Search results for: Mojtaba Barzegar

Authors: Shima Soltanzadeh, Mohammad Hosain Fazel Zarandi, Mojtaba Barzegar Astanjin

Abstract:

Diagnosis of male infertility by the laboratory tests is expensive and, sometimes it is intolerable for patients. Filling out the questionnaire and then using classification method can be the first step in decision-making process, so only in the cases with a high probability of infertility we can use the laboratory tests. In this paper, we evaluated the performance of four classification methods including naive Bayesian, neural network, logistic regression and fuzzy c-means clustering as a classification, in the diagnosis of male infertility due to environmental factors. Since the data are unbalanced, the ROC curves are most suitable method for the comparison. In this paper, we also have selected the more important features using a filtering method and examined the impact of this feature reduction on the performance of each methods; generally, most of the methods had better performance after applying the filter. We have showed that using fuzzy c-means clustering as a classification has a good performance according to the ROC curves and its performance is comparable to other classification methods like logistic regression.

Keywords: classification, fuzzy c-means, logistic regression, Naive Bayesian, neural network, ROC curve

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Authors: Atrin Barzegar, Yas Barzegar, Stefano Marrone, Francesco Bellini, Laura Verde

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The aim of this research is to develop an intelligent system to analyze the risk level of wheat flour product manufacturing system. The model consists of five Fuzzy Inference Systems in two different layers to analyse the risk of a wheat flour product manufacturing system. The first layer of the model consists of four Fuzzy Inference Systems with three criteria. The output of each one of the Physical, Chemical, Biological and Environmental Failures will be the input of the final manufacturing systems. The proposed model based on Mamdani Fuzzy Inference Systems gives a performance ranking of wheat flour products manufacturing systems. The first step is obtaining data to identify the failure modes from expert’s opinions. The second step is the fuzzification process to convert crisp input to a fuzzy set., then the IF-then fuzzy rule applied through inference engine, and in the final step, the defuzzification process is applied to convert the fuzzy output into real numbers.

Keywords: failure modes, fuzzy rules, fuzzy inference system, risk assessment

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Authors: Yas Barzegar, Atrin Barzegar

Abstract:

Drinking water quality assessment is a major issue today; technology and practices are continuously improving; Artificial Intelligence (AI) methods prove their efficiency in this domain. The current research seeks a hierarchical fuzzy model for predicting drinking water quality in Rome (Italy). The Mamdani fuzzy inference system (FIS) is applied with different defuzzification methods. The Proposed Model includes three fuzzy intermediate models and one fuzzy final model. Each fuzzy model consists of three input parameters and 27 fuzzy rules. The model is developed for water quality assessment with a dataset considering nine parameters (Alkalinity, Hardness, pH, Ca, Mg, Fluoride, Sulphate, Nitrates, and Iron). Fuzzy-logic-based methods have been demonstrated to be appropriate to address uncertainty and subjectivity in drinking water quality assessment; it is an effective method for managing complicated, uncertain water systems and predicting drinking water quality. The FIS method can provide an effective solution to complex systems; this method can be modified easily to improve performance.

Keywords: water quality, fuzzy logic, smart cities, water attribute, fuzzy inference system, membership function

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Authors: Mojtaba Barzegar, Alireza Shirazi, Saied Rabi Mahdavi

Abstract:

Intraoperative radiation therapy (IORT) is an innovative treatment modality that the delivery of a large single dose of radiation to the tumor bed during the surgery. The radiotherapy success depends on the absorbed dose delivered to the tumor. The achievement better accuracy in patient treatment depends upon the measured dose by standard dosimeter such as ionization chamber, but because of the high density of electric charge/pulse produced by the accelerator in the ionization chamber volume, the standard correction factor for ion recombination Ksat calculated with the classic two-voltage method is overestimated so the use of dose/pulse independent dosimeters such as chemical Fricke and ethanol chlorobenzene (ECB) dosimeters have been suggested. Dose measurement is usually calculated and calibrated in the Zmax. Ksat calculated by comparison of ion chamber response and ECB dosimeter at each applicator degree, size, and dose. The relative output factors for IORT applicators have been calculated and compared with experimentally determined values and the results simulated by Monte Carlo software. The absorbed doses have been calculated and measured with statistical uncertainties less than 0.7% and 2.5% consecutively. The relative differences between calculated and measured OF’s were up to 2.5%, for major OF’s the agreement was better. In these conditions, together with the relative absorbed dose calculations, the OF’s could be considered as an indication that the IORT electron beams have been well simulated. These investigations demonstrate the utility of the full Monte Carlo simulation of accelerator head with ECB dosimeter allow us to obtain detailed information of clinical IORT beams.

