Integrating Goal Programming, Taylor Series, Kuhn-Tucker Conditions, and Penalty Function Approaches to Solve Linear Fractional Bi-level Programming Problems 2 2 In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to fractional objective functions. Then on using the Kuhn-Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty, that can be reduce to a single objective function. In the other words, suitable transformations can be applied to formulate FBLP problems. Finally a numerical example is given to illustrate the complexity of the procedure to the solution. 1 10 2012/02/15 1390/11/26 2015/04/26 1394/2/6 M. Saraj M. Saraj Shahid Chamran University Iran msaraj@scu.ac.ir N. Safaei N. Safaei Shahid Chamran University Iran n_safaei@ymail.com Bi-level programming Fractional programming Taylor Series Kuhn-Tucker conditions Goal programming Penalty function. W. Bialas, M. Karwan, Two-level linear programming, Management Science, 30, (1984), 1004-1020.##W. Bialas, M. Karwan, J. Shaw, A parametric complementary pivot approach for two level linear programming, Technical Report 80-2, State University of New York at Buffalo, 1980.##H. I. Calvetea, C. Gal, Solving linear fractional bilevel programs, Operations Research Letters, 32, (2004), 143-151.##P. Hansen, B. Jaumard, G. Savard, New branch-and-bound rules for linear bilevel programming, SIAM Journal on Scientific and Statistical Computing, 13, (1992), 1194-1217.##S. M. Karbassi, F. Soltanian, A new approach to the solution of sensitivity minimization in linear state feedback control, Iranian Journal of Mathematical Sciences and Informatics, 2(1), (2007), 1-13.##H. L. Li, An efficient method for solving linear goal programming problems, Journal of Optimization Theory and Applications, 90(2), (1996), 465-469.##Y. Lv, T.Hu, G. Wang and Z. Wan, A penalty function method based on KuhnTucker condition for solving linear bi-level programming, Applied Mathematics and Computation, 188(1), (2007), 808-813.##A. Nagoorgania, P. Palaniammalb, A fuzzy production model with probabilistic resalable returns, Iranian Journal of Mathematical Sciences and Informatics, 3(1), (2008), 77-86##M. Saraj, N. Safaei, solving Bi-Level Programming Problems on Using Global Criterion Method with an Interval Approach, Applied Mathematical Sciences, 6, (2012), 1135-l141.##S. Schaible, Fractional programming, Kluwer Academic Publishers, Dordrecht, 1995, 495-608.##C. Shi, J. Lu, Guangquan Zhang, An extended KuhnTucker approach for linear bi-level programming, Applied Mathematics and Computation, 162, (2005), 51-63.##L. N. Vicente, P. H. Calamai, Bi-level and multilevel programming: a bibliography review, Journal of Global Optimization, 5(3), (1994), 291-306.##D. White, G. Anandalingam, A penalty function approach for solving bi-level linear programs, Journal of Global Optimization, 3, (1993), 397-419## ##

Optimal Linear Codes Over GF(7) and GF(11) with Dimension 3 2 2 Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes presented before. Our given codes in $GF(11)$ are all new. 11 22 2012/02/152013/02/1 1391/11/13 2015/04/262014/12/22 1393/10/1 M. Emami M. Emami Univ. of Zanjan Iran mojgan.emami@yahoo.com L. pedram L. pedram Univ. of Zanjan Iran leilapedram@yahoo.com Linear codes Optimal codes Griesmer bound. T. L. Alderson, Extending MDS codes, Annals of combinatorics, 9, (2005), 125-135.##M. Amini, Quantum error-correcting codes on Abelian groups, Iranian journal of mathematical sciences and informations, 5(1), (2010), 55-67.##I. Boukliev, S. Kapralov, T. Maruta, M. Fukui, Optimal linear codes of dimension 4 over F5, IEEE Transactions on Information Theory, 43, (1997), 308-313.##R. N. Daskalov, T. A. Gulliver, Bounds in Minimum Distance for Linear Codes over GF(7), JCMCC, 36, (2001), 175-191.##A. Cheraghi, On the pixel expansion of hypergraph acess structures in visual cryptography schemes, Iranian journal of mathematical sciences and informations, 5 (2), (2010), 45-54.##M. Grassl, Tables of minimum-distance bounds for linear codes, http://www.codetable.de/.##P. P. Greenough, R. Hill, Optimal linear codes over GF(4), Discrete Mathematics, 125, (1994), 187-199.##P. P. Greenough, R. Hill, Optimal ternary quasi-cyclic codes, Designs, Codes and Cryptography, 2, (1992), 81-91.