A linear (qd, q, t)-perfect hash family of size s in a vector space V of order qd over a field F of order q consists of a set φ1, . . . , φs of linear functionals from V to F with the following property: for all t subsets X ⊆ V there exists i ∈ {1, . . . , s} such that φi is injective when restricted to F . A linear (qd, q, t)-perfect hash family of minimal size d(t− 1) is said to be optimal. I...

Abstract Leptophobic Z ′ gauge boson appears naturally in many grand unified theories, such as flipped SU(5) or string-inspired E6 models. This elusive particle easily escapes the direct/indirect detections because it does not couple to charged leptons. However, it can generate flavor changing neutral current at tree level. In this letter, we show that the recently measured mass difference, ∆ms...

Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. Recently, Gronau et al determined the existence of super-simple (v, 5, 2)-BIBDs with possible exceptions of v ∈ {75, 95, 115, 135, 195, 215, 231, 285, 365, 385, 515}. In this article, we investigate the existence of a super-simple (v, 5, 4)-BIBD and show that such a design exi...

We present two new perfect hashing schemes that can be used for efficient bitboard move generation for sliding pieces in chess-like board games without the need to use rotated bitboards. Moreover, we show that simple variations of these schemes give minimal perfect hashing schemes. The new method is applicable provided N , the number of k-bit spaced positions that may be set to 1, is not more t...

We study the neutrino mixing matrix (MNS matrix) in seesaw model. Assuming large mass hierarchy for heavy right-handed Majorana mass, we show that MNS matrix is determined by a unitary matrix which transforms neutrino yukawa term into a triangular form. Large mixing may occur even if yukawa matrix for charged lepton and that for neutrino is simultaneously diagonalized by biunitary transformatio...

We consider the Generalised Normal Variance-Mean (GNVM) model in which the mixing random variable is Gamma distributed for financial return data. This model generalises the popular Variance-Gamma (VG) distribution. This GNVM model can be interpreted as the addition of noise to a (skew) VG base. In this presentation, we will not only discuss the parameter estimation of the general model, but als...