Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. Its evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. The present first part of this investigation is devoted to the introduction of basic concepts on which the fibre bundle approach to quantum mechanics rests. We show that the evolution of pure quantum-mechanical states can be described as a suitable linear transport along paths, called evolution transport, of the state sections in the Hilbert fibre bundle of states of a considered quantum system.Comment: 26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Revised: new material, references, and comments are added. Minor style chages. Continuation of quan-ph/9803083. For continuation of the this series see http://www.inrne.bas.bg/mathmod/bozhome

Models and metaphors: complexity theory and through-life management in the built environment

Complexity thinking may have both modelling and metaphorical applications in the through-life management of the built environment. These two distinct approaches are examined and compared. In the first instance, some of the sources of complexity in the design, construction and maintenance of the built environment are identified. The metaphorical use of complexity in management thinking and its application in the built environment are briefly examined. This is followed by an exploration of modelling techniques relevant to built environment concerns. Non-linear and complex mathematical techniques such as fuzzy logic, cellular automata and attractors, may be applicable to their analysis. Existing software tools are identified and examples of successful built environment applications of complexity modelling are given. Some issues that arise include the definition of phenomena in a mathematically usable way, the functionality of available software and the possibility of going beyond representational modelling. Further questions arising from the application of complexity thinking are discussed, including the possibilities for confusion that arise from the use of metaphor. The metaphor of a 'commentary machine' is suggested as a possible way forward and it is suggested that an appropriate linguistic analysis can in certain situations reduce perceived complexity

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Factors that affect proliferation of Salmonella in tomatoes post-harvest: the roles of seasonal effects, irrigation regime, crop and pathogen genotype

MAIN OBJECTIVES: Fresh fruits and vegetables become increasingly recognized as vehicles of human salmonellosis. Physiological, ecological, and environmental factors are all thought to contribute to the ability of Salmonella to colonize fruits and vegetables pre- and post-harvest. The goal of this study was to test how irrigation levels, fruit water congestion, crop and pathogen genotypes affect the ability of Salmonella to multiply in tomatoes post-harvest. EXPERIMENTAL DESIGN: Fruits from three tomato varieties, grown over three production seasons in two Florida locations, were infected with seven strains of Salmonella and their ability to multiply post-harvest in field-grown tomatoes was tested. The field experiments were set up as a two-factor factorial split plot experiment, with the whole-plot treatments arranged in a randomized complete-block design. The irrigation treatment (at three levels) was the whole-plot factor, and the split-plot factor was tomato variety, with three levels. The significance of the main, two-way, and three-way interaction effects was tested using the (type III) F-tests for fixed effects. Mean separation for each significant fixed effect in the model was performed using Tukey's multiple comparison testing procedure. MOST IMPORTANT DISCOVERIES AND SIGNIFICANCE: The irrigation regime per se did not affect susceptibility of the crop to post-harvest proliferation of Salmonella. However, Salmonella grew significantly better in water-congested tissues of green tomatoes. Tomato maturity and genotype, Salmonella genotype, and inter-seasonal differences were the strongest factors affecting proliferation. Red ripe tomatoes were significantly and consistently more conducive to proliferation of Salmonella. Tomatoes harvested in the driest, sunniest season were the most conducive to post-harvest proliferation of the pathogen. Statistically significant interactions between production conditions affected post-harvest susceptibility of the crop to the pathogen. UV irradiation of tomatoes post-harvest promoted Salmonella growth

Nutritional and Metabolic Requirements for the Infection of HeLa Cells by Salmonella enterica Serovar Typhimurium

Salmonella is the causative agent of a spectrum of human and animal diseases ranging from gastroenteritis to typhoid fever. It is a food - and water - borne pathogen and infects via ingestion followed by invasion of intestinal epithelial cells and phagocytic cells. In this study we employed a mutational approach to define the nutrients and metabolic pathways required by Salmonella enterica serovar Typhimurium during infection of a human epithelial cell line (HeLa). We deleted the key glycolytic genes, pfkA and pfkB to show that S. Typhimurium utilizes glycolysis for replication within HeLa cells; however, glycolysis was not absolutely essential for intracellular replication. Using S. Typhimurium strains deleted for genes encoding components of the phosphotransferase system and glucose transport, we show that glucose is a major substrate required for the intracellular replication of S. Typhimurium in HeLa cells. We also deleted genes encoding enzymes involved in the utilization of gluconeogenic substrates and the glyoxylate shunt and show that neither of these pathways were required for intracellular replication of S. Typhimurium within HeLa cells

Applicability of the Ussing chamber technique to permeability determinations in functionally distinct regions of the gastrointestinal tract in the rat

Ussing chambers are commonly utilized for in vitro investigations into gastrointestinal permeability. However, their sensitivity and applicability to the small intestine have not been well characterized. Methods: In order to investigate the effects of experimentally induced damage and the relative contribution of the mucosa and muscularis externa layers to transmural permeability in the small intestine, stomach and colon, normal rat intestinal tissues were mounted in Ussing chambers with or without removal of the muscularis externa or mucosal layers. Gastric tissues were damaged in vivo by exposure to indomethacin (100 mg kg -1 ), while ileal tissues were damaged in vitro by 0.4 M NaCl. Tissue damage was assessed histologically, while permeability parameters included conductance (G), potential difference (PD) and mucosal to serosal flux of horseradish peroxidase (HRP). Results: Damage localized to the tissue edges (edge damage) accounted for 25%-50% of the exposed epithelial length in the ileum, while less than 20% of stomach and colon epithelium was affected by edge damage. In the damaged stomach, a 20% reduction in epithelialization was accompanied by increases in G ( P < 0.001) and HRP ( P < 0.01) flux. Removal of the muscularis externa did not affect mucosal viability in the undamaged ileum or colon although HRP flux in the colon, but not ileum, was increased ( P < 0.01). Removal of the ileal mucosa produced increases in G and HRP flux, while PD was maintained. Conclusion: We conclude that the Ussing chamber technique is suitable for application to studies of gastric and colonic permeability in rats. However, owing to the prevalence and extent of edge damage in the small intestine, we would caution against the use of this technique for permeability studies in this region of the gastrointestinal tract in the rat