PARTITIONING THE BLOCKS OF A STEINER TRIPLE SYSTEM INTO PARTIAL PARALLEL CLASSES

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [v⁄3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks can be partitioned into partial parallel classes of size 4.

Extension and Partitioning in an Oblique Subduction Zone, New Zealand: Constraints from Three-Dimensional Numerical Modeling

Contraction, strike slip, and extension displacements along the Hikurangi margin northeast of the North Island of New Zealand coincide with large lateral gradients in material properties. We use a finite- difference code utilizing elastic and elastic-plastic rheologies to build large- scale, three-dimensional numerical models which investigate the influence of material properties on velocity partitioning within oblique subduction zones. Rheological variation in the oblique models is constrained by seismic velocity and attenuation information available for the Hikurangi margin. We compare the effect of weakly versus strongly coupled subduction interfaces on the development of extension and the partitioning of velocity components for orthogonal and oblique convergence and include the effect of ponded sediments beneath the Raukumara Peninsula. Extension and velocity partitioning occur if the subduction interface is weak, but neither develops if the subduction interface is strong. The simple mechanical model incorporating rheological variation based on seismic observations produces kinematics that closely match those published from the Hikurangi margin. These include extension within the Taupo Volcanic Zone, uplift over ponded sediments, and dextral contraction to the south.

Occurrence, gas/particle partitioning and carcinogenic risk of polycyclic aromatic hydrocarbons and their oxygen and nitrogen containing derivatives in Xi'an, central China

29 parent- and alkyl-polycyclic aromatic hydrocarbons (PAHs), 15 oxygenated-PAHs (OPAHs), 11 nitrated-PAHs (NPAHs) and 4 azaarenes (AZAs) in both the gaseous and particulate phases, as well as the particulate-bound carbon fractions (organic carbon, elemental carbon, char, and soot) in ambient air sampled in March and September 2012 from an urban site in Xi'an, central China were extracted and analyzed. The average concentrations (gaseous+particulate) of 29PAHs, 15OPAHs, 11NPAHs and 4AZAs were 1267.0±307.5, 113.8±46.1, 11.8±4.8 and 26.5±11.8ngm(-3) in March and 784.7±165.1, 67.2±9.8, 9.0±1.5 and 21.6±5.1ngm(-3) in September, respectively. Concentrations of 29PAHs, 15OPAHs and 11NPAHs in particulates were significantly correlated with those of the carbon fractions (OC, EC, char and soot). Both absorption into organic matter in particles and adsorption onto the surface of particles were important for PAHs and OPAHs in both sampling periods, with more absorption occurring in September, while absorption was always the most important process for NPAHs. The total carcinogenic risk of PAHs plus the NPAHs was higher in March. Gaseous compounds, which were not considered in most previous studies, contributed 29 to 44% of the total health risk in March and September, respectively.

Variations of clinopyroxene/melt element partitioning during assimilation of olivine/peridotite by low-Mg diorite magma

The effects of crystal chemistry and melt composition on the control of clinopyroxene/melt element partitioning (D) during the assimilation of olivine/peridotite by felsic magma have been investigated in Mesozoic high-Mg diorites from North China. The assimilation resulted in significant increase of Mg, Cr and Ni and only slight (< 30%) decrease of incompatible elements of the magma, and the compositional variations have been mirrored by the normally and reversely zoned clinopyroxene microphenocrysts formed at the early stage of the magma evolution. The Mg# [100 × Mg / (Mg + Fe)] values of the reversely zoned clinopyroxenes increase from 65 to 75 in the core to 85–90 in the high-Mg midsection, and reduce back to 73–79 at the rim. Trace element profiles across all these clinopyroxene domains have been measured by LA-ICP-MS. The melt trace element composition has been constrained from bulk rock analyses of the fine-grained low- and high-Mg diorites. Clinopyroxene/melt partition coefficients for rare earth elements (REE) and Y in the high-Mg group zonings (Mg# > 73–79, DDy < 1.2) are positively correlated with tetrahedral IVAl and increase by a factor of 3–4 as tetrahedral IVAl increases from 0.01 to 0.1 per formula unit (pfu). These systematic variations are interpreted to be controlled by the clinopyroxene composition. In contrast, partition coefficients for low-Mg group zonings (Mg# < 75–79, DDy > 1.2) are elevated by up to an order of magnitude (for REE and Y) or more (for Zr and Hf) at similar IVAl, indicating dominant control of melt composition/structure. DZr and DHf show a larger sensitivity to the compositional change of crystal and melt than DREE. DTi values for the low- and high-Mg zonings show a uniform dependence on IVAl. DSr and DLi are insensitive to the compositional change of clinopyroxene and melt, resulting in Sr depletions in the clinopyroxene zonings with elevated REE without crystallization of plagioclase. Our observations show that crystal chemistry and melt composition/structure may alternatively control clinopyroxene/melt partitioning during the assimilation of peridotite by felsic magma, and may be useful for deciphering clinopyroxene compositions and related crust–mantle processes.

