Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Neural correlates of mental transformations of the body-in-space.

Regional cerebral blood flow was measured with positron emission tomography in human subjects during the performance of a task requiring mental rotation of their hand and a perceptually equivalent control task that did not require such a process. Comparison of the distribution of cerebral activity between these conditions demonstrated significant blood flow increases in the superior parietal cortex, the intraparietal sulcus, and the adjacent rostralmost part of the inferior parietal lobule. These findings demonstrated that, in the human brain, there is a specific system of parietal areas that are involved in mental transformations of the body-in-space.

Extraterrestrial amino acids in Orgueil and Ivuna: Tracing the parent body of CI type carbonaceous chondrites

Amino acid analyses using HPLC of pristine interior pieces of the CI carbonaceous chondrites Orgueil and Ivuna have found that β-alanine, glycine, and γ-amino-n-butyric acid (ABA) are the most abundant amino acids in these two meteorites, with concentrations ranging from ≈600 to 2,000 parts per billion (ppb). Other α-amino acids such as alanine, α-ABA, α-aminoisobutyric acid (AIB), and isovaline are present only in trace amounts (<200 ppb). Carbon isotopic measurements of β-alanine and glycine and the presence of racemic (D/L ≈ 1) alanine and β-ABA in Orgueil suggest that these amino acids are extraterrestrial in origin. In comparison to the CM carbonaceous chondrites Murchison and Murray, the amino acid composition of the CIs is strikingly distinct, suggesting that these meteorites came from a different type of parent body, possibly an extinct comet, than did the CM carbonaceous chondrites.