Abstract/Overview In this paper we consider the price dynamics of a portfolio consisting of risk-free and risky assets. The paper discusses the pricing process of a contingent claim, the pricing equation and the risk-neutral valuation under the Martingale representation property. A partial differential equation with an unknown price function is formulated. The solution of this PDE gives a unique pricing formula

Abstract/Overview In this paper, we present results on the necessary and sufficient condi-tions for positivity of operators in non-unital C*- algebras

Abstract/Overview In this paper, attempt to study effects of extreme observations on two estimators of finite population total theoretically and by simulation is made. We compare the ratio estimate with the local linear polynomial estimate of finite population total given different finite populations. Both classical and the non parametric estimator based on the local linear polynomial produce good results when the auxiliary and the study variables are highly correlated. It is however note...

Abstract/Overview In this paper, attempt to study effects of outliers on two estimators of finite population total theoretically and by simulation is made. We compare the ratio estimate with the local linear polynomial estimate of finite population total given different finite populations. Both classical and the non parametric estimator based on the local linear polynomial produce good results when the auxiliary and the study variables are highly correlated. It is however noted that in th...

Abstract/Overview In this paper, we examine conservative autonomous dynamic vibration equation, f(x) = sech x which is time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Numerical results using New mark method are tabulated and then represented graphically. Further the stability of the algorithms employed is also discussed

Abstract/Overview Modeling of some physical phenomena and technological processes taking into account dissipation leads to the Sine-Gordon equation with the first time derivative. The (2+1) Sine-Gordon equation with the first time derivative is used in explaining a number of physical phenomena including the propagation of fluxons in Josephson junctions. This study uses Finite Difference Method to solve (2+1) dimensional Sine-Gordon equation with the first time derivative that models dissi...

Abstract/Overview Finite element method is a class of mathematical tool which approximates solutions to initial and boundary value problems. Finite element, basic functions, stiffness matrices, systems of ordinary differential equations and hence approximate solutions of partial differential equations which involves rendering the partial differential equation into system of ordinary differential equations. The ordinary differential equations are then numerically integrated. We present a f...

Abstract/Overview The nonlinear (1+1) Sine-Gordon equation that governs the vibrations of the rigid pendula attached to a stretched wire is solved. The equation is discretized and solved by Finite Difference Method with specific initial and boundary conditions. A Crank Nicolson numerical scheme is developed with concepts of stability of the scheme analysed using matrix method. The resulting systems of linear algebraic equations are solved using Mathematica software. The solutions are pres...

Abstract/Overview In this paper we establish the exact time of death of a murdered person. This leads to an ordinary differential equation whose solution has been analyzed to provide the approximate time of death. Forensic expert will try to estimate this time from body’s current temperature and calculating how long it would have taken to lose heat to reach this point. This provides an accurate approach to establish the approximate time when crime is committed

Abstract/Overview Numerical range is useful in studying operators on Hilbert spaces. In particular, the geometrical properties of numerical range often provide useful information about algebraic and analytic properties of an operator. The theory of numerical range played a crucial role in the study of some algebraic structures especially in the non-associative context. The numerical range of an operator depends strongly upon the base field. Motivated by theoretical study and applications,...

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.

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 ...

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.

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...

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...