Thermodynamic studies on the complete phase diagram of aqueous two phase system containing polyethylene glycol dimethyl ether 2000 and di-potassium hydrogen phosphate at different temperatures

The liquid-liquid equilibrium of polyethylene glycol dimethyl ether 2000 (PEGDME₂₀₀₀)+K₂HPO₄+H₂O system has been determined experimentally at T=(298.15,303.15,308.15 and 318.15) K. The liquid-solid and complete phase diagram of this system was also obtained at T=(298.15 and 308.15) K. A nonlinear temperature dependent equation was successfully used for the correlation of the experimental binodal data. Furthermore, a temperature dependent Setschenow-type equation was successfully used for the correlation of the tie-lines of the studied system. Moreover, the effect of temperature on the binodal curves and the tie-lines for the investigated aqueous two-phase system have been studied. Also, the free energies of cloud points for this system and some previously studied systems containing PEGDME₂₀₀₀ were calculated from which it was concluded that the increase of the entropy is the driving force for formation of aqueous two-phase systems. Additionally, the calculated free energies for phase separation of the studied systems were used to investigate the salting-out ability of the salts having different anions. Furthermore, the complete phase diagram of the investigated system was compared with the corresponding phase diagrams of previously studied systems, in which the PEGDME₂₀₀₀ has been used, in order to obtain some information regarding the phase behavior of these PEGDME₂₀₀₀+salt+water systems.     

Exploring factors influencing consumers’ behavioral intention to adopt broadband in Malaysia

The purpose of this paper is to examine various normative, attitudinal and control factors influencing consumers’ intention to adopt broadband internet in a developing country such as Malaysia. This study is based on empirical data collected using a self-administered questionnaire relating to the normative, attitudinal and control variables. Structural equation modeling analysis is conducted to test the role of numerous variables on consumers’ behavioral intentions to adopt broadband internet in Malaysia. Results revealed that Primary Influences (PI), Relative Advantage (RA), Hedonic Outcomes (HO), Facilitating Conditions Resources (FCR), and Self-Efficacy (SE) are positively associated with consumers’ Behavioral Intention (BI) to adopt broadband in Malaysia. The significance of this research study is twofold. Practically, this research study provide some useful guidelines to industry players, be it the internet service providers (ISPs) or the policy makers, to understand which are the factors (primary influences, self-efficacy, relative advantage, hedonic outcomes and facilitating conditions resources) that can have an influence on consumers’ intention to adopt broadband technology. It was found that primary influences, self-efficacy and relative advantage are the key determinants that influences consumers’ broadband adoption. From here, practitioners could take into consideration our findings when revising and restructuring their marketing strategy. Theoretically, the research framework used in this study is an extension from the past research models used (i.e. TPB, DOI and MATH). With the newly integrated framework, a greater level of comprehension can be attained with regards to the broadband acceptance among the Malaysian consumers.     

Numerical inversions of a source term in the FADE with a Dirichlet boundary condition using final observations

This paper deals with an inverse problem of determining a source term in the one-dimensional fractional advection-dispersion equation (FADE) with a Dirichlet boundary condition on a finite domain, using final observations. On the basis of the shifted Grünwald formula, a finite difference scheme for the forward problem of the FADE is given, by means of which the source magnitude depending upon the space variable is reconstructed numerically by applying an optimal perturbation regularization algorithm. Numerical inversions with noisy data are carried out for the unknowns taking three functional forms: polynomials, trigonometric functions and index functions. The reconstruction results show that the inversion algorithm is efficient for the inverse problem of determining source terms in a FADE, and the algorithm is also stable for additional data having random noises.     

Stochastic differential equations driven by a Wiener process and fractional Brownian motion: Convergence in Besov space with respect to a parameter

A stochastic differential equation involving both a Wiener process and fractional Brownian motion, with nonhomogeneous coefficients and random initial condition, is considered. The coefficients and initial condition depend on a parameter. The assumptions on the coefficients and the initial condition supplying continuous dependence of the solution on a parameter, with respect to the Besov space norm, are established.     

Anti-periodic fractional boundary value problems

We study a class of anti-periodic boundary value problems of fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.     

Existence results for impulsive differential inclusions with nonlocal conditions

In this paper, we shall establish sufficient conditions for the existence of mild solutions for nonlocal impulsive differential inclusions. On the basis of the fixed point theorems for multivalued maps and the technique of approximate solutions, new results are obtained. Examples are also provided to illustrate our results.     

On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

In this paper, we investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. The results are obtained by using the α-resolvent family (S_α(t))_t≥0 on a complex Banach space X combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.     

Numerical analysis and physical simulations for the time fractional radial diffusion equation

We do the numerical analysis and simulations for the time fractional radial diffusion equation used to describe the anomalous subdiffusive transport processes on the symmetric diffusive field. Based on rewriting the equation in a new form, we first present two kinds of implicit finite difference schemes for numerically solving the equation. Then we strictly establish the stability and convergence results. We prove that the two schemes are both unconditionally stable and second order convergent with respect to the maximum norm. Some numerical results are presented to confirm the rates of convergence and the robustness of the numerical schemes. Finally, we do the physical simulations. Some interesting physical phenomena are revealed; we verify that the long time asymptotic survival probability ∝t^−α, but independent of the dimension, where α is the anomalous diffusion exponent.     

The Dirichlet problem for a 3D elliptic equation with two singular coefficients

In the present work, we investigate the Dirichlet problem for a three-dimensional (3D) elliptic equation with two singular coefficients. We find four fundamental solutions of the equation, containing hypergeometric functions of Appell. Then using an “a-b-c” method, the uniqueness for the solution of the Dirichlet problem is proved. Applying a method of Green’s function, we are able to find the solution of the problem in an explicit form. Moreover, decomposition formulas, formulas of differentiation and some adjacent relations for Appell’s hypergeometric functions were used in order to find the explicit solution for the formulated problem.