ORIGINAL_ARTICLE
The analysis of a disease-free equilibrium of Hepatitis B model
In this paper we study the dynamics of Hepatitis B virus (HBV) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring and also through contact with infective individuals. Stability of the disease-free steady state is investigated. The basic reproductive rate, $R_0$, is derived. The results show that the dynamics of the model is completely determined by the basic reproductive number $R_0$. If $R_0<1$, the disease-free equilibrium is globally stable and the disease always dies out and if $R_0>1$, the disease-free equilibrium is unstable and the disease is uniformly persistent.
http://scma.maragheh.ac.ir/article_19749_d6277da45d18a2b9e2617791b8dbcc92.pdf
2016-06-01T11:23:20
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1
11
Hepatitis B virus (HBV)
Basic reproduction number ($R_0$)
Compound matrices
Disease-Free equilibrium state
Global stability
Reza
Akbari
r9reza@yahoo.com
true
1
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
LEAD_AUTHOR
Ali
Vahidian Kamyad
avkamyad@yahoo.com
true
2
Department of Mathematics Sciences, University of Ferdowsi, Mashhad, Iran.
Department of Mathematics Sciences, University of Ferdowsi, Mashhad, Iran.
Department of Mathematics Sciences, University of Ferdowsi, Mashhad, Iran.
AUTHOR
Ali akbar
Heydari
heydariaa@mums.ac.ir
true
3
Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
AUTHOR
Aghileh
Heydari
a_heidari@pnu.ac.ir
true
4
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
Department of Mathematical Sciences, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.
AUTHOR
[1] R.M. Anderson and R.M. May, Infectious Disease of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
1
[2] S. Bhattacharyyaa and S. Ghosh, Optimal control of vertically transmitted disease, Computational and Mathematical Methods in Medicine. 11(4) (2010) 369-387.
2
[3] S. Bowong, J.J. Tewa, and J.C. Kamgang, Stability analysis of the transmission dynamics of tuberculosis models, World Journal of Modelling and Simulation. 7(2) (2011) 83-100.
3
[4] P.V.D. Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math Biosci. 180 (2002) 29-48.
4
[5] Y. Enatsu, Y. Nakata, and Y. Muroya, Global stability of SIRS epidemic models with a class of nonlinear incidence rates and distributed delays, Published in Acta Mathematica Scientia, 32 (2012) 851-865.
5
[6] H. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000) 599-653.
6
[7] J.C. Kamgang and G. Sallet, Computation of threshold conditions for epidemio-logical models and global stability of the disease-free equilibrium (DFE), Mathematical Biosciences, 213 (2008) 1-12.
7
[8] A.V. Kamyad, R. Akbari, A.A. Heydari, and A. Heydari, Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus, Computational and Mathematical Methods in Medicine. Volume 2014, Article ID 475451, 15 pages.
8
[9] T.K. Kar and S. Jana, A theoretical study on mathematical modelling of an infectious disease with application of optimal control, Bio Systems, 111(1) (2013) 3750.
9
[10] T.K. Kar and A. Batabyal, Stability analysis and optimal control of an SIR epidemic model with vaccination, Biosystems. 104 (2011) 127-135.
10
[11] X. Liu and L. Yang, Stability analysis of an SEIQV epidemic model with saturated incidence rate, Nonlinear Analysis: Real World Applications, 13 (2012) 2671-2679.
11
[12] J. Mann and M. Roberts, Modelling the epidemiology of hepatitis B in New Zealand, Journal of Theoretical Biology. 269 (2011) 266-272.
12
[13] G.F. Medley and N.A. Lindop, Hepatitis-B virus endemicity: heterogeneity, catastrophic dynamics and control, Nature Medicine, 7(5) (2001) 619-624.
13
[14] A.A. Momoh, M.O. Ibrahim, and B.A. Madu, Stability Analysis of an Infectious Disease Free Equilibrium of Hepatitis B Model, Research Journal of Applied Sciences, Engineering and Technology, 3(9) (2011) 905-909.
14
[15] J.S. Muldowney, Compound matrices and ordinary differential equations, Rocky Mountain J. Math. 20 (1990) 857-872.
