Ueber den Einfluss des Bleiessigs bei der Bestimmung des Zuckers durch Polarisation

Ohne Zusammenfassung     

Calibration of estimator-weights via semismooth Newton method

Weighting is a common methodology in survey statistics to increase accuracy of estimates or to compensate for non-response. One standard approach for weighting is calibration estimation which represents a common numerical problem. There are various approaches in the literature available, but quite a number of distance-based approaches lack a mathematical justification or are numerically unstable. In this paper we reformulate the calibration problem as a system of nonlinear equations. Although the equations are lacking differentiability properties, one can show that they are semismooth and the corresponding extension of Newton’s method is applicable. This is a mathematically rigorous approach and the numerical results show the applicability of this method.     

Univalent Gallium and Indium Phosphane Complexes: From Pyramidal M(PPh3)3+ to Carbene‐Analogous Bent M(PtBu3)2+ (M=Ga,In) Complexes

In a new oxidative route, Ag⁺[Al(OR^F)₄]^? (R^F=C(CF₃)₃) and metallic indium were sonicated in aromatic solvents, such as fluorobenzene (PhF), to give a precipitate of silver metal and highly soluble [In(PhF)_n]⁺ salts (n=2, 3) with the weakly coordinating [Al(OR^F)₄]^? anion in quantitative yield. The In⁺ salt and the known analogous Ga⁺[Al(OR^F)₄]^? were used to synthesize a series of homoleptic PR₃ phosphane complexes [M(PR₃)_n]⁺, that is, the weakly PPh₃‐bridged [(Ph₃P)₃In–(PPh₃)–In(PPh₃)₃]²⁺ that essentially contains two independent [In(PPh₃)₃]⁺ cations or, with increasing bulk of the phosphane, the carbene‐analogous [M(PtBu₃)₂]⁺ (M=Ga, In) cations. The M^I? P distances are 27 to 29 pm longer for indium, and thus considerably longer than the difference between their tabulated radii (18 pm). The structure, formation, and frontier orbitals of these complexes were investigated by calculations at the BP86/SV(P), B3LYP/def2‐TZVPP, MP2/def2‐TZVPP, and SCS‐MP2/def2‐TZVPP levels.     

Black swans,power laws,and dragon-kings: Earthquakes,volcanic eruptions,landslides, wildfires,floods, and SOC models

Extreme events that change global society have been characterized as black swans. The frequency-size distributions of many natural phenomena are often well approximated by power-law (fractal) distributions. An important question is whether the probability of extreme events can be estimated by extrapolating the power-law distributions. Events that exceed these extrapolations have been characterized as dragon-kings. In this paper we consider extreme events for earthquakes, volcanic eruptions, wildfires, landslides and floods. We also consider the extreme event behavior of three models that exhibit self-organized criticality (SOC): the slider-block, forest-fire, and sand-pile models. Since extrapolations using power-laws are widely used in probabilistic hazard assessment, the occurrence of dragon-king events have important practical implications.