Search results for "Gradient"
showing 10 items of 725 documents
The annular decay property and capacity estimates for thin annuli
2016
We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted $\mathbf{R}^n$ and in metric spaces, primarily under the assumptions of an annular decay property and a Poincar\'e inequality. In particular, if the measure has the $1$-annular decay property at $x_0$ and the metric space supports a pointwise $1$-Poincar\'e inequality at $x_0$, then the upper and lower bounds are comparable and we get a two-sided estimate for thin annuli centred at $x_0$, which generalizes the known estimate for the usual variational capacity in unweighted $\mathbf{R}^n$. Most of our estimates are sharp, which we show by supplying several key counterexamples. We also character…
Neumann p-Laplacian problems with a reaction term on metric spaces
2020
We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincare inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.
QR-Factorization Algorithm for Computed Tomography (CT): Comparison With FDK and Conjugate Gradient (CG) Algorithms
2018
[EN] Even though QR-factorization of the system matrix for tomographic devices has been already used for medical imaging, to date, no satisfactory solution has been found for solving large linear systems, such as those used in computed tomography (CT) (in the order of 106 equations). In CT, the Feldkamp, Davis, and Kress back projection algorithm (FDK) and iterative methods like conjugate gradient (CG) are the standard methods used for image reconstruction. As the image reconstruction problem can be modeled by a large linear system of equations, QR-factorization of the system matrix could be used to solve this system. Current advances in computer science enable the use of direct methods for…
Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
2006
We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having a first order term which grows quadratically in the gradient. The model problem we refer to is the following (1){ut−div(α(u)∇u)=β(u)|∇u|2+f(x,t),in Ω×]0,T[;u(x,t)=0,on ∂Ω×]0,T[;u(x,0)=u0(x),in Ω. Here Ω is a bounded open set in RN, T>0. The unknown function u=u(x,t) depends on x∈Ω and t∈]0,T[. The symbol ∇u denotes the gradient of u with respect to x. The real functions α, β are continuous; moreover α is positive, bounded and may vanish at ±∞. As far as the data are concerned, we require the following assumptions: ∫ΩΦ(u0(x))dx<∞ where Φ is a convenient function which …
A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets
2004
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.
Optimizing auditory images and distance metrics for self‐organizing timbre maps*
1996
Abstract The effect of using different auditory images and distance metrics on the final configuration of a self‐organized timbre map is examined by comparing distance matrices, obtained from simulations, with a similarity rating matrix, obtained using the same set of stimuli as in the simulations. Gradient images, which are intended to represent idealizations of physiological gradient maps in the auditory pathway, are constructed. The optimal auditory image and distance metric, with respect to the similarity rating data, are searched using the gradient method.
Data from: Ecological and historical determinants of population genetic structure and diversity in the Mediterranean shrub Rosmarinus officinalis (La…
2016
Population genetic studies of widespread Mediterranean shrubs are scarce compared with those of trees and narrow endemics or studies from phylogeographical perspectives, despite the key role these species may play in Mediterranean ecosystems. Knowledge on the effect of ecological factors in shaping their genetic patterns is also limited. In this study we investigate genetic diversity and population structure across 18 populations of Rosmarinus officinalis, a Mediterranean shrubland plant. Populations were sampled along two elevational gradients, one each on calcareous and siliceous soils in a mountain system in the eastern Iberian Peninsula, to decipher the effect of ecological factors on t…
Microbial analysis of raw cows' milk used for cheese-making: influence of storage treatments on microbial composition and other technological traits
2010
Raw milk used to produce Grana cheese was subjected to several treatment regimes, including varying temperatures and storage times. Milk from morning and evening milking were transferred to a dairy factory sepa- rately (double delivery) or together (single delivery), after storage at the farm for 12 h; in the former case, milk was stored at 12 or 8°C, whereas, in the latter, it was kept at ambient temperature or 18°C. Values of pH of the vat milk were lower for milk samples kept at room temperature, while other physico-chemical parameters and rheological characteristics tested did not show significant differ- ences linked to the different storage temperatures of milk used for ‘‘Grana Trenti…
Kinetics of streptolysin O self-assembly.
1995
Streptolysin O is a member of a family of membrane-damaging toxins that bind to cell membranes containing cholesterol and then polymerize to form large pores. We have examined the kinetics of toxin action using 125I-labelled streptolysin O. Binding of toxin monomers to membranes displays first-order kinetics and is reversible; the rate of desorption from red cells shows a marked dependence on temperature. To study oligomerization, toxin was bound to erythrocytes at 0 degrees C. Oligomer formation was then triggered by a sudden temperature shift and stopped by solubilization of membranes with deoxycholate. While at moderately high streptolysin O concentrations oligomerization behaves as a re…
Image-based MRI Gradient Estimation
2017
In order to reduce geometric distortion phenomena in MR images, every MRI system main magnet undergoes a shimming process. Since this process aims at optimizing magnetic field homogeneity within a so-called uniformity sphere, image quality outside this sphere is neglected. Since the fields vary smoothly in space, MR signal-to-noise ratio is still non-zero just outside the uniformity region, but correction of MR image distortion fails due to lack of magnetic field knowledge outside it. We propose a novel algorithm for measuring all the fields involved in the generation of images. Our proposal is based on exploitation of the distortion which can be observed in images of a known phantom. The p…