University of KashanIranian Journal of Mathematical Chemistry2228-64897220160901Type-Itemized Enumeration of RS-Stereoisomers of Octahedral Complexes1131531337910.22052/ijmc.2016.13379ENS.FujitaShonan Institute of Chemoinformatics and Mathematical ChemistryJournal Article20151116Stereoisograms of octahedral complexes are classified into five types (type I--typeV) under the action of the corresponding RS-stereoisomeric group. Their enumeration is accomplished in a type-itemized fashion, where Fujita's proligand method developed originally for combinatorial enumeration under point groups (S. Fujita, Theor. Chem. Acc., 113, 73--79 (2005)) is extended to meet the requirement of Fujita's stereoisogram approach. The cycle index with chirality fittingness (CI-CF) of the point group O_h is modulated by taking account of the CI-CF for calculating type-V quadruplets contained in stereoisograms. The modulated CI-CF is combined with a CI-CF of the maximum chiral point group (O), a CI-CF of the maximum RS-permutation group, a CI-CF of the maximum ligand-reflection group, and a CI-CF of the RS-stereoisomeric group, so as to generate CI-CFs for evaluating type-I to type-V quadruplets. By introducing ligand-inventory functions into the CI-CFs, 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/A-descriptors are discussed on the basis of Fujita's stereoisogram approach.https://ijmc.kashanu.ac.ir/article_13379_257b1e5f2c420db08065377bd4bbdc79.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64897220160901Half-Century Journey from Synthetic Organic Chemistry to Mathematical Stereochemistry through Chemoinformatics1552211388210.22052/ijmc.2016.13882ENS.FujitaShonan Institute of Chemoinformatics and Mathematical ChemistryJournal Article20151010My half-century 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 computer-oriented 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 unit-subduced-cycle-index (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.https://ijmc.kashanu.ac.ir/article_13882_f2efa6612f707e0e8842f415a197c907.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64897220160901Enumeration of Conformers of Octahedral [M(ABC)_{6}] Complex on the Basis of Computational Group Theory2232341392610.22052/ijmc.2016.13926ENH.SakiyamaYamagata UniversityK.WakiYamagata UniversityJournal Article20160218Conformers 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.https://ijmc.kashanu.ac.ir/article_13926_10d6298ef8e8a0cc7cd78f6cdd3d149a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64897220160901QSPR Modeling of Heat Capacity, Thermal Energy and Entropy of Aliphatic Aldehydes by using Topological Indices and MLR Method2352511565610.22052/ijmc.2016.15656ENA.AlaghebandiDepartment of Chemistry, Science Faculty, Arak Branch, Islamic Azad University, Arak, IranF.ShafieiDepartment of Chemistry, Science Faculty, Arak Branch, Islamic Azad University, Arak, IranJournal Article20160624https://ijmc.kashanu.ac.ir/article_15656_15cda36e3c4738750662d2bf376a5cbb.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64897220160901On the Mark and Markaracter Tables of Finite Groups2532661509610.22052/ijmc.2016.15096ENM.GhorbaniDepartment of mathematics, Shahid Rajaee Teacher Training University0000-0002-5324-0847Journal Article20160422Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H,K-entry 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.https://ijmc.kashanu.ac.ir/article_15096_277e66c395cff3391a684c5737ec351e.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64897220160901Weak Algebraic Hyperstructures as a Model for Interpretation of Chemical Reactions2672831397510.22052/ijmc.2016.13975ENB.DavvazYazd UniversityJournal Article20141122The concept of weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known 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.https://ijmc.kashanu.ac.ir/article_13975_687ed25a7221a0475772ca3a4ef9be97.pdf