15
[16] J. Pang, J.A. Cui, and X. Zhou, Dynamical behavior of a hepatitis B virus transmission model with vaccination, Journal of Theoretical Biology. 265 (2010) 572-578.
16
[17] S. Sun, Global Dynamics of a SEIR Model with a Varying Total Population Size and Vaccination, Int. Journal of Math. Analysis, 6(40) (2012) 1985-1995.
17
[18] C. Sun, Y. Lin, and S. Tang, Global stability for an special SEIR epidemic model with nonlinear incidence rates, Chaos, Solitons and Fractals, 33 (2007) 290-297.
18
[19] S. Thornley, C. Bullen, and M. Roberts, Hepatitis B in a high prevalence New Zealand population: A mathematical model applied to infection control policy, Journal of Theoretical Biology. 254 (2008) 599-603.
19
[20] P. Van Den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibrium for compartmental models of disease transmission, Mathe- matical Biosciences, 180 (2002) 29-48.
20
[21] K. Wanga, A. Fan, and A. Torres, Global properties of an improved hepatitis B virus model, Nonlinear Analysis: Real World Applications, 11 (2010) 3131-3138.
21
[22] WHO, Hepatitis B Fact Sheet No. 204, The World Health Organisation, Geneva, Switzerland, 2013, http://www.who.int/mediacentre/factsheets/fs204/en/.
22
[23] S. Zhang and Y. Zhou, The analysis and application of an HBV model, Applied Mathematical Modelling, 36 (2012) 1302-1312.
23
[24] S.J. Zhao, Z.Y. Xu, and Y. Lu, A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int.J.Epidemiol. 29 (2000) 744-752.
24
[25] L. Zou, W. Zhang, and S. Ruan, Modeling the transmission dynamics and control of hepatitis B virus in China, Journal of Theoretical Biology, 262 (2010) 330-338.
25
ORIGINAL_ARTICLE
Growth analysis of entire functions of two complex variables
In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.
http://scma.maragheh.ac.ir/article_19750_9a173f57343ef9c61aa8f0ee7cdf9b6d.pdf
2016-06-01T11:23:20
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13
24
Entire functions
Generalized relative order
Generalized relative lower order
Two complex variables
Composition
growth
Sanjib
Kumar Datta
sanjib_kr_datta@yahoo.co.in
true
1
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
LEAD_AUTHOR
Tanmay
Biswas
tanmaybiswas_math@rediffmail.com
true
2
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
AUTHOR
[1] A.K. Agarwal, On the properties of entire function of two complex variables, Canadian Journal of Mathematics, 20 (1968) 51-57.
1
[2] L. Bernal, Crecimiento relativo de funciones enteras. Contribucion al estudio de lasfunciones enteras con ndice exponencial nito, Doctoral Dissertation, University of Seville, Spain, 1984.
2
[3] L. Bernal, Orden relativo de crecimiento de funciones enteras, Collect. Math., 39 (1988) 209-229.
3
[4] D. Banerjee and R. K. Dutta, Relative order of entire functions of two complex variables, International J. of Math. Sci. & Engg. Appls. (IJMSEA), 1(1) (2007) 141-154.
4
[5] A.B. Fuks, Theory of analytic functions of several complex variables, Moscow, 1963.
5
[6] S. Halvarsson, Growth properties of entire functions depending on a parameter, Annales Polonici Mathematici, 14(1) (1996) 71-96.
6
[7] O.P. Juneja, G.P. Kapoor, and S.K. Bajpai, On the (p,q)-order and lower $(p,q)$-order of an entire function, J. Reine Angew. Math., 282 (1976) 53-67.
7
[8] C.O. Kiselman, Order and type as measure of growth for convex or entire functions, Proc. Lond. Math. Soc., 66(3) (1993) 152-186.
8
[9] C.O. Kiselman, Plurisubharmonic functions and potential theory in several complex variable, a contribution to the book project, Development of Mathematics, 1950-2000, edited by Hean-Paul Pier.
9
[10] B.K. Lahiri and D. Banerjee, A note on relative order of entire functions, Bull. Cal. Math. Soc., 97(3) (2005) 201-206.
