2018
13
1
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166
Integral Inequalities for h(x)-Riemann-Liouville Fractional Integrals
2
2
In this article, we obtain generalizations for Grüss type integral inequality by using h(x)-Riemann-Liouville fractional integral.
1
13
E.
Kacar
E.
Kacar
University of Kahramanmaraş Sütçü İmam
Turkey
kacarergun@gmail.com
Z.
Kacar
Z.
Kacar
University of Maryland, Department of Statistics
USA
H.
Yildirim
H.
Yildirim
University of Kahramanmaraş Sütçü İmam
Turkey
Fractional Integral
Grüss İnequality
Gruss Type Inequalities
Riemann-Liouville Fractional Integral.
[ G. Gr"{u}ss, Uber das maximum des absoluten Betrages von% begin{equation*} frac{1}{b-a}intlimits_{a}^{b}f(x)g(x)dx-frac{1}{(b-a)^{2}}% intlimits_{a}^{b}f(x)dxintlimits_{a}^{b}g(x)dx end{equation*}%, textit{Math. Z}, textbf{39}, (1935), 215-226 .##Z. Dahmani, L. Tabharit, S. Taf, New Generalisations of Gr¨uss inequality using RiemannLiouville fractional integrals, Bulletin of mathematical Anslysis and Applications, 2(3), (2010), 93-99.##J. Tariboon, S. K. Ntouyas, W. Sudsutad, Some new Riemann-Liouville fractional integral inequalities, International Journal of Mathematics and Mathematical Sciences, 2014, Article ID 869434, (2014).##H. Yue, Ostrowski Inequality for Fractional Integrals and Related Fractional Inequalities,TJMM5, 5(1), (2013), 85-89.##S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, 10 (3), (2009), article 86.##Z. Dahmani, New inequalities in fractional integrals, International Journal of Nonlinear Science, 9 (4), (2010), 493-497.##Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonlinear Science Letters A, 1 (2), (2010), 155-160.##P. -L Butzer, A. -A. Kilbas, J. -J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, Journal of Mathematical Analysis and Applications, 269(2), (2002), 387-400.##M. -Z Sarıkaya, H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstract and Applied Analysis, 2012, Article ID 428983, (2012), 10 pages.##H. Yıldırım, Z. Kırtay, "Ostrowski Inequality for Generalized Fractional Integral and Related Inequalities," Malaya Journal of Matematik, 2 (3) (2014), 322-329.##U. -N. Katugampola, Approach to a generalized fractional integral, Applied Mathematics and Computation, 218(3), (2011), 860-865.##S. -G Samko, A. -A Kilbas, O. -I Marichev, Fractional Integral and Derivatives, Theory and Applications, Gordon and Breach, Yverdon et alibi., (1993).##E. Kacar, H. Yıldırım, Gr¨uss Type Integral Inequalities for Generalized RiemannLiouville Fractional Integrals, IJPAM., 101(1), (2015), 55-70.##S. Kılınc, H. Yıldırım, Generalized Fractional Integral Inequalities Involving Hypergeometric Operators, IJPAM., 101( 1), (2015), 71-82.##H.H.G. Hashem, On The Solution of a Generalized Fractional Order Integral Equation and Some Applications, Journal of Calculus and Applications, 6(1) Jan. (2015), 120-130.##G. Anastassiou, M.R. Hooshmandasl, A. Ghasemi, F. Moftakharzadeh, Montgomery identities for fractional integrals and related fractional inequalities, J. Ineq. Pure and Appl. Math., 10(4), (2009).#### ##]
On the Means of the Values of Prime Counting Function
2
2
In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.
15
22
M.
Hassani
M.
Hassani
University of Zanjan
Iran
mehdi.hassani@znu.ac.ir
Primes counting function
Means of the values of function.
[M. Cipolla, La determinazione assintotica dell’nimo numero primo (asymptotic determination of the n-th prime), Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche, Series 3, 8, (1902), 132-166.## M. Hassani, On the ratio of the arithmetic and geometric means of the prime numbers and the number e, International Journal of Number Theory, 9(6), (2013), 1593-1603.## J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois Journal of Mathematics, 6, (1962), 64-94.## ##]
On the Notion of Fuzzy Shadowing Property
2
2
This paper is concerned with the study of fuzzy dynamical systems. Let (X,M,* ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map defined on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.
23
37
M.
Fatehi Nia
M.
