Seminars from until »

A semi-quantum key distribution protocol is presented and its proof of security is detailed.

We give a simple proof of the boundedness of Bergman projection in various Banach spaces of functions on the unit disc in the complex plain. The approach of the paper is based on the idea of V. P. Zaharyuta, V. I. Yudovich (1962) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderon-Zygmund operators. We exploit this approach and treat the cases of variable exponent Lebesgue space, Orlicz space and variable exponent generalized Morrey space. In the case of variable exponent Lebesgue space the boundedness results is known, so in that case we provide a simpler proof. The other two cases are new. The major idea of this paper is to show that the approach can be applied to a wide range of function spaces. This opens a door in a sense for introducing and studying new function spaces of Bergman type in complex analysis.

We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollifying dilations.

This is a joint work with Stefan Samko and Humberto Rafeiro.

In Finance it is quite usual to assume that a process behaves according to a previously specified target GARCH process. The impact of rumours or other events on this process can be frequently described by an outlier responsible for a short-lived shift in the process mean or by a sustained change in the process variance. This calls for the use of joint schemes for the process mean and variance, such as the ones proposed by Schipper (2001) and Schipper and Schmid (2001).

Since changes in the mean and in the variance require different actions from the traders/brokers, this paper provides an account on the probabilities of misleading and unambiguous signals (PMS and PUNS) of those joint schemes, thus adding valuable insights on the out-of-control performance of those schemes.

We are convinced that this talk is of interest to business persons/traders/brokers, quality control practitioners, and statisticians alike.

Joint work with:

Beatriz Sousa (MMA; CGD);

Yarema Okhrin (Faculty of Business and Economics, University of Augsburg, Germany);

Wolfgang Schmid (Department of Statistics, European University Viadrina, Germany)

References

Schipper, S. (2001). Sequential Methods for Detecting Changes in the Volatility of Economic Time Series. Ph.D. thesis, European University, Department of Statistics, Frankfurt (Oder), Germany.

Schipper, S. and Schmid, W. (2001). Control charts for GARCH processes. Nonlinear Analysis: Theory, Methods & Applications 47, 2049-2060.

Introduz-se um modelo de computação analógico-digital em que a componente digital é o modelo padrão (e.g. máquina de Turing) e a componente analógica é o resultado de uma medição, e.g. obtida através de sensor de grandeza física. A medição atua como oráculo e a troca de informação entre a componente digital e a componente analógica decorre no tempo intrínseco ao processo físico. As medições realizadas pelo acoplamento analógico-digital podem ser executadas através de diferentes protocolos, de estocástico a determinístico, nomeadamente fazendo variar a precisão da medição entre finita e infinita. Discute-se a natureza das medições que podem ser efetuadas pelos sistemas analógico-digitais. Estabelece-se que o poder computacional destes sistemas que operam num número polinomial de passos é o das classes computacionais $\mathit{BPP//}\log^{(k)}\!\star$. Por fim discutem-se os limites da simulação computacional de sistemas físicos e comparam-se os conceitos de número mensurável segundo a abordagem de Geroch e Hartle e a nossa.

We consider a particle system which is equivalent to a process valued on the space of nonentropy solutions of the inviscid Burgers equation. Such solutions are conjectured to be relevant for the study of the KPZ fixed point. We prove ergodicity and obtain some properties of the stationary measure.

Joint work with C.-E. Bréhier (Lyon) and M. Mariani (Rome).