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”).

In this paper we describe G/G/R+s multi- repairmen machining system with balking. The system consists of M operating machines, S spare machines, R permanent and s additional repairmen. Assuming the discrete flow of machines by continuous one, the Diffusion approximation technique for the machine repair system has developed. The system will be in normal working mode if there is M operating machines. When there are less than M and £m, the system is called as short system. The failure rates of operating units in short and normal modes are different. By using the mean and square coefficient of variation of failure and repair time distributions, the queue size distribution has been established. Various performance indices viz. expected number of failed machines, average operating machines etc. have been derived.

boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad’e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for solving singular boundary value problems arising in the reaction cum Diffusion process in a spherical biocatalyst. ChFD method can be regarded as a non-uniform finite difference scheme and DTM is a numerical method based on the Taylor series expansion, which constructs an analytical solution in the form of a polynomial. The main advantage of DTM is that it can be applied directly to nonlinear ordinary without requiring linearization, discretization or perturbation. Therefore, it is not affected by errors associated to discretization. The results obtained, are in good agreement with those obtained numerically or by optimal homotopy analysis method.

Diffusion and dispersion are considered as the two fundamental mechanisms for the miscible gas injection process in the oil reservoirs, which unfortunately are mostly disregarded in the reservoir simulators. In fact, these two phenomena tend to control the miscibility of the injected fluid with oil in the porous media. Neglecting theses (existing) phenomena in reservoir simulators may bring about erroneous results, which may subsequently role an unreliable basis to be applied into the gas injection projects. The aim of this work is to exhibit the error that should be emerged in case of neglecting these phenomena, in a quantitative manner. Initially, the effects of Diffusion and dispersion are shown during a miscible gas-injection process using a one-dimensional model under different scenarios. Such scenarios include both considering and neglecting the Diffusion and dispersion terms. A comparison between the results from each scenario should demonstrate if a considerable error should arise in the simulation results by neglecting these effects. It would also show if such neglecting will result in inaccurate estimation of gas composition change, oil recovery factor, and the gas breakthrough time. Based on the expected results, an appropriate dispersion coefficient for accurate design of miscible gas injection processes will be estimated and introduced.

In the present investigation transient, GX/G/m queuing model with balking and reneging has been studied. The Diffusion process with elementary return boundary has been used for modeling purpose. The probability density function (p. d. f.) for the number of customers in the system has been obtained. In special case, the steady state results which tally with those of Kimura and Ohsone (1984) have been established as a limiting case.

Small and medium industries are some of the most important economic sectors in any country. These industries, usually transforming to business incubator by economies of agglomeration in industrial centers, while large industries are becoming growth poles based on economies of scale. In the regional economics framework, SMEs affect the geographic space and large industries affect the economic space. While small industries by relying on the Diffusion effects play their role in industrial development and economic growth as a business incubator. The present article is examining and modeling two issues in the field of small and medium industries’ activities effects: the Diffusion process modeling and the modeling of how information transmission (or similarly, technology and innovation). Both issues can be brought up in the wave theories. Among two given regions, differences between the type and function of industries can usually make the difference between the waves. considering that each industry has its own preceding and following effects, each region also proportion to the type of established industries in it can have preceding and following effects on the other regions in geographic space and economic space. For the Diffusion process model, the approach of gravity model, and for the process pattern and how information transmission, a hierarchical system is used. In both methods, the results are shown in form of the Diffusion models in general and under specific conditions. The extracted theoretical functions indicate how the regions interact based on the types of established industries in them. The effects of the considered models show that the SMEs can have significant effects on the surrounding regions around via sending permanent innovation waves, information, and other development waves.

Background: Prostate cancer is the third leading cause of death and is the most common cause of cancer in elderly men. Regarding to the low accuracy of screening methods such as prostate-specific antigen (PSA), Digital Rectal Examination (DRE) and trans rectal ultrasound (TRUS) in detection and localization of tumor, Magnetic Resonance Imaging (MRI) and Diffusion Weighted Imaging (DWI) attracted many attentions in the past years. DWI reveals micro-molecular Diffusion, which is the Brownian motion of the spins in biologic tissues. This technique can delineate pathologic lesions with high tissue contrast against generally suppressed background signal. In this paper, the value of DWI in detection of prostate cancer is studied.Methods: In this cross-sectional study, the studied population are suspicious patients to prostate cancer based on high Prostatic Specific Antigen level or abnormal Digital Rectal Examination who refered for prostate biopsy to radiology department of Hazrate- Rasoul Hospital during the year 2011. The results of DWI are compared to biopsy results for all patients.Results: Eighty five patients are selected. The DWI sensitivity in detecting of prostate cancer is 100%, specificity 97.1% and positive and negative predictive values are 89.5% and 100%, respectively. The results showed that if DWI reports the prostate cancer as negative, the result was highly reliable and if it reports as positive, although the report was not 100% reliable, but it still had high reliability, more than 90%.Conclusion: DWI had high accuracy in detecting prostate cancer for patients with cancer. Also the accuracy of this method for patients without prostate cancer was acceptable compared to the other common methods.

Diffusion of small molecules through the polymers has significant importance in different scientific and engineering fields such as medicine, textile industry, membrane separations, packaging in food industry, extraction of solvents and of contaminants, and etc. This paper reports the use of Fourier transform infrared-attenuated total reflectance (FTIR-ATR) and partial least squares (PLS) analysis to study the compositional change of polymer solution exposed to the certain atmosphere. Diffusion coefficient of tetrahydrofuran (THF) in solution of polystyrene was obtained by means of analyzing the spectral data collected by FTIR-ATR instrument. Desorption by which the solvent evaporates from boundary of polymer solution, with respect to the time, showed that three regions of compositional change appeared: plateau, steep slope, and gentle slope regions. Providing the desorption data from the second region which is the essential part of mass transfer, the value of Diffusion coefficient of THF was obtained 5.8´10-6 cm2/sec. Finally, affecting factors and limitations of FTIR-ATR technique on reliability of spectral data are discussed.