##R. Hill, D. E. Newton, Optimal ternary linear codes, Codes and Cryptography, 22, (1992), 137-157.##R. Hill, D. E. Newton, Some optimal ternary linear codes, Ars Combinatoria, 25, (1988), 61-72.##R. Hill, Optimal linear codes, in: C. Mitchell. ed., Pro. 2nd IMA Conf. on Cryptography and Coding (Oxford Univ. Press, Oxford, (1992)) 75-104.##R. Hill, E. Kolev, A survey of recent results on optimal linear codes, Combinatorial Designs and their Application, CRC Research Notes in Mathematics, 403, (1999), 127-152.##A. Klein, On codes meeting the Griesmer bound, Discrete Mathematics, 274, (2004), 289-297.##I. Landjev, Optimal linear codes of dimension 4 over F5, Lecture Notes in Comp. Science, 1225, (1997), 212-220.##I. Landjev, A. Rousseva, T. Maruta and R. Hill, On optimal codes over the field with five elements, Codes and Cryptography, 29, (2003), 165-175.##F. J. MacWilliams, N. J. A. Sloan, The theory of error correcting codes, Amsterdam. North Holland. ##T. Maruta, On the minimum length of q-ray linear codes of dimension four, Discrete Mathematics, 208/209, (1999), 427-435.##T. Maruta, I. N. Landjev, A. Rousseva, On the minimum size of some minihypers and related linear codes, Designs, Codes and Cryptography, 34, (2005), 5-15.##V. Pless, Introduction to the theory of error-correcting codes, New York; Wiley (1982).##G. E. Seguin, G. Drolet, The theory of 1-generator quasi-cyclic codes, Royal Military College of Canada, Kingston, ON, (1991).##H. C. A. VanTilborg, The smallest length of binary 7-dimensional linear codes with prescribed minimum distance, Discrete Mathematics, 33, (1981), 197-207.##T. Verhoef, An updated table of minimum distance bounds for binary linear codes, IEEE Transactions on Information Theory, 33, (1987), 665-680.##H. N. Ward, The nonexistence of a [207,4,165]-code over GF(5), Designs, Codes and Cryptography, 22, (2001), 139-148.## ##

OD-characterization of Almost Simple Groups Related to displaystyle D4(4) 2 2 Let $G$ be a finite group and $pi_{e}(G)$ be the set of orders of all elements in $G$. The set $pi_{e}(G)$ determines the prime graph (or Grunberg-Kegel graph) $Gamma(G)$ whose vertex set is $pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$ and $q$ are adjacent if and only if $pqinpi_{e}(G)$. The degree $deg(p)$ of a vertex $pin pi(G)$, is the number of edges incident on $p$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$ with $p_{1} 23 43 2012/02/152013/02/12013/01/21 1391/11/2 2015/04/262014/12/222014/12/22 1393/10/1 G. R. Rezaeezadeh G. R. Rezaeezadeh university of shahrekord Iran rezaeezadeh@sci.sku.ac.ir M. R. Darafsheh M. R. Darafsheh university of tehran Iran darafsheh@ut.ac.ir M. Bibak M. Bibak university of shahrekord Iran m.bibak62@gmail.com M. Sajadi M. Sajadi university of shahrekord Iran sajadi−mas@yahoo.com Degree pattern $k$-fold OD-characterizable Almost simple group. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of finite groups, Clarendon Press (Oxford), London - New York, 1985.##M. R. Darafsheh, G. R. Rezaeezadeh, M. bibak, M. Sajjadi, OD-Characterization of almost simple groups related to 2E6(2), Advances in Aljebra, 6, (2013), 45-54.##M. R. Darafsheh, G. R. Rezaeezadeh, M. Sajjadi, M. Bibak, OD-Characterization of almost simple groups related to U3(17), Quasigroups and related systems, 21, (2013), 49-58.##M. Foroudi ghasemabadi, N. Ahanjideh, Characterization of the simple groups Dn(3) by prime graph and spectrum, Iranian Journal of Mathematical Sciences and Informatics, 7(1), (2012), 91-106.##D. Gorenstein, Finite groups, New York: Harper and Row, 1980.##A. A. Hoseini, A. R. Moghaddamfar, Recognizing alternating groups Ap+3 for certain primes p by their orders and degree patterns, Front. Math. China, 5(3), (2010), 541-553.##A. R. Moghaddamfar, A. R. Zokayi, M. R. Darafsheh, A characterization of finit simole groups by the degree of vertices of their prime graphs, Algebra Colloquium, 12(3), (2005), 431-442.##A. R. Moghaddamfar, A. R. Zokayi, Recognizing finite groups through order and degree patterns, Algebra Colloquium, 15(3), (2008), 449-456.