1,415 research outputs found
New Reverse Inequalities for Normal Operators in Hilbert Spaces
No full textIn this paper, more reverse inequalities for the class of normal
operators, are established. Some of the obtained results are based on recent
reverse results for the Schwarz inequality in Hilbert spaces due to the author
Crepant resolutions and A-Hilbert schemes in dimension four
No full textThe aim of this thesis is to improve our understanding of when crepant resolutions
exist in dimension four.
In three dimensions [BKR01] proved that for any finite subgroup G ⊂ SL(3,C)
the G-Hilbert scheme G-Hilb(C3) gives a crepant resolution of the quotient singularity
C3/G.
In four dimensions very little is known about when crepant resolutions exist.
In this thesis I present several approaches to this problem. I give an algorithm
which determines, for quotients by cyclic subgroups of SL(4,C) whether or not
a crepant resolution exists. This algorithm seeks to find a crepant resolution by
performing a tree search.
In Chapter 4, building on the work of [CR02] in three dimensions, I calculate
the A-Hilbert scheme for a family of abelian subgroups A ⊂ SL(4,C). I show
that this can be used to find a crepant resolution of C4/A
A Framework for Proving Hilbert's Double Integral Inequality and Related Results
No full textThe classical Hilbert and Hardy integral inequalities are derived within a functional analytic framework. That framework is further used to generate a new inequality, sharper than Hilbert's
Upper Bounds for the Euclidean Operator Radius and Applications
No full textThe main aim of the present paper is to establish various sharp
upper bounds for the Euclidean operator radius of an n−tuple of bounded
linear operators on a Hilbert space. The tools used are provided by several
generalisations of Bessel inequality due to Boas-Bellman, Bombieri and the
author. Natural applications for the norm and the numerical radius of bounded
linear operators on Hilbert spaces are also given
Inequalities for some Functionals Associated with Bounded Linear Operators in Hilbert Spaces
No full textSome inequalities between the operator norm, numerical radius
and functional are established. New upper bounds for the nonnegative
quantity that complement some recent results of the author are given as well
A quantized Riemann-Hilbert problem in Donaldson-Thomas theory
No full textWe introduce Riemann-Hilbert problems determined by refined Donaldson-Thomas theory. They involve piecewise holomorphic maps from the complex plane to the group of automorphisms of a quantum torus algebra. We study the simplest case in detail and use the Barnes double gamma function to construct a solution
Advancing Thalamic Nuclei Segmentation: The Impact of Compressed Sensing on MRI Processing
No full textThe thalamus is a collection of gray matter nuclei that play a crucial role in sensorimotor processing and modulation of cortical activity. Characterizing thalamic nuclei non-invasively with structural MRI is particularly relevant for patient populations with Parkinson's disease, epilepsy, dementia, and schizophrenia. However, severe head motion in these populations poses a significant challenge for in vivo mapping of thalamic nuclei. Recent advancements have leveraged the compressed sensing (CS) framework to accelerate structural MRI acquisition times in MPRAGE sequence variants, while fast segmentation tools like FastSurfer have reduced processing times in neuroimaging research. In this study, we evaluated thalamic nuclei segmentations derived from six different MPRAGE variants with varying degrees of CS acceleration (from about 9 to about 1-min acquisitions). Thalamic segmentations were initialized from either FastSurfer or FreeSurfer, and the robustness of the thalamic nuclei segmentation tool to different initialization inputs was evaluated. Our findings show minimal sequence effects with no systematic bias, and low volume variability across sequences for the whole thalamus and major thalamic nuclei. Notably, CS-accelerated sequences produced less variable volumes compared to non-CS sequences. Additionally, segmentations of thalamic nuclei initialized from FastSurfer and FreeSurfer were highly comparable. We provide the first evidence supporting that a good segmentation quality of thalamic nuclei with CS T1-weighted image acceleration in a clinical 3T MRI system is possible. Our findings encourage future applications of fast T1-weighted MRI to study deep gray matter. CS-accelerated sequences and rapid segmentation methods are promising tools for future studies aiming to characterize thalamic nuclei in vivo at 3T in both healthy individuals and clinical populations
The nonperturbative Hilbert space of quantum gravity with one boundary
No full textWe discuss a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. We use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space
Notes on Hilbert and Cauchy matrices
No full textAbstractInspired by examples of small Hilbert matrices, the author proves a property of symmetric totally positive Cauchy matrices, called AT-property, and consequences for the Hilbert matrix
Contractible Hilbert cube manifolds
No full textIn this note we give an example of a contractible Hilbert cube manifold which cannot be embedded as an open subset of the Hilbert cube Q so that its complement (in Q) lies in a face of the boundary of Q. This example provides a negative answer to a question raised by the author.</p
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