ORIGINAL_ARTICLE
Bayesian Inference Based on type-I Hybrid Censored Data from a Two-Parameter Exponential Distribution
A hybrid censoring is a mixture of type-I and type-II censoring schemes. It is categorized to type-I and type-II hybrid censored based on how the experiment set to terminate. In this paper, we describe the type-I hybrid censoring where lifetime variables have a two-parameters exponential distribution. Bayes estimation of unknown parameters under squared error loss function is developed. Among several methods of constructing the optimal procedures in the context of robust Bayesian methodology, we obtain posterior regret gamma minimax estimation of unknown parameters under squared error loss function. Finally, we discuss minimaxity and admissibility of the generalized Bayes estimator under squared error loss.
https://jamm.scu.ac.ir/article_10026_664c25b7d9acc63f46cfd2172a89bc7f.pdf
2012-08-22
1
26
Admissible Estimator
Bayes Estimator
Minimax estimator
Ahmad
Parsian
ahmad_p@khayam.ut.ac.ir
1
Department of Statistics, Tehran University, Tehran, Iran.
AUTHOR
Fariba
Azizi
2
Department of Statistics, Tehran University, Tehran, Iran.
LEAD_AUTHOR
[1] Epstein, B. (1954), Truncated life-tests in the exponential case, Annals of Mathematical Statistics, 25, 555-564. [2] Fairbanks, K., Madsan, R. and Dykstra, R. (1982), A confidence interval for an exponential parameter from hybrid life-test, Journal of American Statistical Association, 77, 137-140. استنباط بیزی از توزیع نمایی دوپارامتری در سانسور هیبرید نوع اول 24 [3] Chen, S.M. and Bhattacharyya, G.K. (1988), Exact confidence bound for an exponential parameter under hybrid censoring. Communication in Statistics, Theory and Methods, 17, 1857-1870. [4] Childs, A., Chandrasekar, B., Balakrishnan, N. and Kundu, D. (2003), Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Annals of Institute of Statistical Mathematics, 55, 319-225. [5] Draper, N. and Guttman, T. (1987), Bayesian analysis of Hybrid life-test with
1
exponential failure times, Annals of Institute of Statistical Mathematics, 39, 219-225. [6] Gupta, R.D. and Kundu, D. (1998), Hybrid censoring with exponential failure distributions. Communication in Statistics, Theory and Methods, 27, 3065-3083. [7] Ebrahimi, N. (1990), Estimating the parameter of an exponential distribution from hybrid life test. Journal of Statistical Planning and Inference, 23, 255-261. [8] Ebrahimi, N. (1992), Prediction intervals for future failures in the exponential distribution under
2
hybrid censoring. IEEE Transactions on Reliability., 41, 127-132. [9] Kundu, D. (2007), On Hybrid censored weibull distribution, Journal of Statistical Planning and Inference, 137, 2127-2142. [10] Balakrishnan , N. and QihaoXie (2007), Exact inference for a simple Step-Stress model with Type-I hybrid censored data from the exponential distribution , Journal of Statistical Planning and
3
Inference, 137, 3268-3290. [11] Zen, M. M. and Das Gupta, A. (1993), Estimating a binomial parameter: Is robust Bayes real Bayes?, Statistics and Decisions, 11, 37-60. [12] Gnedenko, B.V., Belyayev, Yu. K. and Solovyev, A.D. (1969), Mathematical Method of Reliability Theory, Academic Press, New York. [13] Berger, J.O. (1985), Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York. [14] Royden, H.L. (1963), Real Analysis, Macmillan, New York. [15] Rudin, W. (1964), Principles of Mathematical Analysis, McGrow-Hill, New York.
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ORIGINAL_ARTICLE
Optimization of the Adomian Decomposition Method for Solving Differential Equation with Fractional Order
Up to now, Adomian Decomposition Method (ADM) has been widely employed in solving different kinds of differential equations. However, in many cases it is observed that the ADM has a lower precision in comparison with other methods, especially that of Homotopic ones. ADM is a relatively general and powerful method for finding analytical approximate results from different equations. In this paper, we seek to raise Optimal Adomian Decomposition Method (OADM) precision by employing the standard pattern of ADM. The main character of this repetitive method is based on employment of a controlling parameter in convergence, which resemble the parameters used in Homotopy Analysis Method (HAM). This parameter is indicated in such a way to reasonably increase the precision of obtained results. To indicate the optimizing parameter, the Least Squares Method has been used. The presented examples demonstrate that, how the above mentioned method has validity, applicability and a high degree of precision in solving differential equations of fractional order so that it can be generally used in solving differential equations.
