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

On infinite-dimensional differential equations

AbstractDifferential equations ·x(t) = f(x(t), t) are exhibited in a general infinite-dimensional Banach space, failing each of the following in turn. (i) The set St of solution values x(t) from a given point x(0) is compact. (ii) St is connected. (iii) Any point on the boundary ∂St of St can be reached by a solution x with x(s) ϵ ∂ Ss, 0 ⩽ s ⩽ t

On a necessary aspect for the Riesz basis property for indefinite Sturm-Liouville problems

In 1996, H. Volkmer observed that the inequality $$(\int_{-1}^1\frac{1}{|r|}|f'|dx)^2 \le K^2 \int_{-1}^1|f|^2dx\int_{-1}^1\Big|\Big(\frac{1}{r}f'\Big)'\Big|^2dx$$ is satisfied with some positive constant $K>0$ for a certain class of functions $f$ on $[-1,1]$ if the eigenfunctions of the problem $$-y"=\lambda\, r(x)y,\quad y(-1)=y(1)=0$$ form a Riesz basis of the Hilbert space $L^2_{|r|}(-1,1)$. Here the weight $r\in L^1(-1,1)$ is assumed to satisfy $xr(x)>0$ a.e. on $[-1,1]$. We present two criteria in terms of Weyl-Titchmarsh $m$-functions for the Volkmer inequality to be valid. Using these results we show that this inequality is valid if the operator associated with the spectral problem satisfies the linear resolvent growth condition. In particular, we show that the Riesz basis property of eigenfunctions is equivalent to the linear resolvent growth if $r$ is odd.Comment: 26 page

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

Code-switching strategies in science lessons in Kenyan primary schools : an analysis of their contribution to the meaning making process

This study investigates how teachers in a rural Kenyan primary school use code-switching to help pupils to understand scientific concepts. The study takes place in a teaching and learning environment where English is the 'official' language of teaching beyond year three but where it is accepted by the education ministry that the English proficiency of most of the pupils may not be sufficient for them to fully access the science curriculum. It is, therefore, also accepted that teachers may use three languages, English, Kiswahili and Kigiryama, in the classroom, to explain scientific ideas. The study begins by considering some of the barriers to learning science concepts experienced by those who are taught in a second language. There is then an exploration of code-switching strategies as observed by other researchers many of which have been recorded within science lessons in other Kenyan primary schools. This study then uses observational and interview methods to investigate the actual use of code-switching within the lessons of standard four and five pupils at the target school. These observations, combined with those of other researchers are then used to produce a typology of codeswitching interventions commonly used by teachers during science lessons at the school at Mida Primary School. Following this a second literature review outlines a framework of the key features of explanation, clarifying how teachers use language to explain scientific concepts. The code-switching typology and this framework are then utilised to enable the analysis of six transcripts of science lessons at the target school. The analysis is carried out with the purpose of examining the contribution that each code-switching intervention makes to the meaning-making process. Some implications for teacher training are presented concerning how actual teacher behaviour, with respect of their use of code-switching, compares with what might be expected if trained for a planned use of code-switching when explaining scientific concepts. Also included in the study is a brief examination of other contextual factors that might affect the use of code-switching by teachers in science lessons and the implications that these might have on teacher training for the effective use of codeswitching. Finally, some suggestions for further research and an evaluation of the approach taken in this study are presented

An interview with Paul Binding

Paul Binding is a British writer who has worked in many fields: he is a literary critic, novelist, reviewer and renowned expert in Scandinavian literature. His novels are Harmonica’s Bridegroom (1984, recently reprinted by Valancourt Books), Kingfisher Weather (1989), My Cousin the Writer (2002) and After Brock (2013). He has given lectures at universities and participated in cultural events in Norway, Sweden, Denmark, Finland and Estonia. His memoir St Martin’s Ride, which focuses on his childhood in Germany soon after the end of the Second World War, was Sir Stephen Spender’s Book of the Year, and was awarded the J.R. Ackerley Prize for the best autobiographical book of 1990. He has frequently spent long periods abroad, and his time in Jackson, Mississipi as a visiting professor led to The Still Moment: Eudora Welty, Portrait of a Writer (1994). The book draws on the many conversations he had with Welty about her work. More recently, he published Imagined Corners: Exploring the World’s First Atlas (2003). He has frequently reviewed books for the Times Literary Supplement and The Independent. His most recent book is Hans Christian Andersen: European Witness (2014), which was very well reviewed and described by Amanda Craig in the Literary Review as his best work yet. An in-depth and wide-ranging literary biography, it sets Andersen’s work within a European context and pays close attention to his unjustly neglected work outside the fairy tales, such as the novel Improvisatore, which Binding argues was a great influence on Charles Dickens. I met and became friends with Paul through our mutual interest in the novelist Barbara Pym, and have since had many discussions with him about writers; he was the plenary speaker at the Barbara Pym Centenary Conference I organised in 2013. He lives in the beautiful small town of Bishop’s Castle, Shropshire, in the Welsh Marches – the border country of England and Wales. His website is http://www.paulbinding.co.uk/index.html

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