Il problema di Dirichlet per equazioni lineari ellittiche in forma di divergenza

The purpose of this dissertation is to prove that the Dirichlet problem in a bounded domain is uniquely solvable for elliptic equations in divergence form. The proof can be achieved by Hilbert space methods based on generalized or weak solutions. Existence and uniqueness of a generalized solution for the Dirichlet problem follow from the Fredholm alternative and weak maximum principle.

Problema di Cauchy-Dirichlet per l'equazione del calore di una sbarra omogenea

In questa tesi vengono forniti risultati sulle serie di Fourier e successivamente sulle serie di Fejér, utili per poter analizzare il cosiddetto problema di Cauchy-Dirichlet per l'equazione del calore di una sbarra omogenea. Lo scopo è trovare soluzioni classiche del problema che presenta come dato iniziale dapprima una funzione di classe C^1 e successivamente una funzione solamente continua.

Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

INTERACTIVE CONTROLS OF WATER TABLE POSITION AND PLANT FUNCTIONAL TYPES ON PEAT POREWATER CHARACTER IN NORTHERN BOG ECOSYSTEMS: IMPLICATIONS FOR CARBON CYCLING DYNAMICS

Northern wetlands, and particularly peatlands, have been shown to store around 30% of the world's soil carbon and thus play a significant role in the carbon cycle of our planet. Changes in climate are altering peatland hydrology and vegetation communities. These changes are possibly resulting in declines in the ability of peatlands to sequester carbon because losses through carbon oxidation and mineralization are likely to increase relative to C inputs from net primary production in a warmer, drier climate. However, the consequences of interactive effects of altered hydrology and vegetation on carbon storage are not well understood. This research evaluated the importance of plant species, water table, and their interactive effects on porewater quality in a northern peatland with an average pH of 4.54, ranging from 4.15 to 4.8. We assessed the effects of plant functional group (ericaceous shrubs, sedges, and bryophytes) and water table position on biogeochemical processes. Specifically, we measured dissolved organic carbon (DOC), total dissolved nitrogen (TDN), potential enzyme activity, organic acids, anions and cations, spectral indexes of aromaticity, and phenolic content. Our results indicate that acetate and propionate concentrations in the sedge-dominated communities declined with depth and water table drawdown, relative to the control and ericaceous treatments. DOC increased in the lowered water table treatments in all vegetation community types, and the peat porewater C:N ratio declined in the sedge-dominated treatments when the water table was lowered. The relationship between DOC and ferrous iron showed significant responses to vegetation type; the exclusion of Ericaceae resulted in less ferrous iron per unit DOC compared to mixed species treatments and Ericaceae alone. This observation was corroborated with higher mean oxidation redox potential profiles (integrating 20, 40, and 70 cm) measured in the sedge treatments, compared with the mixed and Ericaceae species treatments over a growing season. Enzymatic activities did not show as strong of a response to treatments as expected; the oxidative enzyme peroxidase and the hydrolytic enzyme phosphatase were the only enzymes to respond to water table, where the potential activity of both enzymes increased with water table drawdown. Overall, there were significant interactive effects between changes in vegetation and water table position on peat porewater composition. These data suggest that vegetation effects on oxidation reduction potentials and peat porewater character can be as important as water table position in northern bog ecosystems.

Vermiculite, Occurence, Character, and Concentration of Mineral from the Pony District, Madison County, Montana

The purpose of this paper is to investigate the occurrence and character of the vermiculite deposits approximately four miles northwest of Pony; Madison County, Montana. The deposits are situated in rolling foothills at the northern end of the Tobacco Root Mountains.

The Deprofessionalisation Thesis, Accountability and Professional Character

It is said that the deprofessionalisation of social work and other welfare occupations reduces workers' professional discretion and autonomy, and thus their capacity to act in the best interests of their client. Without necessarily regarding the deprofessionalisation thesis as conclusive, this paper will ask how the state's control of the role and task of social workers impacts on their role-implicated obligations as professionals. If workers are reduced (as claimed) to the status of mere functionaries in systems they neither approve of nor control, does this exonerate them from bad outcomes or service failures? How should we view the dramatic increase in formal regulation now seen in the UK - as professionalisation or deprofessionalisation? The paper will argue that whatever the drift of policy, workers remain in some measure personally accountable. Service failures imply faults of practical reason that are partly attributable to the moral and intellectual character of professionals as individuals. It is therefore up to professionals, and their organisations, to attend to the improvement of professional character.

Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.