10
[11] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963) 411-414.
11
[12] E.C. Titchmarsh, The theory of functions, 2nd ed. Oxford University Press, Oxford, 1968.
12
ORIGINAL_ARTICLE
Menger probabilistic normed space is a category topological vector space
In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces in probabilistic normed spaces.
http://scma.maragheh.ac.ir/article_19784_ea968e7794474539e5edcca66c4af05b.pdf
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32
Category of probabilistic normed space
Category of topological vector space
Fuzzy continuous operator
Ildar
Sadeqi
esadeqi@sut.ac.ir
true
1
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Sahand University of Technology, Tabriz, Iran.
AUTHOR
Farnaz
Yaqub Azari
fyaqubazari@gmail.com
true
2
University of Payame noor, Tabriz, Iran.
University of Payame noor, Tabriz, Iran.
University of Payame noor, Tabriz, Iran.
LEAD_AUTHOR
[1] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, Fuzzy Math. 11 (2003) 687-705.
1
[2] G. Constantin and I. Istratfescu, Elements of probabilistic analysis, Kluwer Academic Publishers, 1989.
2
[3] P. Freyd, Abelian categories, An Introduction to the theory of functors, Happer & Row, New York, Evanston & London and John Weatherhill, INC, Tokyo, 1964.
3
[4] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994) 395-399.
4
[5] U. Hohle, A note on the hyporgraph functor, Fuzzy Sets and Systems, 131 (2002) 353-356.
5
[6] O. Kaleva and S. Seikala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984) 143-154.
6
[7] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975) 326-334.
7
[8] K. Menger, Statistical metrics. Proc. Nat. Acad. Sci, USA, 28 (1942) 53-57.
8
[9] S.E. Rodabaugh, Fuzzy addition in the L-fuzzy real line, Fuzzy Sets and Systems, 8 (1982) 39-51.
9
[10] S.E. Rodabaugh, Complete fuzzy topological hyperelds and fuzzy multiplication in the fuzzy real lines, Fuzzy Sets and Systems, 15 (1985) 285-310.
10
[11] S.E. Rodabaugh, A theory of fuzzy uniformities with applications to the fuzzy real lines, J. Math. Anal. Appl., 129 (1988) 37-70.
11
[12] W. Rudin, Functional Analysis, Tata McGraw-Hill Publishing Company, 1990.
12
[13] I. Sadeqi and F. Solaty kia, Fuzzy normed linear space and it's topological structure, Chaos, fractal, solution & Fractals, 40 (2007) 2576-2589.
13
[14] I. Sadeqi and F. Solaty kia, The category of fuzzy normed linear space, The journal of fuzzy mathematics, 3 (2010) 733-742.
14
[15] I. Sadeqi, F. Solaty kia and F. Yaqub azari, Menger probabilistic normed linear spaces and its topological structure, Fuzzy Inteligent and Systems, (On published data).
15
[16] E.S. Santos, Topology versus fuzzy topology, preprint, Youngstown State University, 1977.
16
[17] B. Schweizer and A. Sklar, Probablisitic metric spaces, North-Holand, Amesterdam, 1983.
17
ORIGINAL_ARTICLE
On certain fractional calculus operators involving generalized Mittag-Leffler function
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide extensions of the results given by Gupta and Parihar [3], Saxena and Saigo [30], Samko et al. [26]. On account of the general nature of the generalized Mittag-Leffler function and generalized Wright function, a number of known results can be easily found as special cases of our main results.
http://scma.maragheh.ac.ir/article_19751_f8cba31ae3575443d6bc568443f37036.pdf
2016-06-01T11:23:20
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33
45
Marichev-Saigo-Maeda fractional calculus operators
Generalized Mittag-Leffler function
Generalized Wright hypergeometric function
Dinesh
Kumar
dinesh_dino03@yahoo.com
true
1
Department of Mathematics \& Statistics, Jai Narain Vyas University, Jodhpur - 342005, India.
Department of Mathematics \& Statistics, Jai Narain Vyas University, Jodhpur - 342005, India.
Department of Mathematics \& Statistics, Jai Narain Vyas University, Jodhpur - 342005, India.
LEAD_AUTHOR
[1] J. Choi and D. Kumar, Certain unied fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials, Journal of Inequalities and Applications, 2014 (2014), 15 pages.
1
[2] A. Erdelyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Tables of Integral Transforms, McGraw-Hill, New York, 1, 1954.
2
[3] A. Gupta and C.L. Parihar, Fractional dierintegral operators of the generalized Mittag-Leer function, Bol. Soc. Paran. Math., 33(1) (2015), 137-144.
3
[4] H.J. Haubold, A.M. Mathai, and R.K. Saxena, Mittag-Leer functions and their applications, J. Appl. Math. (Article ID 298628) (2011), 1-51.
4
[5] A.A. Kilbas and M. Saigo, Fractional integrals and derivatives of Mittag-Leer type function, Doklady Akad. Nauk Belarusi, 39(4) (1995), 22-26.
5
[6] A.A. Kilbas, M. Saigo and R.K. Saxena, Generalized Mittag-Leer function and generalized fractional calculus operators, Integral Transform Special Function, 15 (2004), 31-49.
6
[7] A.A. Kilbas, M. Saigo and J.J. Trujillo, On the generalized Wright function, Fract. Calc. Appl. Anal., 5(4) (2002), 437460.
7
[8] Y.C. Kim, K.S. Lee and H.M. Srivastava, Some applications of fractional integral operators and Ruscheweyh derivatives, J. Math. And. Appl., 197(2) (1996), 505-517.
8
[9] V. Kiryakova, All the special functions are fractional dierintegrals of elementary functions, Journal of Physics A: Mathematical and General, 30(14) (1997), 5085-5103.
9
[10] D. Kumar and J. Daiya, Fractional calculus pertaining to generalized H-functions, Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 14(3) (2014), 25-36.
10
[11] D. Kumar and S. Kumar, Fractional Calculus of the Generalized Mittag-Leer Type Function, International Scholarly Research Notices 2014 (2014), Article ID 907432, 6 pages.
11
[12] D. Kumar and S.D. Purohit, Fractional dierintegral operators of the generalized Mittag-Leer type function, Malaya J. Mat., 2(4) (2014), 419-425.
12
[13] D. Kumar and R.K. Saxena, Generalized fractional calculus of the M-Series involving F3 hypergeometric function, Sohag J. Math., 2(1) (2015), 17-22.
13
[14] O.I. Marichev, Volterra equation of Mellin convolution type with a Horn function in the kernel, Izvestiya Akademii Nauk BSSR. Seriya Fiziko-Matematicheskikh Nauk, 1 (1974), 128-129, (Russian).
14
[15] A.M. Mathai and H.J. Haubold, Special Functions for Applied Scientists, Springer, New York, 2008.
15
[16] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Dierential Equations, John Wiley & Sons, New York, NY, USA, 1993.
16
[17] G.M. Mittag-Leer, Sur la nouvelle fonction E (x), C.R. Acad. Sci. Paris 137 (1903), 554-558.
17
[18] G.M. Mittag-Leer, Sur la representation analytique d'une branche uniforme d'une function monogene, Acta Math. 29 (1905), 101-181.
18
[19] J. Paneva-Konovska, Inequalities and asymptotic formulae for the three para-metric Mittag-Leer functions, Math. Balkanica, 26 (2012), 203-210.
19
[20] J. Paneva-Konovska, Convergence of series in three parametric Mittag-Leer functions, Math. Slovaca 62, 2012.
20
[21] T.R. Prabhakar, A singular integral equation with a generalized Mittag-Leer function in the Kernel, Yokohama Math. J. 19 (1971), 7-15.
21
[22] M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep., College General Ed. Kyushu Univ. 11 (1978), 135-143.
22
[23] M. Saigo and N. Maeda, More generalization of fractional calculus Transform Methods and Special Functions, Varna, Bulgaria, (1996), 386-400.
23
[24] T.O. Salim, Some properties relating to the generalized Mittag-Leer function, Adv. Appl. Math. Anal., 4 (2009), 21-30.
24
[25] T.O. Salim and A.W. Faraj, A generalization of Mittag-Leer function and Integral operator associated with fractional calculus, Journal of Fractional Calculus and Application, 3(5) (2012), 1-13.
25
[26] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon et alibi, 1993.
26
[27] R.K. Saxena and D. Kumar, Generalized fractional calculus of the Aleph-function involving a general class of polynomials, Acta Mathematica Scientia, 35(5) (2015), 1095-1110.
27
[28] R.K. Saxena, J. Ram and D. Kumar, Generalized fractional dierentiation of the Aleph-Function associated with the Appell function F3 , Acta Ciencia Indica, 38M(4) (2012), 781-792.
28
[29] R.K. Saxena, J. Ram and D. Kumar, On the Two-Dimensional Saigo-Maeda fractional calculus associated with Two-Dimensional Aleph Transform, Le Matematiche, 68 (2013), 267-281.
29
[30] R.K. Saxena and M. Saigo, Certain properties of the fractional calculus operators associated with generalized Mittag-Leer function, Fract. Calc. Appl. Anal., 8(2) (2005), 141-154.
30
[31] H.M. Srivastava and Z. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leer function in the kernel, Appl. Math. Comput., 211 (2009), 198-210.
31
[32] A. Wiman, Uber de fundamental satz in der theorie der funktionen E(x), Acta Math. 29 (1905), 191-201.
32
[33] E.M. Wright, The asymptotic expansion of generalized hypergeometric function, J. London Math. Soc., 10 (1935), 286-293.
33
ORIGINAL_ARTICLE
Multistep collocation method for nonlinear delay integral equations
The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the multistep collocation method when used to approximate smooth solutions of delay integral equations. Finally, numerical results are given showing a marked improvement in comparison with exact solution.
http://scma.maragheh.ac.ir/article_19832_4aa04e21bad2368df51e6e1a4c4fdbda.pdf
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47
65
Delay integral equations
Collocation method
Multistep collocation method
Convergence
Parviz
Darania
p.darania@urmia.ac.ir
true
1
Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 5756151818, Urmia-Iran.
Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 5756151818, Urmia-Iran.
Department of Mathematics, Faculty of Science, Urmia University, P.O.Box 5756151818, Urmia-Iran.
LEAD_AUTHOR
[1] D. Conte and B. Paternoster, Multistep collocation methods for Volterra integral equations, Appl. Numer. Math., 59 (2009) 1721-1736.
1
[2] V. Horvat, On collocation methods for Volterra integral equations with delay arguments, Mathematical Communications, 4 (1999) 93-109.
2
[3] H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, 2004.
3
[4] H. Brunner, High-order collocation methods for singular Volterra functional equations of neutral type, Applied Numerical Mathematics, 57 (2007) 533-548.
4
[5] H. Brunner, Iterated collocation methods for Volterra integral equations with delay arguments, Math. Comp., 62 (1994) 581-599.
5
[6] H. Brunner, Implicitly linear collocation methods for nonlinear Volterra integral equations, Appl. Numer. Math., 9 (1992) 235-247.
6
[7] I. Ali, H. Brunner, and T. Tang, Spectral methods for pantograph-type dierential and integral equations with multiple delays, Front. Math. China, 4 (2009) 49-61.
7
[8] H. Brunner, The numerical solution of weakly singular Volterra functional integro-dierential equations with variable delays, Comm. Pure Appl. Anal. 5 (2006) 261-276.
8
[9] Y. Liu, Stability analysis of θ-methods for neutral functional-dierential equations, Numer. Math., 70 (1995) 473-485.
9
[10] T. Tang, X. Xu, and J. Cheng, On the spectral methods for Volterra type integral equations and the convergence analysis, J. Comput. Math., 26 (2008) 825-837.
10
[11] V. Volterra, Lecons sur les equations integrals et les equations integro-dierentielles, Gauthier-Villars, Paris, 1913.
11
[12] J. Cerha, On some linear Volterra delay equations, Casopis Pest Mat., 101 (1976) 111-123.
