A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.

Towards the Noosphere of Intangible (Esotericism from Materialistic Viewpoint)

Exploration of intangible world is under the serious influence of esotericism. Mystics, religions, unrestrained use of metaphors, fairy tales, gossips, unverified and uncertified “facts” – all this needs accurate well-disposed, but sound scientific consideration. Our society really needs new ideas, new approaches and new paradigms. Technological civilization becomes more and more complicated, risky and ecologically critical. The current level of AI research cannot guarantee successful solution of societal control and management. Besides, the human being itself practically did not change its mental and psychological abilities for many thousands years. We can lose control over our society and its technology, if we do not change cardinally ourselves. In this text, I tried to approach this problem – the problem of our noosphere from materialistic viewpoint.

Starting from Scratch: Creating an Information Technology Infrastructure for MEMS-Related Research and Development

Micro Electro Mechanical Systems (MEMS) have already revolutionized several industries through miniaturization and cost effective manufacturing capabilities that were never possible before. However, commercially available MEMS products have only scratched the surface of the application areas where MEMS has potential. The complex and highly technical nature of MEMS research and development (R&D) combined with the lack of standards in areas such as design, fabrication and test methodologies, makes creating and supporting a MEMS R&D program a financial and technological challenge. A proper information technology (IT) infrastructure is the backbone of such research and is critical to its success. While the lack of standards and the general complexity in MEMS R&D makes it impossible to provide a “one size fits all” design, a systematic approach, combined with a good understanding of the MEMS R&D environment and the relevant computer-aided design tools, provides a way for the IT architect to develop an appropriate infrastructure.

An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

This paper presents the main achievements of the author’s PhD dissertation. The work is dedicated to mathematical and semi-empirical approaches applied to the case of Bulgarian wildland fires. After the introductory explanations, short information from every chapter is extracted to cover the main parts of the obtained results. The methods used are described in brief and main outcomes are listed. ACM Computing Classification System (1998): D.1.3, D.2.0, K.5.1.

Algorithmic Methods in Queues and in the Exploration of Point Processes

This is a review of methodology for the algorithmic study of some useful models in point process and queueing theory, as discussed in three lectures at the Summer Institute at Sozopol, Bulgaria. We provide references to sources where the extensive details of this work are found. For future investigation, some open problems and new methodological approaches are proposed.

Mapping and Merging of Anatomical Ontologies

This article presents the principal results of the Ph.D. thesis Intelligent systems in bioinformatics: mapping and merging anatomical ontologies by Peter Petrov, successfully defended at the St. Kliment Ohridski University of Sofia, Faculty of Mathematics and Informatics, Department of Information Technologies, on 26 April 2013.

Policy Framework and Roadmap for Open Access, Open Research Data and Open Science

Overview of the growth of policies and a critical appraisal of the issues affecting open access, open data and open science policies. Example policies and a roadmap for open access, open research data and open science are included.

Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size

2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.