Genus bounds for minimal surfaces arising from min-max constructions

In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubistein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces. This result is proved in the second part of the paper.Comment: Accepted for publication on Journal for Pure and Applied Mathematic

Repository profile: University of Glasgow: "Enlighten" IR & Research System

The University of Glasgow has established the “Enlighten” IR and Research system. The IR holds 72,000 items for institutional peer-reviewed journal articles, published conference papers, books and book chapters.<p></p> The Research System is an in-house-built system holding research information for institutional research activity, including people, organisations, projects and outputs. It is dynamically linked to the Enlighten IR.<p></p&gt

Russian manufacturing and the threat of ‘Dutch disease’: a comparison of competitiveness developments in Russian and Ukrainian industry

This paper examines the development of Russian industry in comparison with that of Ukrainian industry during 1995–2004 in an effort to ascertain to what extent, if any, Russian manufacturing showed signs of succumbing to ‘Dutch disease’. Ukraine and Russia began the market transition with broadly similar institutions, industrial structures and levels of technology, and the economic reforms implemented in the two countries were also similar, although Ukraine was reckoned to lag behind Russia in many areas. The main difference between them is Russia’s far greater resource wealth. It follows that differences in industrial development since 1991 may to some degree be attributable to differences in initial natural resource endowments. In short, Ukraine could provide a rough approximation of how a resource-poor Russia might have developed over the transition

Admissible Clustering of Aggregator Components: A Necessary and Sufficient Stochastic Semi-Nonparametric Test for Weak Separability.

In aggregation theory, the admissibility condition for clustering together components to be aggregated is blockwise weak separability, which also is the condition needed to separate out sectors of the economy. Although weak separability is thereby of central importance in aggregation and index number theory and in econometrics, prior attempts to produce statistical tests of weak separability have performed poorly in Monte Carlo studies. This paper deals with semi- nonparametric tests for weak separability. It introduces both a necessary and su¢ cient test, and a fully stochastic procedure allowing to take into account measurement error. Simulations show that the test performs well, even for large measurement errors.weak separability, quantity aggregation, clustering, sectors, index number theory, semi-nonparametrics

The observable structure of persistence modules

In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However, unlike persistence modules indexed over a totally ordered finite set or the natural numbers, such diagrams do not provide a complete invariant of q-tame modules. The purpose of this paper is to show that the category of persistence modules can be adjusted to overcome this issue. We introduce the observable category of persistence modules: a localization of the usual category, in which the classical properties of q-tame modules still hold but where the persistence diagram is a complete isomorphism invariant and all q-tame modules admit an interval decomposition

Review Article: MHD Wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a β=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing