We present a proof due to Duistermaat that the gradient flow of the norm squared of the moment map defines a deformation retract of the appropriate piece of the manifold onto the zero level set of the moment map. Duistermaat’s proof is an adaptation of Lojasiewicz’s argument for analytic functions to functions which are locally analytic.

In this study, the hot deformation processing map of AISI 304 austenitic stainless steel in two initial grain sizes of 15 and 40 μm was investigated. For this purpose, cylindrical samples were used in the hot compression test at the temperature range of 950-1100 °C and the strain rate of 0.005-0.5% s-1. At first, the relationship between the peak stress and Zener-Hollomon parameter w...

Spatial normalization is a crucial step in assessing patterns of neuroanatomical structure and function associated with health and disease. Errors that occur during spatial normalization can influence hypothesis testing due to the dimensionalities of mapping algorithms and anatomical manifolds (landmarks, curves, surfaces, volumes) used to drive the mapping algorithms. The primary aim of this p...

This is a comment on the Kuranishi method of constructing analytic deformation spaces. It is based on a simple observation that the Kuranishi map can always be inverted in the category of L ∞-algebras. The L ∞-structure obtained by this inversion is used to define an " unobstructed " deformation functor which is always representable by a smooth pointed moduli space. The singular nature of the o...

In the framework of C-algebraic deformation quantization we propose a notion of deformation groupoid which could apply to known examples e.g. Connes’ tangent groupoid of a manifold, its generalisation by Landsman and Ramazan, Rieffel’s noncommutative torus, and even Landi’s noncommutative 4-sphere. We construct such groupoid for a wide class of T-spaces, that generalizes the one given for C by ...