The Non-Existence of Certain PBIB Designs

Construction of Rectangular Pbib Designs

In this paper, some methods of constructing rectangular PBIB design are presented using the incidence matrix of a known PBIB design and Hadanard matrix. The rectangular design so constructed has nice block structure properties. The dual of these rectangular designs generate semiregular GD designs. A rectangular design is also constructed by using treatments arranged in n square array. Dual of t...

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

Non-Existence of isomorphisms between certain unitals

We show that the Ree-Tits unitals are neither classical nor isomorphic to the polar unitals found in the Coulter-Matthews planes. To this end, we determine the full automorphism groups of the (finite) Ree unitals.

" Applications of Pbib Designs in Cluster Sar''lpling*

On the strong non-rigidity of certain tight Euclidean designs

We study the non-rigidity of Euclidean t-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean t-designs. We show that certain tight Euclidean t-designs are non-rigid, and in fact satisfy a stronger form of non-rigidity which we call strong non-rigidity. This shows that there are plenty of non-isom...