Relative (pa, pb, pa, pa−b-Difference Sets: A Unified Exponent Bound and a Local Ring Construction

On (pa, p, pa, pa-1)-Relative Difference Sets

An Exponent Bound for Relative Difference Sets in p-Groups

An exponent bound ia presented for abelian (pi+j, p0, p•+;, pi) relative c:liffere.nce sets: this botllld can be met for i $ j. RESULT For background in Relative Difference Sets (RDS), see [3]. The basic group ring equation for a RDS Din a group G with a forbidden subgroup N is nn<-1> = k + A(GN) If x is a character on the abelian group G, then we have three possibilities for I x(D) l=I L:dED x...

Introducing a Lightweight Structural Model via Simulation of Vernacular “Pa Tu Pa” Arch

The knowledge of Iranian vernacular structures is based on geometry, and there is a possibility of recreating such structural patterns aimed at producing movable structures. The purpose of this research was to utilize the patterns of vernacular structures to provide a lightweight structural model. The questions raised included how to create various forms based on the structural history of any r...

Independence, Relative Randomness, and PA Degrees

We study pairs of reals that are mutually Martin-Löf random with respect to a common, not necessarily computable probability measure. We show that a generalized version of van Lambalgen’s Theorem holds for non-computable probability measures, too. We study, for a given real A, the independence spectrum of A, the set of all B so that there exists a probability measure μ so that μ{A,B} = 0 and (A...

Pa Learning Pa Algorithm with Unlabeled Data

We analyze the combination of online learning and semisupervised learning. Online learning is an approach to supervised machine learning, which is effective at processing a large amount of training data. Semi-supervised learning is employed when a large amount of unlabeled data is available. While both setting occurs frequently in real applications of machine learning, thus far, their theoretic...