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On Prime and Semiprime Ideals in Ordered AG-Groupoids 2 2 The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them. 1 11 2014/02/12 1392/11/23 2016/11/6 1395/8/16 P. Yiarayong P. Yiarayong University Phitsanuloke 65000 Thailand pairote0027@hotmail.com Ordered AG-Groupoids Prime Semiprime quasi-prime Quasi-semiprime. 1-F. Yousafzai, N. Yaqoob, A. Borumand Saeid, Some results in bipolar-valued fuzzy ordered AG-groupoids, Discussiones Mathematicae General Algebra and Applications, 32, (2012), 55–76.##2-A. Gharibkhajeh, H. Doostie, On the graphs related to green relations of finite semigroups, Iranian Journal of Mathematical Sciences and Informatics, 9(1), (2014), 43–51.## 3-S. H. Ghazavi, S. M. Anvariyeh, S. Mirvakili, Elhyperstructures derived from (partially) quasi ordered hyperstructures, Iranian Journal of Mathematical Sciences and Informatics, 10(2), (2015), 99 –114.##4- P. Holgate, Groupoids satisfying a simple invertive law, Math. Stud., 61, (1992), 101–106.##5- M.K. Kazim, M. Naseeruddin, On almost semigroups, The Alig. Bull. Math, 2, (1972), 1–7.##6-M. Khan, N. Ahmad, Characterizations of left almost semigroups by their ideals, Journal of Advanced Research in Pure Mathematics, 2(3), (2010), 1–733.##7-M. Khan, S. Anis, K.P. Shum, Characterizations of left regular ordered Abel-Grassmann groupoids, International Journal of Algebra, 5(11), (2011), 499–521.##8- M. Khan, Faisal, On fuzzy ordered Abel-Grassmann’s groupoids, J. Math. Res., 3, (2011), 27–40.##9-A. Khan, F. Yousafzai, W. Khan, N. Yaqoob, Ordered LA-semigroups in terms of interval valued fuzzy ideals, Journal of Advanced Research in Pure Mathematics, 5(1), (2013), 100–117.##10-H. R. Maimani, Median and center of zero-divisor graph of commutative semigroups, Iranian Journal of Mathematical Sciences and Informatics, 3(2), (2008), 69–76.##11-Q. Mushtaq, Abelian groups defined by LA-semigroups, Studia Scient. Math. Hungar, (1983), 427–428.##12- Q. Mushtaq, Q. Iqbal, Decomposition of a locally associative LA-semigroup, Semigroup Forum, 41, (1990), 154–164.##13- Q. Mushtaq, M. Iqbal, On representation theorem for inverse LA-semigroups, Proc. Pakistan Acad. Sci, 30, (1993), 247–253.##14- Q. Mushtaq, M. Khan, A note on an Abel-Grassmann’s 3-band,Quasigroups and Related 26- Systems, 15, (2007), 295–301.##15- Q. Mushtaq, M. Khan, Ideals in left almost semigroup,arXiv:0904.1635v1 [math.GR], 28- (2009).## 16-M. Shah, I. Ahmad, A. Ali, Discovery of new classes of AG-groupoids, Research Journal of Recent Sciences, 1(11), (2012), 47–49.## 17-T. Shah, I. Rehman and R. Chinram, On M-systems in ordered AG-groupoids, Far East J. Math. Sci., 47(1), (2010), 13–21.##18- T. Shah, T. Rehman, A. Razzaque, Soft ordered Abel-Grassman’s groupoid (AGgroupoid), International Journal of the Physical Sciences, 6(25), (2011), 6118–6126.## ##

Modeling Dynamic Production Systems with Network Structure 2 2 This paper deals with the problem of optimizing two-stage structure decision making units (DMUs) where the activity and the performance of two-stage DMU in one period effect on its efficiency in the next period. To evaluate such systems the effect of activities in one period on ones in the next term must be considered. To do so, we propose a dynamic DEA approach to measure the performance of such network units. According to the results of proposed dynamic model the inefficiencies of DMUs improve considerably. Additionally, in models which measure efficiency score, undesirable outputs are mostly treated as inputs, which do not reflect the true production process. We propose an alternative method in dealing with bad outputs. Statistical analysis of sub-efficiencies, i.e. efficiency score of each stage, during all periods represents useful information about the total performance of the stage over all periods. 13 26 2014/02/122013/08/24 1392/6/2 2016/11/62016/11/13 1395/8/23 F. Koushki F. Koushki Qazvin Branch, Islamic Azad University Iran fkoushki@gmail.com Data envelopment analysis (DEA) Network DEA Bad outputs Dynamic DEA Sub-efficiency. 1-A. Amirteimoori, ADEA two-stage decision processes with shared resources, Central European Journal of Operations Research,21, (2013), 141-151.##2-G. Aslani, S.H. Momeni-Masuleh, A. Malek, F. Ghorbani, Bank efficiency evaluation using a neural network-DEA method, Iranian Journal of Mathematical Sciences and Information, 4(2), (2009), 33-48.##3-L. Botti , W. Briec , G. Cliquet, Plural forms versus franchise and company-owned systems: a DEA approach of hotel chain performance, Omega, The International Journal of Management Science, 37, (2009), 566-78.##4-Y. Chen, J. Zhu , Measuring information technologys indirect impact on firm performance, Information Technology and Management, 5(12), (2004), 9-22.##5-Y. Chen, W.D. Cook, N. Li, J.Zhu, Additive efficiency decomposition in two-stage DEA, European Journal of Operational Research, 196, (2009), 1170-1176.##6- R. Fare, S. Grosskopf, Productivity and intermediate products: a Frontier approach, Economics Letters, 50(1), (1996), 65–70.##7-R. Fare, S. Grosskopf, w. Gerald, Network Dea, Modeling data irregularities and structural complexities in data envelopment analysis, Springer US, (2007), 209–240.##8- R. Fare, D. Primont, Efficiency measures for multi plant firms, Operations Research Letters, 3, (1984), 257–260.##9-H. Fukuyama, S.M. Mirdehghan, Identifying the efficiency status in network DEA, European Journal of Operational Research, 220(1), (2012), 85–92.