##G. R. Rezaeezadeh, M. Bibak, M. Sajjadi, Characterization of Projective Special linear Groups in Dimension three by their orders and degree patterns, Bulletin of the Iranian Mathematical Society, in press.##G. R. Rezaeezadeh, M. R. Darafsheh, M. Sajjadi, M. Bibak, OD-characterization of almost simple groups related to L3(25), Bulletin of the Iranian Mathematical Society, in press.##J. S. Robinson Derek, A course in the theory of groups, 2nd ed. New York-HeidelbergBerlin: Springer-Verlag, 2003.##A. Zavarnitsin, Finite simple groups with narrow prime spectrum, Siberian Electronic Mathematical Reports, 6, (2009), 1-12.##L. C. Zhang, W. J. Shi, OD-characterization of almost simple groups related to L2(49), Archivum Mathematicum (Brno) Tomus, 44, (2008), 191-199.##L. C. Zhang, W. J. Shi, OD-Characterization of simple K4-groups, Algebra Colloquium, 16(2), (2009), 275-282.##L. C. Zhang, W. J. Shi, OD-characterization of almost simple groups related to U3(5), Acta Mathematica Scientia, 26(1), (2010), 161-168.##L. C. Zhang, W. J. Shi, OD-characterization of almost simple groups related to U6(2), Acta Mathematica Scientia, 31(2), (2011), 441-450.##L. C. Zhang, W. J. Shi, OD-Characterization of the projective special linear groups L2(q), Acta Mathematica Scientia, 19, (2012), 509-524.## ##

Associated Graphs of Modules Over Commutative Rings 2 2 Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete, tree or complete bipartite are studied and several characterizations are given. 45 58 2012/02/152013/02/12013/01/212013/04/27 1392/2/7 2015/04/262014/12/222014/12/222014/10/27 1393/8/5 A. Abbasi A. Abbasi Uni. Guilan Iran aabbasi@guilan.ac.ir H. Roshan-Shekalgourabi H. Roshan-Shekalgourabi Uni. Guilan Iran hroshan@guilan.ac.ir D. Hassanzadeh-Lelekaami D. Hassanzadeh-Lelekaami Uni. Guilan Iran dhmath@guilan.ac.ir Associated Graph of module Prime spectrum Connected graph Diameter. A. Abbasi, Sh. Habibi, Zero-divisor graph in commutative rings with decomposable zero ideal, Far East J. Math. Sci. (FJMS), 59 (1), (2011), 65–72.##A. Abbasi, Sh. Habibi, The total graph of a commutative ring with respect to proper ideals, J. Korean Math. Soc., 49 (1), (2012), 85–98.##A. Abbasi, D. Hassanzadeh-Lelekaami, Modules and spectral spaces, Comm. Algebra, to appear.##S. Akbari, H. R. Maimani, S. Yassemi, When a zero-divisor graph is planar or a complete r-partite graph, J. Algebra, 270, (2003), 169–180.##S. Akbari, A. Mohammadian, Zero-divisor graphs of non-commutative rings, J. Algebra, 296, (2006), 462–479.##D. D. Anderson, M. Naseer, Beck’s coloring of a commutative ring, J. Algebra, 159, (1993), 500–514.##D. F. Anderson, A. Badawi, On the zero-divisor graph of a ring, Comm. Algebra, 36, (2008), 3073–3092.##D. F. Anderson, P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217, (1999), 434–447.##D. F. Anderson, S. B. Mulay, On the diameter and girth of a zero-divisor graph, J. Pure Appl. Algebra, 210 (2), (2007), 543–550.##F. W. Anderson, K. R. Fuller, Rings and categories of modules, Springer-Verlag, New York, (13), Graduate Texts in Math., 1992.##M. Axtell, J. Coykendall, J. Stickles, Zero-divisor graphs of polynomial and power series over commutative rings, Comm. Algebra, 33, (2005), 2043–2050.##F. Azarpanah, M. Motamedi, Zero-divisor graph of C(X), Acta Math. Hungar, 108, (2005), 25–36.##A. Barnard, Multiplication modules, J. Algebra, 71 (1), (1981), 174–178.##I. Beck, Coloring of commutative rings, J. Algebra, 116 (1), (1988), 208–226.##M. P. Brodmann, R. Y. Sharp, Local cohomology an algebraic introduction with geometric applications, Cambridge University Press, 1998.##Z. A. El-Bast, P. F. Smith, Multiplication modules, Comm. Algebra, 16 (4), (1988), 755–779.##J. Hausen, Supplemented modules over dedekind domains, Pacific J. Math., 100 (2), (1982), 387–402.##J. D. LaGrange, Complemented zero-divisor graphs and boolean rings, J. Algebra, 315, (2007), 600–611.##Chin-Pi Lu, Prime submodules of modules, Comment. Math. Univ. St. Pauli, 33 (1), (1984), 61–69. ##Chin-Pi Lu, Spectra of modules, Comm. Algebra, 23 (10), (1995), 3741–3752.##Chin-Pi Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math., 33 (1), (2007), 125–143.##H. R. Maimani, Median and center of zero-divisor graph of commutative semogroups, Iranian J. Math. Sci. and Inf., 3 (2), (2008), 69-76.