Generalized DPW method and an application to isometric immersions of space forms

Let $G$ be a complex Lie group and $\Lambda G$ denote the group of maps from the unit circle ${\mathbb S}^1$ into $G$, of a suitable class. A differentiable map $F$ from a manifold $M$ into $\Lambda G$, is said to be of \emph{connection order $(_a^b)$} if the Fourier expansion in the loop parameter $\lambda$ of the ${\mathbb S}^1$-family of Maurer-Cartan forms for $F$, namely F_\lambda^{-1} \dd F_\lambda, is of the form $\sum_{i=a}^b \alpha_i \lambda^i$. Most integrable systems in geometry are associated to such a map. Roughly speaking, the DPW method used a Birkhoff type splitting to reduce a harmonic map into a symmetric space, which can be represented by a certain order $(_{-1}^1)$ map, into a pair of simpler maps of order $(_{-1}^{-1})$ and $(_1^1)$ respectively. Conversely, one could construct such a harmonic map from any pair of $(_{-1}^{-1})$ and $(_1^1)$ maps. This allowed a Weierstrass type description of harmonic maps into symmetric spaces. We extend this method to show that, for a large class of loop groups, a connection order $(_a^b)$ map, for $a<0<b$, splits uniquely into a pair of $(_a^{-1})$ and $(_1^b)$ maps. As an application, we show that constant non-zero curvature submanifolds with flat normal bundle of a sphere or hyperbolic space split into pairs of flat submanifolds, reducing the problem (at least locally) to the flat case. To extend the DPW method sufficiently to handle this problem requires a more general Iwasawa type splitting of the loop group, which we prove always holds at least locally.Comment: Some typographical correction

Bailouts in a common market: a strategic approach

Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Socio-economic Impacts—Fisheries

Fishers and scientists have known for over 100 years that the status of fish stocks can be greatly influenced by prevailing climatic conditions. Based on historical sea surface temperature data, the North Sea has been identified as one of 20 ‘hot spots’ of climate change globally and projections for the next 100 years suggest that the region will continue to warm. The consequences of this rapid temperature rise are already being seen in shifts in species distribution and variability in stock recruitment. This chapter reviews current evidence for climate change effects on fisheries in the North Sea—one of the most important fishing grounds in the world—as well as available projections for North Sea fisheries in the future. Discussion focuses on biological, operational and wider market concerns, as well as on possible economic consequences. It is clear that fish communities and the fisheries that target them will be very different in 50 or 100 years’ time and that management and governance will need to adapt accordingly

Industry concentration and strategic trade policy in successive oligopoly

We study a policy game between exporting and importing countries in vertically linked industries. In a successive international Cournot oligopoly, we analyse incentives for using tax instruments strategically to shift rents vertically, between exporting and importing countries, and horizontally, between exporting countries. We show that the equilibrium outcome depends crucially on the relative degree of competitiveness in the upstream and downstream parts of the industry. With respect to national welfare, a more competitive upstream industry may benefit an exporting (upstream) country and harm an importing (downstream) country. On the other hand, a more competitive downstream industry may harm exporting countries.Financial support from the Norwegian Research Council, through the PETROPOL research programme, is gratefully acknowledged. The paper has been greatly improved by the suggestions of two anonymous referees. We also thank Hisashi Hokari and Frode Meland for valuable comments and suggestions

Urinary iodine concentration during pregnancy in an area of unstable dietary iodine intake in Switzerland

We prospectively investigated urinary iodine concentration (UIC) in pregnant women and in female, non-pregnant controls in the canton of Berne, Switzerland, in 1992. Mean UIC of pregnant women [205±151 μg iodine/g creatinine (μg I/g Cr); no.=153] steadily decreased from the first (236±180 μg I/g Cr; no.=31) to the third trimester (183±111 μg I/g Cr, p<0.0001; no.=66) and differed significantly from that of the control group (91±37 μg I/g Cr, p<0.0001; no.=119). UIC increased 2.6-fold from levels indicating mild iodine deficiency in controls to the first trimester, demonstrating that high UIC during early gestation does not necessarily reflect a sufficient iodine supply to the overall population. Pregnancy is accompanied by important alterations in the regulation of thyroid function and iodine metabolism. Increased renal iodine clearance during pregnancy may explain increased UIC during early gestation, whereas increased thyroidal iodine clearance as well as the iodine shift from the maternal circulation to the growing fetal-placental unit, which both tend to lower the circulating serum levels of inorganic iodide, probably are the causes of the continuous decrease of UIC over the course of pregnancy. Mean UIC in our control group, as well as in one parallel and several consecutive investigations in the same region in the 1990s, was found to be below the actually recommended threshold, indicating a new tendency towards mild to moderate iodine deficiency. As salt is the main source of dietary iodine in Switzerland, its iodine concentration was therefore increased nationwide in 1998 for the fourth time, following increases in 1922, 1965 and 198

Churn, Baby, Churn: Strategic Dynamics Among Dominant and Fringe Firms in a Segmented Industry

This paper integrates and extends the literatures on industry evolution and dominant firms to develop a dynamic theory of dominant and fringe competitive interaction in a segmented industry. It argues that a dominant firm, seeing contraction of growth in its current segment(s), enters new segments in which it can exploit its technological strengths, but that are sufficiently distant to avoid cannibalization. The dominant firm acts as a low-cost Stackelberg leader, driving down prices and triggering a sales takeoff in the new segment. We identify a “churn” effect associated with dominant firm entry: fringe firms that precede the dominant firm into the segment tend to exit the segment, while new fringe firms enter, causing a net increase in the number of firms in the segment. As the segment matures and sales decline in the segment, the process repeats itself. We examine the predictions of the theory with a study of price, quantity, entry, and exit across 24 product classes in the desktop laser printer industry from 1984 to 1996. Using descriptive statistics, hazard rate models, and panel data methods, we find empirical support for the theoretical predictions

Orbital characterization of GJ1108A system, and comparison of dynamical mass with model-derived mass for resolved binaries

We report an orbital characterization of GJ1108Aab that is a low-mass binary system in pre-main-sequence phase. Via the combination of astrometry using adaptive optics and radial velocity measurements, an eccentric orbital solution of $e$=0.63 is obtained, which might be induced by the Kozai-Lidov mechanism with a widely separated GJ1108B system. Combined with several observed properties, we confirm the system is indeed young. Columba is the most probable moving group, to which the GJ1108A system belongs, although its membership to the group has not been established. If the age of Columba is assumed for GJ1108A, the dynamical masses of both GJ1108Aa and GJ1108Ab ($M_{\rm dynamical,GJ1108Aa}=0.72\pm0.04 M_{\odot}$ and $M_{\rm dynamical,GJ1108Ab}=0.30\pm0.03 M_{\odot}$) are more massive than what an evolutionary model predicts based on the age and luminosities. We consider the discrepancy in mass comparison can attribute to an age uncertainty; the system is likely older than stars in Columba, and effects that are not implemented in classical models such as accretion history and magnetic activity are not preferred to explain the mass discrepancy. We also discuss the performance of the evolutionary model by compiling similar low-mass objects in evolutionary state based on the literature. Consequently, it is suggested that the current model on average reproduces the mass of resolved low-mass binaries without any significant offsets.Comment: Accepted in Ap