##10-H. Fukuyama, L. Wiliam, A.Weber, Slacks-based inefficiency measure for a two-stage system with bad outputs, Omega, 38, (2010), 398–409.##11-C. Kao, S.N. Hwang, Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan, European Journal of Operational Research, 185(1), (2008), 418–429.##12- S.T. Liu, Fuzzy efficiency ranking in fuzzy two-stage data envelopment analysis, Optimization Letters, (2013).##13- J.C. Paradi, S. Rouatt, H. Zhu, Two-stage evaluation of bank branch efficiency using data envelopment analysis, Omega, 39(1), (2011), 99–109.##14- M. Saraj, N. Safaei, Integrating goal programming, Taylor Series, Kuhn-Tucker conditions, and penalty function approaches to solve linear fractional bi-level programming problems, Iranian Journal of Mathematical Sciences and Information, 10(1), (2015).##15- L.M. Seiford, J.Zhu , Profitability and marketability of the top 55 US commercial banks, MANAGE SCI, 45(9), (1999), 1270–88.##16-C.H. Wang, R. Gopal, S. Zionts, Use of data envelopment analysis in assessing information technology impact on firm performance, Annals of Operations Research, 73, (1997), 191-213.##17-K. Wang, W. Huang, J. Wu, Y.N. Liu, Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA , Omega, (2014), 45-20.##18-F. Yang, D.Wu, L. Liang, G.Bi, D.D. Wu, Supply chain DEA: production possibility set and performance evaluation model, Annals of Operations Research, 185, (2011), 195-211.## ##

A Note on Twists of (y^2=x^3+1) 2 2 ‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic twists of (E_1) cite{Kih}. 27 34 2014/02/122013/08/242014/06/23 1393/4/2 2016/11/62016/11/132015/05/6 1394/2/16 F. Izadi F. Izadi Urmia University Iran farzali.izadi@azaruniv.edu A. Shamsi Zargar A. Shamsi Zargar Shahid Madani University, Tabriz Iran shzargar.arman@azaruniv.edu Elliptic curve‎ ‎Mordell curve‎ ‎(Mordell-Weil) rank‎ ‎Twist. 1-H. Daghigh, M. Bahramian, Generalized jacobian and discrete logarithm problem on elliptic curves, Iran. J. Math. Sci. Inform., 4(2), (2009), 55–64.##2-A. Dujella, I. Gusic, L. Lasic, On quadratic twists of elliptic curves y2 = x(x − 1)(x − λ), Rad HAZU, Mat. Znan., 18, (2014), 27–34.##3-I. Gusic, P. Tadic, Injectivity of specialization homomorphism of elliptic curves, J. Number Theory, 148, (2015), 137–152.##4-S. Kihara, On the rank of elliptic curve y2 = x3 + k. II, Proc. Japan Acad. Ser. A Math. Sci., 72, (1996), 228–229.##5-A. Knapp, Elliptic Curves, Princeton University Press, 1992.##6-NMBRTHRY Home Page, https://listserv.nodak.edu/archives/nmbrthry.html.##7-A. Rastegar, Deformation of outer representations of Galois group, Iran. J. Math. Sci. Inform., 6(1), (2011), 33–52.##8-A. Rastegar, Deformation of outer representations of Galois group II, Iran. J. Math. Sci. Inform., 6(2), (2011), 33–41.##9-K. Rubin, A. Silverberg, Rank frequencies for quadratic twists of elliptic curves, Exp. Math., 10, (2001), 559–569.##10-K. Rubin, A. Silverberg, Twists of elliptic curves of rank at least four, in: Ranks of Elliptic Curves and Random Matrix Theory, Cambridge University Press, 2007, 177–188.##11-SAGE software, Version 4.5.3, http://www.sagemath.org.##12-S. Schmitt, H. G. Zimmer, Elliptic curves: A Computational Approach, De Gruyter studies in mathematics, 31, Berlin, Germany, 2003.##13-J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, New York, 1986.##14-J. H. Silverman, Heights and the specialization map for families of abelian varieties, J. Reine Angew. Math., 342, (1983), 197–211.##15-J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986.## ##

Graph Convergence for H(.,.)-co-Accretive Mapping with over-Relaxed Proximal Point Method for Solving a Generalized Variational Inclusion Problem 2 2 In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem in Banach spaces. Our results can be viewed as an extension of some previously known results in this direction. 35 46 2014/02/122013/08/242014/06/232014/12/29 1393/10/8 2016/11/62016/11/132015/05/62015/10/8 1394/7/16 M. Rahaman M. Rahaman Aligarh Muslim University India mrahman96@yahoo.com R. Ahmad R. Ahmad Aligarh Muslim University India raisain_123@rediffmail.com H. A. Rizvi H. A. Rizvi Aligarh Muslim University India haider.alig.abbas@gmail.com Graph convergence Over-relaxed Accretive Variational inclusion Convergence. 1-M. Abbasi, Kh. Pourbarat, The system of vector variational-like inequalities with weakly relaxed {ηγ − αγ}γ∈Γ pseudomonotone mapping in Banach spaces, Iranian Journal of Mathematical Sciences and Informatics, 5(2), (2010), 1-11.##2-R.P. Agarwal, Y.J. Cho, N.J. Huang, Sensitivity analysis for strongly nonlinear quasivariational inclusions, Applied Mathematics Letters, 13(6), (2000), 19-24.##3-R.P. Agarwal, N.J. Huang, Y.J Cho, Generalized nonlinear mixed implicit quasivariational inclusions with set-valued mappings, Journal of Inequalities and Applications, 7(6), (2002), 807-828.##4-R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(·, ·)-co-accretive mapping with an application, Bulletin of the Malaysian Mathematical Sciences Society, 38(4), (2015), 1481-1506..##5-R. Ahmad, Q.H. Ansari, An iterative algorithm for generalized nonlinear variational inclusions, Applied Mathematics Letters, 13(5), (2000), 23-26.##6-S.S. Chang, Y.J. Cho, H.Y. Zhou, Iterative methods for nonlinear operator equations in Banach spaces, Nova Science Publishers, New York, 2002.##7-J.Y. Chen, N.C. Wong, J.C. Yao, Algorithm for generalized co-complementarity problems in Banach spaces, Computers & Mathematics with Applications, 43, (2002), 49-54.