1,169 research outputs found
On Pythagoras' theorem for products of spectral triples
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual
Pythagoras theorem can be formulated in terms of Connes' distance, between pure
states, in the product of commutative spectral triples. We investigate the
generalization to both non pure states and arbitrary spectral triples. We show
that Pythagoras theorem is replaced by some Pythagoras inequalities, that we
prove for the product of arbitrary (i.e. non-necessarily commutative) spectral
triples, assuming only some unitality condition. We show that these
inequalities are optimal, and provide non-unital counter-examples inspired by
K-homology.Comment: Paper slightly shortened to match the published version; Lett. Math.
Phys. 201
A rare case of leiomyoma of the bladder
Bladder leiomyoma is a benign tumour of the bladder and constitute <0.5% of all bladder tumors. We report a clinical case of a 51âyearâold female who presented with with symptomatic bladder leiomyoma. An ultrasound examination showed well-defined bladder leiomyoma in the right posterior bladder wall, which was excised through a transurethral resection. The pathologic diagnosis was bladder leiomyoma
Dirac Operators on Quantum Projective Spaces
We construct a family of self-adjoint operators D_N which have compact
resolvent and bounded commutators with the coordinate algebra of the quantum
projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional
equivariant even spectral triples. If l is odd and N=(l+1)/2, the spectral
triple is real with KO-dimension 2l mod 8.Comment: 54 pages, no figures, dcpic, pdflate
The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
Equivariance under the action of Uq(so(5)) is used to compute the left
regular and (chiral) spinorial representations of the algebra of the orthogonal
quantum 4-sphere S^4_q. These representations are the constituents of a
spectral triple on this sphere with a Dirac operator which is isospectral to
the canonical one on the round undeformed four-sphere and which gives metric
dimension four for the noncommutative geometry. Non-triviality of the geometry
is proved by pairing the associated Fredholm module with an `instanton'
projection. We also introduce a real structure which satisfies all required
properties modulo smoothing operators.Comment: 40 pages, no figures, Latex. v2: Title changed. Sect. 9 on real
structure completely rewritten and results strengthened. Additional minor
changes throughout the pape
Open and / or laparoscopic surgical treatment of liver hydatic cysts
Hydatid disease is a severe parasitic disease with a widely ranging distribution. In the human being the liver is the most frequent organ affected. 1 The treatment should be individualized to the morphology, size, number and location of the cysts, that is why a variety of surgical operations have been advocated from complete resection like total pericystectomy or partial hepatectomy to laparoscopy to a minimally invasive procedures like percutaneous aspiration of cysts to conservative drug therapy. 3-4 This study compares laparoscopic versus open management of the hydatid cyst of liver the surgical approach to liver echinococcosis is still a controversial issue and shows our results of surgical treatment of liver hydatid cysts during a 3-years period
Quantum Isometries of the finite noncommutative geometry of the Standard Model
We compute the quantum isometry group of the finite noncommutative geometry F
describing the internal degrees of freedom in the Standard Model of particle
physics. We show that this provides genuine quantum symmetries of the spectral
triple corresponding to M x F where M is a compact spin manifold. We also prove
that the bosonic and fermionic part of the spectral action are preserved by
these symmetries.Comment: 29 pages, no figures v3: minor change
Cholinergic innervation of human mesenteric lymphatic vessels
Background: The cholinergic neurotransmission within the human mesenteric lymphatic vessels has been poorly studied. Therefore, our aim is to analyse the cholinergic nerve fibres of lymphatic vessels using the traditional enzymatic techniques of staining, plus the biochemical modifications of acetylcholinesterase (AChE) activity.Materials and methods: Specimens obtained from human mesenteric lymphatic vessels were subjected to the following experimental procedures: 1) drawing, cutting and staining of tissues; 2) staining of total nerve fibres; 3) enzymatic staining of cholinergic nerve fibres; 4) homogenisation of tissues; 5) biochemical amount of proteins; 6) biochemical amount of AChE activity; 6) quantitative analysis of images; 7) statistical analysis of data.Results: The mesenteric lymphatic vessels show many AChE positive nerve fibres around their wall with an almost plexiform distribution. The incubation time was performed at 1 h (partial activity) and 6 h (total activity). Moreover, biochemical dosage of the same enzymatic activity confirms the results obtained with morphological methods.Conclusions: The homogenates of the studied tissues contain strong AChE activity. In our study, the lymphatic vessels appeared to contain few cholinergic nerve fibres. Therefore, it is expected that perivascular nerve stimulation stimulates cholinergic nerves innervating the mesenteric arteries to release the neurotransmitter AChE, which activates muscarinic or nicotinic receptors to modulate adrenergic neurotransmission. These results strongly suggest, that perivascular cholinergic nerves have little or no effect on the adrenergic nerve function in mesenteric arteries. The cholinergic nerves innervating mesenteric arteries do not mediate direct vascular responses.
Spectral changes of near-infrared spectroscopy signals in migraineurs with aura reveal an impaired carbon dioxide-regulatory mechanism
Differential and Twistor Geometry of the Quantum Hopf Fibration
We study a quantum version of the SU(2) Hopf fibration and its
associated twistor geometry. Our quantum sphere arises as the unit
sphere inside a q-deformed quaternion space . The resulting
four-sphere is a quantum analogue of the quaternionic projective space
. The quantum fibration is endowed with compatible non-universal
differential calculi. By investigating the quantum symmetries of the fibration,
we obtain the geometry of the corresponding twistor space and
use it to study a system of anti-self-duality equations on , for which
we find an `instanton' solution coming from the natural projection defining the
tautological bundle over .Comment: v2: 38 pages; completely rewritten. The crucial difference with
respect to the first version is that in the present one the quantum
four-sphere, the base space of the fibration, is NOT a quantum homogeneous
space. This has important consequences and led to very drastic changes to the
paper. To appear in CM
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