2018
13
2
0
186
Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
2
2
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+|E(G)|)deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper we find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of complete bipartite graphs.
1
13
Ph.
Inpoonjai
Ph.
Inpoonjai
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi
Thailand
phaisatcha_in@outlook.com
T.
Jiarasuksakun
T.
Jiarasuksakun
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi
Thailand
thiradet.jia@mail.kmutt.ac.th
Complete bipartite graphs
Supermagic graphs
Degree-magic graphs
Balanced degree-magic graphs
[1- L. Bezegova, Balanced Degree-Magic Complements of Bipartite Graphs, Discrete Math., 313, (2013), 1918-1923.##2. L. Bezegova, J. Ivanco, An Extension of Regular Supermagic Graphs, Discrete Math., 310, (2010), 3571-3578.##3. L. Bezegov´a, J. Ivanco, On Conservative and Supermagic Graphs, Discrete Math., 311, (2011), 2428-2436.##4. L. Bezegov´a, J. Ivanco, A Characterization of Complete Tripartite Degree-Magic Graphs, Discuss. Math. Graph Theory, 32, (2012), 243-253.##5. L. Bezegova, J. Ivanˇco, Number of Edges in Degree-Magic Graphs, Discrete Math., 313, (2013), 1349-1357.##6. J.A. Gallian, A Dynamic Survey of Graph Labeling, Electron. J. Combin., 16, (2009), #DS6.##7. E. Salehi, Integer-Magic Spectra of Cycle Related Graphs, Iranian Journal of Mathematical Sciences and Informatics, 1(2), (2006), 53-63.##8. J. Sedlacek, Problem 27. Theory of Graphs and Its Applications, Proc. Symp. Smolenice, Praha, (1963), 163-164.##9. B.M. Stewart, Magic Graphs, Canad. J. Math., 18, (1966), 1031-1059.##10. M.T. Varela, On Barycentric-Magic Graphs, Iranian Journal of Mathematical Sciences and Informatics, 10(1), (2015), 121-129.## ##]
New Approaches to Duals of Fourier-like Systems
2
2
The sequences of the form ${E_{mb}g_{n}}_{m, ninmathbb{Z}}$, where $E_{mb}$ is the modulation operator, $b>0$ and $g_{n}$ is the window function in $L^{2}(mathbb{R})$, construct Fourier-like systems. We try to consider some sufficient conditions on the window functions of Fourier-like systems, to make a frame and find a dual frame with the same structure. We also extend the given two Bessel Fourier-like systems to make a pair of dual frames and prove that the window functions of Fourier-like Bessel sequences share the compactly supported property with their extensions. But for polynomials windows, a result of this type does not happen.
15
27
E.
Osgooei
E.
Osgooei
Department of Sciences, Urmia University of Technology, Urmia, Iran.
Iran
e.osgooei@uut.ac.ir
Fourier-like systems
Shift-invariant systems
A pair of dual frames
Polynomials.
[.1- O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003.##2- O. Christensen, H. O. Kim, R. Y. Kim, Extensions of Bessel sequences to dual pairs of frames, Appl. Comput. Harmon. Anal., 34(2), (2013), 224-233.##3- O. Christensen, H. O. Kim, R. Y. Kim, Regularity of dual Gabor windows, Abstr. Appl. Anal. 2013, Art. ID 747268, 8 pp.##4. O. Christensen, R. Y. Kim, On dual Gabor frame pairs generated by polynomials, J.Fourier Anal. Appl., 16(1), (2010), 1–16.##5. O. Christensen, E. Osgooei, On frame properties for Fourier-like systems, J. Approx.Theory, 172 (2013), 47-57.##6. O. Christensen, W. Sun, Explicity given pairs of dual frames with compactly supported generators and applications to irregular B-splines, J. Approx. Theory, 151(2), (2008), 155-163.##7. L. H. Christiansen, O. Christensen, Construction of smooth compactly supported windows generating dual pairs of Gabor frames, Asian-European Journal of Mathematics, 6(1), (2013), 1-13.##8. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, PA, 1992.##9. M. H. Faroughi, E. Osgooei, A. Rahimi, (X_d, {X_d}^*)-multipliers in Banach spaces, Banach J. Math. Anal., 7(2), (2013), 146-161.##10. A. J. E. M. Janssen, The duality condition for Weyl-Heisenberg frames, in: H.G. Feichtinger, T. Strohmer (Eds.), Gabor Analysis: Theory and Application, Birkhauser, Boston, MA, 1998.##11. A. Ron, Z. Shen, Frames and stable for shift-invariant subspaces of L2 (R), Canad. J. Math., 47 (1995), 1051-1094.## ##]
Existence Results for Generalized ε-Vector Equilibrium Problems
2
2
This paper studies some existence results for generalized epsilon-vector equilibrium problems and generalized epsilon-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.
29
43
M.
Abbasi
M.
Abbasi
university of Isfahan, department of mathematics
Iran
malek.abbasi@sci.ui.ac.ir
M.
Rezaei
M.
Rezaei
university of Isfahan, department of mathematics
Iran
mrezaie@sci.ui.ac.ir
Generalized epsilon-vector equilibrium problems
Generalized epsilon-vector variational inequalities
KKM theorem
Existence results
Painleve-Kuratowski set-convergence.
