Interpolating sequences and the Nevanlinna pick problem

The extremal solutions to the Nevanlinna Pick problem are studied. If there is more than one solution, Nevanlinna showed that all extremal solutions are inner functions. With some extra information on the interpolation data we find that the extremal solutions are Blaschke products whose zeroes form a finite union of interpolating sequence

Mergelyan type theorems for some function spaces

Let $F$ be a relatively closed subset of the unit disc $D$. If $A$ is any of the Hardy spaces $H^p(D)$, 0 < p < \infty, $\overline{A|_F}$ denotes the functions on $F$ being uniform limits of elements from $H^p(D)$. Let $\tilde F$ consist of all $z\in D$ such that $|f(z)|\le\sup \{|f(z)| z\in F\}$ for any bounded analytic function in $D$. It is proved that $\overline{A|_F}$ consist of all functions $f$ that can be decomposed as $f=u+v$, where $u$ belongs to $H^p(D)$ and $v$ is a uniformly continuous function on the set $\tilde F$, analytic at interior points of $\tilde F$

Blaschke products and Nevanlinna-Pick interpolation

For a Nevanlinna{Pick problem with more than one solution, Rolf Nevanlinna proved that all extremal solutions are inner functions. If the interpolation points are contained in dinitely many cones terminating at the unit circle, it is shown that all extremal solutions are Blaschke products

Conference 2014 speaker series: an interview with Jonathan Stray

Ahead of the Polis Annual Journalism Conference on Friday March 28th, we are interviewing some of our speakers. Jonathan Stray is the man behind Overview, a project from the Associated Press that aims to help journalists find stories in large quantities of documents. The tool uses keyword searches to automatically sort documents according to topic, making patterns and trends far easier to spot. Jonathan is a fellow at the Tow Center for Digital Journalism at Columbia University, teaching and researching computational journalism. He developed Overview with a Knight News Challenge grant

Autonomous agile teams: Challenges and future directions for research

According to the principles articulated in the agile manifesto, motivated and empowered software developers relying on technical excellence and simple designs, create business value by delivering working software to users at regular short intervals. These principles have spawned many practices. At the core of these practices is the idea of autonomous, self-managing, or self-organizing teams whose members work at a pace that sustains their creativity and productivity. This article summarizes the main challenges faced when implementing autonomous teams and the topics and research questions that future research should address

Stability of Weak Confined Wake Behind a Cylinder in Fully Developed Turbulent Channel Flow

AbstractThe motivation for the study of instability of turbulent wake flow in a confined turbulent channel was multi-fold. First, the instability of confined wake flows has not been studied much. Second, confined wakes are found to retain their mean velocity profile for a considerable downstream distance. Third, wakes have two points of inflection, one each on either side of the centre line. The basic aim of the present study was to investigate the correlation between the turbulence in the wake region and the inflection points in the wake region using stability theory. The wake behind a cylinder of diameter d in a turbulent channel with half width h, is a weak confined wake when d/h ≈ 0.2. Thus, d/h=0.2 was chosen for the present work. Experimental results are obtained by introducing organized disturbances in the wake and tracking these downstream. Theoretical results were obtained by solving the Orr-Sommerfeld equation by numerical methods

The classicism of Hugh Trevor-Roper

Hugh Trevor-Roper was educated as a classicist until he transferred to history, in which he made his reputation, after two years at Oxford. His schooling engendered in him a classicism that was characterised by a love of classical literature and style, but rested on a repudiation of the philological tradition in classical studies. This reaction helps to explain his change of intellectual career. His classicism, however, endured: it influenced his mature conception of the practice of historical studies, and can be traced throughout his life. This essay explores a neglected aspect of Trevor-Roper's intellectual biography through his ‘Apologia transfugae’ (1973), which explains his rationale for abandoning classics, and published and unpublished writings attesting to his classicism, especially his first publication ‘Homer unmasked!’ (1936) and his wartime notebooks

Detection of intermediates and kinetic control during assembly of bacteriophage P22 procapsid

Bacteriophage P22 serves as a model for the assembly and maturation of other icosahedral double-stranded DNA viruses. P22 coat and scaffolding proteins assemble in vitro into an icosahedral procapsid, which then expands during DNA packaging (maturation). Efficient in vitro assembly makes this system suitable for design and production of monodisperse spherical nanoparticles (diameter ≈50 nm). In this work we explore the possibility of controlling the outcome of assembly by scaffolding protein engineering. The scaffolding protein exists in monomer-dimer-tetramer equilibrium. We address the role of monomers and dimers in assembly by using three different scaffolding proteins with altered monomer-dimer equilibrium (weak dimer, covalent dimer, monomer). The progress and outcome of assembly was monitored by time-resolved X-ray scattering which allowed us to distinguish between closed shells and incomplete assembly intermediates. Binding of scaffolding monomer activates the coat protein for assembly. Excess dimeric scaffolding protein resulted in rapid nucleation and kinetic trapping yielding incomplete shells. Addition of monomeric wild type scaffold with excess coat protein completed these metastable shells. Thus, the monomeric scaffolding protein plays an essential role in the elongation phase by activating the coat and effectively lowering its critical concentration for assembly