Asplund Functions and Projectional Resolutions of the Identity

*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.

The Structure of Information Dialogues: A Case Study

In the paper we consider the structure of information dialogues. Our study is based on Estonian dialogue corpus which contains two kinds of dialogues – transcriptions of spoken conversations, and dialogues collected with the Wizard of Oz method. We are using two ways for describing the structure of dialogues – a typology of dialogue acts, and a system of communicative strategies. We depart from the notion of communicative strategy introduced by Kristiina Jokinen in her Constructive Dialogue Model. The analysis of our empirical material shows that people are using similar communicative strategies in telephone conversations and computer interactions. In the same time, the structure of human-human conversation is much more complicated.

Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.