Fatehi Nia
Department of Mathematics, Yazd University
Iran
fatehiniam@yazd.ac.ir
Fuzzy metric
Fuzzy discrete dynamical systems
Fuzzy shadowing
Fuzzy ergodic shadowing
Fuzzy topological mixing
[R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Springer Lecture Notes in Math, 1975.## J. S. Canovas, J. Kupka, Topological Entropy of Fuzzified Dynamical Systems, Fuzzy Sets and Systems, 165, (2011), 37-49.## L. Chen, S. Li, Shadowing Property for Inverse Limit Spaces, Trans. Amer. Math. Soc., 115 (2), (1992), 573-580.## E. M. Coven, I. Kan, J.A. Yorke, Pseudo-orbit Shadowing in the Family of Tent Maps. Trans. Amer. Math. Soc., 308 (1), (1988), 227-241.## A. Fakhari, F. Helen Ghane, On Shadowing: Ordinary and Ergodic, J. Math. Anal. Appl., 364 (1), (2010), 151-155.## M. Fatehi Nia, Parameterized IFS with the Asymptotic Average Shadowing Property, Qual. Theory Dyn. Syst., 15(2), (2016), 367-381.## M. Fatehi Nia, Iterated function systems with the average shadowing property, Topology Proc., 48, (2016), 261-275.## A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (3), (1997), 365-368.## A. George, P. Veeramani, On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64 (3), (1994), 395-399.## M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27, (1988), 385-389.## V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, Fuzzy Sets and Systems, 170, (2011), 95-111.## V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems, 115(3), (2000), 485-489.##R. Gu, Shadowing Techniques and Chaotic Phenomena, In Advances in Discrete Dynamics, Nova Science Publishers, New York, 65-90, 2012.## R. Gu, The asymptotic average shadowing property and transitivity, Nonlinear Analysis, 67, (2007), 1680-1689.## I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika (Prague), 11(5), (1975), 336-344.## J. Kupka, On devaney chaotic induced dynamical systems, Fuzzy Sets and Systems, 177, (2011), 34-44.## J. Kupka, On fuzzifications of discrete dynamical systems, Inform Sciences, 181, (2011), 2858-2872.## D. Mihet, A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets and Systems, 144(3), (2004), 431-439.## K. Palmer, Shadowing in dynamical systems: theory and applications, Kluwer Acad. Publ., Dordrecht, 2000.##D. Richeson, J. Wiseman, Chain Recurrence Rates and Topological Entropy, Topology Appl. 156, (2008), 251-261.## J. Rodriguesz-Lopez, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147, (2004), 273-283.## H. Roman-Flores, Y. Chalco-Cano, Some Chaotic Properties of Zadeh’s Extensions, Chaos Solitons and Fractals, 35(3), (2008), 452-459.## K. Sakai, Various Shadowing Properties for Positively Expansive Maps, Topology. Appl. 131 (10), (2003), 15-31.## S. Sedaghat, Y. Ordokhani, Stability and numerical solution of time variant linear systems with delay in both the state and control, Iran. J. Math. Sci. Inform., 7, (2012), 43-57.## P. Walters, On the Pseudo-orbit Tracing Property and its Relationship to Stability, Lecture Notes in Math, Springer-Verlag, 668, (1978), 231-244.## R. S. Yang, The Pseudo-orbit Tracing Property and Chaos, Acta Math. Sinica., 39, (1996), 382-386.## R. S. Yang, Pseudo-orbit tracing property and completely positive entropy, Acta Math. Sinica., 42, (1999), 99-104.## M. Yarahmadi, S.M. Karbassi, Design of robust controller by neuro-fuzzy system in a prescribed region via state feedback, Iran. J. Math. Sci. Inform., 4, (2009), 1-16.## ##]
The e-Theta Hopes
2
1
2
The largest class of hyperstructures is the Hv-structures, introduced in 1990, which proved to have a lot of applications in mathematics and several applied sciences, as well. Hyperstructures are used in the Lie-Santilli theory focusing to the hypernumbers, called e-numbers. We present the appropriate e-hyperstuctures which are defined using any map, in the sense the derivative map, called theta-hyperstructures.
39
50
R.
Mahjoob
R.
Mahjoob
Department of Mathematics-Semnan University
Iran
mahjoob@profs.semnan.ac.ir
Hyperstructures
Hv−structures
Hopes
Theta-structures
[R. Ameri, R. Mahjoob, Spectrum of prime L-submodules, Fuzzy sets and Systems, 159, (2008), 1107-1115.## P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993.## P. Corsini, V. Leoreanu, Applications of Hypergroup Theory, Kluwer Academic Publ., 2003.## P. Corsini, R. Mahjoob, Multivalued functions, Ratio Mathematica, 20, (2010), 1-41.## P. Corsini, T. Vougiouklis, From groupoids to groups through hypergroups, Rendiconti Mat. Serie VII, 9, (1989), 173-181.## B. Davvaz, Groups in Polygroups, Iranian Journal of Mathematicsl Science and Informatics, 1(1), (2006), 25-31.## B. Davvaz, Polygroup Theory and Related Systems, World Scientific, 2013.## B. Davvaz, V. Leoreanu, Hyperring Theory and Applications, Int. Academic Press, 2007.## B. Davvaz, R. M. Santilli, T. Vougiouklis, Multi-valued hypermathematics for characterization of matter and antimatter systems, Journal of Computational Methods in Sciences and Engineering (JCMSE), 13, (2013), 37-50.##B. Davvaz, R. M. Santilli, T. Vougiouklis, Mathematical prediction of Ying’s twin universes, American Journal of Modern Physics, 4(3), (2015), 5-9.## S. H. Gazavi, S. M. Anvariyeh, S. Mirvakili, EL2-Hyperstructures derived from partially quasiordered hyperstructures, Iranian Journal of Mathematicsl Science and Informatics, 10(2), (2015), 99-114.## P. Raja, S. M. Vaezpour, Normed Hypervector Spaces, Iranian Journal of Mathematics Science and Informatics, 2(2), (2007), 1-16.## R. M. Santilli, T. Vougiouklis, Isotopies, Genotopies, Hyperstructures and their Applications, Proc. Int. Workshop in Monteroduni: New Frontiers in Hyperstructures and Related Algebras, Hadronic Press (1996), 1-48.## R. M. Santilli, T. Vougiouklis, Lie-admissible hyperalgebras, Italian J. Pure Applied Mathematics, 31, (2013), 239-254.## T. Vougiouklis, Generalization of P-hypergroups, Rendiconti Circolo Matematico diPalermo, S.II, 36, (1987), 114-121.##T. Vougiouklis, The Fundamental Relation in Hyperrings. The General Hyperfield, 4th AHA Congress, World Scientific, 203-211, 1991.## T. Vougiouklis, Hyperstructures and their Representations, Monographs Math., Hadronic Press, 1994.## T. Vougiouklis, Some remarks on hyperstructures, Contemporary Mathematics, Amer.Math. Society, 184, (1995), 427-431.## T. Vougiouklis, On Hv-rings and Hv-representations, Discrete Math., 208/209, (1999), 615-620.## T. Vougiouklis, Enlarging Hv-structures, Algebras and Combinatorics, ICAC’97, Hong Kong, Springer-Verlag, 455-463, 1999.## T. Vougiouklis, -operations and Hv-fields, Acta Math. Sinica, (Engl. Ser.), 24(7), (2008), 1067-1078.## T. Vougiouklis, From Hv-rings to Hv-fields, Int. J. Alg. Hyperstruc. Appl., 1, (2014), 1-13.## T. Vougiouklis, S. Vougiouklis, The helix hyperoperations, Italian Journal of Pure and Applied Mathematics, (18), (2005), 197-206.## M. M. Zahedi, A Review on Hyper K-algebras, Iranian Journal of Mathematicsl Science and Informatics, 1(1), (2006), 55-112.## ##]
Spectra of Some New Graph Operations and Some New Class of Integral Graphs
2
2
In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.
