Sturm bounds for Siegel modular forms of degree 2 and odd weights

Mathematische Zeitschrift - We correct the proof of the theorem in the previous paper presented by Kikuta, which concerns Sturm bounds for Siegel modular forms of degree 2 and of even weights...     

Formal Total Synthesis of (−)‐Taxol through Pd‐Catalyzed Eight‐Membered Carbocyclic Ring Formation

A formal total synthesis of (?)‐taxol by a convergent approach utilizing Pd‐catalyzed intramolecular alkenylation is described. Formation of the eight‐membered carbocyclic ring has been a problem in the convergent total synthesis of taxol but it was solved by the Pd‐catalyzed intramolecular alkenylation of a methyl ketone affording the cyclized product in excellent yield (97 %), indicating the high efficiency of the Pd‐catalyzed intramolecular alkenylation. Rearrangement of the epoxy benzyl ether through a 1,5‐hydride shift, generating the C3 stereogenic center and subsequently forming the C1–C2 benzylidene, was discovered and utilized in the preparation of a substrate for the Pd‐catalyzed reaction.     

Graph Neural Networks with Multiple Feature Extraction Paths for Chemical Property Estimation

Feature extraction is essential for chemical property estimation of molecules using machine learning. Recently, graph neural networks have attracted attention for feature extraction from molecules. However, existing methods focus only on specific structural information, such as node relationship. In this paper, we propose a novel graph convolutional neural network that performs feature extraction with simultaneously considering multiple structures. Specifically, we propose feature extraction paths specialized in node, edge, and three-dimensional structures. Moreover, we propose an attention mechanism to aggregate the features extracted by the paths. The attention aggregation enables us to select useful features dynamically. The experimental results showed that the proposed method outperformed previous methods.     

Symmetric and Skew‐Symmetric ‐Matrices with Large Determinants

We show that the existence of ‐matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum.     

Raman studies of lattice and local vibrational modes of GaInNAs prepared by molecular beam epitaxy

Polarized Raman spectra have been studied on the lattice-matched Ga_0.94In_0.06N_0.025As_0.975 epitaxial layers grown on (100) GaAs by molecular beam epitaxy. Polarization dependence of TO and LO phonon modes has been examined. The N-related local vibrational mode (LVM) in GaInNAs has been studied with emphasis on the light polarization and the effect of the thermal annealing. The thermal annealing-induced change of the N-related LVM in GaInNAs is discussed in terms of the local atomic arrangement around N atoms.