Partial difference sets and partially balanced weighing designs for calibration and tournaments

Partial Difference Sets and Partially Balanced Weighing Designs for Calibration and Tournaments

Partially continuous pretopological and topological operators for intuitionistic fuzzy sets

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced...

Supplementary difference sets and optimal designs

D-optimal designs of order n = 2v ≡ 2 (mod 4), where q is a prime power and v = q2 + q + 1 are constructed using two methods, one with supplementary difference sets and the other using projective planes more directly. An infinite family of Hadamard matrices of order n = 4v with maximum excess (n) = n√n 3 where q is a prime power and v = q2 + q + 1 is a prime, is also constructed. Disciplines Ph...

Applying Balanced Generalized Weighing Matrices to Construct Block Designs

Balanced generalized weighing matrices are applied for constructing a family of symmetric designs with parameters (1 + qr(rm+1 − 1)/(r − 1), rm, rm−1(r − 1)/q), where m is any positive integer and q and r = (qd − 1)/(q − 1) are prime powers, and a family of non-embeddable quasi-residual 2−((r+1)(rm+1−1)/(r−1), rm(r+ 1)/2, rm(r− 1)/2) designs, where m is any positive integer and r = 2d− 1, 3 · 2...

Difference balanced functions and their generalized difference sets

Difference balanced functions from F∗ q to Fq are closely related to combinatorial designs and naturally define p-ary sequences with the ideal two-level autocorrelation. In the literature, all existing such functions are associated with the d-homogeneous property, and it was conjectured by Gong and Song that difference balanced functions must be d-homogeneous. First we characterize difference b...