12
ORIGINAL_ARTICLE
On the topological centers of module actions
In this paper, we study the Arens regularity properties of module actions. We investigate some properties of topological centers of module actions ${Z}^\ell_{B^{**}}(A^{**})$ and ${Z}^\ell_{A^{**}}(B^{**})$ with some conclusions in group algebras.
http://scma.maragheh.ac.ir/article_19748_3fb8c456b2e4d1f04f48b4146fde0d2d.pdf
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67
74
Arens regularity
Topological centers
Module actions
Kazem
Haghnejad Azar
haghnejad@uma.ac.ir
true
1
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
LEAD_AUTHOR
[1] R.E. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848.
1
[2] J. Baker, A.T. Lau and J.S. Pym Module homomorphism and topological centers associated with weakly sequentially compact Banach algebras, Journal of Functional Analysis. 158 (1998), 186-208.
2
[3] F.F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, Berlin 1973.
3
[4] H.G. Dales, Banach algebra and automatic continuity, Oxford 2000.
4
[5] H.G. Dales, F. Ghahramani and N. Grnbk, Derivation into iterated duals of Banach algebras, Studia Math. 128 1 (1998), 19-53.
5
[6] M. Eshaghi Gordji and M. Filali, Arens regularity of module actions, Studia Math. 181 3 (2007), 237-254.
6
[7] E. Hewitt and K.A. Ross, Abstract harmonic analysis, Springer, Berlin, Vol I 1963.
7
[8] A.T. Lau and V. Losert, On the second Conjugate Algebra of locally compact groups, J. London Math. Soc. 37 (2)(1988), 464-480.
8
[9] A.T. Lau and A. Ulger, Topological center of certain dual algebras, Trans. Amer. Math. Soc. 348 (1996), 1191-1212.
9
[10] S. Mohamadzadeh and H.R.E. Vishki, Arens regularity of module actions and the second adjoint of a derivation, Bulletin of the Australian Mathematical Society 77 (2008), 465-476.
10
[11] J.S. Pym, The convolution of functionals on spaces of bounded functions, Proc. London Math Soc. 15 (1965), 84-104.
11
[12] A. Ulger, Some stability properties of Arens regular bilinear operators, Proc. Amer. Math. Soc. (1991) 34, 443-454.
12
[13] A. Ulger, Arens regularity of weakly sequentialy complte Banach algebras, Proc. Amer. Math. Soc. 127 (11) (1999), 3221-3227.
13
ORIGINAL_ARTICLE
Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions
In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining a new Hilbert space and using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at some interior point and parts of two sets of eigenvalues.
http://scma.maragheh.ac.ir/article_17973_6df44ee2ee8037955d17cb29c9f1d581.pdf
2016-06-01T11:23:20
2019-08-19T11:23:20
75
89
Inverse Sturm-Liouville problem
Jump conditions
Non self-adjoint operator
Parameter dependent condition
Mohammad
Shahriari
shahriari@maragheh.ac.ir
true
1
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
LEAD_AUTHOR
[1] Z. Akdogan, M. Demirci, and O. Sh. Mukhtarov, Green function of discontinuous boundary value problem with transmission conditions, Math. Meth. Appl. Sci., 30 (2007) 1719-1738.
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[2] S. Albeverio, F. Gesztesy, R. Hegh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics, 2nd ed., AMS Chelsea Publishing, Providence, RI, 2005.
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[4] R.Kh. Amirov, On Sturm-Liouville operators with discontinuity conditions inside an interval, J. Math. Anal. Appl. 317 (2006) 163-176.
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[5] P.A. Binding, P.J. Browne, and B.A. Watson, Inverse spectral problems for left denite Sturm-Liouville equations with indenite weight, J. Math. Anal. Appl. 271 (2002) 383-408.
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[6] G. Borg, Eine umkehrung der Sturm-Liouvilleschen eigenwertaufgabe, Acta Math. 78 (1945) 1-96.
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[7] J. Eckhardt and G. Teschl, Uniqueness results for Schrodinger operators on the line with purely discrete spectra, arXiv:1110.2453.
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[8] G. Freiling and V.A. Yurko, Inverse Sturm-Liouville problems and their applications, NOVA Science Publishers, New York, 2001.
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[10] O. Hald, Discontinuous inverse eigenvalue problem, Commun. Pure. Appl. Math. 37 (1984) 539-577.
