We introduce the concept of a prehomogeneous determinant as a possibly nonreduced version of a linear free divisor. Both are special cases of prehomogeneous vector spaces. We show that the roots of the b-function are symmetric about −1 for reductive prehomogeneous determinants and for regular special linear free divisors. For general prehomogeneous determinants, we describe conditions under whi...

We study expectation values related to the dynamical lattice spacing that occurs in the recent 2d lattice super-Yang-Mills constructions of Cohen et al. [hep-lat/0307012]. The corresponding observable in the fully-quenched ensemble would appear to indicate a difficulty with the proposed continuum limit. However, we find that the same observable in the phase-quenched ensemble takes a very differ...

Using a cohomological characterization of the consistent and the covariant Lorentz and gauge anomalies, derived from the complexification of the relevant algebras, we study in d = 2 the definition of the Weyl determinant for a non-abelian theory with Riemannian background. We obtain two second order operators that produce, by means of ζ-function regularization, respectively the consistent and t...

I Let Tn be the set of congruence classes of simplices in Euclidean space E . The set Tn is an open manifold (also a semi-algebraic set) of dimension (n + 1)n/2. Coincidentally, a simplexT ∈ Tn is determined by the (n+1)n/2 lengths of its edges. Furthermore, the square of the volume of T ∈ Tn is a polynomial in the squares of the edgelengths. This polynomial is given by the Cayley-Me...

We investigate the continuum limit of the rooted staggered action in the 2-dimensional Schwinger model. We match both the unrooted and rooted staggered determinants with an overlap fermion determinant of two (one) flavors and a local pure gauge effective action by fitting the coefficients of the effective action and the mass of the overlap operator. The residue of this fit measures the differen...

We use a " hybrid " method, mixing variationally-determined triaxial nuclear Slater determinants, to calculate the response of 73 Ge to hypothetical dark-matter particles such as neutralinos. The method is a hybrid in that rota-tional invariance is approximately restored prior to variation and then fully restored before the mixing of intrinsic states. We discuss such features of 73 Ge as shape ...

The scientific legacy of Zvi Griliches’ contribution to the economic analysis of the diffusion of technological innovations is the subject of this paper. It begins with an examination of the relationship between Griliches’ pioneering empirical work on the introduction and adoption of hybrid corn and the subsequent development of theoretical models and econometric research on the microeconomic d...

A global error bound is given on the distance between an arbitrary point in the n-dimensional real space R n and its projection on a nonempty convex set determined by m convex, possibly nondiierentiable, inequalities. The bound is in terms of a natural residual that measures the violations of the inequalities multiplied by a new simple condition constant that embodies a single strong Slater con...

We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a reduction of the associated dynamical partial differential equations to a system of ordinary differential equations, and provide a nonlinear counterpart to quasi-exactly solvable quantum Hamiltonian...

In the simplified setting of the Schwinger model we present a systematic study on the simulation of dynamical fermions by global accept/reject steps that take into account the fermion determinant. A family of exact algorithms is developed, which combine stochastic estimates of the determinant ratio with the exploitation of some exact extremal eigenvalues of the generalized problem defined by th...