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Kosmos
Astronomia Astrofizyka
Inne

Kultura
Sztuka dawna i współczesna, muzea i kolekcje

Metoda
Metodologia nauk, Matematyka, Filozofia, Miary i wagi, Pomiary

Materia
Substancje, reakcje, energia
Fizyka, chemia i inżynieria materiałowa

Człowiek
Antropologia kulturowa Socjologia Psychologia Zdrowie i medycyna

Wizje
Przewidywania Kosmologia Religie Ideologia Polityka

Ziemia
Geologia, geofizyka, geochemia, środowisko przyrodnicze

Życie
Biologia, biologia molekularna i genetyka

Cyberprzestrzeń
Technologia cyberprzestrzeni, cyberkultura, media i komunikacja

Działalność
Wiadomości | Gospodarka, biznes, zarządzanie, ekonomia

Technologie
Budownictwo, energetyka, transport, wytwarzanie, technologie informacyjne

Asian Journal of Mathematics & Statistics

An algorithmic solution of constrained linear programming problems is presented.
The method is based on the Quick Convergent Inflow Algorithm (QCIA) used in
solving linear programming problems but considers the effect of segmentation
of the design or feasible regions on the algorithm. A stopping rule based on
the concepts of variance exchange algorithms is proposed. The algorithm converges
to the global optimizer of the objective function as demonstrated using numerical
illustrations.

http://scialert.net/abstract/?doi=ajms.2014.40.59 2014/09/14 - 07:32

New Statistical method on delay differential equation is proposed for growth
rate modeling. The method is compared with two conventional approaches, illustrating
the application on mice tumor growth data. Significance drug treatment effect
is observed through different methods. The proposed method can be applied in
tumor growth data.

http://scialert.net/abstract/?doi=ajms.2014.60.67 2014/09/14 - 07:32

In the present study, we generalize a problem dealing with the minimum distance
between two disjoint, closed and compact subsets of real line. This result asserts
that the disjointness of a closed set and a compact set in a metric space implies
that the distance between these sets is always nonzero.

http://scialert.net/abstract/?doi=ajms.2014.68.69 2014/09/14 - 07:32

The aim of this study is to give upper bounds for ruin probabilities of generalized
risk processes under interest force with homogenous Markov chain claims. Generalized
Lundberg inequalities for ruin probabilities of these processes are derived
by the martingale approach.

http://scialert.net/abstract/?doi=ajms.2014.1.11 2014/03/30 - 11:46

In this study, we propose some new fuzzy directed divergence measure and study its particular cases. We also establish some fuzzy coding theorems. Some of the known results are the particular cases of our proposed divergence measure.

http://scialert.net/abstract/?doi=ajms.2014.12.20 2014/03/30 - 11:46

Calcium, a second messenger for signal transduction in cells plays an important role in almost every cell of our human body. In oocytes calcium plays a significant role in oocyte maturation. In the process of reproduction calcium concentration is regulated at high levels in oocytes through various mechanisms so as to meet the requirements of oocytes maturation. Thus modelling of calcium distribution in oocytes can help us in understanding this mechanism in a better way. Here an attempt has been made to develop a finite element model to study calcium distribution in oocytes. The model incorporates the parameters like diffusion coefficient, Na+/K+ pump, Na+/Ca2+ exchanger and buffers like BAPTA and EGTA. The proposed model is solved numerically using appropriate initial and boundary conditions. The program has been developed in MATLAB 7.10 for the entire problem and simulated on a 64 bit machine to compute the numerical results.

http://scialert.net/abstract/?doi=ajms.2014.21.28 2014/03/30 - 11:46

This manuscript is a description of pre A*-Homomorphism and established the concept of kernel of pre A*-homomorphism and prove some theorems on these pre A*-homomorphisms, establish its useful theorems. It distinguish theorems related with these concepts of pre A*-homomorphism.