[1-M. Abbasi, Kh. Pourbarat, The System of vector variational-like inequalities with weakly relaxed {ηγ − αγ}γ∈Γ pseudomonotone mappings in Banach spaces, Iranian Journal of Mathematical Sciences and Informatics, 2, (2010), 1-11.##2- Q. H. Ansari, I. V. Konnov, J. C. Yao, Existence of a solution and variational principles for vector equilibrium problems. Journal of Optimization Theory and Applications, 110, (2001), 481-492.##3- Q. H. Ansari, I. V. Konnov, J. C. Yao, Characterizations of solutions for vector equilibrium problems. Journal of Optimization Theory and Applications, 113, (2000), 435-447.##4. Q. H. Ansari, X.Q. Yang, J. C. Yao, Existence and duality of implicit vector variational problems, Numerical Functional Analysis and Optimization, 22, (2001), 815-829.##5. R. I. Bo, S. M. Grad, G. Wanka, Duality in Vector Optimization, Springer-Verlag, Berlin, Heidelberg, 2009.##6. F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, 1983.##7. K. Fan, A generalization of Tychonoffs fixed point theorem, Mathematische Annalen, 142, (1991), 305310.##8. F. Giannessi, Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Nonconvex Optimization and its Applications, Kluwer Academic Publishers, Dordrecht, Holland, 2000.##9. A. Jofre, D.T. Luc, M. Thera, ε-subdifferential and ε-monotonicity, Nonlinear Anal., 33, (1998), 71-90.##10. A. A. Khan, Ch. Tammer, C. Zalinescu, set-valued optimization, Springer-Verlag, 2015.##11. S. Kum, G. S. Kim, G. M. Lee, Duality for ε-variational inequality, Journal of Optimization Theory and Applications, 139, (2008), 649-655.##12. C. S. Lalitha, G. Bhatia, Duality in ε-variational inequality problems, J. Math. Anal. Appl., 356, (2009), 168-178. ##13. G. M. Lee, D. S. Kim, B. S. Lee, Generalized vector variational inequality, Applied Mathematics Letters, 9, (1996), 39-42.##14. G. M. Lee, D. S. Kim, B. S. Lee, G. Y. Chen, Generalized vector variational inequality and its duality for set-valued maps, Applied Mathematics Letters, 11, (1998), 21-26.##15. G. M. Lee, D. S. Kim, B. S. Lee, G. Y. Chen, Generalized vector variational inequality and its duality for set-valued maps, Applied Mathematics Letters, 11, (1998), 21-26.##16. S. J. Li, P. Zhao, A method of duality for a mixed vector equilibrium problem, Optimization Letters, 4, (2010), 85-96.##17. H. V. Ngai, D. T. Luc, M. Th´era, Approximate convex functions, J. Nonlinear Convex Anal., 1, (2000), 155-176.##18. Kh. Pourbarat, M. Abbasi, On the Vector variational-like inequalities with relaxed η − α pseudomonotone mappings, Iranian Journal of Mathematical Sciences and Informatics,1, (2009), 37-42.##19. R. T. Rockafellar, R. J. B. Wets, Variational Analysis, Grundlehren der Mathematischen Wissenschaften, 317, Springer-Verlag, Berlin 1998.##20. P. H. Sach, D. S. Kim, L. A. Tuan, G. M. Lee, Duality results for generalized vector variational inequalities with set-valued maps, Journal of Optimization Theory and Applications, 136, (2006), 105-123.##21. E. U. Tarafdar, M.S.R. Chowdhury, Topological methods for Set-Valued nonlinear Analysis, World Scientific Publishing Co. Pte. Ltd, 2008.##22. X. Q. Yang, Vector variational inequality and its duality, Nonlinear Analysis, 21, (1993), 869-877.## ##]
Szeged Dimension and $PI_v$ Dimension of Composite Graphs
2
2
Let G be a simple connected graph. In this paper, Szeged dimension and PI_v dimension of graph G are introduced. It is proved that if G is a graph of Szeged dimension 1 then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Szeged and PI_v indices for these composite graphs is obtained.
45
57
Y.
Alizadeh
Y.
Alizadeh
Hakim Sabzevary University
Iran
y.alizadeh@hsu.ac.ir
Szeged dimension
PI_v dimension
Composite graphs
Strongly regular graph.
[1. Y. Alizadeh, A. Iranmanesh, T. Doslic, Additively weighted Harary index of some composite graphs, Discrete Math., 313, (2013), 2634.##2. Y. Alizadeh, A. Iranmanesh, S. Klavzar, Interpolation method and topological indices: the case of fullerenes C12k+4, Match Commun. Math. Comput. Chem., 68, (2012), 303-310.##3. Y. Alizadeh, S. Klavzar, Interpolation method and topological indices: 2-parametric families of graphs, Match Commun. Math. Comput.Chem., 69, (2013), 523-534.##4. M. An, L. Xiong, Multiplicatively Weighted Harary index of some Composite graphs, Filomat, 29, (2015), 795-805.##5. M.R. Darafsheh, Computation of topological indices of some graphs, Acta Appl.Math., 110, (2010), 1225-1235.##6. T. Doˇsli´c, A. Graovac, F. Cataldo, O. Ori, Notes on some distancebased invariants for 2-dimensional square and comb lattices, Iran. J. Math. Sci. Inf., 5, (2010), 61-68.##7. M. Ghorbani, M. A Hosseinzadeh, New version of Zagreb indices. Filomat., 26(1), (2012), 93-100.##8. I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes New York., 27, (1994), 9-15.##9. I. Gutman, P. V. Khadikar, P. V. Ra jput, S. Kamarkar, The Szeged index of polyacenes, J. Serb. Chem. Soc., 60, (1995), 759-764.##10. H. Hua, A. R. Ashrafi, L. Zhang, More on Zagreb coindices of graphs, Filomat, 26, (2012), 1215-1225.##11. A. Iranmanesh, Y. Alizadeh, Computing Wiener Index of HAC5C7[p,q] Nanotubes by GAP Program, Iran. J. Math. Sci. Inf., (1), (2008), 1-12.##12. P. V. Khadikar, P. P. Kale, N. V. Deshpande, S. Karmarkar, V. K. Agrawal, Novel PI indices of hexagonal chains, J. Math. Chem., 29, (2001), 143-150.