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[11] H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math., 34(4) (1978), 676-680.
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[12] H. Hochstadt, On inverse problems associated with Sturm-Liouville operators, J. Dierential Equations, 17 (1975) 220-235.
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[14] M. Kobayashi, A uniqueness proof for discontinuous inverse Sturm-Liouville problems with symmetric potentials, Inverse Problems 5 (1989) 767-781.
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[15] H. Koyunbakan, A new inverse problem for the diusion operator, Applied Mathematics Letters, 19 (2006) 995-999.
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[16] H. Koyunbakan and E.S. Panakhov, Inverse problem for a singular dierential operator, Mathematical and Computer Modeling, 47 (2008) 178-185.
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[18] B.M. Levitan, Inverse Sturm-Liouville Problems, VNU Science Press, 1987.
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[19] V.A. Marchenko, Sturm-Liouville operators and applications, American Mathematical Society, 2011.
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[20] J.R. McLaughlin, Analytical methods for recovering coecients in dierential equations from spectral data, SIAM Rev. 28 (1986) 53-72.
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[21] K. Mochizuki and I. Trooshin, Inverse problem for interior spectral data of the dirac operator, Comm. Korean Math. Soc. 16, No. 3 (2001) 437-442.
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[22] K. Mochizuki and I. Trooshin, Inverse problem for interior spectral data of the Dirac operator on a nite interval, Publ. RIMS, Kyoto Univ. 38 (2002), 387-395.
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[23] O.Sh. Mukhtarov, Mahir Kadakal, and F.S. Muhtarov, On discontinuous Sturm-Liouville problems with transmission conditions, J. Math. Kyoto Univ. (JMKYAZ), 44-4 (2004) 779-798.
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[24] Y. Pingwang, An interior inverse problem for Sturm-Liouville operator with eigenparameter dependent boundary conditions, TAMKANG J. Math., Volume 42, Number 3, 395-403, Autumn 2011.
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[25] M. Shahriari and A. Jodayree Akbarfam, Inverse Sturm-Liouville problem with discontinuity conditions, Sahand Communications in Mathematical Analysis (SCMA) Vol. 1 No. 1(2014), 29-40.
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[26] M. Shahriari and A. Jodayree Akbarfam, Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions, Caspian journal of Mathematical Sciences, preprint.
26
[27] M. Shahriari, A. Jodayree Akbarfama, and G. Teschl, Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions, J. Math. Anal. Appl., 395 (2012) 19-29.
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[28] C.T. Shieh and V.A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl. 347 (2008) 266-272.
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[29] G. Teschl, Mathematical Methods in Quantum Mechanics; With Applications to Schrodinger Operators, Graduate Studies in Mathematics 99, Amer. Math. Soc., Providence, RI, 2009.
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[30] C.F. Yang, Hochstadt-Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions, Nonlinear Analysis, 74(2011)2475-2484.
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[31] C.F. Yang, Inverse spectral problems for the Sturm-Liouville operator on a d-star graph, J. Math. Anal. Appl. 365 (2010) 742-749.
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[32] C.F. Yang and X.P. Yang, An interior inverse problem for the Sturm-Liouville operator with discontinuous conditions, Applied Mathematics Letters, 22 (2009) 1315-1319.
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[33] V. Yurko, Integral transforms connected with discontinuous boundary value problems, Int. Trans. Spec. Functions, 10 (2000) 141-164.
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[34] C. Willis, Inverse Sturm-Liouville problems with two discontinuities, Inverse Problems I (1985) 263-289.
34
ORIGINAL_ARTICLE
On multiplicative (strong) linear preservers of majorizations
In this paper, we study some kinds of majorizations on $\textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e. linear or strong linear preservers like $\Phi $ with the property $\Phi (AB)=\Phi (A)\Phi (B)$ for every $A,B\in \textbf{M}_{n}$.
http://scma.maragheh.ac.ir/article_18507_6efe0e20f27345279deaf253dedbf98a.pdf
2016-06-01T11:23:20
2019-08-19T11:23:20
91
106
Doubly stochastic matrix
Linear preserver
Multiplicative map
Mohammad Ali
Hadian Nadoshan
ma.hadiann@gmail.com
true
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
LEAD_AUTHOR
Ali
Armandnejad
armandnejad@vru.ac.ir
true
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
AUTHOR
[1] T. Ando, Majorization, Doubly stochastic matrices, and comparision of eigenvalues, Linear Algebra and its Applications, 118 (1989) 163-248.
