Dirac Operator on a disk with global boundary conditions

We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the connection between our result and the index theorem.Comment: RevTeX, 11 pages. References adde

Determinants of Dirac operators with local boundary conditions

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.Comment: standard LaTeX, 24 pages. To appear in Jour. Math. Phy

Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model

Understanding why individuals delay reproduction is a classic problem in evolutionary biology. In plants, the study of reproductive delays is complicated because growth and survival can be size and age dependent, individuals of the same size can grow by different amounts and there is temporal variation in the environment. We extend the recently developed integral projection approach to include size- and age-dependent demography and temporal variation. The technique is then applied to a long-term individually structured dataset for Carlina vulgaris, a monocarpic thistle. The parameterized model has excellent descriptive properties in terms of both the population size and the distributions of sizes within each age class. In Carlina, the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy approach. Considering each year separately, we show that both the direction and the magnitude of selection on the flowering strategy vary from year to year. Provided the flowering strategy is constrained, so it cannot be a step function, the model accurately predicts the average size at flowering. Elasticity analysis is used to partition the size- and age-specific contributions to the stochastic growth rate, λs. We use λs to construct fitness landscapes and show how different forms of stochasticity influence its topography. We prove the existence of a unique stochastic growth rate, λs, which is independent of the initial population vector, and show that Tuljapurkar's perturbation analysis for log(λs) can be used to calculate elasticities

A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the main framework. The final value heat conduction problem on a smooth open set is also proved to be well posed, and non-zero Dirichlet data are shown to require an extended compatibility condition obtained by adding an improper Bochner integral.Comment: 16 pages. To appear in "Applied and numerical harmonic analysis"; a reference update. Conference contribution, based on arXiv:1707.02136, with some further development

Ellipticity Conditions for the Lax Operator of the KP Equations

The Lax pseudo-differential operator plays a key role in studying the general set of KP equations, although it is normally treated in a formal way, without worrying about a complete characterization of its mathematical properties. The aim of the present paper is therefore to investigate the ellipticity condition. For this purpose, after a careful evaluation of the kernel with the associated symbol, the majorization ensuring ellipticity is studied in detail. This leads to non-trivial restrictions on the admissible set of potentials in the Lax operator. When their time evolution is also considered, the ellipticity conditions turn out to involve derivatives of the logarithm of the tau-function.Comment: 21 pages, plain Te

Input-output Analysis - Texas High Plains Labor Employment Potentials to 1980

The regional economy of the Texas High Plains (56 counties) is confronted with limited and exhaustable supplies of natural resources. This study was conducted to provide estimates of the direct labor requirements per $10,000 of production, to estimate dollar value of finished goods and services in 1980 required of each sector, and to estimate, in specific instance, the effects of irrigation water resource shortages upon labor employment opportunities. Direct, indirect and induced employment effects were derived through use of a Leontief Input-Output model. The analyses showed that final demand could increase from$5.5 billion in 1967 to $8.7 billion in 1980. In order to meet this level of production, labor employment in the region could increase from the 1967 level of 254 thousand to an estimated 406 thousand in 1980

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functions for free massive scalar fields in $\mathbb{R}^{n}$, scalar fields in three-dimensional hyperbolic space $H_{3}$ (the Euclidean Anti-de Sitter space $AdS_{3}$), in $H_{3}/Z$ (the geometry of the Euclidean BTZ black hole), and in $S^{1}$, and the Higgs model in a $(1+1)$-dimensional finite interval. Moreover, in the above cases, we also calculate the spectra from the counting functions. Besides exact solutions, we give a general discussion on approximate solutions and construct the general series expansion for one-loop effective actions, vacuum energies, and spectral counting functions. In doing this, we encounter divergences. In order to remove the divergences, renormalization procedures are used. In this approach, these three physical quantities are regarded as spectral functions in the spectral problem.Comment: 37 pages, no figure. This is an enlarged and improved version of the paper published in JHE

Isobutylmethylxanthine fails to stimulate chloride secretion in cystic fibrosis airway epithelia.

It has been proposed that a combination of an activated adenylyl cyclase and a high concentration of a phosphodiesterase inhibitor (isobutylmethylxanthine [IBMX], 5 mM) stimulates Cl- secretion mediated by the heterologously expressed cystic fibrosis transmembrane regulator protein carrying the most common cystic fibrosis (CF) mutation (delta F508). We tested whether Cl- secretion could be stimulated by this protocol in vitro and in vivo in CF airway epithelia expressing endogenous delta F508 CFTR protein. In cultured airway preparations, forskolin (a direct adenylyl cyclase activator) stimulated Cl- secretion in amiloride-pretreated normal (delta Isc = 7.1 +/- 1.7 microA.cm-2) but not CF tissues (delta Isc = -02 +/- 0.1 microA.cm-2). Unexpectedly, IBMX partially inhibited the forskolin-induced Cl- secretion in normal tissues; IBMX addition had no effect on CF tissues. Direct measurements of cell cAMP concentrations revealed that 0.1 mM IBMX and forskolin produced the maximum levels of cell cAMP levels attainable with this drug combination, and 5 mM IBMX was without further effect. The combination of forskolin (10(-5) M) and isoproterenol, an adenylyl cyclase activator (10(-5) M), produced approximately 3 times higher levels of cAMP than forskolin/IBMX but also did not induce Cl- secretion in CF tissues