##H. R. Maimani, M. Salimi, A. Sattari, S. Yassemi, Comaximal graph of commutative rings, J. Algebra, 319, (2008), 1801–1808.##R. L. McCasland, M. E. Moore, P. F. Smith, On the spectrum of a module over a commutative ring, Comm. Algebra, 25 (1), (1997), 79–103.##P. K. Sharma, S. M. Bhatwadekar, A note on graphical representation of rings, J. Algebra, 176, (1995), 124–127.##A. Tehranian, H. R. Maimani, A study of total graph, Iranian J. Math. Sci. and Inf., 6 (2), (2011), 75-80.##H. J. Wang, Graphs associated to co-maximal ideals of commutative rings, J. Algebra, 320, (2008), 2917–2933.##R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, 1991.##H. Zoschinger, Koatomare moduln, Math. Z., 170, (1980), 221–232.## ##

Filters and the Weakly Almost Periodic Compactification of a Semitopological Semigroup 2 2 Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of the $wap-$compactification of a semitopological semigroup is constructed as a space of $z-$filters. Also we obtain the cardinality of $S^{wap}$ and show that if $S^{wap}$ is the one point compactification then $(S^{Lmc}-S)*S^{Lmc}$ is dense in $S^{Lmc}-S$. 59 80 2012/02/152013/02/12013/01/212013/04/272013/06/9 1392/3/19 2015/04/262014/12/222014/12/222014/10/272014/12/31 1393/10/10 M. Akbari Tootkaboni M. Akbari Tootkaboni Shahed University Iran akbari@shahed.ac.ir Semigroup compactification $Lmc$-compactification $wap$-compactification $z$-filter. M. Amini, A. R. Medghalchi, Spectrum of the Fourier-Stieltjes algebra of a semigroup, Iranian Journal of Mathematical Sciences and Informatics, 1 (2), (2006), 1-8.##J. F. Berglund, H. D. Junghenn, P. Milnes, Analysis on Semigroups: Function Spaces, Compactifications, Representations, Wiley, New York, 1989.##J. F. Berglund, N. Hindmani, Filters and the weak almost periodic compactification of discrete semigroup, Trans. Amer. Math. Soc., 284, (1984), 1-38.##W. Comfort, S. Negrepontis, The Theory of Ultrafilters, Springer-Verlag, Berlin, 1974.##L. Gilman, M. Jerison, Ring of Continuous Functions, Van Nostrand, Princeton, N. J., 1960.##M. Filali, On the action of a locally compact group on same of its semigroup compactifications, 2007, Math. Proc. Camb. Phil. Soc., 143, 25-39.##N. Hindman, D. Strauss, Algebra in the Stone-Cech Compactification, Theory and Application, Springer Series in Computational Mathematics, Walter de Gruyter, Berlin, 1998.##R. Safari, S. M. Bagheri, On the Ultramean Construction, Iranian Journal of Mathematical Sciences and Informatics, 9 (2), (2014), 109-119.##M. A. Tootkaboni, Comfort order on topological space, Ultramath Con. 2008.##M. A. Tootkaboni, Quotient space of LMC-compactification as a space of z−filters, Acta Math Scientia., 32 (5), (2012), 2010-2020.##M. A. Tootkaboni, Z. Eslami, Density in Locally Compact Topological Groups, Topology and its Applications, 165, (2014), 2638##M. A. Tootkaboni, A. Riazi, Ultrafilters on Semitopological Semigroup, Semigroup Forum, 70 (3), (2005), 317-328.##M. A. Tootkaboni, H. R. E. Vishki, Filters and semigroup compactification properties, Semigroup Forum, 78 (2), (2009), 349-359.##Y. Zelenyuk, Ultrafilters and Topologies on Groups, Walter de Gruyter, Berlin, 2011.## ##

Gravitational Search Algorithm to Solve the K-of-N Lifetime Problem in Two-Tiered WSNs 2 2 Wireless Sensor Networks (WSNs) are networks of autonomous nodes used for monitoring an environment. In designing WSNs, one of the main issues is limited energy source for each sensor node. Hence, offering ways to optimize energy consumption in WSNs which eventually increases the network lifetime is strongly felt. Gravitational Search Algorithm (GSA) is a novel stochastic population-based meta-heuristic that has been successfully designed for solving continuous optimization problems. GSA has a flexible and well-balanced mechanism to enhance intensification (intensively explore areas of the search space with high quality solutions) and diversification (move to unexplored areas of the search space when necessary) abilities. In this paper, we will propose a GSA-based method for near-optimal positioning of Base Station (BS) in heterogeneous two-tiered WSNs, where Application Nodes (ANs) may own different data transmission rates, initial energies and parameter values. Here, we treat with the problem of positioning of BS in heterogeneous two-tiered WSNs as a continuous optimization problem and show that proposed GSA can locates the BS node in an appropriate near-optimal position of heterogeneous WSNs. From the experimental results, it can be easily concluded that the proposed approach finds the better location when compared to the PSO algorithm and the exhaustive search. 