scholarly journals Quantum Molecular Polyhedra and Atomic Populations

2021 ◽  
Vol 14 (14) ◽  
pp. 6-13
Author(s):  
Ramon Carbó-Dorca

The present paper uses the LCAO MO theory formalism. The structure of the first order electronic density function is decomposed in two kinds of quantum polyhedra to discuss the behavior of quantum atomic populations. Among the many aspects one can consider about atomic populations here, the quantum mechanical structure of the density function is taken as the most important characteristic to think about. Apart of the usual one-electron basis set, centered in the molecular atoms, there is also discussed the possibility that the three-dimensional space where the molecular structures are described can be also the site of basis functions centered in points non-coincident with atomic positions.

2013 ◽  
Vol 48 (4) ◽  
pp. 141-145 ◽  
Author(s):  
Bartlomiej Oszczak ◽  
Eliza Sitnik

ABSTRACT During the process of satellite navigation, and also in the many tasks of classical positioning, we need to calculate the corrections to the initial (or approximate) location of the point using precise measurement of distances to the permanent points of reference (reference points). In this paper the authors have provided a way of developing Hausbrandt's equations, on the basis of which the exact coordinates of the point in two-dimensional space can be determined by using the computed correction to the coordinates of the auxiliary point. The authors developed generalised equations for threedimensional space introducing additional fixed point and have presented proof of derived formulas.


Author(s):  
Chris Christou

Virtual Reality is implemented by a combination of technologies that are used in order to visualize and provide interaction with a virtual environment. These environments often depict three-dimensional space which may be realistic or imaginary, macroscopic or microscopic and based on realistic physical laws of dynamics, or on imaginary dynamics. The multitude of scenarios that VR may be used to depict make it broadly applicable to the many areas in education. A key feature of VR is that it allows multi-sensory interaction with the space being visualized. Here we look at how this combination of multi-sensory visualization and interactivity make VR ideally suited for effective learning and try to explain this effectiveness in terms of the advantages afforded by active learning through experiences. We also consider some of the applications of VR in education and also some of its drawbacks.


1988 ◽  
Vol 53 (11) ◽  
pp. 2675-2713 ◽  
Author(s):  
Jaroslav Jonas

Isomerism is a notion of a considerably broad meaning. Not only chemists but also physicists, biologists and philosophers come across it. In the sequel, some basic problems of the contemporary understanding of the phenomenon of isomerism of molecular structures and related problems of topic relationships between homomorphic ligands and faces are dealt with. Illustrating factual material is selected within the domain of organic chemistry. With the rapid development of nomenclature in this area in mind, the issues are presented from a point of view stressing the unity of historical and logical moments. Problems arising when moving from the analysis of molecular structure models towards the analysis of real sets of molecules are highlighted. Differences between the analysis of static molecular structures in three-dimensional space and the analysis of real dynamic molecular structures in four-dimensional space are dealt with in greater detail. The method of NMR spectroscopy is discussed from this standpoint as an example of the most widespread research tool for investigating intramolecular dynamism at present. Stereo-differentiating reactions are also treated briefly and a suggestion is made to introduce into the teaching of isomerism and topicity a classification of differentiating interactions. The relationships discussed are demonstrated comprehensively using the chemical behaviour of an optically active trisubstituted cycloheptatriene-norcaradiene system as an example and, are also discussed in connection with some new findings concerning actual chiral geometries in some conventionally achiral systems. Attention is paid to didactic presentation of the topic and an attempt is made to show probable trends in future development in this domain.


Sapere Aude ◽  
2019 ◽  
Vol 10 (19) ◽  
pp. 184-202
Author(s):  
Raquel Anna Sapunaru

A ideia de um espaço tridimensional começou a se formar no século XV. Antes disso, em um mundo dominado pelo aristotelismo, o espaço era vinculado à superfície e não ao volume. Foi através das artes que essa realidade começou a mudar. A perspectiva racional, definida aqui como um recurso gráfico que utiliza o efeito visual de linhas convergentes para criar a ilusão de tridimensionalidade do espaço e das formas representadas sobre uma superfície plana de um papel ou tela, nascida a partir de uma retomada da geometria euclidiana, entrou em cena para ficar no século XVI. Entre os muitos nomes que poderiam ser citados, destacaram-se o matemático e filósofo John Dee, o arquiteto e designer Filippo Brunelleschi, e o pintor e matemático Pierro della Francesca. Através da combinação das ideias e realizações desses três atores é possível entender uma época de transição entre o antigo e o moderno, em termos de ciência e arte.PALAVRAS-CHAVE: Espaço tridimencional. Geometria. Perspectiva racional. Filosofia e arte. ABSTRACTThe idea of a three-dimensional space began to form in the fifteenth century. Before that, in a world dominated by Aristotelianism, space was bound to the surface and not to the volume. It was through the arts that this reality began to change. The rational perspective, defined here as a graphic resource that uses the visual effect of converging lines to create the illusion of three-dimensionality of space and forms represented on a flat surface of a paper or canvas, born from a resumption of Euclidean geometry, came into the scene to stay in the sixteenth century. Among the many names that could be cited were the mathematician and philosopher John Dee, the architect and designer Filippo Brunelleschi, and the painter and mathematician Pierro della Francesca. By combining the ideas and achievements of these three actors it is possible to understand a time of transition between the old and the modern, in terms of science and art.KEYWORDS: Three-dimensional space. Geometry. Rational Perspective. Philosophy and Art.


1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.


2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>


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