The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

By applying projection operators to state vectors of coordinates we obtain subspaces in which these states are no longer normalized according to Dirac's delta function but normalized according to what we call " incomplete delta functions ". We show that this class of functions satisfy identities similar to those satisfied by the Dirac delta function. The incomplete delta functions may be employ...

The ‘‘pre-processing’’ procedure and the ‘‘break-point’’ analysis developed in a previous work based on the ADO (analytical discrete ordinates) method are used, along with a nascent delta function to describe the polar-angle dependence of an incident beam, to solve the classical albedo problem for radiative transfer in a plane-parallel, multi-layer medium subject to Fresnel boundary and interfa...

Using the concept of Hukuhara difference, in this paper we introduce a class of new derivatives called Hukuhara delta derivative and a class of new integrals called Hukuhara delta integral for fuzzy setvalued functions on time scales. Moreover, some corresponding properties of Hukuhara delta derivative and Hukuhara delta integral are discussed. Furthermore, sufficient conditions are established...

Existence criteria for two positive solutions to a nonlinear, even-order stacked deltanabla boundary value problem with stacked, vanishing conditions at the two endpoints are found using the method of Green’s functions. A few examples are given for standard time scales. The corresponding even-order nabla-delta problem is also discussed in detail. c © 2003 Elsevier Science Ltd. All rights reserv...

Recent research has found that the entrance of a low cost carrier leads to lower prices on routes it has entered. This paper extends this analysis by examining the impact of route entry by a discount carrier, ValuJet into an established carrier's hub, Delta, and by examining price changes on routes not entered by the low cost carrier. We found that Delta lowered its fares on competitive routes ...

We consider a one-dimensional fractional diffusion equation: ∂α t u(x, t) = ∂ ∂x ( p(x) ∂u ∂x (x, t) ) , 0 < x < `, where 0 < α < 1 and ∂α t denotes the Caputo derivative in time of order α. We attach the homogeneous Neumann boundary condition at x = 0, ` and the initial value given by the Dirac delta function. We prove that α and p(x), 0 < x < `, are uniquely determined by data u(0, t), 0 < t ...

We write down the local equations that characterize the sub-manifolds N of a Dirac manifold M which have a normal bundle that is either a coisotropic or an isotropic submanifold of T M endowed with the tangent Dirac structure. In the Poisson case, these formulas prove again a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of T M with the tangent Poisson s...