81 93 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/7 1391/4/17 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/26 1394/2/6 M. Kuchaki Rafsanjani M. Kuchaki Rafsanjani Shahid Bahonar University of Kerman Iran marjankuchaki@yahoo.com M. B. Dowlatshahi M. B. Dowlatshahi Shahid Bahonar University of Kerman Iran H. Nezamabadi-Pour H. Nezamabadi-Pour Shahid Bahonar University of Kerman Iran Wireless sensor network (WSN) Two-tiered WSNs Base station location Energy consumption Network lifetime Gravitational search algorithm (GSA). G. Aslania, S. H. Momeni-Masuleh, A. Malekb, F. Ghorbanib, Bank efficiency evaluation using a neural network-DEA method, Iranian Journal of Mathematical Sciences and Informatics, 4(2), (2009), 33-48##J. Chou, D. Petrovis, K. Ramchandran, A distributed and adaptive signal processing approach to reducing energy consumption in sensor networks, The 22nd IEEE Conference on Computer Communications (INFOCOM), p. 1054-1062, San Francisco, USA, March, 2003.##D. Estrin et al., Embedded, Everywhere: A Research Agenda for Networked Systems of Embedded Computers, Nat Research Council Report, 2001.##D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, John Wiley and Sons, 1993.##W. Heinzelman, A. Chandrakasan, H. Balakrishnan, Energy-efficient communication protocols for wireless microsensor networks, The Hawaiian International Conference on Systems Science, 2000.##W. Heinzelman, J. Kulik, H. Balakrishnan, Adaptive protocols for information dissemination in wireless sensor networks, The 5th ACM International Conference on Mobile Computing and Networking, p. 174-185, 1999.##T. P. Hong, G. N. Shiu, Solving the K-of-N Lifetime Problem by PSO, International Journal of Engineering, Science and Technology, 1(1), (2009), 136-147.##C. Intanagonwiwat, R. Govindan, D. Estrin, Directed diffusion: a scalable and robust communication paradigm for sensor networks, The ACM International Conference on Mobile Computing and Networking, 2000.##V. Kawadia, P. R. Kumar, Power control and clustering in ad hoc networks, The 22nd IEEE Conference on Computer Communications (INFOCOM), 2003.##S. Lee, W. Su, M. Gerla, Wireless ad hoc multicast routing with mobility prediction, Mobile Networks and Applications, 6(4), (2001), 351-360.##N. Li, J. C. Hou, L. Sha, Design and analysis of an mst-based topology control algorithm, The 22nd IEEE Conference on Computer Communications (INFOCOM), 2003.##J. Pan, L. Cai, Y. T. Hou, Y. Shi, S. X. Shen, Optimal base-station locations in twotiered wireless sensor networks, IEEE Transactions on Mobile Computing, 4(5), (2005), 458-473.##J. Pan, Y. Hou, L. Cai, Y. Shi, X. Shen, Topology control for wireless sensor networks, The 9th ACM International Conference on Mobile Computing and Networking, p. 286-299, 2003.##R. Ramanathan, and R. Hain, Topology control of multihop wireless networks using transmit power adjustment, The 19th IEEE Conference on Computer Communications (INFOCOM), 2000.##E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, GSA: A Gravitational Search Algorithm, Information Sciences, 179(13), (2009), 2232-2248.##V. Rodoplu, and T. H. Meng, Minimum energy mobile wireless networks, IEEE Journal on Selected Areas in Communications, 17(8), (1999), 1333-1344.## D. Tian, N. Georganas, Energy efficient Routing with guaranteed delivery in wireless sensor networks, The IEEE Wireless Communication & Networking Conference, 2003.##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.##F. Ye, H. Luo, J. Cheng, S. Lu, L. Zhang, A two-tier data dissemination model for large scale wireless sensor networks, The ACM International Conference on Mobile Computing and Networking, 2002.## ##

