376 research outputs found
Sequences of Willmore surfaces
In this paper we develop the theory of Willmore sequences for Willmore
surfaces in the 4-sphere. We show that under appropriate conditions this
sequence has to terminate. In this case the Willmore surface either is the
twistor projection of a holomorphic curve into complex projective space or the
inversion of a minimal surface with planar ends in 4-space. These results give
a unified explanation of previous work on the characterization of Willmore
spheres and Willmore tori with non-trivial normal bundles by various authors.Comment: 10 page
Is diagnosis enough to guide interventions in mental health? Using case formulation in clinical practice
While diagnosis has traditionally been viewed as an essential concept in medicine, particularly when selecting treatments, we suggest that the use of diagnosis alone may be limited, particularly within mental health. The concept of clinical case formulation advocates for collaboratively working with patients to identify idiosyncratic aspects of their presentation and select interventions on this basis. Identifying individualized contributing factors, and how these could influence the person\u27s presentation, in addition to attending to personal strengths, may allow the clinician a deeper understanding of a patient, result in a more personalized treatment approach, and potentially provide a better clinical outcome.<br /
NR4A Gene Expression Is Dynamically Regulated in the Ventral Tegmental Area Dopamine Neurons and Is Related to Expression of Dopamine Neurotransmission Genes
The NR4A transcription factors NR4A1, NR4A2, and NR4A3 (also known as Nur77, Nurr1, and Nor1, respectively) share similar DNA-binding properties and have been implicated in regulation of dopamine neurotransmission genes. Our current hypothesis is that NR4A gene expression is regulated by dopamine neuron activity and that induction of NR4A genes will increase expression of dopamine neurotransmission genes. Eticlopride and Îł-butyrolactone (GBL) were used in wild-type (+/+) and Nurr1-null heterozygous (+/â) mice to determine the mechanism(s) regulating Nur77 and Nurr1 expression. Laser capture microdissection and real-time PCR was used to measure Nurr1 and Nur77 mRNA levels in the ventral tegmental area (VTA). Nur77 expression was significantly elevated 1Â h after both GBL (twofold) and eticlopride (fourfold). In contrast, GBL significantly decreased Nurr1 expression in both genotypes, while eticlopride significantly increased Nurr1 expression only in the +/+ mice. In a separate group of mice, haloperidol injection significantly elevated Nur77 and Nor1, but not Nurr1 mRNA in the VTA within 1Â h and significantly increased tyrosine hydroxylase (TH) and dopamine transporter (DAT) mRNA expression by 4Â h. These data demonstrate that the NR4A genes are dynamically regulated in dopamine neurons with maintenance of Nurr1 expression requiring dopamine neuron activity while both attenuation of dopamine autoreceptors activation and dopamine neuronal activity combining to induce Nur77 expression. Additionally, these data suggest that induction of NR4A genes could regulate TH and DAT expression and ultimately regulate dopamine neurotransmission
Mean Curvature Flow of Spacelike Graphs
We prove the mean curvature flow of a spacelike graph in of a map from a closed Riemannian
manifold with to a complete Riemannian manifold
with bounded curvature tensor and derivatives, and with
sectional curvatures satisfying , remains a spacelike graph,
exists for all time, and converges to a slice at infinity. We also show, with
no need of the assumption , that if , or if and
, constant, any map is trivially
homotopic provided where
, in case , and
in case . This largely extends some known results for
constant and compact, obtained using the Riemannian structure
of , and also shows how regularity theory on the mean
curvature flow is simpler and more natural in pseudo-Riemannian setting then in
the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages:
we replace the condition by the the weaker one .
The proofs are essentially the same. We change the title to a shorter one. We
add an applicatio
On the Evolution Equation for Magnetic Geodesics
In this paper we prove the existence of long time solutions for the parabolic
equation for closed magnetic geodesics.Comment: In this paper we prove the existence of long time solutions for the
parabolic equation for closed magnetic geodesic
QCD Strings as Constrained Grassmannian Sigma Model:
We present calculations for the effective action of string world sheet in R3
and R4 utilizing its correspondence with the constrained Grassmannian sigma
model. Minimal surfaces describe the dynamics of open strings while harmonic
surfaces describe that of closed strings. The one-loop effective action for
these are calculated with instanton and anti-instanton background, reprsenting
N-string interactions at the tree level. The effective action is found to be
the partition function of a classical modified Coulomb gas in the confining
phase, with a dynamically generated mass gap.Comment: 22 pages, Preprint: SFU HEP-116-9
THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS
We consider rotating black hole configurations of self-gravitating maps from
spacetime into arbitrary Riemannian manifolds. We first establish the
integrability conditions for the Killing fields generating the stationary and
the axisymmetric isometry (circularity theorem). Restricting ourselves to
mappings with harmonic action, we subsequently prove that the only stationary
and axisymmetric, asymptotically flat black hole solution with regular event
horizon is the Kerr metric. Together with the uniqueness result for
non-rotating configurations and the strong rigidity theorem, this establishes
the uniqueness of the Kerr family amongst all stationary black hole solutions
of self-gravitating harmonic mappings.Comment: 18 pages, latex, no figure
On paraquaternionic submersions between paraquaternionic K\"ahler manifolds
In this paper we deal with some properties of a class of semi-Riemannian
submersions between manifolds endowed with paraquaternionic structures, proving
a result of non-existence of paraquaternionic submersions between
paraquaternionic K\"ahler non locally hyper paraK\"ahler manifolds. Then we
examine, as an example, the canonical projection of the tangent bundle, endowed
with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.Comment: 13 pages, no figure
Remarks on symplectic twistor spaces
We consider some classical fibre bundles furnished with almost complex
structures of twistor type, deduce their integrability in some cases and study
\textit{self-holomorphic} sections of a \textit{symplectic} twistor space. With
these we define a moduli space of -compatible complex structures. We
recall the theory of flag manifolds in order to study the Siegel domain and
other domains alike, which is the fibre of the referred twistor space. Finally
the structure equations for the twistor of a Riemann surface with the canonical
symplectic-metric connection are deduced, based on a given conformal coordinate
on the surface. We then relate with the moduli space defined previously.Comment: 20 pages, title changed since v2, accepted in AMPA toda
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