Amongst resolvable incomplete block designs, affine resolvable designs are optimal in many conventional senses. However, different affine resolvable designs for the same numbers of treatments, replicates, and block size can differ in how well they estimate elementary treatment contrasts. An aberration criterion is employed to distinguish the best of the affine resolvable designs for this task. ...

Generalized Bhaskar Rao n-ary are defined. This paper studies with elements from abelian groups of Generalized Bhaskar Rao nary called Bhaskar Rao Bhaskar Rao a v b matrix of ±1 and such that the inner product of any two rows 0 and the matrix obtained of X by its absolute value the incidence matrix of the construction of infinite families of Balanced Balanced are Some construction methods and n...

We propose a new scheme for managing files of variable-length dynamic records, based on storing the records in large, fixed-length blocks. We demonstrate the effectiveness of this scheme for text indexing, showing that it achieves space utilisation of over 95%. With an appropriate block size and caching strategy, our scheme requires on average around two disk accesses—one read and one write—for...

Assaf, A.M., A. Hartman and N. Shalaby, Packing designs with block size 6 and index 5, Discrete Mathematics 103 (1992) 121-128. A (v, K, A) packing design of order v, block size K and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most I blocks. The packing problem is to determine the maximum number of blocks in a packing des...

We investigate the spectrum for {4}-GDDs of type g u m 1. We determine, for each admissible pair (g, u) (with some exceptions), the maximum and minimum values of m for which a {4}-GDD of type g u m 1 exists.

A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine spaces over various finite fields. Then algebro-geometric transformations on those spaces is transported back to provide encryption. For a specific block size <...

We introduce, for block size 3, the problem of minimal enclosings of GDDs with u groups of size g into GDDs with u groups of size g + 1. We prove the necessary conditions are sufficient for the embedding of any GDD with group size 1, i.e., a BIBD(v, 3, λ), into a GDD with v groups of size 2. Minimal faithful enclosings of GDDs are given for group size 2 with any index into GDDs with group size ...

Each parallel class of a uniformly resolvable design (URD) contains blocks of only one block size. AURDwith v points andwith block sizes three and fourmeans that at least one parallel class has block size three and at least one has block size four. Danziger [P. Danziger, Uniform restricted resolvable designs with r = 3, ARS Combin. 46 (1997) 161–176] proved that for all v ≡ 12 (mod 24) there ex...

The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007

A novel methodology to quantify displacements and strain in musculoskeletal ultrasound sequences is presented. We extend the principles of 2D interframe displacements produced by our earlier work using hierarchical variable block size matching, to quantify displacement trajectories. We provide novel solutions for probe motion, quantification of objects moving in the 3D volume traversing the 2D ...