Recovery of the m-function from spectral data for generalized Sturm–Liouville problems

AbstractThe Sturm–Liouville problem −y″+qy=λy, y(0)cosα=y′(0)sinα, (y′/y)(1)=h(λ)/g(λ) is studied, where h and g are real polynomials. Generalized norming constants ρnk associated with eigenvalues Λn are defined and formulae are given for recovering the m-function from these constants. This leads to a uniqueness theorem for the associated inverse problem

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

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

Novel B(Ar')2(Ar'') hetero-tri(aryl)boranes: a systematic study of Lewis acidity

A series of homo- and hetero-tri(aryl)boranes incorporating pentafluorophenyl, 3,5-bis(trifluoromethyl)phenyl, and pentachlorophenyl groups, four of which are novel species, have been studied as the acidic component of frustrated Lewis pairs for the heterolytic cleavage of H2. Under mild conditions eight of these will cleave H2; the rate of cleavage depending on both the electrophilicity of the borane and the steric bulk around the boron atom. Electrochemical studies allow comparisons of the electrophilicity with spectroscopic measurements of Lewis acidity for different series of boranes. Discrepancies in the correlation between these two types of measurements, combined with structural characterisation of each borane, reveal that the twist of the aryl rings with respect to the boron-centred trigonal plane is significant from both a steric and electronic perspective, and is an important consideration in the design of tri(aryl)boranes as Lewis acids

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

An Electrochemical Study of Frustrated Lewis Pairs: A Metal-free Route to Hydrogen Oxidation

[Image: see text] Frustrated Lewis pairs have found many applications in the heterolytic activation of H(2) and subsequent hydrogenation of small molecules through delivery of the resulting proton and hydride equivalents. Herein, we describe how H(2) can be preactivated using classical frustrated Lewis pair chemistry and combined with in situ nonaqueous electrochemical oxidation of the resulting borohydride. Our approach allows hydrogen to be cleanly converted into two protons and two electrons in situ, and reduces the potential (the required energetic driving force) for nonaqueous H(2) oxidation by 610 mV (117.7 kJ mol(–1)). This significant energy reduction opens routes to the development of nonaqueous hydrogen energy technology

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