ORIGINAL_ARTICLE
General Linear Model Specification Error Test with Missing Data
In this paper, we consider a general linear model where missing data may occur in response and covariate variables. We propose a new test based on Ramsy's test to identify goodness of fit for general linear model with missing data. We show that under the null hypothesis, our test functions for complete case analysis follow a Fisher distribution and the other test function used for analysis with available data converges in distribution to Quasi-Fisher distribution. Furthermore, we compare proposed test functions by using some simulation studies. Also, we apply our methods in analyzing a real data set.
https://jamm.scu.ac.ir/article_13854_ccbba435dbe7b45aa7a7e0cee582812b.pdf
2019-03-21
1
26
10.22055/jamm.2018.24634.1541
General linear model
Missing data
Goodness of fit
Ramsey's test
Quasi-Fisherd distribution
fayyaz
bahari
fayyaz.bahari@yahoo.com
1
Department of statistics and computer sciences, University of mohaghegh ardabili< Ardabil< Iran
AUTHOR
Safar
Safar
parsi@uma.ac.ir
2
Department of Statistics and Computer Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
LEAD_AUTHOR
Mojataba
Ganjali
m-ganjali@sbu.ac.ir
3
Department of statistics, Shahid beheshti university, Tehran, Iran
AUTHOR
[1] Madsen, H. and Thyregod, P. 2010. Introduction to general and generalized linear models. CRC Press.
1
[2] Ramsey, G. B. (1969). Test for specification error in classical linear least square regression analysis. Journal of the Royal Statistical Society, 31, 350-71.
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[3] Griffith, D. A. and Chun, Y. (2016). Evaluating eigenvector spatial filter corrections for omitted georeference variables. Econometrics, 21, 1-12.
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[4] Shukur, G. and Mantalos, P. (2004). Size and power of the RESET test as applied to systems of equations. A Bootstrap Approach, Journal of Modern Applied Statistical Methods, 3, 370-385.
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[5] Sapra, S. (2005). A regression error specification test (RESET) for generalized linear model. Economics Bulletin, 3, 1-6.
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[6] Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581-592.
6
[7] Little, R. J. A. and Rubin, D. B. (2002). Statistical analysis with missing data. Second Edition, Wiley-Interscience, New York.
7
[8] Basilevsky, A., Sabourin, D., Hum, D. and Anderson, A. (1985). Missing data estimators in the general linear model: an evaluation of simulated data as an experimental design. Communications in Statistics-Simulation and Computation, 14(2), 371-394.
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[9] Little, R. J. A. (1992). Regression with missing X's: A review. Journal of the American Statistical Association, 87, 1227-1237.
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[10] Wang, S. and Wang, C.Y. (2001). A note on kernel assisted estimators in missing covariate regression. Statistics and Probability letters, 55, 439-449.
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[11] Hardle, W. and Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. Annals of Statistics, 21, 1921-1947.
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[12] Hardle, W., Mammen, E. and Muller, M. (1998). Testing parametric versus semiparametric modeling in generalized linear models. Journal of the American Statistical Association, 93(444), 1461-1474.
12
[13] Zhu, L.X. and Cui, H.J. (2005). Testing lack-of-fit for general linear errors in variables models. Statistica Sinica, 15, 1049--1068.
13
[14] Guo, X. and Xu, W. (2012). Goodness-of-fit tests for general linear models with covariates missed at random. Journal of Statistical Planning and Inference, 142, 2047-2058.
14
[15] Li, X. (2012). Lack-of-fit testing of a regression model with response missing at random. Journal of Statistical Planning and Inference, 142(1), 155-170.
15
[16] Zhao, L. P. and Lipsitz, S. (1992). Design and analysis of two-stage studies. Statistics in Medicine, 11, 769-782.
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[17] Carpenter, J. R. and Kenward, M. G. (2006). A comparison of multiple imputation and doubly robust estimation for analyses with missing data. Journal of the Royal statistical Society, 169, 571-584.
17
[18] Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. A. (1983). Graphical methods for data analysis. Belmont, CA: Wadsworth.
18
ORIGINAL_ARTICLE
Bayesian analysis of Gastric Cancer rate in Gilan Province by using the
Auto-beta binomial model
The climatic and environmental conditions in each region contribute to the outbreak of certain diseases. Therefore, providing a map of the event rate of a disease or mortality from various diseases on a geographic area is one issue of concern for physicians and health experts. Considering that gastric cancer is the most common cancer in Gilan province, Iran, in this paper, we study the impact of some risk factors on the rate of this cancer for the cities of Gilan province by using two auto-binomial and auto-beta-binomial Bayesian spatial models. The other purposes of this study are providing the gastric cancer rate prediction map and comparing the performance of the two proposed models. We used a dataset from the Razi Educational Center of Rasht in which the data were collected for sixteen cities of Gilan during the period of 2012-2017. We fitted the proposed models for these data by using an approximate Bayesian approach, called the integrated nested Laplace approximation (INLA). Based on the results, it was found that prediction of the rates of cancer in most of the cities of Gilan are similar by using of both models; in cities where there is a difference, the auto-binomial model predicts a higher rate than the auto-beta-binomial model. The reason for this is also that the auto-binomial model is over-fitted, which reduces its ability to predict.
https://jamm.scu.ac.ir/article_13892_d0c4b99ea065677ab646ed3f26319842.pdf
2019-03-21
27
43
10.22055/jamm.2018.25994.1586
Zoning map
Binomial model
Beta-binomial model
Gastric cancer
leila
abedinpour liiajadmeh
leila.abedinpour@yahoo.com
1
Departmant of Statistics, Shahrood University of Technology, Shahrood, Iran
LEAD_AUTHOR
Hossein
Baghishani
hbaghishani@shahroodut.ac.ir
2
Departmant of Statistics, Shahrood University of Technology, Shahrood, Iran
LEAD_AUTHOR
negar
eghbal
n.eghbal@shahroodut.ac.ir
3
Departmant of Statistics, Shahrood University of Technology, Shahrood, Iran
AUTHOR
[1] Rao, J. N. (2015). Small‐Area Estimation. John Wiley and Sons, Ltd.
