Search results for "values."

On attracting sets in artificial networks: cross activation

2018

Mathematical models of artificial networks can be formulated in terms of dynamical systems describing the behaviour of a network over time. The interrelation between nodes (elements) of a network is encoded in the regulatory matrix. We consider a system of ordinary differential equations that describes in particular also genomic regulatory networks (GRN) and contains a sigmoidal function. The results are presented on attractors of such systems for a particular case of cross activation. The regulatory matrix is then of particular form consisting of unit entries everywhere except the main diagonal. We show that such a system can have not more than three critical points. At least n–1 eigenvalu…

Tunnel effect and symmetries for Kramers–Fokker–Planck type operators

2011

AbstractWe study operators of Kramers–Fokker–Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number n0 of local minima. Under suitable additional assumptions, we show that the first n0 eigenvalues are real and exponentially small, and establish the complete semiclassical asymptotics for these eigenvalues.

The ∞-Eigenvalue Problem

1999

. The Euler‐Lagrange equation of the nonlinear Rayleigh quotient \( \left(\int_{\Omega}|\nabla u|^{p}\,dx\right) \bigg/ \left(\int_{\Omega}|u|^{p}\,dx\right)\) is \( -\div\left( |\nabla u|^{p-2}\nabla u \right)= \Lambda_{p}^{p} |u |^{p-2}u,\) where \(\Lambda_{p}^{p}\) is the minimum value of the quotient. The limit as \(p\to\infty\) of these equations is found to be \(\max \left\{ \Lambda_{\infty}-\frac{|\nabla u(x)|}{u(x)},\ \ \Delta_{\infty}u(x)\right\}=0,\) where the constant \(\Lambda_{\infty}=\lim_{p\to\infty}\Lambda_{p}\) is the reciprocal of the maximum of the distance to the boundary of the domain Ω.

Lower bounds for eigenvalues of a quadratic form relative to a positive quadratic form

1968

Abstract : A method is presented for the calculation of lower bounds to eigenvalues of operators that arise from variational problems for one quadratic form relative to a positive definite quadratic form. Eigenvalue problems of this kind occur, for example, in the theory of buckling of continuous linear elastic systems. The technique used is a modification of one introduced earlier, (1) sections II and IVB, for the determination of lower bounds to eigenvalues of semi-bounded self-adjoint operators. Other methods for the latter problem can be carried over without essential changes. The particular difficulty in the case we consider is that some operators which enter the calculation for the lo…

Diagnostic use of fructosamine assay in the control of type II diabetes mellitus.

1988

In an attempt to evaluate the usefulness of fructosamine assay in monitoring type II diabetes, 142 diabetic patients were investigated. Fructosamine values were found to be higher in patients on insulin treatment than on oral hypoglycemic agents. In order to evaluate the metabolic control by using the correlated variations of F, Gm and HbAlc, the patients were subdivided into many control classes: mean values of fructosamine were higher in poorly controlled patients. Fructosamine however correlated better with glycemia in patients with recent variations in metabolic state than HbAlc. It was concluded that fructosamine is a good index for short-term metabolic control, and if used in an integ…

Atrial natriuretic peptide and CD34 overexpression in human idiopathic dilated cardiomyopathies.

2007

Idiopathic dilated cardiomyopathy (IDCM) is a primary myocardial disease of unknown cause characterized by ventricular chamber enlargement with impaired contractile function. In familial forms of IDCM, mutations of genes coding for cytoskeletal proteins related to force transmission, such as dystrophin, cardiac actin, desmin, and delta-sarcoglycan, have been identified. Here, we report the data of a retrospective investigation carried out to evaluate the expression of atrial natriuretic peptide (ANP), CD34, troponin T and nestin in the myocardium of patients affected with IDCM. Formalin-fixed and paraffin-embedded consecutive tissue sections from the ventricular wall of 10 human normal hear…

Value Co-Creation Through Digitalization

2017

The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models

2007

Characteristic-based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen-decomposition of the Jacobian matrix of the system. For the Multi-Class Lighthill-Witham-Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen-vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mutations of mitochondrial DNA and human death.

1990

In the skeletal muscle of patients with mitochondrial myopathies (Kearns-Sayre syndrome and chronic progressive external ophthalmoplegia) and in the heart and skeletal muscle of healthy persons cells lacking cytochrome c oxidase are found. The respiratory-defective cells have the following features in common: onset of the defect at juvenile or adult age; progressive character of the defect with increasing age; and focal pattern of respiratory-deficient cells (fibers). A statistic mutation of mtDNA in affected cells is suggested to cause the defect of mitochondrial function. It is postulated that the continuous accumulation of respiratory-deficient cells, mainly in the human heart with incre…

Steroidal saponins from Raphia vinifera and their cytotoxic activity

2020

Abstract Phytochemical analysis of the fruits of Raphia vinifera led to the isolation of four new steroidal saponins (1–4), along with six known secondary metabolites (6–10). The structures of the isolated compounds were determined based on the analyses of NMR and mass spectrometric data, and chemical degradation reactions. Among the compounds tested, 1 and 4 showed the most promising cytotoxic activity against the drug-sensitive CCRF-CEM leukemia cell lines, with IC50 values of 3.55 µM and 7.14 µM, respectively.