2016
6
2
2
0
ON THE FUNCTION OF BLOCK ANTI DIAGONAL MATRICES AND ITS APPLICATION
2
2
The matrix functions appear in several applications in engineering and sciences. The computation of these functions almost involved complicated theory. Thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. The aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. Moreover, some theorems will be proven and applications will be given.
1

105
117


A.
Sadeghi
Department of Mathematics, Islamic Azad University, Robat Karim Branch, Tehran,
Iran.
Department of Mathematics, Islamic Azad University
Iran
Matrix functions
Block anti diagonal matrix
Central symmetric Xform matrix
Matrix exponential
Matrix differential function
[B. N. Datta, Numerical Methods for Linear Control Systems. Elsevier Academic Press,(2004). ##G. Golub, C.F. Van Loan, Matrix Computations, Johns Hopkins Univ. Press, Baltimore,MA, (1989). ##N. J. Higham, Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics, Philadelphia (2008). ##Roger A. Horn and Charles R. Johnson. Matrix Analysis. Cambridge University Press,xiii+561 pp. ISBN 0521305861, (1985). ##A. M. Nazari, E. Afshari and A. Omidi Bidgoli, Properties of Central Symmetric XForm Matrices, Iranian Journal of Mathematical Sciences and Informatics, 6(2), pp: 920, (2011). ##A. Sadeghi, Some new formulas for the exponential of central symmetric X form matrices, To appear (2016)##]
ANALYSIS OF A DISCRETETIME IMPATIENT CUSTOMER QUEUE WITH BERNOULLISCHEDULE VACATION INTERRUPTION
2
2
This paper investigates a discretetime impatient customer queue with Bernoullischedule vacation interruption. The vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain the steadystate probabilities at arbitrary and outside observer's observation epochs using recursive technique. Cost analysis is carried out using particle swarm optimization. Computational experiences with a variety of numerical results are discussed.
1

119
128


P.
Vijaya Laxmi
Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India.
Department of Applied Mathematics, Andhra
Iran


K.
Jyothsna
Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India.
Department of Applied Mathematics, Andhra
Iran
discretetime
balking
reneging
Bernoullischedule vacation interruption
particle swarm optimization
[[1] V. Goswami, Analysis of discretetime multiserver queue with balking, Int. J. Manage. Sci. Eng. ##Manage, 9 (1) (2014) 21–32. ##[2] V. Goswami, A discretetime queue with balking, reneging and working vacations, Int. J. Stoch. ##Anal., Article ID 358529, http://dx.doi.org/10.1155/2014/358529,(2014). ##[3] M. Lozano and P. Moreno, A discrete time singleserver queue with balking: economic applications, ##Appl. Econ, 40 (6) (2008) 735–748. ##[4] S. S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, Hoboken, New ##Jersey, USA, (2009). ##[5] L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/W V ), Perf. Eval, 50 ##(1) (2002) 41–52. ##[6] N. Tian, Z. Ma and M. Liu, The discrete time Geom/Geom/1 queue with multiple working vacations, ##Appl. Math. Model, 32 (12) (2008) 2941–2953. ##[7] P. Vijaya Laxmi, V. Goswami and K. Jyothsna, Analysis of finite buffer Markovian queue with ##balking, reneging and working vacations, Int. J. Strat. Dec. Sci, 4 (1) (2013) 1–24. ##[8] P. Vijaya Laxmi and K. Jyothsna, Impatient customer queue with Bernoulli schedule vacation interruption, ##Comput. Oper. Res, 56 (2015) 1–7. ##[9] H. Zhang and D. Shi, The M/M/1 queue with Bernoullischedulecontrolled vacation and vacation ##interruption, Int. J. Inform. Manage. Sci, 20 (2009) 579–587.##]
STABILITY ANALYSIS FROM FOURTH ORDER NONLINEAR EVOLUTION EQUATIONS FOR TWO CAPILLARY GRAVITY WAVE PACKETS IN THE PRESENCE OF WIND OWING OVER WATER.
2
2
Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillarygravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution equations,the stability analysis is made for a uniform capillary gravity wave train in the presence of another wave train having the same group velocity. Instability condition is obtained and graphs are plotted for maximum growth rate of instability and for wave number at marginal stability against wave steepness for some different values of dimensionless wind velocity.
1

129
147


J.
Mondal
Department of Mathematics,Indian Institute of Engineering Science and Technology, P.
O. Botanical Garden, Howrah  711103, West Bengal, India;
Department of Mathematics,Indian Institute
Iran


K.
Dhar
Department of Mathematics,IIEST, Howrah  711103,
West Bengal, India.
Department of Mathematics,IIEST, Howrah 
Iran
[T.B.Benjamin and J.E.Feir, The disintegration of wave trains on deep water, Part I Theory, J.Fluid ##Mech 27(1967)417. ##S.Bhattacharyya and K.P. Das, Fourth order nonlinear evolution equations for surface gravity waves ##in the presence of a thin thermocline, J.Austral, Math. Soc.Sec.B 39(1997)214. ##S.Debsarma and K.P. Das Fourth order nonlinear evolution equations for gravitycapillary waves in ##the the presence of a thin thermocline in deep water, ANZIAM J. 43,(2002)513. ##A.K.Dhar and K.P. Das, A fourth order nonlinear evolution equation for deep water surface gravity ##waves in the presence of wind blowing over water, Phys. Fluids A 2(5)(1990)778 783. ##A.K.Dhar and K.P.Das, Stability analysis from fourth order evolution equation for small but finite ##amplitude interfacial waves in the presence of a basic current shear, J.Austral. Math.Soc. Ser.B ##(1994)348365. ##A. K. Dhar and K.P. Das, Fourth order nonlinear evolution equation for two Stokes wave trains in ##deep water, Phys. Fluids A 3(12)(1991)3021. ##A.K.Dhar and K.P. Das, Effect of capillarity on f ourthorder nonlinear evolution equations for two ##Stokes wave trains in deep water, J.Indian Inst.Sci. 73(1993)579 ##A. K. Dhar and J.Mondal,,Stability analysis from fourth order evolution equation for counterpropagating ##gravity wave packets in the presence of wind owing over water, ANZIAM J. 56(E)(2015) pp ##K. B. Dysthe, Note on a modification to the nonlinear Schrdinger equation for application to deep ##water waves, Proc. R. Soc. Lond.A 369(1979) 105. ##P.A.E.M.Janssen, On a fourth order envelope equation for deep water waves, J.Fluid Mech. ##T.Hara and C.C.Mei, Frequency downshift in narrowbanded surface waves under the influence of ##wind, J.Fluid Mech. 230(1991)429. ##T.Hara and C.C.Mei, Wind effects on nonlinear evolution of slowly varying gravitycapillary waves, ##J.Fluid Mech. 267(1994)221. ##S. J. Hogan, The fourth order evolution equation for deep water gravity capillary waves, Proc.R.Soc. ##Lond.A 402(1985)359. ##S. Ahmadi, Applications of Partial Differential Equations in Stability Index and Critical Length in ##Avalanche Dynamics,IJM2C, 02  02 (2012) 137 144. ##S. J. Hogan,I.Gruman and M.Stiassine, On the changes in phase speed of one train of water waves ##in the presence of another., J.Fluid Mech. 192(1988)97. ##V.P. Krasitskii, On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves, ##J.Fluid Mech. 273(1994)1. ##M.S.LonguetHiggins and O.M.Philips, Phase velocity effects interraction, J.Fluid Mech. ##(1962)333.##]
HYBRID OF RATIONALIZED HAAR FUNCTIONS METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER
2
2
Abstract. In this paper, we implement numerical solution of diﬀerential equations of frac tional order based on hybrid functions consisting of blockpulse function and rationalized Haar functions. For this purpose, the properties of hybrid of rationalized Haar functions are presented. In addition, the operational matrix of the fractional integration is obtained and is utilized to convert computation of fractional diﬀerential equations into some algebraic equa tions. We evaluate application of present method by solving some numerical examples.
1

149
158


Y.
Ordokhani
Department of Applied Mathematics, Faculty of Mathematical Sciences, Alzahra
University, Tehran, Iran.
Department of Applied Mathematics, Faculty
Iran


