LetM be a compact spin manifold with a smooth action of the ntorus. Connes and Landi constructed θ-deformations Mθ of M , parameterized by n×n real skew-symmetric matrices θ. TheMθ’s together with the canonical Dirac operator (D,H) on M are an isospectral deformation of M . The Dirac operator D defines a Lipschitz seminorm on C(Mθ), which defines a metric on the state space of C(Mθ). We show th...

Let M be a compact spin manifold with a smooth action of the ntorus. Connes and Landi constructed θ-deformations Mθ of M , parameterized by n × n skew-symmetric matrices θ. The Mθ’s together with the canonical Dirac operator (D,H) on M are an isospectral deformation of M . The Dirac operator D defines a Lipschitz seminorm on C(Mθ), which defines a metric on the state space of C(Mθ). We show tha...

The linear adiabatic pulsation-periods of Mira variable stars have been derived. Approximately 2701[1]models were calculated for M = 0.7 MΘ to 2 MΘ stars with radii from 180 RΘ to 340 RΘ and luminosities from 2800 LΘ to 10,000 LΘ. The chemical composition of all models is (X,Z) = (0.7,0.02). From the result of this study, linear relations on Luminosity-Period-Mass relationship and luminosity-pe...

the linear adiabatic pulsation-periods of mira variable stars have been derived. approximately 2701[1]models were calculated for m = 0.7 mθ to 2 mθ stars with radii from 180 rθ to 340 rθ and luminosities from 2800 lθ to 10,000 lθ. the chemical composition of all models is (x,z) = (0.7,0.02). from the result of this study, linear relations on luminosity-period-mass relationship and luminosity-pe...

Let M be a separable compact Hausdorff space with dim M ≤ 2 and θ : M → M be a homeomorphism with prime period p (p ≥ 2). Set Mθ = {x ∈ M | θ(x) = x} 6= ∅ and M0 = M\Mθ. Suppose that M0 is dense in M and H(M0/θ,Z) ∼= 0, H(χ(M0/θ),Z) ∼= 0. Let M ′ be another separable compact Hausdorff space with dim M ′ ≤ 2 and θ′ be the self–homeomorphism of M ′ with prime period p. Suppose that M ′ 0 = M ′\M ...

the linear adiabatic pulsation-periods of mira variable stars have been derived. approximately 2701[1]models were calculated for m = 0.7 mθ to 2 mθ stars with radii from 180 rθ to 340 rθ and luminosities from 2800 lθ to 10,000 lθ. the chemical composition of all models is (x,z) = (0.7,0.02). from the result of this study, linear relations on luminosity-period-mass relationship and luminosity-pe...

In this article we prove the problem on isometric mappings of S posed by Th. M. Rassias. We prove that any map f : S → S, p ≥ n > 1, preserving two angles θ and mθ (mθ < π, m > 1) is an isometry. With the assumption of continuity we prove that any map f : S → S preserving an irrational angle is an isometry.

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 C/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/...