##8-A. Deepmala, A study on fixed point theorems for nonlinear contractions and its applications, Ph.D. Thesis, Pt. Ravishankar Shukla University, Raipur-492010, India, 2014.##9-X.P. Ding, C.L. Luo, Perturbed proximal point algorithms for generalized quasivariational-like inclusions, Journal of Computational and Applied Mathematics, 210, (2000), 153-165.##10-A. Hassouni, A. Moudafi, A perturbed algorithm for variational inclusions, Journal of Mathematical Analysis and Applications, 185, (1994), 706-712.##11-N.J. Huang, A new class of generalized set-valued implicit variational inclusions in Banach spaces with an application, Computers & Mathematics with Applications, 41(7-8), (2001), 937-943.##12-N.J. Huang, Nonlinear implicit quasi-variational inclusions involving generalized maccretive mappings, Archives of Inequalities and Applications, 2(4), (2004), 413-426.##13-N.J. Huang, Generalized nonlinear variational inclusions with noncompact valued mappings, Applied Mathematics Letters, 9(3), (1996), 25-29.##14-S. Husain, S. Gupta, V.N. Mishra, An existence theorem of solutions for the systems of generalized vector quasi-variational inequalities, American Journal of Operations Reseach, 3(03), (2013), 329-336.##15-S. Husain, S. Gupta, V.N. Mishra, Generalized H(·, ·, ·)-η-cocoercive operators and generalized set-valued variational-like inclusions, Journal of Mathematics, 2013, (2013): 738491.##16-S. Husain, S. Gupta, V.N. Mishra, Graph convergence for the H(·, ·)-mixed mapping with an application for solving the system of generalized variational inclusions, Fixed Point Theory and Applications, 2013(1), (2013): 304.##17-F. Li, On over-relaxed proximal point algorithm for generalized nonlinear operator equation with (A, η, m)-monotonicity framework, International Journal of Modern Nonlinear Theory and Application, 1, (2012), 67-72.##18-X. Li, N.J. Huang, Graph convergence for the H(·, ·)-accretive operator in Banach spaces with an application, Applied Mathematics and Computation, 217, (2011), 9053-9061.##19-H.Y. Lan, Graph-convergent analysis of over-relaxed (A, η, m)-proximal point iterative methods with errors for general nonlinear operator equations, Fixed Point Theory and Applications, 2014(1), (2014): 161.## ##

Integrating Differential Evolution Algorithm with Modified Hybrid GA for Solving Nonlinear Optimal Control Problems 2 2 ‎Here‎, ‎we give a two phases algorithm based on integrating differential evolution (DE) algorithm with modified hybrid genetic algorithm (MHGA) for solving the associated nonlinear programming problem of a nonlinear optimal control problem‎. ‎In the first phase‎, ‎DE starts with a completely random initial population where each individual‎, ‎or solution‎, ‎is a random matrix of control input values in time nodes‎. ‎After phase 1‎, ‎to achieve more accurate solutions‎, ‎we increase the number of time nodes‎. ‎The values of the associated new control inputs are estimated by linear or spline interpolations using the curves computed in the phase 1‎. ‎In addition‎, ‎to maintain the diversity in the population‎, ‎some additional individuals are added randomly‎. ‎Next‎, ‎in the second phase‎, ‎MHGA starts by the new population constructed by the above procedure and tries to improve the obtained solutions at the end of phase 1‎. ‎We implement our proposed algorithm on some well-known nonlinear optimal control problems‎. ‎The numerical results show the proposed algorithm can find almost better solution than other proposed algorithms‎. 47 67 2014/02/122013/08/242014/06/232014/12/292014/06/26 1393/4/5 2016/11/62016/11/132015/05/62015/10/82015/05/24 1394/3/3 S. Nezhadhosein S. Nezhadhosein Payame Noor University, Tehran Iran s_nezhadhossin@yahoo.com A. Heydari A. Heydari Payame Noor University, Tehran Iran R. Ghanbari R. Ghanbari Ferdowsi University of Mashhad Iran Nonlinear optimal control problem‎ ‎Differential evolution‎ ‎Modified hybrid genetic algorithm‎ ‎Successive quadratic programming‎ ‎Spline interpolation‎. Z.S. Abo-Hammour, A.Gh. Asasfeh, A.M. Al-Smadi, Othman M.K. Alsmadi, A novel continuous genetic algorithm for the solution of optimal control problems,Optimal Control Applications and Methods 32(4), (2011), 414-432.##M.M. Ali, C. Storey, A. T¨orn, Application of stochastic global optimization algorithms to practical problems,Journal of Optimization Theory and Applications, 95(3), (1997), 545-563.##M. Senthil Arumugam, G. Ramana Murthy, C. K. Loo, On the optimal control of the steel annealing processes as a two stage hybrid systems via PSO algorithms, International Journal Bio-Inspired Computing, 1(3), (2009), 198-209.##M. Senthil Arumugam, M. V. C. Rao, On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems, Application Soft Computing, 8(1), (2008), 324–336.## S. Babaie-Kafaki, R. Ghanbari, N. Mahdavi-Amiri, Two effective hybrid metaheuristic algorithms for minimization of multimodal functions, International Journal Computing Mathematics, 88(11), (2011), 2415–2428.## J.J.F. Bonnans, J.C. Gilbert, C. Lemar´echal, C.A. Sagastiz´abal, Numerical optimization: Theoretical and practical aspects, Springer London, Limited, 2006.##I.L. Lopez Cruz, L.G. Van Willigenburg, G. Van Straten, Efficient differential evolution algorithms for multimodal optimal control problems, Applied Soft Computing, 3(2), (2003), 97-122.## F. Dong, O. Petzold, W. Heinemann, R. Kasper, Time-optimal guidance control for an agricultural robot with orientation constraints, Computers and Electronics in Agriculture, 99(0), (2013), 124-131.