Composite materials play an increasingly important role in our everyday life and technology from skis and golf clubs to sensors and actuators in high tech components. By “composite” we mean a perfectly bonded homogeneous mixture of two or more materials on a length scale much smaller than human size and much larger than interatomic distances. The physical properties of a composite (conducting, ...

Notation: In the sequel K is a field and Σn is the group of permutation over n elements. If A is an operad, then the K-vector space of n-ary operations is denoted as usual by A(n). Recall that if A is regular, then A(n) := An⊗KΣn, where An is the K-vector space of n-ary operations without permutations of the entries. We adopt Sweedler notation for binary cooperation ∆ on a K-vector space V and ...

For each 1 < s < ∞, a Popa algebra As is constructed that embeds as a weakly dense C∗–subalgebra of the interpolated free group factor L(Fs). Certain approximation properties for As are shown. It follows that L(Fs) has the weak expectation property of Lance with respect to As. In the course of the demonstration, it is proved that under certain conditions, full amalgamated free products of matri...

It has been studied that, the fine-irresolute mapping introduced in [13] includes all mappings defined by Császár (cf. [5]) in a fine space which is a special case of generalized topological space. It has been also noted that g-α-irresolute function defined by Bai et al [1] is also included in the same fine-irresolute mapping.

The Nagano-Yagi-Goldmann theorem states that on the torus T, every affine (or projective) structure is invariant or is constructed on the basis of some Goldmann rings [N-Y]. It shows the interest to study the invariant affine structure on the torus T or on abelian Lie groups. Recently, the works of Kim [K] and Dekempe-Ongenae [D-O] precise the number of non equivalent invariant affine structure...

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as...

This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler’s dual.

This paper classifies the blocks of the cyclotomic Hecke algebras of type G(r, 1, n) over an arbitrary field. Rather than working with the Hecke algebras directly we work instead with the cyclotomic Schur algebras. The advantage of these algebras is that the cyclotomic Jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic Schur algebras. We obtain an e...

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finitedimensional are explo...