Partitioning the Choice Task Makes Starbucks Coffee Taste Better

Consumers are often less satisfied with a product chosen from a large assortment than a limited one. Experienced choice difficulty presumably causes this as consumers have to engage in a great number of individual comparisons. In two studies we tested whether partitioning the choice task so that consumers decided sequentially on each individual attribute may provide a solution. In a Starbucks coffee house, consumers who chose from the menu rated the coffee as less tasty when chosen from a large rather than a small assortment. However, when the consumers chose it by sequentially deciding about one attribute at a time, the effect reversed. In a tailored-suit customization, consumers who chose multiple attributes at a time were less satisfied with their suit, compared to those who chose one attribute at a time. Sequential attribute-based processing proves to be an effective strategy to reap the benefits of a large assortment.

Apatite as an indicator of fluid salinity: An experimental study of chlorine and fluorine partitioning in subducted sediments

In order to constrain the salinity of subduction zone fluids, piston-cylinder experiments have been conducted to investigate the partitioning behaviour of Cl and F in subducted sediments. These experiments were performed at H2O-undersaturated conditions with a synthetic pelite starting composition containing 800 ppm Cl, over a pressure and temperature range of 2.5–4.5 GPa and 630–900 °C. Repetitive experiments were conducted with 1900 ppm Cl + 1000 ppm F, and 2100 ppm Cl. Apatite represents the most Cl-abundant mineral phase, with Cl concentration varying in the range 0.1–2.82 wt%. Affinity for Cl decreases over the following sequence: aqueous fluid > apatite ⩾ melt > other hydrous minerals (phengite, biotite and amphibole). It was found that addition of F to the Cl-bearing starting composition significantly lowers the Cl partition coefficients between apatite and melt (DClAp–melt) and apatite and aqueous fluid (DClAp–aq). Cl–OH exchange coefficients between apatite and melt (KdCl–OHAp–melt) and apatite and aqueous fluid (KdCl–OHAp–aq) were subsequently calculated. KdCl–OHAp–melt was found to vary from 1 to 58, showing an increase with temperature and a decrease with pressure and displaying a regular decrease with increasing H2O content in melt. Mole fractions of Cl and OH in melt were calculated based on an ideal mixing model for H2O, OH, O, Cl and F. The Cl contents of other hydrous minerals (phengite, biotite and amphibole) fall between 200 and 800 ppm, with resultant Cl partition coefficients from 0.02 to 0.49, appearing independent of the bulk Cl and F content. Preliminary data from this study show that the partitioning behaviour of F is strongly in favour of apatite relative to melt and phengite, with DFAp–melt = 15–51. Apatites from representative eclogite facies metasediments were examined and found to have low Cl contents close to ∼100 ppm. Calculations using our experimentally determined KdCl–OHAp–aq of 0.004 at 2.5 GPa, 630 °C indicate a low salinity character (0.5–2 wt% NaCleq) for the fluid formed during dehydration of subducted oceanic sediment at ∼80 km depth.

Combined effects of CO2 and temperature on carbon uptake and partitioning by the marine diatoms Thalassiosira weissflogii and Dactyliosolen fragilissimus

Carbon uptake and partitioning of two globally abundant diatom species, Thalassiosira weissflogii and Dactyliosolen fragilissimus, was investigated in batch culture experiments under four conditions: ambient (15°C, 400 µatm), high CO2 (15°C, 1000 µatm), high temperature (20°C, 400 µatm), and combined (20°C, 1000 µatm). The experiments were run from exponential growth into the stationary phase (six days after nitrogen depletion), allowing us to track biogeochemical dynamics analogous to bloom situations in the ocean. Elevated CO2 had a fertilizing effect and enhanced uptake of dissolved inorganic carbon (DIC) by about 8% for T. weissflogii and by up to 39% for D. fragilissimus. This was also reflected in higher cell numbers, build-up of particulate and dissolved organic matter, and transparent exopolymer particles. The CO2 effects were most prominent in the stationary phase when nitrogen was depleted and CO2(aq) concentrations were low. This indicates that diatoms in the high CO2 treatments could take up more DIC until CO2 concentrations in seawater became so low that carbon limitation occurs. These results suggest that, contrary to common assumptions, diatoms could be highly sensitive to ongoing changes in oceanic carbonate chemistry, particularly under nutrient limitation. Warming from 15 to 20 °C had a stimulating effect on one species but acted as a stressor on the other species, highlighting the importance of species-specific physiological optima and temperature ranges in the response to ocean warming. Overall, these sensitivities to CO2 and temperature could have profound impacts on diatoms blooms and the biological pump.