Search results for: radiation stability

Authors: Chundong Li, V. V. Neshchimenko, M. M. Mikhailov

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The effect of the modification of ZnO powders by ZrO₂, Al₂O₃, TiO₂, SiO₂, CeO₂ and Y₂O₃ nanoparticles with a concentration of 1-30 wt % is investigated by diffuse reflectance spectra within the wavelength range 200 to 2500 nm before and after 100 keV proton and electron irradiation. It has been established that the introduction of nanoparticles ZrO₂, Al₂O₃ enhances the optical stability of the pigments under proton irradiation, but reduces it under electron irradiation. Modifying with TiO₂, SiO₂, CeO₂, Y₂O₃ nanopowders leads to decrease radiation stability in both types of irradiation. Samples modified by 5 wt. % of ZrO₂ nanoparticles have the highest stability of optical properties after proton exposure. The degradation of optical properties under electron irradiation is not high for this concentration of nanoparticles. A decrease in the absorption of pigments modified with nanoparticles proton exposure is determined by a decrease in the intensity of bands located in the UV and visible regions. After electron exposure the absorption bands have in the whole spectrum range.

Keywords: Irradiation, nanopowders, radiation stability, zinc oxide.

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Authors: Ali M. Jawarneh, Ahmad S. AL-Shyyab

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The purpose of this work is to present the potential of solar energy in Zarqa region. The solar radiation along year 2009 was obtained from Pyranometer which measures the global radiation over horizontal surfaces. Solar data in several different forms, over period of 5 minutes, hour-by-hour, daily and monthly data radiation have been presented. Briefly, the yearly global solar radiation in Zarqa is 7297.5 MJ/m2 (2027 kWh/m²) and the average annual solar radiation per day is 20 MJ/m2 (5.5 Kwh/m2). More specifically, the average annual solar radiation per day is 12.9 MJ/m2 (3.57 Kwh/m2) in winter and 25 MJ/m2 (7 Kwh/m2) in summer.

Keywords: Solar Energy, Pyranometer, Zarqa Region

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Authors: Muhammed A. Ahmed, Sidra A. Shaikh

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Global Solar Radiation (H) for Dubai and Sharjah, Latitude 25.25oN, Longitude 55oE and 25.29oN, Longitude 55oE respectively have been studied using sunshine hour data (n) of the areas using various methods. These calculated global solar radiation values are then compared to the measured values presented by NASA. Furthermore, the extraterrestrial (H0), diffuse (Hd) and beam radiation (Hb) are also calculated. The diffuse radiation is calculated using methods proposed by Page and Liu and Jordan (L-J). Diffuse Radiation from the Page method is higher than the L-J method. Moreover, the clearness index (KT) signifies a clear sky almost all year round. Rainy days are hardly a few in a year and limited in the months December to March. The temperature remains between 25oC in winter to 44oC in summer and is desirable for thermal applications of solar energy. From the estimated results, it appears that solar radiation can be utilized very efficiently throughout the year for photovoltaic and thermal applications.

Keywords: Dubai, Sharjah, Global Solar Radiation, Diffuse Radiation

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Authors: Priyanka R. Oberoi, Chandra B. Maurya, Prakash A. Mahanwar

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Ionizing radiation can cause a drastic change in the physical and chemical properties of the material exposed. Numerous medical devices are sterilized by ionizing radiation. In the current research paper, an attempt was made to develop precise and inexpensive polymeric film dosimeter which can be used for controlling radiation dosage. Polymeric film containing (pH sensitive dye) indicator dye Bromophenol blue (BPB) was casted to check the effect of Gamma radiation on its optical and physical properties. The film was exposed to gamma radiation at 4 kGy/hr in the range of 0 to 300 kGy at an interval of 50 kGy. Release of vinyl acetate from an emulsion on high radiation reacts with the BPB fading the color of the film from blue to light blue and then finally colorless, indicating a change in pH from basic to acidic form. The change was characterized by using CIE l*a*b*, ultra-violet spectroscopy and FT-IR respectively.

Keywords: Bromophenol blue, dosimeter, gamma radiation, polymer.

