2014
3
2
2
60
On the construction of symmetric nonnegative matrix with prescribed Ritz values
2
2
In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.
1

61
66


A. M.
Nazaria
Department of Mathematics, Arak University, P.O. Box 3815688349, Iran
Department of Mathematics, Arak University,
Iran
anazari@araku.ac.ir


E.
Afshari
Department of Mathematics, Khomein Branch, Islamic Azad University, Khomein, Iran
Department of Mathematics, Khomein Branch,
Iran
Ritz values
Nonnegative matrix
[[1] Bertram Kostant, Nolan Wallach, GelfandZeitlin theory from the perspective of classical mechanics I, Prog. Math. 243 (2006) 319364. ##[2] Bertram Kostant, Nolan Wallach, GelfandZeitlin theory from the perspective of classical mechanics II, Prog. Math. 244 (2006) 387420. ##[3] Beresford Parlett, Gilbert Strang, Matrices with prescribed Ritz values, Linear Algebra and its Applications 428 (2008) 17251739. ##[4] A. M. Nazari, F. Sherafat, On the inverse eigenvalue problem for nonnegative matrices of order two to five, Linear Algebra Appl. 436 (2012) 17711790.##]
Existence and uniqueness of solution of Schrodinger equation in extended Colombeau algebra
2
2
In this paper, we establish the existence and uniqueness result of the linear Schrodinger equation with Marchaud fractional derivative in Colombeau generalized algebra. The purpose of introducing Marchaud fractional derivative is regularizing it in Colombeau sense.
1

67
78


M.
Alimohammady
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Department of Mathematics, University of
Iran
amohsen@umz.ac.ir


F.
Fattahi
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Department of Mathematics, University of
Iran
Colombeau algebra
Marchaud fractional differentiation
Schrodinger equation
[[1] J. F. Colombeau, New generalized functions and Multiplication of distributions, NorthHolland, Amsterdam, 1984. ##[2] J. F. Colombeau and A. Y. L. Roux, Multiplications of distributions in elasticity and hydrodynamics, J. Math. Phys., 29 (1988), 315319. ##[3] J. F. Colombeau, Elementary Introduction to New Generalized Functions, NorthHolland Math. Studies Vol. 113, NorthHolland, Amsterdam 1985. ##[4] I. M. Gel'fand and G. E. Shilov, Generalized functions, Academic press, New York, Vol. I, 1964. ##[5] D. RajterCiric, Fractional derivatives of Colombeau Generalized stochastic processes defined on R+, Appl. Anal. Discrete Math. 5 (2011), 283297. ##[6] M. Stojanovic , Extension of Colombeau algebra to derivatives of arbitrary order $D^{alpha}$, Application to ODEs and PDEs with entire and fractional derivatives, Nonlinear Analysis 5 (2009), 54585475.##]
Product of normal edgetransitive Cayley graphs
2
2
For two normal edgetransitive Cayley graphs on groups H and K which have no common direct factor and $gcd(H/H^prime,Z(K))=1=gcd(K/K^prime,Z(H))$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edgetransitive.
1

