We explore the connection between the concepts “excess” and “duality gap” from epigraphical analysis and optimization, and the functional analytic concepts of weak* and weak compactness. We also discuss briefly the connection with R. C. James’s “sup theorem”.

Course construction using reusable learning objects is becoming ever more popular due to its’ efficiency. The course creator who uses this methodology may face problems due to the fact that he or she is not as intimately involved in the creation of every element of the course. In this paper we discuss one such problem faced by course creator known as “the competency gap”. Here, we define the co...

In this paper we reconsider the connectedness effect discussed by Kayne (1983), and illustrated in the examples (1)-(3). Kayne observed that in VO languages, left branch constituents are strong islands for extraction; however, an illegitimate gap inside a left branch island can be rescued by another gap embedded in a lower right branch constituent. The examples in (1)-(2) illustrate preverbal s...

A number of concepts exist regarding how urbanization can be described as a process. Understanding this process that affects billions of people and its future development in a spatial manner is imperative to address related issues such as human quality of life. In the focus of spatially explicit studies on urbanization is typically a city, a particular urban region, an agglomeration. However, g...

In this work, we achieve gap amplification for the Small-Set Expansion problem. Specifically, we show that an instance of the Small-Set Expansion Problem with completeness ε and soundness 12 is at least as difficult as Small-Set Expansion with completeness ε and soundness f (ε), for any function f (ε) which grows faster than √ ε. We achieve this amplification via random walks – the output graph...

A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter ...

Servitization in the manufacturing industry implies a shift from an offer based mainly on standard goods, to a wider value proposition composed of solutions aimed at solving specific customers’ problems, obtained by integrating tangible and intangible elements. The purpose of this paper is to investigate the servitization strategies of manufacturing firms, more specifically about: (i) how manuf...