Mathematics Research Papers/Topics

Generalizations on normal self-ad joint operators

Abstract/Overview We consider certain properties of operators. A lot of studies have been done on reflexivity, compactness and numerical radius attainability on Hilbert space operators [1-12] and the reference therein.

Operators with slowly growing resolvents towards the spectrum

Abstract/Overview A closed densely defined operator H, on a Banach space X, whose spectrum is contained in R and satisfies (z −H)−1 ≤ c hziα |=z|β ∀ z 6∈ R (0.1) for some α , β ≥ 0; c > 0, is said to be of (α, β)−type R . If instead of (0.1) we have (z −H)−1 ≤ c |z|α |=z|β ∀ z 6∈ R, (0.2) then H is of (α, β)0−type R . Examples of such operators include self-adjoint operators, Laplacian on L1(R), Schro¨dinger operators on Lp(Rn) and operators H whose ...

Numerical solution of dynamic vibration equations

Abstract/Overview In this paper, we examine conservative autonomous dynamic vibration equation, , which is time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Numerical results using Newmark are tabulated. The stability of the algorithm employed is also discussed.

The similarities in properties of essential numerical range and Davis-Wielandt shell of Hilbert space operators

Abstract/Overview Let be an operator on an infinite dimensional Hilbert space . Denote the essential numerical range of the operator by and the Davis-Wielandt shell of the operator by . We review the properties of the essential numerical range and those of the Davis-Wielandt shell. This review is aimed at striking similarities in the properties shared. The results of this study show that some of the properties shared are, for instance, unitary invariance and convexity. However, it is note...

Symmetry group approach to the solution of generalized burgers equation: Ut + UUx = λUxx

Abstract/Overview Symmetry of a system of differential equations is a transformation that maps any solution to another solution of the system. In Lie’s framework such transformations are groups that depend on continuous parameters and consist of point transformations (point symmetries), acting on the system’s space of independent and dependent variables, or, more generally, contact transformations (contact symmetries), acting on independent and dependent variables as well as on all fi...

Analytic solution of a nonlinear black-scholes partial differential equation

Abstract/Overview We study a nonlinear Black-Scholes partial differential equation whose nonlinearity is as a result of a feedback effect. This is an illiquid market effect arising from transaction costs. An analytic solution to the nonlinear Black-Scholes equation via a solitary wave solution is currently unknown. After transforming the equation into a parabolic nonlinear porous medium equation, we find that the assumption of a traveling wave profile to the later equation reduces it to o...

On the structures of quotient groups

Abstract/Overview Let J be the Jacobson radical of a commutative completely primary finite ring R such that J k 6= (0) and J k+1 = (0). Then R/J ∼= GF(p r ), the finite field of p r elements, and the characteristic of R is p k where k ≥ 2 and p is some prime integer. In this paper, we determine the structures of the quotient groups 1 + J i/1 + J i+1 for every characteristic of R and 1 ≤ i ≤ k − 1.

Modeling co-infection of paediatric Malaria and Pneumonia

Abstract/Overview Malaria and persistent childhood diseases are a major threat to child survival in the developing world. In this paper, we develop and analyse a mathematical model for paediatric malaria and pneumonia co-infection. We establish the existence of equilibria points in terms of the basic reproduction numbers Rm and Rp. The analysis shows that the diseasefree equilibrium of the model is globally asymptotically stable whenever the co-infection reproduction number Rmp is less th...

Functions of multi-pendula system spatial motion

Abstract/Overview A study has been done using generalized coordinates system with the application of the Lagrangian formalism for n mass units linearly connected to move in space. Lagrangian equations have been developed and used throughout the research to determine the equations of motion for multi-pendula system for several as well as many mass units involved. These equations were solved using various mathematical techniques to determine the zenith angular accelerations for each system....

Two dimensional mathematical models for convective-dispersive flow of pesticides in porous media

Abstract/Overview The transport of solutes through porous media where chemicals undergo adsorption or change process on the surface of the porous materials has been a subject of research over the years. Use of pesticides has resulted in production of diverse quantity and quality for the market. Disposal of excess material has also become an acute problem. The concept of adsorption is essential in determining the movement pattern of pesticides in soil in order to assess the effect of migra...

Extraction of zero coupon yield curve for Nairobi securities exchange: finding the best parametric model for East African securities markets

Abstract/Overview We seek to construct a zero coupon yield curve (ZCYC) for Nairobi Securities Exchange (NSE). The objective of this paper is to construct a ZCYC that is differentiable at all points and at the same time, produces continuous and positive forward curve. We will use the classical Nelson-Siegel model, Svensson Model, Rezende-Ferreira model and Svensson extended model. These models have linear and nonlinear guidelines making them have multiple local minima. This condition caus...

Mathematical modeling of insulin therapy in patients with diabetes mellitus

Abstract/Overview This study presents a Mathematical Model Insulin Therapy in Patients with Diabetes Mellitus which includes external rate at which blood glucose, insulin and epinephrine are being increased in the form, Y =AY+r  (t) and whose solution was analyzed to provide the systems natural frequency, 0 , which is the basic descriptor of saturation level of the drug. It was established that the resonance period for the final model, that is, T 0 =3.76912 hrs, is in the accepta...

The algebra of smooth functions of rapid descent

Abstract/Overview A bounded operator with the spectrum lying in a compact set V ⊂ R, has C∞ (V) functional calculus. On the other hand, an operator H acting on a Hilbert space H, admits a C(R) functional calculus if H is self-adjoint. So in a Banach space setting, we really desire a large enough intermediate topological algebra A, with C∞ 0 (R) ⊂ A ⊆ C(R) such that spectral operators or some sort of their restrictions, admit a A functional calculus. In this paper we construct su...

On Compact Operators Whose Norms Are Eigenvalues and Completeness

Abstract/Overview Let X be a Banach space and T: X→Y be a linear operator, then Tis compact if it maps bounded sequences in X to sequences in Y with convergent subsequences, that is, if xn ∈ X is a bounded sequence, then T xn ∈ Y has a convergent subsequence say, T xnk in Y. The eigenvalue of an operator T, is a scalar λ if there is a nontrivial solution x such that T x=λ x. Such an x is called an eigenvector corresponding to the eigenvalue λ. A vector space is complete if every ...

Choi Matrices of 2-positive Maps on Positive Semidefinite Matrices

Abstract/Overview Several investigations have been done on positive maps on their algebraic structures with more emphasis on completely positive maps. In this study we have described the structure of the Choi matrices for 2−positive maps on positive semidefinite matrices and the conditions for complete positivity of positive linear maps fromMntoMn+1. The motivation behind these objectives is work done by Majewski and Marciniak on the structure of positive mapsφfromMntoMn+1(2≥2) betwe...


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