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Authors: Ashok K. Satapathy, Prerana Nashine

Abstract:

Radiative heat transfer in participating medium was carried out using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab and by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient radiation equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: Participating media, finite volume method, radiation coupled with conduction, heat transfer.

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Authors: Ali M. Jawarneh

Abstract:

Beam and diffuse radiation data are extracted analytically from previous measured data on a horizontal surface in Zarqa city. Moreover, radiation data on a tilted surfaces with different slopes have been derived and analyzed. These data are consisting of of beam contribution, diffuse contribution, and ground reflected contribution radiation. Hourly radiation data for horizontal surface possess the highest radiation values on June, and then the values decay as the slope increases and the sharp decreasing happened for vertical surface. The beam radiation on a horizontal surface owns the highest values comparing to diffuse radiation for all days of June. The total daily radiation on the tilted surface decreases with slopes. The beam radiation data also decays with slopes especially for vertical surface. Diffuse radiation slightly decreases with slopes with sharp decreases for vertical surface. The groundreflected radiation grows with slopes especially for vertical surface. It-s clear that in June the highest harvesting of solar energy occurred for horizontal surface, then the harvesting decreases as the slope increases.

Keywords: Beam and Diffuse Radiation, Zarqa City

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Authors: J. Mlýnek, R. Srb

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This article is focused on the calculation of heat radiation intensity and its optimization on an aluminum mould surface. The inside of the mould is sprinkled with a special powder and its outside is heated by infra heaters located above the mould surface, up to a temperature of 250°C. By this way artificial leathers in the car industry are produced (e. g. the artificial leather on a car dashboard). A mathematical model of heat radiation of infra heaters on a mould surface is described in this paper. This model allows us to calculate a heat-intensity radiation on the mould surface for the concrete location of infra heaters above the mould surface. It is necessary to ensure approximately the same heat intensity radiation on the mould surface by finding a suitable location for the infra heaters, and in this way the same material structure and color of artificial leather. In the model we have used a genetic algorithm to optimize the radiation intensity on the mould surface. Experimental measured values for the heat radiation intensity by a sensor in the surroundings of an infra heater are used for the calculation procedures. A computational procedure was programmed in language Matlab.

Keywords: Genetic algorithm, mathematical model of heat radiation, optimization of radiation intensity, software implementation

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Authors: M. Ebrahimi Shohani, S. M. Taheri, S. M. Golgoun

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Environmental radiation dosimeter is a kind of detector that measures the dose of the radiation area. Dosimeter registers the radiation and converts it to the dose according to the calibration parameters. The limit of a dose is different at each radiation area and this limit should be notified and reported to the user and health physics department. The stochastic nature of radiation is the reason for the fluctuation of any gamma detector dosimetry. In this research we investigated Geiger-Muller type of dosimeter and tried to improve the dose measurement. Geiger-Muller dosimeter is a counter that converts registered radiation to the dose. Therefore, for better data analysis, it is necessary to apply an algorithm to smooth statistical variations of registered radiation. We proposed a method to smooth these fluctuations much more and also proposed a dynamic way to trace rapid changes of radiations. Results show that our method is fast and reliable method in comparison the traditional method.

Keywords: Geiger-Muller, radiation detection, smoothing algorithms, dosimeter, dose calculation.

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Authors: Sajjad A. Memon, Sadaf T. Qureshi, Naeem A. Laghari, Noor M. Khuhro

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The present study represents the occupational radiation doses received by selected workers of Nuclear Institute of Medicine and Radiotherapy (NIMRA) Jamshoro Pakistan and conducted to discuss about how we be careful and try to avoid make ourselves overconscious. Film badges with unique identification number were issued to radiation worker to detect occupational radiation doses. In this study, only 08 workers with high radiation doses were assessed amongst 35 radiation workers during the period of January 2012 to December 2012. The selected radiation workers’ occupational doses were according to designated work areas and in the range of 1.21 to 7.78 mSv (mili Sieveret) out of the annual dose limit of 20 mSv. By the comparison of different studies and earth’s HNBR (High Natural Background Radiation) locations’ doses, it is concluded that the worker’s high doses are of magnitude of HNBR Regions and were in the acceptable range of National and International regulatory bodies so we must not to show any type of overconsciousness but be careful in handling the radioactive sources.

