ABSTRACT In this paper we push forward results on the invariant F -module of a virtual knot investigated by the first named author where F is the algebra with two invertible generators A,B and one relation ABAB −BAB = BABA− A . For flat knots and links the two sides of the relation equation are put equal to unity and the algebra becomes the Weyl algebra. If this is perturbed and the two sides o...

Long and Reid have shown that some compact flat 3-manifold cannot be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped hyperbolic 4-manifold. Similar to the flat case, we give a negative answer that there exists a 3-dimensional closed Heisenberg infranilmanifold whose diffeomorphism class cannot be arisen as a cusp cross-section of any complete finite volume 1-cusped ...

W e use program slices to model module cohesion. For our purposes, a slice is a projection of program text that includes only the data tokens relevant t o one output. W e define six cohesion metrics in terms of these slices, and evaluate the effects of classes of module changes on these metrics. W e find that the effects on cohesion metrics are notably more predictable when the changes result f...

A W-algebra action is constructed via Hecke transformations on the equivariant Borel–Moore homology of Hilbert scheme points a nonreduced plane in three-dimensional affine space. The resulting W-module then identified to vacuum module. construction based generalization ADHM as well W-action moduli space instantons by Schiffmann and Vasserot.

carbon molecular sieve membranes (cmsms) have been considered as very promising candidates for gas separation, in terms of separation properties as well as thermal and chemical stability. due to the numerous advantages and wide applications of carbon membranes, their application for gas separation is of special importance. because of the importance of carbon membranes and a large number of stud...

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we study notions of ~-adic nonlocal vertex algebra and ~-adic (weak) quantum vertex algebra, slightly generalizing Etingof-Kazhdan’s notion of quantum vertex operator algebra. For any topologically free C[[~]]-module W , we study ~-adic...

One of the most challenging issues for a selfsustaining robotic system is how to use its limited resources to accomplish a large variety of tasks. The scope of such tasks could include transportation, exploration, construction, inspection, maintenance, in-situ resource utilization, and support for astronauts. This paper proposes a modular and reconfigurable solution for this challenge by allowi...

We prove that over a commutative noetherian ring the three approaches to introducing depth for complexes: via Koszul homology, via Ext modules, and via local cohomology, all yield the same invariant. Using this result, we establish a far reaching generalization of the classical AuslanderBuchsbaum formula for the depth of finitely generated modules of finite projective dimension. We extend also ...

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. ...

The two most fundamental conjectures on the structure of generic Hecke algebra $\mathcal{H}(W)$ associated with a complex reflection group $W$ state that is free module rank $|W|$ over its ring definition, and admits canonical symmetrising trace. first conjecture has recently become theorem, while second conjecture, known to hold for real groups, only been proved some exceptional non-real group...