Isomerism and topicity in three- and four-dimensional space: A review

1988 ◽  
Vol 53 (11) ◽  
pp. 2675-2713 ◽  
Author(s):  
Jaroslav Jonas
Keyword(s):  
Dimensional Space ◽  
Rapid Development ◽  
Three Dimensional ◽  
Point Of View ◽  
Molecular Structures ◽  
New Findings ◽  
Chemical Behaviour ◽  
Broad Meaning ◽  
Three Dimensional Space

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.

scholarly journals How Can I Grab That?

i-com ◽  
2020 ◽  
Vol 19 (2) ◽  
pp. 67-85
Author(s):  
Matthias Weise ◽  
Raphael Zender ◽  
Ulrike Lucke
Keyword(s):  
Virtual Reality ◽  
User Experience ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Advantages And Disadvantages ◽  
Multiple Dimensions ◽  
Application Developers ◽  
Three Dimensional Space

AbstractThe selection and manipulation of objects in Virtual Reality face application developers with a substantial challenge as they need to ensure a seamless interaction in three-dimensional space. Assessing the advantages and disadvantages of selection and manipulation techniques in specific scenarios and regarding usability and user experience is a mandatory task to find suitable forms of interaction. In this article, we take a look at the most common issues arising in the interaction with objects in VR. We present a taxonomy allowing the classification of techniques regarding multiple dimensions. The issues are then associated with these dimensions. Furthermore, we analyze the results of a study comparing multiple selection techniques and present a tool allowing developers of VR applications to search for appropriate selection and manipulation techniques and to get scenario dependent suggestions based on the data of the executed study.

scholarly journals Ideals of Herzog–Northcott type

2011 ◽  
Vol 54 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Liam O'Carroll ◽  
Francesc Planas-Vilanova
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Regular Sequence ◽  
Point Of View ◽  
Prime Ideals ◽  
Monomial Curves ◽  
Definition Of ◽  
Minimal Prime ◽  
Special Case ◽  
Three Dimensional Space

AbstractThis paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is the ideals determining monomial curves in three-dimensional space, which were studied by Herzog. In the broader context studied here, these ideals are identified as Northcott ideals in the sense of Vasconcelos, and so their liaison properties are displayed. It is shown that they are set-theoretically complete intersections, revisiting the work of Bresinsky and of Valla. Even when the three elements are taken to be variables in a polynomial ring in three variables over a field, this point of view gives a larger class of ideals than just the defining ideals of monomial curves. We then characterize when the ideals in this larger class are prime, we show that they are usually radical and, using the theory of multiplicities, we give upper bounds on the number of their minimal prime ideals, one of these primes being a uniquely determined prime ideal of definition of a monomial curve. Finally, we provide examples of characteristic-dependent minimal prime and primary structures for these ideals.

scholarly journals Classification of book representations of K6

2017 ◽  
Vol 26 (12) ◽  
pp. 1750075
Author(s):  
Dana Rowland
Keyword(s):  
Complete Graph ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Crossing Number ◽  
Ambient Isotopy ◽  
Three Dimensional Space

A book representation of a graph is a particular way of embedding a graph in three-dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to [Formula: see text], the complete graph with six vertices. We prove there are exactly 59 distinct book representations for [Formula: see text], and we identify the number and type of knotted and linked cycles in each representation. We show that book representations of [Formula: see text] contain between one and seven links, and up to nine knotted cycles. Furthermore, all links and cycles in a book representation of [Formula: see text] have crossing number at most four.

scholarly journals A Clustering Method Applied to the Analysis of Planetary Nebulae

1993 ◽  
Vol 155 ◽  
pp. 44-44
Author(s):  
O.S. Yatsyk
Keyword(s):  
Planetary Nebula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Planetary Nebulae ◽  
Spectral Lines ◽  
Radio Flux ◽  
Clustering Method ◽  
Centroid Method ◽  
Three Dimensional Space

Intensities of the observed spectral lines, radio fluxes and Hβ fluxes are used for the classification of planetary nebulae by centroid method of taxonomical analysis. Two variants of classification are proposed. The first one– in the three–dimensional space of relation of intensity of spectral lines He II λ 4686/HeI λ 4471, [OIII] λ 4959+5007/[OII] λ 3726+29, [OIII] λ 4959+5007/[OIII] 4363. The second variants is the classification in the three-dimensional space with cooordinates being radio flux, Hβ flux and [OIII] λ 4959+5007 intensity. The membership of classes (taxons) are presented. In the diagram joining the planetary nebula descriptors pairwise there are regions of complete (or predominant) of nebulae belonging to the same taxon, but there are also some regions of overlap. The corresponding taxons are not isolated but merge continuously into one another.

scholarly journals Perceptually Valid Facial Expressions for Character-Based Applications

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Ali Arya ◽  
Steve DiPaola ◽  
Avi Parush
Keyword(s):  
Facial Expression ◽  
Language Learning ◽  
Facial Expressions ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Point Of View ◽  
Mixed Emotions ◽  
Dynamic Facial Expressions ◽  
Emotion Model ◽  
Three Dimensional Space

