A stochastic process {Xk, k = 1, 2, ...} is a doubly geometric stochastic process if there exists the ratio (a > 0) and the positive function (h(k) > 0), so that {α 1 h-k }; k ak X k = 1, 2, ... is a generalization of a geometric stochastic process. This process is stochastically monotone and can be used to model a point process with multiple trends. In this paper, we use nonparametric methods to investigate statistical inference for doubly geometric stochastic processes. A graphical technique for determining whether a process is in agreement with a doubly geometric stochastic process is proposed. Further, we can estimate the parameters a, b, μ and σ2 of the doubly geometric stochastic process by using the least squares estimate for Xk a

In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator.  e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated.  e su‰cient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to con‹rm the theoretical results.

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers’ fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution. Furthermore, 3D figures are drawn to exhibit the effect of magneto hydrodynamic and different parameters for the velocity distribution.

The azo dye brilliant reactive red K-2BP (λmax = 534 nm) is widely used for coloring textiles because of its low-cost and tolerance fastness properties. Wastewaters treatment that contains the dye by conventional ways is usually inadequate due to its resistance to biological and chemical degradation. During this study, the continuous reactor of an advanced oxidation method supported the use of H₂O₂/sunlight, H₂O₂/UV, H₂O₂/TiO₂/sunlight, and H₂O₂/TiO₂/UV for decolorization of brilliant reactive red dye from the effluent. The existence of an optimum pH, H₂O₂ concentration, TiO₂ concentration, and d

Generally, statistical methods are used in various fields of science, especially in the research field, in which Statistical analysis is carried out by adopting several techniques, according to the nature of the study and its objectives. One of these techniques is building statistical models, which is done through regression models. This technique is considered one of the most important statistical methods for studying the relationship between a dependent variable, also called (the response variable) and the other variables, called covariate variables. This research describes the estimation of the partial linear regression model, as well as the estimation of the “missing at random” values (MAR). Regarding the

       A reliability system of the multi-component stress-strength model R_(s,k) will be considered in the present paper ,when the stress and strength are independent and non-identically distribution have the Exponentiated Family Distribution(FED) with the unknown  shape parameter α and known scale parameter λ  equal to two and parameter θ equal to three. Different estimation methods of R_(s,k) were introduced corresponding to Maximum likelihood and Shrinkage estimators. Comparisons among the suggested estimators were prepared depending on simulation established on mean squared error (MSE) criteria.

A simple reverse-phase high performance liquid chromatographic method for the simultaneous analysis (separation and quantification) of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) has been developed and validated. The method was carried out on a NUCLEODUR® 100-5 C18ec column (250 x 4.6 mm, i. d.5μm), with a mobile phase comprising of acetonitrile: deionized water (50: 50 v/v, pH adjusted to 3.6 ±0.05 with acetic acid) at a flow rate 1.5 mL.min-1 and the quantification was achieved at 226 nm. The retention times of FURO, CARB, DIAZ and CARV were found to be 1.90 min, 2.79 min, 5.39 min and 9.56 min respectively. The method was validated in terms of linearity, accuracy, precision, limit of detection and li