Holomorphic families of non-equivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \C^k into \C^n ($0<k<n-1$), so that for any two different parameters in the family no holomorphic automorphism of \C^n can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \C^n we derive the existence of families of holomorphic \C^*-actions on \C^n ($n\ge 5$) so that different actions in the family are not conjugate. This result is surprising in view of the long standing Holomorphic Linearization Problem, which in particular asked whether there would be more than one conjugacy class of \C^* actions on \C^n (with prescribed linear part at a fixed point)

Solving q-Virasoro constraints

We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for beta-ensembles. From free-field point of view the models considered have zero momentum of the highest weight, which leads to an extra constraint T_{-1} Z = 0. We then show how to solve these q-Virasoro constraints recursively and comment on the possible applications for gauge theories, for instance calculation of (supersymmetric) Wilson loop averages in gauge theories on D^2 \cross S^1 and S^3.Comment: 31 pag

Elliptic modular double and 4d partition functions

We consider 4d supersymmetric (special) unitary $\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of vertex operators and screening charges of the modular double version of elliptic $W_{q,t;q'}(\Gamma)$ algebras. We also consider a generating function of BPS surface defects supported on $T^2$ and show that it can be identified with a particular coherent state in the Fock module over the elliptic Heisenberg algebra.Comment: v1: 34 pages, 3 figures; v2: corrected few typos, references adde

The effect of a dietary nitrate supplementation in the form of a single shot of beetroot juice on static and dynamic apnoea performance

Introduction: The purpose of the present study was to assess the effects of acute nitrate (NO3-)-rich beetroot juice supplementation on peripheral oxygen saturation (SpO2), heart rate (HR), and pulmonary gas exchange during submaximal static and dynamic apnoea. Methods: Nine (six male, three female) trained apneists (age: 39.6 ± 8.2 years, stature: 170.4 ± 11.5cm, body mass: 72.0 ± 11.5 kg) performed three submaximal static apnoeas at 60%, 70% and 80% of the participant’s current reported personal best time, followed by three submaximal (~ 75% or personal best distance) dynamic apnoeas following the consumption of either a 140 ml concentrated NO3--rich beetroot juice (BRJ; 7.7 mmol NO3-) or a NO3--depleted placebo (PLA; 0.1 mmol NO3-) in double-blind randomised manner. HR and SpO2 were measured via fingertip pulse oximetry at the nadir, and online gas analysis was used to assess pulmonary oxygen uptake (V̇O2) during recovery following breath-holds. Results: There were no differences (P <0.05) between conditions for HR (PLA = 59 ± 11 bpm and BRJ = 61 ± 12 bpm), SpO2 (PLA = 83 ± 14% and BRJ = 84 ± 9%) or V̇O2 (PLA = 1.00 ± 0.22 L.min-1 and BRJ = 0.97 ± 0.27 L.min-1). Conclusion: The consumption of 7.7mmol of beetroot juice supplementation prior to a series of submaximal static and dynamic apnoeas did not induce a significant change in SpO2, HR and V̇O2, when compared to placebo. Therefore there is no apparent physiological response that may benefit free-divers as a result of the supplementation

