We introduce a notion of tangential Alexander polynomials for plane curves and study the relation with θ-Alexander polynomial. As an application, we use these polynomials to study a non-reduced degeneration Ct, → D0 + jL. We show that there exists a certain surjectivity of the fundamental groups and divisibility among their Alexander polynomials.

WINTER 2015 87 The Internet has been strongly gaining prominence as a news medium; in 2012, it overtook the TV as the most used news source for people under 30 in the United States (Kohut 2013). In addition, it has significantly changed the way in which many people find and consume news. Multiple publishers are now reachable more easily than ever before. Social bookmarking sites present us with...

We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.

We determine all Riemannian manifolds for which the tangent sphere bundles, equipped with the Sasaki metric, are local or global Riemannian product manifolds.

The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants ∆i(u1, . . . , ud, v), i = 0, 1, . . . , is obtained. When l is a classical link, ∆i reduces to the well-known ith Alexander polynomial of the link in the d variables u1v, . . . , udv; in particular, ∆0 vanishes.

Let S be a proper partial geometry pg(s, t, 2), and let G be an abelian group of automorphisms of S acting regularly on the points of S. Then either t ≡ 2 (mod s+1) or S is a pg(5, 5, 2) isomorphic to the partial geometry of van Lint and Schrijver [11]. This result is a new step towards the classification of partial geometries with an abelian Singer group and further provides an interesting cha...

INTRODUCTION The correction of a deep overbite with the subsequent achievement of long-term stability is a difficult problem for orthodontists. The role of leveling the curve of Spee (COS) in bite opening and the success of orthodontic treatment has been well documented in the literature. The aim of this study was to investigate whether leveling the COS, by using 2 orthodontic treatment techniq...

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