Supersymmetric quantum theory and (non-commutative) differential geometry

We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in algebraic data consisting of an algebra of functions on a manifold and a family of supersymmetry generators represented on a Hilbert space. We show that known types of differential geometry can be classified in terms of the supersymmetries they exhibit. Replacing commutative algebras of functions by non-commutative *-algebras of operators, while retaining supersymmetry, we arrive at a formulation of non-commutative geometry encompassing and extending Connes' original approach. We explore different types of non-commutative geometry and introduce notions of non-commutative manifolds and non-commutative phase spaces. One of the main motivations underlying our work is to construct mathematical tools for novel formulations of quantum gravity, in particular for the investigation of superstring vacua.Comment: 125 pages, Plain TeX fil

Supersymmetric quantum theory and non-commutative geometry

Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes' non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)Kaehler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in some detail.Comment: 77 pages, PlainTeX, no figures; present paper is a significantly extended version of the second half of hep-th/9612205. Assumptions in Sect. 2.2.5 clarified; final version to appear in Commun.Math.Phy

The Gravitational Sector in the Connes-Lott Formulation of the Standard Model

We study the Riemannian aspect and the Hilbert-Einstein gravitational action of the non-commutative geometry underlying the Connes-Lott construction of the action functional of the standard model. This geometry involves a two-sheeted, Euclidian space-time. We show that if we require the space of forms to be locally isotropic and the Higgs scalar to be dynamical, then the Riemannian metrics on the two sheets of Euclidian space-time must be identical. We also show that the distance function between the two sheets is determined by a single, real scalar field whose VEV sets the weak scale.Comment: Latex file, 29 page

Family Carabodidae (Acari: Oribatida) V. The genus Congocepheus Balogh, 1958 (second part), with a redescription of Congocepheus involutus Mahunka, 1997, and descriptions of two new species

The species Congocepheus involutus Mahunka, 1997 is redescribed, and two newspecies are described, Congocepheus gabonensis n. sp. and Congocepheus ektactesin. sp., using optical and scanning electron microscopy.La Famille Carabodidae (Acari: Oribatida) V. Le genre Congocepheus, Balogh, 1958 (deuxième partie) avec la redescription de Congocepheus involutus Mahunka, 1997 et les descriptions de deux nouvelles espèces. L'espèce Congocepheus involutus Mahunka, 1997 est redécrite et deux espèces nouvelles sont décrites Congocepheus gabonensis n. sp. et Congocepheus ektactesi n. sp. sur la base d'observations en microscopie optique et électronique à balayage.Fil: Fernandez, Nestor Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Rioja; ArgentinaFil: Theron, Pieter. North-West University; SudáfricaFil: Rollard, Christine. Centre National de la Recherche Scientifique; Francia. Museum National D; FranciaFil: Tiedt, Louvrens. North-West University; Sudáfric

Umbilical Cord Mercury Concentration as Biomarker of Prenatal Exposure to Methylmercury

Biomarkers are often applied to assess prenatal exposure to methylmercury in research and surveillance. In a prospective study in the Faroe Islands, the main exposure biomarkers were the mercury concentrations in cord blood and maternal hair obtained at parturition. We have now supplemented these exposure biomarkers with mercury analyses of umbilical cord tissue from 447 births. In particular, when expressed in relation to the dry weight of the tissue, the cord mercury concentration correlated very well with that in cord blood. Structural equation model analysis showed that these two biomarkers have average total imprecision of about 30%, which is much higher than the laboratory error. The imprecision of the dry-weight–based concentration was lower than that of the wet-weight–based parameter, and it was intermediate between those of the cord blood and the hair biomarkers. In agreement with this finding, regression analyses showed that the dry-weight cord mercury concentration was almost as good a predictor of methylmercury-associated neuropsychologic deficits at 7 years of age as was the cord-blood mercury concentration. Cord mercury analysis can therefore be used as a valid measure of prenatal methylmercury exposure, but appropriate adjustment for the imprecision should be considered

Further Comments on Engineering Shape Anisotropy of Fe3o4-Γ-Fe2o3hollow Nanoparticles for Magnetic Hyperthermia

In their earlier paper, Niraula et al. (ACS Appl. Nano Mater. 2021, 4, 3148-3158) described the morphological, compositional, and magnetic properties of three different magnetite/maghemite or Fe3O4/γ-Fe2O3, hollow nanoparticles, referred to herein as nanorings, short-nanotubes, and long-nanotubes. Scanning electron microscopy indicates that these nanoparticles have lengths of 275 ± 51, 411 ± 92, and 515 ± 98 nm and outer diameters of 201 ± 55, 251 ± 46, and 229 ± 42 nm, respectively, dimensions that are all rather similar in view of their distributions, as is shown in a figure herein. Further, the lengths indicate that these nanoparticles are far larger than what are normally considered nanoparticles. Rietveld refinement of the powder X-ray diffraction patterns presumably reveals the presence of Fe3O4, γ-Fe2O3, and small amounts of α-Fe2O3in some of the nanoparticles; unfortunately, the lack of refinement details make the validity of these compositions at least problematic. The published iron-57 Mössbauer spectral analysis is marginal. An alternative analysis of both the reported X-ray lattice parameters and the Mössbauer spectral results for the three nanoparticles in terms of solid solutions of magnetite and maghemite, AFe3+[BFe1-3δ2+Fe1+2δ3+□δ]O4, where □ represents a vacancy, δ= 0 corresponds to magnetite, Fe3O4, and δ= 0.333 corresponds to maghemite, γ-Fe2O3, is proposed herein. In the presence of the expected magnetite Verwey transition, the Mössbauer spectral analysis is formulated with the stoichiometry AFe3+[BFe2(1-3δ)2.5+Fe5δ3+□δ]O4, and as far as we can tell, this model is consistent with the Rietveld X-ray diffraction analysis. The values of δ= 0.28(2) and 0.30(1) obtained from the X-ray diffraction and Mössbauer spectral analyses, respectively, indicate that the composition of the nanoparticles is very close to γ-Fe2O3, in contrast to the earlier conclusion. During the course of this reformulation, numerous errors in the mathematical expressions, and in some cases their subsequent misuse, have been discovered and corrected herein whenever possible

A liquid crystal analogue of the cosmic string

We consider the propagation of light in a anisotropic medium with a topological line defect in the realm of geometrical optics. It is shown that the effective geometry perceived by light propagating in such medium is that of a spacial section of the cosmic string spacetime.Comment: 3 pages, 2 figures. Modern Physics Letters A, accepted for publicatio

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available