##13. P. V. Khadikar, S. Karmarkar, V. K. Agrawal, A novel PI index and its applications to QSRP/QSAR studies, J. Chem. Inf. Comput. Sci., 41, (2001), 934-949.##14. M. H. Khalifeh, H. YouseAzari, A. R. Ashrafi, A matrix method for computing Szeged and vertex PI indices of join and composition of graphs, Lin. Algebra Appl., 429, (2008), 2702-2709.##15. M. H. Khalifeh, H. YouseAzari, A. R. Ashrafi, Vertex and edge PI indices of Cartesian product graphs, Disc. Appl. Math., 156, (2008), 1780-1789.##16. S. Klavzar, I. Gutman, The Szeged and the Wiener Index of Graphs Appl. Math. Lett., 9, (1996) 45-49.##17. S. Klavzar, A. Rajapakse, I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett., 9, (1996), 45-49.##18. A. Mahmiani, O. Khormali, A. Iranmanesh, The explicit relations among the edge versions of detour index, Iran. J. Math. Sci. Inf., 3 (2), (2008), 112.##19. T. Mansour, M. Schork, The PI index of bridge and chain graphs, MATCH Commun.Math. Comput. Chem. 61 (2009), 723-734.##20. T. Mansour, M. Schork, The vertex PI index and Szeged index of bridge graphs, Discr. Appl. Math., 157, (2009), 1600-1606.##21. H. Wiener, Structural determination of the paran boiling points, J. Amer. Chem. Soc., 69, (1947), 17-20.##22. L. Xu, S. Chen, The PI Index of polyomino chains, Appl. Math. Lett., 21, (2008), 1101-1104.##23. H. Yousefi Azari, B. Manoochehrian, A. R. Ashrafi, Szeged index of some nanotubes, Curr. Appl. Phys., 8, (2008), 713715.## ##]
L_1-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures
2
2
Chen's biharmonic conjecture is well-known and stays open: The only
biharmonic submanifolds of Euclidean spaces are the minimal ones. In
this paper, we consider an advanced version of the conjecture,
replacing Delta by its extension, L_1-operator
(L_1-conjecture). The L_1-conjecture states that any
L_1-biharmonic Euclidean hypersurface is 1-minimal. We prove that
the L_1-conjecture is true for L_1-biharmonic hypersurfaces with
three distinct principal curvatures and constant mean curvature of a
Euclidean space of arbitrary dimension.
59
70
A.
Mohammadpouri
A.
Mohammadpouri
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Iran
pouri@tabrizu.ac.ir
F.
Pashaie
F.
Pashaie
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh.
Iran
S.
Tajbakhsh
S.
Tajbakhsh
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Iran
Linearized operators L_r
L_1-biharmonic hypersurfaces
1-minimal
[1. G.B. Airy, On the Strains in the Interior of Beams, Philosophical Transactions of the Royal Society, 153, (1863), 49-79.##2. K. Akutagawa, S. Maeta, Biharmonic Properly Immersed Submanifolds in Euclidean Spaces, Geometriae Dedicata, 164(1), (2013), 351-355.##3. L. J. Alias, N. Gurbuz, An Extension of Takahashi Theorem for the Linearized Operators of the Higher Order Mean Curvatures, Geometriae Dedicata, 121(1), (2006), 113-127.##4. M. Aminian, S. M. B. kashani, Lk-Biharmonic Hypersurfaces in Euclidean Space, Taiwanese Journal of Mathematics, 19(3), (2015), 659-976.##5. B. Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics, 2. World Scientific Publishing Co, Singapore, 2014.##6. B. Y. Chen, M. I. Munteanu, Biharmonic Ideal hypersurfaces in Euclidean Spaces, Differential Geometry and its Applications, 31, (2013), 1-16.##7. I. Dimitric, Submanifolds of Em with Harmonic Mean Curvature Vector, Bulletin of the Institute of Mathematics Academia Sinica, 20(1), (1992), 53-65.##8. J. Eells, J.H. Sampson, Harmonic Mappings of Riemannian Manifolds, American Journal of Mathematics, 86(1), (1964), 109-160.##9. J. Eells, J. C. Wood, Restrictions on Harmonic Maps of Surfaces, Topology 15(3), (1976), 263-266.##10. Y. Fu, Biharmonic Hypersurfaces with Three Distinct Principal Curvatures in Euclidean 5-Space, Journal of Geometry and Physics, 75, (2014), 113-119.##11. R. Gupta, On Biharmonic Hypersurfaces in Euclidean Space of Arbitary Dimension, Glasgow Mathematical Journal, 57, (2015), 633-642.##12. T. Hasanis, T. Vlachos, Hypersurfaces in E4 with Harmonic Mean Curvature Vector Field, Mathematische Nachrichten, 172(1), (1995), 145-169.##13. W. Hussain, The Effect of Pure Shear on the Reflection of Plane Waves at the Boundary of an Elastic Half-Space, Iranian Journal of Mathematical Sciences and Informatics, 2(2), (2007), 1-16.##14. J. A. Jerline , L. B. Michaelraj, On Harmonic Index and Diameter of Unicyclic Graphs,Iranian Journal of Mathematical Sciences and Informatics, 11(1), (2016), 115-122.##15. S. M. B. Kashani, On Some L1-Finite Type (Hyper)surfaces in Rn+1, Bulletin of the Korean Mathematical Society, 46(1), (2009), 35-43.##16. J. C. Maxwell, On Reciprocal Diagrams in Space, and Their Relation to Airys Function of Stress, Proc. London. Math. Soc. 102(2), 1868.##17. R. C. Reilly, Variational Properties of Functions of the Mean Curvatures for Hypersurfaces in Space Forms, Journal of Differential Geometry, 8(3), (1973), 465-477.##18. B. Segre, Famiglie di Ipersuperficie Isoparametrische Negli Spazi Euclidei ad un Qualunque Numero di Dimensioni, Atti della Accademia dItalia, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali, 27, (1938), 203-207.## ##]
On Generalizations of Hadamard Inequalities for Fractional Integrals
2
2
Fejer Hadamard inequality is generalization of Hadamard inequality. In this paper we prove certain Fejer Hadamard inequalities for k-fractional integrals.
