after a lifting session. Sometimes for me the DOMS doesn't set in until 24 hrs. so usually I can manage this ok. If it's my legs or hamstrings that are sore I tend to take it more easy until the soreness goes away. Good luck so glad your getting back in Maranda. Thanks for linking up.
I use to run after the gym all the time last summer because there is a great route by the gym.
sounds like your summer is coming together nicely! Cute bracelet! You know I am getting old so I gotta keep moving! have a great week!
I suppose keep moving is not such a bad idea!
I'll be going on another cruise and then to the beach!
I love the momentum jewelry it's so cute and yes motivating! 5k's are great in the summer when it's so hot. Have a great week!
This is my first piece of Momentum jewelry!
I have the same momentum wrap and love it !
I love the Momentum wraps! Although I haven't gotten one for myself yet. Good luck with the races that you've chosen.


Two ACCES Employment alumni, Carla Ramos, who now works at Rogers Communications, and Fraje Nersesian, who now works at TD Wealth Management, share their job search journey and provide helpful advice.
They are amongst many newcomers who have come through ACCES and have successfully launched their careers in Canada. Both Carla and Fraje are from the Leadership Connections bridging program in Toronto.