Let F be a function from Fpn to itself and δ a positive integer. F is called zerodifference δ-balanced if the equation F (x+a)−F (x) = 0 has exactly δ solutions for all nonzero a ∈ Fpn . As a particular case, all known quadratic planar functions are zero-difference 1-balanced; and some quadratic APN functions over F2n are zerodifference 2-balanced. In this paper, we study the relationship betwe...

In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. Commutative fundamental rings and the fundamental relation α which is the smallest strongly regular relation in hyperringswere introduced by Davvaz and Vougiouklis (2007). Recently, another strongly regular relation named θ on hyperrings has been studied by Ameri and Norouzi (2013). Ameri...

We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not always specialize to convex polytopes; however, in a number of cases where we can realize it, it produces interesting classes of polytopes. Thus we produce ...

For strongly regular graphs with adjacency matrix A, we look at the binary codes generated by A and A+ I . We determine these codes for some families of graphs, we pay attention to the relation between the codes of switching equivalent graphs and, with the exception of two parameter sets, we generate by computer the codes of all known strongly regular graphs on fewer than 45 vertices.

This paper presents a new and enhanced fusion module for the Multi-Sensor Precipitation Estimator (MPE) that would objectively blend real-time satellite quantitative precipitation estimates (SQPE) with radar and gauge estimates. This module consists of a preprocessor that mitigates systematic bias in SQPE, and a two-way blending routine that statistically fuses adjusted SQPE with radar estimate...

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Testing is a validation activity used to check the system’s correctness with respect to the specification. In this context, test based on refusals is studied in theory and tools are effectively constructed. This paper addresses, a formal testing based on stochastic refusals graphs (SRG) in order to test stochastic system represented by maximality-based stochastic labeled transition systems (MSL...

Strongly regular graphs lie on the cusp between highly structured and unstructured. For example, there is a unique strongly regular graph with parameters (36,10,4,2), but there are 32548 non-isomorphic graphs with parameters (36,15,6,6). (The first assertion is a special case of a theorem of Shrikhande, while the second is the result of a computer search by McKay and Spence.) In the light of th...

We explore twoor three-class association schemes. We study aspects of the structure of the relation graphs in association schemes which are not easily revealed by their parameters and spectra. The purpose is to develop some combinatorial methods to characterize the graphs and classify the association schemes, and also to delve deeply into several specific classification problems. We work with s...