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We present selected known results and some new observations, involving Gurariĭ Spaces. A Banach space is Gurariĭ Spaces if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the word \almost", we get the notion of a strong Gurariĭ Spaces. There exists a unique (up to isometry) separable Gurariĭ Spaces, however strong Gurariĭ Spaces cannot be separable. The structure of the class of non-separable Gurariĭ Spaces seems to be not very well understood. We discuss some of their properties and state some open questions. In particular, we characterize nonseparable Gurariĭ Spaces in terms of skeletons of separable subspaces, we construct a nonseparable Gurariĭ Spaces with a projectional resolution of the identity and we show that no strong Gurariĭ Spaces can be weakly Lindelӧf determined. Research of the first author is supported by the ESF Human Capital Operational Program grant 6/1/8.2.1./POKL/2009. peerReviewed

We propose a computational model to study (the evolution of) post-secondary education. “Consumers” who differ in quality shop around for desirable colleges or universities. “Firms” that differ in quality signal the availability of their services to desirable students. As long as they have capacity, colleges and universities make offers to students, who apply and qualify. Our model generalizes an earlier literature (namely, Vriend 1995) in an important dimension: quality, the model confirms key predictions of an analytical model that we also supply, and the model allows us to systematically explore the emergence of macro regularities and the consequences of various strategies that sellers might try. We supply three such exercises. In our baseline treatment we establish the dynamics and asymptotics of our generalized matching model. In the second treatment we study the consequences of opportunistic behavior of firms and thus demonstrate the usefulness of our computational laboratory for the analysis of this or similar questions (e.g., the problem of early admission). In the third treatment we equip some firms with economies of scale. This variant of our matching model is motivated by the entry of for-profit providers into low-quality segments of post-secondary education in the USA and by empirical evidence that, while traditional nonprofit or state-supported providers of higher education do not have significant economies of scale, the new breed of for-profit providers seems to capture economies in core functions such as curricular design, advertising, informational infrastructure, and regulatory compliance. Our computational results suggest that this new breed of providers is likely to continue to move up the quality ladder, albeit not necessarily all the way up to the top.

Microalgae are a known source of proteins, prebiotics, lipids, small molecules, anti-oxidants and bioactives with health benefits that can be harnessed for the development of functional foods, feeds, cosmeceuticals and pharmaceuticals. This review collates information on the supply, processing costs, target markets and value of microalgae, as well as microalgal proteins, lipids, vitamins and minerals. It discusses the potential impact that microalgae could have on global food and feed supply and highlights gaps that exist with regards to the use of microalgal proteins and ingredients as foods and supplements.

It is proved that epimorphisms are surjective in a range of varieties of residuated structures, including all varieties of Heyting or Brouwerian algebras of finite depth, and all varieties consisting of Goedel algebras, relative Stone algebras, Sugihara monoids or positive Sugihara monoids. This establishes the infinite deductive Beth definability property for a corresponding range of substructural logics. On the other hand, it is shown that epimorphisms need not be surjective in a locally finite variety of Heyting or Brouwerian algebras of width 2. It follows that the infinite Beth property is strictly stronger than the so-called finite Beth property, confirming a conjecture of Blok and Hoogland.

The rate of TEA+ ion transfer across the water/1,2-dichloroethane interface has been\nmeasured using steady-state cyclic voltammetry at a capillary with an orifice of nano-sized\ndimension. It was found that the average rate constant for TEA+ transfer from water to oil and\nfrom oil to water is 0.64 cm/s. The results are repeatable using the same capillary. This value\nis similar to that measured previously using electrochemical impedance spectroscopy and\nfluctuation analysis at the micro-interface.

We consider the full Navier-Stokes-Fourier system in the singular limit for the small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on the three dimensional Euclidean space. The Euler-Boussinesq approximation is identified as the limit system.