Search results for " solution"

Analytic solution for a class of discrete-time Riccati equations arising in Nash games

1990

On the solutions to 1-Laplacian equation with L1 data

2009

AbstractIn the present paper we study the behaviour, as p goes to 1, of the renormalized solutions to the problems(0.1){−div(|∇up|p−2∇up)=finΩ,up=0on∂Ω, where p>1, Ω is a bounded open set of RN (N⩾2) with Lipschitz boundary and f belongs to L1(Ω). We prove that these renormalized solutions pointwise converge, up to “subsequences,” to a function u. With a suitable definition of solution we also prove that u is a solution to a “limit problem.” Moreover we analyze the situation occurring when more regular data f are considered.

Best proximity point theorems for rational proximal contractions

2013

Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.

On Different Type Solutions of Boundary Value Problems

2016

We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].

A meshfree method for transverse vibrations of anisotropic plates

2003

A meshfree approach, called displacement boundary method, for anisotropic Kirchhoff plate dynamic analysis is presented. This method is deduced from a variational principle, which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables. The discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional. The stiffness and mass matrices obtained for the dynamic model are frequency-independent, symmetric and positive definite and their computation involves bound…

A Boundary/Interior Element Discretization Method for the Analysis of Two- and Three-Dimensional Elastic-Plastic Structures

1992

A coupled boundary/interior element method is presented for the analysis of elastic-plastic structures with material models endowed of dual internal variables. The domain field modelling is limited to the only plastic strains and strain-like internal variables, represented by their node values at a set of strain points in each interior element. The formulation, based on a Galerkin-type approach, is variationally consistent and leads to a fully symmetric-definite equation system. The backward difference method is adopted for the step-by-step integration procedure, and each step is addressed by an iterative predictor/corrector solution scheme. The analysis method is expected to be most approp…

The Dissociation Constant of Pyruvic Acid: Determination by Spectrophotometric Measurements

1991

Aqueous solutions of sodium pyruvate/hydrochloric acid mixtures were studied with regard to changes in the intensity of optical absorption at 317 nm wavelength, caused by varying pH and temperature. The data were evaluated to determine the pyruvic acid apparent dissociation constant at infinite dilution. Its temperature dependence followed the relation ln Kod = −(0.55 ± 0.47) − (1538 ± 135)/T or, if previous results of Pedersen at two temperatures are included, In Kod = −(0.97 ± 0.35) − (1418 ± 102)T. The effective absorption coefficient for pyruvic acid and its anion differ because the former species is largely hydrated, whereas the latter is not. The known hydration constant and its tempe…

Natural Organic Compounds in Soil Solution: Potential Role as Soil Quality Indicators

2013

This review focuses on the chemical nature of that fraction of already dissolved organic matter into soil solution, or extracted by mild extractants, which is truly readily available for microbial activity and, consequently, more sensitive than total soil organic matter to changes in management and/or environmental conditions. In particular, we deal with low molecular weight compounds such as monosaccharides, amino sugars and amino acids. Soil sampling strategy and extraction procedure, prior to analyses, are crucial to make comparable results among laboratories. Although soil management and climatic conditions may cause large variability, extractable organic C and N may indicate the amount…

Localization and separation of solutions for Fredholm integral equations

2020

[EN] In this paper, we establish a qualitative study of nonlinear Fredholm integral equations, where we will carry out a study on the localization and separation of solutions. Moreover, we consider an efficient algorithm to approximate a solution. To do this, we study the semilocal convergence of an efficient third order iterative scheme for solving nonlinear Fredholm integral equations under mild conditions. The novelty of our work lies in the fact that this study involves first order Frechet derivative and mild conditions. A numerical example involving nonlinear Fredholm integral equations, is solved to show the domains of existence and uniqueness of solutions. The applicability of the it…

The Existence of Nitrate Radicals in Irradiated TiO 2 Aqueous Suspensions in the Presence of Nitrate Ions

2018

Evidence of the existence of nitrate radical in irradiated aqueous TiO2 suspensions in the presence of nitrate ions are reported for the first time. The joint use of UV/Vis and EPR spectroscopy showed that nitrate radicals are formed by hole induced oxidation of nitrate ions. Photocatalytic degradation of a model alkene compound allowed to highlight the presence of an intermediate organic nitrate deriving from nitrate radical attack to the double bond of the substrate. These results not only allow deeper understanding of photocatalytic processes, but open the route to new green photocatalytic syntheses initiated by nitrate radicals and to new insights in the field of atmospheric chemistry.