Distance-Balanced Closure of Some Graphs 2 2 In this paper we prove that any distance-balanced graph $G$ with $Delta(G)geq |V(G)|-3$ is regular. Also we define notion of distance-balanced closure of a graph and we find distance-balanced closures of trees $T$ with $Delta(T)geq |V(T)|-3$. 95 102 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/72015/04/29 1394/2/9 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/262015/04/29 1394/2/9 N. Ghareghani N. Ghareghani University of Tehran Iran ghareghani@ut.ac.ir B. Manoochehrian B. Manoochehrian University of Tehran Iran behzad@khayam.ut.ac.ir M. Mohammad-Noori M. Mohammad-Noori University of Tehran Iran morteza@ipm.ir Distances in graphs Distance-balanced graphs Distance-balanced closure. H. J. Bandelt, V. Chepoi, Metric graph theory and geometry: a survey, manuscript, 2004.##F. Buckley, F. Harary, Distance in graphs, Addison-Wesley, 1990.##V. Chepoi, Isometric subgraphs of hamming graphs and d-convexity, Cybernetics, 24, (1988), 6-10 (Russian, English transl.)##D. Z. Dijokovic, Dictance preserving subgraphs of hypercubes, J. Combin. Theory Ser B., 14, (1973), 263-267.##D. Eppstein, The lattice dimention of a graph, European J. Combin., 26, (2005), 585-592.##A. Graovac, M. Juvan, M.Petkovsek, A. Vasel, J. Zerovnik, The Szged index of fascia-graphs, MATCH Commun. Math. Comput. Chem., 49, (2003), 47-66.##I. Gutman, L. Popovic, P. V. Khadikar S. Karmarkar, S. Joshi, M. Mandloi, Relations between Wiener and Szeged indices of monocyclic molecules, MATCH Commun. Math. Comput. Chem., 35, (1997), 91-103.##J. Fathali, N. Jafari Rad, S. Rahimi Sherbaf, The p-median and p-center Problems on Bipartite Graphs, Iranian Journal of Mathematical Sciences and Informatics, 9 (2), (2014), 37-43.##J. Jerebic, S. Klavzar, D. F. Rall, Dictance-balanced graphs, Ann. Combin., 12, (2008), 71-79.##H. S. Ramane, I. Gutman, A. B. Ganagi, On Diameter of Line Graphs, Iranian Journal of Mathematical Sciences and Informatics, 8 (1), (2013), 105-109.#### ##

($phi,rho$)-Representation of $Gamma$-So-Rings 2 2 A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-representation of $Gamma$-so-rings. 103 119 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/72015/04/292013/08/22 1392/5/31 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/262015/04/292014/12/22 1393/10/1 M. Siva Mala M. Siva Mala V.R.Siddhartha Engineering College, Kanuru India sivamala_aug9@yahoo.co.in K. Siva Prasad K. Siva Prasad Acharya Nagarjuna University India siva235prasad@yahoo.co.in Subdirectly irreducible $Gamma$-so-ring Subdirect product $(phi rho)$-product of $Gamma_i$-so-rings $(phi rho)$-representation of a $Gamma$-so-ring. G. V. S. Acharyulu, A Study of Sum-Ordered Partial Semirings, Doctoral thesis, Andhra University, 1992.## M. A. Arbib, E. G. Manes, Partially Additive Categories and Flow-diagram Semantics, Journal of Algebra, 62, (1980), 203-227.## A. Iampan, Characterizing Ordered Bi-ideals in Ordered Gamma-semigroups, Iranian Journal of Mathematical Sciences and Informatics, 4 (1),(2009), 17-25.##A. Iampan, Some Properties of Ideal Extensions in Ternary semigroups, Iranian Journal of Mathematical Sciences and Informatics, 8 (1), (2013), 67-74.##E. G. Manes, D.B. Benson, The Inverse Semigroup of a Sum-Ordered Semiring, Semigroup Forum, 31, (1985), 129-152.##M. Murali Krishna Rao, Γ-Semirings, Doctoral thesis, Andhra University, 1995.##M. Siva Mala, K. Siva Prasad, Partial Γ-Semirings, Southeast Asian Bulletin of Mathematics, 38 (6),(2014), 873-885.## M. E. Streenstrup, Sum-Ordered Partial Semirings, Doctoral thesis, Graduate school of the University of Massachusetts, Feb 1985 (Department of Computer and Information Science).##P. V. Srininvasa Rao, φ- Representation of So-Rings, Intenational Journal of Computational Cognition, 7 (2),(2009), 65-70.##P. V. Srinivasa Rao, Ideal Theory of Sum-Ordered Partial Semirings, Doctoral thesis, Acharya Nagarjuna University, 2011.##A. Walendziak, A Common Generalization of Subdirect and Direct product of Algebras, Annales Societatis Mathematicae Polanae, Series I, Commentationes Mathemathicae, 17, (1992).## ##

