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The purpose of this paper is to perform Shariah review of Brownian motion that is used for prediction of Islamic stock prices and their volatility.

It uses the Shariah compliant development model guidelines to review the Brownian motion and its applications.

The model of Brownian motion does not involve any variable that renders it non-Shariah compliant; neither all applications of Brownian motion are Shariah compliant. Because the model is based on stochastic properties that involve randomness, therefore the issue of gharar takes the utmost important to handle in the applications of the model. The results need to be analyzed strictly in accordance with the Shariah whether they create any element of gharar or uncertainty in case of expected price and volatility estimates.

The research suffers from the limitation that it analyses only one model of physics, i.e. Brownian motion model from Shariah perspective.

The research opens an area for Shariah analysis of results generated from the application of advanced models of physics on matters related to Islamic financial markets.

The originality of this study stems from the fact that to the best of the authors’ knowledge, it is the first study that extends Shariah guidelines into Financial physics for making the foundations of Islamic econophysics.

Discusses the recent research interest in the relationship between cybernetics and creativity. Uses Brownian motion to review the metaphorical value of cybernetics. Points out that, although an examination from the cybernetics perspective is largely retrospective in nature, the lessons learned from this examination may provide interesting hindsight to guide our future creative activities.

The purpose of this paper is to argue that a stationary-differenced autoregressive (AR) process with lag greater than 1, AR(q > 1), has certain properties that are consistent with a fractional Brownian motion (fBm). What the authors are interested in is the investigation of approaches to identifying the existence of persistent memory of one form or another for the purposes of simulating commodity (and other asset) prices. The authors show in theory, and with application to agricultural commodity prices the relationship between AR(q) and quasi-fBm.

In this paper the authors develop mathematical relationships in support of using AR(q > 1) processes for simulating quasi-fBm.

From theory the authors show that any AR(q) process is a stationary, self-similar process, with a lag structure that captures the essential elements of scaling and a fractional power law. The authors illustrate through various means the approach, and apply the quasi-fractional AR(q) process to agricultural commodity prices.

While the results can be applied to most time series of commodity prices, the authors limit the evaluation to the Gaussian case. Thus the approach does not apply to infinite-variance models.

The approach to using the structure of an AR(q > 1) model to simulate quasi-fBm is a simple approach that can be applied with ease using conventional Monte Carlo methods.

The authors believe that the approach to simulating quasi-fBm using standard AR(q > 1) models is original. The approach is intuitive and can be applied easily.

The purpose of this paper is to discuss a widespread idea in the financial literature: information in financial markets is free. Indeed, whenever an investor wants to intervene to purchase and/or to sell, he/she faces the need to access the information, which he/she judges to ensure an optimal decision.

The paper uses the entropy statistics in order to estimate the information cost of the assets of the Tunisian stock market over the period extending from 2002 to 2005.

The obtained results show that the information costs follow a Brownian motion. This finding lends empirical support to the theoretical position that has always been adopted in the relevant literature: in finance, as in economy, the majority of the series follow a Brownian motion.

The proposed methodology offers investors the opportunity to estimate the information cost by taking into account the quotation probability, a simple approach that can be used not only by fund managers, but also by financial market investors.

The paper uses entropy as a relatively new tool applied in financial theory. It offers a new understanding of information cost. The paper will be of interest for financial market investors and academics.

The purpose of this paper is to present a boundary layer analysis for the mixed convection past a vertical wedge in a porous medium saturated with a power law type non-Newtonian nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le and the power law exponent n. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

This general non-linear problem cannot be solved in closed form and, therefore, a numerical solution is necessary to describe the physics of the problem. An implicit, tri-diagonal finite-difference method has proven to be adequate and sufficiently accurate for the solution of this kind of problems. Therefore, it is adopted in the present study. Variable step sizes were used. The convergence criterion employed in this study is based on the difference between the current and the previous iterations. When this difference reached 10−5 for all the points in the η directions, the solution was assumed to be converged, and the iteration process was terminated.

The results indicate that as the buoyancy ratio parameter (Nr) and thermophoresis parameter (Nt) increase, the friction factor increases whereas the heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) decrease. As the Brownian motion parameter (Nb) increases, the friction factor and surface mass transfer rates increase whereas the surface heat transfer rate decreases. As Le increases, mass transfer rates increase. As the power law exponent n increases, the heat and mass transfer rates increase.

The analysis is valid for natural convection dominated regime. The combined forced and natural convection dominated regimes will be reported in a future work.

The approach used is useful in optimizing the porous media heat transfer problems in geothermal energy recovery, crude oil extraction, ground water pollution, thermal energy storage and flow through filtering media.

The results of the study may be of some interest to the researchers of the field of porous media heat transfer. Porous foam and microchannel heat sinks used for electronic cooling are optimized utilizing the porous medium. The utilization of nanofluids for cooling of microchannel heat sinks requires understanding of fundamentals of nanofluid convection in porous media.

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

The purpose of this paper is to present a proportional-integral (PI) observer design on a linear system with stochastic noises.

The noised disturbances are modeled as independent Brownian motions for various affections, such as radiation, heat, and material fatigue. These phenomena are common in applications, such as biomolecules, nonlinear control, and biochemical networks. Under this framework, this paper proposes a new approach on a PI observer in terms of four crucial theorems, and an illustrative numerical example is given to verify the proposed design.

The results provide potential solutions for system fault tolerance and isolation.

This paper proposes a design, solvability, and controllability analysis on a PI observer in terms of four crucial theorems.

This paper aims to present the effect of entropy generation on the unsteady flow of upper-convected Maxwell nanofluid past a wedge embedded in a porous medium in view of buoyancy force. Cattaneo-Christov double diffusion theory simulates the processes of energy phenomenon and mass transfer. Meanwhile, Brownian motion, thermophoresis and convective boundary conditions are discussed to further visualize the heat and mass transfer properties.

Coupled ordinary differential equations are gained by appropriate similar transformations and these equations are manipulated by the Homotopy analysis method.

The result is viewed that velocity distribution is a diminishing function with boosting the value of unsteadiness parameter. Moreover, fluid friction irreversibility is dominant as the enlargement in Brinkman number. Then controlling the temperature and concentration difference parameters can effectively regulate entropy generation.

This paper aims to address the effect of entropy generation on unsteady flow, heat and mass transfer of upper-convected Maxwell nanofluid over a stretched wedge with Cattaneo-Christov double diffusion, which provides a theoretical basis for manufacturing production.

This study aims to employ a modern numerical approach for conducting the simulations, which uses the smoothed-profile lattice Boltzmann method. Two separate distribution functions for flow and temperature fields are used to solve the Navier–Stokes equations in the most efficient manner. In addition, the Koo–Kleinstreuer–Li model is used to calculate the dynamic viscosity and thermal conductivity in the desired volume fractions, and the effect of Brownian motion is taken into consideration.

Nowadays, because of enhanced global price of oil and critical issue of global warming, a significant demand for using renewable energy exists. The solar energy is one of the most popular forms of renewable energy. The solar collector can be used to collect and trap the energy received from the sun. The present work focuses on introducing and investigating a parabolic-trough solar collector.

To analyze all hydrodynamic and thermal views of the solar collector, the structure of nanofluid stream, distribution of temperature, local dissipations because of flow and heat transfer, volumetric entropy production, Bejan number vs Rayleigh number and volume fraction are presented. Also, three different configurations for profile of solar receiver are designed and studied.

The originality of the present work is in using a modern numerical approach for a well-known application. Also, the effect of Brownian motion is taken into account which significantly enhances the accuracy.