We deduce Fejer Hadamard-type inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for k-fractional as well as fractional integrals are given.
71
81
Gh.
Farid
Gh.
Farid
Department of Mathematics COMSATS University Islamabad Attock Campus, Pakistan.
Pakistan
A.
Ur Rehman
A.
Ur Rehman
Department of Mathematics COMSATS University Islamabad Attock Campus, Pakistan.
Pakistan
M.
Zahra
M.
Zahra
Department of Mathematics COMSATS University Islamabad Attock Campus, Pakistan.
Pakistan
Convex functions
Hermite-Hadamard inequalities
Fejer Hadamard inequality
Riemann-Liouville fractional integrals
[1. Y.-M. Chu, M. Adil Khan, T. Khan, T. Ali, Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9(6), (2016), 4305-4316.##2. Y.-M. Chu, G.-D. Wang, X.-H. Zhang, Schur convexity and Hadamard’s inequality, Math. Inequal. Appl., 13(4), (2010), 725-731.##3. M. Dalir, M. Bashour, Applications of fractional calculus, Appl. Math. Sci., 4(21), (2010), 1021–1032.##4. S. A. David, J. L. Linares, E. M. J. A. Pallone, Fractional order calculus: Historical apologia, basic concepts and some applications, Rev. Bras. Ensino Fıs. 33(4), (2011), Article ID 4302, 1–7.##5. S. S. Dragomir, New Jensen and Ostrowski type inequalities for general Lebesgue integral with applications, Iran. J. Math. Sci. Inform, 11(2), (2016), 1–22.##6. G. Farid, Some new Ostrowski type inequalities via fractional integrals, Int. J. Anal. App., 14(1), (2017), 64-68.##7. G. Farid, A. U. Rehman, M. Zahra, On Hadamard inequalities for k-Fractional integrals, Nonlinear Funct. Anal. Appl., 21(3), (2016), 463–478.##8. I. Iscan, Hermite Hadamard Fejer type inequalities for convex functions via fractional integrals, Stud. Univ. Babe¸s-Bolyai Math., 60(3), (2015), 355–366.##9. S. Mubeen, G. M. Habibullah, k-Fractional integrals and applications, Int. J. Contemp. Math. Sci., 7, (2012), 89–94.##10. J. Pecaric, F. Proechan, Y. L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991.##11. M. Z. Sarikaya, A. Saglamb, H. Yildirim, On generalization of Cebysev type inequalities, Iran. J. Math. Sci. Inform., 5(1), (2010), 41–48.##12. M. Z. Sarikaya, E. Set, H. Yaldiz, N. Basak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, J. Math. Comput. Model., 57, (2013), 2403–2407.##13. L. Fejer, Uberdie fourierreihen II, Math. Naturwise. Anz Ungar. Akad., Wiss, 24, (1906), 369–390. (In Hungarian)##14. J. Wang, C. Zhu, Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means, J. Inequal. Appl., 2013, (2013), Article ID 325, 15pp.##15. X-M. Zhang, Y.-M. Chu, X.-H. Zhang, The Hermite-Hadamard type inequality of GAconvex functions and its applications, J. Inequal. Appl., 2010 (2010), Article ID 507560, 11 pages.## ##]
Vector Space semi-Cayley Graphs
2
2
The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever $v_1-v_2in S$ or $-S$, where $S$ is a basis of $mathcal{V}$. This fact causes a new connection between vector spaces and graphs. The vector space Cayley graph is made of copies of the cycles of length $t$, where $t$ is the cardinal number of the field that $mathcal{V}$ is constructed over it. The vector space Cayley graph is generalized to the graph $Gamma(mathcal{V},S)$. It is a graph with vertex set whole vectors of $mathcal{V}$ and two vertices $v$ and $w$ are adjacent whenever $c_{1}upsilon+ c_{2}omega = sum^{n}_{i=1} alpha_{i}$, where $S={alpha_1,cdots,alpha_n}$ is an ordered basis for $mathcal{V}$ and $c_1,c_2$ belong to the field that the vector space $mathcal{V}$ is made of over. It is deduced that if $ S'$ is another basis for $mathcal{V}$ which is constructed by special invertible matrix $P$, then $Gamma(mathcal{V},S)cong Gamma(mathcal{V},S')$.
83
91
B.
Tolue
B.
Tolue
Department of Mathematics,Hakim Sabzevari University
Iran
b.tolue@gmail.com
Cayley graph
Vector space
Basis.
[A. Abbasi, H. Roshan-Shekalgourabi, D. Hassanzadeh-Lelekaami, Associated graphs of modules over commutative rings, Iranian J. Math. Sci. and Inf., 10 (1), (2015), 45-58.##J. A. Bondy, J. S. R. Murty, Graph theory with applications, Elsevier, 1977.##T. Chalapathi, L. Madhavi, S. Venkataramana, Enumeration of triangles in a divisor Cayley graph, Momona Ethiopian Journal of Science (MEJS), 5(1), (2013), 163-173.##C. Godsil, Algebric graph theory, Springer-Verlag, 2001.##R. Gould, Graphs and vector spaces, J. Math. and Phys., 37, (1958), 193-214.## J. D. Halpern, Bases for vector spaces and the axiom of choice, Proc. Amer. Math. Soc., 17, (1966), 670 - 673.##K. Hoffman, Linear algebra, Prentice-Hall, Inc., 1971.##T. W. Hungerford, Algebra, Springer-Verlag, 1980.##W. Klotz, T. Sander, Some properties of unitary Cayley graphs, Electron. J. Combin.14(3), (2007), 1-12.##A. Medrano, P. Myers, H.M. Stark, A. Terras, Finite analogues of Euclidean space, J. Comput. Appl. Math. 68, (1996), 221-238.##S. Sesi-iu, M. B. Reed, Linear Graphs and Electrical Networks, Addison-Wesley, Reading, Mass., 1961.##A. Tehranian, H. R. Maimani, A study of the total graph, Iranian J. Math. Sci. and Inf., 6 (2), (2011), 75-80.## ##]
Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds
2
2
If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of graph(f)
is as big as possible and the lower box dimension of graph(f) is as small as possible.
