General quadratic gauge theory. Constraint structure, symmetries, and physical functions

How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially relate the constraint structure with the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether can we identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present article is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfill such a program, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyze a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analyzing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.Comment: LaTex file, 18 page

Canonical form of Euler-Lagrange equations and gauge symmetries

The structure of the Euler-Lagrange equations for a general Lagrangian theory is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter in the right hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proven that for local theories all the gauge generators are local in time operators.Comment: 27 pages, LaTex fil

NAA and STS effects on bract survival time, carbohydrate content, respiration rate and carbohydrate balance of potted Bougainvillea spectabilis Willd

The aims of this work were to deepen the knowledge on the physiology of bract abscission in Bougainvillea spectabilis ‘Killie Campbell’ plants, in what relates to respiration and carbon balance. Using the effects induced by Silver Thiosulphate (STS) and/or Naphtalene Acetic Acid (NAA, at high concentration: 500 mg.l-1) on bract abscission under interior conditions, the relationship between bract survival time (longevity) and, respiration rate or carbohydrate levels, was investigated. Treatments that included NAA were the ones that reduced significantly bract abscission. Unexpectedly, the higher the levels of bract soluble and total carbohydrates, measured at day 10 postproduction (PP), the higher the abscission of bracts. These results show, for the first time, that abscission can positively correlate with non structural carbohydrates levels in the organ that abscise. Bract respiration rate was significantly affected by treatment and postproduction day (PP). Treatments that had higher bract respiration rates (WATER and STS) also had higher levels of non structural carbohydrates in the bracts. Bract respiration rate decreased from day 10 to day 17 PP by approximately 50% (on average of all treatments) and was negatively correlated with bract survival time. In the carbon balance per gram of bract dry weight, the treatments WATER and STS, showed the largest decrease in the content of total carbohydrates and had the highest consumption of carbohydrates through respiration. So, these were the bracts that needed to import a higher amount of carbohydrates per gram of bract dry weight. In the carbon balance for the whole mass of bracts and adjacent stems in an average plant, the treatments WATER and STS continued to allow for the largest decreases in total carbohydrate during postproduction. However, and contradicting the results per gram of bract dry weight, the highest total consumption of carbohydrates by respiration was obtained for the NAA and STS+NAA treatments. It makes sense that bracts that last longer have lower individual carbon consumption while, at the plant level, the increased number of remaining bracts causes a higher overall expenditure. Respiration rate has been used as an indicator of flower longevity, this correlation is here extended for the flower+bract system. Plants that had higher bract respiration rates, most probably, had a higher flow of carbohydrates through the bracts (and flowers), which, in the end, was sensed as a higher carbohydrate level.Bolsa Praxis XXI/BD/15640/98 e o Projecto PBIC/C/2286/95, financiados pela Fundação para a Ciência e Tecnologia. Financiamento Plurianual e instalações do CDCTPV/Universidade do Algarve (incluindo o Projecto de unidade I&D: CDCTPV 2003-2005, POCTI/POCI,2010

Estimating environmentally adjusted risks of mortgage arrears for different socioeconomic groups of borrowers

Purpose: The proper consideration of risk factors that can lead to the failure of a borrower to repay a mortgage is critical for both mortgage borrowers and lending institutions. Models for assessing the risk of mortgage arrears (MA) typically incorporate loan attributes and essential characteristics of the borrower, including net income, family size, age, education, and credit history. However, such standard MA models exclude environmental risk factors, which increase, as we hypothesize, the MA risk. Design/Methodology/Approach: We analyzed 90,000 individual mortgage records obtained from a leading commercial bank in Israel to verify this hypothesis. In the analysis, the mortgage records were geo-referenced by their seven-digit ZIP codes and linked to air pollution data and several other locational attributes. The analysis was performed using a Cox-type proportional hazard model. Findings: The study shows that residential exposure to high levels of air pollution tends to increase the MA risk by about 10%–25%, depending on the type of air pollutant and exposure level. We attribute this finding to the fact that exposure to air pollution may reduce productivity and increase work absenteeism, thus making mortgage repayment more difficult. Practical implications: The importance of the study is due to its three main novelty aspects: First, it suggests an empirical approach to adjusting MA risk estimates by accounting for environmental attributes of residential properties. Second, the analysis shows that borrowers' and mortgage's attributes (such as net monthly income, family size, and LTV ratio) tend to increase the MA risk asymmetrically for different groups of borrowers. Originality: The study demonstrates the utility of adding air pollution variables to the list of MA risk predictors, which helps to introduce important information not captured by other observables. To the best of our knowledge, this is the first study that assesses environmentally adjusted MA risks for different socioeconomic groups of borrowers.peer-reviewe