scholarly journals Inverse resonance scattering on rotationally symmetric manifolds

2020 ◽  
pp. 1-17
Author(s):  
Hiroshi Isozaki ◽  
Evgeny Korotyaev
Keyword(s):  
Hilbert Spaces ◽  
Counting Function ◽  
Resonance Scattering ◽  
Compact Interval ◽  
Large Radius ◽  
One Dimensional ◽  
Symmetric Manifold ◽  
Direct Sum ◽  
Rotationally Symmetric ◽  
Real Analytic

We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = ( 0 , ∞ ) × Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrödinger operators with compactly supported potentials on the half-line. We prove Asymptotics of counting function of resonances at large radius. The rotation radius is uniquely determined by its eigenvalues and resonances. There exists an algorithm to recover the rotation radius from its eigenvalues and resonances. The proof is based on some non-linear real analytic isomorphism between two Hilbert spaces.

Asymptotic variance parameters for the boundary local times of reflected Brownian motion on a compact interval

1992 ◽  
Vol 29 (04) ◽  
pp. 996-1002 ◽  
Author(s):  
R. J. Williams
Keyword(s):  
Brownian Motion ◽  
Asymptotic Variance ◽  
Hitting Time ◽  
Local Times ◽  
Compact Interval ◽  
Reflected Brownian Motion ◽  
Direct Derivation ◽  
One Dimensional ◽  
Brownian Motion With Drift ◽  
Variance Parameters

A direct derivation is given of a formula for the normalized asymptotic variance parameters of the boundary local times of reflected Brownian motion (with drift) on a compact interval. This formula was previously obtained by Berger and Whitt using an M/M/1/C queue approximation to the reflected Brownian motion. The bivariate Laplace transform of the hitting time of a level and the boundary local time up to that hitting time, for a one-dimensional reflected Brownian motion with drift, is obtained as part of the derivation.

One-dimensional error-diffusion technique adapted for binarization of rotationally symmetric pupil filters

1995 ◽  
Vol 114 (3-4) ◽  
pp. 211-218 ◽  
Author(s):  
Marek Kowalczyk ◽  
Manuel Martínez-Corral ◽  
Tomasz Cichocki ◽  
Pedro Andrés
Keyword(s):  
Error Diffusion ◽  
Dimensional Error ◽  
One Dimensional ◽  
Diffusion Technique ◽  
Rotationally Symmetric

scholarly journals Damping estimates for oscillatory integral operators with real-analytic phases and its applications

2019 ◽  
Vol 31 (4) ◽  
pp. 843-865
Author(s):  
Zuoshunhua Shi ◽  
Shaozhen Xu ◽  
Dunyan Yan
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Independent Interest ◽  
One Dimensional ◽  
Oscillatory Integral Operators ◽  
Real Analytic

Abstract In this paper, we investigate sharp damping estimates for a class of one-dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates for suitably damped oscillatory integral operators, we are able to give a new proof of the sharp {L^{p}} estimates, which have been proved by Xiao in [Endpoint estimates for one-dimensional oscillatory integral operators, Adv. Math. 316 2017, 255–291]. The damping estimates obtained in this paper are of independent interest.

scholarly journals A decomposition theorem for homogeneous algebras

2002 ◽  
Vol 72 (1) ◽  
pp. 47-56 ◽  
Author(s):  
L. G. Sweet ◽  
J. A. Macdougall
Keyword(s):  
Nonzero Element ◽  
Decomposition Theorem ◽  
Small Dimension ◽  
Infinite Field ◽  
Left Multiplication ◽  
One Dimensional ◽  
Direct Sum ◽  
Homogeneous Algebras ◽  
The One ◽  
Homogeneous Algebra

AbstractAn algebra A is homogeneous if the automorphism group of A acts transitively on the one dimensional subspaces of A. Suppose A is a homogeneous algebra over an infinite field k. Let La denote left multiplication by any nonzero element a ∈ A. Several results are proved concerning the structure of A in terms of La. In particular, it is shown that A decomposes as the direct sum A = ker La Im La. These results are then successfully applied to the problem of classifying the infinite homogeneous algebras of small dimension.