51
65
Ch.
Adiga
Ch.
Adiga
University of Mysore
India
c_adiga@hotmail.com
B. R.
Rakshith
B. R.
Rakshith
University of Mysore
India
ranmsc08@yahoo.co.in
K. N.
Subba Krishna
K. N.
Subba Krishna
University of Mysore
India
sbbkrishna@gmail.com
Duplication corona
Duplication edge corona
Duplication neighborhood corona
Cospectral graphs
Integral graphs.
[C. Adiga, B. R. Rakshith, On spectra of variants of the corona of two graphs and some new equienergetic graphs, {it Discuss. Math. Graph Theory}, {bf 36} (1), (2016), 127--140.## A. Alwardi, N. D. Soner, I. Gutman, On the common-neighborhood energy of a graph, {it Bull. Acad. Serbe Sci. Arts (Cl. Math. Nat.)}, {bf 143}, (2011), 49-59.##K. Bali$acute{text{n}}$ska, D. Cvetkovi$acute{text{c}}$, Z. Radosavljevi$acute{text{c}}$, S. Simi$acute{text{c}}$, D.Stevanovi$acute{text{c}}$, A survey on integral graphs, {it Univ. Beograd. Publ.Elektrotehn. Fak. Ser. Mat.}, {bf 13}, (2002), 42-65.## S. Barik, S. Pati, B. K. Sarma, The spectrum of the corona of two graphs, {it SIAM J. Discrete Math.}, {bf 21}, (2007), 47--56.##S-Y Cui, G-X Tian, The spectrum and the signless Laplacian spectrum of coronae, {it Linear Algebra Appl.}, {bf 437}, (2012), 1692--1703.## D. Cvetkovi$acute{text{c}}$, New theorems for signless Laplacian eigenvalues, {textit Bull. Acad. SerbeSci. Arts, Cl. Sci. Math. Natur., Sci. Math.}, {textbf 137}, (2008), 131--146.##D. Cvetkovi$acute{text{c}}$, S. K. Simi$acute{text{c}}$, Towards a spectral theory of graphs based on the signless Laplacian, II, {it Linear Algebra Appl.}, {bf 432}, (2010), 2257--2272.##D. M. Cvetkovi$acute{text{c}}$, M. Doob, H. Sachs, {it Spectra of Graphs--Theory and Applications}, third ed., Johann Ambrosius Barth, Heidelberg, 1995.##R. Frucht, F. Harary, On the corona of two graphs, {it Aequationes Math.}, {bf 4}, (1970), 322-325.##F. Harary, A. J. Schwenk, Which Graphs have Integral Spectra?, {it Graphs and Combinatorics} (R. Bari and F. Harary, eds.), Springer-Verlag, Berlin, (1974), 45--51.##Y-P. Hou, W-C.Shiu, The spectrum of the edge corona of two graphs, {it Electronic Journal of Linear Algebra}, {bf20}, (2010), 586--594.##G. Indulal, The spectrum of neighborhood corona of graphs,{it Kragujevac J. Math.}, {bf 35}, (2011), 493--500.##G. Indulal, A. Vijayakumar, On a pair of equienergetic graphs, {it MATCH Commun. Math.Comput. Chem.}, {bf 55}, (2006), 83--90.## G. Indulal, A. Vijayakumar, Some New Integral Graphs, {it Applicable Analysis and Discrete Mathematics}, {bf 1}, (2007),420--426.## J. Lan, B. Zhou,Spectra of graph operations based on $R$-graph, {it Linear and Multilinear Algebra}, {textbf 63}, (2015), 1401--1422.##X. Liu, P. Lu, Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae, {it Linear Algebra Appl.}, {bf 438}, (2013) 3547-3559.## X. Liu, S. Zhou, Spectra of the neighbourhood corona of two graphs, {it Linear and Multilinear Algebra}, {textbf 62}:9, (2014), 1205--1219.##C. McLeman, E. McNicholas, Spectra of coronae, {it Linear Algebra Appl.}, {bf 435}, (2011), 998--1007.## R. Merris, Laplacian matrices of graphs: a survey, {it Linear Algebra Appl.}, {bf 197/198}, (1994), 143--176.## L. G. Wang, A survey of results on integral trees and integral graphs, {it University of Twente, The Netherlands}, (2005).##L. G. Wang, H. J. Broersma, C. Hoede, X. Li, G. Still, Some families of integral graphs, {it Discrete Math.}, {bf 308}, (2008), 6383--6391.##S. Wang, B. Zhou, The signless Laplacian spectra of the corona and edge corona of two graphs, {it Linear and Multilinear Algebra}, {textbf 61}, (2013), 197--204.## ##]
A Graphical Characterization for SPAP-Rings
2
2
Let $R$ be a commutative ring and $I$ an ideal of $R$. The zero-divisor graph of $R$ with respect to $I$, denoted by $Gamma_I(R)$, is the simple graph whose vertex set is ${x in Rsetminus I mid xy in I$, for some $y in Rsetminus I}$, with two distinct vertices $x$ and $y$ are adjacent if and only if $xy in I$. In this paper, we state a relation between zero-divisor graph of $R$ with respect to an ideal and almost prime ideals of $R$. We then use this result to give a graphical characterization for $SPAP$-rings.
