3,880 research outputs found
On Closed Invariant Sets in Local Dynamics
We investigate the dynamical behaviour of a holomorphic map on a
invariant subset of where We
study two cases: when is an open, connected and polynomially convex subset
of and closed in and when
has a p.s.h. barrier at each of its points and is
not relatively compact in In the second part of the paper, we prove a
Birkhoff's type Theorem for holomorphic maps in several complex variables, i.e.
given an injective holomorphic map defined in a neighborhood of
with star-shaped and a Runge domain, we prove the
existence of a unique, forward invariant, maximal, compact and connected subset
of which touches Comment: Exposition has been improved; Corollary 3.6 has been corrected; 8
pages; version close to be publishe
Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation
We study the combinatorial structure of the irreducible characters of the
classical groups , ,
, and the
"non-classical" odd symplectic group , finding new
connections to the probabilistic model of Last Passage Percolation (LPP).
Perturbing the expressions of these characters as generating functions of
Gelfand-Tsetlin patterns, we produce two families of symmetric polynomials that
interpolate between characters of and and between characters of
and . We identify the first family as a
one-parameter specialization of Koornwinder polynomials, for which we thus
provide a novel combinatorial structure; on the other hand, the second family
appears to be new. We next develop a method of Gelfand-Tsetlin pattern
decomposition to establish identities between all these polynomials that, in
the case of characters, can be viewed as describing the decomposition of
irreducible representations of the groups when restricted to certain subgroups.
Through these formulas we connect orthogonal and symplectic characters, and
more generally the interpolating polynomials, to LPP models with various
symmetries, thus going beyond the link with classical Schur polynomials
originally found by Baik and Rains [BR01a]. Taking the scaling limit of the LPP
models, we finally provide an explanation of why the Tracy-Widom GOE and GSE
distributions from random matrix theory admit formulations in terms of both
Fredholm determinants and Fredholm Pfaffians.Comment: 60 pages, 11 figures. Typos corrected and a few remarks adde
Thrombolytics in Pediatric Stroke: Imaging Modalities
Thrombolytics in Pediatric Stroke: Imaging Modalities
Katherine Au, Dept. of Biomedical Engineering, with Dr. Bisi Hollist, Inova Neuroscience and Spine Institute
We report the potential danger associated with an initial neuroimaging-negative cerebral ischemia in pediatrics. For patients who present with clinical features suggestive of acute ischemic stroke but have an alternative diagnosis, there is concern of utilizing thrombolysis. Due to the short time window from symptom onset to treatment, a thorough history and neurologic examination, along with diagnostic imaging and blood tests are important for diagnosis and timely treatment. We present a case of a 14-year old female with a history of thalamic stroke who presented with neurological symptoms consistent with acute stroke. An MRI of her brain was indeterminate and showed no frank evidence of cerebral infarction. Further inspection showed an area of restricted diffusion which clinically correlated to her symptoms. There was no evidence of vessel wall irregularities, high grade stenosis or dissection. This patient was administered intravenous tPA over the course of 1 hour and her symptoms resolved.https://scholarscompass.vcu.edu/uresposters/1295/thumbnail.jp
Log-biharmonicity and a Jensen formula in the space of quaternions
Given a complex meromorphic function, it is well defined its Riesz measure in
terms of the laplacian of the logarithm of its modulus. Moreover, related to
this tool, it is possible to prove the celebrated Jensen formula. In the
present paper, using among the other things the fundamental solution for the
bilaplacian, we introduce a possible generalization of these two concepts in
the space of quaternions, obtaining new interesting Riesz measures and global
(i.e. four dimensional), Jensen formulas.Comment: Final Version. To appear on Annales Academiae Scientiarum Fennicae
Mathematica, Volume 44 (2019
GOE and marginal distribution via symplectic Schur functions
We derive Sasamoto's Fredholm determinant formula for the Tracy-Widom GOE
distribution, as well as the one-point marginal distribution of the process, originally derived by Borodin-Ferrari-Sasamoto, as
scaling limits of point-to-line and point-to-half-line last passage percolation
with exponentially distributed waiting times. The asymptotic analysis goes
through new expressions for the last passage times in terms of integrals of
(the continuous analog of) symplectic and classical Schur functions, obtained
recently in [BZ19a].Comment: 19 pages, 2 figures. Typos corrected, references adde
A remark on the Ueno-Campana's threefold
We show that the Ueno-Campana's threefold cannot be obtained as the blow-up
of any smooth threefold along a smooth centre, answering negatively a question
raised by Oguiso and Truong.Comment: To appear on Michigan Math. Journal, Vol. 65 (2016
Some notions of subharmonicity over the quaternions
This works introduces several notions of subharmonicity for real-valued
functions of one quaternionic variable. These notions are related to the theory
of slice regular quaternionic functions introduced by Gentili and Struppa in
2006. The interesting properties of these new classes of functions are studied
and applied to construct the analogs of Green's functions.Comment: 16 page
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