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3. Words for maximal Subgroups of Fi24‘

Author

Yasin Faisal, Farooq Adeel, and Jung Chahn Yong

Subjects
molecular symmetry, point group, maximal subgroup, fischer group, generators, Chemistry, QD1-999
Abstract

Group Theory is the mathematical application of symmetry to an object to obtain knowledge of its physical properties. The symmetry of a molecule provides us with the various information, such as - orbitals energy levels, orbitals symmetries, type of transitions than can occur between energy levels, even bond order, all that without rigorous calculations. The fact that so many important physical aspects can be derived from symmetry is a very profound statement and this is what makes group theory so powerful. In group theory, a finite group is a mathematical group with a finite number of elements. A group is a set of elements together with an operation which associates, to each ordered pair of elements, an element of the set. In the case of a finite group, the set is finite. The Fischer groups Fi22, Fi23 and Fi24‘ are introduced by Bernd Fischer and there are 25 maximal subgroups of Fi24‘. It is an open problem to find the generators of maximal subgroups of Fi24‘. In this paper we provide the generators of 10 maximal subgroups of Fi24‘.

Published
2019
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4. Valency-based molecular descriptors of Bakelite network BNmn$B\text N_{m}^{n}$

Author

Ahmad Maqsood, Javaid Muhammad, Saeed Muhammad, and Jung Chahn Yong

Subjects
molecular graph, bakelite network, zagreb index, chemical properties, Chemistry, QD1-999
Abstract

Bakelite network BNmn$BN_{m}^{n}$is a molecular graph of bakelite, a pioneering and revolutionary synthetic polymer (Thermosetting Plastic) and regarded as the material of a thousand uses. In this paper, we aim to compute various degree-based topological indices of a molecular graph of bakelite network BNmn$BN_{m}^{n}$. These molecular descriptors play a fundamental role in QSPR/QSAR studies in describing the chemical and physical properties of Bakelite network BNmn$BN_{m}^{n}$. We computed atom-bond connectivity ABC its fourth version ABC4 geometric arithmetic GA its fifth version GA5 Narumi-Katayama, sum-connectivity and Sanskruti indices, first, second, modified and augmented Zagreb indices, inverse and general Randic’ indices, symmetric division, harmonic and inverse sum indices of BNmn$BN_{m}^{n}$.

Published
2019
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10. (p,h)-Convex Functions Associated with Hadamard and Fejér-Hadamard Inequalities via k-Fractional Integral Operators

Author

Zhang, Xiujun, Farid, Ghulam, Demirel, Ayşe Kübra, and Jung, Chahn Yong

Subjects
Article Subject, Mathematics::Classical Analysis and ODEs
Abstract

In this article, generalized versions of the k-fractional Hadamard and Fejér-Hadamard inequalities are constructed. To obtain the generalized versions of these inequalities, k-fractional integral operators including the well-known Mittag-Leffler function are utilized. The class of (p,h)-convex functions for Hadamard-type inequalities give the generalizations of results which have been proved in literature for p-convex, h-convex, and several functions deducible from these two classes.

Published
2022
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14. Inequalities for a Unified Integral Operator for Strongly α,m-Convex Function and Related Results in Fractional Calculus

Author

Jung, Chahn Yong, Farid, Ghulam, Mahreen, Kahkashan, and Shim, Soo Hak

Subjects
Article Subject, QA1-939, Mathematics
Abstract

In this paper, we study integral inequalities which will provide refinements of bounds of unified integral operators established for convex and α,m-convex functions. A new definition of function, namely, strongly α,m-convex function is applied in different forms and an extended Mittag-Leffler function is utilized to get the required results. Moreover, the obtained results in special cases give refinements of fractional integral inequalities published in this decade.

Published
2021

18. Hadamard-Type k-Fractional Integral Inequalities for Exponentially α,h−m-Convex Functions

Author

Jung, Chahn Yong, Farid, Ghulam, Bibi, Sidra, Nisar, Kottakkaran Sooppy, and Kang, Shin Min

Subjects
Article Subject, QA1-939, Mathematics
Abstract

The class of exponentially α,h−m-convex functions has been discovered to unify different kinds of convexities. This paper finds new Riemann–Liouville fractional Hadamard-type inequalities for this generalized class of convex functions. These results further have their consequences which are presented in the form of corollaries. Moreover, some known results are identified in the form of remarks.

Published
2020

19. Refinements of some integral inequalities for (s,m)-convex functions

Author

Farid, Ghulam, Chu, Yu-Ming, Andrić, Maja, Jung, Chahn Yong, Pečarić, Josip, and Kang, Shin Min

Subjects
Article Subject, convex function, Mittag-Leffler function, fractional integral operator, QA1-939, MathematicsofComputing_NUMERICALANALYSIS, TA1-2040, Engineering (General). Civil engineering (General), Mathematics
Abstract

In this paper, the refinements of integral inequalities for all those types of convex functions are given which can be obtained from (s, m)-convex functions. These inequalities not only provide refinements of bounds for unified integral operators but also for various associated fractional integral operators containing Mittag–Leffler function. At the same time, presented results give generalizations of many known fractional integral inequalities.

Published
2020

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