Abstract Customers demand and manufacturers strive for increasingly higher product reliability. Statistics plays a key role in achieving this. Necip Doganaksoy, William Q. Meeker Gerald J. Hahn explain how

Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the well-known exactly solvable difference equations of the Meixner–Pollaczek, continuous Hahn, continuous dual Hahn, Wilson and Askey–Wilson polynomials. Up to ...

We show that for every set of discrete polynomials yn(x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials zk(ξ(t)) of degrees k = s−a and k = b− s− 1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative f...

This paper will introduce and prove several theorems involving the separation of convex sets by hyperplanes, along with other interesting related results. It will begin with some basic separation results in Rn, such as the Hyperplane Separation Theorem of Hermann Minkowski, and then it will focus on and prove the extension of this theorem into normed vector spaces, known as the Hahn-Banach Sepa...

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König’s Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibilit...

Formation of a ZnS/Zn„S,O... bilayer buffer on CuInS2 thin film solar cell absorbers by chemical bath deposition M. Bär ,b Solarenergieforschung (SE2), Hahn-Meitner-Institut Berlin, Glienicker Strasse 100, D-14109 Berlin, Germany and Department of Chemistry, University of Nevada, 4505 Maryland Parkway, Las Vegas, Nevada 89145 A. Ennaoui, ,c J. Klaer, T. Kropp, R. Sáez-Araoz, N. Allsop, I. Lauer...

Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as wel...

We present explicit formulas for the operators providing missing labels tensor product of two irreducible representations $$\mathfrak {su}_3$$ . The result is seen as a particular representation diagonal centraliser through pair tridiagonal matrices. Using these formulas, we investigate symmetry this label problem and find group order 144 larger than what can be expected from natural symmetries...

For the three types of simply connected Riemannian spaces of constant curvature it is shown that the associated spherical functions can be obtained from the corresponding (zonal) spherical functions by application of a differential operator of the form p(i d/dt), where p belongs to a system of orthogonal polynomials: Gegenbauer polynomials, Hahn polynomials or continuous symmetric Hahn polynomi...

Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre, Meixner are reviewed and their connection explored by adopting a probabilistic approach. Hahn and Meixner polynomials are interpreted as posterior mixtures of Jacobi and Laguerre polynomials, respectively. By using known properties of Gamma point processes and related transformations, an infinite-dimension...