Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on [0,π]

Our aim in this paper is to prove an analog of the classical Titchmarsh theorem on the image under the discrete Fourier–Jacobi transform of a set of functions satisfying a generalized Lipschitz condition in the space ${\mathbb{L}}_2^{(\alpha ,\beta )}$.     

Integral methods for computing solutions of a class of singular two-point boundary value problems

In this paper, we establish three iteration methods to compute solutions for a class of (weakly) singular two-point boundary value problems (xy^′)^′=f(x,y), where x(0,1) and <2. We obtain the sufficient conditions for existence of a unique solution on . Finally, we given some numerical examples.     

Some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity

The paper deals with some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity by direct variational method, Galerkin approach, and sub‐super solutions method. Our results are natural extension of Boulaaras' work in (Math Methods Appl Sci; 41(13):5203‐5210).     

An Optimal L∞–error Estimate for an Approximation of a Parabolic Variational Inequality

In this article, an optimal error estimate for parabolic variational inequalities is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L^∞-asymptotic behavior in uniform norm is proved using the semi-implicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolutions.     

Composite mix design in the production of asbestos/cement pipes

A mathematical model is presented for the determination of optimal mix of asbestos fibres to satisfy a set of desired pipe properties which vary with pipe size, class, and material availability. The approach utilizes a linear/separable programming model which is aimed at minimizing the total cost of fibres used. The fibre properties, such as reinforcing strength, processability, and length as well as cost and stocks available are taken into account in the model. Also represented are the profile of the ideal mix relative to the required composite strength, processability, and ‘dust content’. Asbestos mixes designed using the model have been implemented in the production of asbestos/cement pipes in one of the asbestos/cement pipe manufacturing plants in the Gulf area. Optimum model mixes have demonstrated significant technical and economic merits over the conventionally designed mixes.     

Spectral Properties of <Emphasis Type="Italic">k</Emphasis>-Quasi-<Emphasis Type="Italic">M</Emphasis>-hyponormal Operators

In this paper, we study the k-quasi-M-hyponormal operator and mainly prove that if T is a k-quasi-M-hyponormal operator, then \(\sigma _{ja}(T)\backslash \{0\}=\sigma _{a}(T)\backslash \{0\}\), and the spectrum is continuous on the class of all k-quasi-M-hyponormal operators; let \(d_{AB}\in B(B(H))\) denote either the generalized derivation \(\delta _{AB}= L_{A}-R_{B}\) or the elementary operator \(\Delta _{AB} =L_{A}R_{B}- I\), we show that if A and \(B^{*}\) are k-quasi-M-hyponormal operators, then \(d_{AB}\) is polaroid and generalized Weyl’s theorem holds for \(f(d_{AB})\), where f is an analytic function on \(\sigma (d_{AB})\) and f is not constant on each connected component of the open set U containing \(\sigma (d_{AB})\). In additon, we discuss the hyperinvariant subspace problem for k-quasi-M-hyponormal operators.     

Anisotropic parameter identification using inhomogeneous tensile test

In this contribution, an inverse identification strategy of constitutive laws for elastoplastic behaviour is presented. The proposed inverse algorithm is composed on an appropriate finite element calculation combined with an optimisation procedure. It is applied to identify material anisotropic coefficients using a set up of easy performed laboratory tests. The used experimental data are the plane tensile test and the off axes tensile tests. The identified behaviour models are mainly based on Hill's quadratic yield criterion. Two cases of this yield criterion have been considered: the transverse isotropic and the orthotropic one under an associated and non-associated flow rule assumptions for each case. The yield surface has been assumed to expand isotropically (isotropic strain hardening law) as a function of the plastic work.In order to better describe anisotropic plastic properties of the studied materials, a recently planar anisotropic yield function is used. It is a non-quadratic yield criterion which takes account of anisotropic yield stresses as well as anisotropic strain ratios. It is subsequently shown that the agreement between inverse identification results and experimental measurements were improved.We prove also that the presented strategy is a good alternative to the simplified homogeneous tests assumption, especially for the plane tensile test.     

A generalized equation for rheology of emulsions and suspensions of deformable particles subjected to simple shear at low Reynolds number

We present analyses to provide a generalized rheological equation for suspensions and emulsions of non-Brownian particles. These multiparticle systems are subjected to a steady straining flow at low Reynolds number. We first consider the effect of a single deformable fluid particle on the ambient velocity and stress fields to constrain the rheological behavior of dilute mixtures. In the homogenization process, we introduce a first volume correction by considering a finite domain for the incompressible matrix. We then extend the solution for the rheology of concentrated system using an incremental differential method operating in a fixed and finite volume, where we account for the effective volume of particles through a crowding factor. This approach provides a self-consistent method to approximate hydrodynamic interactions between bubbles, droplets, or solid particles in concentrated systems. The resultant non-linear model predicts the relative viscosity over particle volume fractions ranging from dilute to the the random close packing in the limit of small deformation (capillary or Weissenberg numbers) for any viscosity ratio between the dispersed and continuous phases. The predictions from our model are tested against published datasets and other constitutive equations over different ranges of viscosity ratio, volume fraction, and shear rate. These comparisons show that our model, is in excellent agreement with published datasets. Moreover, comparisons with experimental data show that the model performs very well when extrapolated to high capillary numbers (C a?1). We also predict the existence of two dimensionless numbers; a critical viscosity ratio and critical capillary numbers that characterize transitions in the macroscopic rheological behavior of emulsions. Finally, we present a regime diagram in terms of the viscosity ratio and capillary number that constrains conditions where emulsions behave like Newtonian or Non-Newtonian fluids.