79
85


A.
Assari
Department of Basic Science, JundiShapur University of Technology, Dezful, Iran
Department of Basic Science, JundiShapur
Iran
amirassari@jsu.ac.ir
Cayley graph
Normal edgetransitive
Product of graphs
[[1] M. Alaeiyan. On normal edgetransitive Cayley graphs of some abelian groups. Southeast Asian Bull. Math. 33 (2009), no. 1, 1319. ##[2] M. R. Darafsheh, A. Assari. Normal edgetransitive Cayley graphs on nonabelian groups of order 4p, where p is a prime number. Sci. China Math. 56 (2013), no. 1, 213219. ##[3] J. N. S. Bidwell, M. J. Curran, D. J. McCaughan. Automorphisms of direct products of nite groups. Arch. Math. (Basel) 86 (2006), no. 6, 481489. ##[4] G. B. Cagaanan, S. R. J. Canoy. On the hull sets and hull number of the Cartesian product of graphs. Discrete Math. 287 (2004), no. 13, 141144. ##[5] P. Dorbec, M. Mollard, S. Klavzar, S. Spacapan. Power domination in product graphs. SIAM J. Discrete Math. 22 (2008), no. 2, 554567. ##[6] X. G. Fang, C. H. Li, M. Y. Xu. On edgetransitive Cayley graphs of valency four. European J. Combin. 25 (2004), no. 7, 11071116. ##[7] C. D. Godsil. On the full automorphism group of a graph. Combinatorica 1 (1981), no. 3, 243256. ##[8] C. Godsil, G. Royle. Algebraic graph theory. Graduate Texts in Mathematics, 207. SpringerVerlag, New York, 2001. ##[9] P. C. Houlis. Quotients of normal edgetransitive Cayley graphs. University of Western Australia, 1998. ##[10] N. Hosseinzadeh, A. Assari. Graph operations on Cayley graphs of semigroups. International Journal of Applied Mathematical Research, 3 (1) (2014) 5457. ##[11] C. H. Li, Z. P. Lu, H. Zhang. Tetravalent edgetransitive Cayley graphs with odd number of vertices. J. Combin. Theory Ser. B 96 (2006), no. 1, 164181. ##[12] D. Marusic, R. Nedela. Maps and halftransitive graphs of valency 4. European J. Combin. 19 (1998), no. 3, 345354. ##[13] C. E. Praeger. Finite normal edgetransitive Cayley graphs. Bull. Austral. Math. Soc. 60 (1999), no. 2, 207220. ##[14] C. Wang, D. Wang, M. Xu. Normal Cayley graphs of nite groups. Sci. China Ser. A 41 (1998), no. 3, 242251. ##[15] M. Y. Xu. Automorphism groups and isomorphisms of Cayley digraphs. Graph theory (Lake Bled, 1995). Discrete Math. 182 (1998), no. 13, 309319. ##[16] J. M. Xu, C. Yang. Connectivity and superconnectivity of Cartesian product graphs. Ars Combin. 95 (2010), 235245. ##[17] J. M. Xu, C. Yang. Connectivity of Cartesian product graphs. Discrete Math. 306 (2006), no. 1, 159165.##]
Compact composition operators on real Banach spaces of complexvalued bounded Lipschitz functions
2
2
We characterize compact composition operators on real Banach spaces of complexvalued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
1

87
105


D.
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, Arak, 3815688349, Iran
Department of Mathematics, Faculty of Science,
Iran
dalimohammadi@araku.ac.ir


S.
Sefidgar
Department of Mathematics, Faculty of Science, Arak University, Arak, 3815688349, Iran
Department of Mathematics, Faculty of Science,
Iran
Compact operator
composition operator
Lipschitz function
Lipschitz involution
spectrum of an operator
[[1] D. Alimohammadi and A. Ebadian, Hedberg;s theorem in real Lipschitz algebras, Indian J. Pure Appl. Math. 32 (10)(2001), 14791493. ##[2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer Verlag, 1973. ##[3] A. Ebadian and S. Ostadbashi, Compact homomorphisms of real Lipschitz algebras, Southeast Asian Bull. Math. 30(4) (2006), 653661. ##[4] A. JimenezVargas and M. VillegasVallecillos, Compact composition operators on noncompact Lipschitz spaces, J. Math. Anal. Appl. 398(2013), 221229. ##[5] H. Kamowitz and S. Scheinberg, Some properties of endomorphisms of Lipschitz algebras, Studia Math. 96 (1990), 6167. ##[6] S. H. Kulkarni and B. V. Limaye, Gleason parts of real function algebras, Canad. J. Math. (33) (1) (1981), 181200. ##[7] S. H. Kulkarni and B. V. Limaye, Real Function Algebras, Marcel Dekker, New Yorke, 1992. ##[8] D. R. Sherbert, Banach algebras of Lipschitz functions, Pacic J. Math. 13(1963), 13871399. ##[9] D. R. Sherbert, The structure of ideals and point derivations of Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc. 111(1964). 240272. ##[10] N. Weaver, Lipschitz Algebras, World Scientic, New Jersey, 1999.##]
Hereditary properties of amenability modulo an ideal of Banach algebras
2
2
In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neounital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered by the neounital modulo I Banach algebra over A.
1

107
114


H.
Rahimi
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
PO. Code 13185768, Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran
rahimi@iauctb.ac.ir


