Infinite Transitivity on Affine Varieties

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

Carbon sequestration in Himalaya's alpine meadows: Mitigating cropping encroachment on pastures in Northern Pakistan

Rangelands store about 30% of the world’s carbon and support over 120 million pastoralists globally. Adjusting the management of remote alpine pastures bears a substantial climate change mitigation potential that can provide livelihood support for marginalized pastoralists through carbon payment. Landless pastoralists in Northern Pakistan seek higher income by cropping potatoes and peas over alpine pastures. However, tilling steep slopes without terracing exposes soil to erosion. Moreover, yields decline rapidly requiring increasing fertilizer inputs. Under these conditions, carbon payment could be a feasible option to compensate pastoralists for renouncing hazardous cropping while favoring pastoral activities. The study quantifies and compares C on cropped and grazed land. The hypothesis was that cropping on alpine pastures reduces former carbon storage. The study area located in the Naran valley of the Pakistani Himalayas receives an annual average of 819 mm of rain and 764 mm of snow. Average temperatures remain below 0°C from November to March while frost may occur all year round. A total of 72 soil core samples were collected discriminating land use (cropping, pasture), aspect (North, South), elevation (low 3000, middle 3100, and high 3200 m a.s.l.), and soil depth (shallow 0-10, deep 10-30 cm). Thirty six biomass samples were collected over the same independent variables (except for soil depth) using a 10x10x20 cm steal box inserted in the ground for each sample. Aboveground biomass and coarse roots were separated from the soil aggregate and oven-dried. Soil organic carbon (SOC) and biomass carbon (BC) were estimated through a potassium dichromate oxidation treatment. The samples were collected during the second week of October 2010 at the end of the grazing and cropping season and before the first snowfall. The data was statistically analyzed by means of a one-way analysis of variance. Results show that all variables taken separately have a significant effect on mean SOC [%]: crop/pasture 1.33/1.6, North/South 1.61/1.32, low/middle/high 1.09/1.62/1.68, shallow/deep 1.4/1.53. However, for BC, only land use has a significant effect with more than twice the amount of carbon in pastures [g m-2]: crop/pasture 127/318. These preliminary findings suggest that preventing the conversion of pastures into cropping fields in the Naran valley avoids an average loss of 12.2 t C ha-1 or 44.8 t CO2eq ha-1 representing a foreseeable compensation of 672 € ha-1 for the Naran landless pastoralists who would renounce cropping. The ongoing study shall provide a complete picture for carbon payment integrating key aspects such as the rate of cropping encroachment over pastures per year, the methane leakage from the system due to livestock enteric fermentation, the expected cropping income vs. livestock income and the transaction costs of implementing the mitigation project, certifying it, and verifying carbon credits. A net present value over an infinite time horizon for the mitigation scenario shall be estimated on an iterative simulation to consider weather and price uncertainties. The study will also provide an estimate of the minimum price of carbon at which pastoralists would consider engaging in the mitigation activity.

The Meta in Meta-object Architectures

Behavioral reflection is crucial to support for example functional upgrades, on-the-fly debugging, or monitoring critical applications. However the use of reflective features can lead to severe problems due to infinite metacall recursion even in simple cases. This is especially a problem when reflecting on core language features since there is a high chance that such features are used to implement the reflective behavior itself. In this paper we analyze the problem of infinite meta-object call recursion and solve it by providing a first class representation of meta-level execution: at any point in the execution of a system it can be determined if we are operating on a meta-level or base level so that we can prevent infinite recursion. We present how meta-level execution can be represented by a meta-context and how reflection becomes context-aware. Our solution makes it possible to freely apply behavioral reflection even on system classes: the meta-context brings stability to behavioral reflection. We validate the concept with a robust implementation and we present benchmarks.

Spontaneous supersymmetry breaking in the 2d N=1 Wess-Zumino model

We study the phase diagram of the two-dimensional N = 1 Wess-Zumino model using Wilson fermions and the fermion loop formulation. We give a complete non-perturbative determination of the ground state structure in the continuum and infinite volume limit. We also present a determination of the particle spectrum in the supersymmetric phase, in the supersymmetry broken phase and across the supersymmetry breaking phase transition. In the supersymmetry broken phase we observe the emergence of the Goldstino particle.

