A stereochemistry-oriented hierarchical tree for classification of point groups of symmetry

1986 ◽  
Vol 26 (4) ◽  
pp. 633-633 ◽  
Author(s):  
V. I. Sokolov
Keyword(s):  
Hierarchical Tree ◽  
Point Groups

scholarly journals Hierarchical text classification using Relative Inverse Document Frequency

2021 ◽  
Vol 15 (2) ◽  
pp. 166-176
Author(s):  
Boonthida Chiraratanasopha ◽  
Thanaruk Theeramunkong ◽  
Salin Boonbrahm
Keyword(s):  
Text Classification ◽  
Term Weighting ◽  
Hierarchical Tree ◽  
Inverse Document Frequency ◽  
Document Frequency ◽  
Relative Inverse ◽  
The Hierarchical Structure ◽  
Family Based ◽  
Hierarchical Text Classification

Automatic hierarchical text classification has been a challenging and in-needed task with an increasing of hierarchical taxonomy from the booming of knowledge organization. The hierarchical structure identifies the relationships of dependence between different categories in which can be overlapped of generalized and specific concepts within the tree. This paper presents the use of frequency of the occurring term in related categories among the hierarchical tree to help in document classification. The four extended term weighting of Relative Inverse Document Frequency (IDFr) including its located category, its parent category, its sibling categories and its child categories are exploited to generate a classifier model using centroid-based technique. From the experiment on hierarchical text classification of Thai documents, the IDFr achieved the best accuracy and F-measure as 53.65% and 50.80% in Top-n features set from family-based evaluation in which are higher than TF-IDF for 2.35% and 1.15% in the same settings, respectively.

Molecular Rovibronic Symmetries in Electric and Magnetic Fields

1975 ◽  
Vol 53 (19) ◽  
pp. 2210-2220 ◽  
Author(s):  
James K. G. Watson
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Symmetry Groups ◽  
Nuclear Spins ◽  
Symmetry Classification ◽  
Electric And Magnetic Fields ◽  
Field Symmetry ◽  
Point Groups

The structures of the symmetry groups for the rovibronic levels of a molecule in a homogeneous electric or magnetic field are derived, and the symmetry classification of the levels in terms of the representations and corepresentations of these groups is discussed. Specific results are given for molecules of the point groups C3, C2v, C3v, D2d, and Td in an electric field. Symmetry in combined electric and magnetic fields and the inclusion of nuclear spins are considered briefly.

CROSS-COUNTRY HIERARCHICAL STRUCTURE AND CURRENCY CRISES

2006 ◽  
Vol 17 (03) ◽  
pp. 333-341 ◽  
Author(s):  
GUILLERMO J. ORTEGA ◽  
DAVID MATESANZ
Keyword(s):  
Currency Crises ◽  
Correlation Coefficients ◽  
Relevant Information ◽  
Hierarchical Tree ◽  
Ultrametric Analysis ◽  
Exchange Rate Movements ◽  
The Matrix ◽  
Using Data ◽  
Metric Distance

Using data from a sample of 28 representatives countries, we propose a classification of currency crises consequences based on the ultrametric analysis of the real exchange rate movements time series, without any further assumption. By using the matrix of synchronous linear correlation coefficients and the appropriate metric distance between pairs of countries, we were able to construct a hierarchical tree of countries. This economic taxonomy provides relevant information regarding liaisons between countries and a meaningful insight about the contagion phenomenon.

scholarly journals Cooperation of enterprises in innovative activities on the example of Polish regions

Equilibrium ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. 839-857
Author(s):  
Paulina Nowak
Keyword(s):  
Central Government ◽  
Value Added ◽  
Business Environment ◽  
Economic Life ◽  
Regional Environment ◽  
Hierarchical Tree ◽  
Low Level ◽  
Innovation Activities ◽  
Scientific Institutions