On Barycentric-Magic Graphs 2 2 Let $A$ be an abelian group. A graph $G=(V,E)$ is said to be $A$-barycentric-magic if there exists a labeling $l:E(G)longrightarrow Asetminuslbrace{0}rbrace$ such that the induced vertex set labeling $l^{+}:V(G)longrightarrow A$ defined by $l^{+}(v)=sum_{uvin E(G)}l(uv)$ is a constant map and also satisfies that $l^{+}(v)=deg(v)l(u_{v}v)$ for all $v in V$, and for some vertex $u_{v}$ adjacent to $v$. In this paper we determine all $hinmathbb{N}$ for which a given graph G is $mathbb{Z}_{h}$-barycentric-magic and characterize $mathbb{Z}_{h}$-barycentric-magic labeling for some graphs containing vertices of degree 2 and 3. 121 129 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/72015/04/292013/08/222013/09/25 1392/7/3 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/262015/04/292014/12/222015/04/26 1394/2/6 M. T. Varela M. T. Varela Universidad Simon Bolıvar Venezuela mtvarela@usb.ve Magic graph Barycentric sequences Barycentric magic graph. C. Delorme, S. Gonzalez, O. Ordaz, M.T. Varela, Barycentric Sequences and Barycentric Ramsey Numbers Stars, Discrete Math., 277, (2004), 45-56.##C. Delorme, I. Marquez, O. Ordaz, A. Ortuno, Existence Conditions for Barycentric Sequences , Discrete Math., 281, (2004), 163-172.##S. Gonzalez, L. Gonzalez, O. Ordaz, Barycentric Ramsey Numbers for Small Graphs, Bull. Malays. Math. Sci. Soc. (2), 32(1), (2009), 1-17.##S.-M. Lee, E. Salehi, H. Sun, Integer- Magic Spectra of Trees with Diameter at most Four, J. Comb. Math. Comb. Comput., 50, (2004), 3-15.##O. Ordaz, D. Quiroz, Barycentric-sum problem: a survey , Divulg. Mat, 8, (2007), 193-206.##E. Salehi, Zero-Sum Magic Graphs and Their Null Sets , Ars Comb., 82, (2007), 41-53.## ##

On the 2-absorbing Submodules 2 2 Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of $M$ and $M/N$ is Noetherian, then a chain of 2-absorbing submodules of $M$ is constructed. Furthermore, the annihilation of $E(R/frak p)$ is studied whenever $0$ is a 2-absorbing submodule of $E(R/frak p)$, where $frak p$ is a prime ideal of $R$ and $E(R/frak p)$ is an injective envelope of $R/frak p$. 131 137 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/72015/04/292013/08/222013/09/252013/10/30 1392/8/8 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/262015/04/292014/12/222015/04/262014/07/2 1393/4/11 Sh. Payrovi Sh. Payrovi Imam Khomeini International University Iran shpayrovi@sci.ikiu.ac.ir S. Babaei S. Babaei Imam Khomieni International University Iran sbabaei@edu.ikiu.ac.ir 2-absorbing ideal 2-absorbing submodule A chain of 2-absorbing submodule. D. F. Anderson, A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra, 39, (2011), 1646-1672.## A. Badawi, On 2-absorbing ideals of commutavie rings, Bull. Austral. Math. Soc., 75, (2007), 417-429.##A. Badawi, A. Y. Darani, On weakly 2-absorbing ideals of commutative rings, Houston J. Math., 39 (2), (2013), 441-452.## A. Y. Darani, E. R. Puczylowski, On 2-absorbing commutative semigroups and their applications to rings, Semigroup Forum, 86, (2013), 83-91.##A. Y. Darani, F. Soheilnia, On n-absorning submodules, Math. Commun., 17, (2012), 547-557.##A. Y. Darani, F. Soheilnia, 2-Absorning and weakly 2-Absorbing submodules, Thai J. of Math., 9, (2011), 577-584.##R. Jahani-Nezhad, The Dual of a Strongly Prime Ideal, Iranian Journal of Mathematical Sciences and Informatics, 5, (2010), 19-26.##H. Matsumura, Commutative Rings Theory, Second edition, Cambridge Studies in Advanced Mathematics, 8, Cambridge University Press, Cambridge, 1989.##Sh. Payrovi, S. Babaei, On 2-absorbing submodules, Algebra Collq., 19, (2012), 913-920.##Sh. Payrovi, S. Babaei, On the 2-absorbing ideals, Int. Math. Forum, 7, (2012), 265-271.## ##

On Tensor Product of Graphs, Girth and Triangles 2 2 The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out. 139 147 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/72015/04/292013/08/222013/09/252013/10/302014/05/22 1393/3/1 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/262015/04/292014/12/222015/04/262014/07/22015/04/29 1394/2/9 H. P. Patil H. P. Patil Pondicherry University India hpppondy@gmail.com V. Raja V. Raja Pondicherru university India vraja.math@gmail.com Tensor product Bipartite graph Connected graph Eulerian graph Girth Cycle Path. J. A. Bondy, U. S. R. Murthy, Graph Theory with Applications, Macmillan Press Ltd, 1976.