Showing 11 results for Linear
Volume 9, Issue 1 (10-2010)
Abstract
This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, so that the solution of this system yields the Taylor expansion coefficients of the solution function. Then, the performance of the method is evaluated with some examples
Volume 10, Issue 1 (3-2010)
Abstract
In this paper, estimation of survey precision for nonlinear estimators is considered and an equation is presented based on sampling and nonsampling variances. Furthermore, by considering the response error model in surveys and the estimators of variance components, some relations are presented to computation of survey precision for nonlinear estimators. As an application case for the results, two typical data sets are considered and survey precisions of a nonlinear estimator are computed in the both data sets.
Esmaeil Babolian, Ar Vahidi,
Volume 11, Issue 2 (2-2011)
Abstract
In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) for analytic treatment of nonlinear Volterra integral equations, and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations.
Mohsen Mohammadzadeh Darrodi, ,
Volume 12, Issue 1 (11-2012)
Abstract
Spatial generalized linear mixed models are usually used for modeling non-Gaussian and discrete spatial responses. In these models, spatial correlation of the data can be considered via latent variables. Estimation of the latent variables at the sampled locations, the model parameters and the prediction of the latent variables at un-sampled locations are of the most important interest in SGLMM. Often the normal assumption for latent variables is considered just for convenient in practice. Although this assumption simplifies the calculations, in practice, it is not necessarily true or possible to be tested. In this paper, a closed skew normal distribution is proposed for the spatial latent variables. This distribution includes the normal distribution and also remains closed under linear conditioning and marginalization. In these models, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, for maximum likelihood estimation of the model parameters and predictions of latent variables, an approximate algorithm is introduced that is faster than the former method. The performance of the proposed model and algorithm are illustrated through a simulation study.
S Davaeefar, Yadollah Ordokhani,
Volume 13, Issue 2 (7-2013)
Abstract
In this article, the efficient numerical methods for finding solution of the linear and nonlinear Fredholm integral equations of the second kind on base of Bernstein multi scaling functions are being presented. In the beginning the properties of these functions, which are a combination of block-pulse functions on , and Bernstein polynomials with the dual operational matrix are presented. Then these properties are used for the purpose of conversion of the mentioned integral equation to a matrix equation that are compatible to a algebraic equations system. The imperative of the Bernstein multi scaling functions are, for the proper quantitative value of and have a high accuracy and specifically the relative errors of the numerical solutions will be minimum. The presented methods from the standpoint of computation are very simple and attractive and the numerical examples which were presented at the end shows the efficiency and accuracy of these methods.
Kazem Haghnejad Azar,
Volume 13, Issue 2 (7-2013)
Abstract
In this paper, we study the Arens regularity properties of module actions and we extend some proposition from Baker, Dales, Lau and others into general situations. We establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. In 1951 Arens shows that the second dual of Banach algebra endowed with the either Arens multiplications is a Banach algebra, see [1]. The constructions of the two Arens multiplications in lead us to definition of topological centers for with respect to both Arens multiplications. The topological centers of Banach algebras, module actions and applications of them were introduced and discussed in [3, 5, 6, 9, 15, 16, 17, 18, 19, 24, 25]. In this paper, we extend some problems from [3, 5, 6, 16, 22] to the general criterion on module actions with some applications in group algebras. Baker, Lau and Pym in [3] proved that for Banach algebra with bounded right approximate identity, is an ideal of right annihilators in and . In the following, for a Banach , we study the similar discussion on the module actions and for Banach , we show that
Fatemeh Hosseini, Omid Karimi, Mohsen Mohammadzadeh,
Volume 13, Issue 3 (11-2013)
Abstract
Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed models, such that the spatial correlation of the data can be introduced via normal latent variables. The model parameters and the prediction of the latent variables at unsampled locations are of the most important interest in SGLMM by estimating of the latent variables at sampled locations. In these models, since there are the latent variables and non-Gaussian spatial response variables, likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper, a new algorithm is introduced for maximum likelihood estimation of the model parameters and predictions, that is faster than the former method. This algorithm obtains to combine the pseudo maximum likelihood method, the Expectation maximization Gradient algorithm and an approximate method. The performance and accuracy of the proposed model are illustrated through a simulation study. Finally, the model and the algorithm are applied to a case study on rainfall data observed in the weather stations of Semnan in 2012.
Zahra Bahrami, Ali Mahdifar,
Volume 14, Issue 1 (4-2014)
Abstract
This paper aimed to investigate the relation between the coherent states and the wavelets. So first the standard, generalized and nonlinear coherent states were reviewed and then their properties were presented. As an example of the nonlinear coherent states, the coherent states of a two-dimensional harmonic oscillator on a flat space were examined. Using the Dirac notation, the admissibility condition of the mother wavelets was studied. Then by means of the resolution of the identity of the generalized coherent states and the admissibility condition of the wavelets, a systematic method was presented to calculate the polynomial wavelets. At the end, as an illustrative example, the polynomial wavelets were constructed by using the nonlinear coherent states on a flat space.
Milad Rahimi, Mousa Golalizadeh,
Volume 17, Issue 40 (9-2015)
Abstract
Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been under considerations of the researchers in various scientific disciplines including biological sciences. It is usually assumed that the outcomes of these processes
are lied on the Euclidean spaces. However, some data are appeared in physical, chemical and biological phenomena that cannot be considered as the observations in Euclidean spaces due to various features
such as the periodicity of the data. Hence, we cannot analysis them using the common mathematical methods available in Euclidean spaces. In addition, studying and analyzing them using common linear statistics are not possible. One of these typical data is the dihedral angles that are utilized to identifying, modeling and predicting the proteins backbones. Because these angles are representatives of points on the surface of torus, it seems that proper statistical modeling of diffusion processes on the torus could be of a great help for the research activities on dynamic molecular simulations in predicting the proteins backbones. In this article, using the Riemannian distance on the torus, the stochastic differential equations to describe the Brownian motions and Ornstein-Uhlenbeck processes on this geometrical objects will be derived. Then, in order to evaluate the proposed models, the statistical simulations will be performed using the equilibrium distributions of aforementioned stochastic processes. Moreover, the link between the gained results with the available concepts in the non-linear statistics will be highlighted.
Azhdar Soleymanpour Bakefayat, Nader Dastranj,
Volume 17, Issue 40 (9-2015)
Abstract
In this paper, We Stabilize a subclass of nonlinear control systems by using neural networks and Zobov's theorem. Zobov’s Theorem is one of the theorems which indicates the conditions for the stability of a nonlinear systems with specific attraction region. We applied neural networks to approximate some functions mentioned in Zobov’s theorem, So as to find the controller of a nonlinear controlled system which is difficult task to find its law in mathematic manner. also we apply nelder meed optimization method to learning neural network. Finally, the effectiveness and the applicability of the proposed method are demonstrated by using some numerical examples.
Volume 18, Issue 44 (10-2009)
Abstract
Hybrid of rationalized Haar functions are developed to approximate the solution of the differential equations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. These properties together with the Newton-Cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.