Due to the condition of the original material, there are unavoidable flaws in this reproduction. We have made every effort possible to provide you with the best copy available. If you are dissatisfied with this product and find it unusable, please contact Document Services as soon as possible. ABSTRACT Simultaneous determination of the lamellar morphological length scale and the grain size of s...

we develop a two phase sampling procedure to determine the sample size necessary to estimatethe population mean of a normally distributed random variable and show that the resulting estimator has preassigned variance and is unbiased under a regular condition. we present a necessary and sufficient condition under which the final sample mean is an unbiased estimator for the population mean.

This paper revisits the existence and construction problems for polygonal designs (a special class of partially balanced incomplete block designs associated with regular polygons). We present new polygonal designs with various parameter sets by explicit construction. In doing so we employ several construction methods – some conventional and some new. We also establish a link between a class of ...

In 1963, Shrikhande and Raghavarao [5] published a recursive construction for designs that starts with a resolvable design (the “master design”) and then uses a second design (“the indexing design”) to take certain unions of blocks in each parallel class of the master design. Several variations of this construction have been studied by different authors. We revisit this construction, concentrat...

We show that if G is a finite Abelian group and the block size is 3, then the necessary conditions for the existence of a (v, 3, λ;G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated (v, 3, λ) BIBD plus λ ≡ 0 (mod |G|), plus some extra conditions when |G| is even, namely that the number of blocks be divisible by 4 and, if...

It is shown here that the necessary conditions for the existence of MGD[4, A m, n] for A ~ 2 are sufficient with the exception of MGO(4, 3, 6,23].

In a t-(v, k, λ) directed design the blocks are ordered k-tuples and every ordered t-tuple of distinct points occurs in exactly λ blocks (as a subsequence). We study t-(v, 5, 1) directed designs with t = 3 and t = 4. In particular, we construct the first known examples, and an infinite class, of 3-(v, 5, 1) directed designs, and the first known infinite class of 4-(v, 5, 1) directed designs.

In this paper, we investigate the existence of a super-simple (4, 5)-GDD of type gu and show that such a design exists if and only if u ≥ 4, g(u − 2) ≥ 10, g(u − 1) ≡ 0 (mod 3) and u(u− 1)g2 ≡ 0 (mod 12). © 2009 Elsevier B.V. All rights reserved.

We study three similar bijections on set partitions. The first is an involution defined by Kasraoui and Zeng which proves the symmetry of the distribution of crossings and nestings. We show that a stronger result can be deduced. The second gives a bijective proof of the equivalence of two statistics with a q-Stirling distribution. The third proves the equivalence of a multivariate block size di...

We propose a new indexing scheme, called the CRB-tree, for efficiently answering range-aggregate queries. The range-aggregate problem is defined as follows: Given a set of weighted points in R, compute the aggregate of weights of points that lie inside a d-dimensional query rectangle. In this paper we focus on range-COUNT, SUM, AVG aggregates. First, we develop an indexing scheme for answering ...