93
99
R.
Mirzaie
R.
Mirzaie
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University
Iran
r.mirzaei@sci.ikiu.ac.ir
Manifold
Fractal
Box dimension.
[ S. Banach, Uberdie Baire’sche kategorie gewisser funktionenmengen, Studia Math, 3, (1931), 147-179.## A. S. Besicovitch, H. D. Ursell, On dimensional numbers of some curves, J. London Math.Soc., 12, (1937), 18-25.##J. Hyde, V. Laschos, L. Olsen, I. Petrykiewicz, A. Shaw, On the box dimensions of graphs of typical continuous functions, J. Math. Anal. Appl., 391, (2012), 567-581.##K. Falconer, Fractal Geometry: Mathematical foundations, Wiley, New york, 1990.##P. Gruber, Dimension and structure of typical compact sets, Continua and curvs, Mh. Math., 108, (1989), 149-164.##R. D. Mauldin, S. C. Williams, On the Hausdorff dimension of some graphs, Trans. Am. Math. Soc., 298, (1986), 793-803.##R. Mirzaie, On images of continous functions from a compact manifold in to Euclidean space, Bulletin Of The Iranian Mathematical Society, 37, (2011), 93-100.##J. R. Munkres, Topology a first course, Appleton Century Grotfs, 2000.##A. Ostaszewski, Families of compact sets and their universals, Mathematica, 21, (1974), 116-127.##W. Rudin, Principles of mathematical analysis, MGH, 1976.##J. A. Wieacker, The convex hull of a typical compact set, Math. Ann., 282, (1998), 637-644.## ##]
On I-statistical Convergence
2
2
In the present paper, we investigate the notion of I -statistical convergence
and introduce I -st limit points and I -st cluster points of real number sequence and also
studied some of its basic properties.
101
109
Sh.
Debnath
Sh.
Debnath
Tripura University
India
shyamalnitamath@gmail.com
D.
Rakshit
D.
Rakshit
Tripura University
India
debjanirakshit88@gmail.com
I -limit point
I -cluster point
I -statistically convergent
[ R. C. Buck, The measure theoretic approach to density, Amer. J. Math., 68, (1946), 560-580.## R. C. Buck, Generalized asymptotic density, Amer. J. Math., 75, (1953), 335-346.##S. Debnath, J. Debnath, On I -statistically convergent sequence spaces defined by sequences of Orlicz functions using matrix transformation, Proyecciones J. Math., 33(3), (2014), 277-285.##K. Dems, On I -Cauchy sequences, Real Anal. Exchange, 30(1), (2004/2005), 123-128.##M. Et, A. Alotaibi, S. A. Mohiuddine, On (4m, I)-statistical convergence of order α,The Scientific world journal, vol 2014.##H. Fast, Sur la convergence statistique, Colloq. Math., 2, (1951), 241-244.##J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc., 4, (1993), 1187-1192.##J. A. Fridy, On statistical convergence, Analysis, 5, (1985), 301-313.##M. Gurdal, H. Sari, Extremal A-statistical limit points via ideals, J. Egyptian Math. Soc., 22(1), (2014), 55-58.##M. Gurdal, M. O. Ozgur, A generalized statistical convergence via moduli, Electronic J. Math. Anal. & Appl., 3(2), (2015), 173-178.##P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I -convergence and extremal I -limit points, Math. Slov., 4, (2005), 443-464.##P. Kostyrko, T. Salat, W. Wilczynski, I -convergence, Real Anal. Exchange, 26(2), (2000/2001), 669-686.##M. Mamedov, S. Pehlivan, Statistical cluster points and turnpike theorem in non convex problems, J. Math. Anal. Appl., 256, (2001), 686-693.##D. S. Mitrinovic, J. Sandor, B. Crstici, Handbook of Number Theory, Kluwer Acad. Publ.Dordrecht-Boston-London, 1996.##M. Mursaleen, S. Debnath, D. Rakshit, I-statistical limit superior and I-statistical limit inferior, Filomat, 31(7), (2017), 2103-2108.##E. Savas, P. Das, A generalized statistical convergence via ideals, App. Math. Lett., 24,(2011), 826-830.##E. Savas, P. Das, On I -statistically pre-Cauchy sequences, Taiwanese J. Math., 18(1),(2014), 115-126.##H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math.,2, (1951), 73-74.##T. Salat, On statistically convergent sequences of real numbers, Math. Slov., 30, (1980),139-150.##T. Salat, B. Tripathy, M. Ziman, On some properties of I -convergence, Tatra. Mt. Math.Publ., 28, (2004), 279-286.##B. C. Tripathy, On statistically convergent and statistically bounded sequences, Bull. Malaysian. Math. Soc., 20, (1997), 31-33.##U. Yamanci, M. Gurdal, I -statistical convergence in 2-normed space, Arab J. Math.Sci., 20(1), (2014), 41-47.##U. Yamanci, M. Gurdal, I -statistically pre-Cauchy double sequences, Global J. Math.Anal., 2(4), (2014), 297-303## ##]
A Numerical Scheme for Solving Nonlinear Fractional Volterra Integro-Differential Equations
2
2
In this paper, a Bernoulli pseudo-spectral method for solving
nonlinear fractional Volterra integro-differential equations is considered.