1
[2] Wilkinson, D., and Tanser, F. (1999). GIS/GPS to document increased access to community-based treatment for tuberculosis in Africa. The Lancet, 354(9176), 394-395.
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[3] رمضانی، بهمن؛ حنیفی، اعظم (1387). شناخت پراکندگی جغرافیایی شیوع سرطان معـده در استان گیلان. فصلنامه علوم و تکنولوژی محیطزیست، دورهی 13، شمارهی 2، ص92-79.
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[4] رضوانی، محمود و همکاران 1374، طرح ثبت سرطان در استان گیلان، معاونت بهداشتی استان گیلان، ص 1.
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[5] Ali, M., Rasool, S., Park, J. K., Saeed, S., Ochiai, R. L., Nizami, Q., and Bhutta, Z. (2004). Use of satellite imagery in constructing a household GIS database for health studies in Karachi, Pakistan. International Journal of Health Geographics, 3(1), 20.
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[6] Cressie, N. (1993). Statistics for Spatial Data: Revised Edition. John Wiley and Sons.
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[7] Snow, J. (1854). The cholera near Golden-square, and at Deptford. Medical Times and Gazette, 9, 321-322.
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[8] Clayton, D., and Kaldor, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43, 671-681.
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[9] Kaiser, M. S., and Cressie, N. (1997). Modeling Poisson variables with positive spatial dependence. Statistics and Probability Letters, 35(4), 423-432.
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[10] Lajaunie, C. (1991). Local risk estimation for a rare noncontagious disease based on observed frequencies. Note N-36/91/G, Centre de Géostatisque, Ecole des Mines de Paris.
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[11] Oliver, M. A., Webster, R., Lajaunie, C., Muir, K. R., Parkes, S. E., Cameron, A. H., and Mann, J. R. (1998). Binomial cokriging for estimating and mapping the risk of childhood cancer. Mathematical Medicine and Biology: A Journal of the IMA, 15(3), 279-297.
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[12] Monestiez, P., Dubroca, L., Bonnin, E., Durbec, J. P., and Guinet, C. (2006). Geostatistical modelling of spatial distribution of Balaenoptera physalus in the Northwestern Mediterranean Sea from sparse count data and heterogeneous observation efforts. Ecological Modelling, 193(3-4), 615-628.
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[13] Goovaerts P. (2010). Geostatistical Analysis of County-Level Lung Cancer Mortality Rates in the Southeastern United States, Geographical analysis, 42(1), 32-52.
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[14] Goovaerts, P. (2005). Geostatistical analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging. International Journal of Health Geographics, 4(1), 31.
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[15] Goovaerts, P. (2009). Medical geography: a promising field of application for geostatistics. Mathematical Geosciences, 41(3), 243.
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[16] Shao, C., Mueller, U., and Cross, J. (2009). Area-to-point Poisson kriging analysis for lung cancer in Perth areas. Proceedings of the 18th World IMACS/MODSIM Congress, Jul 13-17, Caire, Australia.
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[17] Kerry, R., Goovaerts, P., Smit, I., and Ingram, P. R. (2010). A Comparison of Indicator and Poisson Kriging of Herbivore Species Abundance in Kruger National Park. South Africa [Online].
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[18] Bandyopadhyay, D., Reich, B. J., and Slate, E. H. (2011). A spatial beta-binomial model for clustered count data on dental caries. Statistical Methods in Medical Research, 20(2), 85-102.
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[19] Harrison, X. A. (2015). A comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in Binomial data in ecology and evolution, PeerJ, 3, e1114.
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[20] Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B (Methodology), 36(2), 192-236.
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[21] Ferrari, S., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799-815.
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[22] Rue, H., Martino, S., and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society, Series B (Methodology), 71(2), 319-392.
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[23] Rue, H., and Held, L. (2005). Gaussian Markov random fields: theory and applications, CRC press, London.
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[24] Isaksson, A., Wallman, M., Göransson, H., and Gustafsson, M. G. (2008). Cross-validation and bootstrapping are unreliable in small sample classification. Pattern Recognition Letters, 29(14), 1960-1965.
24
[25] Varoquaux, G. (2017). Cross-validation failure: small sample sizes lead to large error bars. Neuroimage, 180, 68-77.
25
ORIGINAL_ARTICLE
A constrained optimization problem for determining the smallest Pareto confidence region under progressive Type-II censoring
In this paper, a constrained optimization problem is formulated and solved to determine the smallest joint confidence region for Pareto parameters based on the progressively Type-II censored samples. The objective function is the area of the confidence region and the problem constraint is the specified confidence level. The proposed joint confidence region is also valid for the complete samples and right censored samples. The area of the smallest proposed confidence region and the area of the balanced confidence region are compared. Finally, two numerical examples are presented to describe the proposed optimization method.
https://jamm.scu.ac.ir/article_13855_a5564d4d6073f68a56ab9561e036a727.pdf
2019-03-21
44
57
10.22055/jamm.2018.23489.1492
Joint confidence region
Progressive Type-II censoring
Lagrangian method
Pareto distribution
Marjan
Zare
mrjn.zare@yahoo.com
1
Department of Statistics, University of Mazandaran, Babolsar, IRAN
AUTHOR
Akbar
Asgharzadeh
a.asgharzadeh@umz.ac.ir
2
Department of Statistics, University of Mazandaran, Babolsar, IRAN
LEAD_AUTHOR
[1] Johnson, N.L. and Kotz, Balakrishnan, N. (1994). Continuous Uinvariare Distributions, Vol. 1, 2nd ed. John Wiley & Sons, New York.
1
[2] Fernandez, A.J. (2012). Minimizing the area of a Pareto confidence region, European Journal of Operational research, 221, 205–212.
2
[3] Fernandez, A.J. (2013). Smallest Pareto confidence regions and applications, Computational Statistics and Data Analysis, 62, 11–25.
3
[4] Fernandez, A.J. (2014). Computing optimal confidence sets for Pareto models under progressive censoring, Journal of Computational and Applied Mathematics, 258, 168–180
4
[5] Asgharzadeh, A., Abdi, M. and Kus, C. (2011). Interval estimation for the two-parameter Pareto distribution based on record values, Selçuk Journal of Applied Mathematics, 149–161. Special Issue.
5
[6] Asgharzadeh, A., Fernandez, A.J. and Abdi, M. (2017). Confidence sets for two-parameter Rayleigh distribution under progressive censoring, Applied Mathematical modelling, 47, 656–667.
6
[7] Balakrishnan, N., and Aggarwala, R. (2000). Progressive censoring: Theory, Methods and Applications, Birkhauser Publishers, Boston.
7
[8] Balakrishnan, N. and Cramer, E. (2014). The Art of Progressive Censoring, Springer, New York.
8
[9] Kus, C. and Kaya, M.F. (2007). Estimation for the parameters of the Pareto distribution under progressive censoring, Communications in Statistics - Theory and Methods, 36, 1359–1365.
9
[10] Nelson, W. B. (1970). Statistical methods for accelerated life test datathe inverse power law model, General Electric Co. Tech. Rep.71-C011, New York: Schenectady.
10
[11] Asgharzadeh, A., Mohammadpour, M. and Ganji, Z.M. (2014). Estimation and reconstruction Based on Left Censored Data from Pareto Model, Journal of Iranian Statistical Society, 13, 151–175.
11
[12] Parsi, S., Ganjali, M. and Sanjari Farsipour, N. (2010). Simultaneous confidence intervals for the parameters of Pareto distribution under progressive censoring, Communications in Statistics-Theory and Methods, 39, 94–106.
12
ORIGINAL_ARTICLE
A generalization of δ- shock model
Suppose that a system is exposed to a sequence of shocks that occur randomly over time, and δ_1 and δ_2 are two critical levels such that 0 < δ_1
https://jamm.scu.ac.ir/article_14239_c58e924649302aad37cd99bc91c0fbe5.pdf
2019-03-21
58
70
10.22055/jamm.2019.26715.1618
δ-Shock model
Interarrival distribution
Survival function
Mohamad hosein
Poursaeed
poursaeed.m@lu.ac.ir
1
Department of Statistics, Lorestan university, Khoramabad, Iran
LEAD_AUTHOR
[1] Li, Z.H. (1984). Some distributions related to Poisson processes and their application in solving the problem of traffic jam. J. Lanzhou Univ. Nat. Sci., 20, 127–136.
1
[2] Sumita, U. and Shanthikumar, J.G. (1985). A class of correlated cumulative shock models. Ann. Appl. Probab., 17, 347–366.
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[3] Aven, T. and Gaarder, S. (1987). Optimal replacement in a shock model: Discrete-time, J. Appl. Probab., 24, 281–287.
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[4] Gut, A. (1990). Cumulative shock models. Ann. Appl. Probab., 22, 504–507.
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[5] Mallor, F. and Omey, E. (2001). Shocks, runs and random sums. J. Appl. Probab., 38, 438–448.
5
[6] Wang, G.J. and Zhang, Y.L. (2001). -shock model and its optimal replacement policy. J. Southeast Univ., 31, 121–124.
6
[7] Li, Z.H. and Kong, X.B. (2007). Life behavior of -shock model. Statist. Probab. Lett., 77, 577–587.
7
[8] Li, Z.H. and Zhao, P. (2007). Reliability analysis on the -shock model of complex systems. IEEE Trans. Reliab., 56, 340–348.
8
[9] Finkelstein, M. and Cha, J. H. (2013). Stochastic Modeling for Reliability, Shocks, Burn-in and Heterogeneous Populations. London, U.K.: Springer-Verlag.
9
[10] Eryilmaz,S. and Bayromoglu, K. (2014). Life behavior of -shock models for uniformly distributed inter-arrival times, Stat. Papers, 55, 841-852.
10
[11] Parvardeh, A. and Balakrishnan, N. (2015). On mixed -shock models, Statist. Probab. Lett., 102, 51-60.
11
ORIGINAL_ARTICLE
On the Stochastic Properties of Unfailed Components in Used Networks
We consider a two-state network consists of n components and assume that the failure of components occur according to a nonhomogeneous Poisson process. Some networks have the property that after the failure, some of the components remain unfailed. The remaining unfailed components might be resumed from the network and be used again in a new network. In this paper, we explore some aging properties and stochastic comparisons of the residual lifetime of remaining unfailed components of the failed network.
https://jamm.scu.ac.ir/article_14240_ed9a6a218e837c116bb7edb5d8b7b689.pdf
2019-03-21
71
97
10.22055/jamm.2019.24420.1526
Stochastic Ordering
Record values
Two-state networks
Nonhomogeneous Poisson Process
Signature
Somayeh
Zarezadeh
s.zarezadeh@shirazu.ac.ir
1
Department of Statistics, Shiraz University, Shiraz, Iran
LEAD_AUTHOR
[1] Boland, P.J., Samaniego, F.J. and Vestrup, E.M. (2003). Linking dominations and signatures in network reliability theory, In: Lindquist, B.H., Doksum, K.A. (Eds) Mathematical and statistical methods in reliability. World Scientific, Singapore, 89-103.
1
[2] Samaniego, F.J. (1985). On closure of the IFR class under formation of coherent systems, IEEE Transactions on Reliability, 34, 69-72.
2
[3] Zarezadeh, S., Mohammadi, L. and Balakrishnan, N. (2018). On the joint signature of several coherent systems with some shared components, European Journal of Operational Research, 264(3), 1092-1100.
3
[4] Navarro, J., Balakrishnan, N. and Samaniego. F.J. (2008). Mixture representations of residual lifetimes of used systems. Journal of Applied Probability, 45, 1097-1112.
4
[5] Eryilmaz, S. (2014). A study on reliability of coherent systems equipped with a cold standby component, Metrika, 77, 349-359.
