Infinite dimensional moment problem: open questions and applications

Infinite dimensional moment problems have a long history in diverse applied areas dealing with the analysis of complex systems but progress is hindered by the lack of a general understanding of the mathematical structure behind them. Therefore, such problems have recently got great attention in real algebraic geometry also because of their deep connection to the finite dimensional case. In particular, our most recent collaboration with Murray Marshall and Mehdi Ghasemi about the infinite dimensional moment problem on symmetric algebras of locally convex spaces revealed intriguing questions and relations between real algebraic geometry, functional and harmonic analysis. Motivated by this promising interaction, the principal goal of this paper is to identify the main current challenges in the theory of the infinite dimensional moment problem and to highlight their impact in applied areas. The last advances achieved in this emerging field and briefly reviewed throughout this paper led us to several open questions which we outline here.Comment: 14 pages, minor revisions according to referee's comments, updated reference

Microservices Validation: Methodology and Implementation

Due to the wide spread of cloud computing, arises actual question about architecture, design and implementation of cloud applications. The microservice model describes the design and development of loosely coupled cloud applications when computing resources are provided on the basis of automated IaaS and PaaS cloud platforms. Such applications consist of hundreds and thousands of service instances, so automated validation and testing of cloud applications developed on the basis of microservice model is a pressing issue. There are constantly developing new methods of testing both individual microservices and cloud applications at a whole. This article presents our vision of a framework for the validation of the microservice cloud applications, providing an integrated approach for the implementation of various testing methods of such applications, from basic unit tests to continuous stability testing

Necessary and sufficient optimality conditions for optimization problems in function spaces and applications to control theory

We consider an abstract formulation for optimization problems in some Lp spaces. The variables are restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type. Second-order necessary and sufficient optimality conditions are established, where the cone of critical directions is arbitrarily close to the form which is expected from the optimization in finite dimensional spaces. The results are applied to an optimal control problem governed by a partial differential equation. Finally we compare the conditions obtained by applying this abstract procedure and those ones derived by using the methods adapted to the optimal control problem