Thermodynamics of Salts in Aqueous Fluids at Low Concentrations

In geothermal power plants, high-temperature aqueous fluids are extracted from boreholes in the Earth's crust and then expanded and cooled to drive turbines for electricity production. A particularly promising geothermal resource is reservoirs with vapor-like aqueous fluids under so-called superhot conditions, where temperatures and pressures reach approximately 400–600 °C and 160–440 bar. Projections suggest these reservoirs could be used to generate ten times the power of a conventional geothermal system operating below 300 °C with the same volumetric flow rate. Still, several issues must be addressed for them to become economically viable. One such issue is scaling, which refers to the accumulation of precipitated solutes that can lead to the clogging of wellbores and damage to production equipment. Precipitation is governed by solubility, which can to some extent be calculated by thermodynamic models when experimental data are lacking. However, new fundamental understanding is needed as the theoretical basis for current models breaks down under superhot conditions. In this work, a theoretically robust Helmholtz energy model is developed for sodium chloride dissolved in water vapor. It provides quantitative agreement with solubility data in the coexistence region between the vapor phase and crystalline NaCl (halite), which largely overlaps with the conditions of interest for superhot power generation. The model is derived by combining an accurate equation of state for pure water and a truncated virial equation for molecular H2O and NaCl. Interactions between H2O and NaCl are taken into account through three temperature-dependent cross virial coefficients, determined by regression to solubility data. The first of these coefficients also shows qualitative agreement with a theoretical pair potential obtained from ab initio calculations. Finally, pressure–enthalpy and pressure–entropy phase diagrams are calculated and used for discussion of the thermodynamics of halite scaling in idealized geothermal energy processes. An extension of the model beyond the vapor–halite coexistence region must consider the dissociation of salt molecules into ions. The thermodynamic behavior of the resulting electrolyte solution is in part described by the Debye–Hückel limiting law. This famous law follows from the seminal work of Debye and Hückel, which includes a rudimentary electrolyte solution model and consecutive approximations that somewhat obscure the underlying molecular-scale phenomena captured by their theory. In this work, an alternative explanation of the law is presented using a mixture of combinatorics, computer simulation, and fundamental statistical mechanics. The central claim is that a system satisfies the Debye–Hückel limiting law if the energies of its microstates follow an asymmetric distribution with a specific exponential form for negative energies. This distribution is a direct manifestation of the predominance of molecular configurations with alternating cations and anions in 3D space and the long-range nature of the Coulomb potential. The nature of this potential leads to a fundamentally different trend for the distribution of significant ion–ion interactions (with salt concentration), compared to the molecular interactions in a similar system of uncharged molecules

The statistics of the Debye-Hückel limiting law

The Debye–Hückel Limiting Law (DHLL) correctly predicts the thermodynamic behavior of dilute electrolyte solutions. Most articles and books explain this law using Peter Debye and Erich Hückel’s original formalism of linearizing the Poisson–Boltzmann equation for a simple electrolyte model. Brilliant in its own right, this approach does not fully explain which microstates contribute in the range of the Debye–Hückel theory. Notably, the original formalism does not establish the Energy Multiplicity Distribution (EMD), which is the energy distribution of a system’s microstates. This work establishes an analytical expression for the EMD that satisfies the DHLL. Specifically, an EMD that is proportional to exp(��3el) satisfies the DHLL for a monovalent electrolyte solution. Here, Uel is the effective electrostatic energy due to ion–ion interactions. The proposed proportionality shows quantitative agreement with the simulated EMDs of a Coulomb lattice gas that corresponds to an aqueous sodium chloride solution at a concentration of 3.559 × 10−4 M. The lattice gas that is used does not incorporate solvent molecules, but the Coulomb interactions are scaled through a permittivity that emulates the solvent—similar to the Debye–Hückel theory. Moreover, this work explains the proportionality by partitioning Uel into a set of energy contributions using minimal spanning graphs. This discussion on the EMD is new in the field. It widens the scope of the Debye–Hückel theory and could lead to a new parameterization option for developing equations of state.publishedVersio

Window dressing inequalities and constructing women farmers as problematic—gender in Rwanda’s agriculture policy

Rwanda is often depicted as a success story by policy makers when it comes to issues of gender. In this paper, we show how the problem of gendered inequality in agriculture nevertheless is both marginalized and instrumentalized in Rwanda’s agriculture policy. Our in-depth analysis of 12 national policies is informed by Bacchi’s What’s the problem represented to be? approach. It attests that gendered inequality is largely left unproblematized as well as reduced to a problem of women’s low agricultural productivity. The policy focuses on framing the symptoms and effects of gendered inequality and turns gender mainstreaming into an instrument for national economic growth. We argue that by insufficiently addressing the socio-political underlying causes of gendered inequality, Rwanda’s agriculture policy risks reproducing and exacerbating inequalities by reinforcing dominant gender relations and constructing women farmers as problematic and men as normative farmers. We call for the policy to approach gendered inequality in alternative ways. Drawing on perspectives in feminist political ecology, we discuss how such alternatives could allow policy to more profoundly challenge underlying structural constraints such as unequal gender relations of power, gender norms, and gender divisions of work. This would shift policy’s problematizing lens from economic growth to social justice, and from women’s shortcomings and disadvantages in agriculture to the practices and relations that perpetuate inequality. In the long term, this could lead to transformed gender norms and power relations, and a more just and equal future beyond what the dominant agricultural development discourse currently permits

