358 research outputs found
Derivations of the Lie Algebras of Differential Operators
This paper encloses a complete and explicit description of the derivations of
the Lie algebra D(M) of all linear differential operators of a smooth manifold
M, of its Lie subalgebra D^1(M) of all linear first-order differential
operators of M, and of the Poisson algebra S(M)=Pol(T*M) of all polynomial
functions on T*M, the symbols of the operators in D(M). It turns out that, in
terms of the Chevalley cohomology, H^1(D(M),D(M))=H^1_{DR}(M),
H^1(D^1(M),D^1(M))=H^1_{DR}(M)\oplus\R^2, and
H^1(S(M),S(M))=H^1_{DR}(M)\oplus\R. The problem of distinguishing those
derivations that generate one-parameter groups of automorphisms and describing
these one-parameter groups is also solved.Comment: LaTeX, 15 page
Time-Varying Gravitomagnetism
Time-varying gravitomagnetic fields are considered within the linear
post-Newtonian approach to general relativity. A simple model is developed in
which the gravitomagnetic field of a localized mass-energy current varies
linearly with time. The implications of this temporal variation of the source
for the precession of test gyroscopes and the motion of null rays are briefly
discussed.Comment: 10 pages; v2: slightly expanded version accepted for publication in
Class. Quantum Gra
Direction of light propagation to order G^2 in static, spherically symmetric spacetimes: a new derivation
A procedure avoiding any integration of the null geodesic equations is used
to derive the direction of light propagation in a three-parameter family of
static, spherically symmetric spacetimes within the post-post-Minkowskian
approximation. Quasi-Cartesian isotropic coordinates adapted to the symmetries
of spacetime are systematically used. It is found that the expression of the
angle formed by two light rays as measured by a static observer staying at a
given point is remarkably simple in these coordinates. The attention is mainly
focused on the null geodesic paths that we call the "quasi-Minkowskian light
rays". The vector-like functions characterizing the direction of propagation of
such light rays at their points of emission and reception are firstly obtained
in the generic case where these points are both located at a finite distance
from the centre of symmetry. The direction of propagation of the
quasi-Minkowskian light rays emitted at infinity is then straightforwardly
deduced. An intrinsic definition of the gravitational deflection angle relative
to a static observer located at a finite distance is proposed for these rays.
The expression inferred from this definition extends the formula currently used
in VLBI astrometry up to the second order in the gravitational constant G.Comment: 19 pages; revised introduction; added references for introduction;
corrected typos; published in Class. Quantum Gra
General post-Minkowskian expansion of time transfer functions
Modeling most of the tests of general relativity requires to know the
function relating light travel time to the coordinate time of reception and to
the spatial coordinates of the emitter and the receiver. We call such a
function the reception time transfer function. Of course, an emission time
transfer function may as well be considered. We present here a recursive
procedure enabling to expand each time transfer function into a perturbative
series of ascending powers of the Newtonian gravitational constant (general
post-Minkowskian expansion). Our method is self-sufficient, in the sense that
neither the integration of null geodesic equations nor the determination of
Synge's world function are necessary. To illustrate the method, the time
transfer function of a three-parameter family of static, spherically symmetric
metrics is derived within the post-linear approximation.Comment: 10 pages. Minor modifications. Accepted in Classical and Quantum
Gravit
Radioscience simulations in General Relativity and in alternative theories of gravity
In this communication, we focus on the possibility to test GR with
radioscience experiments. We present a new software that in a first step
simulates the Range/Doppler signals directly from the space time metric (thus
in GR and in alternative theories of gravity). In a second step, a
least-squares fit of the involved parameters is performed in GR. This software
allows one to get the order of magnitude and the signature of the modifications
induced by an alternative theory of gravity on radioscience signals. As
examples, we present some simulations for the Cassini mission in
Post-Einsteinian gravity and with the MOND External Field Effect.Comment: 4 pages; Proceedings of "Les Rencontres de Moriond 2011 - Gravitation
session
'Thank you for loving me': A qualitative study on perceptions of gratitude and their effects in palliative care patients and relatives.
Empirical studies suggest that gratitude positively influence the quality of life of palliative patients and relatives. However, the literature is marked by a lack of conceptual clarity about what gratitude is and whether it can bring about individual and social benefits.
This paper explores how palliative care patients and relatives understand gratitude, how discursive representations of gratitude may affect their positions, perceptions and relations, and how to conceptualise gratitude in the palliative context.
We examine 33 gratitude letters written by patients and relatives and 25 semi-structured interviews conducted as part of a pilot gratitude intervention study. We use a qualitative approach, thematic analysis, within a conceptual framework of discourse analysis.
Data were collected from 23 patients and 13 relatives recruited through three hospital palliative care services in French-speaking Switzerland.
Participants articulate gratitude in five ways: (1) appreciating others; (2) love; (3) need to reciprocate; (4) appreciating the little things; (5) solace amid serious illness. While some of these representations are sources of positive emotions and outlook, wellbeing and hope, others may confirm self-perceptions of powerlessness and burden. These results support a tridimensional conceptualisation of gratitude in palliative care as source of individual benefits, valuing closest relationships and moral obligation.
Our study suggests that gratitude is a key to a good (end of) life, whilst highlighting potential negative effects. It could help healthcare professionals to better understand what gratitude means to patients and relatives, which may facilitate awareness and fostering of gratitude in palliative care
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