67
73
E.
Rostami
E.
Rostami
Department of Pure Mathematics, Faculty of Mathematics and Computer,Shahid Bahonar University of Kerman, Kerman, Iran
Iran
e_rostami@uk.ac.ir
SPAP-Ring
Almost prime ideal
Zero-divisor graph with respect to an ideal
[A. Abbasi, H. Roshan-Shekalgourabi, D. Hassanzadeh-Lelekaami, Associated Graphs of Modules Over Commutative Rings, Iran. J. Math. Sci. Inform., 10(1), (2015), 45-58.## S. Akbari, R. Nikandish, M. J. Nikmehr, Some results on the intersection graphs of ideals of rings, J. Algebra Appl., 12(4), (2013), 125-200. [13 pages] DOI:10.1142/S0219498812502003.## D. D. Anderson, M. Bataineh, Generalization of Prime Ideals, Comm. Algebra, 36, (2008), 686-696.## A. Barnard, Multiplication modules, J. Algebra, 71, (1981), 174-178. ## I. Chakrabarty, S. Ghosh, T. K. Mukherjee, M. K. Sen, Intersection graphs of ideals of rings, Discrete Math., 309, (2009), 5381-5392.## I. Beck, Coloring of commutative rings, J. Algebra, 116, (1988), 208-226.## S. M. Bhatwadekar, P. K . Sharma, Unique factorization and birth of almost primes, Comm. Algebra, 33, (2005), 43-49.## H. R. Maimani, Median and center of zero-divisor graph of commutative semogroups, Iran. J. Math. Sci. Inform., 3(2), (2008), 69-76.## S. Mori, Allgemeine Z.P.I.-Ringe, J. Sci. Hirosima Univ. Ser. A., 10, (1940), 117-136.## S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra, 31, (2003), 4425-4443 .## E. Rostami, R. Nekooei, On SPAP -rings, Bull. Iranian Math. Soc., 41(4), (2015), 907-921.## A. Tehranian, H. R. Maimani, A study of the Total graph, Iran. J. Math. Sci. Inform.,6(2), (2011), 75-80.## ##]
Generalized Approximate Amenability of Direct Sum of Banach Algebras
2
2
In the present paper for two $mathfrak{A}$-module Banach algebras $A$ and $B$, we investigate relations between $varphi$-$mathfrak{A}$-module approximate amenability of $A$, $psi$-$mathfrak{A}$-module approximate amenability of $B$, and $varphioplus psi$-$mathfrak{A}$-module approximate amenability of $Aoplus B$ ($l^1$-direct sum of $A$ and $B$), where $varphiin$ Hom$_{mathfrak{A}}(A)$ and $psiin$ Hom$_{mathfrak{A}}(B)$.
75
87
H.
Sadeghi
H.
Sadeghi
Department of Mathematics, Faculty of Science, University of Isfahan, Isfahan, Iran.
Iran
sadeghi@sci.ui.ac.ir
Banach algebra
Module derivation
Module approximate amenability.
[ M. Amini, Module amenability for semigroup algebras, Semigroup Forum, 69, (2004), 243-254.## M. Amini, A. Bodaghi, D. Ebrahimi Bagha, Module amenability of the second dual and module topological center of semigroup algebras, Semigroup Forum, 80, (2010), 302-312.## 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.## A. Bodaghi, M. Amini, Module character amenability of Banach algebras, Arch. Math., 99, (2012), 353-365.## F. Ghahramani, R.J. Loy, Generalized notions of amenability, J. Funct. Anal., 208, (2004), 229-260.## F. Ghahramani, R. J. Loy, Y.Zhang, Generalized notions of amenability, II, J. Funct. Anal., 254, (2008), 1776-1810.## F. Ghahramani, C. J. Read, Approximate identities in approximate amenability, J. Funct. Anal., 262, (2012), 3929-3945.## Z. Ghorbani, M. Lashkarizadeh Bami, ’-Amenable and ’-biflat Banach algebras, Bull. Iran. Math. Soc., 39 (3), (2013), 507-515.## Z. Ghorbani, M. Lashkarizadeh Bami, ’-Approximate biflat and ’-amenable Banach algebras, Proc. Rom. Acad. Ser. A, 13 (1), (2012), 3-10.## Z. Ghorbani, M. Lashkarizadeh Bami, ’-n-Approximate weak amenability of abstract Segal algebras, U.P.B. Sci. Bull., Series A, 74 (4), (2012), 507-515.## M. Mirzavaziri, M. S. Moslehian, σ-derivations in Banach algebras, Bull. Iran. Math. Soc., 32 (1), (2006), 65-78.## M. Mirzavaziri, M.S. Moslehian, Automatic continuity of σ-derivations in C∗-algebras, Proc. Amer. Math. Soc., 134 (11), (2006), 3319-3327.##M. Momeni, T. Yazdanpanah,σ-Approximately module amenable Banach algebras,Math Sci, (2014), 8:113.## H. Pourmahmood Aghababa, (Super) module amenability, module topological center and semigroup algebras,Semigroup Forum,81, (2010), 344-356.## H. Pourmahmood Aghababa, A. Bodaghi, Module approximate amenability of Banach algebras, Bull. Iran. Math. Soc.,39(6), (2013), 137-1158.## M. Shams Yousefi, p-Analog of the semigroup Fourier-Steiltjes algebras,Iranian Journal of Mathematical Sciences and Informatics,10(2), (2015), 55-66.## ##]
Serre Subcategories and Local Cohomology Modules with Respect to a Pair of Ideals
2
2
This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.
89
96
F.
Dehghani-Zadeh
F.
