2019
10
2
0
101
Chemical salt reactions as algebraic hyperstructures
2
2
A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of hyperstructures associated with salt metathesis reactions, and we observe that these chemical reactions are examples of the phenomena when composition of two elements is a set of elements.
1

93
102


Dariush
Heidari
Faculty of science, Mahallat Institute of Higher Education, Mahallat, Iran
Faculty of science, Mahallat Institute of
Iran
dheidari82@gmail.com


Davood
Mazaheri
Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran
Faculty of Engineering, Mahallat Institute
Iran
davood.mazaheri@gmail.com


Bijan
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
Iran
davvaz@yazd.ac.ir
Hyperstructures
semihypergroup
$H_v$semigroup
salt reaction
[1. K. M. Chun, Chemical hyperstructures of chemical reactions for iron and##idium, J. Chungcheong Math. Soc. 27 (2) (2014) 319−325.##2. S. C. Chung, Chemical hyperstructures for vanadium, J. Chungcheong##Math. Soc. 27 (2) (2014) 309−317.##3. S. C. Chung, K. M. Chun, N. J. Kim, S. Y. Jeong, H. Sim, J. Lee and H.##Maeng, Chemical hyperalgebras for three consecutive oxidation states of##elements, MATCH Commun. Math. Comput. Chem. 72 (2) (2014) 389−402.##4. P. Corsini and V. Leoreanu, Applications of Hyperstructures Theory,##Advanced in Mathematics, Kluwer Academic Publisher, 2003.##5. B. Davvaz, Weak algebraic hyperstructures as a model for interpretation of##chemical reactions, Iranian J. Math. Chem. 7 (2) (2016) 267−283.##6. B. Davvaz and A. DehganNezhad, Chemical examples in hypergroups,##Ratio Mat. 14 (2003) 71−74.##7. B. Davvaz, A brief survey of the theory of Hstructures, Proc. 8th##International Congress on Algebraic Hyperstructures and Applications, 1−9##September 2002, Samothraki, Greece, Spanidis Press, 2003, pp. 39−70.##8. B. Davvaz, A. Dehghan Nezhad and A. Benvidi, Chemical hyperalgebra:##Dismutation reactions, MATCH Commun. Math. Comput. Chem. 67 (2012)##55−63.##9. B. Davvaz, A. Dehghan Nezhad and A. Benvidi, Chain reactions as##experimental examples of ternary algebraic hyperstructures, MATCH##Commun. Math. Comput. Chem. 65 (2) (2011) 491−499.##10. B. Davvaz and A. Dehghan Nezhad, Dismutation reactions as experimental##verifications of ternary algebraic hyperstructures, MATCH Commun. Math.##Comput. Chem. 68 (2012) 551−559.##11. B. Davvaz, A. Dehghan Nezhad and M. MazloumArdakani, Chemical##hyperalgebra: Redox reactions, MATCH Commun. Math. Comput. Chem.##71 (2014) 323−331.##12. B. Davvaz, Semihypergroup Theory, Elsevier/Academic Press, London,##13. F. Marty, Sur une generalization de la notion de group, In 8th Congress##Math. Scandenaves, 1934, pp. 45−49.##14. Ch. E. Mortimer, Chemistry, Wadsworth Pub Co, 6 Sub edition, 1986.##15. T. Vougiouklis, Hgroups defined on the same set, Discrete Math. 155##(1996) 259−265.##16. T. Vougiouklis, Hyperstructures and Their Representations, Hadronic##Press, Inc, 115, Palm Harber, USA, 1994.##17. T. Vougiouklis, The fundamental relation in hyperrings. The general##hyperfield, Proc. Fourth Int. Congress on Algebraic Hyperstructures and##Appl. (AHA 1990), World Scientific, 1991, pp. 203−211.##]
Solving Multiobjective Optimal Control Problems of chemical processes using Hybrid Evolutionary Algorithm
2
2
Evolutionary algorithms have been recognized to be suitable for extracting approximate solutions of multiobjective problems because of their capability to evolve a set of nondominated solutions distributed along the Pareto frontier. This paper applies an evolutionary optimization scheme, inspired by Multiobjective Invasive Weed Optimization (MOIWO) and Nondominated Sorting (NS) strategies, to find approximate solutions for multiobjective optimal control problems (MOCPs). The desired control function may be subjected to severe changes over a period of time. In response to deficiency, the process of dispersal has been modified in the MOIWO. This modification will increase the exploration power of the weeds and reduces the search space gradually during the iteration process. The performance of the proposed algorithm is compared with conventional Nondominated Sorting Genetic Algorithm (NSGAII) and Nondominated Sorting Invasive Weed Optimization (NSIWO) algorithm.The results show that the proposed algorithm has better performance than others in terms of computing time, convergence rate and diversity of solutions on the Pareto frontier.
1