## M. Farzan, D. A. Waller, Kronecker Products and local joins of graphs, Canad. J. Math., 29 (2), 1977, 255-269.##G. H. Fath-Tabar, A. R. Ashrafi, The Hyper-Wiener Polynomial of Graphs, Iran. J. Math. Sci. Inf., 6 (2), (2011), 67-74.##R. Hammack, W. Imrich, S. Klavzar, Handbook of product graphs, Discrete Mathematics and its Applications, CRC-Press, New York, 2011.##H. P. Patil, Isomorphisms of duplicate graphs with some graph valued functions, Joul. of Combinatorics Inf. and System Sciences, 10 (1-2), (1985), 36-40.##E. Sampathkumar, On duplicate graphs, Joul. of Indian Math. Soc, (N.B.), 37, (1973), 285-293.##Sirous Moradi, A Note on Tensor Product of Graphs, Iran. J. Math. Sci. Inf., 7 (1), (2012), 73-81.##P. M. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc., 13, (1962), 47-52.## ##

Epi-Cesaro Convergence 2 2 Since the turn of the century there have been several notions of convergence for subsets of metric spaces appear in the literature. Appearing in as a subset of these notions is the concepts of epi-convergence. In this paper we peresent definitions of epi-Cesaro convergence for sequences of lower semicontinuous functions from $X$ to $[-infty,infty]$ and Kuratowski Cesaro convergence of sequences of sets. Also we characterize the connection between epi-Cesaro convergence of sequences of functions and Kuratowski Cesaro convergence of their epigarphs. 149 155 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/72015/04/292013/08/222013/09/252013/10/302014/05/222014/11/2 1393/8/11 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/262015/04/292014/12/222015/04/262014/07/22015/04/292015/02/21 1393/12/2 F. Nuray F. Nuray Afyon Kocatepe University India fnuray@aku.edu.tr R. F. Patterson R. F. Patterson University of North Florida India rpatters@unf.edu Cesaro convergence Epi-convergence Epi-Cesaro convergence Lower semicontinuous function. A. A. Arefijamaal, G. Sadeghi, Frames in 2-inner Product Spaces, Iranian Jour. Math. Sci. Inform., 8 (2), (2013), 123-130.##J. P. Aubin, H. Frankowska, Set-valued analysis, Boston, Birkhauser, 1990.##H. Attouch, Variational convergence for functions and operators, Pitman, New York,1984.##H. Attouch, R. Wets, Quantitative stability of variational systems: I. The epigraphical distance, Trans. Amer. Math. Soc., 328, (1991), 695-730.##S. Banach, Theorie des operations linearies, Warsaw, 1932.##G. Beer, R. T. Rockafeller ,J. B. Roger, R. Wets, A characterization of epi-convergence in terms of convergence of level sets, Proc. Amer. Math. Soc., 3 (116), (1992), 753-761.##J. Boos, Classical and modern methods in summability, Oxford University Press, Oxford, 2000.##J. Connor, The statistical and strong p-Cesro convergence of sequences, Analysis, 8, (1988), 47-63.##S. Dolecki, G. Salinetti , J. B Roger, R Wets, Convergence of functions: Equisemicontinuity I, Trans. Amer Math. Soc., 1 (276), (1980), 409-429.##G. H. Hardy, Divergent series, Clarendon Press, Oxford, 1949.##B. Hazarika, Strongly Almost Ideal Convergent Sequences in a Locally Convex Space Defined by Musielak-Orlicz Function, Iranian Jour. Math. Sci. Inform., 9 (2), (2014), 15-35.##K. Pall, Approximation to Optimization Problems: An Elementary Review, Mathematics of Operations Research, 11, (1986), 9-18.##I. J. Maddox, Elements of functional analysis, Cambridge University Press, Cambridge, 1970.##I. J. Maddox, I. J., A new type of convergence, Math. Proc. Cambridge Phil. Soc., 83, (1978), 61-64.##G. Petersen, Regular Matrix Transformations, Mc-Graw Hill Publ. Comp., London-New York-Toronto-Sydney, 1966.##I. J. Schoenberg, The integrability of certain functions and related sumability methods, Amer. Math. Monthly, 66, (1959), 361-375.## ##

ABSTRACTS IN PERSIAN - Vol. 10, No. 1 2 2 Please see the full text contains the Pesian abstracts for this volume. 157 169 2012/02/152013/02/12013/01/212013/04/272013/06/92012/07/72015/04/292013/08/222013/09/252013/10/302014/05/222014/11/22016/01/27 1394/11/7 2015/04/262014/12/222014/12/222014/10/272014/12/312015/04/262015/04/292014/12/222015/04/262014/07/22015/04/292015/02/212016/01/27 1394/11/7 Name of Authors in This Volume Name of Authors in This Volume jahade daneshgahi Iran All references of vol10,no1## ##