this paper presents an exact analytical solution for two-dimensional conductive heat transfer in spherical composite pressure vessels .the vessels are in spherical shape and fibers are winded in circumferential direction. the analytical solution is obtained under the general boundary conditions which consist of convection, conduction and radiation inside/outside of vessel. the heat transfer equ...

A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is computed.

We give a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant to consider in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations...

Following the recent work by Chan [4] and Morton and Hadji [7] on the Homflypt polynomials of some generalized Hopf links, we investigate the Kauffman polynomials of generalized Hopf links. By studying the Kauffman skein module of the solid torus S × D, we establish a similar skein map on the Kauffman skein module of S × D which has distinct eigenvalues. Furthermore we are able to calculate the...

We compute the Kauffman skein module of the complement of torus knots in S3. Precisely, we show that these modules are isomorphic to the algebra of Sl(2, C)-characters tensored with the ring of Laurent polynomials. Skein modules were introduced indenpendantly by V. Turaev in 1988 and J. Przytycki in 1991 (see [TU88, HP92]) as a C[A±1]-module associated to a 3-manifold M generated by banded link...

We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.

Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach algebra situs. When looking at the panorama of skein modules1, we see, past the rolling hills of homologies and homotopies, distant mountains the Kauffman bracket skein module, and farther off in the distance skein modules based on other quantum inva...

For a ring R, we denote by R[L] the free R-module spanned by the isotopy classes of singular links in S. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in S (relative to the triple (R, t, x)) is the quotient of R[L] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (...

For each Frobenius algebra there is defined a skein module of surfaces embedded in a given 3manifold and bounding a prescribed curve system in the boundary. The skein relations are local and generate the kernel of a certain natural extension of the corresponding topological quantum field theory. In particular the skein module of the 3-ball is isomorphic to the ground ring of the Frobenius algeb...

We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on obtain and use knots, proving that these are knotoid isotopy invariant. Secondly, define type directly knotoids, by extending singular via skein relation. Then, spherical show there non-trivial type-1 invariants, in contrast with classical knot where v...