Generic initial ideals of some monomial complete intersections in four variables

Let R = K[x ₁, x ₂, x ₃, x ₄] be the polynomial ring over a field of characteristic zero. For the ideal (x₁^a, x₂^b, x₃^c, x₄^d) ì R{(x_1^a, x_2^b, x_3^c, x_4^d) \subset R}, where at least one of a, b, c and d is equal to two, we prove that its generic initial ideal with respect to the reverse lexicographic order is the almost revlex ideal corresponding to the same Hilbert function.     

Enhancement of Chiroptical Responses of trans-Bis[(β-iminomethyl)naphthoxy]platinum(II) Complexes with Distorted Square Planar Coordination Geometry

The relationship between the coordination geometry and photophysical properties of trans-bis[(β-iminomethyl)naphthoxy]platinum(II) was investigated both experimentally and theoretically. A series of platinum(II) complexes with differently substituted iminomethyl groups were synthesized, and their photophysical properties were examined in solution, in the crystalline, and in the PMMA film-dispersed state, respectively (PMMA=poly(methyl methacrylate)). These complexes showed structure-dependent emission spectra, in which the color of the luminescence in the crystalline state varied over a range of about 40 nm depending on the specific bowl-shaped molecular structure. The chiral complexes with (R,R)- and (S,S)-configurations were found to have structure-dependent chiroptical properties both in solution and the PMMA film-dispersed state such that the intensity of circular dichroism (CD) and circularly polarized luminescence (CPL) were enhanced with bulky cyclic substituents at the nitrogen atoms. A theoretical study using density functional theory (DFT) and time-dependent (TD)-DFT calculations revealed that the enhancement of chiroptical responses is due to the amplification of the magnetic dipole moment caused by the distortion of the square planar geometry.