Dehghani-Zadeh
Islamic Azad University, Yazd Branch
Iran
fdzadeh@gmail.com
Local cohomology modules
Pair of ideals
Serre subcategory
[M. Aghapournahr, A. J. Taherizadeh, A. Vahidi, Extension functors of local cohomology modules, Bulletin of the Iranian Mathematical Society, 37(3), (2011), 117-134.## M. P. Brodmann, Sharp. R. Y, Local cohomology: An Algebraic introduction with geometric applications, Cambridge studies in advanced Mathematics, 60, Cambridge University Press, Cambridge, 1998.## K. Borna Lorestani, P. Sahandi, S. Yassemi, Artinian local cohomology modules, Canadian Mathematical Bulletin, 50(4), (2007), 98-602.## W. Bruns, J. Herzog, Cohen-Macaulay Rings, Cambridge studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1993.## L. Chu, Q. Wang, Some results on local cohomology modules defined by a pair of ideals, Kyoto Journal of Mathematics, 49(1), (2009), 193-200.## L. Chu, Top local cohomology modules with respect to a pair of ideals, Proceedings of the American Mathematical Society, 139(3), (2011), 777-782.## F. Dehghani-Zadeh, On the finiteness properties of generalized local cohomology modules, International Electronic Journal of Algebra, 10, (2011), 113-122.## F. Dehghani-Zadeh, Finiteness properties generalized local cohomology with respect to an ideal containing the irrelevant ideal, Journal of the Korean Mathematical Society, 49(6), (2012), 1215-1227.## F. Dehghani-Zadeh, Results of generalized local cohomology with respect to a pair of ideals, International Journal of Pure and Applied Mathematics, 99 (4), (2015), 471-476.## A. Mafi, A. Pour Eshmanan Talemi, Results of certain local cohomology modules, Bulletin of the Korean Mathematical Society, 51(3), (2014), 653-657.##H. Matsumura, Commutative Ring Theory, Cambridge University Press 1986.## L. Melkersson, Modules cofinite with respect to an ideal, Journal of Algebra, 285(2), (2005), 619-668.## Sh. Payrovi, M. Lotfi Parsa, Artinianness of Local Cohomology Modules Defined by a pair of Ideals, Bulletin of the Malaysian Mathematical Sciences Society, 35(4), (2012), 877-883.##A. Pour Eshmanan Talemi, A. Tehranian, Local cohomology with respect to a cohomologically complete intersection pair of ideals, Iranian Journal of Mathematical Sciences and Informatics, 9(2), (2014), 7-13.##J. Rotman, An Introduction to Homological Algebra, Academic Press, orlando, 1979.## R.Takahashi, Y. Yoshino, T. Yoshinawa, Local cohomology based on a nonclosed support defined by a pair of ideals, Journal of Pure and Appllied Algebra, 213(4), (2009), 582-600.## A. Tehranian, A. Pour Eshmanan Talemi, Cofiniteness of local cohomology based on a non-closed support defined by a pair of deals, Bulletin of the Iranian Mathematical Society, 36(2), (2010), 145-155.## ##]
A Shorter and Simple Approach to Study Fixed Point Results via b-Simulation Functions
2
2
The purpose of this short note is to consider much shorter and nicer proofs
about fixed point results on b-metric spaces via b-simulation function introduced very recently by Demma et al. [M. Demma, R. Saadati, P. Vetro, emph{Fixed point results on b-metric space via Picard sequences and b-simulation functions}, Iranian J. Math. Sci. Infor. 11 (1) (2016) 123--136].
97
102
Gh.
Soleimani Rad
Gh.
Soleimani Rad
Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Iran
gha.soleimani.sci@iauctb.ac.ir
S.
Radenovic
S.
Radenovic
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia & State University of Novi Pazar, Serbia
Serbia
radens@beotel.net
D.
Dolicanin-Dekic
D.
Dolicanin-Dekic
Faculty of Technical Sciences, Kneza Miov{s}a 7, 38 220 Kosovska Mitrovica, Serbia
Serbia
diana.dolicanin@pr.ac.rs
b-Metric space
b-Simulation function
Cauchy sequence
Lower semi-continuous
[H. Argoubi, B. Samet, C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8, (2015), 1082-1094.## M. Demma, R. Saadati, P. Vetro, Fixed point results on b-metric space via Picard sequences and b-simulation functions, Iranian Journal of Mathematical Sciences and Informatics, 11(1), (2016), 123-136.## M. Jovanovi´c, Z. Kadelburg, S. Radenovi´c, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010, 978121, 15 pages.## F. Khojasteh, S. Shukla, S. Radenovi´c, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29(6), (2015), 1189-1194.## S.K. Mohanta, Coincidence points and common fixed points for expansive type pappings in b-metric spaces, Iranian Journal of Mathematical Sciences and Informatics, 11(1), (2016), 101-113.## A. Nastasi, P. Vetro, Existence and uniqueness for a first-order periodic differential problem via fixed point results, Results. Math., (2016), doi: 10.1007/s00025-016-0551-x.## A. Nastasi, P. Vetro, Fixed point results on metric and partial metrric spaces via simulations functions, J. Nonlinear Sci. Appl., 8, (2015), 1059-1069.## A. Roldan, E. Karapınar, C. Roldan, J. Martinez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comut. Appl. Math., 275, (2015), 345-355.## ##]
Atomic Systems in 2-inner Product Spaces
2
2
In this paper, we introduce the concept of family of local atoms in a 2-inner product space and then this concept is generalized to an atomic system. Besides, a characterization of an atomic system lead to obtain a new frame. Actually this frame is a generalization of previous works.
103
110
B.
Dastourian
B.
Dastourian
Department of Pure Mathematics Ferdowsi University of Mashhad
Iran
M.
Janfada
M.