## S. Effati, H. Saberi Nik, Solving a class of linear and non-linear optimal control problems by homotopy perturbation method, IMA Journal of Mathematical Control and Information, 28(4), (2011), 539-553.## A.P. Engelbrecht, Computational intelligence: An introduction, Wiley, 2007.##B.C. Fabien, Numerical solution of constrained optimal control problems with parameters,Applied Mathematics and Computation, 80(1), (1996), 43-62.## B.C. Fabien, Some tools for the direct solution of optimal control problems, Advances Engineering Software, 29(1), (1998), 45-61.## F. Ghomanjani, M.H Farahi, M Gachpazan, B´ezier control points method to solve constrained quadratic optimal control of time varying linear systems, Computational and Applied Mathematics, 31, (2012), 433-456.##A. Ghosh, S. Das, A. Chowdhury, R. Giri, An ecologically inspired direct search method for solving optimal control problems with B´ezier parameterization, Engineering Applications of Artificial Intelligence, 24(7), (2011), 1195-1203.## C.J. Goh, K.L. Teo, Control parametrization: A unified approach to optimal control problems with general constraints, Automatica, 24(1), (1988), 3-18.## D.E. Kirk, Optimal control theory: An introduction, Dover Publications, 2004.## A. Vincent Antony Kumar, P. Balasubramaniam, Optimal control for linear system using genetic programming, Optimal Control Applications and Methods 30(1), (2009), 47-60.## Moo Ho Lee, Ch. Han, K.S. Chang, Dynamic optimization of a continuous polymer reactor using a modified differential evolution algorithm, Industrial and Engineering Chemistry Research, 38(12), (1999), 4825-4831.## R. Li, Y.J. Shi, The fuel optimal control problem of a hypersonic aircraft with periodic cruising mode, Mathematical and Computer Modelling, 55(11-12), (2012), 2141-2150.##Y. Li, X. Zhang, Y. Chen, H. Zhou, Particle swarm optimization for time-optimal control design, Journal of Control Theory and Applications, 10(3), (2012), 365–370.##J. Antonio Delgado San Martn, M. Nicols Cruz Bournazou, P. Neubauer, T. Barz, Mixed integer optimal control of an intermittently aerated sequencing batch reactor for wastewater treatment, Computers & Chemical Engineering, 71(0), (2014), 298-306.## W. Mekarapiruk, R. Luus, Optimal control of inequality state constrained systems, Industrial and Engineering Chemistry Research, 36(5), (1997), 1686-1694.## H. Modares, M.B. Naghibi-Sistani, Solving nonlinear optimal control problems using a hybrid IPSO - SQP algorithm, Engineering Applications of Artificial Intelligence, 24(3), (2011), 476-484.## H. Moradi, Gh. Vossoughi, H. Salarieh, Optimal robust control of drug delivery in cancer chemotherapy: A comparison between three control approaches, Computer Methods and Programs in Biomedicine, 112(1), (2013), 69-83.## G.M. Ostrovsky, N.N. Ziyatdinov, T.V. Lapteva, Optimal design of chemical processes with chance constraints, Computers & Chemical Engineering, 59(0), (2013), 74-88.## Th. Penzl, Algorithms for model reduction of large dynamical systems, Linear Algebra and its Applications, 415(2-3), (2006), 322-343.##J. Rajesh, K. Gupta, H.Sh. Kusumakar, V.K. Jayaraman, B.D. Kulkarni, Dynamic optimization of chemical processes using ant colony framework, Computers & Chemistry, 25(6), (2001), 583-595.## A.F. Ribeiro, M.C.M. Guedes, G.V. Smirnov, S. Vilela, On the optimal control of a cascade of hydro-electric power stations, Electric Power Systems Research, 88(0), (2012), 121-129.## S. Sedaghat, Y. Ordokhani, Stability and numerical solution of time variant linear systems with delay in both the state and control, Iranian Journal of Mathematical Sciences and Informatics, 7(1), (2012), 43-57.## X. H. Shi, L. M. Wan, H. P. Lee, X. W. Yang, L. M. Wang, Y. C. 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Zhong, A hybrid improved genetic algorithm and its application in dynamic optimization problems of chemical processes, Chinese Journal of Chemical Engineering, 21(2), (2013), 144-154.## K.L. Teo, C.J. Goh, K.H. Wong, A unified computational approach to optimal control problems, Pitman monographs and surveys in pure and applied mathematics, Longman Scientific and Technical, 1991.## J. M. van Ast, R. Babuˇska, B. De Schutter, Novel ant colony optimization approach to optimal control, International Journal of Intelligent Computing and Cybernetics, 2(3), (2009), 414-434.##F.Sh. Wang, J.P. Chiou, Optimal control and optimal time location problems of differential-algebraic systems by differential evolution, Industrial and Engineering Chemistry Research, 36(12), (1997), 5348-5357.##M. Yaghini, M. Karimi, M. Rahbar, A hybrid metaheuristic approach for the capacitated p-median problem, Applied Soft Computing, 13(9), (2013), 3922-3930.##M. Yarahmadi, S. M. Karbassi, Design of robust controller by neuro-fuzzy system in a prescribed region via state feedback, Iranian Journal of Mathematical Sciences and Informatics, 4(1), (2009), 1-16.##B. Zhang, D. Chen, W. Zhao, Iterative ant-colony algorithm and its application to dynamic optimization of chemical process, Computers & Chemical Engineering 29(10), (2005), 2078-2086.##W. Zhang, H.p. Ma, Chebyshev-legendre method for discretizing optimal control problems, Journal of Shanghai University, 13(2), (2009), 113-118.## ##

