We show that the Kauffman bracket skein modules of certain manifolds obtained from integral surgery on a (2, 2b) torus link are finitely generated, and list the generators for select examples.

We give a simple unified proof for several disparate bounds on Thurston–Bennequin number for Legendrian knots and self-linking number for transverse knots in R, and provide a template for possible future bounds. As an application, we give sufficient conditions for some of these bounds to be sharp.

The composite materials are extensively used in the structures of civil, aerospace, marine, and automobile engineering due to their tailorable capability. The objective of this article is to address the issue of resonance-free lightweight design of such composite structures coupled with the notion of reliability. Laminated composite spherical shell is considered in this study to optimize width ...

Core-shell composite structures are potential candidates for Li-ion battery electrodes as they can take advantage of materials with higher energy density and materials with higher cyclability. This paper derives an analytical solution for isotropic 1-dimensional diffusion with galvanostatic boundary condition in composite slab, cylinder and sphere using separation of variables method. A general...

In [2] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying the skein relations: [ ] = A[ ] + B[ ] + [ ] [ ] = a[ ], [ ] = a[ ] and is defined in terms of a state-sum and the Dubrovnik polynomial for l...

Hydrogels are promising materials for bioengineering applications, and are good model materials for the study of hydrated biological tissues. As these materials often have a structural function, the measurement of their mechanical properties is of fundamental importance. In the present study gelatin gels reinforced with ceramic microspheres are produced and their poroviscoelastic response in sp...