103
126


Gholam
Askarirobati
Department of Mathematics, Payame Noor University, P.O.Box 193953697, Tehran, Iran
Department of Mathematics, Payame Noor University,
Iran
askary2010@gmail.com


Akbar
Hashemi Borzabadi
Department of Mathematics and Computer Science, Damghan University, Damghan, Iran
Department of Mathematics and Computer Science,
Iran
a.hashemi.bor@gmail.com


Aghileh
Heydari
Department of Mathematics, Payame Noor University, Tehran, Iran
Department of Mathematics, Payame Noor University,
Iran
a_heidari@pnu.ac.ir
Multiobjective optimal control
Pareto optimal frontier
Nondominated sorting
invasive weed optimization
Fed Batch Reactor
[1. L. Biegler, Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation, Comput. Chem. Eng. 8 (1984) 243−248.##2. L. Biegler, An overview of simultaneous strategies for dynamic optimization, Chem. Eng Process: Process Intensif. 46 (11) (2007) 1043−1053.##3. H. Bock and K. Plitt, A multiple shooting algorithm for direct solution of optimal control problems. In: Proceedings of the 9th IFAC world congress, Budapest. Pergamon Press, 1984, pp. 243247.##4. C. A. Coello, A comprehensive survey of evolutionarybased multiobjective optimization techniques, Knowl. Inf. Syst.1 (3) (1999) 269−308.##5. C. A. Coello andM. S. Lechuga, MOPSO: A proposal for multiple objective particle swarm optimization, In: Proceeding of Congress on Evolutionary Computation (CEC2002), Honolulu, HI. 1 (2002) 1051−1056.##6. I. Das and J. E. Dennis, Normalboundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems, SIAM. J.Optimiz. 8 (3) (1998) 631−657.##7. K. Deb, MultiObjective Optimization Using Evolutionary Algorithms,Wiley 2001.##8. K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multiobjective geneticalgorithm: NSGAII, IEEE. Trans. Evolut. Comput. 6 (2) (2002) 182−197.##9. T. Erickson, A. Mayer andJ. Horn, The niched Pareto genetic algorithm 2 applied to the design of ground water remediation systems, Evolutionary MultiCriterion Optimization: First International Conference, EMO. (2001) 681−695.##C. M. Fonseca, MultiObjective Genetic Algorithms with Application to Control Engineering Problems, Ph.D. Thesis, University of Sheffield. Sheffield, 1995.##S. M. K. Heris and H. Khaloozadeh, Open and closedloop multiobjective optimal strategies for HIV therapy using NSGAII, IEEE. Trans. Biomed. Eng. 58 (6) (2011) 1678−1685.##J. Knowles andD. Corne, ThePareto archived evolution strategy: A new baseline algorithm for Pareto multiobjective optimization, Proceedings of the 1999 IEEE Congress on Evolutionary Computation 1999.##S. Kukkonen and K. Deb, Improved Pruning of NonDominated Solutions Based on Crowding Distance for BiObjective Optimization Problems, IEEE Congress on Evolutionary Computation, pp. 91−98, 2007.##D. Kundu, K. Suresh, S. Ghosh, S. Das and B. K. Panigrahi, Multiobjective optimization with artificial weed colonies, J. Inf. Sci. 181 (2011) 2441−2454.##D. Leineweber, I. Bauer, H. Bock and J. Schlder, An efficient multiple shooting based reduced SQP strategy for largescale dynamic process optimization, Part I: Theoretical aspects, Comput. Chem. Eng. 27 (2003) 157−166.##F. Logist, P. M. Van Erdeghem and J. F. Van Impe, Efficient deterministic multiple objective optimal control of (bio)chemical processes, Chem. Eng. Sci. 64 (2009) 2527−2538.##F. Logist, B. Houska, M. Diehl and J. Van Impe, Fast Pareto set generation for nonlinear optimal control problems with multiple objectives, Struct. Multidisc. Optim. 42 (2010) 591−603.##F. Logist, B. Houska, M. Diehl and J. Van Impe, Robust multiobjective optimal control of uncertain (bio)chemical processes, Chem. Eng. Sci. 66 (2011) 4670−4682.##F. Logist, S. Sager, C. Kirchesand and J. Van Impe, Efficient multiple objective optimal control of dynamic systems with integer controls, J. Process Control 20 (2010) 810−822.