Choice of tree species in the aftermath of two major storms

The forests in Götaland, the most southern part of Sweden, are dominated by Norway spruce (Picea abies (L.) H. Karst). This species is very important for the Swedish forest sector, but also associated with certain risks, such as wind-throw. Götaland was hit by the storm Gudrun in 2005, causing damages of a magnitude never experienced in the modern Swedish history. Two years later the same region suffered severe damages in another storm, Per. Due to the ownership structure in southern Sweden the reforestation efforts after the storms were largely made by small-scale private forest owners. Disproportionally high losses of Norway spruce exposed the risks associated with previous practices. In addition, reforestation grants were available through the Swedish Forest Agency that compensated for the higher regeneration costs associated with broadleaves. Despite this, the vast majority of the storm felled areas were regenerated with Norway spruce. Through qualitative interviews and subsequent analysis, this study examined how small-scale private forest owners’ reasoned in their choice of species and which factors that were of decisive importance for the final outcome. Regeneration with Norway spruce was mainly an expression of forest owners evaluating the different alternatives based on economic rationality. Past and current economic conditions have been and still are favorable for this species, and forest owners therefore relayed on experiencebased knowledge in their reforestation decision. Meanwhile, there are other contextual factors that steered forest owners towards planting spruce, such as a high browsing pressure and influence from dominant forest management norms. Regeneration with other species reflects situations where forest owners incorporated other aspects in their decision-making processes. Regeneration with broadleaves was favored by consideration of aesthetical values and an awareness of potential future risks with Norway spruce. In addition, since large areas had to be regenerated, forest owners ceased the opportunity to vent their curiosity with new species (especially exotic conifers/broadleaves) on smaller areas. The soft policy instruments that characterize Swedish forest policy also had a facilitating effect. Forest owners received information about alternatives through various pathways and the reforestation grants were of crucial importance for the owners that planted broadleaves. This study also suggests that the higher share of naturally regenerated birch found in regenerations surveys after Gudrun cannot simply be regarded as an effect of lower level of ambition, but also expresses a shift towards a more positive attitude concerning this species.Skogen i Götaland, den sydligaste delen av Sverige, domineras av Gran (Picea abies (L.) H. Karst). Denna art är mycket viktig för svensk skogsindustrin, men kopplas också samman med vissa risker, såsom en högre risk för stormfällning. 2005 så drabbades Götaland av stormen Gudrun, som orsakade skador av en omfattning som aldrig tidigare upplevts i modern svensk historia. Två år senare så drabbades samma region av stormen Per. Ägandestrukturen i södra Sverige innebar att föryngringsbesluten efter stormarna i hög grad utfördes av småskaliga skogsägare. Disproportionellt stora skador på granskog visade på riskerna med tidigare skogsbruksmetoder, samtidigt som skogsstyrelsens återväxtstöd kompenserade för lövträdens högre föryngringskostnad. Trots detta föryngrades de stormfällda områdena i mycket stor utsträckning med gran. Med kvalitativa intervjuer och efterföljande analys undersöktes i denna studie hur privata skogsägare resonerade i sina föryngringsbeslut och vilka faktorer som var av avgörande betydelse för det slutgiltiga utfallet. Föryngring med gran var främst ett uttryck för skogsägare som värderade de olika alternativen utifrån ett ekonomiskt perspektiv. Förhållandena för ett graninriktat skogsbruk har varit stabilt gynnsamma under lång tid, vilket gjorde att skogsägare planterade arten grundat i en erfarenhetsbaserad kunskap. Samtidigt så är det andra kontextuella faktorer som styrt skogsägares trädslagsval mot gran, såsom ett högt betestryck och påverkan från normer i omgivningen. Föryngring med andra arter återspeglar situationer där skogsägare vägt in andra aspekter i beslutsprocessen. Föryngring med lövträd gynnades av beaktandet av estetiska värden och en medvetenhet om framtida risker förenande med gran. Eftersom stora områden skulle föryngras så tog skogsägare tillfället i akt att prova nya arter som de var nyfikna på (framförallt exotiska barrträd/lövträd). De mjuka styrinstrument som karaktäriserar svensk skogspolitik har också haft en positiv påverkan. Skogsägare fick på olika sätt information om alternativ och återväxtstödet var av avgörande betydelse för de som planterade lövträd. Enligt den här studien så kan den högre andelen av naturligt föryngrad björk i föryngringarna efter Gudrun inte endast förklaras av en lägre ambitionsnivå i föryngringsarbetet, utan ska också ses som ett uttryck för en utveckling mot en mer positiv inställning till björk