https://jamm.scu.ac.ir/article_10025_4b99c78e70d70e2e592ee3de04f00d70.pdf
2012-08-22
27
45
Esmail
Hesameddini
1
Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
LEAD_AUTHOR
Mohsen
Riahi
2
Department of Mathematics, Shiraz University of Technology, Shiraz, Iran
AUTHOR
[1] He, J.H. (1999), Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 257-262. [2] Hesameddini, E. and Latifizadeh, H. (2009), A new vision of the He’s homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 10, 1415-1424. [3] Hesameddini, E. and Latifizadeh, H. (2009), An optimal choice of initial solutions in the homotopy perturbation method. International اسماعیل حسامالدینی، محسن ریاحی 42 Journal of Nonlinear Sciences
1
and Numerical Simulation, 10, 1389- 1398. [4] Liao, S.J. (1992), On the proposed homotopy analysis technique for nonlinear problems and its applications, Ph.D. Dissertation. Shanghai Jiao Tong University, Shanghai, China. [5] Liao, S.J. (2004), On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation, 147(2), 499-513. [6] West, B.J. and
2
Bolognab, M. and Grigolini, P. (2003), Physics of Fractal Operators, Springer, New York. [7] Miller, K.S. and Ross, B. (1993), An
3
introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York. [8] Samco, S.G. and Kilbas, A.A. and Marichev, O.I. (1993), Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon. [9] Einicke, G.A. and White, L.B. and Bitmead, R.R. (2003), The use of fake algebraic Riccati Equations for co-channel demodulation, IEEE Transactions on Signal Processing, 51(9) 129-134. [10] Adomian, G. (1990), A review of the decomposition method and
4
some recent results for nonlinear equation, Mathematical and Computer Modelling, 13(7) 17-42. [11] Adomian, G. (1994), Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, HA. [12] Hosseini, M.M. (2006), Adomian decomposition method with Chebyshev polynomials, Applied Mathematics and Computation, 175, 1685-1693. [13] Duan, J.S. and Rach, R. (2011), A new modification of the adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations, Applied Mathematics and Computation, 218, 4090-4118. [14] Kumar, M. and Singh, N. (2010), Modified Adomian Decomposition Method and computer implementation for solving singular boundary value problems arising in
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various physical problems, Computers and Chemical Engineering, 34, 1750-1760. [15] Abbaoui, K. and Cherruaul, Y. (1995), New ideas for proving convergence of decomposition methods, Computers & Mathematics with Applications, 29, 103-8.
6
ORIGINAL_ARTICLE
A Stable Numerical Solution of an Inverse Moving Boundary Problem of Heat Conduction Using Discrete Mollification Approach
In this paper the application of marching scheme and mollification approach to solve a one dimensional inverse moving boundary problem for the heat equation is investigated. The problem is considered with noisy data. A regularization method based on marching scheme and discrete mollification approach is developed to solve the proposed problem and the stability and convergence of numerical solution is proved. To show the ability and efficiency of the proposed method, some numerical experiments are investigated.
https://jamm.scu.ac.ir/article_10027_58c19a69aea4102de28b5fc4bf7caa83.pdf
2012-08-22
47
60
Morteza
Garshasbi
garshasbi@idu.ac.ir
1
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
LEAD_AUTHOR
Hatef
Dastour
2
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
AUTHOR
Mehdi
Jalalvand
m_djalal@iust.ac.ir
3
Department of Mathematics, Shahid Chamran University, Ahvaz, Iran
AUTHOR
[3] Rubinsteĭn L.I. (1979), The Stefan problem: Comments on its present state, Journal of the Institute of Mathematics and its Applications, 24, 259-277. [4] Grzymkowski R., Slota D. (2006), One-phase inverse Stefan problem solved by Adomain decomposition method, Computers & Mathematics with Applications, 51, 33-40. [5] Johansson B.T., Lesnic D., Reeve T. (2011), A method of fundamental solutions for the one-dimensional inverse Stefan problem, Applied Mathematical Modelling, 35, 4367-
1
4378. [6] Murio D.A. (2002), Mollification and space marching, in: K. Woodbury (Ed.), Inverse Engineering Handbook, CRC Press. [7] Garshasbi M., Reihani P., Dastour H. (2012), A stable numerical solution of a class of semi-linear Cauchy problems, Journal of Advanced Research in Dynamical and Control Systems, 4, 56-67. [8] Murio D.A., (1993), The Mollification Method and the Numerical Solution of Ill-Posed Problems, John Wiley and Sons, New York. [9] Anderssen B., de Hogg F., Hegland M. (1998), A
2
stable finite difference ansatz for higher order differentiation of nonexact data, Bulletin of the Australian Mathematical Society, 58, 223-232. [10] Ang D.D., Pham Ngoc Dinh A., Tranh D. (1996), An inverse Stefan problem: identification of boundary value, Journal of Computational and Applied Mathematics, 66, 75-84. [11] Beck J.V., Blackwell B., C.R.S.C. Jr. (1985), Inverse Heat Conduction, John Wiley-Interscience Publication, New York. [12] Garshasbi M., Damirchi J., Reihani P. (2010), Parameter
3
estimation in an inverse initial-boundary value problem of heat equation, Journal of Advances in Differential Equations, 2, 49-60. [13] Murio D.A., Paloschi J.R. (1988), Combined mollification-future temperatures procedure for solution of inverse heat
4
conduction problem, Journal of Computational and Applied Mathematics, 23, 235-244. [14] Murio D.A., Yi ZH. (2002), Source Term Identification in 1-D IHCP, Computers & Mathematics with Applications, 47, 1921-1933
5
ORIGINAL_ARTICLE
P-spaces and Artin-Rees Property
In this article, we study the Artin-Rees property in C(X), in the rings of fractions of C(X) and in the factor rings of C(X) . We show that C(X)/(f) is an Artin-Rees ring if and only if Z(f) is an open P-space. A necessary and sufficient condition for the local rings of C(X) to be Artin-Rees rings is that each prime ideal in C(X) becomes minimal and it turns out that every local ring of C(X) is an Artin-Rees ring if and only if X is a P-space. Finally we have shown that whenever XZ(f) is dense C-embedded in X , then C(X)f is regular if and only if Xz(f) is a P-space.
