Department of Pure Mathematics (1996 - Present)
Math
, Tarbiat Modares University,
Pure Mathematics
, Tarbiat Modares University,
applied mathematics
, Shiraz university,
ALI IRANMANESH received his B.Sc. from Shiraz University and Ph.D. degree from the University of Tarbiat Modares, Tehran, Iran, in 1995. Since 1995, he has been employed in the same university and currently he is a full Professor of mathematics. He is the author of 10 books in Persian, and has been involved in the writing of some chapters of 10 English books published by reputable international publications, including Springer. So far, about 250 articles by Dr. Iranmanesh have been published in prestigious international and domestic journals, and he has appeared as a supervisor in 6 postdoctoral dissertations, 35 doctoral dissertations, and 90 masters theses. He has 29 completed research projects (national and international) in his scientific record. In 2018, he was a Visiting Scholar at the University of California, Berkeley, USA. He also served as president of the Iranian Nanotechnology Society from 2014 to 2020. Membership in the Iranian Mathematical Society, the American Mathematical Society, the London Mathematical Society, the European Mathematical Society and the European Mathematical-Chemistry Society, as well as the titles of national best professor in 1399, top researcher of Iranian Universities in basic sciences in 1391 and fourth place in the third best competition Nanotechnology in 2010 is one of the honors and activities of Dr. Iranmanesh in the field of mathematical sciences. His research interests include representation and character theory of finite groups, characterization of finite groups , mathematical chemistry , theory of hyperstructures , algebraic graph theory, combinatorics, computational graph theory and biomathematics.
Given a finite group G, the character graph, denoted by Δ (G), for its irreducible character degrees is a graph with vertex set ρ (G) which is the set of prime numbers that divide the irreducible character degrees of G, and with {p, q} being an edge if there exists a non-linear χ∈ Irr (G) whose degree is divisible by p q. In this paper, on one hand, we proceed by discussing the graphical shape of Δ (G) when it has cut vertices or small number of eigenvalues, and on the other hand we give some results on the group structure of G with such Δ (G). Recently, Lewis and Meng proved the character graph of each solvable group has at most one cut vertex. Now, we determine the structure of character graphs of solvable groups with a cut vertex
The aim of this article is to contribute to a question of R. Brauer that “when do non-isomorphic groups have isomorphic complex group algebras?” Let H and G be finite groups where and let denote the first column of the complex character table of H. In this article, we show that if then provided that q + 1 divides neither n nor n – 1. Consequently, it is shown that G is uniquely determined by the structure of its complex group algebra. This in particular extends a recent result of Bessenrodt et?al. [Algebra Number Theory 9 (2015), 601–628] to the almost simple groups of arbitrary rank.
Let G be a finite group and let N (G) denote the set of conjugacy class sizes of G. Thompson’s conjecture states that if G is a centerless group and S is a non-abelian simple group satisfying N (G)= N (S), then G≅ S. In this paper, we investigate a variation of this conjecture for some symmetric groups under a weaker assumption. In particular, it is shown that G≅ Sym (p+ 1) if and only if| G|=(p+ 1)! and G has a special conjugacy class of size (p+ 1)!/p, where p> 5 is a prime number. Consequently, if G is a centerless group with N (G)= N (Sym (p+ 1)), then G≅ Sym (p+ 1).
The Wiener index is a topological index of a molecular graph, defined as the sum of distances between all pairs of its vertices. Benzenoid graphs include molecular graphs of polycyclic aromatic hydrocarbons. An edge thorny graph G is constructed from a catacondensed benzenoid graph H by attaching new graphs to edges of a perfect matching of H. A formula for the Wiener index of G is derived. The index of the resulting graph does not contain distance characteristics of elements of H and depends on the Wiener index of H and distance properties of the attached graphs.
The rapid increment of biological sequences in next generation sequencing (NGS) techniques has highlighted the key role of multiple genome alignment in comparative structure and function analysis of biological sequences. Sequence alignment is usually the first step
Let be a finite group and be the set of all irreducible complex characters of In this paper, we consider as a polygroup, where for each the product is the set of those irreducible constituents which appear in the element wise product We call that simple if it has no proper normal subpolygroup and
Supercharacter theory is developed by P. Diaconis and IM Isaacs as a natural generalization of the classical ordinary character theory. Some classical sums of number theory appear as supercharacters which are obtained by the action of certain subgroups of GLd (Zn) on Zdn. In this paper we take Zdp, p prime, and by the action of certain subgroups of GLd (Zp) we find supercharacter table of Zdp.