Some Families of Graphs whose Domination Polynomials are Unimodal 2 2 Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal. 69 80 2014/02/122013/08/242014/06/232014/12/292014/06/262014/09/16 1393/6/25 2016/11/62016/11/132015/05/62015/10/82015/05/242017/01/2 1395/10/13 S. Alikhani S. Alikhani Yazd University Iran alikhani@yazd.ac.ir S. Jahari S. Jahari Yazd University Iran s.jahari@gmail.com Domination polynomial unimodal family. S. Akbari, S. Alikhani, Y.H. Peng, Characterization of graphs using domination polynomial, Europ. J. Combin., 31, (2010), 1714-1724.## S. Alikhani, On the domination polynomial of some graph operations, ISRN Combin., 2013, Article ID 146595, 3 pages.## S. Alikhani, On the domination polynomials of non P4-free graphs, Iran. J. Math. Sci. Inform., 8(2), (2013), 49–55.## S. Alikhani, On the graphs with four distinct domination roots, Int. J. Comp. Math., 88(13), (2011), 2717-2720.## S. Alikhani, Graphs whose their certain polynomials have few distinct roots, ISRN Discrete Math., 2013, Article ID 195818, 8 pages. ## S. Alikhani, J.I. Brown, S. Jahari, On the domination polynomials of friendship graphs,Filomat, 30(1), (2016), 169-178.## S. Alikhani, F. Jafari, On the unimodality of independence polynomial of certain classes of graphs, Trans. Combin., 2(3), (2013), 33–41.## S. Alikhani, Y.H. Peng, Introduction to domination polynomial of a graph, Ars Combin., 114, (2014), 257-266.## F. Brenti, Log-concave and unimodal sequences in algebra, combinatorics, and geometry: An update, Contemp. Math. 178, (1994),417-441.## F. Brenti, Unimodal, log-concave, and P´ olya frequency sequences in combinatorics, Mem. Amer. Math. Soc., 413, (1989).## G. H. Fath-Tabar, A. R. Ashra, The Hyper-Wiener polynomial of graphs, Iran. J. Math.Sci. Inform., 6(2), (2011), 67–74.## R. Frucht, F. Harary, On the corona of two graphs, Aequationes Math., 4, (1970), 322–325.## J.A. Gallian, A dynamic survey of graph labeling, Elec. J. Combin. 16, (2013), #DS6.## C.D. Godsil, B.D. McKay, A new graph product and its spectrum, Bull. Austral. Math.Soc., 18, (1978), 21-28.## E. Ghorbani, Graphs with few matching roots, Graphs and Combin., 29(5), (2013),1377–1389.## T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of domination in graphs, Marcel Dekker, NewYork, 1998.## T. Kotek, J. Preen, F. Simon, P. Tittmann, M. Trinks, Recurrence relations and splitting formulas for the domination polynomial, Elec. J. Combin., 19(3), (2012), # P47.## V.E. Levit, E. Mandrescu, A family of graphs whose independence polynomials are both palindromic and unimodal, Carpathian J. Math., 23, (2007), 108-116.## V.E. Levit, E. Mandrescu, On the independence polynomial of the corona of graphs, Disc Appl. Math., (2015), http://doi:10.1016/j.dam.2015.09.021.## E. Mandrescu, Unimodality of some independence polynomials via their palindromicity, Australasian J. Combin., 53, (2012), 77-82.## V.R. Rosenfeld, The independence polynomial of rooted products of graphs, Disc. Appl.Math., 158, (2010), 551-558.## R.P. Stanley, Log-concave and unimodal sequences in algebra, combinatorics and geometry, Ann. New York Acad. Sci., 576, (1989), 500-534.## M. Walsh, The hub number of a graph, Int. J. Math. Comput. Sci., 1, (2006), 117-124.## http://mathworld.wolfram.com/DutchWindmillGraph.html.## The On-Line Encyclopedia of Integer Sequences. http://oeis.org, 2012.## ##

On Lorentzian two-Symmetric Manifolds of Dimension-fou‎r 2 2 ‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎. 81 94 2014/02/122013/08/242014/06/232014/12/292014/06/262014/09/162014/09/28 1393/7/6 2016/11/62016/11/132015/05/62015/10/82015/05/242017/01/22015/05/10 1394/2/20 A. Zaeim A. Zaeim ‎Payame noor University Iran zaeim@pnu.ac.ir M. Chaichi M. Chaichi ‎Payame noor University Iran chaichi@pnu.ac.ir Y. Aryanejad Y. Aryanejad ‎Payame noor University Iran y.aryanejad@pnu.ac.ir Pseudo-Riemannian metric‎ ‎Einstein-like metrics‎ ‎Ricci soliton‎ ‎Homogeneous spac‎e‎. 1-E. Abbena, S. Garbiero, L. Vanhecke, Einstein-like metrics on three-dimensional Riemannian homogeneous manifolds, Simon Stevin Quart. J. Pure Appl. Math., 66, (1992), 173-182.##2-E. Abbena, S. Garbiero, Curvature forms and Einstein-like metrics on Sasakian manifolds, Math. J. Okayama Univ., 34, (1992), 241-248.##3-D. V. Alekseevsky, A. S. Galaev, Two-symmetric Lorentzian manifolds, Geom. Phys., 61, (2011), 2331-2340.##4-W. Ambrose, I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J., 25, (1958), 647-669.##5-A. Arvanitogeorgos, An Introduction to Lie Groups and the Geometry of Homogeneous Spaces, Student Mathematical Library, 22.##6-A. R. Ashrafi, M. R. Ahmadi, Symmetry of fullerene C60, Iranian Journal of Mathematical Sciences and Informatics, 1(1), (2006), 1-13.##7-W. Batat, Curvature properties and Ricci solitons of Lorentzian pr-Waves manifolds, J.Geom. Phys., 75, (2014), 7-16.##8-O. F. Blanco, M. Sanchez, J. M. Senovilla, Complete classification of second-order symmetric spacetimes, J. Phys. Conf. Ser., 229, (2010).##9-M. Blau, M. O’Loughlin, Homogeneous plane waves, Nuc. Phys. B., 654, (2003), 135-176.##10-E. Boeckx, Einstein-like semi-symmetric spaces, Arch. Math. (Brno), 16, (1997), 789-800.##11-M. Brozos-Vazquez, E. Garcıa-Rıo, S. Gavino-Fernandez, Locally conformally flat Lorentzian gradient Ricci solitons, J. Geom. Anal., 23, (2013), 1196-1212.##12-M. Brozos-Vazquez, E. Garcıa-Rıo, S. Gavino-Fernandez, Locally conformally flat Lorentzian quasi-Einstein manifolds, Monatsh Math., 173, (2014), 175-186.##13-P. Bueken, L. Vanhecke, Three- and four-dimensional Einstein-like manifolds and homogeneity, Geom. Dedicata, 75, (1999), 123–136.##14-G. Calvaruso, Homogeneous structures on three-dimensional Lorentzian manifolds, J.Geom. Phys., 57, (2007), 1279–1291. Addendum: J. Geom. Phys., 58, (2008), 291–292.