##F. Logist, M. Vallerio, B. Houska, M. Diehl and J. Van Impe, Multiobjective optimal control of chemical processes using ACADO toolkit, Comput. Chem. Eng. 37 (2012) 191−199.##R. Mehrabian and C. Lucas, A novel numerical optimization algorithm inspired from weed colonization, Ecol. Inform. 1 (4) (2006) 355−366.##A. Messac, A. IsmailYahaya and C. A. Mattson, The normalized normal constraint method for generating the Pareto frontier, Struct. Multidisc. Optim. 25 (2) (2003) 86−98.##K. Miettinen, Nonlinear MultiObjective Optimization, Kluwer, Boston, 1999.##A. H. Nikoofard, H. Hajimirsadeghi, A. RahimiKian and C. Lucas, Multiobjective invasive weed optimization: Application to analysis of Pareto improvement models in electricity markets, Appl. Soft. Comput. 12 (2012) 100−112.##H. Modares and M. N. Sistani, Solving nonlinear optimal control problems using a hybrid IPSOSQP algorithm, Eng. Appl. Artif. Intel. 24 (2011) 476−484.##H. Ohno, E. Nakanishi and T. Takamatsu, Optimal control of a semibatch fermentation, Biotechnol. Bioeng. 18 (1976) 847−864.##G. C. Onwubolu and B. V. Babu, New Optimization Techniques in Engineering, Springer Verlag, Heidelberg, Germany 2004.##N. Patel and N. Padhiyar, Modified genetic algorithm using box complex method: Application to optimal control problems, J. Process Control 26 (2015) 35−50.##N. Patel and N. Padhiyar, Multiobjective dynamic optimization study of fedbatch bioreactor, Chem. Eng. Res. Des. 119 (2017) 160−170.##S. Panuganti, P. Roselyn John, D. Devraj and S. Sekhar Dash, Voltage stability constrained optimal power flow using NSGAII, Comput. Water Energy Envir. Eng. 2 (2013) 1−8.##S. Park and W. Fred Ramirez, Optimal production of secreted protein in fedbatch reactors, AIChE. J. 34 (1988) 1550−1558.##D. Sarkar and J. Modak, Genetic algorithms with filters for optimal control problems infedbatch bioreactors, Bioprocess Biosyst. Eng. 26 (2004) 295−306.##D. Sarkar and J. M. Modak, Paretooptimal solutions for multiobjective optimization offedbatch bioreactors using nondominated sorting genetic algorithm, Chem. Eng. Sci. 60 (2) (2005) 481−492.##J. D. Schafier, Multiple objective optimization with vector evaluated genetic algorithms, Proceedings of the First International Conference of Genetic Algorithms, Pittsburgh, pp. 93−100, 1985.##N. Srinivas and K. Deb, Multiobjective function optimization using nondominated sorting genetic algorithms, Evolut.Comput.2 (3) (1995) 221−248.##F. Sun, W. Du, R. Qi, F. Qian and W. Zhong, A hybrid improved genetic algorithm and its application in dynamic optimization problems of chemical processes, Chin. J. Chem. Eng. 21 (2013) 144−154.##E. Zitzler and L. Thiele, Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evolut. Comput. 3 (1999) 257−271.##E. Zitzler, M. Laumanns and L. Thiele, SPEA2: Improving the strength Pareto evolutionary algorithm, Zurich, Switzerland: Swiss Federal Institute Technology, 2001.##X. Zhang, J. Xu and G. Cui, Research on invasive weed optimization based on the cultural framework, 3rd International Conference on BioInspired Computing: Theories and Applications, IEEE Conference Publications, pp. 129–134, 2008.##P. Zhang, H. Chen, X. Liu and Z. Zhang, An iterative multiobjective particle swarm optimizationbased control vector parameterization for state constrained chemical and biochemical engineering problems, Biochem. Eng. J. 103 (2015) 138−151.##]
Mpolynomial of some graph operations and Cycle related graphs
2
2
In this paper, we obtain Mpolynomial of some graph operations and cy cle related graphs. As an application, we compute Mpolynomial of some nanostruc tures viz., TUC4C8[p; q] nanotube, TUC4C8[p; q] nanotorus, line graph of subdivision graph of TUC4C8[p; q] nanotube and TUC4C8[p; q] nanotorus, Vtetracenic nanotube and Vtetracenic nanotorus. Further, we derive some degree based topological indices from the obtained polynomials.
1

