Mathematical Researches

In this paper we introduce a word-based stream cipher consisting of a chaotic part operating as a chaotic permutation and a linear part, both of which designed on a finite field. We will show that this system can operate in both synchronized and self-synchronized modes. More specifically, we show that in the self-synchronized mode the stream cipher has a receiver operating as an unknown input observer. In addition, we evaluate the statistical uniformity of the output and also show that the system in the self-synchronized mode is much faster and lighter for implementation compared to similar self-synchronized systems with equal key size.

Zobov’s Theorem is one of the theorems which indicate the conditions for the stability of a nonlinear system with specific attraction region. We have applied neural networks to approximate some functions mentioned in Zobov’s theorem in order to find the controller of a nonlinear controlled system whose law in a mathematical manner is difficult to make. Finally, the effectiveness and the applicability of the proposed method are demonstrated through using numerical examples.

Fractional derivatives and integrals are new concepts of derivatives and integrals of arbitrary order. Partial differential equations whose derivatives can be of fractional order are called fractional partial differential equations (FPDEs). Recently, these equations have received special attention due to their high practical applications. In this paper, we survey a rather general case of FPDE to obtain a numerical scheme. The fractional derivatives in the equation are replaced by common definitions such as Grundwald-Letnikov, Riemann-Liouville and Caputo. To improve the numerical solution, partial derivatives inside the equation are discrete using non-standard finite difference scheme. Then, we survey the stability of numerical scheme and prove that the proposed method is unconditionally stable. Eventually, in order to approve the theoretical results, we use the presented technique to solve wave equation with fractional-order, which is very practical and widely used in physics and its branches. Numerical results confirm the findings of the theory and show that this technique is effective.

A new technique to find the optimization parameter in TSVD regularization method is based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter, then the above-mentioned curve is also discrete. In this paper we present a mathematical analysis of this curve, showing that the curve has L-shaped path very similar to that of the classical L-curve and its corner point can represent the optimization regularization parameter very well. In order to find the corner point of the L-curve (optimization parameter), two methods are applied: pruning and triangle. Numerical results show that in the considered test problems the new curve is better than the classical L-curve.

In this paper, a new method to selecting different viewing angles feature vector is introduced to recognition different types of Helicopters. Feature vector 32 components based on characteristics of the shape, Area and a length to describe a binary two-dimensional image was created, shape feature and length feature not only effective but area features effective and were used. New features vector based on the number of components (parameter nf) and the grouping frame (parameter ns ) at 13 various manners were examined and the results showed that nf=400 and ns=5 best mode for the feature vector area marks.

An important issue in survival data analysis is the identification of risk factors. Some of these factors are identifiable and explainable by presence of some covariates in the Cox proportional hazard model, while the others are unidentifiable or even immeasurable. Spatial correlation of censored survival data is one of these sources that are rarely considered in the literatures. In this paper, a spatial survival model is introduced to analyze such kinds of data. Then a simulation method is introduced to study the performance of Cox, frailty and spatial survival models for modeling spatially correlated survival data. Next, the proposed spatial survival model is used to model the time disease of Cercosporiose in olive trees. Finally, results and discussion are presented

In this Paper, We propose a new three-parameter lifetime of Power Series distributions of the Family Gampertz with decreasing, increasing, increasing-decreasing and unimodal Shape failure rate. The distribution is a Compound version of of the Gampertz and Zero-truncated Possion distributions, called the Gampertz-Possion distribution (GPD). The density function, the hazard rate function, a general expansion for moments, the density of the order statistic, and the maen and median deviations of the GPD are derived and studied in detail. The maximum likelihood estimation procedure is discussed and an algorithm EM is provided for estimating the parameters. The asymptotic confidence Intervals for the parameters are also obtained based on asymptotic variance covariance matrix.

In this a‌r‌t‌i‌c‌l‌e we will find n‌e‌c‌e‌s‌s‌a‌r‌y and s‌u‌f‌f‌i‌c‌i‌e‌n‌t c‌o‌n‌d‌i‌t‌i‌o‌n‌s for a f‌i‌x‌e‌d  p‌o‌i‌n‌t f‌r‌e‌e autom‌o‌r‌p‌h‌i‌s‌m (f‌p‌f a‌u‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m) o‌f a g‌r‌o‌u‌p t‌o b‌e a c‌o‌m‌m‌u‌t‌i‌n‌g a‌u‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m. F‌o‌r a given prim‌e ‌ we  f‌i‌n‌d t‌h‌e s‌m‌a‌l‌l‌e‌s‌t o‌r‌d‌e‌r o‌f a n‌o‌n a‌b‌e‌l‌i‌a‌n p-g‌r‌o‌u‌p a‌d‌m‌i‌t‌t‌i‌n‌g a c‌o‌m‌m‌u‌t‌i‌n‌g f‌i‌x‌e‌d p‌o‌i‌n‌t f‌r‌e‌e a‌u‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m. W‌e p‌r‌o‌v‌e t‌h‌a‌t a g‌r‌o‌u‌p o‌f o‌r‌d‌e‌r p³ h‌a‌v‌i‌n‌g a c‌o‌m‌m‌u‌t‌i‌n‌g f‌p‌f autom‌o‌r‌p‌h‌i‌s‌m, h‌a‌s a r‌e‌s‌t‌r‌i‌c‌t‌e‌d s‌t‌r‌u‌c‌t‌u‌r‌e. M‌o‌r‌e‌o‌v‌e‌r w‌e p‌r‌o‌v‌e t‌h‌a‌t i‌f a f‌i‌n‌i‌t‌e g‌r‌o‌u‌p  a‌d‌m‌i‌t‌s a f‌p‌f au‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m o‌f o‌r‌d‌e‌r 4, t‌h‌e‌n t‌h‌e c‌o‌n‌v‌e‌r‌s‌e of Laffey’s result holds in G¹.

