Research Papers/Topics in Mathematics

On Application of Mathematical Modeling in the Spread of HIV/AIDS Epidemic

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,...

Dynamic Buckling of a Clamped Finite Column Resting on a Non – linear Elastic Foundation

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 inc...

Application of Unbounded Hilbert Linear Operations in Quantum Mechanics

 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...

The Implicit Midpoint Rule of Non-expansive Mappings and Applications in Uniformly Smooth Banach Space

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...

It is Time to Move Research Expenditures to the Denominator in University Metrics

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.

Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure"[1]) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.[2]The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the...

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