##15-G. Calvaruso, L. Vanhecke, Special ball-homogeneous spaces, Z. Anal. Anwendungen, 16, (1997), 789-800.##16-G. Calvaruso, Einstein-like and conformally flat contact metric three-manifolds, Balkan J. Geom., 5(2), (2000), 17–36.##17-G. Calvaruso, A. Fino, Ricci solitons and geometry of four-dimensional non-reductive homogeneous spaces, Canad. J. Math., 64, (2012), 778–804.##18-G. Calvaruso, A. Zaeim, Geometric structures over non-reductive homogeneous 4-spaces, Advances in Geometry, 14(2), (2014), 191–214.##19-H. D. Cao, Recent progress on Ricci solitons, Recent advances in geometric analysis, Adv. Lect. Math. (ALM), 11, Int. Press, Somerville, MA, (2010), 1–38.##20-M. Dabirian, A. Iranmanesh, The molecular symmetry group theory of trimethylamineBH3 addend (BH3 free of rotation),Iranian Journal of Mathematical Sciences and Informatics, 1(1), (2006), 15-26.##21-M.E. Fels and A.G. Renner, Non-reductive homogeneous pseudo-Riemannian manifolds of dimension four, Canad. J. Math., 58, (2006), 282–311.##22-P.M. Gadea, J.A. Oubina, Homogeneous pseudo-Riemannian structures and homogeneous almost para-Hermitian structures, Houston J. Math., 18(3), (1992), 449–465.##23-A. Gray, Einstein-like manifolds which are not Einstein, Geom. Dedicata, 7, (1978), 259-280.##24-V. R. Kaigorodov, Structure of the curvature of space time, J. Sov. Laser Res., 28(2), (1985), 256-273.##25-B. Komrakov Jnr., Einstein-maxwell equation on four-dimensional homogeneous spaces, Lobachevskii J. Math., 8, (2001), 33-165.##26-V. Patrangenaru, Locally homogeneous pseudo-Riemannian manifolds, J. Geom. Phys., 17, (1995), 59-72.##27-F. Podesta, A. Spiro, Four-dimensional Einstein-like manifolds and curvature homogeneity, Geom. Dedicata, 54, (1995), 225-243.##28-J. M. Senovilla, Second-order symmetric Lorentzian manifolds. I. Characterization and general results, Classical Quantum Gravity, 25(24), (2008).##29-S. Tanno, Curvature tensors and covariant derivatives, Ann. Mat. Pura Appl., 96(4), (1972), 233-241.##30-F. Tricerri, L. Vanhecke, Homogeneous structures on Riemannian manifolds, London Math. Soc. Lect. Notes, 83, Cambridge Univ. Press, (1983).##31-J.A. Wolf, Homogeneous manifolds of constant curvature, Comment, Math. Helv., 36, (1961), 112–147.## ##

On the Zero-divisor Cayley Graph of a Finite Commutative Ring 2 2 Let R be a fnite commutative ring and N(R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma(R), is the graph obtained by setting all the elements of N(R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin N(R). In this paper, the basic properties of Gamma(R) are investigated and some characterization results regarding connectedness, girth and planarity of Gamma(R) are given. 95 106 2014/02/122013/08/242014/06/232014/12/292014/06/262014/09/162014/09/282014/10/11 1393/7/19 2016/11/62016/11/132015/05/62015/10/82015/05/242017/01/22015/05/102015/10/10 1394/7/18 A. R. Naghipour A. R. Naghipour Shahrekord University Iran Connectivity Diameter Girth Planar graph Clique. 1-G. Aalipour, S. Akbari, On the Cayley graph of a commutative ring with respect to its zero-divisors, Communications in Algebra, 44(4), (2016), 1443-1459.##2- A. Abbasi, H. Roshan-Shekalgourabi, D. Hassanzadeh-Lelekaami, Associated graphs of modules over commutative rings, Iranian Journal of Mathematical Sciences and Informatics, 10(1), (2015), 45–58.##3- R. Akhtar, M. Boggess, T. Jackson-Henderson, I. Jim´enez, R. Karpman, A. Kinzel, D. Pritikin, On the unitary Cayley graph of a finite ring, Electron. J. Combin., 16(1), (2009), #R117.##4- D. F. Anderson, A. Badawi, The total graph of a commutative ring, J. Algebra, 320(7), (2008), 2706–2719.##5- M. F. Atiyah, I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, Mass., 1969.##6- B. Corbas, G. D. Williams, Rings of order p5. I. Nonlocal rings, J. Algebra, 231(2), (2000), 677–690.##7- D. Dolzan, Group of units in a finite ring, ring. J. Pure Appl. Algebra, 170, (2002), 175–183.##8- C. Godsil, G. Royle, Algebraic Graph Theory, Springer-Verlag, New York, 2001.##9- R. Y. Sharp, Steps in Commutative Algebra, Cambridge University Press, Cambridge, 1990.##10- A. Theranian, H. R. Maimani, A study of the total graph, Iranian Journal of Mathematical Sciences and Informatics, 6(2), (2011), 75–80. ##11- D. B. West, Introduction to Graph Theory, Second Edition, Prentice-Hall, 2000.## ##

On Open Packing Number of Graphs 2 2 In a graph G = (V,E), a subset $S⊂V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds. 107 117 2014/02/122013/08/242014/06/232014/12/292014/06/262014/09/162014/09/282014/10/112015/06/26 1394/4/5 2016/11/62016/11/132015/05/62015/10/82015/05/242017/01/22015/05/102015/10/102016/05/2 1395/2/13 I. Sahul Hamid I. Sahul Hamid The Madura College(Autonomous) Madurai India S. Saravanakumar S. Saravanakumar The Madura College(Autonomous) Madurai India Open packing Maximum degree Clique Split graphs. 1-A. Alwardi, B. Arsic, I. Gutman, N.D. Soner, The common neighbourhood graph and its energy, Iranian Journal of Mathematical Sciences and Informatics, 7(2), (2012), 1–8.##2- S. Arumugam, M. Sundarakannan, Equivalence dominating sets in graphs, Utilitas. Math., 91, (2013), 231–242.##3- G. Chartrand, L. Lesniak, P. Zhang, Graphs and digraphs, Fourth edition, CRC press, Boca Raton, 2005.##4- T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of domination in graphs, Marcel Dekker, New York, 1988.##5- M.A. Henning, Upper bounds on the lower open packing number of a tree, Quaestiones Mathematicae, 21, (1998), 235–245.##6- M.A. Henning, P.J. Slater, Open packing in graphs, JCMCC, 29, (1999), 3–16.##7- A. Meir, J.W. Moon, Relations between packing and covering numbers of a tree, Pacific J. Math., 61, (1975), 225-233.##8- I. Sahul Hamid, S. Saravanakumar, Packing parameters in graphs, Discussiones Mathematicae Graph Theory, 35, (2015), 5–16.##9- H. Yousefi-Azari, A. Goodarzi, 4-placement of rooted trees, Iranian Journal of Mathematical Sciences and Informatics, 1(2), (2006), 65-77## ##

