Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Partial-Cycle-Index Method of the USCI Approach

2012 ◽  
Vol 85 (7) ◽  
pp. 793-810 ◽  
Author(s):  
Shinsaku Fujita
Keyword(s):  
Three Dimensional ◽  
Cycle Index ◽  
Index Method ◽  
Partial Cycle ◽  
Usci Approach

scholarly journals Application of GAP (groups, algorithms and programming) system to stereoisograms for characterizing RS-stereoisomers of cubane derivatives

2021 ◽  
Vol 87 (2) ◽  
pp. 207-270
Author(s):  
Shinsaku Fujita ◽  
Keyword(s):  
Permutation Group ◽  
Point Group ◽  
Gap Functions ◽  
Programming System ◽  
Cycle Index ◽  
Index Method ◽  
Type V ◽  
Partial Cycle

The PCI (Partial-Cycle-Index) method of Fujita’s USCI (Unit-Subduced-CycleIndex) approach has been applied to symmetry-itemized enumerations of cubane derivatives, where groups for specifying three-aspects of symmetry, i.e., the point group for chirality/achirality, the RS-stereogenic group for RS-stereogenicity/RS-astereogenicity, and the LR-permutation group for sclerality/ascrelarity are considered as the subgroups of the RS-stereoisomeric group . Five types of stereoisograms are adopted as diagrammatical expressions of , after combined-permutation representations (CPR) are created as new tools for treating various groups according to Fujita’s stereoisogram approach. The use of CPRs under the GAP (Groups, Algorithms and Programming) system has provided new GAP functions for promoting symmetry-itemized enumerations. The type indices for characterizing stereoisograms (e.g., for a type-V stereoisogram) have been sophisticated into RS-stereoisomeric indices (e.g., for a cubane derivative with the composition ). The type-V stereoisograms for cubane derivatives with the composition are discussed under extended pseudoasymmetry as a new concept.

scholarly journals Standard mark table and standard USCI-CF table of the point group D6h. Unification of candidates derived from different D6h-skeletons

2021 ◽  
Vol 87 (3) ◽  
pp. 481-525
Author(s):  
Shinsaku Fujita ◽  
Keyword(s):  
Point Group ◽  
Gap Function ◽  
Combinatorial Enumeration ◽  
Cycle Index ◽  
Single Standard ◽  
Partial Cycle ◽  
Unit Subduced Cycle Index ◽  
Chirality Fittingness ◽  
Usci Approach ◽  
Cycle Indices

Combined-permutation representations (CPRs) for characterizing -skeletons (a benzene skeleton, a Haworth-projected skeleton, a superphane skeleton, and a coronene skeleton) are constructed by starting from respective sets of generators, where the permutation of each generator is combined with a mirror-permutation of 2-cycle to treat both achiral and chiral substituents under the GAP system. Thereby, the CPR of degree 8 (= 6 + 2) for the benzene skeleton, the CPR of degree 14 (= 12 + 2) for the Haworth-projected skeleton, the CPR of degree 14 (= 12 + 2) for the superphane skeleton, the CPR of degree 14 (= 12 + 2) for the coronene skeleton are generated to give primary mark tables (tables of marks) based on these CPRs. These primary mark tables generated by the GAP system are different in the sequence of subgroups from each other, although they stem from the same point group . They are unified into a single standard mark table by means of a newly-devised GAP function MarkTableforUSCI. Moreover, another newly-devised GAP function constructUSCITable is employed to construct a standard USCI-CF (unit-subduced-cycle-index-with-chirality-fittingness) table concordantly. After a set of PCI-CFs (partial cycle indices with chirality fittingness) is calculated for each skeleton, symmetry-itemized combinatorial enumeration is conducted by means of the PCI method of Fujita’s USCI approach (S. Fujita, Symmetry and Combinatorial Enumeration in Chemistry, Springer-Verlag, Berlin-Heidelberg, 1991).

scholarly journals Research on Water Quality Assessment Model Based on Improved Three-Dimensional Nemerow Index Method and Firefly Algorithm

2017 ◽  
Vol 7 (2) ◽  
pp. 47
Author(s):  
Jian Cao ◽  
Zheng-Long Li ◽  
Yuan-Biao Zhang
Keyword(s):  
Water Quality ◽  
Quality Assessment ◽  
Firefly Algorithm ◽  
Human Life ◽  
Three Dimensional ◽  
Water Quality Assessment ◽  
Assessment Model ◽  
Index Method ◽  
Threshold Setting ◽  
Ongoing Concern

Monitoring water quality is a subject of ongoing concern and study since water quality is closely related to human life. Although Nemerow index method is widely used in water quality assessment, the artificial threshold setting may lead to some errors. In this study, we improved the traditional Nemerow index method and built a three-dimensional water quality assessment model combined with the modified firefly algorithm (FA). Then, we applied the improved three-dimensional Nemerow index method to evaluate 100 random water samples. Compared with the traditional method, the improved one proved to be more objective, scientific and practical.

scholarly journals RISK PERFORMANCE INDEXES AND MEASUREMENT SYSTEMS FOR MEGA CONSTRUCTION PROJECTS

2010 ◽  
Vol 16 (4) ◽  
pp. 586-594 ◽  
Author(s):  
Seon-Gyoo Kim
Keyword(s):  
Performance Measurement ◽  
Performance Index ◽  
Construction Projects ◽  
Three Dimensional ◽  
Urban Regeneration ◽  
Performance Measurement System ◽  
Index Method ◽  
Performance Guarantees ◽  
Performance Indexes ◽  
Integrated Performance

In recent years, interest in and studies on urban regeneration projects have increased. New urban regeneration projects, i.e., redevelopment projects, are being used to help solve the social and economic problems caused by antiquated buildings and degraded infrastructure. However, such projects can offer no performance guarantees because they have various and complex stakeholders and their huge scale exposes them to many risks. We propose a risk performance index to improve the efficiency of general performance measurement for mega projects by extending the existing cost/schedule‐based performance measurement system to include the risks of such mega projects. The risk performance index method proposed in this study is similar to the conventional EVMS and makes it possible to perform a three‐dimensional integrated performance measurement of cost/schedule/risk through 18 indexes and variables. Santrauka Pastaraisiais metais miestu atnaujinimo projektai vis dažniau atsiduria demesio centre ir yra tyrinejami. Nauji miestu atnaujinimo projektai, t. y. pertvarkymo projektai, naudojami sprendžiant socialines ir ekonomines problemas, kylančias del pasenusiu pastatu ir yrančios infrastruktūros. Tačiau tokie projektai nežada jokiu efektyvumo garantiju, nes juose dalyvauja ivairiausios ir sudetingos interesu grupes, o del stambaus masto jiems gresia daugybe rizikos rūšiu. Siūlomas efektyvaus rizikos valdymo indeksas, padedantis geriau ivertinti bendra efektyvuma stambiuose projektuose, nes esama sanaudomis ir terminais pagrista efektyvumo vertinimo sistema papildoma rizikos rūšimis, būdingomis tokiems stambiems projektams. Šiame tyrime siūlomas efektyvaus rizikos valdymo indekso metodas yra panašus i iprastas atliktu darbu vertinimo sistemas (EVMS). Jis leidžia atlikti trimati integruota efektyvaus sanaudu, terminu ir rizikos valdymo vertinima pagal 18 indeksu ir kintamuju.

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