We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christooel symbols of a symmetric Ehresmann "-connection.

Given a finite planar graph, a grove is a spanning forest in which every component tree contains one or more of a specified set of vertices (called nodes) on the outer face. For the uniform measure on groves, we compute the probabilities of the different possible node connections in a grove. These probabilities only depend on boundary measurements of the graph and not on the actual graph struct...

We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals. AMS 2000 subject classifications: Primary 60K35; secondary 94A17.

We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.

In part 1 of this study, it was discussed that dental occlusion/temporomandibular joint (TMJ) status is functionally connected to general body health. The purpose of this part of the study was to attempt to formulate a conceptual account, the "fascial connection theory for TMJ and other parts of the body," to explain the functional connection between TMJ and other parts of the body. The first h...

tooth/implant supported fixed prostheses may present biomechanical design problems, as the implant is rigidly anchored within the alveolus, whereas the tooth is attached by the periodontal ligament to the bone allowing movement. many clinicians prefer tooth/implant supported fixed prosthesis designs with rigid connectors. however, there are some doubts about the effect of attachment placement i...

We present a histories version of the connection formalism of general relativity. Such an approach introduces a spacetime description—a characteristic feature of the histories approach—and we discuss the extent to which the usual loop variables are compatible with a spacetime description. In particular, we discuss the definability of the Barbero connection without any gauge fixing. Although it ...

We consider filtered holomorphic vector bundles on a compact Riemann surface X equipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. If Q is a stable vector bundle of rank r and degree (1−genus(X))nr , then any holomorphic connection on the jet bundle Jn(Q) satisfies this transversality condition for the natural filtration of Jn(Q) ...