First existence of a unique solution for the problem under study is proved.
Then the Caputo fractional derivative and Riemman-Liouville fractional
integral properties are employed to derive the new approximate formula
for unknown function of the problem. The suggested technique transforms
these types of equations to the solution of systems of algebraic equations.
In the next step, the error analysis of the proposed method is investigated.
Finally, the technique is applied to some problems to show its validity and
applicability.
111
132
P.
Rahimkhani
P.
Rahimkhani
Alzahra University
Iran
Y.
Ordokhani
Y.
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University
Iran
E.
Babolian
E.
Babolian
Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University
Iran
Fractional Volterra integro-differential equations
Bernoulli pseudo- spectral method
Caputo derivative.
[A. Azizia, J. Saeidianb, S. Abdi, Applying Legendre Wavelet Method with Regularization for a Class of Singular Boundary Value Problems, Iranian Journal of Mathematical Sciences and Informatics, 11(2), (2016), 57−69.##R. L. Bagley, P. J. Torvik, Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures, AIAA. J., 23(6), (1985), 918−925.##R. T. Baillie, Long Memory Processes and Fractional Integration in Econometrics, J. Econometrics, 73(1), (1996), 5−59.##R. P. Boas, R. C. Buck, Polynomial Expansions of Analytic Functions, New York, Springer-Verlag, 1964.##T. S. Chow, Fractional Dynamics of Interfaces Between Soft-Nanoparticles and Rough Substrates, Phys. Lett. A., 342(1−2), (2005), 148−155.##E. H. Doha, A. H. Bhrawy, S. S. Ezz-Eldien, Efficient Chebyshev Spectral Methods for Solving Multi-Term Fractional Orders Differential Equations, Appl. Math. Model., 35(12), (2011), 5662−5672.##B. Doyon, J. Lepowsky J, A. Milas, Twisted Vertex Operators and Bernoulli Polynomials, Commun. Contemp. Math., 8(2), (2006), 247−307.##D. B. Fairlie, A. P. Veselov, Faulhaber and Bernoulli Polynomials and Solitons, Physica D: Nonlinear Phenomena, 152−153, (2001), 47−50.##M. P. Grosset, A. P. Veselov, Elliptic Faulhaber Polynomials and Lame Densities of States, Int. Math. Res. Not., 2016(5), (2006), 1−21.##I. Hashim, O. Abdulaziz, S. Momani, Homotopy Analysis Method for Fractional IVPs,Commun. Nonl. Sci. Numer. Simul., 14(3), (2009) 674−684.##J. H. He, Nonlinear Oscillation with Fractional Derivative and its Applications, International Conference on Vibrating Engineering , (1998), 288−291.##J. H. He, Some Applications of Nonlinear Fractional Differential Equations and Their Approximations, Bull. Sci. Technol., 2, (1999), 86−90.##M. H. Heydari, M. R. Hooshmandasl, F. Mohammadi, C. Cattani, Wavelets Method for Solving Systems of Nonlinear Singular Fractional Volterra Integro-Diffrential Equations, Communications in Nonlinear Science and Numerical Simulation, 19(1), (2014), 37−48.##J. K. Hunter, B. Nachtergaele, Applied Analysis, University of california, 2000.##S. Karimi Vanani, A. Amintaei, Operational Tau Approximation for a General Class of Fractional Integro-Differential Equations, Comput. Appl. Math., 30(3), (2011), 655−674.##E. Keshavarz, Y. Ordokhani, M. Razzaghi, Bernoulli Wavelet Operational Matrix of Fractional Order Integration and its Applications in Solving the Fractional Order Differential Equations, Appl. Math. Model., 38(24), (2014), 6038−6051.##N. Koblitz, p-Adic Numbers, p-adic Analysis and Zeta-Functions, Second ed, New York, Springer-Verlag, 1984.##E. Kreyszig, Introductory Functional Analysis with Applications, New York, John Wiley and Sons Press, 1978.##S. Lang, Introduction to Modular Forms, Springer-Verlag, 1976.##R. L. Magin, Fractional Calculus in Bioengineering, Crit. Rev. Biomed. Eng., 2004.##F. Mainardi, Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics. Fractals and Fractional Calculus in Continuum Mechanics, New York, Springer Verlag, 1997.##B. Mandelbrot, Some Noises with 1/f Spectrum, a Bridge between direct Current and White Noise, IEEE Trans Inform Theory, 2, (1967), 289−98.##S. Mashayekhi, Y. Ordokhani, M. Razzaghi, Hybrid Functions Approach for Optimal Control described by Integro−Differential Equations, Appl. Math. Model., 37(5), (2013), 3355− 3368.##M. Meerschaert, C. Tadjeran, Finite Difference Approximations for Two-Sided SpaceFractional Partial Differential Equations, Appl. Numer. Math., 56(1), (2006), 80−90.##R. Metzler, J. Klafter, The Restaurant at the End of the Random Walk: Recent Developments in the Description of Anomalous Transport by Fractional Dynamics, Journal of Physics A: Mathematical and General, 37, (2004), 161−208.##K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, New York, Wiley, 1993.##S. Momani, K. Al-Khaled, Numerical Solutions for Systems of Fractional Differential Equations by the Decomposition Method, Appl. Math. Comput., 162(3), (2005), 1351−1365.##P. Rahimkhani, Y. Ordokhani, E. Babolian, A New Operational Matrix based on Bernoulli Wavelets for Solving Fractional Delay Differential Equations, Numer. Algor., 74, (2017), 223−245.##P. Rahimkhani, Y. Ordokhani, E. Babolian, Fractional-order Bernoulli Wavelets and Their Applications, Appl. Math. Model., 40, (2016), 8087−8107.##Y. A. Rossikhin, M. V. Shitikova, Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids, Appl. Mech. Rev., 50(1), (1997), 15−67.##A. Saadatmandi, M. Dehghan, A Legendre Collocation Method for Fractional IntegroDifferential Equations, Vibration and Control, 17(13), (2011), 2050−2058.##H. Saeedi, M. Mohseni Moghadam, Numerical Solution of Nonlinear Volterra IntegroDifferential Equations of Arbitrary Order by CAS Wavelets, Commun. Nonl. Sci. Numer. Simul., 16(3), (2011), 1216−1226.## ##]
Isoclinic Classification of Some Pairs $(G,G')$ of $p$-Groups
2
2
The equivalence relation isoclinism partitions the class of all pairs of groups into families. In this paper, a complete classification of the set of all pairs $(G,G')$ is established, whenever $G$ is a $p$-group of order at most $p^5$ and $p$ is a prime number greater than 3. Moreover, the classification of pairs $(H,H')$ for extra special $p$-groups $H$ is also given.