Research background: Cooperation is an indispensable element of innovation activities of enterprises. Undertakings in innovation, by nature, require not only significant expenditures or creative human capital, but also cooperation with other enterprises, scientific institutions, and the business environment. Cooperating companies have a greater chance to compete in the international arena while building the innovative potential of the regional environment. Stimulating the permanent cooperation of enterprises operating in the region, in its various forms, is a key challenge for central government authorities, local government authorities, and other actors in social and economic life. The existing literature on the cooperation of enterprises focuses on the motives of cooperation and their effects, but to a lesser extent on the spatial similarity of these processes, i.e. in individual regions of the country. Purpose of the article: The purpose of the article is to diagnose and evaluate regional differences in the level of cooperation between companies conducting innovation activities in Poland. The study used data on innovation activities published by Statistics Poland and data on enterprises participating in cluster cooperation published by the Polish Agency for Enterprise Development. Methods: The cluster analysis was used, allowing to identify voivodeships that are similar to each other in terms of the analyzed phenomenon. The spatial classification of voivodeships was performed using the Ward method, which is classified as hierarchical and is often used to group objects. The result is a hierarchical tree that groups the regions in increasingly larger clusters. Findings & value added: The results indicate a low level of cooperation and the existence of significant differences in the cooperation of enterprises as part of innovation activities in Polish regions. The low level of cooperation between companies in individual regions corresponds to the number of marketed innovations. There are similarities between some regions in terms of cooperation on innovation activities. The results of the analysis may provide an indication for national and European Union economic policy entities in the field of creating instruments to support the cooperation of companies on innovation activities.

The crystallographic point groups as semi-direct products

1963 ◽  
Vol 255 (1054) ◽  
pp. 216-240 ◽  
Keyword(s):  
Direct Product ◽  
Invariant Subgroup ◽  
Projection Operators ◽  
Direct Products ◽  
Finite Rotations ◽  
Space Groups ◽  
Symmetry Adapted Functions ◽  
Point Groups ◽  
Definition Of

This paper aims at providing a systematic treatment of the crystallographic point groups. Some well-known properties of them, in terms of the theory of the poles of finite rotations, are first discussed, so as to provide a simple way for recognizing their invariant subgroups. A definition of the semi-direct product is then given, and it is shown that all crystallographic point groups can be expressed as a semi-direct product of one of their invariant subgroups by a cyclic subgroup. Many useful relations between point groups can be obtained by exploiting the properties of the triple and mixed triple semi-direct products, which are defined. Much of the rest of the paper is devoted to the theory of the representations of semi-direct products. The treatment here parallels that given by Seitz (1936) for the reduction of space groups in terms of the representations of its invariant subgroups (the translation groups). The latter, however, are always Abelian and this is not always the case for point groups. The full treatment of the general case, such as given by McIntosh (1958), is laborious and it is shown that, if the emphasis is placed on the bases of the representations, rather than the representations themselves, it is possible to achieve the reduction of the point groups by a method hardly more involved than that required when the invariant subgroup is Abelian. It is also shown that, just as for space groups, the representations of the invariant subgroups can be denoted and visualized by means of a vector, which allows a very rapid classification of the representations, very much as the k vector as used by Bouckaert, Smoluchowski & Wigner (1936) allows the formalism of the Seitz method for space groups to be carried out in a graphical fashion. One of the major consequences of this work is that it affords a substantial simplification in the use of the symmetrizing and projection operators that are required to obtain symmetry-adapted functions: a very systematic alternative to the method given by Melvin (1956) is therefore provided. In the last section of the paper all the techniques discussed are applied in detail, as an example, to the cubic groups. The projection operators are used to obtain symmetry-adapted spherical harmonics for these groups. The paper might be found useful as an introduction to the methods for the reduction of space groups.

scholarly journals Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors

2018 ◽  
Vol 98 (16) ◽  
Author(s):  
Satoru Hayami ◽  
Megumi Yatsushiro ◽  
Yuki Yanagi ◽  
Hiroaki Kusunose
Keyword(s):  
Linear Response ◽  
Atomic Scale ◽  
Point Groups
Sign in / Sign up

Export Citation Format

Share Document