Keywords: Natural background radiation, Occupational dose, Overconscious, Personal monitoring.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

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In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.

Keywords: Hopfield neural networks, uniform asymptotic stability, global asymptotic stability, exponential stability.

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Authors: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop

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In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.

Keywords: Heat transfer, Radiation effect, Shrinking sheet Unsteady flow.

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Authors: M. Kidouche, H. Habbi, M. Zelmat

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In this paper, the decomposition-aggregation method is used to carry out connective stability criteria for general linear composite system via aggregation. The large scale system is decomposed into a number of subsystems. By associating directed graphs with dynamic systems in an essential way, we define the relation between system structure and stability in the sense of Lyapunov. The stability criteria is then associated with the stability and system matrices of subsystems as well as those interconnected terms among subsystems using the concepts of vector differential inequalities and vector Lyapunov functions. Then, we show that the stability of each subsystem and stability of the aggregate model imply connective stability of the overall system. An example is reported, showing the efficiency of the proposed technique.

Keywords: Composite system, Connective stability, Lyapunovfunctions.

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Authors: N. W. K. Jayatissa, R. Attalage, Prabath Hewageegana, P. A. A. Perera, M. A. Punyasena

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Per capita energy usage in any country is exponentially increasing with their development. As a result, the country’s dependence on the fossil fuels for energy generation is also increasing tremendously creating economic and environmental concerns. Tropical countries receive considerable amount of solar radiation throughout the year, use of solar energy with different energy storage and conversion methodologies is a viable solution to minimize the ever increasing demand for the depleting fossil fuels. Salinity gradient solar pond is one such solar energy application. This paper reports the characteristics and performance of a thermally insulated, experimental salinity-gradient solar pond, built at the premises of the University of Kelaniya, Sri Lanka. Particular stress is given to the behavior of the evolution of the three layer structure exist at the stable state of a salinity gradient solar pond over a long period of time, under different environmental conditions. The operational procedures required to maintain the long term thermal stability are also reported in this article.

Keywords: Salt-gradient, solar pond, solar radiation, renewable energy.

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Authors: C. M. De Marco Muscat-Fenech, A.M. Grech La Rosa

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The application of stability theory has led to detailed studies of different types of vessels; however, the shortage of information relating to multihull vessels demanded further investigation. This study shows that the position of the hulls has a very influential effect on both the transverse and longitudinal stability of the tricore. HSC stability code is applied for the optimisation of the hull configurations. Such optimization criteria would undoubtedly aid the performance of the vessel for both commercial or leisure purposes

Keywords: Stability, Multihull, Tricore

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Authors: Lai Xuejiang, Huang Li, Yang Yi

Abstract:

To study the potential hazards of the sudden emergency relief of flare stack, the thermal radiation and noise calculation of flare stack is carried out by using Flaresim program 2.0. Thermal radiation and noise analysis should be considered as the sudden emergency relief takes place. According to the Flaresim software simulation results, the thermal radiation and noise meet the requirement.

Keywords: Flare stack, thermal radiation, noise, safety assessment.

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Authors: Muhammad Waqar, Touqir Ahmad Afridi, Quratulain Soomro

Abstract:

Radiation is a ghost causing unimaginable physical damage, but its harm is not inevitable. The panic created by previously reported worst-case scenarios i.e., Three Mile Island, Fukushima, Chernobyl, has adversely affected the attitude of radiation workers towards the profession. The psychological effect of radiation-related catastrophes creates an invisible barrier that reduces the efficiency of radiation workers. Careful handling and proper monitoring of radiation decreases the hazards of radiation and proves that the psychological impairment of radiation is myriad fold adverse than its physiological damage. Thermoluminescent Dosimeter (TLD) badges with unique identity numbers were provided to 36 radiation workers for a period of one year (2021). TLDs were read quarterly, and doses were recorded for every radiation worker. Annual doses were recorded and compared with national and international standards. Moreover, the period for which an individual worker is expected to reach one year limit of 20 mSv was also calculated. The highest radiation dose for the radiation worker in 2021 was found at 3.2 mSv, which was 16% of the permissible annual dose limit. The average occupational radiation doses ranged from 1.0 mSv to 3.20 mSv. 64% of the employees did not exceed the 10% of the annual limit, receiving less than 2 mSv. The least time for 20 mSv completion was found 6.25 years for the hot-lab technician. As a whole, the 20 mSv completion period ranged from 6.25 to 20 years. We concluded that the annual professional radiation doses were well within the permissible limits of Pakistan Nuclear Regulatory Authority (PNRA) and International Commission on Radiological Protection (ICRP). The fear of radiation is unnecessary and it creates reluctance towards performing their assigned duties and it is also not favorable for the institute. It must be abolished through education and training sessions.

Keywords: TLD, thermoluminescent dosimeter, psychological impact, radiation dose, annual dose limit, PNRA, ICRP, IAEA.

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Authors: Bhanu Gupta, Sanjay K. Srivastava

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In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.

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Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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Authors: Yusuff Idowu Moshood, Sanni Mohammed

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Natural radiations such as ultraviolet (UV) radiation sourced from sun are known to be the main causes of skin cancer, sunburn, eye damage, premature aging of skin and other skin related diseases. Its percentage of radiation reaching the earth populace and its impacts are not well known. Its variability in near-surface relating to its impacts on populace depends on some atmospheric parameters. Hence, this work was embarked on to determine the variability in near-surface UV radiation and its dependency on some atmospheric parameters at different time of the day in Offa, Nigeria. The variability was determined using the data obtained from meteorological garden, Science Laboratory Technology Department, Federal Polytechnic Offa, Nigeria. The data obtained were solar UV radiation, solar radiation, temperature, humidity and pressure at 30 minutes interval. Relationships were determined and correlations were derived using SPSS Pearson Correlation tool. The results showed a significant level of correlation with p-value of 0.01 and 0.05 levels. Thus, the results revealed some good relationships between the solar UV radiation and other atmospheric parameters with significance level less than p-value obtained. Inferentially, interdependent relationships were found to exist. Therefore, the nature of relationship obtained could be a yardstick for decision making in short term environmental planning on solar UV radiation depending of some atmospheric parameters within Offa locality.

Keywords: Correlation, inferential, radiation, yardstick.

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Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri

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In this paper, the 1-D conduction-radiation problem is solved by the lattice Boltzmann method. The effects of various parameters such as the scattering albedo, the conduction–radiation parameter and the wall emissivity are studied. In order to check on the accuracy of the numerical technique employed for the solution of the considered problem, the present numerical code was validated with the published study. The found results are in good agreement with those published

Keywords: Conduction, lattice Boltzmann method, planar medium, radiation.

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: Fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability.

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Authors: N. Todorovic, I. Bikit, J. Nikolov, S. Forkapic, D. Mrdja, S. Todorovic

Abstract:

Interventional cardiologists are at greater risk from radiation exposure as a result of the procedures they undertake than most other medical specialists. A study was performed to evaluate operator dose during interventional cardiology procedures and to establish methods of operator dose reduction with a radiation protective device. Different procedure technique and use of protective tools can explain big difference in the annual equivalent dose received by the professionals. Strategies to prevent and monitor radiation exposure, advanced protective shielding and effective radiation monitoring methods should be applied.

Keywords: absorbed dose rate measurements, annualequivalent dose, protective device.

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Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.

Abstract:

The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.

Keywords: Acoustic radiation, boundary element

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Authors: Ren Jian, Yang Shulin

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In this paper, the difference between the Alternating Direction Method (ADM) and the Non-Splitting Method (NSM) is investigated, while both methods applied to the simulations for 2-D multimaterial radiation diffusion issues. Although the ADM have the same accuracy orders with the NSM on the uniform meshes, the accuracy of ADM will decrease on the distorted meshes or the boundary of domain. Numerical experiments are carried out to confirm the theoretical predication.

Keywords: Alternating Direction Method, Non-SplittingMethod, Radiation Diffusion.