133
142
S.
Kayvanfar
S.
Kayvanfar
Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Iran
skayvanf@um.ac.ir
A.
Kaheni
A.
Kaheni
Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Iran
azamkaheni@yahoo.com
Pairs of groups
Isoclinism
Classification of $p$-groups
[F. Ayatollah Zadeh Shirazi, A. Hosseini, On (α, β)- linear connectivity, Iranian Journal of Mathematical Sciences and Informatics, 11 (1), (2016), 85-100.##G. Ellis, Capability, homology, and central series of a pair of groups, J. Algebra, 179, (1996), 31-46.##G. Ellis, The Schur multiplier of a pair of groups, Applied Categorical Structures, 6, (1998), 355-371.##P. Hall, The classification of prime-power groups, J. Reine Angew. Math., 182, (1940), 130-141.##M. Hassanzadeh, A. Pourmirzaei, S. Kayvanfar, On the nilpotency of a pair of groups, Southeast Asian Bulletin of Mathematics, 37, (2013), 67-77.##R. James, The groups of order p6, Mathematics of Computation, 34, (1980), 613-637.##M. Keshavarzi, M. A. Dehghan, M. Mashinchi, Classification based on 3-similarity, Iranian Journal of Mathematical Sciences and Informatics, 6 (1), (2011), 7-21.##M. R. R. Moghaddam, A. R. Salemkar, K. Chiti, Some properties on the Schur multiplier of a pair of groups, J. Algebra , 312, (2007), 1-8.##A. Pourmirzaei, A. Hokmabadi, S. Kayvanfar, On the capability of a pair of groups, Bull. Malays. Math. Sci. Soc. 2, (2011), 205-213.## A. R. Salemkar, F. Saeedi, T. Karimi, The structure of isoclinism classes of pair of groups, Southeast Asian Bulletin of Math., 31, (2007), 1173-1181.## ##]
Extended Jacobi and Laguerre Functions and their Applications
2
1
2
The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre
polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We
prove some important properties of these operators such as: These sets of functions are
orthogonal with respect to a positive de nite inner product de ned over the compact
intervals [-1, 1] and [0,1), respectively and also these sequences form two new orthog-
onal bases for the corresponding Hilbert spaces. Finally, the spectral and Rayleigh-Ritz
methods are carry out using these basis functions to solve some examples. Our nu-
merical results are compared with other existing results to con rm the eciency and
accuracy of our method.
143
161
M.R.
Eslahchi
M.R.
Eslahchi
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University
Iran
A.
Abedzadeh
A.
Abedzadeh
Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University
Iran
Sturm-Liouville theory
Orthogonal polynomials
Ordinary dierential equations
Non-classical Sturm-Liouville problems
Spectral method
Collocation method
Galerkin.
[M. Al-Gwaiz, Sturm-Liouville Theory and its Applications, Springer, 2007.##M. Aristidou, M. Davidson, G. Olafsson, Laguerre functions on symmetric cones and recursion relations in the real case, Journal of computational and applied mathematics, 199(1), (2007), 95–112.##W. Bao, J. Shen, A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates, Journal of Computational Physics, 227(23), (2008), 9778–9793.##S. Bochner, Uber Sturm-Liouvillesche Polynomsysteme, ¨ Mathematische Zeitschrift,29(1), (1929), 730–736.##J. P. Boyd, Rational Chebyshev series for the Thomas-Fermi function: Endpointsin gularities and spectral methods, Journal of computational and applied mathematics, 244, (2013), 90–101.##A. R. Davies, A. Karageorghis, T. N. Phillips, Spectral Galerkin methods for the primary two point boundary value problem in modelling viscoelastic flows, International Journal for Numerical Methods in Engineering, 26(3), (1988), 647–662.##M. Dehghan, E. A. Hamedi, H. Khosravian-Arab, A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials, Journal of Vibration and Control, (2014), 1077546314543727.##E. H. Doha, W. M. Abd-Elhameed, On the Coefficients of Integrated Expansions and Integrals of Chebyshev Polynomials of Third And Fourth Kinds, Bulletin of the Malaysian Mathematical Sciences Society, 2014.##G. A. Frolov, M. Y. Kitaev, A problem of numerical inversion of implicitly defined Laplace transforms, Computers & Mathematics with Applications, 36(5), (1998), 35–44. erential Equations, Springer Verlag, New York, 1992.##D. Gomez-Ullate, N. Kamran, R. Milson, An extended class of orthogonal polynomials defined by a Sturm-Liouville problem, Journal of Mathematical Analysis and Applications, 359(1), (2009), 352–367.##K. Hoffman, R. Kunze, Linear Algebra, Englewood Cliffs, New Jersey, 1971.##H. Khan, H. Xu, Series solution to the Thomas-Fermi equation, Physics Letters A, 365,(2007), 111–115.##H. Khosravian-Arab, M. Dehghan, M. R. Eslahchi, Fractional SturmLiouville boundary value problems in unbounded domains: Theory and applications, Journal of Computational Physics, 299, (2015), 526–560.##S. Liao, Beyond perturbation: introduction to the homotopy analysis method, CRC press, 2003.