Averaging diffeomorphisms is a challenging problem, and it has great applications in areas like medical image atlases. The simple Euclidean average can neither guarantee the averaged transformation is a diffeomorphism, nor get reasonable result when there is a local rotation. The goal of this paper is to propose a new approach to averaging diffeomorphisms based on the Jacobian determinant and t...

The common way to define a curl operator considers Stoke’s Theorem and the concept of circulation. Common numerical discretizations for this operator also use this approach. In this work, we revisit the construction of the curl operator using an extended form of Gauss’ Divergence Theorem instead. This new approach allows us to present a discretization framework that naturally inherits all the d...

1. SOBOLEV SPACES AND WEAK FORMULATIONS Let Ω be a bounded Lipschitz domain in R. We introduce the Sobolev spaces H(curl ; Ω) = {v ∈ L(Ω), curlv ∈ L(Ω)}, H(div; Ω) = {v ∈ L(Ω),div v ∈ L(Ω)} The vector fields (E,H) belong to H(curl ; Ω) while the flux (D,B) in H(div; Ω). We shall use the unified notation H(d; Ω) with d = grad , curl , or div. Note that H(grad ; Ω) is the familiar H(Ω) space. The...

Abstract Consider the differential equation curl for a 3dimensional differentiable vector field We prove that is analytic and then prove an existence and uniqueness theorem for the differential equation with a prescribed boundary data. We also outline with a few variations Professor J. Ericksen’s work on a unit vector field that equals its own curl. AMS Subject Classification 2000 15A72, 35A10,...

BACKGROUND The ultimate goal of rhinoplasty is to achieve a controllable, reliable and an aesthetically pleasing result. Various approaches and instruments have been introduced for the correction of the bony walls of the nose to improve predictability of the procedure and to minimize the associated trauma. We conducted a cadaveric study comparing the results of osteotomy of the nasal wall using...

Abstract In this work we test the numerical behaviour of matrix-valued fields approximated by finite element subspaces $$[{{\,\mathrm{\textit{H}^1}\,}}]^{3\times 3}$$ [ H 1 ] 3 ×</mml:m...

BACKGROUND The pedicle screw placement in scoliosis correction at the apex underlies potential risk for neurological injury. This research is to investigate the relative position of spinal cord at the apex in idiopathic thoracic scoliosis and to explore the risk of spinal cord injury from pedicle screw at the apex. METHODS Thirty-three adolescents with thoracic scoliosis were recruited in thi...

PURPOSE Coronary artery bypass graft (CABG) surgery represents the standard treatment of advanced coronary artery disease. Two major types of anastomosis exist to connect the graft to the coronary artery, i.e., by using an end-to-side or a side-to-side anastomosis. There is still controversy because of the differences in the patency rates of the two types of anastomosis. The purpose of this pap...

[Purpose] The aim of this study was to examine the effect of resistance exercise on carotid intima-media thickness, luminal diameter, peak systolic flow velocity, end diastolic flow velocity, and wall shear rate in healthy elderly men. [Subjects and Methods] Thirty healthy elderly men (age ≥65 years) were randomly divided into a control (n=15) and resistance exercise (n=15) groups. The 24-week ...