Computational aspects of modular parametrizations of elliptic curves

Thesis (Ph.D.)--University of Washington, 2016-06

Microspectrophotometry of visual pigments and oil droplets in a marine bird, the wedge-tailed shearwater Puffinus pacificus: Topographic variations in photoreceptor spectral characteristics

Microspectrophotometric examination of the retina of a procellariiform marine bird, the wedge-tailed shearwater Puffinus pacificus, revealed the presence of five different types of vitamin A(1)-based visual pigment in seven different types of photoreceptor. A single class of rod contained a medium-wavelength sensitive visual pigment with a wavelength of maximum absorbance (lambda(max)) at 502 nm. Four different types of single cone contained visual pigments maximally sensitive in either the violet (VS, lambda(max) 406 nm), short (SWS, lambda(max) 450 nm), medium (MWS, lambda(max) 503 nm) or long (LWS, lambda(max) 566 nm) spectral ranges. In the peripheral retina, the SWS, MWS and LWS single cones contained pigmented oil droplets in their inner segments with cut-off wavelengths (lambda(cut)) at 445 (C-type), 506 (Y-type) and 562 nm (R-type), respectively. The VS visual pigment was paired with a transparent (T-type) oil droplet that displayed no significant absorption above at least 370 run. Both the principal and accessory members of the double cone pair contained the same 566 nm lambda(max) visual pigment as the LWS single cones but only the principal member contained an oil droplet, which had a lambda(cut) at 413 nm. The retina had a horizontal band or 'visual streak' of increased photoreceptor density running across the retina approximately 1.5 mm dorsal to the top of the pecten. Cones in the centre of the horizontal streak were smaller and had oil droplets that were either transparent/colourless or much less pigmented than at the periphery. It is proposed that the reduction in cone oil droplet pigmentation in retinal areas associated with high visual acuity is an adaptation to compensate for the reduced photon capture ability of the narrower photoreceptors found there. Measurements of the spectral transmittance of the ocular media reveal that wavelengths down to at least 300 nm would be transmitted to the retina.

Existence and multiplicity results for quasilinear elliptic equations

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f (x, s), we show the following problem: -Delta(p)u = lambda f(x,u) in Omega, u/(partial derivative Omega) = 0, where Omega is a bounded open subset of R-N, N >= 2, with smooth boundary, lambda is a positive parameter and Delta(p) is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large lambda.

Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

Development of an integrated reverse osmosis-greenhouse system driven by solar photovoltaic generators

The development of a system that integrates reverse osmosis (RO) with a horticultural greenhouse has been advanced through laboratory experiments. In this concept, intended for the inland desalination of brackish groundwater in dry areas, the RO concentrate will be reduced in volume by passing it through the evaporative cooling pads of the greenhouse. The system will be powered by solar photovoltaics (PV). Using a solar array simulator, we have verified that the RO can operate with varying power input and recovery rates to meet the water demands for irrigation and cooling of a greenhouse in north-west India. Cooling requires ventilation by a fan which has also been built, tested and optimised with a PV module outdoors. Results from the experiments with these two subsystems (RO and fan) are compared to theoretical predictions to reach conclusions about energy usage, sizing and cost. For example, the optimal sizing for the RO system is 0.12–1.3 m2 of PV module per m2 of membrane, depending on feed salinity. For the fan, the PV module area equals that of the fan aperture. The fan consumes <30 J of electrical energy per m3 of air moved which is 3 times less than that of standard fans. The specific energy consumption of the RO, at 1–2.3 kWh ?m-3, is comparable to that reported by others. Now that the subsystems have been verifi ed, the next step will be to integrate and test the whole system in the field.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

An iterative procedure for solving a Cauchy problem for second order elliptic equations

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Experiences on Application Generators

The National Institute for Statistics is the organism responsible for acquiring economical data for governmental statistics purposes. Lisbon agreements establish a framework in which this acquisition process shall be available through Internet, so each survey should be considered as a little software project to be developed and maintained. Considering the great amount of different surveys and all changes produced per year on each make impossible this task. An application generator has been developed to automate this task, taking as a start point the Word or PDF template of a survey, and going through a graphical form designer as all human effort, all HTML, Java classes and Oracle database resources are generated and sent from backoffice to frontoffice servers, reducing the team to carry out the whole set of electronic surveys to two people from non I.T. staff.

On a Class of Generalized Elliptic-type Integrals

The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication [1] we have obtained recurrence relations and asymptotic formula for this generalized elliptic-type integral. Here we shall obtain some more results which are single and multiple integral formulae, differentiation formula, fractional integral and approximations for this class of generalized elliptic-type integrals.

Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30