The Deformation Space Smooth

Smooth biproximity spaces and P-smooth quasi-proximity spaces

The notion of smooth biproximity space  where $delta_1,delta_2$ are gradation proximities defined by Ghanim et al. [10]. In this paper, we show every smooth biproximity space $(X,delta_1,delta_2)$ induces a supra smooth proximity space $delta_{12}$ finer than $delta_1$ and $delta_2$. We study the relationship between $(X,delta_{12})$ and the $FP^*$-separation axioms which had been introduced by...

Murphy’s Law in Algebraic Geometry: Badly-behaved Deformation Spaces

We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible.” We show this for a number of important moduli spaces. More precisely, every singularity of finite type overZ (up to smooth parameters) appears on: the Hilbert scheme of curves in projective space...

A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

Plane Strain Deformation of a Poroelastic Half-Space Lying Over Another Poroelastic Half-Space

The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...

On Unitary Deformations of Smooth Modular Representations

Let G be a locally Qp-analytic group and K a finite extension of Qp with residue field k. Adapting a strategy of B. Mazur (cf. [Maz89]) we use deformation theory to study the possible liftings of a given smooth G-representation ρ over k to unitary G-Banach space representations over K. The main result proves the existence of a universal deformation space in case ρ admits only scalar endomorphis...