1 Let D be either the unit ball B1(0) or the half ball B + 1 (0), let f be a strictly positive and continuous function, and let u and Ω ⊂ D solve the following overdetermined problem: ∆u(x) = χ Ω (x)f(x) in D, 0 ∈ ∂Ω, u = |∇u| = 0 in Ω, where χ Ω denotes the characteristic function of Ω, Ωc denotes the set D \Ω, and the equation is satisfied in the sense of distributions. When D = B 1 (0), then...

The sets and curves of fractional dimension have been constructed and found to be useful at number of places in science [1]. They are used to model various irregular phenomena. It is wellknown that the usual calculus is inadequate to handle such structures and processes. Therefore a new calculus should be developed which incorporates fractals naturally. Fractional calculus, which is a branch of...

We study the L2-time regularity of the Z-component of a Markovian BSDE, whose terminal condition is a function g of a forward SDE (Xt)0≤t≤T . When g is Lipschitz continuous, Zhang [1] proved that the related squared L2-time regularity is of order one with respect to the size of the time mesh. We extend this type of result to any function g, including irregular functions such as indicator functi...

Let P = fP0; :::; Png be a partition of a nite abelian group A and L(P ) the complex vector space generated by the indicator functions of the sets P0; :::; Pn. In [1] it was proved that P de nes an abelian association scheme on A if L(P ) equals the space L(P ) of all Fourier transforms of functions in L(P ). In this paper it is shown that P de nes an abelian association scheme on A if and only...

A characterization of geometric distribution is given, which is based on the ratio of the real and imaginary part of the characteristic function.

This article considers optimal foldover plans for nonregular designs. By using the indicator function, we deŽ ne words with fractional lengths. The extended word-length pattern is then used to select among nonregular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors...

We provide a short proof of the validity and unimodality of Linnik’s characteristic function l/(1 + 1 t I”), 0 < a < 2, by noting that it corresponds to the distribution of S,V’/a, where S, is a symmetric stable random variable with parameter OL, and V is an independent exponential random variable. AMS 1980 Subject Classifications: 65C10, 68505.

In this paper we will show how a suitably developed decomposition of the characteristic function of the logarithm of the likelihood ratio test statistic to test independence in a set of variates may be used to obtain extremely wellt near-exact distributions both for this test statistic as well as for the likelihood ratio test statistic for sphericity, based on a decomposition of this latter tes...

A new simple model has recently been proposed for land mobile satellite channels. In this paper we study the secondorder statistics of the new model. First we develop a characteristic function-based approach for calculating the level crossing rate of the new model in diversity systems, where the branches can have different fading statistics. Then we compare the level crossing rate and the avera...