##C. Liu, S. Zhu, Laguerre pseudospectral approximation to the Thomas-Fermi equation, Journal of Computational and Applied Mathematics, 282 (2015) 251–261.##M. Lorente, Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom, Physics Letters A, 285(3), (2001), 119–126.##S. Odak, R. Sasaki, Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials, Journal of Mathematical Physics, 51(5), (2010), 053513.##S. Odak, R. Sasaki, Another set of infinitely many exceptional (Xl)-Laguerre polynomials, Physics Letters B, 684.2 (2010) 173–176.##K. Ozawa, A functional fitting Runge-Kutta method with variable coefficients, Japan journal of industrial and applied mathematics, 18(1), (2001), 107–130.##K. Parand, M. Dehghan, A. Pirkhedri, The Sinc-collocation method for solving the Thomas-Fermi equation, Journal of Computational and Applied Mathematics, 237(1), (2013), 244–252.##K. R. Pandey, N. Kumar, A. Bhardwaj, G. Dutta, Solution of LaneEmden type equations using Legendre operational matrix of differentiation, Applied Mathematics and Computation, 218(14), (2012), 7629–7637.##S. Pooseh, R. Almeida, D. F. Torres, Discrete direct methods in the fractional calculus of variations, Computers & Mathematics with Applications, 66(5), (2013), 668–676.##S. Pooseh, R. Almeida, D. F. Torres, A discrete time method to the first variation of fractional order variational functionals, Open Physics, 11(10), (2013), 1262–1267.##J. Shen, T. Tang, L. L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer Science & Business Media, Vol. 41, 2011.##A. Azizi, J. Saeidian, S. Abdi, Applying Legendre Wavelet Method with Regularization for a Class of Singular Boundary Value Problems, Iranian Journal of Mathematical Sciences and Informatics, 11(2), 57–69.##M. Jahanshahi, A. Ahmadkhanlu, The Wave Equation in Non-classic Cases: Non-self Adjoint with Non-local and Non-periodic Boundary Conditions, Iranian Journal of Mathematical Sciences and Informatics, 9(1), 1–12.##G. Szego, Orthogonal Polynomials, American Mathematical Soc, 1939.##Z. Q. Wang, B. Y. Guo, W. Zhang, Mixed spectral method for three-dimensional exterior problems using spherical harmonic and generalized Laguerre functions, Journal of Computational and Applied Mathematics, 217(1), (2008), 277–298.##D. Wang, A. Xiao, Fractional variational integrators for fractional Euler-Lagrange equations with holonomic constraints, Communications in Nonlinear Science and Numerical Simulation, 18(4), (2013), 905–914.##J. Wu, H. Tian, Functionally-fitted block methods for ordinary differential equations, Journal of Computational and Applied Mathematics, 271, (2014), 356–368.##S. Zhu, H. Zhu, Q. Wu,Y. Khan, An adaptive algorithm for the Thomas-Fermi equation, Numerical Algorithms, 59(3), (2012), 359–372.## ##]
On Almost n-Layered QTAG-modules
2
2
We define the notion of almost $n$-layered $QTAG$-modules and study their basic properties. One of the main result is that almost 1-layered modules are almost $(omega+1)$-projective exactly when they are almost direct sum of countably generated modules of length less than or equal to $(omega+1)$. Some other characterizations of this new class are also established.
163
171
A.
Hasan
A.
Hasan
Jazan University, KSA
Kingdom of Saudi Arabia
ayaz.maths@gmail.com
$QTAG$-modules
Almost $Sigma$-uniserial modules
Almost $(omega+n)$-projective modules
Almost 1-layered modules.
[A. Hasan, On essentially finitely indecomposable QTAG-modules, Afrika Mat., 27(1), (2016), 79-85.##A. Mehdi, A. Hasan, F. Sikander, On submodules of QT AG-modules, Int. J. Engg., Sci.Tech., 6(2), (2014), 20-30.##A. Mehdi, F. Sikander, S.A.R.K. Naji, A study of elongations of QTAG-modules, Afrika Mat., 27(1), (2016), 133-139.##A. Mehdi, M.Y. Abbasi, F. Mehdi, Nice decomposition series and rich modules, South East Asian J. Math. & Math. Sci., 4(1), (2005), 1-6.##A. Mehdi, M.Y. Abbasi, F. Mehdi, On (ω + n)-projective modules, Ganita Sandesh, 20(1), (2006), 27-32.##F. Sikander, A. Hasan, A. Mehdi, On n-layered QT AG-modules, Bull. Math. Sci., 4(2),(2014), 199-208.##H. Mehran, S. Singh, On σ-pure submodules of QTAG-modules, Arch. Math., 46, (1986),501-510.##L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, New York, 1970.##L. Fuchs, Infinite Abelian Groups, Vol. II, Academic Press, New York, 1973.##S. Singh, Abelian groups like modules, Act. Math. Hung, 50, (1987), 85-95.## ##]
ABSTRACTS IN PERSIAN Vol.13, No.2
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Please see the full text contains the Pesian abstracts for this volume.
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The Name of Authors
In This Volume
The Name of Authors
In This Volume
the affiliations of all authors
The country of all authors
fatemeh.bardestani@gmail.com
ABSTRACTS
PERSIAN
Vol. 13
No. 2
[1-All references of this volume## ##]