This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.

Division of Removable Prosthodontics, Department of Oral Rehabilitation, Fukuoka Dental College, Fukuoka, Japan, Division of Dental Biomaterials Science, Department of Oral Health Science, Course for Oral Science, Niigata University Graduate School of Medical and Dental Sciences, Niigata, Japan, and Department of Biomaterials Science, Baylor College of Dentistry, Texas A&M University System Hea...

A series class P of a connected matroid M is removable if M \ P is connected. In this paper, we prove that a connected matroid M with r(M) ≥ 2 has at least r(M) + 1 removable series classes. Further, we obtain certain results from which the following result of Oxley and its graph theoretic version follow: If C is a circuit of a connected matroid M with C 6= M such that M \ x is not connected fo...

Let α be a differential form defined on an open set D ⊂ . If (D) is a class of functions defined on D, then we say that the differential form α is in this class provided that αi1···ik ∈ (D). For instance, the differential form α is in the class Lp(D) if all its coefficients are in this class. A differential form α of degree k on the manifold with coefficients αi1···ik ∈ L loc( ) is called weakl...

Tutte proved that every 3-connected graph on more than 4 nodes has a contractible edge. Barnette and Grünbaum proved the existence of a removable edge in the same setting. We show that the sequence of contractions and the sequence of removals from G to the K4 can be computed in O(|V | ) time by extending Barnette and Grünbaum’s theorem. As an application, we derive a certificate for the 3-conne...

Abstract. We construct a sequence of compact embedded minimal disks in the unit ball in Euclidean 3-space whose boundaries are in the boundary of the ball and where the curvatures blow up at every point of a line segment of the vertical axis, extending from the origin. We further study the transversal structure of the minimal limit lamination and find removable singularities along the line segm...

This paper describes tools and methods used to manage DEIMOS removable elements (filters, gratings, and slitmasks). The iterative process of adapting and refining our basic strategy to the working conditions and requirements of Keck Observatory staff is not yet complete; hence this paper should be read as a Work In Progress report.

In 1971 Trotter (or Bogart and Trotter) conjectured that every finite poset on at least 3 points has a pair whose removal does not decrease the dimension by more than 1. In 1992 Brightwell and Scheinerman introduced fractional dimension of posets, and they made a similar conjecture for fractional dimension. This paper settles this latter conjecture.

AIM Residual ridges change in shape and reduce in size due to alveolar bone resorption. Therefore, the purpose was to investigate changes in denture base thickness (DBT) and interocclusal rest space (IRS) with regard to the denture relining procedure. METHODS The IRS and DBT were measured (before and after denture relining) in the case of 74 patients and their removable dental prostheses by u...

T individuals rendered edentulous and provided with complete dentures display marked changes in jaw relations due to resorption of the residual alveolar ridges. The changes are characterized by an upward rotation of the mandible with a resulting decrease in occlusal vertical dimension and increase in mandibular prognathism. I-3 The most rapid changes occur during the first year, when the rate o...