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergence, efficiency and simplicity of the method.

Mathematics Subject Classification: 45J05, 65T60

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van der Pol and Bagley-Torvik equations for the application of the method. Illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method. 

Let S be a semigroup with a left multiplier  on S. A new product on S is defined by  related to S and  such that S and the new semigroup S_T have the same underlying set as S. It is shown that if  is injective then where, is the extension of  on  Also, we show that if  is bijective then is amenable if and only if is so. Moreover, if  S completely regular, then is weakly amenable. 

In this paper‎, two inverse problems of determining an unknown source term in a parabolic‎ equation are considered‎. ‎First‎, ‎the unknown source term is ‎estimated in the form of a combination of Chebyshev functions‎. ‎Then‎, ‎a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem‎. ‎For solving the problem‎, ‎the operational matrices of integration and derivation are introduced and utilized to reduce the mentioned problem into the matrix equations which correspond to a system of linear algebraic equations with unknown Chebyshev coefficients‎. Due‎ to ill-posedness of these inverse problems‎, ‎the Tikhonov regularization method with generalized cross validation (GCV) criterion is applied to find stable‎ solutions. ‎Finally‎, some examples are presented to illustrate the efficiency of this numerical method‎. The numerical results show that the proposed method is a reliable method and can give high accuracy approximate solutions.

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new system by using matrix decomposition and linear matrix inequality (LMI) technique. Some numerical examples are given to illustrate the efficiency of our method. 

    In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagrange multipliers identified optimally via the variational theory.This method provides a sequence of function which converges to the exact solution of the problem. This technique does not require any discretization, linearization or small perturbations and therefore reduces the numerical computations a lot. Numerical examples are examined to show the efficiency of the technique. 

In this paper, we will use a modified  variational iteration method (MVIM) for solving an inverse heat conduction problem (IHCP). The approximation of the temperature and the heat flux at  are considered. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional in Euclidian space. Applying this technique, a rapid convergent sequence to the exact solution is produced. Moreover, this method does not require any discretization, linearization or small perturbation, thus it can be considered as an efficient method to solve this problem. To show the strength  and capability of this method, some examples are given

To investigate the spatial error correlation in panel regression models, various statistical hypothesizes and testings have been proposed. This paper, within introduction to spatial panel data regression model, existence of spatial error correlation and random effects is investigated by a joint Lagrange Multiplier test, which simultaneously tests their existence. For this purpose, joint Lagrange Multiplier test statistic and its asymptotic distribution is introduced. A simulation study is performed for considering the size and power of the test this test for joint hypothesizes. Then the application of this test is shown with investigating spatial errors correlation and random effects in data of agricultural product exports of ECO member states. Finally, discussion and conclusion are given.

 This article is concerned with the comparison P-value and Bayesian measure for the variance of Normal distribution with mean as nuisance paramete. Firstly, the P-value of null hypothesis is compared with the posterior probability when we used a fixed prior distribution and the sample size increases. In second stage the P-value is compared with the lower bound of posterior probability when the prior distribution is belonged to a class of reasonable distributions. It was shown that even for fixed sample size the P-value is less than the lower bound. This is not the case for one-sided hypothesis. There is a reconcilability between these two criterion.

Tries are the most popular data structure on strings. We can construct d-ary tries by using strings over an alphabet leading to d-ary tries. Throughout the paper we assume that strings stored in trie are generated by an appropriate memory less source. In this paper, with a special combinatorial approach we extend their analysis for average profiles to d-ary tries. We use this combinatorial approach for studying of average profile, since its probability distribution is unknown. We obtain the probability distribution of depth and the distribution function of height as n is large. These results follow from the study of certain recurrence equations that we solve by a analytic method. 

Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In this paper, the obtained results will be extended to orbital normal form and one of the three aforementioned cases will be discussed. The orbital obtained normal form will be simpler than the previous simplest normal form.