The Kauffman bracket skein modules, S(M,A), have been calculated for A = ±1 for all 3-manifolds M by relating them to the SL2(C)-character varieties. We extend this description to the case when A is a 4th root of 1 and M is either a surface × [0, 1] or a rational homology sphere (or its submanifold).

We use Polyak’s skein relation to give a new proof that Milnor’s string link invariants μ12...n are finite type invariants, and to develop a recursive relation for their associated weight systems. We show that the obstruction to the triviality of these weight systems is the presence of a certain kind of spanning tree in the intersection graph of a chord diagram.

The aim of this paper is to study the skein exact sequence for knot Floer homology. We prove precise graded version of this sequence, and also one using HF−. Moreover, a complete argument is also given purely within the realm of grid diagrams.

We construct a polynomial invariant, for links in a large class of rational homology 3-spheres, which generalizes the 2-variable Jones polynomial (HOMFLY). As a consequence, we show that the dual of the HOMFLY skein module of a homotopy 3-sphere is isomorpic to that of the genuine 3-sphere .

in this paper, the propagation of the waves in the laminated composite plates which is subjected to low velocity impact is investigated using the finite element method. a rigid metallic projectile with spherical nose is considered and the impact of this projectile with laminated composite is studied in this study. considering a finite element model the governing equations of the problem is disc...

It is natural to try to place the new polynomial invariants of links in algebraic topology (e.g. to try to interpret them using homology or homotopy groups). However, one can think that these new polynomial invariants are byproducts of a new more delicate algebraic invariant of 3-manifolds which measures the obstruction to isotopy of links (which are homotopic). We propose such an algebraic inv...

The objective of this work was to characterize the cinnamon oil nanocapsule that contained alginate-chitosan as coating agents. In this work, cinamonn oil loaded chitosan nanoparticles (CS-alginate NP-cinamonn) are prepared by a two-step process including oil/water emulsion and ionic gelation. In this study, cinamon as a core material was nanoencapsulated with chitosan alginate at a ratio of 1:...

All impact analyses performed so far for the composite plates, have treated central impacts. Furthermore, investigations on influences of the in-plane biaxial compression, tension, or tension-compression preloads on various responses of the low-velocity impact, especially the indentation, have not been performed so far. In the present research, a finite element formulation is presented for resp...