2016
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2
2
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TypeItemized Enumeration of RSStereoisomers of Octahedral Complexes
2
2
Stereoisograms of octahedral complexes are classified into five types (type ItypeV) under the action of the corresponding RSstereoisomeric group. Their enumeration is accomplished in a typeitemized fashion, where Fujita's proligand method developed originally for combinatorial enumeration under point groups (S. Fujita, Theor. Chem. Acc., 113, 7379 (2005)) is extended to meet the requirement of Fujita's stereoisogram approach. The cycle index with chirality fittingness (CICF) of the point group O_h is modulated by taking account of the CICF for calculating typeV quadruplets contained in stereoisograms. The modulated CICF is combined with a CICF of the maximum chiral point group (O), a CICF of the maximum RSpermutation group, a CICF of the maximum ligandreflection group, and a CICF of the RSstereoisomeric group, so as to generate CICFs for evaluating typeI to typeV quadruplets. By introducing ligandinventory functions into the CICFs, the numbers of quadruplets ofoctahedral complexes are obtained and shown in tabular forms. Several stereoisograms for typical complexes are depicted. Their configuration indices and C/Adescriptors are discussed on the basis of Fujita's stereoisogram approach.
1

113
153


S.
Fujita
Shonan Institute of Chemoinformatics and Mathematical Chemistry
Shonan Institute of Chemoinformatics and
Japan
shinsaku_fujita@nifty.com
Enumeration
Stereoisogram
Octahedral complex
RSstereoisomeric group
HalfCentury Journey from Synthetic Organic Chemistry to Mathematical Stereochemistry through Chemoinformatics
2
2
My halfcentury journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of imaginary transition structures (ITSs) as computeroriented representation of organic reactions. My interest was stimulated to attack combinatorial enumeration through the investigation on enumeration of subgraphs of ITSs. Stereochemistry and combinatorial enumeration was combined in my interest, so that I reached mathematical stereochemistry as the final stage of my journey. Fujita's unitsubducedcycleindex (USCI) approach, Fujita's proligand method, and Fujita's stereoisogram approach were developed, so as to integrate van't Hoff's way (asymmetry, stereogenicity) and Le Bel's way (dissymmetry, chirality), which caused continuous confusion in the history of stereochemistry.
1

155
221


S.
Fujita
Shonan Institute of Chemoinformatics and Mathematical Chemistry
Shonan Institute of Chemoinformatics and
Japan
shinsaku_fujita@nifty.com
Sphericity
Combinatorial enumeration
Stereoisogram
Stereochemistry
Enumeration of Conformers of Octahedral [M(ABC)6] Complex on the Basis of Computational Group Theory
2
2
Conformers of [M(ABC)6] complex have been enumerated on the basis of computational group theory, where M is the central metal, and ABC is the ligand, bound to M through A. Based on the 16 conformers of the M(AB)6 core unit, 7173 conformers have been found for the [M(ABC)6] complex, which are assigned to nine point groups, 1 D3d, 4 D3, 4 S6, 5 C2h, 7 C3, 182 C2, 15 Cs, 23 Ci, and 6932 C1.
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223
234


H.
Sakiyama
Yamagata University
Yamagata University
Japan
saki@sci.kj.yamagatau.ac.jp


K.
Waki
Yamagata University
Yamagata University
Japan
waki@sci.kj.yamagatau.ac.jp
Enumeration
Conformer
Octahedral [M(ABC)6] Complex
Computational Group Theory
QSPR Modeling of Heat Capacity, Thermal Energy and Entropy of Aliphatic Aldehydes by using Topological Indices and MLR Method
2
2
1

235
251


A.
Alaghebandi
Department of Chemistry, Science Faculty, Arak Branch, Islamic Azad University, Arak, Iran
Department of Chemistry, Science Faculty,
I R Iran


F.
Shafiei
Department of Chemistry, Science Faculty, Arak Branch, Islamic Azad University, Arak, Iran
Department of Chemistry, Science Faculty,
I R Iran
Topological indices
Aldehydes
QSPR
MLR method
On the Mark and Markaracter Tables of Finite Groups
2
2
Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H,Kentry is the number of fixed points of the set G/K under the action of H is called the table of marks of G where H,K run through all elements in C(G). Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representations and characters for linear representations in a common basis. In this paper, we compute these tables for some classes of finite groups.
1

253
266


M.
Ghorbani
Department of mathematics, Shahid Rajaee Teacher Training University
Department of mathematics, Shahid Rajaee
I R Iran
mghorbani@srttu.edu
Group action
Automorphism group
Mark table
Markaracter table
Weak Algebraic Hyperstructures as a Model for Interpretation of Chemical Reactions
2
2
The concept of weak algebraic hyperstructures or Hvstructures constitutes a generalization of the wellknown algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper after an introduction of basic definitions and results about weak algebraic hyperstructures, we review: (1) Weak algebraic hyperstructures associated with chain reactions. (2) Weak algebraic hyperstructures associated with dismutation reactions (3) Weak algebraic hyperstructures associated with redox reactions.
1

267
283


B.
Davvaz
Yazd University
Yazd University
I R Iran
davvaz@yazd.ac.ir
Weak algebraic hyperstructure
Hypergroup
H_{v}group
Chain reaction
Dismutation reaction
Redox reaction