A Hilbert module over a planar algebra is essentially a Hilbert module over a eanonieally defined algebra spanned by the annular tangles in It follows that any planar algebra containing is a module over and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar...

Let be any -type Lie algebra with ≥ 2 over an algebraically closed field of characteristic 5. Let be an irreducible -module corresponding to some points and let be its corresponding representation. In this paper, in order to prove that the equality about the versus problem out of the 7 Clay...

A formal linear vector field representation for scientific equations is developed to rationalize the intuitive methods that are constantly employed. It is shown that unlike mechanical units that appear in the basis of the space, the reduced temperature and Boltzmann parameter cannot be described...

We present a method based on degree one extensions of Lie algebras by a derivation to compute the Casimir operator of perfect Lie algebras having only one invariant for the coadjoint representation and an abelian radical. In particular, the Casimir operator of the special affine Lie algebras...

1 Motivation -- 1–1 Introduction -- 1–2 Miscellaneous Examples -- 1–3 Conclusion: Our Present Aim -- 2 The Initial Axioms -- 2–1 Some Logical Geography -- 2–2 Commutative Bands -- 2–3 Isotone Functions -- 2–4 Belts -- 2–5 Belt Homomorphisms -- 2–6 Types of Belt -- 2–7 Dual...

As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations...

This book presents recent theoretical and practical aspects in the field of optimization and convex analysis. The topics covered in this volume include: - Equilibrium models in economics. - Control theory and semi-infinite programming. - Ill-posed variational problems. - Global optimization. -...

1. Convex Cones and linear Inequalities -- 1. Separation theorems -- 2. Cones and duals -- 3. Linear inequalities over cones -- 4. Theorems of the alternative -- 2. Mathematical Programming over Cones -- 5. Linear programming -- 6. Quadratic programming -- 7. The complementarity problem -- 8....

We present some formal systems in the language of linearly ordered rings with finite sets whose nonlogical axioms are strictly mathematical, which correspond to polynomially bounded arithmetic. With an additional strictly mathematical axiom, the systems correspond to exponentially bounded arithmetic