http://scialert.net/abstract/?doi=ajms.2014.29.34 2014/03/30 - 11:46

This study dealt with the queues system in one of the industrial workshops
which it was composed of four queues, the first and the fourth queues were connected
in series, while the second and the third queues were connected in parallel
to repair defective machines such that the repairing process included two parts,
it were electric and mechanic parts. The first stage was the dismantling of
the machine into two parts with the time represented by a continuous random
variable T1. The continuous random variables T2 and T3
represented the time of the repairing stages which it were electrical and mechanical
repairing respectively and the continuous random variable T4 represented
a compile-time of the machine after repairing it. All the random variables had
a normal distribution with different means and variances. The joint probability
distribution function FT(t) was obtained as multiple linear regression
form by calculating the probability density function f(Ti), i = 1,
2, 3, 4 where T is a continuous random variable represented the whole time repairs
in the system and t represented a maximum value of T. On the other hand the
probability that the system will be failure or defective at T>t is equal
to (1-FT(t)) can be computed and predicted its value easily by using
the multiple linear regression form of FT(t) without performed many
mathematical processes.

http://scialert.net/abstract/?doi=ajms.2014.35.39 2014/03/30 - 11:46

A common problem in autoregressive regression models is outliers, which produces undesirable effects on the least squares estimators. Many regression estimation techniques have been suggested to deal with this problem. The majority of such techniques are developed from the classical least squares. Some other robust approaches have been investigated in the regression case both on theoretical and empirical grounds. However, the behavior of these alternative methods has not received more attention in the context of time series. In this study, we present a comparative simulation study for three robust alternatives to the least squares estimator under innovation and additives outliers. The empirical study indicated that, the Reweighted Least Squares estimator (RLS) seems to be very reasonable because of having smaller "total" root normalized absolute bias and "total" root normalized variance. The RLS estimator was recommended as worthy robust alternative to the least squares estimator in the case of autoregressive models with the two kinds of outliers schemes.

http://scialert.net/abstract/?doi=ajms.2013.57.66 2013/07/18 - 16:41

We investigate the asymptotic finite properties of estimator to ascertain its
behaviour from small to large sample when there is presence of heteroscedasticity.
We explore full Bayesian experiments with Generalized Least Squares estimator
incorporating heteroscedastic error structure. Estimates were obtained through
Markov Chain Monte Carlo approach that draws simulated sample of parameters
from joint posterior distribution. Burnin and thinning were chosen as 1000 and
5, respectively. Bias and Mean Squares Error criteria were used to evaluate
finite properties of the estimator. We choose the following sample sizes: 25,
50, 100, 200, 500 and 1000. Thus, 10,000 simulations with varying degree of
heteroscedasticity were carried out. This is subjected to the level of convergence.
Bias and Minimum Mean Squares Error criteria revealed improving performance
asymptotically regardless of the degree of heteroscedasticity. Considering heteroscedasticity
at scale 0.3, from the results, we observed an increase in sample sizes: 25,
50, 100, 200, 500 and 1000 led to decrease in mean squares error: 0.068436,
0.033896, 0.015071, 0.006772, 0.001935 and 0.00101, respectively. This implies
efficiency of the estimator asymptotically, ditto for all other scales.

http://scialert.net/abstract/?doi=ajms.2013.67.75 2013/07/18 - 16:41

Solving nonlinear ordinary differential equations is relevant because phenomena on the frontiers of modern sciences are often nonlinear in nature; therefore this article proposes Perturbation Method (PM) to solve nonlinear problems. As case study PM is employed to obtain a handy approximate solution for Gelfand’s differential equation which governing combustible gas dynamics. Comparing figures between approximate and exact solutions, it is shown that PM method result extremely efficient.

http://scialert.net/abstract/?doi=ajms.2013.76.82 2013/07/18 - 16:41

Although, the concept of conditional probability is useful tool in theory as
well as in applications, some configurations are not considered. This paper
suggests some ideas showing the effect of the events order in the application
of conditional probability and provides some results allowing the calculation
of the probability of any event in a given sample space. The results have been
illustrated by numerical examples.

http://scialert.net/abstract/?doi=ajms.2013.83.88 2013/07/18 - 16:41

In this study, a class of product-cum-dual to product estimators have been
proposed for estimating finite population mean of the study variate. The bias
and mean square error of the proposed estimator have been obtained. The asymptotically
optimum estimator (AOE) in this class has also been identified along with its
approximate bias and mean square error. Theoretical and empirical studies have
been done to demonstrate the superiority of the proposed estimator over the
other estimators.