127
150


Bommanahal
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
India
b.basavanagoud@gmail.com


Anand
Barangi
Department of Mathematics
Karnatak University
Dharwad, Karnatak580003
India.
Department of Mathematics
Karnatak University
Dhar
India
apb4maths@gmail.com


Praveen
Jakkannavar
Department of Mathematics
Karnatak University
Dharwad, Karnataka580003
India.
Department of Mathematics
Karnatak University
Dhar
India
jpraveen021@gmail.com
Mpolynomial
Degreebased topological index
line graph
subdivision graph
wheel graph
[1. M. S. Anjum and M. U. Safdar, K Banhatti and K hyperBanhatti indices of##nanotubes, Eng. Appl. Sci. Lett. 2 (1) (2019) 19−37.##2. A. R. Ashrafi, T. Došlić and A. Hamzeh, Extremal graphs with respect to the##Zagreb coindices, MATCH Commun. Math. Comput. Chem. 65 (2011) 85−92.##3. A. R. Ashrafi, B. Manoochehrian and H. YousefiAzari, On the PI polynomial of a##graph, Util. Math. 71 (2006) 97−108.##4. B. Basavanagoud, A. P. Barangi and S. M. Hosamani, First neighbourhood Zagreb##index of some nano structures, Proc. Inst. Appl. Math. 7 (2) (2018) 178−193.##5. B. Basavanagoud and P. Jakkannavar, KulliBasava indices of graphs, Int. J. Appl.##Eng. Res. 14(1) (2019) 325−342.##6. B. Basavanagoud and P. Jakkannavar, Computing leap Zagreb indices of##generalized xyzpointline transformation graphs T(G) when z = +, J. Comp.##Math. Sci. 9 (10) (2018) 1360−1383.##7. B. Basavanagoud, Chitra E, On the leap Zagreb indices of generalized xyzpointline##transformation graphs T(G) when z = 1, Int. J. Math. Combin., 2 (2018) 44##8. B. Basavanagoud and P. Jakkannavar, Mpolynomial and degreebased topological##indices of graphs, Electronic J. Math. Anal. Appl., 8 (1) (2020) 75−99.##9. G. G. Cash, Relationship between the Hosoya polynomial and the hyperWiener##index, Appl. Math. Lett. 15 (2002) 893−895.##10. E. Deutsch and S. Klavžar, MPolynomial and degreebased topological indices,##Iran. J. Math. Chem. 6 (2) (2015) 93−102.##11. E. Deutsch and S. Klavžar, MPolynomial revisited: Bethe cacti and an extension of##Gutman's approach, J. Appl. Math. Comput. 60 (2019) 253−264.##12. N. De, Computing reformulated first Zagreb index of some chemical graphs as an##application of generalized hierarchical product of graphs. Open J. Math. Sci. 2 (1)##(2018) 338−350.##13. N. De, Hyper Zagreb index of bridge and chain graphs, Open J. Math. Sci. 2 (1)##(2018) 1−17.##14. T. Došlić, Planar polycyclic graphs and their Tutte polynomials, J. Math. Chem. 51##(2013) 1599−1607.##15. E. J. Farrell, An introduction to matching polynomials, J. Combin. Theory Ser. B##27 (1979) 75−86.##16. S. Fajtlowicz, On conjectures of Graffiti  II, Congr. Numer. 60 (1987) 187−197.##17. J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. #DS6,##(2018) 502 pages.##18. W. Gao, M. Asif and W. Nazeer, The study of honey comb derived network via##topological indices, Open J. Math. Anal. 2 (2) (2018) 10−26.##19. I. Gutman, Molecular graphs with minimal and maximal Randić indices, Croat.##Chem. Acta 75 (2002) 357−369.##20. I. Gutman, The acyclic polynomial of a graph, Publ. Inst. Math. 22 (36) (1979)##63−69.##21. I. Gutman, Degreebased topological indices, Croat. Chem. Acta 86 (2013)##351−361.##22. I. Gutman and N. Trinajstić, Graph theory and molecular orbitals, Total electron##energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535−538.##23. I. Gutman, B. Ruščić, N. Trinajstić and C. F. Wilcox, Graph theory and molecular##orbitals, XII. Acyclic polyenes, J. Chem. Phys. 62 (1975) 3399−3405.