5
[6] Gertsbakh, I., Rubinstein, R., Shpungin, Y. and Vaisman, R. (2014). Permutational methods for performance analysis of stochastic flow networks, Probability in the Engineering and Informational Sciences, 28(1), 21-38.
6
[7] Patelli, E., Feng, G., Coolen, F.P. and Coolen-Maturi, T. (2017). Simulation methods for system reliability using the survival signature, Reliability Engineering & System Safety, 167, 327-337.
7
[8] Eryilmaz, S. and Bayramoglu, I. (2012). On extreme residual lives after the failure of the system, Mathematical Problems in Engineering, 1-11.
8
[9] Zarezadeh, S. and Asadi, M. (2013). Network reliability modeling under stochastic process of component failures, IEEE Transactions on Reliability, 62(4), 917-929.
9
[10] Nakagawa, T. (2011). Stochastic Processes: With Applications to Reliability Theory, New York: Springer-Verlag.
10
[11] Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (2011). Records, Wiley.
11
[12] Gupta, R. C. and Kirmani, S.N.U.A. (1988). Closure and monotonicity properties of nonhomogeneous Poisson processes and record values, Probability in the Engineering and Informational Sciences, 2, 475-484.
12
[13] Balakrishnan, N. and Asadi, M. (2012). A proposed measure of residual life of live components of a coherent system, IEEE Transactions on Reliability, 61(1), 41-49.
13
[14] Bairamov, I. and Arnold, B.C. (2008). On the residual life lengths of the remaining components in a (n - k + 1)-out-of-n system, Statistics & Probability Letters, 78, 945-952.
14
[15] Gurler, S. (2012). On residual lifetimes in sequential (n-k+1)-out-of-n systems. Statistical Papers, 53(1), 23-31.
15
[16] Balakrishnan, N., Barmalzan, G. and Haidari, A. (2014). Stochastic orderings and ageing properties of residual life lengths of live components in (n-k+ 1)-out-of-n systems, Journal of Applied Probability, 51(1), 58-68.
16
[17] Balakrishnan, N., Barmalzan, G. and Haidari, A. (2016). Multivariate stochastic comparisons of multivariate mixture models and their applications, Journal of Multivariate Analysis, 145, 37-43.
17
[18] Kelkinnama, M. and Asadi, M. (2014). Stochastic properties of components in a used coherent system, Methodology and Computing in Applied Probability, 16(3), 675-691.
18
[19] Kelkin Nama, M., Asadi, M. and Zhang, Z. (2013). On the residual life lengths of the remaining components in a coherent system, Metrika, 76(7), 979-996.
19
[20] Shaked, M. and Shanthikumar, J.G. (2007). Stochastic Orders, New York: Springer-Verlag.
20
[21] Rao, M., Chen, Y., Vemuri, B.C. and Wang, F. (2004). Cumulative residual entropy: A new measure of information, IEEE Transactions on Information Theory, 50(6), 1220-1228.
21
[22] Elperin, T., Gertsbakh, I. and Lomonosov, M. (1991). Estimation of network reliability using graph evolution models, IEEE Transactions on Reliability, 40(5), 572-581.
22
[23] Khaledi, B.E. and Shaked, M. (2010). Stochastic comparisons of multivariate mixtures. Journal of Multivariate Analysis, 101(10), 2486-2498.
23
[24] Belzunce, F., Mercader, J.A., Ruiz, J.M. and Spizzichino, F. (2009). Stochastic comparisons of multivariate mixture models. Journal of Multivariate Analysis, 100(8), 1657-1669.
24
[25] Ahmadi, J. and Arghami, N.R. (2001). Some univariate stochastic orders on record values. Communications in Statistics - Theory and Methods, 30, 69-74.
25
ORIGINAL_ARTICLE
A new optimization operational matrix algorithm for solving nonlinear variable-order time fractional convection-diffusion equation
In this paper, a new and effective optimization algorithm is proposed for solving the nonlinear time fractional convection-diffusion equation with the concept of variable-order fractional derivative in the Caputo sense. For finding the solution, we first introduce the generalized polynomials (GPs) and construct the variable-order operational matrices. In the proposed optimization technique, the solution of the problem under consideration is expanded in terms of GPs with unknown free coefficients and control parameters. The main advantage of the presented method is to convert the variable-order fractional partial differential equation to a system of nonlinear algebraic equations. Also, we obtain the free coefficients and control parameters optimally by minimizing the error of the approximate solution. Finally, the numerical examples confirm the high accuracy and efficiency of the proposed method in solving the problem under study.
https://jamm.scu.ac.ir/article_13856_dd993b70d3e9af8b5dd7341484258c42.pdf
2019-03-21
98
119
10.22055/jamm.2018.24417.1525
Nonlinear variable-order time fractional convection-diffusion equation
Operational matrices
Optimization algorithm
Generalized polynomials (GPs)
Control parameters
Hossein
Hassani
hosseinhassani40@yahoo.com
1
Department of َApplied Mathematics, Shahrekord University, Shahrekord , Iran
AUTHOR
Eskandar
Naragirad
esnaraghirad@yu.ac.ir
2
Department of Mathematics, Yasouj University, Yasouj, Iran.
LEAD_AUTHOR
[1] Ciombra, C. F. M. (2013). Mechanics with variable-order differential operators, Ann. Phys., 12 (11-12), 692-703.
1
[2] Pedro, H. T. C., Kobayashi, M. H., Pereira, J. M. C. and Coimbra, C. F. M. (2008). Variable order modeling of diffusive-convective effects on the oscillatory flow past a sphere, J. Vib. Control, 14, 1569-1672.
2
[3] Ramirez, L. E. S. and Coimbra, C. F. M. (2011). On the variable order dynamics of the nonlinear wake caused by a sedimenting particle, Physica D, 240, 1111-1118.
3
[4] Shyu, J. J., Pei, S. C. and Chan, C. H. (2009). An iterative method for the design of variable fractional-order FIR different egrators, Signal Process., 89, 320-327.
4
[5] Sun, H. G., Chen, W. and Chen, Y. Q. (2009). Variable-order dractional differential operators in anomalous diffusion modeling, Phys. A, 388, 4586-4592.