Keywords: intra operative radiotherapy, ethanol chlorobenzene, ksat, output factor, monte carlo simulation

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Authors: Ehsanolah Assareh, Mojtaba Biglari, Mojtaba Nedaei

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Sanar village in north of Iran is a remote region with difficult access to electricity, grid and water supply. Thus the aim of this research is to evaluate the potential of wind as a power source either for electricity generation or for water pumping. In this study the statistical analysis has been performed by Weibull distribution function. The results show that the Weibull distribution has fitted the wind data very well. Also it has been demonstrated that wind speed at 40 m height is ranged from 1.75 m/s in Dec to 3.28 m/s in Aug with average value of 2.69 m/s. In this research, different wind speed characteristics such as turbulence intensity, wind direction, monthly air temperature, humidity wind power density and other related parameters have been investigated. Finally it was concluded that the wind energy in the Sanar village may be explored by employing modern wind turbines that require very lower start-up speeds.

Keywords: wind energy, wind turbine, weibull, Sanar village, Iran

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Authors: Saeedeh Barzegar Khalilsaraei, Manoocheher Kelarestaghi, Farshad Eshghi

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The vehicle color, as a prominent and stable feature, helps to identify a vehicle more accurately. As a result, vehicle color recognition is of great importance in intelligent transportation systems. Unlike conventional methods which use only a single Convolutional Neural Network (CNN) for feature extraction or classification, in this paper, four CNNs, with different architectures well-performing in different classes, are trained to extract various features from the input image. To take advantage of the distinct capability of each network, the multiple outputs are combined using a stack generalization algorithm as an ensemble technique. As a result, the final model performs better than each CNN individually in vehicle color identification. The evaluation results in terms of overall average accuracy and accuracy variance show the proposed method’s outperformance compared to the state-of-the-art rivals.

Keywords: Vehicle Color Recognition, Ensemble Algorithm, Stack Generalization, Convolutional Neural Network

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Authors: Zahra A. Barzegar, Maryam B. Golboo

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In this paper, the manner of obtaining hierarchies and privacy entry of traditional houses in providing a safe place in the city of Shiraz will be evaluated by qualitative–descriptive methods and 6 old houses are the case study. The houses of Shiraz, as the houses in other cities in Iran are a response to climate and physical features. The old part of Shiraz has a compressed and dense texture in which the houses are in narrow and tight alleys. In this regard, the principles of traditional house entrance design have been introduced. The results show that every house has a private entrance. Direction of the entry of most houses is toward the south and with a turn to the South-East side. Entrance to yard path in all the cases is not straight, and this had been done by using 90 degrees rotates of the corridor leading to the yard. Vestibule provides a private place for the house and entrance stairway to the rooftop is located inside it.

Keywords: entrance, components of entrance, hierarchy, frontage, Shiraz houses

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Authors: Zahra Barzegar, Reza Deedari, Behzad Pourgharib

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This study examines how metamorphosis in nature is depicted in Charles Tomlinson's poetry through Lawrence Buell's mimesis and referential strategy of adéquation. This study aims to answer the questions that what is the relationship between Tomlinson's selected poems and nature, and how does Tomlinson's poetry bring the reader close to the natural environment. Adéquation is a way that brings the reader close to nature, not by imitating nature but by referring to it imaginatively and creating a stylized image. Using figurative language, namely imagery, metaphor, and analogy, adéquation creates a stylized image of metamorphosis in a nature scene that acts as a middle way between the reader and nature. This paper proves that adéquation reinvents the metamorphosis in natural occurrences in Charles Tomlinson's selected poems. Thus, a reader whose imagination is addressed achieves closeness with nature and a caring outlook toward natural happenings. This article confirms that Tomlinson's poems are potential enough to represent metamorphosis in nature through adéquation. Therefore, the reader understands nature beyond the poem as the poem presents a gist of nature through adéquation.

Keywords: adéquation, metamorphosis, nature, referentiality

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Authors: Yas Barzegaar, Atrin Barzegar

Abstract:

The aim of this research is to develop an intelligent system to analyze the risk level of wheat flour product manufacturing system. The model consists of five Fuzzy Inference Systems in two different layers to analyse the risk of a wheat flour product manufacturing system. The first layer of the model consists of four Fuzzy Inference Systems with three criteria. The output of each one of the Physical, Chemical, Biological and Environmental Failures will be the input of the final manufacturing systems. The proposed model based on Mamdani Fuzzy Inference Systems gives a performance ranking of wheat flour products manufacturing systems. The first step is obtaining data to identify the failure modes from expert’s opinions. The second step is the fuzzification process to convert crisp input to a fuzzy set., then the IF-then fuzzy rule applied through inference engine, and in the final step, the defuzzification process is applied to convert the fuzzy output into real numbers.

