Image reconstruction from scattered Radon data by weighted positive definite kernel functions

We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite–Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite–Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented

Local RBF approximation for scattered data fitting with bivariate splines

In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given

Rendimento e qualidade fisiológica de sementes de duas variedades de azevém com diferentes manejos de adubação e cortes.

CONGREGA URCAMP 2012

Polyelectrolyte multilayer membranes:An experimental review

Within just two decades, polyelectrolyte multilayer (PEM) membranes have moved from invention to their world wide application. One key advantage of these membranes is their versatility, allowing easy optimization through various tuning parameters. But it is exactly this versatility that has made it difficult to fairly compare PEM membranes. Previously, only Krasemann and Tieke (2000) have compared a large set polyelectrolyte pairs for their membrane performance, concluding that the polyelectrolyte charge density was a key tuning parameter. However, in these early days of PEM membrane research, characterization was rather limited. In this work, we have performed a thorough experimental review, studying 9 common polyelectrolyte pairs for their layer properties on model surfaces and their separation properties as pressure driven membranes. All systems were prepared under identical conditions to allow for a fair comparison, and membranes were characterized for their water permeability, molecular weight cut off, and ion retention. We find that the porous support is closed by a PEM when its thickness is in the order of the membrane support pore size, which was expected but not demonstrated before. Of all the PEM parameters, the degree of swelling stands out as a parameter that plays a key role and can be easily experimentally determined. Interestingly, we find that swelling increases with polyelectrolyte charge density, which is opposite to what Krasemann and Tieke proposed. We attribute this to the higher hydrophilicity of polyelectrolytes with a higher charge density. In turn, we find correlations between swelling and the water permeability as well as size exclusion, dielectric exclusion and Donnan exclusion. Still, the connection between polyelectrolyte properties and membrane properties is more complex and cannot be solely understood by swelling. Further understanding of this complexity will provide the tools to develop even better polyelectrolyte multilayer membranes.</p

Exact ground-state correlation functions of the one-dimensional strongly correlated electron models with the resonating-valence-bond ground state

We investigate the one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding non-interacting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing.Comment: 59 pages, REVTeX 3.0, Figures are available on reques

The Short Range RVB State of Even Spin Ladders: A Recurrent Variational Approach

Using a recursive method we construct dimer and nondimer variational ansatzs of the ground state for the two-legged ladder, and compute the number of dimer coverings, the energy density and the spin correlation functions. The number of dimer coverings are given by the Fibonacci numbers for the dimer-RVB state and their generalization for the nondimer ones. Our method relies on the recurrent relations satisfied by the overlaps of the states with different lengths, which can be solved using generating functions. The recurrent relation method is applicable to other short range systems. Based on our results we make a conjecture about the bond amplitudes of the 2-leg ladder.Comment: REVTEX file, 32 pages, 10 EPS figures inserted in text with epsf.st