5
[6] Zahra, W. K. and Hikal, M. M. (2017). Nonstandard finite difference method for solving variable order fractional control problems, J. Vib. Control, 23 (6), 948-958.
6
[7] Ramirez, L. E. S. and Coimbra, C. F. M. (2007). Variable order constitutive relation for viscoelasticity, Ann. Phys., 16, 543-552.
7
[8] Chen, C. M. (2013). Numerical methods for solving a two-dimensional variable-order modified diffusion equation. Appl. Math. Comput., 225, 62-78.
8
[9] Bhrawy, A. H. and Zaky, M. A. (2016). Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation, Nonlinear Dyn., 80 (1), 101-116.
9
[10] Shen, S., Liu, F., Chen, J., Turner, I. and Anh, V. (2012). Numerical techniques for the variable order time fractional diffusion equation, Appl. Math. Comput., 218, 10861-10870.
10
[11] Yang, X. J. and Tenreiro Machado, J. A. (2017). A new fractional operator of variable order: application in the description of anomalous diffusion equation, Physica A: Statistical Mechanics and its Applications, 481, 276-283.
11
[12] Dahaghin, M. Sh. and Hassani, H. (2017). An optimization method based on the generalized polynomials for nonlinear variable-order time fractional diffusion-wave equation, Nonlinear Dyn., 88 (3), 1587-1598.
12
[13] Li, X. Y. and Wu, B. (2015). A numerical technique for variable fractional functional boundary value problems, Appl. Math. Lett., 43, 108-113.
13
[14] Chen, C. M., Liu, F., Anh, V. and Turner, I. (2010). Numerical schemes with high spatial accuracy for a variable-order anomalous subdiffusion equation, SIAM J. Sci. Comput., 32 (4), 1740-1760.
14
[15] Bhrawy, A. H. and Zaky, M. A. (2017). An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations, Appl. Numer. Math., 11, 197-218.
15
[16] Zhang, H., Liu, F., Phanikumar, M, S. and Meerschaert, M. M. (2013). A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model, Comput. Math. Appl., 66, 693-701.
16
[17] Chen, S., Liu, F. and Burrage, K. (2014). Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media, Comput. Math. Appl., 68 (12), 2133-2141.
17
[18] Chen, Y. M., Wei, Y. Q., Liu, D. Y., Boutat, D. and Chen, X. K. (2016). Variable-order fractional numerical differentiation for noisy signals by wavelet denoising, J. Comput. Phys., 311, 338-347.
18
[19] Zhao, X., Sun, Z. Z. and Karniadakis, G. E. (2015). Second-order approximations for variable order fractional derivatives: Algorithms and applications, J. Comput. Phys., 293, 184-200.
19
[20] Li, X. Y. and Wu, B. (2015). A numerical technique for variable fractional functional boundary value problems, Appl. Math. Lett., 43, 108-113.
20
[21] Jia, Y. T., Xu, M. Q. and Lin, Y. Z. (2017). A numerical solution for variable order fractional differential equation, Appl. Math. Lett., 64, 125-130.
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[22] Atangana, A. (2015). On the stability and convergence of the time-fractional variable order telegraph equation, J. Comput. Phys., 293, 104-114.
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[23] Chen, C. M. (2013). Numerical methods for solving a two-dimensional variable-order modified diffusion equation, Appl. Math. Comput., 225, 62-78.
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[24] Zhou, F. and Xu, X. (2016). The third kind Chebyshev wavelet collocation method for solving the time-fractional convection diffusion equations with variable coefficients, Appl. Math. Comput., 280, 11-29.
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[25] Behroozifar, M. and Sazmand, A. (2017). An approximate solution based on Jacobi polynomials for time-fractional convection-diffusion equation, Appl. Math. Comput. 296, 1-17.
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[26] Chen, M. H. and Deng, W. H. (2014). A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation, Appl. Math. Model. 38 (13), 3244-3259.
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35
ORIGINAL_ARTICLE
Existence and Uniqueness of Asymptotic Periodic Solution in the Cyclic Four Species Predator- Prey Model
In the past decades, in the area of mathematical ecology, the dynamical properties occurring in the predator-prey models have been studied. Moreover, the stability and boundedness of the solution for population model such as cyclic, delayed and etc. have been studied. In the present paper, a nonlinear cyclic predator-prey system with sigmoidal type functional response is analyzed. Indeed, a model of four species predator-prey system has been investigated and the sufficient conditions for stability and boundedness of the solutions of predator-prey system have been presented. For this purpose, the differential inequality theory is employed and finally, by constructing a suitable Lyapanov function the existence and uniqueness of asymptotically periodic solution which is globally asymptotically stable are proved.
https://jamm.scu.ac.ir/article_13857_80b5781f975dd4809a792eaaa0a89976.pdf
2019-03-21
143
160
10.22055/jamm.2018.24716.1540
Predator-prey
Functional response
Sigmoidal
Lyapanov function
Stability
Mohammad Hossein
Rahmani Doust
mh.rahmanidoust@gmail.com
1
Department of Mathematics, University of Neyshabur, Neyshabur, Iran
LEAD_AUTHOR
Farzaneh
Motahari Nasab
2
Department of Mathematics, University of Neyshabur, Neyshabur, Iran
AUTHOR
[1] Rahmani Doust, M.H. and Gholizade, S. (2014). An analysis of the modified Lotka-Volterra predator-prey equations, Gen. Math. Notes, 25, 2, 1-5.
1
[2] Rahmani Doust, M.H. and Gholizade, S. (2014). The lotka- Volterra predator-prey equations, Caspian Journal of Mathematical Sciences, 3(1), 227-231.
2
[3] Rahmani Doust, M. H. (2015). The efficiency of harvest factor; Lotka-Volterra predator-prey model, Caspian Journal of Mathematical Sciences, 4(1), 51-59.
3
[4] Li Y. K., and Ye, Y. (2013). Multiple positive almost periodic solutions to an impulsive non-autonomous Lotka-Volterra predator-prey system with harvesting terms, common. Non-linear sci. Number. Simul. 18, 3190-3201.
