shortly we can derive the Cauchy's residue theorem (its general form) just by direct integration of a Taylor series placing an open curve onto a specific domain, in order to satisfy holomorphic properties

The problem of fraction decomposition it's easy to solve by using the cover up method, when there are no repeated linear factors in the denominator . Nevertheless it could turn into a hard work if these factors are raised to a high power, where the cover up method doesn't work . This technique shows how to calculate these coefficients without solving large systems of equations with a clever rearrangement of the numerator.

Abstract Currently, the demand of Pleurotus HK-37 (oyster mushroom) in Tanzania is growing rapidly due to the increasing of awareness on its nutrition, health, and economic benefits. Despite the increasing demand, the availability of strains of Pleurotus HK-37 species is still a challenge due to high cost of tissue culture technology. ,e high cost of importing agar seems to be among the factors for this failure. ,is study aimed at investigating the performance of low-cost agar from local Grac...

Abstract . We obtain new regular exact solutions to the field equations for uncharged relativistic stellar objects with vanishing pressure anisotropy. We assume a quadratic equation of state and a choice of measure of anisotropy and a metric function defining one of the gravitational potentials. In our exact models, we regain anisotropic and isotropic results generated by other researchers as a special case. It is interesting that our results are in agreement with Minkowski space-time and ear...

Abstract We find two new classes of exact solutions for the Einstein-Maxwell equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field equations are integrated by specifying forms for the measure of anisotropy and a gravitational potential which are physically reasonable. The solutions found generalize the Mark-Harko model and the Komathiraj-Maharaj model. A graphical analysis indicates that the matt...

Abstract The aim of this study was to assess the impact on teaching and learning using the LSTT (Language Supportive Teaching and Textbooks) project’s bilingual Mathematics textbook chapters among Form One students in selected rural community secondary schools in Tanzania. LSTT project was introduced in Tanzania in 2013 to enhance language supportive teaching among the disadvantaged rural groups identified as less competent in foreign languages. The study employed both quantitative and qua...

The effects of chemical reaction on a transient MHD mixed convection flow with mass transfer past an impulsively fixed infinite vertical plate under the influence of a transverse magnetic field have been presented. The medium is considered to be non-scattering and the fluid to be non-gray having emitting-absorbing and optically thick radiation limit properties. The dimensionless governing equations of the flow and mass transfer with boundary conditions are solved numerically by using the Ritz...

ABSTRACT This study was set out to examine the barriers to ICT integration into Mathematics teaching and learning in selected Senior High Schools in the Central Region of Ghana. Specifically, the study aimed to examine the effects of internal barriers (constructive teaching beliefs, teaching experience, attitudes toward computer and technology competence) and external barriers (access to technology use, level of training in the use of technology, time adequacy, as well as, the culture of the ...

The mathematical equations and concepts we learned in schools can actually be summed up to be relevant in the prediction, estimation and understanding of certain real world situations or problems that surrounds us. Some examples could be, How can we predict the break of a new infectious disease affecting the country Nigeria? How can reduction in the import of items into the country Nigeria affect the long term economy of the country Nigeria? How can we apply certain mathematical concept in ...

Mathematical models here serve as tools for understanding the epidemiology of Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS) if they are carefully constructed. The research emphasis is on the epidemiological impacts of AIDS and the rate of spread of HIV/AIDS in any given population through the numericalization of the Basic reproductive rate of infection (R0). Applicable Deterministic models, Classic Endemic Model (SIR), Commercial Sex Workers (CSW) model, Dyn...

The analysis of the dynamic buckling of a clamped finite imperfect viscously damped column lying on a quadratic-cubic elastic foundation using the methods of asymptotic and perturbation technique is presented. The proposed governing equation contains two small independent parameters (δ and ϵ) which are used in asymptotic expansions of the relevant variables. The results of the analysis show that the dynamic buckling load of column decreases with its imperfections as well as with the increas...

research work presents an important Banach Space in functional analysis which is known and called Hilbert space. We verified the crucial operations in this space and their applications in physics particularly in quantum mechanics. The operations are restricted to the unbounded linear operators densely defined in Hilbert space which is the case of prime interest in physics, precisely in quantum machines. Precisely, we discuss the role of unbounded linear operators in quantum mechanics partic...

Let K be a nonempty closed convex subset of a Banach space E and T : K → K be a nonexpansive mapping. Using a viscosity approximation method, we study the implicit midpoint rule of a nonexpansive mapping T. We establish a strong convergence theorem for an iterative algorithm in the framework of uniformly smooth Banach spaces and apply our result to obtain the solutions of an accretive mapping and a variational inequality problem. The numerical example which compares the rates of convergence...

An unintended consequence of using “research expenditures” as a figure of merit for universities is to reduce the research output per dollar invested by discouraging the diffusion of superior, lower-cost, open-source scientific equipment.

The laws of Physics and some other related courses are generally written as differential equations. Therefore, all of science and engineering use differential equations to some extent. A good knowledge of differential equations will be an integral part of your study in science and/or engineering classes. You can think of mathematics as the language of science, and differential equations are one of the most important parts of this language as far as science and engineering are concerned. De...