Schur Polynomials and the Yang-Baxter equation

We show that within the six-vertex model there is a parametrized Yang-Baxter equation with nonabelian parameter group GL(2)xGL(1) at the center of the disordered regime. As an application we rederive deformations of the Weyl character formule of Tokuyama and of Hamel and King.Comment: Revised introduction; slightly changed reference

The eight-vertex model and lattice supersymmetry

We show that the XYZ spin chain along the special line of couplings J_xJ_y+J_xJ_z+J_yJ_z=0 possesses a hidden N=(2,2) supersymmetry. This lattice supersymmetry is non-local and changes the number of sites. It extends to the full transfer matrix of the corresponding eight-vertex model. In particular, it is shown how to derive the supercharges from Baxter's Bethe ansatz. This analysis leads to new conjectures concerning the ground state for chains of odd length. We also discuss a correspondence between the spectrum of this XYZ chain and that of a manifestly supersymmetric staggered fermion chain.Comment: 40 pages, 6 figures, Tik

Gender characteristics of urinary excretion of oxalates, calcium and phosphates in children and teenagers

Relevance. The risk factors for urolithiasis include an increase in the daily excretion of lithogenic metabolites. These factors have not been sufficiently studied in childhood. Methods. We conducted a study of the 24-hour urinary excretion of calcium, oxalate and phosphorus in 196 patients (median age was 9.0 [6.0; 14.0] years, boys 23.5% (46/196)) with the urinary syndrome. Results. We found a statistically significantly higher daily urinary excretion of oxalates in boys compared to girls, 18.1 [11.2; 25.6] mg/day and 14.1 [9.6; 21.3] mg/day, respectively, p = = 0.012. However, these differences manifest themselves only at the age of 10 years and older, amounting to 23.85 [11.2; 25.5] mg/day in boys and 13.91 [8.02; 18.9] mg/day in girls, p = 0.005. We did not establish gender differences in daily calcium excretion, p = 0.45. At the same time, we revealed gender differences in daily phosphorus excretion in boys compared with girls 23.25 [15.0; 38.0] mmol/day and 18.9 [10.6; 29.2] mmol/day, respectively, p = 0.013. These patterns were also typical only for the age older than 10 years – in boys 31.7 [21.1; 43.0] mmol/day, in girls 17.9 [11.6; 30.9] mmol/day, p = 0.003. Conclusions. Boys aged 10 years and older have a statistically significantly higher 24-hour urinary excretion of oxalate and phosphorus than girls. This may indicate the gender dependence of some lithogenic factors and the need for increased attention to the prevention of nephrolithiasis during early puberty