4
[5] XU, C. and Zhang, Q. (2014) Permanence and asymptotically periodic solution for a cyclic predator-prey model with sigmoidal type functional response, Wseas transactions on Systems, 13, 668-678.
5
[6] Yang, Y. and Chen, W.C. (2006). Uniformly strong persistence of a nonlinear asymptotically periodic multispecies competition predator-prey system with general functional response, Appl. Math. Comput. 183, 423-426.
6
[7] Yuan, R., (1992). Existence of almost periodic solutions of functional differential equations of neutral type, J. Math. Anal. Appl. 165, 524-538.
7
[8] Murray, J.D. (2002). Mathematical biology (Vol. 1: An Introduction). Springer, New York.
8
[9] Murray, J.D. (2003). Mathematical biology (Vol. 2: Spatial models and biomedical applications). Springer, New York.
9
[10] Cornin, J. (2008). Ordinary differential equations. Third Edition, Chapman & Hall/CRC.New York.
10
[11] Perco, L. (2001). Differential equations and dynamical systems. Springer, New York.
11
[12] Miller, R.K. and Michel A.N. (1982). Ordinary differential equations, Academic press, New York.
12
[13] رحمانی دوست، محمدحسین، (1392). معادلات دیفرانسیل و اکولوژی جلد اول، انتشارات نوروزی، گرگان. دانشگاه نیشابور.
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[14] Montes F. de Oca, and Vivas, M. (2006). Extinction in a two dimensional Lotka-Volterra system with infinite delay. Nonlinear Anal. Real World Appl. 7, 1042-1047.
14
ORIGINAL_ARTICLE
Modeling and solving problems of optimal control of hybrid systems with autonomous switches using particle swarm optimization and direct transcription methods
In this paper, it is focused on a specific category of hybrid optimal control problems with autonomous systems. Because of existence of continuous and discrete dynamic, the numerical solutions of hybrid optimal control are not simple. The numerical direct and indirect methods presented for solving optimal control of hybrid systems have drawbacks due to sensitivity to initial guess and the inability of finding a global minimum solution. Meta-heuristic methods have been proposed. In this method, Meta-heuristic methods (e.g. using PSO) is used to determine the mode sequence, and by the attention to the prescribed the mode sequence, a problem with a determinate mode sequence is obtained, and then the switching times, the optimal value of the target function and the state and control are estimated by using the direct approach. Actually, using the proposed model, we will eliminate basic challenges of solving optimal control of hybrid autonomous systems problems, in which the number of switches and mood sequence are unknown .Finally, numerical results for solving an example presented.
https://jamm.scu.ac.ir/article_14237_3c0aedc9d1bfc2cc60423eca0fae53ab.pdf
2019-03-21
120
142
10.22055/jamm.2019.25112.1559
optimal control
hybrid system
autonomous switch
heuristic methods
Particle Swarm Algorithm
Zeynab
Dalvand
z_dalvand@sbu.ac.ir
1
Department of Industrial and Applied Mathematics, Shahid Beheshti University, Tehran, Iran
AUTHOR
Mostafa
Shamsi
m_shamsi@aut.ac.ir
2
Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran
AUTHOR
Masoud
Hajarian
m_hajarian@sbu.ac.ir
3
Department of Industrial and Applied Mathematics, Shahid Beheshti University, Tehran, IRAN
LEAD_AUTHOR
[1] Witsenhausen, H. (1966). A class of hybrid-state continuous-time dynamic systems. IEEE Transactions on Automatic Control, 11, 161-167.
1
[2] Liberzon, D. (2012). Switching in systems and control. Springer Science & Business Media.
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[3] Eich-Soellner, E. and Führer, C. (1998). Numerical methods in multibody dynamics, Stuttgart: Teubner.
3
[4] Böhme, T. J. and Frank, B. (2017). Hybrid systems and hybrid optimal control. In Hybrid Systems, Optimal Control and Hybrid Vehicles Springer, Cham, 79-115.
4
[5] Lin, H. and Antsaklis, P. J. (2014). Hybrid dynamical systems: An introduction to control and verification. Foundations and Trends in Systems and Control, 1, 1-172
5
[6] Wu, X., Zhang, K. and Sun, C. (2015). Constrained optimal control of switched systems and its application. Optimization, 64, 539-557.
6
[7] Liu, X. and Stechlinski, P. (2017). Hybrid and Switched Systems. In Infectious Disease Modeling, Springer, Cham, 21-39.
7
[8] Hamann, P. and Mehrmann, V. (2008). Numerical solution of hybrid systems of differential-algebraic equations. Computer Methods in Applied Mechanics and Engineering, 197, 693-705.
8
[9] Yu, M., Wang, L, Chu, T. and Xie, G. (2004, December). Stabilization of networked control systems with data packet dropout and network delays via switching system approach. In Decision and Control, 2004. CDC. 43rd IEEE Conference on, 4, 3539-3544.
9
[10] Kröger, T. (2010). Hybrid switched-system control for robotic systems. In On-Line Trajectory Generation in Robotic Systems, Springer, Berlin, Heidelberg, 105-135.
10
[11] Filippov, A. F. (1960). Differential equations with discontinuous right-hand side. Matematicheskii sbornik, 93, 99-128.
11
[12] Xu, X. and Antsaklis, P. J. (2004). Optimal control of switched systems based on parameterization of the switching instants. IEEE transactions on automatic control, 49(1), 2-16.
12
[13] Kirk, D. E. (2012). Optimal control theory: an introduction. Courier Corporation.
13
[14] Flaßkamp, K. Murphey, T. and Ober-Blöbaum, S. (2012, December). Switching time optimization in discretized hybrid dynamical systems. In Decision and Control (CDC), 2012 IEEE 51st Annual Conference on IEEE, 707-712.
14
[15] Passenberg, B. Caines, P. E. Sobotka, M. Stursberg, O. and Buss, M. (2010, December). The minimum principle for hybrid systems with partitioned state space and unspecified discrete state sequence. In Decision and Control (CDC), 2010 49th IEEE Conference on, IEEE, 6666-6673.