1
[2] A. Armandnejad, F. Akbarzadeh, and Z. Mohammadi, Row and column-majorization on M_{n;m}, Linear Algebra and its Applications, 437 (2012) 1025-1032.
2
[3] A. Armandnejad and H. Heydari, Linear Preserving gd-Majorization Functions from M_{n;m} to M_{n;k}, Bull. Iranian Math. Soc., 37(1) (2011) 215-224.
3
[4] A. Armandnejad and A. Ilkhanizadeh Manesh, gut-Majorization and its Linear Preservers, Electronic Journal of Linear Algebra, 23 (2012) 646-654.
4
[5] A. Armandnejad, Z. Mohammadi, and F. Akbarzadeh, Linear preservers of G-row and G-column majorization on M_{n;m}, Bull. Iranian Math. Soc., 39(5) (2013) 865-880.
5
[6] A.M. Hasani and M. Radjabalipour, The structure of linear operators strongly preserving majorizations of matrices, Electronic Journal of Linear Algebra, 15 (2006) 260-268.
6
[7] C.K. Li and E. Poon, Linear operators preserving directional majorization, Linear Algebra and its Applications, 325 (2001) 15-21.
7
[8] P. Semrl, Maps on matrix spaces, Linear Algebra and its Applications, 413(2-3) (2006) 364-393.
8
ORIGINAL_ARTICLE
On $n$-derivations
In this article, the notion of $n-$derivation is introduced for all integers $n\geq 2$. Although all derivations are $n-$derivations, in general these notions are not equivalent. Some properties of ordinary derivations are investigated for $n-$derivations. Also, we show that under certain mild condition $n-$derivations are derivations.
http://scma.maragheh.ac.ir/article_19780_83b63b675701b909f6b32e3f6bb7c3aa.pdf
2016-06-01T11:23:20
2019-08-19T11:23:20
107
115
$n$-derivation
$n$-homomorphism
Banach algebra
Mohammad Hossein
Sattari
sattari@azaruniv.ac.ir
true
1
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
LEAD_AUTHOR
[1] F. F. Bonsall and J. Duncan, Complete normed algebras, Springpr-Verlag, New York, 1973.
1
[2] G. Dales, Banach Algebra and Automatic Continuity, London Mathematical Society Monographs, Volume 24, Clarendon Press, Oxford, 2000.
2
[3] H. G. Dales, F. Ghahramani, and N. Gronbaek, Derivations into iterated duals of Banach algebras, Studia Math., 128 (1998), 19-54.
3
[4] N. Dunford and J. T. Schwartz, Linear operators, Part I, New York, Interscience, 1958.
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[5] F. Ghahramani, Homomorphisms and derivations on weighted convolution algebras, J. London Math. Soc., 21 (1980), 149-161.
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[6] M. Hejazian, M. Mirzavaziri, and M. S. Moslehian, n-Homomorphism, Bull. Iranian Math. Soc., 31(1) (2005), 13-23.
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[7] B. E. Johnson, Local derivations on C* algebras are derivations, Trans. Amer. Math. Soc., 353 (2000), 313-325.
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[8] I. Kaplansky, Derivations of Banach algebras, In Seminars on analytic functions, Vol. 2, Princeton Univ. Press, Princeton, 1958.
8
[9] E. Samei, Approximately local derivations, J. London Math. Soc., 71(2) (2005), 759-778.
9
[10] A. M. Sinclair, Continuous derivations on Banach algebras , Proc. Amer. Math. Soc., 20 (1969), 166-170.
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[11] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann., 129 (1955) 260-264.
11
[12] S. Watanabe, A Banach algebra which is an ideal in the second dual space, Sci. Rep. Niigata Univ. Ser., A 11 (1974), 95-101.
12