On Twin--Good Rings 2 2 In this paper, we investigate various kinds of extensions of twin-good rings. Moreover, we prove that every element of an abelian neat ring R is twin-good if and only if R has no factor ring isomorphic to‌ $Z_2$ or $Z_3$. The main result of [24] states some conditions that any right self-injective ring R is twin-good. We extend this result to any regular Baer ring R by proving that every element of a regular Baer ring is twin-good if and only if R has no factor ring isomorphic to  $Z_2$ or $Z_3$. Also we illustrate conditions under which extending modules, continuous modules and some classes of vector space are twin-good. 119 129 2014/02/122013/08/242014/06/232014/12/292014/06/262014/09/162014/09/282014/10/112015/06/262014/10/26 1393/8/4 2016/11/62016/11/132015/05/62015/10/82015/05/242017/01/22015/05/102015/10/102016/05/22015/04/28 1394/2/8 N. Ashrafi N. Ashrafi Semnan University Iran nashrafi@semnan.ac.ir N. Pouyan N. Pouyan Semnan University Iran neda.pouyan@gmail.com Twin-good ring Neat ring Regular Baer ring π-Regular. 1-N. Ashrafi, The unit sum number of some projective modules, Glasg. Math. J., 50(1), (2008), 71-74.##2- N. Ashrafi, Z. Ahmadi, Weakly g(x)-Clean Rings, Iranian Journal of Mathematical Sciences and Informatics, 7(2), (2012), 83-91.## 3-N. Ashrafi, N. Pouyan, The unit sum number of discrete modules, Bulletin of the Iranian Mathematical Society, 37(4), (2011) ,243-249.## 4-S. K. Berberian, Baer rings and Baer ∗-rings, The University of Texas at Austin, 1988.##5- V. Camillo, P. P. Nielsen, McCoy rings and zero-divisors, J. Pure Appl. Algebra, 212(3), (2008), 599-615.##6-H. Chen, Exchange rings with artinian primitive factors, Algebra Represent. Theory, 2, (1999), 201-207.##7- H. Chen, Decompositions of linear transformations over division rings, Algebra Colloquium, 19(3), (2012), 459-464.##8- A. A. Estaji, z-Weak Ideals and Prime Weak Ideals, Iranian Journal of Mathematical Sciences and Informatics, 7(2), (2012), 53-62.##9- J. W. Fisher, R. L. Snider, Rings generated by their units, J. Algebra, 42, (1976), 363-368.##10- B. Goldsmith, S. Pabst, A. Scott, Unit sum number of rings and modules, Quart. J. Math. Oxford, 49(2), (1998), 331-344.##11- K. R. Goodearl, P. Menal, Stable range one for ring with many units, J. Pure Appl. Algebra, 54(2-3), (1988), 261-287.##12- X.J. Guo, K.P. Shum, Baer semisimple modules and Baer rings, Algebra Discrete Math., 2, (2008), 42-49.##13- M. Henriksen, Two classes of rings generated by their units, J. Algebra, 31, (1974), 182–193.##14- D. Khurana, A. K. Srivastava, Right Self-injective Rings in Which Each Element is Sum of Two Units, Journal of Algebra and its Applications, 6(2), (2007), 281-286.##15- D. Khurana, A. K. Srivastava, Unit sum numbers of right self-injective rings, Bull. Austral. Math. Soc., 75(3), (2007), 355–360.##16- I. Kaplansky, Rings of Operators, Benjamin, New York, 1965.##17- J. Y. Kim, J. K. Park, On Regular Baer rings, Trends in Math., 1(1), (1998), 37-40.##18-T. Y. Lam, Lectures on Modules and Rings, GTM 189, Berlin-Heidelberg-New York, Springer Verlag, 1999.##19- W. Wm. McGovern, Neat rings, J. Pure Applied Alg., 205(2), (2006), 243-265.## 20-S.H. Mohamed, B.J. M¨uller, Continuous and Discrete Modules, London Math. Soc., LN 147, Cambridge Univ. Press, 1990.## 21-W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229, (1977), 269-278.## 22-S. L. Perkins, Masters thesis, Saint Louis University, St. Louis, MO, 2011.## 23-R. Raphael, Rings which are generated by their units, J. Algebra, 28, (1974), 199-205.## 24-S.T. Rizvi, C.S. Roman, Baer and quasi-Baer modules, Comm. Algebra, 32(1), (2004), 10–123.## 25-F. Siddique, A. K. Srivastava, Decomposing elements of a right self-injective ring , J. Algebra and Appl., 12(6), (2013).## 26-A. A. Tuganbaev, Rings and modules with exchange properties, J. Math. Sci. , 110(1), (2002), 2348-2421.##27- P. Vamos, 2-Good Rings, The Quart. J. Math., 56, (2005), 417-430.## 28-L. N. Vaserstein, Basss first stable range condition, J. Pure Appl. Algebra, 34(2-3), (1984), 319-330.## 29-L.Wang, Y. Zhou, Decomposing Linear Transformations, Bull. Aust. Math. Soc., 83(2), (2011), 256-261.## ##

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function 2 2 In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) function nor logarithmic barrier function, the primal-dual IPMs based on this kernel function enjoy the worst case iteration bound $Oleft(sqrt{n}log nlog frac{n}{epsilon}right)$ for the large-update methods with the special choice of its parameters. This bound coincides to the so far best known complexity results obtained from SR kernel functions for linear and semidefinite optimization problems. Finally some numerical issues regarding the practical performance of the new proposed kernel function is reported. 131 152 2014/02/122013/08/242014/06/232014/12/292014/06/262014/09/162014/09/282014/10/112015/06/262014/10/262014/12/30 1393/10/9 2016/11/62016/11/132015/05/62015/10/82015/05/242017/01/22015/05/102015/10/102016/05/22015/04/282016/07/11 1395/4/21 M. R. Peyghami M. R. Peyghami K.N. Toosi Univ. of Tech. Iran peyghami@kntu.ac.ir S. Fathi Hafshejani S. Fathi Hafshejani Shiraz Univ. of Tech. Iran sajadfathi85@gmail.com Convex quadratic semidefinite optimization problem Primal-dual interior-point methods Kernel function Iteration complexity. 