Daoud Bshouty
Technion – Israel Institute of Technology
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Featured researches published by Daoud Bshouty.
Journal of Theoretical Probability | 1994
Shaul K. Bar-Lev; Daoud Bshouty; Peter Enis; Gérard Letac; I-Li Lu; Donald St. P. Richards
A natural exponential family (NEF)F in ℝn,n>1, is said to be diagonal if there existn functions,a1,...,an, on some intervals of ℝ, such that the covariance matrixVF(m) ofF has diagonal (a1(m1),...,an(mn)), for allm=(m1,...,mn) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ℝk and ℝn-k, for somek=1,...,n−1. This paper shows that there are only six types of irreducible diagonal NEFs in ℝn, that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ℝn, under what conditions is its projectionp(F) in ℝk, underp(x1,...,xn)∶=(x1,...,xk),k=1,...,n−1, still an NEF in ℝk? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofVF(m1,...,mn) does not depend on (mk+1,...,mn).
Journal D Analyse Mathematique | 1997
Daoud Bshouty; Walter Hengartner
AbstractThis article is divided into two parts. In the first part, we consider univalent harmonic mappings from the unit diskU onto a Jordan domain Ω whose dilatation functions
Journal of Computer and System Sciences | 1998
Daoud Bshouty; Nader H. Bshouty
Journal D Analyse Mathematique | 1995
Daoud Bshouty; Walter Hengartner; Tiferet Suez
a = \bar f_{\bar z} /f_z
Probability Theory and Related Fields | 1992
Shaul K. Bar-Lev; Daoud Bshouty; Peter Enis
Complex Variables and Elliptic Equations | 1993
Daoud Bshouty; W. Hengartner
have modulus one on an interval of the unit circle. The boundary values off depend very strongly on the values ofa(eit). A complete characterization of the inverse imagef-1(q) of a pointq on ∂Ω is given. We then consider the case where the dilatation functiona(z) is a finite Blaschke product of degreeN. It is shown that in this case, Ω can have at mostN+2 points of convexity. Finally, we give a complete characterization of simply connected Jordan domains Ω with the property that there exists a nonparametric minimal surface over Ω such that the image of its Gaussian map is the upper half-sphere covered exactly once.
Complex Variables and Elliptic Equations | 2013
Daoud Bshouty; S.S. Joshi; S.B. Joshi
A formula is a read-once formula if each variable appears at most once in it. An arithmetic read-once formula (AROF) with exponentiation is one in which the operations are addition, substraction, multiplication, division and exponentiation to an arbitrary integer. We present a polynomial time algorithm for interpolating AROF withexponentiationusing randomized substitutions. Interpolating AROF without exponentiation is studied in (Bshouty, Hancock, and Hellerstein,SIAM J. Comput.24, No. 4, 1995). To add the exponentiation operation to the basis we develop a new technique.
Computational Methods and Function Theory | 2004
Daoud Bshouty; Abdallah Lyzzaik
A harmonic polynomial of degreen has at mostn2 zeros. It is shown that this bound is exact.
Statistics & Probability Letters | 1992
Shaul K. Bar-Lev; Daoud Bshouty; Gérard Letac
SummaryLet ℱ be a natural exponential family onℝ and (V, Ω) be its variance function. Here, Ω is the mean domain of ℱ andV, defined on Ω, is the variance of ℱ. A problem of increasing interest in the literature is the following: Given an open interval Ω⊂ℝ and a functionV defined on Ω, is the pair (V, Ω) a variance function of some natural exponential family? Here, we consider the case whereV is a polynomial. We develop a complex-analytic approach to this problem and provide necessary conditions for (V, Ω) to be such a variance function. These conditions are also sufficient for the class of third degree polynomials and certain subclasses of polynomials of higher degree.
Complex Variables | 2003
Daoud Bshouty; Allen Weitsman
Let ф be a simple closed convex curve of and let f∗ be a homeomorphism from the circle onto ф. Let p be the mean value of f∗over . Then the solution of the Dirichlet problem f=f∗on and on is univalent on the annulus .