##24. F. Harary, Graph Theory, AddisonWesely, Reading, 1969.##25. F. Hassani, A. Iranmanesh and S. Mirzaie, Schultz and modified Schultz##polynomials of fullerene, MATCH Commun. Math. Comput. Chem. 69 (2013)##87−92.##26. H. Hosoya, On some counting polynomials in chemistry, Discrete Appl. Math. 19##(1988) 239−257.##27. I. Javaid and S. Shokat, On the partition dimension of some wheel related graphs, J.##Prime Res. Math. 4 (2008) 154−164.##28. S. M. Kang, W. Nazeer, W. Gao, D. Afzal and S. N. Gillani, Mpolynomials and##topological indices of dominating David derived networks, Open Chem. 16 (2018)##201−213.##29. Y. C. Kwun, M. Munir, W. Nazeer, R. Rafique and S. M. Kang, Mpolynomials and##topological indices of Vphenylenic nanotubes and nanotori, Sci. Reports 7 (2017)##Art. 8756.##30. Y. Kins, Radio labeling of certain graphs, Ph.D. Thesis, University of Madras,##India, November 2011.##31. X. Li and H. Zhao, Trees with the first three smallest and largest generalized##topological indices, MATCH Commun. Math. Comput. Chem. 50 (2004) 57−62.##32. X. Li and Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput.##Chem. 59 (2008) 127−156.##33. M. Munir, W. Nazeer, S. Rafique and S. M. Kang, Mpolynomial and related##topological indices of nanostar dendrimers, Symmetry 8 (2016) 97.##34. M. Munir, W. Nazeer, S. Rafique, A. R. Nizami and S. M. Kang, Mpolynomial and##degreebased topological indices of titania nanotubes, Symmetry 8 (2016) 117.##35. M. Munir, W. Nazeer, S. Rafique, A. R. Nizami and S. M. Kang, MPolynomial##and DegreeBased Topological Indices of Polyhex Nanotubes Symmetry, 8 (2016)##36. M. Randić, On characterization of molecular branching, J. Am. Chem. Soc. 97##(1975) 6609−6615.##37. M. Riaz, W. Gao and A. Q. Baig, MPolynomials and degreebased Topological##Indices of Some Families of Convex Polytopes. Open J. Math. Sci. 2 (1) (2018)##18−28.##38. S. Roy, Packing chromatic number of certain fan and wheel related graphs, AKCE##Int. J. Graphs Comb. 14 (2017) 63−69.##39. Z. Shao, A. R. Virk, M. S. Javed, M. A. Rehman and M. R. Farahani, Degree based##graph invariants for the molecular graph of Bismuth TriIodide, Eng. Appl. Sci. Lett.##2 (1) (2019) 1−11.##40. H. Siddiqui and M. R. Farahani, Forgotten polynomial and forgotten index of##certain interconnection networks, Open J. Math. Sci. 1 (1) (2017) 44−59.##41. Z. Tang, L. Liang and W. Gao, Wiener polarity index of quasitree molecular##structures, Open J. Math. Sci. 2 (1) (2018) 73−83.##42. S. K. Vaidyaa and M. S. Shukla, bChromatic number of some wheel related##graphs, Malaya J. Math. 2 (4) (2014) 482−488.##43. A. R. Virk, M. N. Jhangeer and M. A. Rehman, Reverse Zagreb and reverse hyper##Zagreb indices for silicon carbide [, ] and [, ], Eng. Appl. Sci.##Lett. 1 (2) (2018) 37−50.##44. H. Wiener, Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69##(1947) 17−20.##45. L. Yan, M. R. Farahani and W. Gao, Distancebased indices computation of##symmetry molecular structures, Open J. Math. Sci. 2 (1) (2018) 323−337.##46. H. Zhang, F. Zhang, The Clar covering polynomial of hexagonal systems I,##Discrete Appl. Math. 69 (1996) 147−167.##]
Trees with the greatest Wiener and edgeWiener index
2
2
The Wiener index W and the edgeWiener index W_e of G are defined as the sum of distances between all pairs of vertices in G and the sum of distances between all pairs of edges in G, respectively. In this paper, we identify the four trees, with the first through fourth greatest Wiener and edgeWiener index among all trees of order n ≥ 10.
1

