In the present paper we construct deformations of the Poincaré algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate ansatz for the deformed Lorentz generator. They turn out to be Hopf algebras of quantum universal enveloping algebra type with nontrivial antipodes. In order ...

For a finite subgroup G ⊂ SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C3/G. This paper considers the moduli spaces Mθ, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G -Hilb for a particular choice of GIT parameter θ. For G Abelian, we prove that every projective crepant resolution of C...

Let H m be the reproducing kernel Hilbert space with the kernel function (z, w) ∈ B×B → (1− m ∑ i=1 ziw̄i) . We show that if θ : B → L(E , E∗) is a multiplier for which the corresponding multiplication operator Mθ ∈ L(H m ⊗ E , H 2 m ⊗ E∗) has closed range, then the quotient module Hθ, given by · · · −→ H m ⊗ E Mθ −→ H m ⊗ E∗ πθ −→ Hθ −→ 0, is similar to H m ⊗F for some Hilbert space F if and on...

Divergence functions are the non-symmetric “distance” on the manifold,Mθ, of parametric probability density functions over a measure space, (X,μ). Classical information geometry prescribes, on Mθ: (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint a...

where both m(·) and σ(·) are unknown functions defined over R, the data {(Xt, Yt)}t=1 are weakly dependent stationary time series, and et is an error process with zero mean and unit variance. Suppose that {mθ(·)|θ ∈ Θ} is a family of parametric specification to the regression function m(x) where θ ∈ R is an unknown parameter belonging to a parameter space Θ. This paper considers testing the val...

It is shown that the one-loop quadratic divergences of standard supergravity can be regulated by the introduction of heavy PauliVillars fields belonging to chiral and abelian gauge multiplets. The resulting one-loop correction can be interpreted as a renormalization of the Kähler potential. Regularization of the dilaton couplings to the Yang-Mills sector requires special care, and may shed some...

Classical information geometry prescribes, on the parametric family of probability functions Mθ : (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint actions; and (iii) a family of (non-symmetric) divergence functions (α-divergence) defined on Mθ ×Mθ...

We investigate whether the Affleck-Dine (AD) mechanism works when the contribution of the twoloop thermal correction to the potential is negative in the gauge-mediated supersymmetry breaking models. The AD field is trapped far away from the origin by the negative thermal correction for a long time until the temperature of the universe becomes low enough. The most striking feature is that the Hu...

Anti-decuplet penta-quark baryon is studied with the quenched anisotropic lattice QCD for accurate measurement of the correlator. Both the positive and negative parity states are studied using a non-NK type interpolating field with I = 0 and J = 1/2. After the chiral extrapolation, the lowest positive parity state is found at mΘ ≃ 2.25 GeV, which is too massive to be identified with the experim...