Search results for "value"

Feynman-Kac formulae

2015

In this chapter, we establish the connection between the deterministic EIT forward problem and the class of reflecting diffusion processes. We proceed along the lines of the recent paper [137] by Piiroinen and the author: We derive Feynman-Kac formulae in terms of these processes for the solutions to the forward problems corresponding to the continuum model and the complete electrode model, respectively. These results extend the classical Feynman-Kac formulae for elliptic boundary value problems in smooth domains and with smooth coefficients which were obtained in the 1980s and 1990s using the Feller semigroup approach and Ito stochastic calculus. In contrast to this well-studied situation,…

Green’s function and existence of solutions for a third-order three-point boundary value problem

2019

The solutions of third-order three-point boundary value problem x‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η), where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.

Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type

2021

The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.

Quasilinear elliptic equations with singular quadratic growth terms

2011

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

Determination of sugars in depilatory formulations: a green analytical method employing infrared detection and partial least squares regression.

2011

A green analytical method was developed for the analysis of sugar-based depilatories. Three independent partial least squares (PLS) regression models were built for the direct determination of glucose, fructose and maltose without any sample pretreatment based on their attenuated total reflectance - Fourier transform infrared (ATR-FTIR) spectra. The models showed adequate prediction capabilities with root-mean-square-errors of prediction ranging from 7.04 to 12.55 mg sugar g(-1) sample. As a reference procedure, gradient liquid chromatography with on-line infrared detection, employing background correction based on cubic smoothing splines, was used. The analysis revealed changes in the suga…

Evaluation of DR and CR digital mammography systems based on phantom and breast dosimetry.

2006

Digital mammography has been progressively introduced in screening centers, since recent evolution of CR and DR detectors. However, it is questionable which exposure conditions would be more suitable when these techniques are applied, in order to reduce the glandular breast doses, as they are related with induced carcinogenesis. Several exposures have been performed in CR and DR mammography units for comparing absorbed doses during quality control assessments and during screening, diagnosis and treatment. In the first case, the CIRS11A mammographic phantom has been used with standard exposure conditions (28 kV, AEC mode with blackening +0, 50:50 glandularity and 4.5 compressed breast thickn…

The role of the reporting framework MIATA within current efforts to advance immune monitoring

2014

The course of fatigue in patients with gynecologic and breast cancer

2013

Objective: The objective of this study is to examine the course of fatigue in female cancer patients during the first months after treatment. Methods: We examined a sample of 110 patients suffering from gynecological or breast cancer. Fatigue was assessed with two questionnaires, the Multidimensional Fatigue Inventory (MFI) and the fatigue scale of the quality of life questionnaire European Organisation for Research and Treatment of Cancer (EORTC QLQ-C30). Participants were tested during their stay in the hospital (t1), two weeks after discharge (t2), and three months after discharge (t3). Results: Fatigue in the patients’ sample was markedly higher than the general population reference val…

What is the order of the two-dimensional polymer escape transition?

2007

An end-grafted flexible polymer chain in three-dimensional space between two pistons undergoes an abrupt transition from a confined coil to a flowerlike conformation when the number of monomers in the chain, $N$, reaches a critical value. In two-dimensional (2D) geometry, excluded-volume interactions between monomers of a chain confined inside a strip of finite length $2L$ transform the coil conformation into a linear string of blobs. However, the blob picture raises questions about the nature of this escape transition. To check theoretical predictions based on the blob picture we study 2D single-polymer chains with excluded-volume interactions and with one end grafted in the middle of a st…

Periodic orbits of single neuron models with internal decay rate 0 < β ≤ 1

2013

In this paper we consider a discrete dynamical system x n+1=βx n – g(x n ), n=0,1,..., arising as a discrete-time network of a single neuron, where 0 &lt; β ≤ 1 is an internal decay rate, g is a signal function. A great deal of work has been done when the signal function is a sigmoid function. However, a signal function of McCulloch-Pitts nonlinearity described with a piecewise constant function is also useful in the modelling of neural networks. We investigate a more complicated step signal function (function that is similar to the sigmoid function) and we will prove some results about the periodicity of solutions of the considered difference equation. These results show the complexity of …