Existence and Asymptotics of Eigenvalues of Indefinite Systems of Sturm–Liouville and Dirac Type

AbstractExistence and asymptotic behavior of eigenvalues of indefinite Sturm–Liouville and Dirac systems with integrable coefficients are investigated using Prüfer angle analysis. The results generalize those previously obtained by Atkinson, Mingarelli, Gohberg and Krein and are based on a new theorem that determines the asymptotic behavior of the solution of a Riccati-type equation containing a large parameter

Oscillation results for Sturm–Liouville problems with an indefinite weight function

AbstractWe prove oscillation results for the real eigenvalues of Sturm–Liouville problems with an indefinite weight function. An essential role is played by the signature of an eigenvalue, which is shown to be related to the signs of the corresponding leading coefficients of the Titchmarsh–Weyl m-function and of the Prüfer angle at this eigenvalue

Local distinguishability of quantum states in infinite dimensional systems

We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and classical communications, even for infinite dimensional systems. An estimate of the local discrimination probability is also given for some family of more than two pure states

On the use of continuous spectrum and discrete-mode differential models to predict contraction-flow pressure drops for Boger fluids

Over recent years, there has been slow but steady progress towards the qualitative numerical prediction of observed behaviour when highly elastic Boger fluids flow in contraction geometries. This has led to an obvious desire to seek quantitative agreement between prediction and experiment, a subject which is addressed in the current paper. We conclude that constitutive models of non-trivial complexity are required to make headway in this regard. However, we suggest that the desire to move from qualitative to quantitative agreement between theory and experiment is making real progress. In the present case with differential models, this has involved the introduction of a generalized continuous spectrum model. This is based on direct data input from material functions and rheometrical measurements. The class of such models assumes functional separability across shear and extensional deformation, through two master functions, governing independently material-time and viscous-response. The consequences of such a continuous spectrum representation are compared and contrasted against discrete-mode alternatives, via an averaged single-mode approximation and a multi-modal approximation. The effectiveness of each chosen form is gauged by the quality of match to complex flow response and experimental measurement. Here, this is interpreted in circular contraction-type flows with Boger fluids, where large experimental pressure-drop data are available and wide disparity between different fluid responses has been recorded in the past. Findings are then back-correlated to base-material response from ideal viscometric flow

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels

The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia

Inverse problems for Sturm-Liouville equations with boundary conditions linearly dependent on the spectral parameter from partial information

[[abstract]]Abstract.In this paper, we study the inverse spectral problems for Sturm–Liouville equations with boundary conditions linearly dependent on the spectral parameter and show that the potential of such problem can be uniquely determined from partial information on the potential and parts of two spectra, or alternatively, from partial information on the potential and a subset of pairs of eigenvalues and the normalization constants of the corresponding eigenvalues.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]DE

ARIADNE: A Research Infrastructure for Archaeology

Research e-infrastructures, digital archives, and data services have become important pillars of scientific enterprise that in recent decades have become ever more collaborative, distributed, and data intensive. The archaeological research community has been an early adopter of digital tools for data acquisition, organization, analysis, and presentation of research results of individual projects. However, the provision of e-infrastructure and services for data sharing, discovery, access, and (re)use have lagged behind. This situation is being addressed by ARIADNE, the Advanced Research Infrastructure for Archaeological Dataset Networking in Europe. This EU-funded network has developed an e-infrastructure that enables data providers to register and provide access to their resources (datasets, collections) through the ARIADNE data portal, facilitating discovery, access, and other services across the integrated resources. This article describes the current landscape of data repositories and services for archaeologists in Europe, and the issues that make interoperability between them difficult to realize. The results of the ARIADNE surveys on users’ expectations and requirements are also presented. The main section of the article describes the architecture of the e-infrastructure, core services (data registration, discovery, and access), and various other extant or experimental services. The ongoing evaluation of the data integration and services is also discussed. Finally, the article summarizes lessons learned and outlines the prospects for the wider engagement of the archaeological research community in the sharing of data through ARIADNE

Witchcraft and the Somerset idyll : The depiction of folk belief in Walter Raymond’s novels

The work of Walter Raymond (1852-1931) is now largely forgotten. Yet his Somerset novels, complemented by his ethnographic writings, contain depictions of local witchcraft belief that are worthy of study in literary and historical contexts. They raise issues regarding the fictional depiction of rural life and tradition, and the value of fiction as a folkloric and historical sourcePeer reviewe

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