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Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani

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In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.

Keywords: Markov Chain, regenerative processes, risk models, ruin probability, strong stability.

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Authors: Rehab I. Abdul Rahman, Mazhar B. Tayel

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This paper presents a method of hardening the 8051 micro-controller, able to assure reliable operation in the presence of bit flips caused by radiation. Aiming at avoiding such faults in the 8051 micro-controller, Hamming code protection was used in its SRAM memory and registers. A VHDL code has been used for this hamming code protection.

Keywords: Radiation, hardening, bitflip, hamming code.

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Authors: Zanariah Mohd Yusof, Siti Khuzaimah Soid, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

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Unsteady magnetohydrodynamics (MHD) boundary layer flow and heat transfer over a continuously stretching surface in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to a set of ordinary differential equations. Numerical solutions are obtained by employing the Runge-Kutta-Fehlberg method scheme with shooting technique in Maple software environment. The effects of unsteadiness parameter, radiation parameter, magnetic parameter and Prandtl number on the heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases as the Prandtl number and unsteadiness parameter increase but decreases with magnetic and radiation parameter.

Keywords: Heat transfer, magnetohydrodynamics, radiation, unsteadiness.

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Authors: T. Zalabsky, P. Bezousek, T. Shejbal

Abstract:

The paper describes new concept of the ribbon beam antenna for RFID technology. Antenna is located near to railway lines to monitor tags situated on trains. Antenna works at 2.45 GHz and it is fabricated by microstrip technology. Antenna contains two same mirrored parts having the same radiation patterns. Each part consists of three dielectric layers. The first layer has on one side radiation elements. The second layer is only for mechanical construction and it sets optimal electromagnetic field for each radiating elements. The third layer has on its top side a ground plane and on the bottom side a microstrip circuit used for individual radiation elements feeding.

Keywords: RFID, cosecant radiation pattern, ribbon beam, patch antenna, microstrip.

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Authors: B. I. Lee, S. I. Kim, D. H. Suh, J. I. Kim, Y. K. Lim

Abstract:

A total of 33,680 nuclear power plants (NPPs) workers were monitored and recorded from 1990 to 2007. According to the record, the average individual radiation dose has been decreasing continually from it 3.20 mSv/man in 1990 to 1.12 mSv/man at the end of 2007. After the International Commission on Radiological Protection (ICRP) 60 recommendation was generalized in South Korea, no nuclear power plant workers received above 20 mSv radiation, and the numbers of relatively highly exposed workers have been decreasing continuously. The age distribution of radiation workers in nuclear power plants was composed of mainly 20-30- year-olds (83%) for 1990 ~ 1994 and 30-40-year-olds (75%) for 2003 ~ 2007. The difference in individual average dose by age was not significant. Most (77%) of NPP radiation exposures from 1990 to 2007 occurred mostly during the refueling period. With regard to exposure type, the majority of exposures were external exposures, representing 95% of the total exposures, while internal exposures represented only 5%. External effective dose was affected mainly by gamma radiation exposure, with an insignificant amount of neutron exposure. As for internal effective dose, tritium (3H) in the pressurized heavy water reactor (PHWR) was the biggest cause of exposure.

Keywords: Dose distribution, External exposure, Nuclear powerplant, Occupational radiation dose

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Authors: Kai-Long Hsiao

Abstract:

In this study, an analysis has been performed for free convection with radiation effect over a thermal forming nonlinearly stretching sheet. Parameters n, k0, Pr, G represent the dominance of the nonlinearly effect, radiation effect, heat transfer and free convection effects which have been presented in governing equations, respectively. The similarity transformation and the finite-difference methods have been used to analyze the present problem. From the results, we find that the effects of parameters n, k0, Pr, Ec and G to the nonlinearly stretching sheet. The increase of Prandtl number Pr, free convection parameter G or radiation parameter k0 resulting in the increase of heat transfer effects, but increase of the viscous dissipation number Ec will decrease of heat transfer effect.

Keywords: Nonlinearly stretching sheet, Free convection, Finite-difference, Radiation effect.

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