15
[16] Kennedy, J. (2011). Particle swarm optimization. In Encyclopedia of machine learning, Springer US, 760-766.
16
[17] Clerc, M. and Kennedy, J. (2002). The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE transactions on Evolutionary Computation, 6, 58-73
17
[18] Borrelli, F. (2003). Constrained optimal control of linear and hybrid systems, 290. Springer.
18
[19] Eberhart, R. and Kennedy, J. (1995, October). A new optimizer using particle swarm theory. In Micro Machine and Human Science,Proceedings of the Sixth International Symposium on, 39-43, IEEE
19
[20] Krink, T. VesterstrOm, J.S. and Riget, J. (2002). Particle swarm optimisation with spatial particle extension. In Evolutionary Computation, 2002. CEC'02. Proceedings of the 2002 Congress on, 2, 1474-1479. IEEE.
20
[21] Eberhart, R. Simpson, P. and Dobbins, R. (1996). Computational intelligence PC tools. Academic Press Professional, Inc.
21
[22] Fulcher, J. (2008). Computational intelligence: an introduction. In Computational intelligence: a Compendium, Springer, Berlin, Heidelberg, 3-78.
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[23] Betts J, T. (2010), Practical methods for optimal control and estimation using nonlinear programming, 19, Siam.
23
[24] Passenberg, B. (2012). Theory and algorithms for indirect methods in optimal control of hybrid systems. PhD thesis, Technical University of Munich.
24
[25] Passenberg, B. and Stursberg, O. (2019). Graph search for optimizing the discrete location sequence in hybrid optimal control. IFAC Proceedings Volumes, 42, 304-309.
25
ORIGINAL_ARTICLE
On α-semi Krull modules
In this article we introduce and study the concept of -almost semi Artinian modules. Using this concept we extend some of the basic results of -almost Artinian modules to -almost semi Artinian modules. Moreover we introduce and study the concept of -semi Krull modules. We show that if M is an -semi Krull module, then the perfect dimension of M is either or +1.
https://jamm.scu.ac.ir/article_14241_68d9f819cea933e405c96d022e71034e.pdf
2019-03-21
161
180
10.22055/jamm.2019.26269.1602
Krull dimension
α -semi Krull module
α-almost Noetherian module
Noetherian dimension
α-short module
Maryam
Davoudian
m.davoudian@scu.ac.ir
1
Department of mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran
LEAD_AUTHOR
[1] Gordon, R. and Robson, J.C. (1973). Krull dimension, Mem. Amer. Math. Soc., 133.
1
[2] Krause, G. (1972). On fully left bounded left Noetherian rings, J. Algebra, 23, 88-99.
2
[3] Lemonnier, B. (1972). Deviation des ensembless etgroupes totalement ordonnes, Bull. Sci. Math., 96, 289-303.
3
[4] Chambless, L. (1980). N-Dimension and N-critical modules, Application to Artinian modules, Comm. Algebra, 8, 1561-1592.
4
[5] Karamzadeh, O.A.S. (1974). Noetherian-dimension, Ph.D. thesis, Exeter University, England, UK.
5
[6] Karamzadeh, O.A.S. and Motamedi, M. (1994). On -DICC modules, Comm. Algebra, 22, 1933-1944.
6
[7] Karamzadeh, O.A.S. and Sajedinejad, A.R. (2001). Atomic modules, Comm. Algebra, 29, 2757-2773.
7
[8] Karamzadeh, O.A.S. and Sajedinejad, A.R. (2002). On the Loewy length and the Noetherian dimension of Artinian modules, Comm. Algebra, 30, 1077-1084.
8
[9]. Kirby, D. (1990). Dimension and length for Artinian modules, Quart. J. Math. Oxford, 41, 419-429.
9
[10] Hashemi, J., Karamzadeh, O.A.S. and Shirali, N. (2009). Rings over which the Krull dimension and the Noetherian dimension of all modules coincide, Comm. Algebra, 37, 650-662.
10
[11] Karamzadeh, O.A.S. and Shirali, N. (2004). On the countability of Noetherian dimension of Modules, Comm. Algebra, 32, 4073-4083.
11
[12] Davoudian, M. (2018). Modules with chain condition on non-finitely generated submodules, Mediterr. J. Math., 15, 1-12.
12
[13] Davoudian, M. (2016). Dimension of non-finitely generated submodules, Vietnam J. Math., 44, 817-827.
13
[14] Davoudian, M. (2017). Modules satisfying double chain condition on non-finitely generated submodules have Krull dimension, Turk. J. Math., 41, 1570-1578.
14
[15] Davoudian, M. and Ghayour, O. (2017). The length of Artinian modules with countable Noetherian dimension, Bull. Iranian Math. Soc., 43, 1621-1628.
15
[16] Davoudian, M. (2017). On -quasi short modules, Int. Electron. J. Algebra, 21, 91-102.
16
[17] Davoudian, M. and Shirali, N. (2016). On -tall modules, Bull. Malays. Math. Sci. Soc., 41, 1739-1747.
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[18] Davoudian, M. (2015). Perfect dimension, The 46th Annual Iranian Mathematics Conference, Yazd University, Yazd, Iran.
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[19] Albu, T. and Vamos, P. (1998). Global Krull dimension and Global dual Krull dimension of valuation Rings, Lecture Notes in Pure and Applied Mathematics, 201, 37-54.
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[20] Albu, T. and Smith, P.F. (1999). Dual Krull dimension and duality, Rocky Mountain J. Math., 29, 1153-1164.
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[21] Albu, T. and Smith, P.F. (1996). Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki Theorem (I), Math. Proc. Cambridge Philos. Soc., 120, 87-101.
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[22] Albu, T. and Smith, P.F. (1997). Localization of modular lattices, Krull dimension, and the Hopkins-Levitzki Theorem (II), Comm. Algebra, 25, 1111-1128.
