Riesz Bases of Root Vectors of Indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.Comment: 21 page

Public health careers: mapping information, informing practitioner needs

Public health promotion and ill health prevention is a key priority for the NHS. The public health workforce is central to achieving improved health outcomes for a diverse and changing population. This mixed-methods study explored career practitioners’ views on their knowledge of the public health sector as well as the accessibility of public health career information on selected websites. The research suggested practitioners lacked awareness of public health opportunities and were only somewhat confident in providing public health career information. In response to this a new web site has been developed which provides information on over 350 health care role

A combined "electrochemical-frustrated Lewis pair" approach to hydrogen activation: surface catalytic effects at platinum electrodes

Herein, we extend our “combined electrochemical–frustrated Lewis pair” approach to include Pt electrode surfaces for the first time. We found that the voltammetric response of an electrochemical–frustrated Lewis pair (FLP) system involving the B(C6F5)3/[HB(C6F5)3]− redox couple exhibits a strong surface electrocatalytic effect at Pt electrodes. Using a combination of kinetic competition studies in the presence of a H atom scavenger, 6-bromohexene, and by changing the steric bulk of the Lewis acid borane catalyst from B(C6F5)3 to B(C6Cl5)3, the mechanism of electrochemical–FLP reactions on Pt surfaces was shown to be dominated by hydrogen-atom transfer (HAT) between Pt, [Pt[BOND]H] adatoms and transient [HB(C6F5)3]⋅ electrooxidation intermediates. These findings provide further insight into this new area of combining electrochemical and FLP reactions, and proffers additional avenues for exploration beyond energy generation, such as in electrosynthesis

Hermeneutics and Nature

This paper contributes to the on-going research into the ways in which the humanities transformed the natural sciences in the late Eighteenth and early Nineteenth Centuries. By investigating the relationship between hermeneutics -- as developed by Herder -- and natural history, it shows how the methods used for the study of literary and artistic works played a crucial role in the emergence of key natural-scientific fields, including geography and ecology

Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains

We study the existence and nonexistence of positive (super) solutions to the nonlinear $p$-Laplace equation $$-\Delta_p u-\frac{\mu}{|x|^p}u^{p-1}=\frac{C}{|x|^{\sigma}}u^q$$ in exterior domains of ${\R}^N$ ($N\ge 2$). Here $p\in(1,+\infty)$ and $\mu\le C_H$, where $C_H$ is the critical Hardy constant. We provide a sharp characterization of the set of $(q,\sigma)\in\R^2$ such that the equation has no positive (super) solutions. The proofs are based on the explicit construction of appropriate barriers and involve the analysis of asymptotic behavior of super-harmonic functions associated to the $p$-Laplace operator with Hardy-type potentials, comparison principles and an improved version of Hardy's inequality in exterior domains. In the context of the $p$-Laplacian we establish the existence and asymptotic behavior of the harmonic functions by means of the generalized Pr\"ufer-Transformation.Comment: 34 pages, 1 figur

On the isospectral problem of the dispersionless Camassa-Holm equation

We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa--Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite. The results are applied to deduce several facts for the dispersionless Camassa--Holm equation. In particular, we show that initial conditions with integrable momentum asymptotically split into a sum of peakons as conjectured by McKean.Comment: 26 page

Exploring structural and electronic effects in three isomers of tris{bis(trifluoromethyl)phenyl}borane: Towards the combined electrochemical-frustrated Lewis pair activation of H2

Three structural isomers of tris{bis(trifluoromethyl)phenyl}borane have been studied as the acidic com- ponent of frustrated Lewis pairs. While the 3,5-substituted isomer is already known to heterolytically cleave H2 to generate a bridging-hydride; ortho-substituents in the 2,4- and 2,5-isomers quench such reactivity through electron donation into the vacant boron pz orbital and steric blocking of the boron centre; as shown by electrochemical, structural and computational studies. Electrochemical studies of the corresponding borohydrides identify that the two-electron oxidation of terminal-hydrides occurs at more positive potentials than observed for [HB(C6F5)3]−, while the bridging-hydride oxidizes at a higher poten- tial still, comparable to that of free H2

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

Nähe der Antike : eine Ansprache

Frankfurter gelehrte Reden und Abhandlungen VIII. Heft : Zwei Ansprachen zur Eröffnung der Ortsgruppe Frankfurt am Main der Gesellschaft für antike Kultur am 9. Dezember 1925 Nähe der Antike / Rudolf G. Binding Zeit und Antike / W. F. Otto