151
159


Ali
Ghalavand
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 8731753153, I R Iran
Department of Pure Mathematics, Faculty of
Iran
ali.ghalavand.kh@gmail.com
tree
Wiener index
edgeWiener index
Graph operation
[Y. Alizadeh, A. Iranmanesh, T. Doŝlić, M. Azari, The edge Wiener index of suspensions, bottlenecks, and thorny graphs, Glas. Mat. Ser. III 49 (69) (2014) 1−12.##M. Azari, A. Iranmanesh, A. Tehranian, A method for calculating an edge version of the Wiener number of a graph operation, Util. Math. 87 (2012) 151−164.##F. Buckley, Mean distance in line graphs, Congr. Numer. 32 (1981) 153−162.##A. Chen, X. Xiong, F. Lin, Explicit relation between the Wiener index and the edgeWiener index of the catacondensed hexagonal systems, Appl. Math. Comput. 273 (2016) 1100−1106.##P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, The edge–Wiener index of a graph, Discrete Math. 309 (2009) 3452−3457.##Y. Dou, H. Bian, H. Gao, H. Yu, The polyphenyl chains with extremal edge–Wiener indices, MATCH Commun. Math. Comput. Chem. 64 (2010) 757−766.##J. Devillers, A.T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach Science Publishers, 1999.##H.Y. Deng, The trees on vertices with the first to seventeenth greatest Wiener indices are chemical trees, MATCH Commun. Math. Comput. Chem. 57 (2007) 393−402.##A. Iranmanesh, M. Azari, Edge–Wiener descriptors in chemical graph theory: a survey, Curr. Org. Chem. 19 (2015) 219−239.## A. Iranmanesh, I. Gutman, O. Khormali, A. Mahmiani, The edge versions of Wiener index, MATCH Commun. Math. Comput. Chem. 61 (2009) 663−672.## M. Karelson, Molecular Descriptors in QSAR/QSPR, Wiley, New York, 2000.##M. Knor, P. Potočnik, R. Škrekovski, Relationship between the edgeWiener index and the Gutman index of a graph, Discrete Appl. Math. 167 (2014) 197−201.##M. H. Khalifeh, H. Yousefi Azari, A. R. Ashrafi, S. G. Wagner, Some new results on distance–based graph invariants, European J. Comb. 30 (2009) 1149−1163.##A. Kelenc, S. Klavžar, N. Tratnik, The Edge–Wiener index of benzenoid systems in linear time, MATCH Commun. Math. Comput. Chem. 74 (2015) 521−532.##M. Liu, B. Liu, Q. Li, Erratum to: The trees on vertices with the first to seventeenth greatest Wiener indices are chemical trees, MATCH Commun. Math. Comput. Chem. 64 (2010) 743−756.##M. J. Nadjafi–Arani, H. Khodashenas, A. R. Ashrafi, Relationship between edge Szeged and edge Wiener indices of graphs, Glas. Mat. Ser. III 47 (67) (2012) 21−29.##N. Tratnik, P. Žigert Pleteršek, Relationship between the Hosoya polynomial and the edgeHosoya polynomial of trees, MATCH Commun. Math. Comput. Chem. 78 (2017) 181−187.##H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc.##69 (1947) 17−20.##H. Yousefi–Azari, M. H. Khalifeh, A. R. Ashrafi, Calculating the edge Wiener and edge Szeged indices of graphs, J. Comput. Appl. Math. 235 (2011) 4866−4870.##]
