scholarly journals The Order Continuity of the Regular Norm on Regular Operator Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zi Li Chen ◽  
Ying Feng ◽  
Jin Xi Chen
Keyword(s):  
Regular Operator ◽  
Operator Spaces ◽  
Order Continuity ◽  
Regular Norm

scholarly journals Matrix Regular Operator Spaces

1998 ◽  
Vol 152 (1) ◽  
pp. 136-175 ◽  
Author(s):  
Walter J. Schreiner
Keyword(s):  
Regular Operator ◽  
Operator Spaces

A Stabilized B-Splines FEM Formulation for the Solution of an Inverse Elasticity Problem Arising in Medical Imaging

2008 ◽  
Author(s):  
Carlos E. Rivas ◽  
Paul E. Barbone ◽  
Assad A. Oberai
Keyword(s):  
Mechanical Properties ◽  
Diagnostic Value ◽  
Incompressible Material ◽  
High Order ◽  
Elasticity Problem ◽  
Parameter Distribution ◽  
Order Continuity ◽  
B Splines ◽  
Inverse Elasticity ◽  
Continuous Problem

Soft tissue pathologies are often associated with changes in mechanical properties. For example, breast and other tumors usually present as stiff lumps. Imaging the spatial distribution of the mechanical properties of tissues thus reveals information of diagnostic value. Doing so, however, typically requires the solution of an inverse elasticity problem. In this work we consider the inverse elasticity problem for an incompressible material in plane stress, formulated and solved as a constrained optimization problem. We formulate this inverse problem enforcing high order continuity for our variables. Driven by the requirements for the strong and weak solutions to this problem, we assume that our data field (i.e. the measured displacement) is in H2 and our parameter distribution (i.e. the sought shear modulus distribution) is in H1. This high order regularity requirement for the data is incompatible with standard FEM. We solve this problem using a FEM formulation that is novel in two respects. First, we employ quadratic b-splines that enforce C1 continuity in our displacement field, consistent with the variational requirements of the continuous problem. Second, we include Galerkin-least-squares (GLS) stabilization in the iterative optimization formulation. GLS adds consistent stability to the discrete formulation that otherwise violates an ellipticity condition that is satisfied by the continuous problem. Computational examples validate this formulation and demonstrate numerical convergence with mesh refinement.

scholarly journals On some geometric properties of operator spaces

2019 ◽  
Vol 13 (1) ◽  
pp. 174-191 ◽  
Author(s):  
Arpita Mal ◽  
Debmalya Sain ◽  
Kallol Paul
Keyword(s):  
Operator Spaces ◽  
Geometric Properties

Operator Spaces

2015 ◽  
pp. 1-37
Author(s):  
Ved Prakash Gupta ◽  
Prabha Mandayam ◽  
V. S. Sunder
Keyword(s):  
Operator Spaces

scholarly journals Globally exact operator spaces

2018 ◽  
Vol 53 (1) ◽  
pp. 179-186
Author(s):  
Massoud Amini ◽  
◽  
Alireza Medghalchi ◽  
Hamed Nikpey ◽  
◽  
...  
Keyword(s):  
Operator Spaces

scholarly journals Quasi Cubic Trigonometric Curve and Surface

2019 ◽  
Author(s):  
Guicang Zhang ◽  
Kai Wang
Keyword(s):  
Partition Of Unity ◽  
Shape Features ◽  
Bernstein Basis ◽  
Order Continuity ◽  
B Spline ◽  
Spline Curve ◽  
Totally Positive ◽  
Chebyshev Space ◽  
Spline Basis ◽  
Cutting Algorithm

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.

Sign in / Sign up

Export Citation Format

Share Document