Homogeneous geodesics in solvable Lie groups

After the second author and J. Szenthe [10] proved that every homogeneous Riemannian manifold admits a homogeneous geodesic, several authors studied the set of all homogeneous geodesics in various homogeneous spaces. In this paper, we consider special examples of homogeneous spaces of solvable type of arbitrary odd dimension given in [1] and [7] and we show that their sets of homogeneous geodesics have an interesting structure, closely connected to the notion of Hadamard matrices.     

A multivariate method for relating groups of measurements connected by a causal pathway

The multivariate regression model solved by partial least squares, PLS, is extended to more than one predictor block; two algorithms are discussed in detail. The performance of the method is tested by applying it to a water quality problem. Several underlying factors are revealed. Contributions of the various ions are assigned to the different polluting run-offs.     

Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states

The method of moments of coupled-cluster equations (MMCC), which provides a systematic way of improving the results of the standard coupled-cluster (CC) and equation-of-motion CC (EOMCC) calculations for the ground- and excited-state energies of atomic and molecular systems, is described. The MMCC theory and its generalized MMCC (GMMCC) extension that enables one to use the cluster operators resulting from the standard as well as nonstandard CC calculations, including those obtained with the extended CC (ECC) approaches, are based on rigorous mathematical relationships that define the many-body structure of the differences between the full configuration interaction (CI) and CC or EOMCC energies. These relationships can be used to design the noniterative corrections to the CC/EOMCC energies that work for chemical bond breaking and potential energy surfaces of excited electronic states, including excited states dominated by double excitations, where the standard single-reference CC/EOMCC methods fail. Several MMCC and GMMCC approximations are discussed, including the renormalized and completely renormalized CC/EOMCC methods for closed- and open-shell states, the quadratic MMCC approaches, the CI-corrected MMCC methods, and the GMMCC approaches for multiple bond breaking based on the ECC cluster amplitudes.     

Structure analysis of some α‐(n‐methyl‐n‐formylaminomethyl)‐quinolines

The ¹H and ¹³C nmr spectra of the rotational isomers 3a and 3b of 6‐N‐methyl‐N‐formylaminomefhyl)‐thioquinanthrene were completely assigned with a combination of 1D and 2D nmr techniques. The key‐parts of this methodology were long‐range proton‐carbon correlations and NOE experiments with N‐methyl‐N‐formylaminomethyl substituent. The X‐ray study of 4‐methyl‐2‐N‐methyl‐N‐formylaminomethyl)quinoline 4a as well as ¹H and ¹³C nmr spectra show that N‐methyl‐N‐formylaminomethyl substituent in 4a and 4b has a different steric arrangement than the same substituent in 3a and 3b .