N.
Rahimi
Department of Applied Mathematics, Faculty of Mathematical Sciences, Alzahra
University, Tehran, Iran.
Department of Applied Mathematics, Faculty
Iran
Diﬀerential equation
RiemannLiouville integral
Caputo fractional derivative
Hybrid
Rationalized Haar
Fractional operational matrix
[K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Diﬀerential Equations, Johnwiley and Sons, New York, 1993. ##I. Podlubny, Fractional Diﬀerential Equations: An Introduction to Fractional Derivatives, Fractional Diﬀerential Equations, to Methods of their Solution and Some of Their Application, Mathematics in Science and Engineering, Academic Press, New York, Volume 198, 1999. ##M. U. Rehman and R. A. Khan, The Legendre wavelet method for solving fractional diﬀerential equations, Commun Nonlinear Sci Numer Simmulat, 16 (2011) 41634173. ##H. Jafari and S.A. Youse, M. A. Firroozjaee, S. Momani, C. M. Khalique, Application of Legendre wavelet for solving fractional diﬀerential equations, Computers and Mathematics with Applications, 62 (2011) 10331045. ##Y. Li and W. Zhao, Haar Wavelet operational matrix of fractional order integration and its application in solving the fractional order diﬀerential equations, Applied Mathmatics and Computation, 216 (2010) 22762285. ##Y. Li, Solving a nonlinear fractional diﬀerential equations using Chebyshev wavelets, Communication in Nonlinear Science and Numerical Simulation, 15 (2010) 22842292. ##S. A. ElWakil, A. Elhanblay and M. A. Abdou, Adomian decomposition method for solving fractional nonlinear diﬀerential equations, Applied Mathematical and Computation, 182 (2006) 313324. ##S. Momani and Z. Odibat, Numerical comparison of methods for solving linear diﬀerential equations of fractional order, Chos Solitons and Fractals, 31 (2007) 12481255. ##A. Arikoglu and I. Ozkol, Solution of fractional diﬀerential equations by using diﬀerential transform method, Chos Solitons and Fractals, 34 (2007) 14731481. ##A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional order diﬀerential equations, Computers and Mathematics with Applications, 59 (2010) 13261336. ##M. U. Rehman and R. A. Khan, A numerical method for solving boundary value problems for frac tional diﬀerential equations, Applied Mathematical Modelling, 36 (2011) 894907. ##M. M. Khader, T. S. El danaf and A. S. Hendy, Eﬃcient spectral collocation method for solving multiterm fractional diﬀerential equations based on the generalized Lagurre polynomials, Journal of Fractional Calculus and Application, 3 (12) (2012) 114. ##J. D. Munkhammar, RiemannLiouville Fractional Derivatives and The TaylorRiemmann Series, U. U. D. M. Project Report, 2004. ##A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Diﬀerential Equations, NorthHolland Mathematic Studies, Elsvier, 204 (2006). ##B. Arabzadeh, M. Razzaghi and Y. Ordukhani, Numerical solution of linear timevarying diﬀeren tial equations using hybrid of blockpulse and rationalized Haar functions, Journal of Vibration and Control, 12 (2006) 10811092. ##Y. Ordokhani, Solution of nonlinear VolterraFredholmHammerstein integral equations via rational ized Haar functions, Applied Mathmatics and Computation, 187 (2006) 436443. ##G. M. Philips and P.J. Taylor, Theory and Application of Numerical Analysis, Academic Press, New York, 1973. ##A. Kilicman and Z. A. A. Al Zhour, Kronecker operational matrices for fractional calculus and some applications, Applied Mathematics and Computation, 187 (2007) 250265. ##]
THE ENTROPIES OF THE SEQUENCES OF FUZZY SETS AND THE APPLICATIONS OF ENTROPY TO CARDIOGRAPHY
2
2
In this paper, rstly we have introduced to entropy of sequences of fuzzy sets and given sometheorems about it. Secondly, the waves P and T which appears in electrocardiograms weretransferred to fuzzy sets, by using denition of entropy for sequences of fuzzy sets, and somenumerical values were obtained for sequences of waves P and T. Thus any person can makea medical predictions for some cardiac problems using to the numerical values.
1