E.
Tahmasebi
Department of Mathematics, Islamic Azad University, Central Tehran Branch,
PO. Code 13185768, Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran
Amenability modulo an ideal
Neounital modulo an ideal
Approximate identity modulo an ideal
[[1] M. Amini and H. Rahimi, Amenability of semigroups and their algebras modulo a group congruence, Acta Mathematica Hungarica, Vol 144, Issue 2 , (2014), pp 407415. ##[2] G. K. Dales, A.T.M. Lau and D. Strauss, Banach Algebras on Semigroups and their Compactications, Memoirs American Mathematical Society, American Mathematical Society, Providence, (2010), Vol. 205, No. 966. ##[3] M. Day, Amenable groups, Bull. Amer. Math, Soc, (1950), 56: 4657. ##[4] M. Day, Amenable semigroups, Illinois J. Math, (1957), 1: 509544. ##[5] J. Duncan and A. L. T Paterson, Amenability for discrete convolution semigroup algebras, Math. Scandinavica, (1990), 66: 141146. ##[6] J. Duncan and I. Namioka, Amenability of inverse semigroups and their semigroup algebras, Proc. Royal Soc. Edinburgh Sect, (1978), A 80: 309321. ##[7] G. H. Eslamzadeh, Ideals and representations of certain semigroup algebras, Semigroup Forum 69 (2004), 5162. ##[8] N. Groenbaek, Amenability of discrete convolution algebras, the commutative case, Pacic J. Math, (1990), 143: 243249. ##[9] J. M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford (1995). ##[10] B. E. Johnson, Cohomology in Banach Algebras, American Mathematical Society, Providence, RI, 1972. ##[11] H. Rahimi and E. Tahmasebi, Amenability and Contractibility modulo an ideal of Banach algebras, Abstract and Applied Analysis, (2014), 514761. ##[12] H. Rahimi and E. Tahmasebi, A note on amenability modulo an ideal of unitial Banach algebras, J. Mathematical Extension, In press. ##[13] Yu. V. Selivanov, Banach algebras of small global dimension zero, Uspekhi Mat. Nauk, (1976), 31: 2 (188), 227228. ##[14] J. Von Neumann, Zur allgemeinem Theorie des Mabes, J. Funct. Anal, (1929), 13: 73116.##]
A generalized cost Malmquist index to compare the productivities of units with negative data in DEA
2
2
In some data envelopment analysis (DEA) applications, some inputs of DMUs have negative values with positive cost. This paper generalizes the global cost Malmquist productivity index to compare the productivity of dierent DMUs with negative inputs in any two periods of times under variable returns to scale (VRS) technology, and then the generalized index is decomposed to several components. The obtained components are computed using the nonparametric linear programming models, known as DEA. To illustrate the generalized index and its components, a numerical example at three successive periods of time is given.
1

115
120


G.
Tohidi
Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran


S.
Razavyan
Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran


S.
Tohidnia
Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran
Malmquist Index
Circularity
Data Envelopment Analysis (DEA)
Cost efficiency
Returns to scale (VRS)
Negative data
[[1] D. W. Caves, L. R. Christensen and W. E. Diewert, The economic theory of index numbers and the measurement of input, output and productivity, Econometrica, 50, (1982) 13931414. ##[2] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research, 2, (1978) 429444. ##[3] A. Emrouznejad, A. L. Anouze and E. Thanassoulis, A semioriented radial measure for measuring the efficiency of decision making units with negative data, using DEA, European Journal of Operational Research, 200, (2010) 297304. ##[4] R. Fare, S. Grosskopf, M. Norris and Z. Zhang, Productivity growth, technical progress and efficiency changes in industrialized countries, American Economic Review, 84, (1994) 6683. ##[5] N. Maniadakis and E. Thanassoulis, A cost Malmquist productivity index, European Journal of Operational Research, 154, (2004) 396409. ##[6] M. C. A. S. Portela, E. Thanassoulis and G. P. M. Simpson, Negative data in DEA: A directional distance approach applied to bank branches, Journal of the Operational Research Society, 55, (2004) 11111121. ##[7] M. C. A. S. Portela and E. Thanassoulis, A circular Malmquisttype index for measuring productivity, Aston Working Paper RP0802., Aston University Birmingham B47ET, UK, (2008). ##[8] M. C. A. S. Portela and E. Thanassoulis, Malmquisttype indices in the presence of negative data: An application to bank branches, Journal of banking & Finance, 34, (2010) 14721483. ##[9] J. A. Sharp, W. Meng and W. Liu, A modied slacksbased measure model for data envelopment analysis with natural negative outputs and inputs, Journal of the Operational Research Society, 58, (2007) 16721677. ##[10] G. Tohidi, S. Razavyan and S. Tohidnia, A global cost Malmquist productivity index using data envelopment analysis, Journal of the Operational Research Society, 63 (2012) 7278. ##[11] G. Tohidi, S. Razavyan and S. Tohidnia, A prot Malmquist productivity index, Journal of Industrial En ##gineering International, 6, No. 10, (2010) 2330. ##[12] G. Tohidi, S. Razavyan, A circular global prot Malmquist productivity index in data Envelopment analysis, ##Applied Mathematical Modelling, 37, (2013) 216227. ##[13] G. Tohidi, S. Razavyan and S. Tohidnia, Prot Malmquist index and its global form in the presence of the ##negative data in DEA, Journal of Applied Mathematics, doi.org/10.1155/2014/276092.##]