Keywords: failure modes, fuzzy rules, fuzzy inference system, risk assessment

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Authors: Meysam Doaei, Mojtaba Kavand

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WAQF as a part of Islamic social security system is developed in Islam. Traditional WAQF has some limitations which are resolved in WAQF Sukuk. In regard to acceptability of Islamic finance in the world, WAQF Sukuk also has been developing in Islamic countries. In this paper, concept of WAQF, traditional and modern WAQF financing are presented. Then, WAQF Sukuk, its application and its model in Iran are developed.

Keywords: Al-mawqūfat development, traditional financing, modern financing, WAQF Sukuk

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Authors: Morteza Raei Dehaghi, Mojtaba Molaahmadi, Seyed Mohammad Mirhashemi

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This study aimed to explore the relationship between energy consumption and value-added in Iran’s industry sector during the time period 1973-2011. Annual data related to energy consumption and value added in the industry sector were used. The results of the study revealed a positive relationship between energy consumption and value-added of the industry sector. Similarly, the results showed that there is one-way causality between energy consumption and value-added in the industry sector.

Keywords: economic growth, energy consumption, granger causality test, industry sector

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Authors: Mojtaba Hakimi-Moghaddam

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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions

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Authors: Helia Barzegar Sedigh, Farzaneh Hamedi, Payam Ashtari

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There are some limitations in common structural systems, such as providing appropriate lateral stiffness, adequate ductility, and architectural openings at the same time. Consequently, the concept of T-Resisting Frame (TRF) has been introduced to overcome all these deficiencies. The configuration of TRF in this study is a Vertical Plate Girder (VPG) which is placed within the span and two Horizontal Plate Girders (HPGs) connect VPG to side columns at each story level by the use of rigid connections. System performance is improved by utilizing rigid connections in side columns base joint. Shear yield of HPGs causes energy dissipation in TRF; therefore, high plastic deformation in web of HPGs and VPG affects the ductility of system. Moreover, in order to prevent shear buckling in web of TRF’s members and appropriate criteria for placement of web stiffeners are applied. In this paper, an experimental study is conducted by applying cyclic loading and using finite element models and numerical studies such as push over method are assessed on shear and flexural yielding of HPGs. As a result, seismic parameters indicate adequate lateral stiffness, and high ductility factor of 6.73, and HPGs’ shear yielding achieved as a proof of TRF’s better performance.

Keywords: experimental study, finite element model, flexural and shear yielding, t-resisting frame

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Authors: Minoo Tavakoli, Mojtaba Zebarjad, Golestanipour

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Metallic sandwich structures with aluminum foam core are good energy absorbers. In this paper, perforation test were carried out on different samples to study energy absorption. In the experiments, effect of several parameters, i.e. skin thickness and thickness of foam core, on the energy absorption, delamination zone of back faces and deformation strain(φ) are discussed. Results show that increasing plates thickness will results in more absorbed energy and delamination. Moreover, thickening foam core has the same effect.

Keywords: sandwich panel, aluminium foam, perforation, energy absorption

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Shohreh Rahimi Lascokalayeh, Hasan Yousefnia, Mojtaba Tajik, Samaneh Zolghadri, Bentehoda Abdolhosseini

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In this study, the production of terbium-161 as new therapeutic radionuclide was investigated using TALYS1.6& EMPIRE 3.2 codes. For this purpose, cross section for the reactions reactor to produce 161Tb were extracted by mean of this code In the following step, stopping power of the reactions reactor was calculated by SRIM code. The best reaction in the production of 161Tb is160 Gd(d,n)161Tb Production yield of the 161Tb was obtained by utilization of MATLAB calculation code and based on the charged particle reaction formalism.The results showed that Production yield of the 161Tb was obtained 0.8 (mci/ A*h).

