2,581 research outputs found
Boundary relations and generalized resolvents of symmetric operators
The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint
exit space extensions of a, not necessarily densely defined, symmetric
operator, in terms of maximal dissipative (in \dC_+) holomorphic linear
relations on the parameter space (the so-called Nevanlinna families). The new
notion of a boundary relation makes it possible to interpret these parameter
families as Weyl families of boundary relations and to establish a simple
coupling method to construct the generalized resolvents from the given
parameter family. The general version of the coupling method is introduced and
the role of boundary relations and their Weyl families for the
Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page
Boundary triplets for skew-symmetric operators and the generation of strongly continuous semigroups
We give a self-contained and streamlined exposition of a generation theorem
for C0-semigroups based on the method of boundary triplets. We apply this
theorem to port-Hamiltonian systems where we discuss recent results appearing
in stability and control theory. We give detailed proofs and require only a
basic knowledge of operator and semigroup theory.Comment: 19 page
A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators
Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator
are studied under the assumption that the weight function has one turning
point. An abstract approach to the problem is given via a functional model for
indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues
are obtained. Also, operators with finite singular critical points are
considered.Comment: 38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4,
and 3.12 extended, details added in subsections 2.3 and 4.2, section 6
rearranged, typos corrected, references adde
Schrödinger operators with δ and δ′-potentials supported on hypersurfaces
Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity
Deep learning for inferring cause of data anomalies
Daily operation of a large-scale experiment is a resource consuming task,
particularly from perspectives of routine data quality monitoring. Typically,
data comes from different sub-detectors and the global quality of data depends
on the combinatorial performance of each of them. In this paper, the problem of
identifying channels in which anomalies occurred is considered. We introduce a
generic deep learning model and prove that, under reasonable assumptions, the
model learns to identify 'channels' which are affected by an anomaly. Such
model could be used for data quality manager cross-check and assistance and
identifying good channels in anomalous data samples. The main novelty of the
method is that the model does not require ground truth labels for each channel,
only global flag is used. This effectively distinguishes the model from
classical classification methods. Being applied to CMS data collected in the
year 2010, this approach proves its ability to decompose anomaly by separate
channels.Comment: Presented at ACAT 2017 conference, Seattle, US
Spin-dependent recombination mechanisms for quintet bi-excitons generated through singlet fission
We investigate the physical mechanisms for spin-dependent recombination of a
strongly bound pair of triplet excitons generated by singlet fission and
forming a spin quintet (total spin of two) bi-exciton. For triplet excitons the
spin-dependent recombination pathways can involve intersystem crossing or
triplet-triplet annihilation back to the singlet ground state. However the
modeling of spin-dependent recombination for quintets is still an open
question. Here we introduce two theoretical models and compare their
predictions with the broadband optically detected magnetic resonance spectrum
of a long lived quintet bi-exciton with known molecular structure. This
spectrum measures the change in the fluorescence signal induced by microwave
excitation of each of the ten possible spin transitions within the quintet
manifold as function of the magnetic field. While most of the experimental
features can be reproduced for both models, the behavior of some of the
transitions is only consistent with the quintet spin-recombination model
inspired by triplet intersystem crossing which can reproduce accurately the
experimental two-dimensional spectrum with a small number of kinetic
parameters. Thus quantitative analysis of the broadband optically detected
magnetic resonance signal enables quantitative understanding of the dominant
spin-recombination processes and estimation of the out-of equilibrium spin
populations.Comment: optimization code available at https://github.com/yneter/ampodm
Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices
We give a uniform interpretation of the classical continuous Chebyshev's and
Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie
algebra gl(N), where N is any complex number. One can similarly interpret
Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials
corresponding to Lie superlagebras.
We also describe the real forms of gl(N), quasi-finite modules over gl(N),
and conditions for unitarity of the quasi-finite modules. Analogs of tensors
over gl(N) are also introduced.Comment: 25 pages, LaTe
Prospective serum metabolomic profiling of lethal prostate cancer
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152026/1/ijc32218.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152026/2/ijc32218_am.pd
Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions
© 2020 The Authors. Mathematische Nachrichten published by Wiley‐VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.fi=vertaisarvioitu|en=peerReviewed
The Unitarity Triangle Analysis within and beyond the Standard Model
International audienceWe present the status of the Unitarity Triangle Analysis (UTA) performed by the UTfit Collaboration, with experimental and theoretical inputs updated for the last summer conferences. Several analyses are presented, corresponding to different assumptions for the theoretical model, that is either the Standard Model, or Minimal Flavour Violation orc ompletely generic NewPhysics
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