We obtain stability estimates and derive analytic expansions for local solutions of multidimensional quadratic backward stochastic differential equations. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and d...

Zeros of Random Analytic Functions The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of generality. We study zeros of random analytic functions in one complex variable. It is known that there is a one parameter family o...

The model for the QCD analytic running coupling, proposed recently, is extended to the timelike region. This running coupling naturally arises under unification of the analytic approach to QCD and the renormalization group (RG) formalism. A new method for determining the coefficients of the “analytized” RG equation is elaborated. It enables one to take into account the higher loop contributions...

The two-case pattern recognition problem aims to find the best way of linearly separate two different classes of data points with a good generalization performance. In the context of learning machines proposed to solve the pattern recognition problem, the analytic center machine (ACM) uses the analytic center cutting plane method restricted to spherical shells. In this work we prove existence a...

Until now, the area of symbolic computation has mainly focused on the manipulation of algebraic expressions. It would be interesting to apply a similar spirit of “exact computations” to the field of mathematical analysis. One important step for such a project is the ability to compute with computable complex numbers and computable analytic functions. Such computations include effective analytic...

In the early seventies D. Ray and I. Singer [17] introduced the notion of zeta-regularized determinants. They used it to define the analytic version of Reidemeister torsion as an alternating product of determinants. One way to understand analytic torsion is to consider it as a ”multiplicative index” of an elliptic complex. By the L2-index theorem of M. Atiyah [1] this analogy suggests that one ...

The key point in this paper is the introduction of elastic analytic functions. An elastic analytic function is a function of the form u : C ! C 2 which is diierentiable and satisses equations which are analogous to the Cauchy-Riemann equations of traditional complex analysis such that the following conditions hold: rst the real and imaginary part of the rst complex component of u satisfy the Na...

The present research aimed at investigating the interaction of the classroom talk to have a better understanding of the teachers’ practice teaching which can pave the way for reflection on teaching. The study benefitted from conversation analytic perspective to qualitatively and interpretively examine the classroom discourse of the teacher-learner interaction. The classroom talk was analyzed th...