Modern Scientific Press

ABSTRACT: Let ∆(α) denote the fractional difference operator. In this paper, we define new difference sequence spaces c₀(Γ, ∆(α), u) and c(Γ, ∆(α), u). Also, the β−dual of the spaces c₀(Γ, ∆(α), u) and c(Γ, ∆(α), u) are determined and calculated their Schauder basis. Furthermore, we characterize the classes (µ(Γ, ∆(α), u) : λ) for µ ∈ {c₀, c} and λ ∈ {c₀, c, ℓ_∞, ℓ₁} .

ABSTRACT: : It was proved by Joyal, Labelle and Rahman [A. Joyal, G. Labelle and Q. I. Rahman, On the location of zeros of polynomials, Canad. Math. J., Bull., 10(1967), 53-63] that if p>1, then all the zeros of P(z)= zⁿ + a_(n-1) z^(n-1) + … + a₁z + a₀ are contained in the circle |z| ≤k, where k ≥max(1,|a_(n-1) |) is a root of the equation (|z|- |a_n |)^q (|z|^q- 1)-B^q=0, p^(-1)+ q^(-1)=1. In this paper, we not only generalize the above result but a verity of interesting results can be deduced from it.

ABSTRACT: Lognormal distribution is one of the mostly widely used probability distributions. In this study, maximum likelihood estimates and posterior estimates of the parameters of lognormal distribution are obtained. The posterior estimates are obtained by using different types of prior distributions and loss functions. Finally we calculate the point estimates of mean and variance for making comparison using simulation techniques.

ABSTRACT: A new finite difference Algorithm called the Restrictive Taylor Approximation (RTA) is implemented to find the numerical solution of Kuramoto–Sivashinsky equation which is nonlinear partial differential equation. This method is a new explicit method. The accuracy of the method is assessed in terms of the absolute error which is very close to zero. We solve also Burger’s equation and Viscous Burger equation.

ABSTRACT: The paper deals with the study of existence of solutions of quasilinear mixed Volterra-Fredholm type integrodifferential equations of fractional order with nonlocal impulsive conditions in Banach spaces. The results are established by using fractional calculus, resolvent operator and Banach fixed point theorem.

ABSTRACT: In this paper, a mathematical model for Reductive alkylation at an internal diffusion limitation for non-steady-state conditions is discussed. The model is based on diffusion equations containing a linear term related to the reaction processes. Reductive alkylation of ortho-, meta- and para-phenylenediamines (PDAs) with methyl ethyl ketone (MEK) has been studied in a semi-batch slurry reactor in the presence of catalyst. The activity was found to decrease in the following order: PPDA>OPDA>MPDA. To understand the substrate structure-activity correlation, the homogeneous equilibrium reactions involved in the alkylation step and the overall catalytic reactions are studied separately. Analytical expressions for concentrations are derived using New Homotopy perturbation method. An excellent agreement with experimental data is observed.