Keywords: terbium161, TALYS1.6, EMPIRE3.2, yield, cross-section

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Authors: Mojtaba Ghodsi, Hamidreza Ziaifar, Morteza Mohammadzaheri, Payam Soltani

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In this paper, the performance of a medium power (25 kW/25 kHz) hybrid inverter with a reactive transformer is investigated. To analyze the sensitivity of the inverster, the RSM technique is employed to manifest the effective factors in the inverter to minimize current passing through the Insulated Bipolar Gate Transistors (IGBTs) (current stress). It is revealed that the ratio of the axillary inductor to the effective inductance of resonant inverter (N), is the most effective parameter to minimize the current stress in this type of inverter. In practice, proper selection of N mitigates the current stress over IGBTs by five times. This reduction is very helpful to keep the IGBTs at normal temperatures.

Keywords: analytical analysis, hybrid resonant inverter, reactive transformer, response surface method

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Authors: Mohammad Rahmani Rezaiyeh, Mojtaba Rahmani Rezaiyeh, Mehrdad Rahmani Rezaiyeh

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Smart speed bump is a new invention and I am invented it. Smart speed bump is a system that can change the position of speed bumps either active or passive in necessary situations. The basic system of smart speed bumps is based on a robotic system which includes mechanic, electronic and artificial intelligence. The smart speed bump is capable of smart decision making and can change its position by anticipating the peak of terrific hours. It can be noted to the advantages of this system such as preventing the waste of petrol while crossing speed bumps, traffic management, accelerating, flowing and securing traffic, reducing accidents and judicial records.

Keywords: invention, smart, robotic system, speed bump, traffic, management

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Authors: Anna Romanova, Mojtaba Mahmoodian, Morteza A. Alani

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Concrete sewer pipes are known to suffer from a process of hydrogen sulfide gas induced sulfuric acid corrosion. This leads to premature pipe degradation, performance failure and collapses which in turn may lead to property and health damage. The above work reports on a field study undertaken in working sewer manholes where the parameters of effluent temperature and pH as well as ambient temperature and concentration of hydrogen sulfide were continuously measured over a period of two months. Early results suggest that effluent pH has no direct effect on hydrogen sulfide build up; on average the effluent temperature is 3.5°C greater than the ambient temperature inside the manhole and also it was observed that hydrogen sulfate concentration increases with increasing temperature.

Keywords: concrete corrosion, hydrogen sulfide gas, temperature, sewer pipe

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

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Authors: Hamed Zolfaghari, Mojtaba Kord

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After feasibility study the design phase is started and the rest of other phases are highly dependent on this phase. forecasting the duration of design phase could do a miracle and would save a lot of time. This study provides a fast and accurate Machine learning (ML) and optimization framework, which allows a quick duration estimation of project design phase, hence improving operational efficiency and competitiveness of a design construction company. 3 data sets of three years composed of daily time spent for different design projects are used to train and validate the ML models to perform multiple projects. Our study concluded that Artificial Neural Network (ANN) performed an accuracy of 0.94.

Keywords: time estimation, machine learning, Artificial neural network, project design phase

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Authors: Hossein Kabir, Mojtaba Sadeghi

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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: single-degree-of-freedom system (SDOF), linear acceleration method, nonlinear excited system, equivalent displacement method, equivalent energy method

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Authors: Mojtaba Borhani

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By employing the unique characteristics of a region, its economy, climate, geography, and culture, rural communities can create distinctive products. This approach not only boosts economic opportunities but also promotes sustainable growth and preserves cultural heritage. A strategic focus on branding and intellectual property (IP) is essential. By developing strong brands, rural areas can differentiate their products, increase their market value, and build consumer loyalty. Moreover, IP protection safeguards the creative and innovative output of rural communities, incentivizing further development. Rural branding can serve as a cornerstone for community empowerment. It can help to prevent rural exodus by providing economic incentives and a strong sense of place. Additionally, by protecting traditional knowledge and cultural expressions, branding contributes to the long-term sustainability of rural livelihoods.

Keywords: intellectual property, regional branding, sustainable development, rural economy

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Authors: Fahimeh Hooshyar, Seyyed Mojtaba Abtahi

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Democracy which is, in its greek roots, consisted of “Demo” (People) and “Kratic” (people) is referring to governing of the people or governing by the people. in its widest definition it refers to a common lifestyle in which all the people has the equal potentials for social participating. But in political perspective, democracy is looking for the equal participation right of the citizens in political decision-making process. in this viewpoint, the democracy is solely a political construct or a social-political style in which all the values are relative. In this definition of the democracy emphasis is on equality of the people based on the governing rule and the natural social and political rights of every member of humankind. This notion of democracy by no means is a self reliant idea and the need of an ideological basis for approaching to this idea is inevitable. In this paper we are trying to define the inter-relations of democracy and its philosophical basis to Islamic fundamental ideas. Our approach to this topic would be a philosophical ideological one.