Janfada
Department of Pure Mathematics Ferdowsi University of Mashhad
Iran
2-inner product space
2-norm space
Family of local atoms
Atomic system
Frame.
[1. A. A. Arefijamaal, Gh. Sadeghi, Frames in 2-inner product spaces,Iran. J. Math. Sci.Inform.,8(2), (2013), 123–130.##2. H. Bolcskei, F. Hlawatsch, H. G. Feichtinger, Frame-theoretic analyssis of oversampled filter banks,IEEE Trans. Signal Process.,46, (1998), 3256–3268.##3. Y. J. Cho, P. C. S. Lin, S. S. Kim, A. Misiak, Theorey of 2-inner Product Spaces, Nova Science Publishers, Inc., New York, 2001.##4. Y. J. Cho, M. Matic, J. E. Pecaric, On Gram’s deteminant in 2-inner product spaces,J.Korean Math. Soc.,38(4), (2001), 125–1156.##5. B. Dastourian, M. Janfada,-frames for operators on Hilbert modules,Wavelets and Linear algebras.,3, (2016), 27–43.##6. B. Dastourian, M. Janfada, Frames for operators in Banach spaces via semi-inner products,Int. J. Wavelets Multiresult. Inf. rocess.,14(3), (2016), 1650011 (17 pages).##7. I. Daubechies, A. Grossmann, Y. Meyer, Painless nonorthogonal expansions,J. Math.Phys.,27, (1986), 1271–1283.##8. N. E. Dudey Ward, J. R. Partington, A construction of rational wavelets and frames in Hardy-Sobolev space with applications to system modelling,SIAM J. Control Optim.36, (1998), 654–679.##9. J. Duffin, A.C. Schaeffer, A class of nonharmonic Fourier series,Trans. Amer. Math.Soc.72, (1952), 341–366.##10. Y. C. Eldar, Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors.J. Fourier. Anal. Appl.9(1), (2003), 77–96.##11. Y. C. Eldar, T. Werther, General framework for consistent sampling in Hilbert spaces,Int. J. Wavelets Multiresult. Inf. Process.3(3), (2005), 347–359.##12. H.G. Feichtinger, T. Werther, Atomic systems for subspaces, in:L. Zayed (Ed.),Pro-ceedings SampTA, (2001),Orlando, FL, (2001), 163–165.##13. P. J. S. G. Ferreira, Mathematics for multimedia signal processing II: Discrete finite frames and signal reconstruction, In:Byrnes, S. (ed.) Signal processing for multimedia,IOS Press, Amsterdam (1999), 35–54.##14. S. Gahler, Linear 2-normierte Raume,Math. Nachr.,28, (1965), 1–43.##15. L. G ̆avrut ̧a, Frames for operators,Appl. Comput. Harmon. Anal.,32, (2012), 139–144.##16. S. M. Gozali, H. Gunawan, On b-orthogonality in 2-normed spaces,J. Indones. Math.Soc.16(2), (2010), 127–132.##17. H. Gunawan, Inner products on n-inner product spaces,Soochow J. Math.28(4), (2002),389–398.##18. Z. Lewandowska, Bounded 2-linear operators on 2-normed sets,Glas. Mat. Ser. III,39(59), (2004), 301–312.##19. T. Strohmer, R. Jr. Heath, Grassmanian frames with applications to coding and com-munications,Appl. Comput. Harmon. Anal.,14, (2003), 257–275.##20. X. Xiao, Y. Zhu, L. G ̆avrut ̧a, Some Properties ofK-Frames in Hilbert Spaces,Results.Math.,63(3-4), (2013), 1243–1255.## ##]
A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation
2
2
In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant literature and the references here). In this paper we study the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. Based on the closed Newton-Cotes formulae, we also develop trigonometrically-fitted symplectic methods. An error analysis for the onedimensional Schrodinger equation of the new developed methods and a comparison with previous developed methods is also given. We apply the new symplectic schemes to the well-known radial Schr¨odinger equation in order to investigate the efficiency of the proposed method to these type of problems.
111
129
A.
Shokri
A.
Shokri
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
Iran
shokri@maragheh.ac.ir
H.
Saadat
H.
