Extremal Problems in Bergman Spaces and an Extension of Ryabykh's Theorem

We study linear extremal problems in the Bergman space $A^p$ of the unit disc for $p$ an even integer. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if the Taylor coefficients of $k$ are sufficiently small, then the extremal function $F \in H^{\infty}$. We also show that if $q \le q_1 < \infty$, then $F \in H^{(p-1)q_1}$ if and only if $k \in H^{q_1}$. These results extend and provide a partial converse to a theorem of Ryabykh.Comment: 16 pages. To appear in the Illinois Journal of Mathematic

Wings of Coenagrion puella vary in shape at the northern range margin (Odonata: Coenagrionidae)

A previous study has shown that wing size in Coenagrion puella varied considerably along a latitudinal gradient in the UK. Using landmark data from wing images, patterns of shape variation were also determined along the same transect by geometric morphometric analysis of wing shape. Wing shape was uniform at all sites other than those closest to the range margin, which differed significantly. The potential mechanisms that might have generated such between-population variation are discussed

A method to measure vacuum birefringence at FCC-ee

It is well-known that the Heisenberg-Euler-Schwinger effective Lagrangian predicts that a vacuum with a strong static electromagnetic field turns birefringent. We propose a scheme that can be implemented at the planned FCC-ee, to measure the nonlinear effect of vacuum birefringence in electrodynamics arising from QED corrections. Our scheme employs a pulsed laser to create Compton backscattered photons off a high energy electron beam, with the FCC-ee as a particularly interesting example. These photons will pass through a strong static magnetic field, which changes the state of polarization of the radiation - an effect proportional to the photon energy. This change will be measured by the use of an aligned single-crystal, where a large difference in the pair production cross-sections can be achieved. In the proposed experimental setup the birefringence effect gives rise to a difference in the number of pairs created in the analyzing crystal, stemming from the fact that the initial laser light has a varying state of polarization, achieved with a rotating quarter wave plate. Evidence for the vacuum birefringent effect will be seen as a distinct peak in the Fourier transform spectrum of the pair-production rate signal. This tell-tale signal can be significantly above background with only few hours of measurement, in particular at high energies.Comment: Presented by UIU at the International Symposium on "New Horizons in Fundamental Physics: From Neutrons Nuclei via Superheavy Elements and Supercritical Fields to Neutron Stars and Cosmic Rays," held to honor Walter Greiner on his 80th birthday at Makutsi Safari Farm, South Africa, November 23-29, 201

The African Female Writer and Her Craft: Aspects of Yvonne Vera’s Peculiar Feminist Vision

This paper is particularly concerned with identifying and examining some peculiar features of Yvonne Vera&rsquo;s literary artistry. It essentially explores the varied ways the Zimbabwean writer has articulated some aspects of her feminist viewpoint through the unique manner she crafts her novels. While drawing illustrations from especially Without a Name, Under the Tongue, Butterfly Burning and The Stone Virgins, it discusses some of theirdistinguishing qualities that include the nature of the writer&rsquo;s expression and interpretation of being. The paper also evaluates the significance of her unique craftswomanship (craftsmanship), especially with regard to understanding the nature of the African peoples and their world. It discovers that Vera celebrates the &ldquo;Africanness&rdquo; of the African, insisting as well on the exceptional qualities embedded in the human person and the exulted position she/he occupies in the cosmic arrangement of beings. In addition, the paper reveals that the writer believes in the sentient nature of the cosmos and in the interconnectivity of all existing entities. It, therefore, maintains that in light of these qualities (among others), Vera&rsquo;s feminist endeavour can rightly be branded as peculiar feminism

Spontaneous breaking of the BRST symmetry in the presence of the Gribov horizon : renormalizability

An all orders algebraic proof of the multiplicative renormalizability of the novel formulation of the Gribov-Zwanziger action proposed in Phys. Rev. D 86, 045005 (2012) [arXiv:1205.3934], and allowing for an exact but spontaneously broken BRST symmetry, is provided.Comment: 15 page