This paper addresses the problem of creating facial expression of mixed emotions in a perceptually valid way. The research has been done in the context of a “game-like” health and education applications aimed at studying social competency and facial expression awareness in autistic children as well as native language learning, but the results can be applied to many other applications such as games with need for dynamic facial expressions or tools for automating the creation of facial animations. Most existing methods for creating facial expressions of mixed emotions use operations like averaging to create the combined effect of two universal emotions. Such methods may be mathematically justifiable but are not necessarily valid from a perceptual point of view. The research reported here starts by user experiments aiming at understanding how people combine facial actions to express mixed emotions, and how the viewers perceive a set of facial actions in terms of underlying emotions. Using the results of these experiments and a three-dimensional emotion model, we associate facial actions to dimensions and regions in the emotion space, and create a facial expression based on the location of the mixed emotion in the three-dimensional space. We call these regionalized facial actions “facial expression units.”

scholarly journals THE SANSEVERO CHAPEL, A THREE-DIMENSIONAL POINT OF VIEW

2019 ◽  
Vol XLII-2/W15 ◽  
pp. 299-304
Author(s):  
V. Cera ◽  
D. Marcos González ◽  
L. A. Garcia
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Point Of View ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Survey Techniques ◽  
Representation Systems ◽  
Representation Of Space ◽  
Special Relevance ◽  
Three Dimensional Space

<p><strong>Abstract.</strong> In this article, the importance of the three-dimensional survey in architectural spaces will be studied, taking special relevance in the study of the perception of perspective, since three-dimensional space would not be understood from a two-dimensional representation of space. The project aims to develop a comparison between the representation systems based on the automatic acquisition of various data by different 3D survey techniques. In particular, the document reports the results of an analysis based on the Sansevero Chapel in Naples.</p>

scholarly journals Application of methods of multidimensional statistical analysis for the classification of signal fragments during cutting processing

2021 ◽  
Vol 2091 (1) ◽  
pp. 012073
Author(s):  
A V Belov ◽  
N N Trufanov ◽  
D V Churikov ◽  
O V Kravchenko
Keyword(s):  
Spectral Analysis ◽  
Statistical Analysis ◽  
Vector Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Vibration Sensor ◽  
Average Amplitude ◽  
Average Value ◽  
Three Dimensional Space

Abstract The preliminary processing of the signal coming from the vibration sensor is performed. Spectral analysis methods allow identifying the distinctive zones corresponding to three parameters: the average amplitude of vibrations, the average value of the spectrum, and the complex parameter of the vibration density obtained using interpolation methods. Hence, the vector contains the listed parameters as components produce a vector space, and the equations of separating surfaces in three-dimensional space and classification errors are calculated.

scholarly journals Quantum Molecular Polyhedra and Atomic Populations

2021 ◽  
Vol 14 (14) ◽  
pp. 6-13
Author(s):  
Ramon Carbó-Dorca
Keyword(s):  
Density Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Molecular Structures ◽  
Basis Set ◽  
Electronic Density ◽  
The Many ◽  
Lcao Mo Theory ◽  
Three Dimensional Space ◽  
Atomic Populations

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.

COLORFUL SYMMETRIC IMAGES IN THREE-DIMENSIONAL SPACE FROM DYNAMICAL SYSTEMS

Fractals ◽  
2012 ◽  
Vol 20 (01) ◽  
pp. 53-60 ◽  
Author(s):  
JIAN LU ◽  
YURU ZOU ◽  
ZEYI LIU ◽  
WENXIA LI
Keyword(s):  
Dynamical Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Automatic Generation ◽  
Point Of View ◽  
Density Functions ◽  
Three Dimensional Space

Functions that are invariant with respect to the tetrahedral and cubic symmetries are determined. These invariant mappings are applied to serve as the density functions for automatic generation of the colorful images with such symmetries in three dimensional space from a dynamical system's point of view.

scholarly journals Emotion Recognition: An Evaluation of ERP Features Acquired from Frontal EEG Electrodes

2021 ◽  
Vol 11 (9) ◽  
pp. 4131
Author(s):  
Moon Inder Singh ◽  
Mandeep Singh
Keyword(s):  
Dimensional Space ◽  
Brain Computer Interface ◽  
Three Dimensional ◽  
Event Related Potential ◽  
Computer Interface ◽  
Two Dimensional ◽  
Emotion Classification ◽  
Better Than ◽  
Three Dimensional Space

The challenge to develop an affective Brain Computer Interface requires the understanding of emotions psychologically, physiologically as well as analytically. To make the analysis and classification of emotions possible, emotions have been represented in a two-dimensional or three-dimensional space represented by arousal and valence domains or arousal, valence and dominance domains, respectively. This paper presents the classification of emotions into four classes in an arousal–valence plane using the orthogonal nature of emotions. The average Event Related Potential (ERP) attributes and differential of average ERPs acquired from the frontal region of 24 subjects have been used to classify emotions into four classes. The attributes acquired from the frontal electrodes, viz., Fp1, Fp2, F3, F4, F8 and Fz, have been used for developing a classifier. The four-class subject-independent emotion classification results in the range of 67–83% have been obtained. Using three classifiers, a mid-range accuracy of 85% has been obtained, which is considerably better than existing studies on ERPs.

Sign in / Sign up

Export Citation Format

Share Document