I gave two talks on some of my results on toroidal Lie algebras in the conference Functional Analysis VIII held in Dubrovnik, Croatia in June 2003. But these results have been submitted to research journals and will appear soon. So I decided to write an expository article on Toroidal Lie Algebras covering my results for the proceedings of Functional Analysis VIII. I will introduce the definitio...

Let A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element σ of the parametrized Kasparov group KKX(A,B) is invertible if and only all its fiberwise components σx ∈ KK(A(x), B(x)) are invertible. This criterion does not extend to infinite dimensional spaces since there exist nontrivial unital separable continuous f...

In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point param...

We introduce and develop new techniques to study the complexity of normalization processes of graded algebras. The construction of a new degree function on graded modules, with a global nature, permits a broad extension of recent bounds for the length of the chains of subalgebras that general algorithms must transverse to build the integral closure, particularly of blowup algebras. It achieves ...

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite dimensional superspaces, and construct superanalogs of the classical function spaces with a reproducing kernel – including the Bargmann-Fock representation – and of the Wiener-Segal representation. The latter representation re...

This paper concerned with a comparative study and implementation of Interior orientation manually and automatically for KFA1000. In manually method, firstly, we reproduced the image to its reduced size photographically from the original image to be measurable in a mono comparator from 30*30 cm to 23*23 cm which proceeds by measuring of photo coordinates of four pieces of KFA-1000 photo. After c...

A primal-dual interior point method for optimal control problems with PDE constraints is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed. Numerical results from an inexact continuation method applied to a model problem are shown. AMS MSC 2000: 49M15, 90C48, 90C51

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the q → 1 limit of the q-deformed affine ŝl(2) symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. We describe how radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Li...

We study a class of representations of the Cuntz algebras O N , N = 2, 3,. .. , acting on L 2 (T) where T = R2πZ. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show how the O N-irreducibles decompose when restricted to the subalgebra UHF N ⊂ O N of gauge-invariant elements; and we show that the whole s...

A universal C∗-algebra is constructed which is generated by a partial isometry. Using grading on this algebra we construct an analog of Cuntz algebras which gives a homotopical interpretation of KK-groups. It is proved that this algebra is homotopy equivalent up to stabilization by 2×2 matrices to M2(C). Therefore those algebras are KK-isomorphic. We recall the definition of partial isometry. D...