From appropriation to formal intervention: An analytical framework for understanding the appropriation process in residual spaces of Cairo

The paper addresses the issue of how residual spaces are intervened upon through formal and informal processes. It argues that a profound understanding for the dynamics of informal interventions, denoted by appropriation, could enhance the performance of their formal peers.Adopting a qualitative approach, the paper departs from Lefebvre’s unitary theory of space and arrives at an analytical framework that helps to understand the appropriation processes in residual spaces. It, then, attempts to empirically challenge the applicability of this framework through analyzing a Cairene residual space that has undergone two cycles of intervention: a formal and informal one.     

Fractional Jacobi Galerkin spectral schemes for multi-dimensional time fractional advection–diffusion–reaction equations

One of the ongoing issues with time fractional diffusion models is the design of efficient high-order numerical schemes for the solutions of limited regularity. We construct in this paper two efficient Galerkin spectral algorithms for solving multi-dimensional time fractional advection–diffusion–reaction equations with constant and variable coefficients. The model solution is discretized in time with a spectral expansion of fractional-order Jacobi orthogonal functions. For the space discretization, the proposed schemes accommodate high-order Jacobi Galerkin spectral discretization. The numerical schemes do not require imposition of artificial smoothness assumptions in time direction as is required for most methods based on polynomial interpolation. We illustrate the flexibility of the algorithms by comparing the standard Jacobi and the fractional Jacobi spectral methods for three numerical examples. The numerical results indicate that the global character of the fractional Jacobi functions makes them well-suited to time fractional diffusion equations because they naturally take the irregular behavior of the solution into account and thus preserve the singularity of the solution.

     

Application of liquisolid technology for promoting the renoprotective efficacy of walnut extracts in chronic renal failure rat model

Chronic renal failure (CRF) is among the major health problems that could lead to increased morbidity and mortality among population. ‘Nutraceuticals’ is an emerging field for natural agents from plant foods that could reduce the progression of such disease. Many newly developed drugs are having bioavailability problems owing to their water insolubility. Liquisolid technique is one of the promising technological approaches to increase solubility and hence, drug absorption. The aim of the present research is to prepare and evaluate the renoprotective effect of the walnut extracts liquisolid formulations in CRF rat model. Saturation solubility study claimed PEG 400 and Tween 20 as good solubilizers for walnut extracts, thus chosen for preparation. The angle of slide was determined for the carrier; microcrystalline cellulose and coating material; silicon dioxide and liquid load factor was evaluated. Eight liquisolid systems were prepared employing 25% and 50% of liquid medication. Their flow and compressibility parameters showed good properties. Dissolution study was more in favor of formulations prepared using PEG 400. Of these, formulation F8 comprising carrier/coat ratio (10:1) and 50% liquid medication, showing superior dissolution properties was selected to perform stability and in-vivo evaluations. Two CRF induced rat groups received F8 at two oral doses (50 and 100?mg/kg). Biochemical and nutritional parameters were compared with both normal and CRF control rats. Results showed improvement of renal function, oxidative stress, antioxidant and inflammatory biomarkers as well as increased appetite and body weight gain on administration of both doses of walnut liquisolid formulation, F8.     

An Efficient Numerical Scheme for Solving Multi‐Dimensional Fractional Optimal Control Problems With a Quadratic Performance Index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi‐dimensional fractional optimal control problem (M‐DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M‐DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.     

Shifted fractional Legendre spectral collocation technique for solving fractional stochastic Volterra integro-differential equations

This paper presents a spectral collocation technique to solve fractional stochastic Volterra integro-differential equations (FSV-IDEs). The algorithm is based on shifted fractional order Legendre orthogonal functions generated by Legendre polynomials. The shifted fractional order Legendre–Gauss–Radau collocation (SFL-GR-C) method is developed for approximating the FSV-IDEs, with the objective of obtaining a system of algebraic equations. For computational purposes, the Brownian motion function W(x) is discretized by Lagrange interpolation, while the integral terms are interpolated by Legendre–Gauss–Lobatto quadrature. Numerical examples demonstrate the accuracy and applicability of the proposed technique, even when dealing with non-smooth solutions.

     

Efficient spectral ultraspherical-dual-Petrov–Galerkin algorithms for the direct solution of (2n + 1)th-order linear differential equations

Some efficient and accurate algorithms based on ultraspherical-dual-Petrov–Galerkin method are developed and implemented for solving (2n + 1)th-order linear elliptic differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a spectral discretization. The key idea to the efficiency of our algorithms is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results are presented to demonstrate the efficiency of our proposed algorithms.     

A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order

We are concerned with linear and nonlinear multi-term fractional differential equations (FDEs). The shifted Chebyshev operational matrix (COM) of fractional derivatives is derived and used together with spectral methods for solving FDEs. Our approach was based on the shifted Chebyshev tau and collocation methods. The proposed algorithms are applied to solve two types of FDEs, linear and nonlinear, subject to initial or boundary conditions, and the exact solutions are obtained for some tested problems. Numerical results with comparisons are given to confirm the reliability of the proposed method for some FDEs.     

On the effect of reservation period on performance of IEEE 802.16 R‐MAC protocol

The IEEE 802.16 standard is gaining broad consideration to serve the expanding demand for broadband access networks. In this standard, the best effort traffic uses the reservation multiple access control (MAC) mechanism, which is widely adopted in recent broadband network technologies. The goal of this paper is to study the performance of the MAC protocol of the best effort traffic in the IEEE 802.16 standard with emphasis on the size of the reservation period. We use a two‐stage Markov chain model to capture all possible events on the reservation and service periods. This allows the computation of the inflow and outflow of bandwidth requests (BWRs) and their associated data packets which leads to the delay and throughput formulas. By means of illustrative examples and numerical results, validated through simulation, we investigate the key importance of the size of reservation period. We highlight potential performance improvement, through opportunistic dynamic control of the size of the reservation period to enhance the performance of reservation MAC protocol. Copyright © 2008 John Wiley & Sons, Ltd.