http://scialert.net/abstract/?doi=ajms.2013.1.11 2012/11/22 - 16:40

The theory of approximation is a very extensive field which has various applications
in pure and applied mathematics. Broadly speaking, Signals are treated as functions
of one variable and images are represented by functions of two variables. The
present study deals with the new theorem on the degree of approximation of a
Signal associated with Fourier series and belonging to the generalized weighted
W(Lr, ξ(t)) (r≥1, t>0)- class by product summability (C,
1) (E, q) method, where ξ (t) is non-negative and non-decreasing function
of t. The main result obtained in this study generalizes some well-known results
in this direction. The class W(Lrξ(t)) (r≥1, t>0), we
have used here in the main theorem includes the Lip (ξ(t)), Lip (α,
r) and Lip α classes.

http://scialert.net/abstract/?doi=ajms.2013.12.22 2012/11/22 - 16:40

This study characterizes the distinct partial orders ≤* and ≤⊕
taking place on a Pre A*-algebra A. As a consequence achieve a result that x≤*y
if and only if y~≤⊕x~ . The Hasse diagrams
are sketched for certain Pre A*-algebras with respect to ≤* as
well as ≤⊕. Further derived equivalent conditions for a Pre A*-algebra
A to be a Boolean algebra or a trivial Pre A*-algebra in terms of the partial
orders ≤* and ≤⊕.

http://scialert.net/abstract/?doi=ajms.2013.23.32 2012/11/22 - 16:40

In this research, we have studied the use of splines to solve lacunary interpolation
problem analytically and applied to the solution of initial and boundary value
problems. The analytical results of this model have been obtained in terms of
convergent series with the theorems for errors estimation. Among a number of
numerical methods used to solve differential equations spline methods provide
an efficient tool.

http://scialert.net/abstract/?doi=ajms.2013.33.42 2012/11/22 - 16:40

Agricultural pests are the insects that feed on crops and damaged them. Most
current agricultural pest control methods focused on chemical insecticides.
Research works have shown that these chemicals have many disastrous consequences.
However, effective control of these pests can be obtained through the use of
living organisms to reduce the density of pest below economic damaging level
and this is refers to as biological pest control. If a mathematical model for
the biological system is provided, then the effects of such pests can be controlled
by the methods of optimal control theory. In this study, the biological control
of agricultural pest system via optimal control theory approach was qualitatively
studied. In an attempt to minimize the pest population below injury level and
stabilize the natural enemies’
population. The system was analysed, equilibrium point for the system was determined,
stability and economic loss free equilibrium was equally established. Numerical
values were employed to check for the validity of the method and the result
was found to be effective.

http://scialert.net/abstract/?doi=ajms.2013.43.51 2012/11/22 - 16:40

This study illustrate some narrative and remarkable properties of 1-quasi-total
graphs. It has been acquired results of various graphs such as regular graphs,
complete graphs, complete bipartite, cycles and chromatic number of 1-quasi-total
graphs.

http://scialert.net/abstract/?doi=ajms.2013.52.56 2012/11/22 - 16:40

The handling of missing data is the difficult problem in longitudinal data analysis. There are broad ranges of methods to handle missing observation in longitudinal data. The comparison of different missing observation handling techniques by Last Observation Carry Forward (LOCF), EM algorithm, Missing at Random (MAR) and Missing not at Random (MNAR) with pattern mixture modeling has been applied on clinical trial data set, studying the effect of drug treatment of metformin with pioglitazone respect to pioglitazone with gliclazide in type 2 diabetes patients for three follow up. It has been found by using the MAR and MNAR approach, that pioglitazone with metformin is more effective to reduce the serum creatinine as compared to pioglitazone with gliclazide.

http://scialert.net/abstract/?doi=ajms.2012.71.81 2012/03/22 - 05:33

Partial least squares regression is a statistical method of modeling relationships between YNxM response variable and XNxK explanatory variables which is particularly well suited for analyzing when explanatory variables are highly correlated. In partial least square part, some model selection criteria are used to obtain the latent variables which are the most relevant variables describing the response variables. In this study, we investigate the performance of Partial Least Squares Regression-the Nonlinear Iterative Partial Least Squares (PLSR-NIPALS), Partial Least Squares Regression-the Variable Importance in the Projection (PLSR-VIP) and the Genetic Algorithms Partial Least Square Regression (GAPLSR) when the fitness function is the Information Complexity Criterion (ICOMP) for model selection. We compared the performance of these methods with real world data and simulation data sets and used the adjusted R square (R2adj) values to quantify the adequacy of the models.

