Related papers: Achievement sets -- current results and open probl…
A list of open problems in the field of analysis of boolean functions, compiled February 2012 for the Simons Symposium.
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…
The main aspect of this paper is to introduce a new generalisation of nano open sets namely, nano h-open sets. These newly generalised sets serve as the foundation for the definition of nano h-continuous functions and some results involving…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years
Wearable devices are a trending topic in both commercial and academic areas. Increasing demand for innovation has led to increased research and new products, addressing new challenges and creating profitable opportunities. However, despite…
We survey recent advances in the theory of graph and hypergraph decompositions, with a focus on extremal results involving minimum degree conditions. We also collect a number of intriguing open problems, and formulate new ones.
We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their…
We give a survey on recent developments in the model theory of valued fields since the introduction of the notion of ``tame valued field'', and of the modifications and generalizations of this notion.
We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from…
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…
We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal achievement sets with the notion of ideally supported sum…
We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.
In the past few years, the research on sober spaces and well-filtered spaces has got some breakthrough progress. In this paper, we shall present a brief summarising survey on some of such development. Furthermore, we shall pose and…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
In recent years, the interest in developing adaptive solutions for online testing has grown significantly in the industry. While the advances related to this relative new technology have been developed in multiple domains, it lacks in the…
We survey recent developments on the Restriction conjecture.