22
[23] Davoudian, M. (2012). On perfect dimension of modules, Ph. D. thesis, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
23
[24] Davoudian, M. and Karamzadeh, O.A.S. (2016). Artinian serial modules over commutative (or left Noetherian) rings are at most one step away from being Noetherian, Comm. Algebra, 44, 3907-3917.
24
[25] Hein, J. (1979). Almost Artinian modules, Math. Scand., 45, 198-204.
25
[26] Bilhan, G. and Smith P.F. (2006). Short modules and almost Noetherian modules, Math. Scand., 98, 12-18.
26
[27] Davoudian, M., Karamzadeh O.A.S. and Shirali N. (2014). On -short modules, Math. Scand., 114 (1), 26-37.
27
[28] Davoudian, M., Halali, A. and Shirali, N. (2016). On -almost Artinian modules, Open Math. 14, 404-413.
28
[29] Davoudian, M. On -semi short modules, Journal of Algebric system, to appear.
29
[30] Anderson, F.W. and Fuller, K.R. (1992). Rings and categories of modules, Springer-Verlag.
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[31] McConell, J.C. and Robson, J.C. (1987). Noncommutative Noetherian Rings, Wiley-Interscience, New York.
31
ORIGINAL_ARTICLE
Non-Archimedean stability of nonhomogeneous second order linear differential equations
Let be a non-Archimedean normed space of real numbers. In this paper, we prove the Hyers-Ulam stability of nonhomogeneous second order linear differential equations with non-constant coefficients, where are given continuous functions, in the non-Archimedean normed space . In this paper, we prove the Hyers-Ulam stability of nonhomogeneous second order linear differential equations with non-constant coefficients, where are given continuous functions, in the non-Archimedean normed space .
https://jamm.scu.ac.ir/article_14242_82e39c05f86e3d9365b664ef3b739891.pdf
2019-03-21
181
191
10.22055/jamm.2019.22960.1472
Hyers-Ulam stability
Linear Differential Equations
Non-Archimedean norm
Hamid
Majani
majani.hamid@gmail.com
1
Department of mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran.
LEAD_AUTHOR
[1] Czerwik, S. (2002). Functional Equations and Inequalities in Several Variables, World Scientific, Singapore.
1
[2] Hyers, D.H., Isac, G. and Rassias, T.M. (1998). Stability of Functional Equations in Several Variables, Birkhäuser, Boston.
2
[3] Sahoo, P.K. and Kannappan, P. (2011). Introduction to Functional Equations, CRC Press, Boca Raton.
3
[4] Obłoza, M. (1993). Hyers stability of the linear differential equation, Rocz. Nauk.-Dydakt. Pr. Mat. 13, 259-270.
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[5] Obłoza, M. (1997). Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocz. Nauk.-Dydakt. Pr. Mat. 14, 141-146.
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[6] Alsina, C and Ger, R. (1998). On some inequalities and stability results related to the exponential function, J. Inequal. Appl. 2, 373-380.
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[7] Găvruţa, P., Jung, S-M. and Li, Y. (2011). Hyers-Ulam stability for second-order linear differential equations with boundary conditions, Electronic. J. Differ. Equ., 801-5.
7
[8] Jung, S-M. (2004). Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett. 17, 1135-1140.
8
[9] Jung, S-M. (2006). Hyers-Ulam stability of linear differential equations of first order, II, Appl. Math. Lett. 19, 854-858.
9
[10] Jung, S-M. (2006). Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients, J. Math. Anal. Appl. 320, 549-561.
10
[11] Miura, T., Oka, H., Takahasi, S-E. and Niwa, N. (2007). Hyers-Ulam stability of the first order linear differential equation for Banach space-valued holomorphic mappings, J. Math. Inequal. 3, 377-385.
11
[12] Popa, D. and Raşa, I. (2011). On the Hyers-Ulam stability of the linear differential equation, J. Math. Anal. Appl. 381, 530-537.
12
[13] Popa, D. and Raşa, I. (2012). Hyers-Ulam stability of the linear differential operator with non-constant coefficients, Appl. Math. Comput. 219, 1562-1568.
13
[14] Rus, I.A. (2009). Ulam stability of ordinary differential equations, Stud. Univ. Babeş–Bolyai, Math. 54, 125-134.
14
[15] Wang, G., Zhou, M. and Sun, L. (2008). Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett. 21, 1024-1028.
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[16] Alqifary, Q.H. and Jung, S-M. (2014). On the Hyers-Ulam stability of differential equations of second order, Abstr. Appl. Anal., Article ID 483707.
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[17] Cîmpean, D.S. and Popa, D. (2010). On the stability of the linear differential equation of higher order with constant coefficients, Appl. Math. Comput. 217, 4141-4146.
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[18] Ghaemi, M.B., Gordji, M.E., Alizadeh and B, Park, C. (2012). Hyers-Ulam stability of exact second-order linear differential equations, Adv. Differ. Equ., Article ID 36.
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[19] Li, Y. and Shen, Y. (2010). Hyers-Ulam stability of linear differential equations of second order, Appl. Math. Lett. 23, 306-309.
19
[20] Javadian, A. (2015). Approximately n-order linear differential equations,International Journal of Nonlinear Analysis and Applications, 6(1), Page 135-139.
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[21] S. Shagholi, M. Eshaghi Gordji and M. Bavand Savadkouhi, (2011) Stability of ternary quadratic derivation on ternary Banach algebras, J. Comput. Anal. Appl. 13, 1097–1105.
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[22] Hensel, K. (1899). Uber eine neue begründung der theorie der algebraischen zahlen, Jahresbericht der Deutschen Mathematiker-Vereinigung 6, 83–88.
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[23] Bachman, G. (1964). Introduction to P-Adic Numbers and Valuation Theory, Academic Press inc. (London) LTD.
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[24] Khrennikov, A. (1997). Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer Academic Publishers, Dordrecht.
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[25] Mahler, K. (1981). p-adic numbers and their functions, Cambridge University Press.
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[26] Kreyszig, E. (1979). Advanced Engineering Mathematics, 4th edition. Wiley, New York.
26