159
173


M.
şengönül
Department of Mathematics, Nev¸sehir HBV University, Nev¸sehir, PO. Code 50100,
T¨urkiye;
Department of Mathematics, Nev¸sehir
Iran


K.
Kayaduman
Department of Mathematics, G. Antep University, G. Antep, PO. Code 27000, T¨urkiye.
Department of Mathematics, G. Antep University,
Iran


Z.
Zararsız
Department of Mathematics, Nev¸sehir HBV University, Nev¸sehir, PO. Code 50100,
T¨urkiye
Department of Mathematics, Nev¸sehir
Iran


S.
Atpınar
Department of Mathematics, Nev¸sehir HBV University, Nev¸sehir, PO. Code 50100,
T¨urkiye
Department of Mathematics, Nev¸sehir
Iran
HAAR WAVELET AND ADOMAIN DECOMPOSITION METHOD FOR THIRD ORDER PARTIAL DIFFERENTIAL EQUATIONS ARISING IN IMPULSIVE MOTION OF A AT PLATE
2
2
We present here, a Haar wavelet method for a class of third order partial dierentialequations (PDEs) arising in impulsive motion of a flat plate. We also, present Adomaindecomposition method to find the analytic solution of such equations. Efficiency andaccuracy have been illustrated by solving numerical examples.
1

175
188


I.
Singh
Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology,
Jalandhar, Punjab144011, India
Department of Mathematics, Dr. B. R. Ambedkar
Iran


S.
Kumar
Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology,
Jalandhar, Punjab144011, India
Department of Mathematics, Dr. B. R. Ambedkar
Iran
Linear third order partial differential equation
Haar wavelet
Adomain decomposition method
Operational matrix
[R.A. Van Gorder, K. Vajravelu, Thirdorder partial differential equations arising in the impulsive motion of a at plate, Commun. Nonlinear Sci. Numer. Simul. 14 (6) (2009) 2629{2636. ##A.M. Wazwaz, An analytic study on the thirdorder dispersive partial differential equations, Appl. Math. Comput. 142 (2) (2003) 511520. ##A.M. Wazwaz, Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations, Appl. Math. Comput. 195 (2) (2008) 754761. ##M. Mechee, F. Ismail, Z.M. Hussain, Z. Siri, Direct numerical methods for solving a class of thirdorder partial differential equations, Applied Mathematics and Computation 247 (2014) 663674. ##I. Teipel, The impulsive motion of a at plate in a viscoelastic ##uid. Acta Mech 39 (1981) 2779. ##C.F. Chen, C.H. Hsiao, Haar wavelet method for solving lumped and distributed parameter systems, IEE. Proc. Control Theory Appl. 144 (1997) 8794. ##U. Lepik, Numerical solution of evolution equations by the Haar wavelet method, Applied Mathematics and Computation 185 (2007) 695 704. ##U. Lepik, Numerical solution of dierential equations using Haar wavelets, Math. Comput. Simul. 68 (2005) 127143. ##U. Lepik, Application of the Haar wavelet transform for solving integral and differential equations, Proc. Estonian Acad. Sci. Phys. Math. 56 (1) (2007) 2846. ##I. Celik, Haar wavelet method for solving generalized BurgersHuxley equation, Arab Journal of Mathematical Sciences 18 (2012), 2537. ##G. Hariharan, K. Kannan, K.R. Sharma, Haar wavelet method for solving Fishers equation, Appl. Math. Comput. 211 (2009) 284292. ##G. Hariharan, K. Kannan, Haar wavelet method for solving FitzHughNagumo equation, Int. J. Math. Stat. Sci. 2(2) (2010) 5963. ##A. Haar, Zur theorie der orthogonalen Funktionsysteme, Math. Annal. 69 (1910) 33171. ##G.B. Whitham, Linear and nonlinear waves, Wiley, New York, 1974. ##G. Adomian, Solving Frontier Problems of Physics: The Decomposition Methods, Kluwer Academic Publishers, Boston (1994).##]