http://scialert.net/abstract/?doi=ajms.2012.82.92 2012/03/22 - 05:33

The multiple linear regression formula of the probability of the averaged daily solar energy reaching a specific location on the earth's surface in a calendar month was obtained with the assumption that the arrival process of clouds and solar energy during the day follows the exponential distribution. This formula enables any user to find out some of the required information such as knowing the maximum probability for the averaged daily solar energy and the amount of the corresponding clouds. In addition, the cumulative distribution functions of this probability was obtained.

http://scialert.net/abstract/?doi=ajms.2012.93.98 2012/03/22 - 05:33

In this study, we have introduced an alternative definition of the basic analogue of a generalization of Fox's H-function in terms of I-function using q-Gamma function. This definition has been employed to obtain several results based on q-Integral. Also some special cases have also been discussed.

http://scialert.net/abstract/?doi=ajms.2012.99.103 2012/03/22 - 05:33

This study examined how six estimation methods of a simultaneous equation model cope with varying degrees of correlation between pairs of random deviates using the Average of parameter estimates. A two-equation simultaneous system was considered with assumed covariance matrix. The model was structured to have a mutual correlation between pairs of random deviates, which is a violation of the assumption of mutual independence between pairs of such random deviates. The correlation between the pairs of normal deviates were generated using three scenarios of r = 0.0, 0.3 and 0.5. The performances of various estimators considered were examined at various sample sizes, correlation levels and 50 replications. The sample size, N = 20, 25, 30 each replicated 50 times was considered. Using the Average of parameter estimates criterion, 2-3SLIML are the best estimators followed by Full Information Maximum Likelihood and by Ordinary Least Squares for the three cases studied. Also, as the sample size increases from 20 to 25 and 30, 2-3SLIML still performed the best (i.e., 2-3SLIML is consistent).

http://scialert.net/abstract/?doi=ajms.2012.39.49 2012/02/28 - 00:46

In this study, Homotopy Perturbation Method (HPM) is used to provide an approximate solution to the Blasius nonlinear differential equation that describes the behaviour of a two-dimensional viscous laminar flow over a flat plate. Comparing results between approximate and exact solutions shows that HPM method is extremely efficient, if the initial guess is suitably chosen.

http://scialert.net/abstract/?doi=ajms.2012.50.59 2012/02/28 - 00:46

A graph G is an interval graph if there is a one-one correspondence between its vertices and a family I of intervals, such that two vertices in G are adjacent if and only if their corresponding intervals overlap. In this context, the family I of intervals is referred to as an interval model of G. Recently found minimum independent neighbourhood set of an interval graph. In this study, we exploit the Maximal Independent Neighbourhood Set (MLINS) of an interval graphs. This problem includes finding a maximal independent set, a shortest path between any two vertices in G in terms of directed network.

http://scialert.net/abstract/?doi=ajms.2012.60.64 2012/02/28 - 00:46

This study has discussed various types of pair of non-commuting mappings which were frequently used in arena of Fixed Point Theory. Further, relationship has been established among them with examples and comparison table has been given.

http://scialert.net/abstract/?doi=ajms.2012.65.70 2012/02/28 - 00:46

This paper is a study on Complex integrable lattice functions and μ-free lattices. It initiates the concepts of complex integrable lattice function, positive and negative separations of μ and establishes the separation properties of complex integrable lattice functions. Also it introduce the concepts of free lattice, μ-free lattice and demonstrate that μ is a measure on β, μ is a free lattice in β, β is a μ-free lattice of σ (L). Also it was defined the concept almost free lattice and finally confirm that every almost free lattice is a complex integrable lattice function and a σ-additive.

http://scialert.net/abstract/?doi=ajms.2012.1.20 2012/01/08 - 03:32

Simulation studies involving linear and quadratic functional forms of continuous covariates were carried out under various combinations of two baseline hazards. These include combination of two Weibull baseline hazards, combination of two Lognormal baseline hazards and combination of Weibull and Lognormal baseline hazards. The study examined the performances of various models progressively within the context of model misspecification. Three criteria; Likelihood Ratio (LR), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used for model comparison. Under LR and AIC, the correctly specified models generally performed better than the misspecified models across all the baseline hazards combinations and under both linear and quadratic functional forms of continuous covariates but not for all cases under BIC. Models with combination of two Weibull baseline hazards performed best under the two functional forms of continuous covariates while those having combination of two Lognormal baseline hazards performed least.

