Contents 0 Notations and conventions 5 1 The Eisenstein symbol and the cup product construction 6

The obstruction space T 2 and the cup product T 1×T 1 → T 2 are computed for toric singularities.

Comparing to the Chen-Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods for almost complex orbifolds (see [2]), we define the obstruction bundle for any 3-multisector of the almost contact orbifolds and the Chen-Ruan cup product ...

Consider a simple graph $G$. We call labeling $w:E(G)\cup V(G)\rightarrow \{1, 2, \dots, s\}$ (\textit{total vertex}) \textit{product-irregular}, if all product degrees $pd_G(v)$ induced by this are distinct, where $pd_G(v)=w(v)\times\prod_{e\ni v}w(e)$. The strength of $w$ is $s$, the maximum number used to label members $E(G)\cup V(G)$. minimum value $s$ that allows some irregular called \tex...

Let I be a 3D digital image, and let Q(I) be the associated cubical complex. In this paper we show how to simplify the combinatorial structure of Q(I) and obtain a homeomorphic cellular complex P (I) with fewer cells. We introduce formulas for a diagonal approximation on a general polygon and use it to compute cup products on the cohomology H∗(P (I)). The cup product encodes important geometric...

Eggs of Aedes albopictus were collected in oviposition cups from 3 forested areas of Delta State in south-central Nigeria during September 1991 as part of a post-yellow fever outbreak investigation. These eggs were shipped to the Centers for Disease Control in Colorado, where they were reared to the adult stage and identified. This is the first record of breeding populations of Ae. albopictus i...

The cup drawing is a basic deep drawing process. Thus, understanding the mechanics ofthe cup drawing process helps in determining the general parameters that affect the deep drawingprocess. There are mainly two methods of analysis; experimental and analytical/numerical.Experimental analysis can be useful in analyzing the process to determine the process parameters thatproduce a defect free prod...