Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Fixed-frequency and threshold molecular photoelectron spectra of S 1s, Si 1s and Cl 1s core levels

Fixed-frequency and threshold photoelectron spectra have been recorded for ionization from the S ls shells in SF₆, CS₂ and COS, the Si 1s shells in SiH₄ and SiCl₄ and the Cl 1s shell in SiCl₄ using synchrotron radiation. Fixed-frequency spectra generally showed a single strong ionization feature with associated weak satellite structure due to excited ionized states. Threshold spectra closely resembled X-ray absorption spectra but with an additional feature due to direct ionization. In cases where resonant process enhanced the NEXAFS spectrum direct ionization was not observed.     

Fluorescence line narrowed spectra of Zn and metal-free cytochrome c

Fluorescence line narrowing (FLN) spectroscopy was used to study the role of the polypeptide chain in influencing the spectrum of Zn-substituted cytochrome c (Zn cyt c) and metal-free cyt c (porphyrin cyt c). For both derivatives the spectra show characteristics of relaxed fluorescence from an inhomogeneously broadened sample. Zero phonon lines and phonon wings can be clearly distinguished, and vibrational frequencies of the ground and excited states were identified. The inhomogeneous distribution width for porphyrin cyt c is slightly wider than that of Zn cyt c and a second population of molecules was apparent in the porphyrin cyt c. The phonon coupling was greater for Zn cyt c than for porphyrin cyt c, which may be due to the extra coupling to the polypeptide chain by metal ligation.This work has been done in partial fulfillment of the requirements for the Doctor of Philosophy degree.     

The Design of Single Mode Large Cross-section Glass-based Waveguides for Photonic Integrated Circuits

This paper presents our recent simulation results and novel designs of single mode large cross-section glass-based waveguides for photonic integrated circuits (PICs). Simulations were performed using an in-house Finite Difference (FD) based mode solver and the FD Beam propagation Method (FD-BPM). Our simulation results show that this innovative technology could provide a simplified means to couple optical energy efficiently between optical components in a single chip. This would provide the base for the future large-scale integration of optical components in PICs. The novel idea of using single mode large cross-section glass-based waveguides as an optical integration platform is an evolutionary innovative solution for the monolithic integration of optical components, in which the glass-based structures act both as waveguides and as an optical bench for integration. This allows easy and efficient optical coupling between optical components and optical fibres, removing costly and tedious alignment problems and considerably reducing optical coupling losses in PICs. We expect that the glass-based waveguide PICs technology will enable the emergence of a new generation of compact, reliable, high speed, and multifunctional devices.     

Quantum confinement in layer-by-layer deposited colloidal HgTe nanocrystals determined by spectroscopic ellipsometry

We report spectroscopic ellipsometry studies in the energy range of 0.5-5 eV on samples of 1-10 bilayers of polymer and HgTe nanocrystals, which exhibit strong transitions at higher critical points in the dispersion relation. We show that the dispersion relation for nanocrystals can be modelled with the same concepts for critical points as used in semiconductor bulk optics. We find an energy shift of up to 0.4 eV of the critical points to higher energies compared to the HgTe bulk properties, caused by quantum confinement in the nanocrystals, which increases with decreasing nanocrystal size.     

The Method of Virtual Experts in Mathematical Diagnostics

Mathematical Diagnostics (MD) deals with identification problems arising in different practical areas. Some of these problems can be described by mathematical models where it is required to identify points belonging to two or more sets of points. Most of the existing tools provide some identification rule (a classifier) by means of which a given point is assigned (attributed) to one of the given sets. Each classifier can be viewed as a virtual expert. If there exist several classifiers (experts), the problem of evaluation of experts’ conclusions arises. In the paper for the case of supervised classification the method of virtual experts (the VE-method) is described. Based on this method, a generalized VE method is proposed where each of the classifiers can be chosen from a given family of classifiers. As a result, a new optimization problem with a discontinuous functional is stated. Examples illustrating the proposed approach are provided. The work of the second author was supported by the Russian Foundation for Fundamental Studies (RFFI) under Grant No 03-01-00668.     

Synthesis and peptide-binding properties of a luminescent pyrimidine zinc(II) complex

The synthesis and peptide-binding properties of a Zn(II)nitrilotriacetate complex substituted with pyrimidine hydrazine amides are reported. The metal complex provides millimolar binding affinity in aqueous buffer to peptides bearing N-terminal His. The pyrimidine heterocycles intermolecularly interact with the bound peptide and quench the emission of nearby Trp residues by energy transfer.