Abstract/Overview We present norm inequalities for positive elementary operators via Cauchy-Schwarz inequality and Minkowskis inequality techniques. Norm inequalities are presented in Euclidean algebras linked to Minkowski’s light cones. Lastly, we explore the applications in quantum theory particularly in entanglement of states.

Abstract/Overview Let H be an infinite dimensional complex Hilbert space and B(H) the algebra of all bounded linear operators on H. We establish norm-attainability of operators via projective tensor norm. Moreover, we give results on the convergence of norm-attainable operators.

Abstract/Overview When mixed, two distributions can form another distribution. Binomial distribution and beta distributions combine to form a binomial mixture with the latter being a prior distribution which is a continuous distribution. Skellam pioneered this study when he mixed binomial distribution with its parameter p taking beta distribution. The paper focused on construction of binomial mixtures, their properties, special cases and the application of the mixtures in a two stage grou...

Abstract/Overview Two or more individual distributions can be mixed together to form a new distribution. According to Feller, this can be done using weights that sum up to unit. Also by considering a parameter which is a random variable taking another distribution then a new distribution ca be formed. The nature of the mixing distribution has effect on the new distribution formed. If the mixing distribution is continuous random variable, then the new mixture formed is also continuous. Ske...

Abstract/Overview This research is about an application of survival analysis on broilers in laNyevu poultry farm in Kaloleni sub-county. Chapter one gives an insight into the introduction of the paper, chapter two discusses the methodology used, chapter three gives the results, chapter four discusses the findings briefly and chapter five gives the conclusions arrived at and some recommendations.

Abstract/Overview Sample survey provides reliable current statistics for large areas or sub-population (domains) with large sample sizes. There is a growing demand for reliable small area statistics, however, the sample sizes are too small to provide direct (or area specific) estimators with acceptable and reliable accuracy. This study gives theoretical description of the estimation of small area mean by use of stratified sampling with a linear cost function in the presence of non-respons...

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