Chemistry in four dimensions

Some chemical phenomena, awkward to rationalize, are argued to originate in the four-dimensional nature of matter in curved space-time. The problem is traced back to the separation of space and time variables in the analysis of fourdimensional events. Althoughmathematically sound, this operation is not physically valid. It destroys the essential non-classical entanglement of space and time, which is recognized in relativistic theory, but not in quantum mechanics. We show that without this approximation the state functions of quantum theory have the same quaternion structure that describes Lorentz transformation and spin. Hypercomplex formulation of four-dimensional motion eliminates several bothersome concepts, such as wave-particle duality and probability density, by providing the logical basis for non-zero commutators in non-classical systems. It shows why chiral states are undefined in quantum theory and why many solid-state transitions appear to be sterically forbidden. A brief introduction to hypercomplex algebra is given as an Appendix.http://www.springer.com/series/430hj201

Wave-mechanical model for chemistry

The strength and defects of wave mechanics as a theory of chemistry are critically examined. Without the secondary assumption of wave-particle duality, the seminal equation describes matter waves and leaves the concept of point particles undefined. To bring the formalism into line with the theory of special relativity, it is shown to require reformulation in hypercomplex algebra that imparts a new meaning to electron spin as a holistic spinor, eliminating serious current misconceptions in the process. Reformulation in the curved space-time of general relativity requires the recognition of nonlinear effects that invalidate the practice of linear combination of atomic orbitals, ubiquitous in quantum chemistry, and redefines the electron as a nondispersive wave packet, or soliton.http://link.springer.com/journal/106982016-10-30am201

Molecular shape

Molecular shape is recognized as an emergent property that complements the projection fromfour-dimensional space-time to tangent Euclidean space. Projection from hypercomplex algebra to real algebra necessitates the three-dimensional definition of concepts such as chirality, quantum uncertainty and probability density to compensate for errors of abstraction. The emergent alternative description of extranuclear charge density as spherical standing waves, optimized by a golden spiral, reveals atomic structure in line with the periodic table of the elements and underpinning the concepts of bond order, interatomic distance and stretching force constant, related to chemical interaction. The principles giving rise to molecular structure are shown to depend, like bond order, on the constructive interference of atomic wave fields, optimized by minimal adjustment to bond orders. The procedure is shown to be equivalent to the philosophy of molecular mechanics. Arguments based on the traditional interpretation of electronegativity, are presented to relate the parameters of strain-free bond lengths, dissociation energies and harmonic force constants, used in molecular mechanics, to quantum-mechanically defined ionization radii of atoms. Atomic electron densities and a bond-order function, both obtained by number-theory optimization, enable the direct calculation of interatomic distance, dissociation energy and stretching force constant for all pairwise interactions of any order. Torsional interaction determines the final shape of a molecule and presumably can only be understood as a four-dimensional effect.http://www.springer.com/series/430hj201

The structure Lacuna

Molecular symmetry is intimately connected with the classical concept of three-dimensional molecular structure. In a non-classical theory of wave-like interaction in four-dimensional space-time, both of these concepts and traditional quantum mechanics lose their operational meaning, unless suitably modified. A required reformulation should emphasize the importance of four-dimensional effects like spin and the symmetry effects of space-time curvature that could lead to a fundamentally different understanding of molecular symmetry and structure in terms of elementary number theory. Isolated single molecules have no characteristic shape and macro-biomolecules only develop robust three-dimensional structure in hydrophobic response to aqueous cellular media.http://www.mdpi.com/journal/ijm

In vitro effects of arachidonic acid and prostaglandin E2 on proliferation, osteoclast formation and bone resoption in RAW 264.7 murine macrophages

This study investigated the effects of arachidonic acid and prostaglandin E2 on osteoclast formation and bone resorption in RAW 264.7 murine pre-osteoclasts. Data obtained suggests an inhibitory effect of these compounds on osteoclastogenesis and bone resorption in the cell line tested.Die Mediese Navorsingsraad en die Navorsingsontwikkelingsprogram (Universiteit van Pretoria)http://www.satnt.ac.z

Towards refining the classification of glass trade beads imported into Southern Africa from the 8th to the 16th century AD

Tracing the origin of glass trade beads excavated at archaeological sites can contribute significantly to dating a site and reconstructing prehistoric trade routes. Wood developed a temporally sensitive bead sequence dating from the 8th to the 16th century AD for beads excavated at southern African sites that is commonly used by archaeologists to classify beads according to their morphology. In this study we develop a multidisciplinary methodology to refine the classification of glass beads based on morphology alone. Glass trade beads excavated at 11 sites along the upper reaches of the Limpopo River in east-central Botswana are used as case study. The beads were visually classified according to their morphological properties (colour, size, etc.) and analysed with Raman spectroscopy and portable X-ray fluorescence (XRF). Energy Dispersive Spectroscopy (EDS) of one bead showed that two types of glass were sintered together to form a recycled product, explaining the divergence of Raman spectra recorded on different zones. The study confirms the value of a morphological classification based on existing data sets as a first approach, but demonstrates that both Raman and XRF measurements can contribute to a more exact classification of glass beads imported into southern Africa from the East before the 17th century AD.Farahnaz Koleini and Linda C. Prinsloo acknowledge the financial contribution from the National Research Foundation (NRF) of South Africa and Philippe Colomban from EGIDE PROTEA.http://www.journals.elsevier.com//journal-of-cultural-heritage2017-05-31hb2016Anthropology and ArchaeologyPhysic

Die latere Ystertydperk in Suidoos- en Sentraal-Marico (Afrikaans)

Please read the abstract (Synopsis) in the section, 00front of this document Copyright 1998, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Boeyens, JCA 1998, Die latere Ystertydperk in Suidoos- en Sentraal-Marico (Afrikaans), DPhil thesis, University of Pretoria, Pretoria, viewed yymmdd Thesis (D Phil (Anthropology))--University of Pretoria, 2008.Anthropology and Archaeologyunrestricte

The universe in perspective

Gödel’s rotating-universe solution of Einstein’s gravitational field equations is interpreted in real projective space. The compass of inertia is shown to coincide with the involuted geodesic of the closed manifold and predicts a cosmological redshift for distant events. Other cosmological criteria of antimatter imbalance, the microwave background and nucleogenesis are satisfied in a natural way. The role of black holes in steady-state circulation, universal self-similar symmetry and the need to reinterpret astronomical data in hyperspace are discussed

Commensurability in the solar system

The features in common between the well-known Bode–Titius law, other commensurable astronomical relation- ships, and the organization of self-similar atomic systems, are used to demonstrate that the orbital data of all planets, aster- oids, moons and rings in the solar system, reduce to a simple numerical pattern based on the golden ratio. A set of integers, not unlike the quantum numbers of atomic systems define the mean orbits of all planets and major satellites

Redetermination of the crystal structure of calcium sulphate dihydrate, CaSO4 center dot 2H(2)O

Please read abstract in the article.https://www.degruyter.com/view/j/ncrsam2023Chemistr