Saadat
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
Iran
hosein67saadat@yahoo.com
A. R.
Khodadadi
A. R.
Khodadadi
Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
Iran
ali_reza_khodadadi@yahoo.com
Phase-lag
Schrodinger equation
Numerical solution
Newton-Cotes formulae
Derivative
[ Z.A. Anastassi, T.E., Simos, Trigonometrically-fitted Runge-Kutta methods for the numerical solution of the Schr ̈odinger equation,Journal of Mathematical Chemistry,37(3),(2005), 281-293.## J. C. Chiou, S. D. Wu, Open Newton-Cotes differential methods as multilayer symplectic integrators,Journal of Chemical Physics,107, (1997), 6894-6897.## P. Henrici,Discrete Variable Methods in Ordinary Differential Equations, Wiley, NewYork, 1962.## M.K. Jain, R.K. Jain, U.A. Krishnaiah, Obrechkoff methods for periodic initial value problems of second order differential equations,Journal of Mathematical Physics,15,(1981), 239-250.## B. Jazbi , M. Moini, Application of Hes homotopy perturbation method for Schr ̈odinger equation,Iranian Journal of Mathematical Sciences and Informatics,3(2), (2008), 13-19.## Z. Kalogiratou, T.E. Simos, A P-stable exponentially-fitted method for the numerical integration of the Schr ̈odinger equation,Applied mathematics and Computations,112,(2000), 99-112.## J.D. Lambert,Numerical methods for ordinary differential systems, The initial value problem, John Wiley and Sons, 1991.## J.D. Lambert, I.A. Watson, Symmetric multistep methods for periodic initial value problems,Journal of the Institute of Mathematics and its Applications,18, (1976), 189-202.## P. Mokhtary, S.M. Hosseini, Some implementation aspects of the general linear methods withinherent Runge-Kutta stability,Iranian ournal of Mathematical Sciences and Informatics,3(1), (2008), 63-76.## G. D. Quinlan, S. Tremaine, Symmetric multistep methods for the numerical integration of planetary orbits, The Astro,The stronomical ournal,100(5), (1990), 1694-1700.## A. D. Raptis, A. C. Allison, Exponential-fitting methods for the numerical solution of the Schr ̈odinger equation,Journal of Computer hysics Communications,14, (1978),1-5.## A. Shokri, An explicit trigonometrically fitted ten-step method with phase-lag of order infinity for the numerical solution of radial Schr odinger equation,Applied and Computational Mathematics,14(1), (2015), 63-74.## A. Shokri, The symmetric two-step P-stable nonlinear predictor-corrector methods for the numerical solution of second order initial alue problems,Bulletin of the Iranian Mathematical Society,41(1), (2015), 191-205.## A. Shokri, A.A. Shokri, S. Mostafavi, H. Saadat, Trigonometrically fitted two-step Obrechkoff methods for the numerical solution of eriodic initial value problems,Iranian Journal of Mathematical Chemistry,6(2), (2015), 145-161.## A. Shokri, H. Saadat, Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical olution of radial Schr ̈odinger equation,Journal of Mathematical Chemistry,52(7), (2014), 1870-1894.## A. Shokri, H. Saadat, High phase-lag order trigonometrically fitted two-step Obrechkoff methods for the numerical solution of periodic nitial value problems,Numerical Algorithms,68, (2015), 337-354.## Shokri, A. A. Shokri, The new class of implicit L-stable hybrid Obrechkoff method for the numerical solution of first order initial value roblems,Journal of Computer Physics Communications, 184, (2013), 529-531.## T. E. Simos, Accurately closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schr ̈odinger quation,International Journal of Modern Physics C,24(3), (2013).##T. E. Simos, Closed Newton-Cotes trigonometrically-fitted formulae for long-time integration of orbital problems,Revista Mexicana de stronomia y Astrofysica,42(2),(2006), 167-177.## T. E. Simos, Closed Newton-Cotes trigonometrically-fitted formulae of high-order for long-time integration of orbital problems,Applied athematical Letters,22(10), (2009),1616-1621.## T. E. Simos, Closed Newton-Cotes trigonometrically-fitted formulae for long-time integration,International Journal of Modern Physics ,14(8), (2003), 1061-1074.## T. E. Simos, High order closed Newton-Cotes exponentially and trigonometrically fit-ted formulae as multilayer symplectic integrators nd their application to the radialSchr ̈odinger equation,Journal of Mathematical Chemistry,50(5), (2012), 1224-1261.## T. E. Simos, High-order closed Newton-Cotes trigonometrically-fitted formulae for long-time integration of orbital problems,Journal of omputer Physics Communications,178(3), (2008), 199-207.## T. E. Simos, High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schr ̈odinger equation,Applied Mathematics and Computation,209 (1), (2009), 137-151.## T. E. Simos, New closed Newton-Cotes type formulae as multilayer symplectic integrators,Journal of Chemical Physics,133(10), 2010), 104-108.## W. Zhu, X. Zhao, Y. Tang, Numerical methods with a high order of accuracy in thequantum system,Journal of Chemical Physics,104, 1996) 2275-2286.## ##]
Some Algebraic and Combinatorial Properties of the Complete $T$-Partite Graphs
2
2
In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs.
131
138
S. M.
Seyyedi
S. M.
Seyyedi
Amirkabir University of Technology
Iran
F.
Rahmati
F.
Rahmati
Amirkabir University of Technology
Iran
frahmati@aut.ac.ir
Cohen-Macaulay
shellable
vertex decomposable
edge ideal
[A. Abbasi, H. Roshan-Shekalgourabi, D. Hassanzadeh-Lelekaami, Associated graphs of Modules over commutative rings,Iranian ournal of Mathematical Sciences and Informatics,10(1), (2015), 45-58.## A. Bj ̈orner, Topological methods, Handbook of combinatorics,Elsevier, Amsterdam,2,(1995), 1819-1872.## M. Estrada, R. H. Villarreal, Cohen-Macaulay bipartite graphs,Arch. Math.,68,(1997), 124-128.## C. A. Francisco, A. Van Tuyl, Sequentially Cohen-Macaulay edge ideals,Proc. Amer.Math. Soc.,135(8), (2007), 2327-2337.## J. Herzog, T. Hibi, Componentwise linear ideals,Nagoya Math. J.,153, (1999), 141-153.## J. Herzog, T. Hibi, Distributive lattices, bipartite graphs, and Alexander duality,J.Algebraic Comb.,22, (2005), 289-302.## J. Herzog, T. Hibi and X. Zheng, Cohen-Macaulay chordal graphs,J. Combin. Theory Ser. A,113(5), (2006), 911-916.## H. R. Maimani, Median and center of zero-devisor graph of commutative semigroups,Iranian Journal of Mathematical Sciences and nformatics,3(2), (2008), 69-76.## E. Miller, B. Strumfels,Combinatorial Commutative Algebra, Springer, 2004.## F. Mohammadi, D. Kiani, Sequentially Cohen-Macaulay graphs of form θn1,...,nk,Bull.Iran. Math. Soc.,36(2), (2010), 109-118.## C. Promsakon, C. Uiyyasathian, Edge-chromatic numbers of glued graphs,Thai J. Math.,4( 2), (2010), 395-401.## R. P. Stanleyl,Combinatorics and Commutative Algebra. Second edition, Progress in Mathematics. 41.Birkh ̈auser Boston, Inc., oston, MA, 1996.## A. Tehranian, H. R. Maimani, A study of the total graph,Iranian Journal of Mathematical Sciences and Informatics,6(2), (2011), 75-80.## A. Van Tuyl, Sequentially Cohen-Macaulay bipartite graphs, vertex decompos ability and regularity,Archiv der Mathematik,93(5), 2009), 51-459.## R. H. Villarreal,Combinatorial Optimization Methods in Commutative Algebra, Preliminary version, 2012.## D. R. Wood, On the umber of maximal independent sets in a graph,Discrete Math.and Theor. Computer Science,13(3), (2011), 7-20.## R. Woodroofe, Vertex decomposable graphs and obstructions to shellability,Proc. Amer.Math. Soc.,137(8), (2009), 3235-3246.## ##]
On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture
2
2
The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case of Sroysang’s conjecture (2013) [9] i.e., given a fixed positive integer k, we verify the validity of the following claim: lim x→∞ f(x + k)/f(x) = φ, where φ = (1 + √5)/2 denotes the well-known golden ratio and the real valued function f on R satisfies the functional equation f(x + 2k) =f(x + k) + f(x) for every x ∈ R. We complete the proof of the conjecture by giving out an entirely different approach for the other case.