High-Pressure Behavior and Phase Stability of Al5BO9, a Mullite-Type Ceramic Material

Phase stability, elastic behavior, and pressure-induced structural evolution of synthetic boron-mullite Al5BO9 (a = 5.6780(7), b = 15.035(6), and c =7.698(3) Å, space group Cmc21, Z = 4) were investigated up to 25.6(1) GPa by in situ single-crystal synchrotron X-ray diffraction with a diamond anvil cell (DAC) under hydrostatic conditions. No evidence of phase transition was observed up to 21.7(1) GPa. At 25.6(1) GPa, the refined unit-cell parameters deviated significantly from the compressional trend, and the diffraction peaks appeared broader than at lower pressure. At 26.7(1) GPa, the diffraction pattern was not indexable, suggesting amorphization of the material or a phase transition to a high-pressure polymorph. Fitting the P–V data up to 21.7(1) GPa with a second-order Birch–Murnaghan Equation-of-State, we obtained a bulk modulus KT0 = 164(1) GPa. The axial compressibilities, here described as linearized bulk moduli, are as follows: KT0(a) = 244(9), KT0(b) = 120(4), and KT0(c) = 166(11) GPa (KT0(a):KT0(b):KT0(c) = 2.03:1:1.38). The structure refinements allowed a description of the main deformation mechanisms in response to the applied pressure. The stiffer crystallographic direction appears to be controlled by the infinite chains of edge-sharing octahedra running along [100], making the structure less compressible along the a-axis than along the b- and c-axis.

New copper(II) complexes with isoconazole: Synthesis, structures and biological properties

There is an increasing demand for novel metal-based complexes with biologically relevant molecules in technology and medicine. Three new Cu(II) coordination compounds with antifungal agent isoconazole (L), namely mononuclear complexes CuCl2(L)(2) (1), and Cu(O2CMe)(2)(L)(2)center dot 2H(2)O (2) and coordination polymer Cu(pht)(L)(2)(n) (3) (where H(2)pht - o-phthalic acid) were synthesized and characterized by IR spectroscopy, thermogravimetric analysis and X-ray crystallography. X-ray analysis showed that in all complexes, the isoconazole is coordinated to Cu(II) centres by a N atom of the imidazole fragment. In complex I, the square-planar environment of Cu(II) atoms is completed by two N atoms of isoconazole and two chloride ligands, whereas the Cu(II) atoms are coordinated by two N atoms from two isoconazole ligands and two O atoms from the different carboxylate residues: acetate in 2 and phthalate in 3. The formation of an infinite chain through the bridging phthalate ligand is observed in 3. The biosynthetic ability of micromycetes Aspergillus niger CNMN FD 10 in the presence of the prepared complexes 1-3 as well as the antifungal drug isoconazole were studied. Complexes 2 and 3 accelerate the biosynthesis of enzymes (beta-glucosidase, xylanase and endoglucanase) by this fungus. Moreover, a simplified and improved method for the preparation of isoconazole nitrate was developed.

Flux and resident injection in gaseous advection experiments

The occurrence of gaseous pollutants in soils has stimulated many experimental activities, including forced ventilation in the field as well as laboratory transport experiments with gases. The dispersion coefficient in advective-dispersive gas phase transport is often dominated by molecular diffusion, which leads to a large overall dispersivity gamma. Under such conditions it is important to distinguish between flux and resident modes of solute injection and detection. The influence of the inlet type oil the macroscopic injection mode was tested in two series of column experiments with gases at different mean flow velocities nu. First we compared infinite resident and flux injections, and second, semi-infinite resident and flux injections. It is shown that the macroscopically apparent injection condition depends on the geometry of the inlet section. A reduction of the cross-sectional area of the inlet relative to that of the column is very effective in excluding the diffusive solute input, thus allowing us to use the solutions for a flux Injection also at rather low mean flow velocities nu. If the whole cross section of a column is exposed to a large reservoir like that of ambient air, a semi-infinite resident injection is established, which can be distinguished from a flux injection even at relatively high velocities nu, depending on the mechanical dispersivity of the porous medium.

Scheduling the production of rolling ingots: Industrial context, model, and solution method

We study a real-world scheduling problem arising in the context of a rolling ingots production. First we review the production process and discuss peculiarities that have to be observed when scheduling a given set of production orders on the production facilities. We then show how to model this scheduling problem using prescribed time lags between operations, different kinds of resources, and sequence-dependent changeovers. A branch-and-bound solution procedure is presented in the second part. The basic principle is to relax the resource constraints by assuming infinite resource availability. Resulting resource conflicts are then stepwise resolved by introducing precedence relationships among operations competing for the same resources. The algorithm has been implemented as a beam search heuristic enumerating alternative sets of precedence relationships.

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).