B-orbits in abelian nilradicals of types B, C and D: towards a conjecture of Panyushev

Let $B$ be a Borel subgroup of a semisimple algebraic group $G$ and let $\mathfrak m$ be an abelian nilradical in $\mathfrak b={\rm Lie} (B)$. Using subsets of strongly orthogonal roots in the subset of positive roots corresponding to $\mathfrak m$, D. Panyushev \cite{Pan} gives in particular classification of $B-$orbits in $\mathfrak m$ and ${\mathfrak m}^*$ and states general conjectures on the closure and dimensions of the $B-$orbits in both $\mathfrak m$ and ${\mathfrak m}^*$ in terms of involutions of the Weyl group. Using Pyasetskii correspondence between $B-$orbits in $\mathfrak m$ and ${\mathfrak m}^*$ he shows the equivalence of these two conjectures. In this Note we prove his conjecture in types $B_n, C_n$ and $D_n$ for adjoint case.Comment: 12 page

Visualizing near-coexistence of massless Dirac electrons and ultra-massive saddle point electrons

Strong singularities in the electronic density of states amplify correlation effects and play a key role in determining the ordering instabilities in various materials. Recently high order van Hove singularities (VHSs) with diverging power-law scaling have been classified in single-band electron models. We show that the 110 surface of Bismuth exhibits high order VHS with an usually high density of states divergence $\sim (E)^{-0.7}$. Detailed mapping of the surface band structure using scanning tunneling microscopy and spectroscopy combined with first-principles calculations show that this singularity occurs in close proximity to Dirac bands located at the center of the surface Brillouin zone. The enhanced power-law divergence is shown to originate from the anisotropic flattening of the Dirac band just above the Dirac node. Such near-coexistence of massless Dirac electrons and ultra-massive saddle points enables to study the interplay of high order VHS and Dirac fermions

Right atrial effects on right ventricular ejection fraction derived from thermodilution measurements

The thermodilution technique provides a convenient means to monitor cardiac output, right ventricular (RV) ejection fraction (EF), and volumes at the bedside. To calculate RVEF from the pulmonary artery temperature curve, the bolus thermodilution technique assumes that right atrial (RA) temperature returns to baseline value within 1 beat following the cold saline injection. The authors hypothesized that this assumption is the reason why the thermodilution technique consistently underestimates RVEF. A theoretical analysis and animal study. Laboratory, university, multi-institutional. Animals. Cold saline injections. In 2 porcine experiments, after a rapid injection of cold saline into right atrium, RA temperature took several heartbeats to return to baseline. In a theoretical analysis, if after the cold saline injection RA temperature returned to baseline in 1 beat (RAEF = 1), then thermodilution-derived RVEF(T) = actual RVEF(A). In contrast, if RA temperature took several beats to return to baseline (RAEF = RVEF), then RVEF(T) consistently underestimated RVEF(A). A least square fit of RVEF(A) versus RVEF(T) resulted in RVEF(A) = 1.0 x RVEF(T) + 0.11. Applying this correction (adding 0.11 to RVEF(T)) to the data gave relatively small errors in estimating RVEF over a wide EF range. After injecting cold saline into the right atrium, RA temperature takes several heart beats to return to baseline temperature, leading to underestimating RVEF and overestimating RV volumes. The pulsed thermal energy approach by injecting heat into the RV avoids these problems, but the impact of its small temperature signal on RVEF measurements needs to be determined