Applied Mathematics

This paper is concerned with the analysis of a single server batch arrival retrial G-queue with feedback, multi-types of service and orbital search under a randomized vacation policy. Positive customers arrive in batches according to Poisson processes. Server provides M types of heterogeneous service. If the server is idle upon the arrival of a batch, one of the customers in the batch receives any one of the types immediately and others join the orbit. Otherwise, all the customers in the batch join the orbit. After completion of service, the unsatisfied customer joins the orbit as a feedback customer. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The repair of the failed server starts immediately. Whenever the orbit becomes empty the server takes a vacation of random length. At a vacation completion epoch, if the system is still empty, the server leaves for another vacation of same length or remains idle in the system. This pattern continues until the server finds at least one customer in the orbit or the number of vacations reaches J. At the end of Jth vacation, even if the orbit is empty the server remains in the system for new arrival. If the orbit is non-empty during the idle period, the server may search customers from the orbit. Using supplementary variable technique, various performance measures are derived. Stochastic decomposition property is established.

Looking to the pharmacological importance of 8-hydroxyquinolines,in the present study, a novel bi-dentate ligand N - (3 - (bis (2 - ((8 – hydroxyquinolin – 5 – yl) methoxy) ethyl) amino) – 4 - methoxyphenyl) acetamide (BHQMA) was synthesized by the reaction of N - (3 - (bis (2 - hydroxyethyl) amino) – 4 -methoxyphenyl) acetamide with 5-chloromethyl- 8-hydroxyquinoline hydrochloride. Its co-ordination polymers were also prepared with Mn(II), Fe(II), Co(II), Ni(II) and Cu(II) salts. All the above compounds were investigated by physicochemical analyses, thermogravimetric analysis and spectroscopic techniques. In vitro antimicrobial activity of all synthesized compounds and standard drugs have been evaluated against four strains of bacteria which include two Gram +ve bacteria such as Staphylococcus aureus, Bacillus megaterium and two Gram-ve bacteria such as Es cherichia coli, Proteus vulgaris and one fungi Aspergillus niger.

In this paper, we present a novel algorithm for time series ARMA parameter estimation, namely, artificial neural network with trust region strategy. It combines the merit of neural network which has the capacity of highly parallel computing with the global convergence of trust region algorithm. The convergence of the algorithm is proved under certain conditions. It offers high accuracy for the parameter value of the ARMA model and makes the model is more superior. Numerical experiment shows that the new method is effective and attractive.

Dufour effect on free convection MHD flow past an impulsively started vertical oscillating plate through porous media with variable temperature and constant mass diffusion is studied here. The Laplace transform technique has been used to find the solutions for the velocity profile, temperature profile and concentration profile. The results obtained are discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof number, Prandtl number, permeability parameter, the Hartmann number, Schmidt number, Dufour number, time, inclination of magnetic field and phase angle.

Combined free and forced convection flow in a vertical channel filled with porous and fluid layer is studied with boundary conditions of third kind. The flow is modeled using Brinkman model. The viscous and Darcy dissipation terms are also included in the energy equation. The plate exchanges heat with an external fluid. Separate solutions are matched at the interface using suitable matching conditions. The coupled non-linear governing equations are solved using perturbation series method valid for small values of the perturbation parameter. The condition for perturbation parameter is relaxed by finding the solutions of the governing equations using Differential Transform method. The effects of various parameters on the flow such as mixed convection parameter, porous parameter, viscosity ratio, width ratio, conductivity ratio and Biot numbers on the flow are explored graphically. Further it is also shown that the Differential Transform method solutions agree very well with perturbation method series solutions for small values of the perturbation parameter.

The self-adjointness of product of two singular differential operators generated by a th-order symmetric differential expression is discussed. By means of the construction theory of real parameter on differential operators and matrix computation, the necessary and sufficient conditions which make the product being the self-adjoint operators in are obtained.

In this paper we have investigated the steady plane poiseuille flow of viscous incompressible fluid between two porous parallel plates through porous medium. We have investigated the velocity, average velocity, shearing stress, skin frictions, the volumetric flow, drag coefficients and stream lines.

Strategic planning has always been used as an important management tool in organizations across the world. The use of strategic planning necessitates decisions to be made in order to achieve the intended objectives and ensure continuity and relevance. Organizations may have good strategic planning practices, but the extent to which they are successfully implemented influence service delivery. The aim of the study was to establish the influence of strategic planning practice on service delivery by Trans Nzoia County government. The study was guided by Survival-Based Theory which explains how organizations can come up with ways to ensure that they achieve their objectives. The target population included management staff, employees and citizens of Trans Nzoia County. Semi structured questionnaires and Interview guides were used for data collection. The instruments were checked for both reliability and validity by use of Cronbach’s alpha and construct validity index respectively. Descriptive, quantitative and qualitative designs were used to find out the relationship between the variables. Multiple Linear Regression model was used to explain how strategic planning practice influences service delivery of Trans Nzoia County government. With the values of the beta coefficients for the model = 3.648 and = 0.412 respectively. Setting of vision and mission statement had the most influence on service delivery and identification of objectives had the least influence. The findings are crucial especially to the management of the County government of Trans Nzoia and can also be emulated by other Counties.

MHD peristaltic flow of a conducting fluid with heat transfer in a vertical asymmetric channel through porous medium is investigated under long wave length and low Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave on the walls to have different amplitudes and phase. The analytical solutions have been computed for the axial velocity and temperature. The pressure rise and the frictional force are obtained. The effects of different parameters on the pressure rise, velocity, temperature and shear stress are discussed numerically. The phenomenon of trapping is further investigated.

By using Mawhin continuation theorem and comparison theorem, the sufficient conditions ensuring the existence of exponential periodic attractor and exponential convergence of a class of functional differential equation with time varying delays are established. The results are very different from some previously known results [1,19,28]. Finally, applications and an example are given to illustrate the effectiveness of the results.