Astrogeometry: Toward mathematical foundations

Inimage processing (e.g., inastronomy), the desired black-and-white image is, from the mathematical viewpoint, aset. Hence, to process images, we need to process sets. To define a generic set, we need infinitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to finite-parameter families of sets that will be used to approximate the desired sets. The wrong choice of a family can lead to longer computations and worse approximation. Hence, it is desirable to find the family that it isthe best in some reasonable sense. In this paper, we show how the problems of choosing the optimal family of sets can be formalized and solved. As a result of the described general methodology, forastronomical images, we get exactly the geometric shapes that have been empirically used by astronomers and astrophysicists; thus, we have atheoretical explanation for these shapes.     

General Quantization

In the Darwinian evolution of physical theories, stability (genericity) has survival value. To convert a singular physical theory based on Lie algebras of several levels into a generic quantum theory with the same levels and nearly the same predictions and symmetries in a limited correspondence domain, it suffices to simplify the algebra of each level by a small homotopy (general quantization). This extends and unifies special relativization, general relativization, and canonical quantization. For exercise I general-quantize the scalar meson field in Minkowski space-time. The predictions of the resulting theory are finite, including its zero-point energy.This updates part of a talk given at Glafka 2005, Athens. quant-ph/0601002     

Introduction

Applied Biochemistry and Biotechnology -     

Dendritic molecular capsules for hydrophobic compounds

Reichardt's dye, a highly solvatochromic dye, was encapsulated within poly (glycerol succinic acid) ([Gn]-PGLSA-OH) dendrimers to investigate the interior environment of these dendritic macromolecules. The absorption maximum for the encapsulated Reichardt's dye in water was indicative of a relatively high dielectric constant present within the dye/dendrimer complex. (1)H NMR of the encapsulated complex showed the presence of aromatic protons from Reichardt's dye along with the aliphatic protons of the dendrimer. Additionally, there were substantial changes in T(1) and T(2) times of the encapsulated dye when compared with the free dye, and (1)H NOESY spectra for the complex showed a significant number of intermolecular NOE cross-peaks. These data reveal the close through-space proximity of the dye to the dendrimer and the restricted motion of the encapsulated dye. To demonstrate the potential use of these macromolecules as drug delivery vehicles, the poorly water-soluble anticancer drug 10-hydroxycamptothecin (10HCPT) was encapsulated within a carboxylated PGLSA dendrimer ([G4]-PGLSA-COONa). Cytotoxicity assays with human breast cancer cells showed a significant reduction of cell viability, demonstrating that 10HCPT retains activity upon encapsulation.     

Myoglobin-CO substate structures and dynamics: multidimensional vibrational echoes and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales.     

Sensing the physicochemical nature of he and ne in micropores by adsorption measurements

He and Ne in contact with molecular sieves in the form of crystalline A zeolites and amorphous carbon molecular sieves fibers (CMSF) were studied by adsorption measurements. Classification of the effective enclosure of zeolitic apertures and of graphitic constrictions, as determined by recent temperature-programmed desorption mass spectrometry (TPD-MS) studies of adsorption of He and Ne onto these materials, was utilized in making a prudent choice of samples and experimental conditions. In view of the former TPD information, the behaviors of adsorption and volumetric measurements reported herein are straightforwardly interpreted. The combined TPD, adsorption isotherms, and dead volume data deepen the understanding of the physicochemical nature of adsorbed gas, where gas adsorption in the vicinity of pore constrictions and/or apertures as well as on the inner surface areas of pores and/or cages could be resolved. Previous conclusions that the huge activation energies measured for Ne/CMSF at high temperatures are unlikely to characterize chemical desorption but reflect those required for overcoming the barrier of effectively constricted apertures were confirmed by the volumetric data presented here. At 77 K, considerable He adsorption was observed in the porous solids and found to be responsible for abnormal deduced values of dead volumes. The occurrence of significant adsorption of He onto A zeolites and CMSF at 77 K warrants the realization that in cases concerning porous materials, volumetrically deduced quantities should not be taken for granted, but should be carefully considered and uniquely interpreted in relation to the specific experimental conditions under which they are taken.     

q-transformation theory

We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU _q (2) algebra. To obtain transition probabilities, one must take the Woronowicz square.     

Average and extreme multi-atom Van der Waals interactions: Strong coupling of multi-atom Van der Waals interactions with covalent bonding

Background  

The prediction of ligand binding or protein structure requires very accurate force field potentials – even small errors in force field potentials can make a 'wrong' structure (from the billions possible) more stable than the single, 'correct' one. However, despite huge efforts to optimize them, currently-used all-atom force fields are still not able, in a vast majority of cases, even to keep a protein molecule in its native conformation in the course of molecular dynamics simulations or to bring an approximate, homology-based model of protein structure closer to its native conformation.