J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2019.12908.1252 Research Paper On the moments of order statistics from the standard two-sided power distribution On the moments of order statistics from the STSP distribution Akhter Zuber Department of Statistics, University of Delhi, Delhi 110007, India MirMostafaee S.M.T.K. Department of Statistics, University of Mazandaran, Babolsar, Iran. Athar Haseeb Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah, KSA. 01 12 2019 7 4 381 398 30 03 2019 12 09 2019 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3645.html

In this paper, we obtain  new explicit expressions for the single and product moments of order statistics from the standard two-sided power (STSP) distribution. These expressions can be used to compute the means, variances and the covariances of order statistics from the STSP distribution. We also have a glance at the application of the results  to the lifetimes of the coherent systems.  Two real data examples are given to illustrate the flexibility of the STSP distribution.

Coherent systems explicit expressions product moments standard two-sided power distribution
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2019.13987.1300 Research Paper Solving two-dimensional nonlinear mixed Volterra Fredholm integral equations by using rationalized Haar functions in the complex plane Two-dimensional mixed Volterra Fredholm integral equations Erfanian Majid Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran Zeidabadi Hamed Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran 01 12 2019 7 4 399 416 07 08 2019 19 09 2019 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3646.html

We present a method for calculating the numerical approximation of the   two-dimensional mixed Volterra Fredholm integral equations, using the properties of the rationalized Haar (RH) wavelets and the matrix operator.  Attaining this purpose, first, an operator and then an orthogonal projection should be defined. Regarding the characteristics of Haar wavelet, we solve the integral equation without using common mathematical methods. An upper bound and the convergence of the mentioned method have been proved, by using the Banach fixed point. Moreover, the rate of the convergence  method is  \$O(n(2q) ^n)\$. Finally, several examples of different kinds of functions are presented and solved by this method.

Nonlinear 2D mixed Volterra Fredholm integral equation‎ ‎Haar Wavelet‎ ‎Error estimation
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2019.13057.1257 Research Paper A new iteration method for solving non-Hermitian positive definite linear systems A new iteration method for solving non-Hermitian PD systems Nasabzadeh Hamideh Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P. O. Box 9453155111, Bojnord, Iran 01 12 2019 7 4 337 347 23 04 2019 03 09 2019 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3647.html

In this paper, based on the single-step Hermitian and Skew-Hermitian (SHSS) iteration method [C.-X. Li, S.-L. Wu, A single-step method for non-Hermitian positive definite linear systems, Appl. Math. Lett. 44 (2015) 26-29] and by using the generalized Taylor  expansion method for solving linear systems [F. Toutounian, H. Nasabzadeh, A new method based on the generalized Taylor expansion for computing a series solution of linear systems, Appl. Math. Comput. 248 (2014) 602-609], a new method (GT-SHSS) is introduced to solve non-Hermitian positive definite linear systems. The convergence properties of the new method are discussed. We show that by using suitable parameters, the GT-SHSS iteration method is faster than the corresponding SHSS iteration method. The numerical examples confirm the effectiveness of the new method.

Non-Hermitian HSS method convergence Analysis iterative Method
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2019.13513.1279 Research Paper On the complete convergence of channel hardening and favorable propagation properties in massive-MIMO communications systems On the complete convergence of channel hardening and ... Pourjafari Navid Department of Electrical Engineering, University of Guilan, Rasht, Iran Seifali Harsini Jalil Department of Electrical Engineering, University of Guilan, Rasht, Iran 01 12 2019 7 4 429 443 08 06 2019 08 10 2019 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3671.html

Massive MIMO is known as a core technology for future 5G networks. The major advantage of massive MIMO over the conventional MIMO systems is that different mobile users are allowed to communicate in the same time-frequency resources while the resultant severe interferences can be eliminated using linear signal processing schemes. This is a consequence of the favorable propagation condition and channel hardening which are known as two basic limiting results in mathematics. In this paper we propose new stochastic convergence proofs for these limiting results in terms of the complete convergence in a massive MIMO system with uncorrelated Rayleigh fading.

Massive MIMO systems favorable propagation condition channel hardening stochastic convergence Rayleigh fading
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2019.13259.1265 Research Paper Galerkin finite element method for forced Burgers' equation Galerkin FEM for forced Burgers' equation Kumbhar Sunil S Department of Mathematics, Shivaji University, Kolhapur (Maharashtra), India Thakar Sarita Department of Mathematics, Shivaji University, Kollapur (Maharashtra), India 01 12 2019 7 4 445 467 13 05 2019 23 10 2019 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3709.html

In this paper second order explicit Galerkin finite element method based on cubic B-splines is constructed to compute numerical solutions of one dimensional nonlinear forced Burgers' equation. Taylor series expansion is used to obtain time discretization. Galerkin finite element method is set up for the constructed time discretized form. Stability of the corresponding linearized scheme is studied by using von Neumann analysis. The accuracy, efficiency, applicability and reliability of the present method is demonstrated by comparing numerical solutions of some test examples obtained by the proposed method with the exact and numerical solutions available in literature.

Forced Burgers' equation cubic B-splines Galerkin Finite Element Method Taylor series von Neumann analysis
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2019.14278.1314 Research Paper Stabilized IMLS based element free Galerkin method for stochastic elliptic partial differential equations Stabilized IMLS based element free Galerkin ... Izadpanah Komeil Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran Mesforush Ali Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran Nazemi Ali Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran 01 12 2019 7 4 469 496 31 08 2019 30 09 2019 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3717.html

In this paper, we propose a numerical method to solve the elliptic stochastic partial differential equations (SPDEs) obtained by Gaussian noises using an element free Galerkin method based on stabilized interpolating moving least square shape functions. The error estimates of the method is presented. The method is tested via several problems. The numerical results show the usefulness and  accuracy of the new method.

Element free Galerkin method Stabilized interpolating moving least square Stochastic elliptic equation Error estimates