A novel two-dimensional cadmium(II) complex: poly[diaquatris(μ4-cyclohexane-1,4-dicarboxylato)bis[2-(pyridin-4-yl)-1H-benzimidazole]tricadmium(II)

2015 ◽  
Vol 71 (5) ◽  
pp. 369-373 ◽  
Author(s):  
Xiu-Hong Yang ◽  
Ming-Xing Yang ◽  
Li-Juan Chen ◽  
Jing Guo ◽  
Shen Lin
Keyword(s):  
Water Molecule ◽  
Title Compound ◽  
Aqua Ligand ◽  
Coordination Geometry ◽  
Two Dimensional ◽  
Asymmetric Unit ◽  
One Dimensional ◽  
Dimensional Network ◽  
Rotationally Symmetric ◽  
Coordinated Water

The title compound, [Cd3(C8H10O4)3(C12H9N3)2(H2O)2]nor [Cd3(chdc)3(4-PyBIm)2(H2O)2]n, was synthesized hydrothermally from the reaction of Cd(CH3COO)2·2H2O with 2-(pyridin-4-yl)-1H-benzimidazole (4-PyBIm) and cyclohexane-1,4-dicarboxylic acid (1,4-chdcH2). The asymmetric unit consists of one and a half CdIIcations, one 4-PyBIm ligand, one and a half 1,4-chdc2−ligands and one coordinated water molecule. The central CdIIcation, located on an inversion centre, is coordinated by six carboxylate O atoms from six 1,4-chdc2−ligands to complete an elongated octahedral coordination geometry. The two terminal rotationally symmetric CdIIcations each exhibits a distorted pentagonal–bipyramidal geometry, coordinated by one N atom from 4-PyBIm, five O atoms from three 1,4-chdc2−ligands and one O atom from an aqua ligand. The 1,4-chdc2−ligands possess two conformations,i.e.e,e-trans-chdc2−ande,a-cis-chdc2−. Thecis-1,4-chdc2−ligands bridge the CdIIcations to form a trinuclear {Cd3}-based chain along thebaxis, while thetrans-1,4-chdc2−ligands further link adjacent one-dimensional chains to construct an interesting two-dimensional network.

scholarly journals Lorentz-Marcinkiewicz property of direct sum of operators

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 391-398
Author(s):  
Ala Ipek
Keyword(s):  
Hilbert Spaces ◽  
Direct Sum

In this paper, the relations between Lorentz-Marcinkiewicz property of the direct sum of operators in the direct sum of Hilbert spaces and its coordinate operators are studied. Then, the obtained results are supported by applications.

scholarly journals Diffusion and Superdiffusion from Hydrodynamic Projections

2022 ◽  
Vol 186 (2) ◽  
Author(s):  
Benjamin Doyon
Keyword(s):  
Lower Bounds ◽  
Hilbert Spaces ◽  
Fibonacci Sequence ◽  
Maximal Entropy ◽  
Many Body ◽  
One Dimensional ◽  
Covariant Derivatives ◽  
Many Body Systems ◽  
Nonlinear Fluctuating Hydrodynamics ◽  
Natural Expression

AbstractHydrodynamic projections, the projection onto conserved charges representing ballistic propagation of fluid waves, give exact transport results in many-body systems, such as the exact Drude weights. Focussing one one-dimensional systems, I show that this principle can be extended beyond the Euler scale, in particular to the diffusive and superdiffusive scales. By hydrodynamic reduction, Hilbert spaces of observables are constructed that generalise the standard space of conserved densities and describe the finer scales of hydrodynamics. The Green–Kubo formula for the Onsager matrix has a natural expression within the diffusive space. This space is associated with quadratically extensive charges, and projections onto any such charge give generic lower bounds for diffusion. In particular, bilinear expressions in linearly extensive charges lead to explicit diffusion lower bounds calculable from the thermodynamics, and applicable for instance to generic momentum-conserving one-dimensional systems. Bilinear charges are interpreted as covariant derivatives on the manifold of maximal entropy states, and represent the contribution to diffusion from scattering of ballistic waves. An analysis of fractionally extensive charges, combined with clustering properties from the superdiffusion phenomenology, gives lower bounds for superdiffusion exponents. These bounds reproduce the predictions of nonlinear fluctuating hydrodynamics, including the Kardar–Parisi–Zhang exponent 2/3 for sound-like modes, the Levy-distribution exponent 3/5 for heat-like modes, and the full Fibonacci sequence.

Spectral asymptotics for Krein–Feller operators with respect to 𝑉-variable Cantor measures

2020 ◽  
Vol 32 (1) ◽  
pp. 121-138
Author(s):  
Lenon Alexander Minorics
Keyword(s):  
Borel Measure ◽  
Differential Operators ◽  
Counting Function ◽  
Second Order ◽  
Spectral Asymptotics ◽  
Compact Interval ◽  
Limiting Behavior ◽  
Convergence Behavior ◽  
Neumann Eigenvalue

AbstractWe study the limiting behavior of the Dirichlet and Neumann eigenvalue counting function of generalized second-order differential operators {\frac{\mathop{}\!d}{\mathop{}\!d\mu}\frac{\mathop{}\!d}{\mathop{}\!dx}}, where μ is a finite atomless Borel measure on some compact interval {[a,b]}. Therefore, we firstly recall the results of the spectral asymptotics for these operators received so far. Afterwards, we make a proposition about the convergence behavior for so-called random V-variable Cantor measures.

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