139
151
J. F.
Rabago
J. F.
Rabago
University of the Philippines Baguio
Iran
jfrabago@gmail.com
Golden ratio
Fibonacci functional equation
Horadam functional equation
convergence.
[S. Alikhani, M. A. Iranmanesh, Energy of graphs, matroids and Fibonacci numbers,Iranian J. Math. Sci. Inform.,5(2), (2010), 55–60.## J. B. Bacani, J. F. T. Rabago, On linear recursive sequences with coefficients inarithmetic-geometric progressions,Appl. Math. Sci. Hikari),9(52), (2015), 2595 –2607.## J. B. Bacani, J. F. T. Rabago, On two nonlinear difference equations,Dyn. Contin.Discrete Impuls. Syst. Ser. A Math. Anal., to appear.## M. Bahramian, H. Daghigh, A generalized Fibonacci sequence and the Diophantine equations x2±kxy−y2±x= 0,Iranian J. Math. Sci. nform.,8(2), (2013), 111–121.## R. A. Dunlap,The Golden Ratio and Fibonacci Numbers, World Scientific, Singapore,1998.## A. Hakami, An application of Fibonacci sequence on continued fractions,Int. Math.Forum,10(2), (2015), 69–74.## J. Hambidge,Dynamic Symmetry: The Greek Vase, New Haven CT: Yale UniversityPress, 1920.## J. S. Han, H. S. Kim, J. Neggers, On Fibonacci functions with Fibonacci numbers,Adv.Differ. Equ.,2012, (2012), Article 126, 7 pages.## A. F. Horadam, Basic properties of a certain generalized sequence of numbers,Fib.Quart.,3, (1965), 161–176.## T. Koshy,Fibonacci and Lucas Numbers with Applications, Pure and Applied Mathematics, Wiley-Interscience, New York, 2001.## P. J. Larcombe, O. D. Bagdasar, E. J. Fennessey, Horadam sequences: a survey,Bull.Inst. Combin. Appl.,67(2013), 49–72.## P. J. Larcombe, Horadam sequences: a survey update and extension,Bull. Inst. Combin.Appl.,80, (2017), 99–118.## M. Livio,The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number,New York: Broadway Books, 2002.##E. Lucas, Th ́eorie des Fonctions Num ́eriques Simplement P ́eriodiques,American Journal of Mathematics,1, (1878), 184–240, 89–321; reprinted as “The Theory of SimplyPeriodic Numerical Functions”, Santa Clara, CA: The Fibonacci Association, 1969.##O.E.I.S. Foundation Inc. (2011), The On-Line Encyclopedia of Integer Sequences,http://oeis.org.## L. Pacioli, Luca,De divina proportione, Luca Paganinem de Paganinus de Brescia (An-tonio Capella), 1509, Venice.## R. Padovan,Proportion, Taylor & Francis, pp. 305–306, 1999.## R. Padovan, Proportion: Science, Philosophy, Architecture,Nexus Network Journal,4(1), (2002), 113–122.##J. F. T. Rabago, On second-order linear recurrent homogeneous differential equations with period k,Hacet. J. Math. Stat.,43(6), (2014), 923–933.## J. F. T. Rabago, On second-order linear recurrent functions with periodk and proofs totwo conjectures of Sroysang,Hacet. J. Math. tat.,45(2), (2016), 429–446.## J. F. T. Rabago, Onk-Fibonacci numbers with applications to continued fractions,Journal of Physics: Conference Series,693, (2016), 12005.## T. Rowland,Cantor’s Intersection Theorem. From Math World–A Wolfram Web Resource, created by Eric W. eisstein.http://mathworld.wolfram.com/CantorsIntersectionTheorem.html## B. Sroysang, On Fibonacci functions with period k,Discrete Dyn. Nat. Soc.,2013,(2013), Article ID 418123, 4 pages.## J. J. Tattersall, Elementary Number Theory in Nine Chapters (2nd ed.),Cambridge University Press, 2005.## D. T. Tollu, Y. Yazlik, N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers,Adv. iffer. qu.,2013, (2013), Article 174,7 pages.## S. A. Vajda,Fibonacci & Lucas Numbers and The Golden Section: Theory and Applications, Ellis Horwood Ltd., Chishester, 1989.## ##]
ABSTRACTS IN PERSIAN Vol.13, No.1
2
2
Please see the full text contains the Pesian abstracts for this volume.
153
166
Name of Authors
In This Volume
Name of Authors
In This Volume
Iranian Journal of Mathematical Sciences and Informatics
Iran
fatemeh.bardestani@gmail.com
ABSTRACTS
PERSIAN
Vol. 13
No. 1
[References of all articles in##this volume## ##]