determinant Samuel Picton Drake, Brian D. O. Anderson, and Changbin Yu Defence Science and Technology Organisation, Edinburgh, South Australia 5111, Australia and School of Chemistry and Physics, The University of Adelaide, Adelaide, South Australia 5005, Australia Research School of Information Sciences and Engineering, Australian National University, Canberra, Australian Capital Territory 020...

We discuss the Attractor Equations of N = 2, d = 4 supergravity in an extremal black hole background with arbitrary electric and magnetic fluxes (charges) for field-strength two-forms. The effective one-dimensional Lagrangian in the radial (evolution) variable exhibits features of a spontaneously broken supergravity theory. Indeed, non-BPS Attractor solutions correspond to the vanishing determi...

We answer a question in [10], showing the regular determinantal complexity of the determinant detm is O(m ). We answer questions in, and generalize results of [2], showing there is no rank one determinantal expression for perm m or detm when m ≥ 3. Finally we state and prove several “folklore” results relating different models of computation.

Multiple Input Double Output (MIDO) asymmetric space-time codes for 4 transmit antennas and 2 receive antennas can be employed in the downlink from base stations to portable devices. Previous MIDO code constructions with low Maximum Likelihood (ML) decoding complexity, full diversity and the nonvanishing determinant (NVD) property are mostly based on cyclic division algebras. In this paper, a n...

Very recently, we have proposed an approximate scheme for calculating the PD on the basis of the extended constrained-search theory [10–14]. By introducing a noninteracting reference system [10,11], the resultant PD corresponds to the best solution within the set of PDs that are constructed from a single Slater determinant (SSD). This PD functional theory has two kinds of merit. The first is th...

We introduce various families of irreducible homaloidal hypersurfaces in projective space Pr, for all r ≥ 3. Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the consideration of the classes of homaloidal hypersur...

We discuss three applications of NJLand PNJL-like models to assess aspects of the QCD phase diagram: First, we study the effect of mesonic correlations on the pressure below and above the finite temperature phase transition within a nonlocal PNJL model beyond the mean-field approximation. Second, we reconstruct the phase boundary of an NJL model from a Taylor expansion of the chiral susceptibil...

The geometric picture of the star-product based on its Fourier representation kernel is utilized in the evaluation of chains of star-products and the intuitive appreciation of their associativity and symmetries. Such constructions appear even simpler for a variant asymmetric product, and carry through for the standard star-product supersymmetrization. §1. Groenewold’s noncommutative ⋆-product [...

Introduction The notion of a quasideterminant and a quasiminor of a matrix A = (a ij) with not necessarily commuting entries was introduced in GR1-3]. The ordinary determinant of a matrix with commuting entries can be written (in many ways) as a product of quasiminors. Furthermore, it was noticed in GR1-3, KL, GKLLRT, Mo] that such well-known noncommutative determinants as the Berezinian, the C...

Some time ago we presented a lattice method for chiral gauge theories that involves the introduction of auxiliary Dirac species [1,2]. Here we elaborate on an alternative approach [2] that achieves the effects of the auxiliary species through a direct modification of the fermion determinant. This alternative method has the advantage that the computational algorithm is simpler, involving two det...