Predeiction of ∆H0f(gas) ,∆H0f(Liq) of Amines Derivatives Using chemometrics (A Quantitative StructureProperty Relationship Study)
2
2
In this study, multiple linear regression method that is based on propertystructure model has been used to predict the standard enthalpies of formation for the gas and liquid phases of the 33 different types of amines. It was indicated that among studied topological and geometric descriptors to predict the ∆H˚f(liquid), descriptors as PSA, H, MaxZL and V have more importance than the other descriptors. Also, the results of experiments on studied amines were compared with the results of multiple linear regression calculations and it was observed that such descriptors as MaxZL MaxPA, DE, J and WW are the best descriptors for predicting the values of ∆H˚f(gas) of this class of amines.
1

161
179


Morteza
Rezaei
Department of Chemistry, Arak Branch, Islamic Azad University, Arak, Iran
Department of Chemistry, Arak Branch, Islamic
Iran
mortezarezaei211@gmail.com


Esmat
Mohammadinasab
Department of Chemistry, Arak Branch, Islamic Azad University, Arak, Iran
Department of Chemistry, Arak Branch, Islamic
Iran
esmohammadinasab@gmail.com
Amines Derivatives
Standard Enthalpy of Formation
Molecular Descriptors
chemometrics
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The new high approximation of stiff systems of first order IVPs arising from chemical reactions by kstep Lstable hybrid methods
2
2
In this paper, we present a new class of hybrid methods for the numerical solution of first order ordinary differential equations (ODEs). The accuracy and stability properties of the new methods are investigated. In the final section, we apply new hybrid methods to solve two stiff chemical problems such as Roberston problem.
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Mohammad
Mehdizadeh Khalsaraei
Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, Iran
Department of Mathematics, Faculty of Sciences,
Iran
muhammad.mehdizadeh@gmail.com


Ali
Shokri
Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, Iran
Department of Mathematics, Faculty of Sciences,
Iran
shokri2090@gmail.com


Maryam
Molayi
Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, Iran
Department of Mathematics, Faculty of Sciences,
Iran
m.molayi.66@gmail.com
Stiff initial value problems
Hybrid methods
Roberston problem
AStability
LStability
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