Structure constants for Chern classes of Schubert cells

AbstractThe first author with B. Sturmfels studied in [16] the variety of matrices with eigenvectors in a given linear subspace, called the Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the irreducibility of the Kalman variety and computing its codimension and degree. Furthermore, we consider the Kalman variety of tensors having singular t-tuples with the first component in a given linear subspace and we prove analogous results, which are new even in the case of matrices. Main techniques come from Algebraic Geometry, using Chern classes for enumerative computations.

Download Full-text

Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0326 ◽

2021 ◽

Vol 76 (4) ◽

pp. 299-304

Author(s):

Fu Chen ◽

Jian-Rong Yang ◽

Zi-Fa Zhou

Keyword(s):

Crystal Field ◽

Elongation Ratio ◽

Paramagnetic Resonance ◽

Local Structures ◽

Epr Parameters ◽

Structure Constants ◽

Crystal Field Parameters ◽

Electron Paramagnetic ◽

Theoretical Results ◽

Good Agreement

Abstract The electron paramagnetic resonance (EPR) parameters (g factor g i , and hyperfine structure constants A i , with i = x, y, z) and local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) are theoretically investigated using the high order perturbation formulas of these EPR parameters for a 3d 9 ion under orthorhombically elongated octahedra. In the calculations, contribution to these EPR parameters due to the admixture of d-orbitals in the ground state wave function of the Cu2+ ion are taken into account based on the cluster approach, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied EPR parameters with the local structures of the Cu2+ centers. Based on the calculations, the Cu–H2O bonds are found to suffer the axial elongation ratio δ of about 3 and 2.9% along the z-axis, meanwhile, the planar bond lengths may experience variation ratio τ (≈3.8 and 1%) along x- and y-axis for Cu2+ center in (NH4)2Zn(SO4)2·6H2O and Rb2Zn(SO4)2·6H2O, respectively. The theoretical results show good agreement with the observed values.

Download Full-text

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

Journal of High Energy Physics ◽

10.1007/jhep07(2020)037 ◽

2020 ◽

Vol 2020 (7) ◽

Author(s):

Yunfeng Jiang ◽

Shota Komatsu ◽

Edoardo Vescovi

Keyword(s):

Structure Constants

Download Full-text

A Residue Formula for Chern Classes Associated with Logarithmic Connections

Tokyo Journal of Mathematics ◽

10.3836/tjm/1270215030 ◽

1982 ◽

Vol 05 (1) ◽

pp. 13-21 ◽

Cited By ~ 11

Author(s):

Makoto OHTSUKI

Keyword(s):

Chern Classes ◽

Residue Formula

Download Full-text

Isotope shift and hyperfine structure in the atomic spectrum of tin

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1973.0016 ◽

1973 ◽

Vol 332 (1588) ◽

pp. 129-138 ◽

Cited By ~ 20

Keyword(s):

Stable Isotopes ◽

Hyperfine Structure ◽

Nuclear Charge ◽

Light Sources ◽

Atomic Spectrum ◽

Nuclear Charge Distribution ◽

Fabry Perot ◽

Self Consistent ◽

Structure Constants ◽

Good Agreement

Three lines in the atomic spectrum of tin, λ 3262 Å, λ 3283 Å and λ 6454Å have been studied in emission under high resolution with the use of light sources containing enriched isotopic samples. Results are reported for isotope shifts in these lines for the abundant stable isotopes ( A ≽ 116). Pressure-scanned Fabry–Perot etalons provided the necessary resolution; the spectrograms for λ 6454 Å were recorded and analysed by digital techniques, and for this line hyperfine structure constants required in the interpretation of the data were also evaluated. The results for the three lines are not in good agreement with earlier work, but are shown to be self-consistent by means of a King plot. Their interpretation in terms of the nuclear charge distribution is considered in the following paper.

Download Full-text