Schubert puzzles and integrability I: invariant trilinear forms

The puzzle rules for computing Schubert calculus on $d$-step flag manifolds, proven in [Knutson Tao 2003] for $1$-step, in [Buch Kresch Purbhoo Tamvakis 2016] for $2$-step, and conjectured in [Coskun Vakil 2009] for $3$-step, lead to vector configurations (one vector for each puzzle edge label) that we recognize as the weights of some minuscule representations. The $R$-matrices of those representations (which, for $2$-step flag manifolds, involve triality of $D_4$) degenerate to give us puzzle formulae for two previously unsolved Schubert calculus problems: $K_T(2$-step flag manifolds$)$ and $K(3$-step flag manifolds$)$. The $K(3$-step flag manifolds$)$ formula, which involves 151 new puzzle pieces, implies Buch's correction to the first author's 1999 conjecture for $H^*(3$-step flag manifolds$)$.Comment: v5: misleading sentence in the statement of theorem 2 and missing pictures in the statement of theorem 3 fixed. no results or proofs changed. v6: left vs right coset issues fixe

A note on muscle composition and colour of Holstein-Friesian, Piedmontese × Holstein-Friesian and Romagnola × Holstein-Friesian steers.

peer-reviewedHolstein-Friesian (HF), Piedmontese × Holstein-Friesian (PM) and Romagnola × Holstein-Friesian (RO) steers were compared for muscle composition and colour. A total of 120 steers in a 3 breed types (HF, PM and RO) × 2 feeding levels (low and high) × 2 finishing periods (short, S and extended, E) factorial experiment were used. Three samples of m. longissimus were taken for chemical analysis, measurement of drip loss and Hunterlab colour measurements. Muscle moisture and protein concentrations were lower, and lipid concentration was higher for HF than for PM and RO, which were similar. There were no effects of feeding level on chemical composition, but after blooming all colour values except hue were lower for the higher feeding level. The E finishing period reduced moisture, protein, drip-loss, L (lightness), a (redness) and chroma values. It is concluded that PM and RO had similar muscle composition but HF had a higher lipid concentration. Feeding level had few effects on muscle composition, but extended finishing increased all measures of fatness and reduced colour values

Influence of Fr\"ohlich polaron coupling on renormalized electron bands in polar semiconductors. Results for zincblende GaN

\ni We develop a simple method to study the zero-point and thermally renormalized electron energy $\varepsilon_{\mathbf{k}n}(T)$ for $\mathbf{k}n$ the conduction band minimum or valence maximum in polar semiconductors. We use the adiabatic approximation, including an imaginary broadening parameter $i\delta$ to supress noise in the density-functional integrations. Fr\"{o}hlich polaron methods provide analytic expressions for the contribution of the problematic optical phonon mode. We use this to correct the renormalization obtained from the adiabatic approximation. Test calculations are done for zincblende GaN for an 18x18x18 integration grid. The Fr\"ohlich correction is of order -0.02 eV for the zero-point energy shift of the conduction band minimum, and +0.03 eV for the valence band maximum; the correction to renormalization of the 3.28 eV gap is -0.05 eV, a significant fraction of the total zero point renormalization of -0.15 eV.Comment: Information has been added to the introduction and some material has been moved to later sections. Clarifications regarding the method have been adde

Is the Australian Forex Market Efficient? A Test of the Forward Rate Unbiasness Hypothesis

This paper features a test of the forward rate unbiasedness hypothesis (FRUH), using the Australian dollar with the United States and Japanese currencies using daily frequencies. We evaluate the FRUH on the 1-month forward rate, for both currencies, and the 3-month and 6-month forwards rates for the US dollar only. We adopt a cointegration framework for assessing the FRUH applying a cointegrating VAR model involving Johansen's ML approach. Our results indicate that in all cases the spot and forward rates are integrated of order 1. Furthermore there is evidence of cointegration and in all but one case the cointegrating vector is (1, -1). The error correction term in all cases is statistically significant and has the correct sign.Interest parity, Exchange rates, Market efficiency, Cointegration