Elementary Functional Equations on Partially Ordered Linear Algebra

Notes on Elementary Linear Algebra

C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology Revised August 2005 1 Vectors In quantum mechanics, we are generally interested in complex numbers. Let C denote the set of all n-tuples of complex numbers (a complex n-space). The elements of C may be called “points” or “vectors” in complex n-space. The elements of the complex numbers C are scalars. A vector...

Notes on Elementary Linear Algebra

Elementary Linear Algebra

FUZZY FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN PARTIALLY ORDERED METRIC SPACES

In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via  weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.

A Self-dual Hopf Algebra on Double Partially Ordered Sets

Let D be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On ZD we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations ZD is a Hopf algebra, self-dual with respect to a scalar product which counts the number of pictures (in the sense of Zelevinsky) between two do...