http://scialert.net/abstract/?doi=ajms.2012.21.31 2012/01/08 - 03:32

In this study, we consider the class Qn(α, γ, μ, c) consisting of analytic functions with fixed second coefficients. The object is to show coefficient estimates, convex linear combinations, some distortion theorems and radii of starlikeness and convexity for f (z) in the class Qn(α, γ, μ, c).

http://scialert.net/abstract/?doi=ajms.2012.32.38 2012/01/08 - 03:32

In this study, we determined the necessary and sufficient conditions on the coefficients of a quadratic equation such that its square root transformation remains approximately a quadratic equation or exactly a linear equation. Numerical examples are used to illustrate the results obtained.

http://scialert.net/abstract/?doi=ajms.2011.186.199 2011/08/09 - 18:46

The study aimed at studying the effect of irregularity present in the surface layer on the propagation of Love waves. The irregularity is present in form of an infinite rigid strip in the surface. The rigid strip lies along half of the slightly dissipative and homogeneous surface layer while other half of the layer is free surface. The transmitted, reflected and the scattered waves have been obtained by Wiener-Hopf technique and Fourier transform. Numerical computations have been done and conclusions have been drawn on the basis of analysis of results. The scattered waves behave as decaying cylindrical waves originating at the tip of rigid strip and its image in the interface. The scattered wave decreases rapidly as the distance from the strip increases. The transmitted and scattered waves move with a velocity equal to that of shear waves, if whole of the layer is rigid.

http://scialert.net/abstract/?doi=ajms.2011.200.213 2011/08/09 - 18:46

The aim of this research was to study the unreliable nature of the servers under Retrial queueing system. These kinds of models are readily available in real life namely booking in Railway system, Call centres etc., so the analysis of such real models is most important. Consider a multi server retrial queueing system with breakdown and repair of services in which arrival rate follows a Poisson distribution with parameter λ and service time follows an exponential distribution with parameter μ. Let c be the number of servers in the system. The breakdown of service follows an exponential distribution with parameter α and repair of service follows an exponential distribution with parameter β. If any one of the servers is free at the time of a primary call arrival, the arriving call begins to be served immediately by one of the free servers and customer leaves the system after service completion. Otherwise, if c servers are busy or c servers are in breakdown then the arriving customer goes to orbit and becomes a source of repeated calls. The pool of sources of repeated calls may be viewed as a sort of queue. Every such source produces a poisson process of repeated calls with intensity σ. If an incoming repeated call finds any one of the servers is free, it is served and leaves the system after service, while the source which produced this repeated call disappears. The access from the orbit to the service facility follows the classical retrial policy. This model is solved by using direct truncation method. Numerical study have been done for analysis of Mean Number of Customers in the Orbit (MNCO), Mean Number of Busy Servers (MNBS), Mean Number of Servers in Breakdown (MNSB) and various system measures.

http://scialert.net/abstract/?doi=ajms.2011.214.223 2011/08/09 - 18:46

In this study, we presented Normal and Laplace’s methods of approximations for posterior density of gamma distribution. The numerical and graphical illustrations of posterior densities of the parameters of interest has been done in S-PLUS and R-Softwares.

http://scialert.net/abstract/?doi=ajms.2011.224.233 2011/08/09 - 18:46

The ability to forecast accurately the future values of a given variable within the minimum possible time gives organizations, governments and business enterprises the opportunity for appropriate decision and policy making. Accurate predictions can be made with a correctly specified model. It is evident that an estimated model comprises parameter estimates. Hence, different sets of estimates may give rise to different forecasts. Again, researchers and experimenters often report large values in some standard forms which include thousands, millions and billions so as to save time required for compilation and computation. In this study, an attempt was made to provide estimates of the parameters of the models involving the transformation obtained by dividing the variables by constants. The effect of the transformation on the parameter estimates was also emphasized. The relationships between the estimates of the parameters of the original model and those involving the transformed variables were derived. It has been shown that the division of the independent variable by a constant did affect the estimate of the slope only. On the other hand, the estimate of the slope of the original model remained unaffected when both variables were divided by the same constant where as other obtained parameter estimates appeared to differ from those of the original model. The theoretically derived estimates were substantiated by empirical data analysis. Moreover, the regression models fitted based on the various transformed variables differed from that of the original model. As a result, transformation by means of dividing the variables by constants affects the parameter estimates as well as the predictability of the model.

