In this paper the new model of Locally STATIONARY Wavelet (LSW) PROCESSes is introduced which is based on reconstruction of functions using wavelets. This model creates a new class of time series that can have a non-STATIONARY behavior. It is observed that, LSW model has a construction similar to moving average model. Finally time series data for Consumer Price Index (CPI) of the country (Iran) in a definite time interval is investigated using this model.

This paper develops a new class of spatio-temporal PROCESS models that can simultaneously capture skewness and non-stationarity. The proposed approach which is based on using the closed skew-normal distribution in the low-rank representation of stochastic PROCESSes, has several favorable properties. In particular, it greatly reduces the dimension of the spatio-temporal latent variables and induces flexible correlation structures. Bayesian analysis of the model is implemented through a Gibbs MCMC algorithm which incorporates a version of the Kalman filtering algorithm. All fully conditional posterior distributions have closed forms which show another advanta-geous property of the proposed model. We demonstrate the e ciency of our model through an extensive simulation study and an application to a real data set comprised of precipitation measurements.

A new approach of fuzzy PROCESSes, the source of which are expert knowledge reflections on the states on STATIONARY Discrete Extremal Fuzzy Dynamic System (SDEFDS) in extremal fuzzy time intervals, are considered. A fuzzy-integral representation of a STATIONARY discrete extremal fuzzy PROCESS is given. A method and an algorithm for identifying the transition operator of SDEFDS are developed. The SDEFDS transition operator is restored by means of expert knowledge reflections on the states of SDEFDS. The regularization condition for obtaining of the quasi-optimal estimator of the transition operator is represented by the theorem. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of SDEFDS states.

How to profoundly change the beliefs of the polytheists during the age of revelation from the denial of the Prophet (pbuh) to the certainty of his Message and the acceptance of his full guardianship is a question worthy of attention. The order of verses about prophecy based on the order of revelation is the reason to lead a transformative PROCESS and a special Quranic method in institutionalizing the belief of prophecy in the lives of Arabs. In the first stage, the Holy Quran in the first Makkī (Arabic: المکّیّ, suras revealed in Mecca) chapters has prepared the community from the motivational side to accept the truth of the Prophet’s (pbuh) prophecy and briefly stating the key issues surrounding it. The Holy Book of Quran at the time of the emergence of oppositions and doubts (the second stage) destroyed the arguments of the polytheists and explained the prophecy and proved its authenticity from a cognitive perspective in the second stage by presenting clear arguments. and the Holy Book of Quran in the third stage after Madanī (Arabic: المدنیّ, suras revealed in Medina) period has undertaken measures in order to fulfill the goals of the Massage by explaining the true position of the Prophet (pbuh) to deepen and operationalize the Prophetic belief through explaining practical duties for the Prophet (pbuh) and behavior based on the acceptance of Walaya (Arabic: ولایة, meaning “guardianship” or “governance”).

This paper investigates an infinite buffer capacity fluid queueing model driven by a state-dependent birth-death PROCESS prone to catastrophes. We employ the Laplace-Stieltjes transform and the continued fraction techniques to determine explicit expressions for the joint probability of the number of customers in the background queueing model and the content of the buffer in the steady state. The importance of the proposed system is that, in numerous practical situation, the service facility possesses defence mechanisms versus long waiting lines. The servers may increase their rate of service under the pressure of a large backlog of work. Therefore, it is of interest to discuss queueing systems taking into regard the state dependent nature of the systems. For example, the congestion control mechanisms deny the formation of long queue in computer and communication systems by controlling the transmission rates of packets based on the queue length (of packets) at source or destination. Numerical illustrations are added to uphold the theoretical results.

This paper investigates an infinite buffer capacity fluid queueing model driven by a state-dependent birth-death PROCESS prone to catastrophes. We employ the Laplace-Stieltjes transform and the continued fraction techniques to determine explicit expressions for the joint probability of the number of customers in the background queueing model and the content of the buffer in the steady state. The importance of the proposed system is that, in numerous practical situation, the service facility possesses defence mechanisms versus long waiting lines. The servers may increase their rate of service under the pressure of a large backlog of work. Therefore, it is of interest to discuss queueing systems taking into regard the state dependent nature of the systems. For example, the congestion control mechanisms deny the formation of long queue in computer and communication systems by controlling the transmission rates of packets based on the queue length (of packets) at source or destination. Numerical illustrations are added to uphold the theoretical results.

Theft is among the most common crimes committed in all societies. The present study aims at exploring the STATIONARY and non STATIONARY theft rates in the cities of Zanjan. All those who committed theft during 2007 to 2008 in the cities of Zanjan (N=493) were the statistical sample. The required data of this field study were collected via questionnaire, interview, and observation. SPSS was used to analyze the collected data. The sample findings are as follows: 1.There is a significant relationship between "The theft technique and thieves' motivations".2.There are significant relationships between."The theft technique and criminal records", "The theft technique and drug abuse", "The theft technique and the theft type", "The theft technique and residential place", and "The theft technique and the place of birth of thieves".

The accurate estimation of the design Precipitation is one of the requirements for the construction of hydraulic structures, which is done by various methods of frequency analysis. Classical methods of fitting observational data use the assumption of constant parameters of distribution functions,while, many studies have been done on non-STATIONARY data due to factors such as climate change. Therefore, this paper aims to use the functions of non-STATIONARY parameters-if necessary-and compare them with the STATIONARY assumption of the maximum daily precipitation data of the Atrak river basin. Mann-Kendall test and White test were used to check the non-STATIONARY in the mean and variance of annual data. The Generalized extreme value distribution function was also fitted to the data time series. Among the 24 stations with long-term data, 5 stations with trends and 6 stations with variance non-STATIONARY were detected. Evaluation criteria including Akaike (AIC), Bayesian (BIC), Root mean square error (RMSE), and Nash-Sutcliffe efficiency (NSE) coefficient was determined under STATIONARY and non-STATIONARY assumptions, for all stations. The results showed that in all stations with non-STATIONARY, considering the mentioned conditions in the analytical calculations is a good choice. Also, the lower (5%), median (50%), and upper (95%) limit values with the return period of 100 years with both assumptions were determined and compared with the classical maximum likelihood method. The underestimation of the maximum likelihood method compared to the Bayesian method used by using Markov chain Monte Carlo (MCMC) in parameter estimation was observed. Also, Akaike criterion provided better results among the used evaluation criteria.