Quillen bundle and geometric prequantization of non-abelian vortices on a Riemann surface

In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from L ² metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic form. The prequantum line bundle turns out to be Quillen’s determinant line bundle with a modified Quillen metric. Next, as in the case of abelian vortices, we construct line bundles over the moduli space whose curvatures form a family of symplectic forms which are parametrized by Ψ₀, a section of a certain bundle. The equivalence of these prequantum bundles are discussed.     

Isometric embeddings in cosmology and astrophysics

Recent interest in higher-dimensional cosmological models has prompted some significant work on the mathematical technicalities of how one goes about embedding spacetimes into some higher-dimensional space. We survey results in the literature (existence theorems and simple explicit embeddings); briefly outline our work on global embeddings as well as explicit results for more complex geometries; and provide some examples. These results are contextualized physically, so as to provide a foundation for a detailed commentary on several key issues in the field such as: the meaning of ‘Ricci equivalent’ embeddings; the uniqueness of local (or global) embeddings; symmetry inheritance properties; and astrophysical constraints.     

An effective Hamiltonian approach to quantum random walk

In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.     

A DUAL-BEAM SOURCE OF ACTINIC LIGHT FOR PHOTOSYNTHESIS RESEARCH

Abstract— A dual-beam source for providing illumination of white or nearly monochromatic light for photosynthesis studies is presented. The device provides programmed, repetitive sample illumination with variable intensity, pulse duration and sequence and a means of monitoring that program. It utilizes a lamp with an integral heat rejecting reflector, and a fiber optic bundle which efficiently transmits the light, diffusely and evenly illuminating the sample.     

Monotone interpolation of order 3 by C2 cubic splines

We propose a local solution for the problem of interpolatingmonotone data by monotone C² cubic splines with two additionalknots per interval, on an arbitrary partition, and with an approximationof order 3. Our paper extends recent works by Archer & LeGruyer and Pruess.     

THE ORIENTATION OF THE REACTION CENTER CAROTENOID TRIPLET STATE MAGNETIC AXES IN CHROMATOPHORES OF Rhodopseudomonas sphaeroides WILD TYPE

Abstract— The orientation of the principal magnetic axes of the reaction center carotenoid from Rps. sphaeroides wild type is presented. The parameters needed to simulate the observed carotenoid triplet state spectra indicate that the carotenoid adopts a planar structure within the reaction center. A high degree of geometrical and structural specificity is shown to exist for this carotenoid molecule.     

TOPICAL UROCANIC ACID ENHANCES UV-INDUCED TUMOUR YIELD AND MALIGNANCY IN THE HAIRLESS MOUSE

Epidermal urocanic acid has been postulated to be the mediator of the specific state of immunosuppression induced by UV irradiation, by which UV-initiated tumour cells are able to evade normal recognition and can survive to grow progressively into malignant tumours. These experiments demonstrate that topical application of UV-irradiated urocanic acid systemically suppresses the contact type hypersensitivity response to oxazolone in hairless mice. In addition, topically applied urocanic acid markedly increases the overt tumour yield and the degree of malignancy in hairless mice exposed chronically to daily minimally erythemal doses of simulated solar UV light. Topical urocanic acid also increases the number of latent UV-initiated tumours, detectable by croton oil promotion. Therefore UV photoproducts of urocanic acid can both systemically suppress contact hypersensitivity in the epidermis, and also enhance early survival of UV-initiated tumour cells resulting in augmentation of UV photocarcinogenesis.     

Computing stability regions--Runge-Kutta methods for delay differential equations

We discuss the practical determination of stability regionswhen various fixed-stepsize Runge-Kutta (RK) methods, combinedwith continuous extensions, are applied to the linear delaydifferential equation (DDE) y'(t)= y(t)+µ(t–) (t) with fixed delay . It is significant that the delay is not limitedto an integer multiple of the stepsize, and that we considervarious continuous extensions. The stability loci obtained in practice indicate that the standardboundary-locus technique (BLT) can fail to map the RK DDE stabilityregion correctly. The aim of this paper is to present an alternativestability boundary algorithm that overcomes the difficultiesencountered using the BLT. This new algorithm can be used forboth explicit and implicit RK methods.