http://scialert.net/abstract/?doi=ajms.2011.174.180 2011/07/02 - 01:50

This study improves on the alternative method of obtaining least squares estimates of the parameters of a simple linear regression model by virtue of adding constant to at least one of the associated variables. It is observed that the estimate of the slope is not affected by addition of a constant to any or both of the variables. The estimate of the intercept is a function of the added constant(s). The relationships between the several intercepts of those models involving the transformed values of the variables and that of the original model are then obtained so to facilitate comparison and referencing. These theoretically obtained results have been validated with the help of empirical data analysis.

http://scialert.net/abstract/?doi=ajms.2011.181.185 2011/07/02 - 01:50

A two-dimensional sofic system has been defined by using the notion of allowable
block. This definition is an extension of the original definition in the one-dimensional
case. It is shown that the present definition is equivalent to using the notion
of symbolic factors of subshift of finite types and to point out some of the
phenomena which arise in the transition from classical shift of finite type
to
two-dimensional shift of finite type where,
A is the finite alphabet. The rigidity properties of certain two dimensional
shift of finite type and two dimensional sofic system has been discussed. Some
examples are presented to illustrate this notation.

http://scialert.net/abstract/?doi=ajms.2011.109.112 2011/05/26 - 10:06

This study presents discussion on the effects of correlation among response respect to estimator properties in mixed logit model on multivariate binary response. It is assumed that each respondent was observed for T response. Yit is the tth response for the ith individual/subject and each response is binary. Each subject has covariate Xi (individual characteristic) and covariate Zijt (characteristic of alternative j). Individual response i that is represented by Yi = (Yi1,....,YiT), Yit is tnd response on ith individual/subject and the response is binary. In order to simplify, one of individual characteristic was and alternative characteristics. We studied effects of correlations using data simulation. Methods of estimations used in this study are Generalized Estimating Equations (GEE) and Maximum Likelihood Estimator (MLE). We generate data and estimate parameters using software R.2.10. From simulation data, we conclude that MLE on mixed logit model is better than GEE. The higher correlation among utility, the higher deviation estimator to parameter.

http://scialert.net/abstract/?doi=ajms.2011.113.127 2011/05/26 - 10:06

Parametric Seemingly Unrelated Regression (SUR) models are used for multivariate regression analysis. However, statistical literature has revealed that, multicollinearity often affects the efficiency of SUR estimators. One of the popular methods for coping with Multicollinearity problem is ridge regression estimation. In this study, some alternative ridge estimators for SUR parameters are proposed when the explanatory variables are affected by multicollinearity. The efficiency of the proposed estimators is evaluated and compared through simulation study, in terms of the Trace Mean Squared Error (TMSE) and the Proportion of Replications, (PR) criterion, under a variety of data conditions. The empirical results indicated that, under certain conditions, the performance of the multivariate regression estimators based on some SUR ridge parameters are superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high, the unbiased SUR estimator produces a smaller TMSEs.

http://scialert.net/abstract/?doi=ajms.2011.128.139 2011/05/26 - 10:06

The aim of the study is to solve some linear and non-linear differential equations using Homotopy Perturbation Method. The brilliance of the method in obtaining analytical or approximate solutions of some linear and non-linear partial differential equations are compared with earlier results obtained by Adomian Decomposition Method. This method is more efficient and easy to handle such partial differential equation in comparison to other methods. Numerical results show the efficiency, accuracy and validation of the Homotopy Perturbation Method (HPM).

http://scialert.net/abstract/?doi=ajms.2011.140.150 2011/05/26 - 10:06

In this study, we studied the zeta function with a 2-dimensional shift of finite type via left and upward shifts, on a subspace of the space of doubly indexed sequences over a finite abelian compact group and new way to calculate periodic point numbers based on the study of linear algebra of F2 the field and index subgroup. We showed the periodic point data of 2-dimensional shift of finite type via left and upward shifts.

http://scialert.net/abstract/?doi=ajms.2011.151.160 2011/05/26 - 10:06