https://jamm.scu.ac.ir/article_10028_092ddbdf0c048e7187a43a74ccb69407.pdf
2012-08-22
61
76
Fariborze
Azarpanah
azarpanah@ipm.ir
1
Department of Mathematics, Shahid Chamran University, Ahvaz, Iran
LEAD_AUTHOR
Soosan
Afrooz
2
Department of Mathematics, Shahid Chamran University, Ahvaz, Iran
AUTHOR
[1] Anderson, D.F. and ayman badawi (2002), Divisibility conditions in commutative rings with zero divisors, Communications in Algebra, 3(8), 4031-4047. [2] Azarpanah, F. and Mohamadian, R. (2007), √z-ideals and √z -ideals in C(X), Acta Mathematica
1
Sinica. 23(6), 989-996. [3] Azarpanah, F. (1995), Essential ideals in C(X), Periodica Mathematica Hungarica, 31(2), 105-112. [4] Bkouche, R. (1970), Purete mosllesse et paracompacite, C. R. Acad. Sci. Paris Ser. A 270, A1653-1655. [5] Brookshear, J.G.
2
(1977), Projective ideals in rings of continuous functions, Pacific Journal of Mathematics, 71, 574-576 [6] DeMarco, G. (1978), Projectivity of pure ideals, Rend. Sem. Mat. Univ. Padova, 68, 289-304. [7] Gillman, L. and Jerison, M. (1976), Rings of continuous functions, Springer, New York. [8] Henriksen, M. and Jerison, M. (1965), The space of minimal prime ideals of
3
commutative rings, Transactions of the American Mathematical Society, 115, 110-130. [9] Karamzadeh, O.A.S and Rostami, M. (1985), On intrinsic topology and some related ideals of C(X), Proceedings of the American Mathematical Society, 93, 179-184.
4
ORIGINAL_ARTICLE
Three Critical Models in Mathematical Finance
In this paper, using mathematical techniques, we are going to model some of the important financial markets. Due to the close relations between stock exchange and derivatives markets, we introduce models which also indicate the collaboration between mathematicians, statisticians, computer and finance researchers. Moreover, in this way, the weakness of the old models has been compensated, thus the new and modern models have been generated to improve financial and mathematical relations for new researches. The aim of this article is not to present the solution of new models, but it is to introduce one of the applied mathematics branchs in finance science. Finally, we make a model with three important problems in financial instruments, which transfer he partial-integral differential equations. Depending on market, application of inverse problems and free boundary value problems in finance science is being explained.
https://jamm.scu.ac.ir/article_10029_f0dc8061962edec402c3cfe99aff0b1b.pdf
2012-08-22
77
96
Financial Modeling
Financial Derivative
Free Boundary Value Problem
Inverse problem
Stochastric Volatility
Abdolsadeh
Neisy
1
Department of Mathematics, Computer and Statistics, AllamehTabataba'i University, Tehran, Iran
LEAD_AUTHOR
Roya
Chamani Anbaji
2
Department of Mathematics, Computer and Statistics, AllamehTabataba'i University, Tehran, Iran
AUTHOR
Leili
Shojaee Manesh
3
Department of Mathematics, Computer and Statistics, AllamehTabataba'i University, Tehran, Iran
AUTHOR
[1] Hull, J.C. (2007), Fundamentals of Futures and Options Markets and Derivagem Package, 6th Edition, Prentice Hall. [2] Kou, S. G. (2002), A Jump-Diffusion Model for Option Pricing, Management Science, 48(8), 1086-1101. [3] Bates, DS. (1996), Jumps and Stochastic Volatility, Exchange rate Processes Implicit in Deutsche Mark Options, Review of Financial Stadies, 9(1), 69-107. [4] Hamilton, J.D. (1994), Time Series Analysis, Princeton University Press. [5] Andersenm, L. and Brotherton-Ratcliffe, R.
