Inversion principles and introduction rules

Following Gentzen’s practice, borrowed from intuitionist logic, Prawitz takes the introduction rule(s) for a connective to show how to prove a formula with the connective dominant. He proposes an inversion principle to make more exact Gentzen’s talk of deriving elimination rules from introduction rules. Here I look at some recent work pairing Gentzen’s introduction rules with general elimination rules. After outlining a way to derive Gentzen’s own elimination rules from his introduction rules, I give a very different account of introduction rules in order to pair them with general elimination rules in such a way that elimination rules can be read off introduction rules, introduction rules can be read off elimination rules, and both sets of rules can be read off classical truth-tables. Extending to include quantifiers, we obtain a formulation of classical first-order logic with the subformula property

On the spatial distribution of minor species in Jupiter's troposphere as inferred from Juno JIRAM data

The spatial distribution of water, ammonia, phosphine, germane, and arsine in the Jupiter's troposphere has been inferred from the Jovian Infrared Auroral Mapper (JIRAM) Juno data. Measurements allow us to retrieve the vertically averaged concentration of gases between ~3 and 5 bars from infrared‐bright spectra. Results were used to create latitudinal profiles. The water vapor relative humidity varies with latitude from <1% to over 15%. At intermediate latitudes (30–70°) the water vapor maxima are associated with the location of cyclonic belts, as inferred from mean zonal wind profiles (Porco et al., 2003). The high‐latitude regions (beyond 60°) are drier in the north (mean relative humidity around 2–3%) than the south, where humidity reaches 15% around the pole. The ammonia volume mixing ratio varies from 1 × 10−4 to 4 × 10−4. A marked minimum exists around 10°N, while data suggest an increase over the equator. The high‐latitude regions are different in the two hemispheres, with a gradual increase in the south and more constant values with latitude in the north. The phosphine volume mixing ratio varies from 4 × 10−7 to 10 × 10−7. A marked minimum exists in the North Equatorial Belt. For latitudes poleward 30°S and 30°N, the northern hemisphere appears richer in phosphine, with a decrease toward the pole, while the opposite is observed in the south. JIRAM data indicate an increase of germane volume mixing ratio from 2 × 10−10 to 8 × 10−10 from both poles to 15°S, with a depletion centered around the equator. Arsine presents the opposite trend, with maximum values of 6 × 10−10 at the two poles and minima below 1 × 10−10 around 20°S

On the clouds and ammonia in Jupiter’s upper troposphere from Juno JIRAM reflectivity observations

We analyse spectra measured by the Jovian Infrared Auroral Mapper (JIRAM, a payload element of the NASA Juno mission) in the 3150–4910 cm−1 (2.0–3.2 μm) range during the perijiove passage of 2016 August. Despite modelling uncertainties, the quality and the relative uniformity of the data set allow us to determine several parameters characterizing the Jupiter’s upper troposphere in the latitude range of 35°S–30°N. Ammonia relative humidity at 500 millibars varies between 5 per cent to supersaturation beyond 100 per cent for about 3 per cent of the processed spectra. Ammonia appears depleted over belts and relatively enhanced over zones. Local variations of ammonia, arguably associated with local dynamics, are found to occur in several locations on the planet (Oval BA, South Equatorial Belt). Cloud altitude, defined as the level where aerosol opacity reaches unit value at 3650 cm−1 (2.74 μm), is maximum over the Great Red Spot (>20 km above the 1 bar level) and the zones (15 km), while it decreases over the belts and towards higher latitudes. The aerosol opacity scale height suggests more compact clouds over zones and more diffuse clouds over belts. The integrated opacity of clouds above the 1.3-bar pressure level is found to be minimum in regions where thermal emission of the deeper atmosphere is maximum. The opacity of tropospheric haze above the 200-mbar level also increases over zones. Our results are consistent with a Hadley-type circulation scheme previously proposed in literature for belts and zones, with clear hemisphere asymmetries in cloud and haze

Potassium Use Efficiency of Plants

International audienceThere are many terms used to define aspects of potassium (K) use efficiency of plants. The terms used most frequently in an agricultural context are (1) agronomic K use efficiency (KUE), which is defined as yield per unit K available to a crop and is numerically equal to the product of (2) the K uptake efficiency (KUpE) of the crop, which is defined as crop K content per unit K available and (3) its K utilization efficiency (KUtE), which is defined as yield per unit crop K content. There is considerable genetic variation between and within plant species in KUE, KUpE, and KUtE. Root systems of genotypes with greatest KUpE often have an ability (1) to exploit the soil volume effectively, (2) to manipulate the rhizosphere to release nonexchangeable K from soil, and (3) to take up K at low rhizosphere K concentrations. Genotypes with greatest KUtE have the ability (1) to redistribute K from older to younger tissues to maintain growth and photosynthesis and (2) to reduce vacuolar K concentration, while maintaining an appropriate K concentration in metabolically active subcellular compartments, either by anatomical adaptation or by greater substitution of K with other solutes in the vacuole. Genetic variation in traits related to KUpE and KUtE might be exploited in breeding crop genotypes that require less K fertilizer. This could reduce fertilizer costs, protect the environment, and slow the exhaustion of nonrenewable resources