1-A.Y. Alfakih, A. Khandani, H. Wolkowicz, Solving Euclidean Distance Matrix Completion Problems via Semidefinite Programming, Computational Optimization and Applications, 12(1-3), (1999), 13–30.##2-Y.Q. Bai, M. El Ghami, C. Roos, A New Efficient Large-update Primal-dual Interiorpoint Methods Based on a Finite Barrier, SIAM Journal on Optimization, 13(3), (2003),766–782.##3-Y.Q. Bai, M. El Ghami, C. Roos, A Comparative Study of Kernel Functions for Primaldual Interior-point Algorithms in Linear Optimization, SIAM Journal on Optimization,15(1), (2004), 101–128.##4-Y.Q. Bai, G. Lesaja, C. Roos, G.Q. Wang, M. El Ghami, A Class of Large-update and Small-update Primal-dual Interior-point Algorithms for Linear Optimization, Journal of Optimization Theory and Applications, 138, (2008), 341-359.##5-E. De Klerk, Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002.## 6-M. El Ghami, Z.A. Guennoun, S. Boula, T. Steihaug, Interior-point Methods for Linear Optimization Based on a Kernel Function with a Trigonometric Barrier Term, Journal of Computational and Applied Mathematics, 236, (2012), 3613–3623.## 7-M.R. Eslahchi, S. Amani, The Best Uniform Polynomial Approximation of Two Classes of Rational Functions, Iranian Journal of Mathematical Sciences and Informatics, 7(2), (2012), 93–102.##8-M. El Ghami, Primal Dual Interior-point Methods for P∗(κ)-Linear Complementarity Problem Based on a Kernel Function with a Trigonometric Barrier Term, Optimization Theory, Decision Making, and Operations Research Applications, Springer Proceedings in Mathematics & Statistics, 31, (2013), 331–349.##9-R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.##10-N.K. Karmarkar, A New Polynomial-time Algorithm for Linear Programming, in: Proceedings of the 16th Annual ACM Symposium on Theory of Computing, 302–311, 1984.##11-B. Kheirfam, Primal-dual Interior-point Algorithm for Semidefinite Optimization Based on a New Kernel Function with Trigonometric Barrier Term, Numerical Algorithms, 61, (2012), 659–680.##12-M. Kojima, S. Mizuno, A. Yoshise, A Primal-dual Interior Point Algorithm for Linear Programming, in: N. Megiddo (Ed.), Progress in Mathematical Programming: Interior Point and Related Methods, Springer Verlag, New York, 29–47, 1989.##13-M. Kojima, S. Shindoh, S. Hara, Interior-point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices, SIAM Journal on Optimization, 7(1), (1997), 86–125.##14- H. Lutkepohl, Handbook of Matrices, Wiley, 1996.##15-N. Megiddo, Pathways to the Optimal Set in Linear Programming, in: N. Megiddo (Ed.), Progress in Mathematical Programming: Interior Point and Related Methods, SpringerVerlag, New York, 131–158, 1989.##16-Y.E. Nesterov, A.S. Nemirovski, Interior Point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, Volume 13, SIAM, Philadelphia, PA,1994.##17-Y.E. Nesterov, M.J. Todd, Primal Dual Interior Point Methods for Self-scaled Cone,SIAM Journal on Optimization, 8(2), (1998), 324-364.##18-Y.E. Nesterov, M.J. Todd, Self-scaled Barries and Interior Point Methods for Convex Programming, Mathematics of Operations Research, 22(1), (1997), 1–42.##19-J.W. Nie, Y.X. Yuan, A Potential Reduction Algorithm for an Extended SDP Problem, Science China (Series A) 43(1), (2000), 35-46.##20- J.W. Nie, Y.X. Yuan, A Predictorcorrector Algorithm for QSDP Combining Dikin-type and Newton Centering Steps, Annals of Operations Research, 103, (2001), 115–133.## 21-J. Peng, New Design and Analysis of Interior Point Methods, Ph.D. Thesis, Universal Press, 2001.##22-J. Peng, C. Roos, T. Terlaky, Self-Regularity: A New Paradigm for Primal-Dual InteriorPoint Algorithms, Princeton University Press, 2002.##23-M. Reza Peyghami, An Interior-point Approach for Semidefinite Optimization Using New Proximity Functions, Asia-Pacific Journal of Operational Research, 26(3), (2009), 365–382.##24-M. Reza Peyghami, S. Fathi Hafshejani, L. Shirvani, Complexity of Interior-point Methods for Linear Optimization Based on a New Trigonometric Kernel Function, Journal of Computational and Applied Mathematics, 255, (2014), 74–85.##25-H. Qi, D. Sun, A Quadratically Convergent Newton Method for Computing the Nearast Correlation Matrix, SIAM Journal on Matrix Analysis and Applications, 28, (2008), 360–385.##26-C. Roos, T. Terlaky, J-P. Vial, Theory and Algorithms for Linear Optimization: An Interior Point Approach, Springer, New York, 2005.##27-M. Salahi, S. Fallahi, A Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint, Iranian Journal of Mathematical Sciences and Informatics, 9(2), (2014), 65–71.## 28-G. 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ABSTRACTS IN PERSIAN Vol.12, No.1 2 2 Please see the full text contains the Pesian abstracts for this volume. 163 175 2014/02/122013/08/242014/06/232014/12/292014/06/262014/09/162014/09/282014/10/112015/06/262014/10/262014/12/302016/06/172017/07/12 1396/4/21 2016/11/62016/11/132015/05/62015/10/82015/05/242017/01/22015/05/102015/10/102016/05/22015/04/282016/07/112017/03/12017/07/12 1396/4/21 Name of Authors In This Volume Name of Authors In This Volume All the author's Affilliations All the author's countries fatemeh.bardestani@gmail.com ABSTRACTS PERSIAN Vol. 12 No. 1 All references of the papres appeared in Iranian Journal of Mathematical Sciences and Informatics vol.12,no.1, (2017).## ##