Keywords: Islam, democracy, democracy’s philosophical basis, secularism, fundamentalism

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Authors: Maryam Khalilzadeh Poshtegal, Seyed Ahmad Mirbagheri, Mojtaba Noury

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In this paper, by application of the input yearly data of rainfall, temperature and flow to the Urmia Lake, the simulation of water level fluctuation were applied by means of three models. According to the climate change investigation the fluctuation of lakes water level are of high interest. This study investigate data-driven models, support vector machines (SVM), SVM method which is a new regression procedure in water resources are applied to the yearly level data of Lake Urmia that is the biggest and the hyper saline lake in Iran. The evaluated lake levels are found to be in good correlation with the observed values. The results of SVM simulation show better accuracy and implementation. The mean square errors, mean absolute relative errors and determination coefficient statistics are used as comparison criteria.

Keywords: simulation, water level fluctuation, urmia lake, support vector machine

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Authors: Mojtaba Molaahmadi, Morteza Raei Dehaghi, Abdolrahim Arghavan

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The present study aims to explore the effect of computerization on marketing performance in Snowa Company. In other words, this study intends to respond to this question that whether or not there is a relationship between utilization of computerization in marketing activities and marketing performance. The statistical population included 60 marketing managers of Snowa Company. In order to test the research hypotheses, Pearson correlation coefficient was employed. The reliability was equal to 96.8%. In this study, computerization was the independent variable and marketing performance was the dependent variable with characteristics of market share, improving the competitive position, and sales volume. The results of testing the hypotheses revealed that there is a significant relationship between utilization of computerization and market share, sales volume and improving the competitive position

Keywords: computerization, e-marketing information, information technology, marketing performance

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Authors: Mohammad Mohammadi, Mojtaba Askari, Mohammad Farouq Hossaini

Abstract:

An intrinsic property of rock mass known as rock bolt supporting factor (RSF) or rock bolting capability of rock mass was developed and used for explanation of the mechanism of rock bolting practice. Based on the theory of RSF, numeral values can be assigned to each given rock mass to show the capability of that rock mass to be reinforced by rock bolting. For determination of shotcrete thickness, both safety and cost must be taken into account. The present paper introduces a scientific approach for determination of the necessary shotcrete thickness in underground structures for support purposes using the concept of rock bolt supporting factor (RSF). The proposed approach makes the outcome of shotcrete design one step more accurate than before. The actual dataset of 500 meters of Alborz Tunnel length is used as an example of the application of the approach.

Keywords: rock bolt supporting factor (RSF), shotcrete design, underground excavation, Alborz Tunnel

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Authors: Mojtaba Soltani, Edi Suhaimi Bakar, Hamid Reza Naji

Abstract:

Date Palm Wood (D.P.W) specimens were impregnated with Phenol formaldehyde (PF) resin at 15% level, using vacuum/pressure method. Three levels of moisture content (MC) (50%, 60%, and 70% ) before pressing stage and three hot pressing times (15, 20, and 30 minutes) were the variables. The boards were prepared at 20% compression rate. The physical properties of specimens such as spring back, thickness swelling and water absorption, and mechanical properties including MOR, MOE were studied and compared between variables. The results indicated that the percentage of MC levels before compression set was the main factor on the properties of the Date Palm Compreg. Also, the results showed that this compregnation method can be used as a good method for making high-quality bio-composite from Date Palm Wood.

Keywords: Date palm, phenol formaldehyde resin, high-quality bio-composite, physical and mechanical properties

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Authors: Sajjad Rostami-Sani, Mojtaba Valinataj, Amir-Hossein Khojir-Angasi

Abstract:

The cache has an important role in the reduction of access delay between a processor and memory in high-performance embedded systems. In these systems, the energy consumption is one of the most important concerns, and it will become more important with smaller processor feature sizes and higher frequencies. Meanwhile, the cache system dissipates a significant portion of energy compared to the other components of a processor. There are some elements that can affect the energy consumption of the cache such as replacement policy and degree of associativity. Due to these points, it can be inferred that selecting an appropriate configuration for the cache is a crucial part of designing a system. In this paper, we investigate the effect of different cache replacement policies on both cache’s performance and energy consumption. Furthermore, the impact of different Instruction Set Architectures (ISAs) on cache’s performance and energy consumption has been investigated.

Keywords: energy consumption, replacement policy, instruction set architecture, multicore processor

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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