Let G be a finite group and cd (G) be the set of all irreducible complex character degrees of G without multiplicities. The aim of this paper is to propose an extension of Huppert’s conjecture from non-Abelian simple groups to almost simple groups of Lie type. Indeed, we conjecture that if H is an almost simple group of Lie type with cd (G)= cd (H), then there exists an Abelian normal subgroup A of G such that G/A≅ H. It is furthermore shown that G is not necessarily the direct product of H and A. In view of Huppert’s conjecture, we also show that the converse implication does not necessarily hold for almost simple groups. Finally, in support of this conjecture, we will confirm it for projective general linear and unitary groups of di
Mathematical chemistry is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. Chemical graphs, particularly molecular graphs, are models of molecules in which atoms are represented by vertices and chemical bonds by edges of a graph. Physico-chemical or biological properties of molecules can be predicted by using the information encoded in the molecular graphs, eventually translated in the adjacency or connectivity matrix associated to these graphs. The bounds of a topological index are important information of a molecular graph in the sense that they establish the approximate range of the index in terms of molecular structural pa
The core of computer science is algorithms. An algorithm is a set of instructions for solving a problem. The word “algorithm” is a distortion of al-Khwarizmi, a Persian mathematician who wrote an influential treatise about algebraic methods. Some algorithms were proposed to compute topological indices based on distance. These are the so-called shortest path algorithms, and in general, solve even more complicated problems where edges are allowed to carry weights. Some of the well-known algorithms to compute the Wiener index is the Floyd-Warshall algorithm. Many methods and algorithms, for computing the topological indices of a graph, were proposed. In a series of papers, the algorithms for calculating some topological indices, based on d
Chemical graphs, particularly molecular graphs, are models of molecules in which atoms are represented by vertices and chemical bonds by edges of a graph. A graph invariant is any function calculated on a molecular graph irrespective of the labeling of its vertices. The values of the eccentric distance sum of each analog in the data set were computed and active range identified. Subsequently, biological activity was assigned to each analog in the data set, which was then compared with the reported anti-HIV activity of dihydroseselin analogs. Excellent correlations were obtained using the eccentric distance sum in all six data sets employed in Gupta et al. Correlation percentages ranging from 93% to more than 99% were obtained in data sets u
The Wiener index is the sum of distances between all pairs of vertices of a connected graph. q-Analogs find applications in a number of areas, including the study of fractals and multifractal measures, and expressions for the entropy of chaotic dynamical systems. q-Analogs also appear in the study of quantum groups and in q-deformed superalgebras. q-Analogs of the Wiener index, motivated by the theory of hypergeometric series. Usage of topological indices in chemistry began in 1947 when chemist Harold Wiener developed the most widely known topological descriptor, the Wiener index, and used it to determine physical properties of types of alkanes known as paraffin. q-Analogs find applications in a number of areas, including the study of fract
Graph theory has provided chemists with a variety of very useful tools, and one of such tools is the topological indices. In the field of chemical graph theory and mathematical chemistry, a topological index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Among the oldest and most famous topological index, the first and the second are Zagreb indices. Zagreb indices possess many interesting properties. This chapter provides some results of Zagreb indices, for chemical graphs and nanostructures. The Zagreb indices and their variants have been used to study molecular complexity chirality, ZE-isomerism and heterosystems whilst the overall Zagreb indic
Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of molecular structures using mathematical methods without necessarily referring to quantum mechanics. Chemical graph theory is a branch of mathematical chemistry which applies graph theory to mathematical modeling of chemical phenomena. The GA index was first introduced in a paper by Vukicevic and Furtula published in the Journal of Mathematical Chemistry as one of the successors of the Randic connectivity index. This index was named as geometric-arithmetic index, it consists of a geometrical mean of end-vertex degrees of an edge uv, dudv, as numerator and arithmetic mean of end-vertex degrees of the edge uv,(d u+ d v)/2, as denominator. A descriptor
The degree distance seems to have been considered first in connection with certain chemical applications by Dobrynin and Kochetova (1994) and at the same time by Gutman (1994), who named it the Schultz index. For chemists, the use of computing tools became an obligation in order to manipulate molecular information that were, during the last years, numerically stocked on computers in databases with huge quantities. Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. Chemical graph theory is a branch of mathematical chemistry which applies graph theory to mathematical modeling of chemical phenomena. T
The discovery of fullerenes greatly expanded the number of known carbon allotropes, which until recently were limited to graphite, diamond, and amorphous carbon such as soot and charcoal. Topological indices are used for example in biological activities or physic-chemical properties of alkenes which are correlated with their chemical structure. In a series of papers topological indices of fullerenes were studied. As an example, topological indices such as the Wiener index, the Szeged index, edge Wiener index, PI v index and eccentric connectivity index of the family of C 10n fullerenes are computed. Many properties of fullerene molecules can be studied using mathematical tools and results. Fullerene graphs were defined as cubic (ie, 3-regul
no record found