1
(1998), The equity option volatility smile: an implicit finite difference approach, Journal of Computational Finance, 1(2), 5-32. [6] Dupire, B. (1994), Pricing with a smile, Risk, 7(1), 18 20. [7] Jackson, N. Suli, E. and Howison S.(1999), Computation of
2
Deterministic volatility surfaces, Journal of computational finance, 2(2), 5-32. [8] Lagnado, R. and Osher, S. (1997), A Technique for Calibrating Derivative Security Pricing Models: Numerical Solution of an Inverse Problem, The Journal of Computational
3
Finance, 1(1), 13-25. [9] Guo, V. and Lerma, O. (2009) Continuous-Time Markov Decision Processes Theory and Applications, Springer-Verlag, New York . [10] Cont, R. and Tankov, P. (2003), Financial Modelling with Jump Processes, Chapman
4
andHall/CRC, Boca Raton, Florida. [11] Björk, T. (2004), Arbitrage theory in continuous time, 2nd edition, Oxford University Press.
5
[12] Heston, S. (2007), A closed-form solution for options with stochastic volatility with applicationsto bond and currency options, Review of Financial Studies, 6 327–343. [13] Wilmott, J. (2006) Paul WilmottOn Quantitative Finance, 2 nd edition, John Wiley, New York.
6
ORIGINAL_ARTICLE
Extension of Cell Cycle Model
In this paper we consider a delayed mathematical model of cell cycle. Adding drug toxicity, the model is modified and developed. A proper Lyapunov function is suggested for stability analysis. Furthermore, by obtaining a criterion for appropriate control, it is shown that any treatment strategy which satisfies the criterion, causes the system converge to tumor free equilibrium point.
https://jamm.scu.ac.ir/article_10030_e938bcf648a7fd25e828f321d4342e07.pdf
2012-08-22
97
106
Delay differential equations
Equilibrium point
Mathematical modeling of cancer
Lyapunov stability criterion
Mohammad
Keyanpour
kianpour@guilan.ac.ir
1
Department of Applied Mathematics, University of Guilan, Rasht, Iran
LEAD_AUTHOR
Tahereh
Akbarian
2
Department of Applied Mathematics, University of Guilan, Rasht, Iran
AUTHOR
[1] Villasana, M. and Ochoa, G. (2004), Heuristic design of cancer chemotherapies, IEEE Transactions of Evolutionary Computation, 8, 513–521. [2] Villasana, M. and Radunskaya, A. (2003), A delay differential equation of the model for tumor
1
growth, Journal of Mathematical Biology, 47, 270–294. [3] Heydari, A., Farahi, M.H. and Heydari, A.A. (2006), Optimal control of treatment of tuberculosis, International Journal of Applied Mathematics, 194, 389-404. [4] Yafia, R. (2006), Dynamics analysis
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and limit cycle in a delayed model for tumor growth with quiescence, Nonlinear Analysis: Modeling and Control, 11, 95–110. [5] Cojocaru, L. and Agur, Z. (1992), A theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs, Math. Biosci., 109, 85–97. [6] Panetta, J.C. and Adam, J. (1995), A mathematical model of cyclespecific chemotherapy, Math. Comput. Modeling, 22(2), 67–82. [7] Birkhead, B.G., Rakin, E.M., Gallivan, S., Dones, L. and Rubens, R.D. (1987), A mathematical model of the development of drug resistance to cancer chemotherapy, European Journal of Cancer and Clinical Oncology, 23(9), 1421-1427. [8] Webb, G.F. (1992), A cell population model of periodic chemotherapy treatment, Biomedical Modelling and Simulation, 83-92. [9] Villasana, M. and Radunskaya, A. (2003), A delay differential equation model for tumor growth, Journal of Mathematical Biology, 47, 270-294. [10] Villasana, M. (2001), A delay differential equation model for tumor growth, Ph.D.
3
dissertation, Claremont University, United State of America. [11] Ghaffari, A. and Nasserifar, N. (2009), Mathematical modeling and Lyapunov based drug administration in cancer chemotherapy, Iranian Journal of Electronical and Electrical Engineering, 5(3), 151-158. [12] Ghaffari, A., Azizi, K. and Amini, M.R. (2011), Mathematical modelling of Cancer and designing of an optimal
4
Lyapunov-Based Chemotherapy, Journal of Isfahan Medical School (JIMS) (In Press). [13] Khalil, H.K. (2002), Nonlinear Systems, 3 rd edition, Prentice-Hall, New York. م
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