Search results for: geotechnical random variables

Authors: Xiaolai Zhang, Haitao Zhang, Qiwen Sun, Weixin Qian, Weiyong Ying

Abstract:

High temperature Fischer-Tropsch synthesis process use fixed fluidized bed as a reactor. In order to understand the flow behavior in the fluidized bed better, the research of how the radial velocity affects the entire flow field is necessary. Laser Doppler Velocimetry (LDV) was used to study the radial velocity distribution along the diameter direction of the cross-section of the particle in a fixed fluidized bed. The velocity in the cross-section is fluctuating within a small range. The direction of the speed is a random phenomenon. In addition to r/R is 1, the axial velocity are more than 6 times of the radial velocity, the radial velocity has little impact on the axial velocity in a fixed fluidized bed.

Keywords: LDV, fixed fluidized bed, velocity, Fischer-Tropsch synthesis.

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Authors: M. Sinecen, M. Makinacı

Abstract:

The purpose of this paper is to assess the value of neural networks for classification of cancer and noncancer prostate cells. Gauss Markov Random Fields, Fourier entropy and wavelet average deviation features are calculated from 80 noncancer and 80 cancer prostate cell nuclei. For classification, artificial neural network techniques which are multilayer perceptron, radial basis function and learning vector quantization are used. Two methods are utilized for multilayer perceptron. First method has single hidden layer and between 3-15 nodes, second method has two hidden layer and each layer has between 3-15 nodes. Overall classification rate of 86.88% is achieved.

Keywords: Artificial neural networks, texture classification, cancer diagnosis.

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Authors: Subrahmanyam Kodukula, Nurbiya Maimaiti

Abstract:

There have been many variations of technologies that helped educators in teaching & learning. From the past research it is evident that Information Technology significantly increases student participation and interactivity in the classrooms. This research started with a aim to find whether adoption of Wi-Fi environment by Malaysian Higher Educational Institutions (HEI) can benefit students and staff equally. The study was carried out in HEI-s of Klang Valley, Malaysia and the data is gathered through paper based surveys. A sample size of 237 units were randomly selected from 5 higher educational institutions in the Klang Valley using the Stratified Random sampling method and from the analysis of the data, it was found that the implementation of wireless technologies in HEIs have created lot of opportunities and also challenges.

Keywords: Wired Technologies, Wireless Classroom, HEI, Dense User Environment.

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Authors: L. Petrovičová, Ž. Balážová, Z. Gálová, M. Wójcik-Jagła, M. Rapacz

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In the present study, RAPD-PCR was used to assess genetic diversity of the rye including landrances and new rye cultivars coming from Central Europe and the Union of Soviet Socialist Republics (SUN). Five arbitrary random primers were used to determine RAPD polymorphism in the set of 38 rye genotypes. These primers amplified altogether 43 different DNA fragments with an average number of 8.6 fragments per genotypes. The number of fragments ranged from 7 (RLZ 8, RLZ 9 and RLZ 10) to 12 (RLZ 6). DI and PIC values of all RAPD markers were higher than 0.8 that generally means high level of polymorphism detected between rye genotypes. The dendrogram based on hierarchical cluster analysis using UPGMA algorithm was prepared. The cultivars were grouped into two main clusters. In this experiment, RAPD proved to be a rapid, reliable and practicable method for revealing of polymorphism in the rye cultivars.

Keywords: Genetic diversity, polymorphism, RAPD markers, Secalecereale L.

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Authors: Hechmi Saidi, Noureddine Hamdi

Abstract:

The performance of hybrid amplify and forward - decode and forward (AF-DF) hybrid radio frequency/free space optical (RF/FSO) communication system, that adopts M-ary pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived. The random variations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the gamma-gamma (GG) statistical distribution. A closed-form expression for the probability density function (PDF) is derived for the whole above system is obtained. Thanks to the use of hybrid AF-DF hybrid RF/FSO configuration and MPPM, the effects of atmospheric turbulence is mitigated; hence the capacity of combating atmospheric turbulence and the transmissitted signal quality are improved.

Keywords: FSO, RF, hybrid, AF, DF, SER, SNR, GG channel.

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Authors: Srinath Shetty K., Shivashankar R., Rashmi P. Shetty

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Earth reinforcing techniques have become useful and economical to solve problems related to difficult grounds and provide satisfactory foundation performance. In this context, this paper uses radial basis function neural network (RBFNN) for predicting the bearing pressure of strip footing on reinforced granular bed overlying weak soil. The inputs for the neural network models included plate width, thickness of granular bed and number of layers of reinforcements, settlement ratio, water content, dry density, cohesion and angle of friction. The results indicated that RBFNN model exhibited more than 84 % prediction accuracy, thereby demonstrating its application in a geotechnical problem.

Keywords: Bearing pressure, granular bed, radial basis function neural network, strip footing.

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Authors: Daniel Morariu, Lucian N. Vintan, Volker Tresp

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Text categorization is the problem of classifying text documents into a set of predefined classes. After a preprocessing step, the documents are typically represented as large sparse vectors. When training classifiers on large collections of documents, both the time and memory restrictions can be quite prohibitive. This justifies the application of feature selection methods to reduce the dimensionality of the document-representation vector. In this paper, three feature selection methods are evaluated: Random Selection, Information Gain (IG) and Support Vector Machine feature selection (called SVM_FS). We show that the best results were obtained with SVM_FS method for a relatively small dimension of the feature vector. Also we present a novel method to better correlate SVM kernel-s parameters (Polynomial or Gaussian kernel).

Keywords: Feature Selection, Learning with Kernels, SupportVector Machine, and Classification.

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Authors: Md. Emaj Uddin

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Family structure that is culturally constructed in every society is the basic unit of social structure. Purpose of the study was to compare family structure, including marriage, residence, family size, type, role sharing, authority, and communication patterns between Muslim and Santal communities in rural Bangladesh. For this we assumed that family structure with the elements was significantly different between the two communities in rural Bangladesh. In so doing, 288 active couples (145 for Muslim and 143 for Santal) selected by cluster random sampling were intensively interviewed with a semi-structured questionnaire method. The results of Pearson Chi-Squire Test reveal that there were significant differences in the family structure followed by the two communities in the study area. Further cross-cultural study should be done on why family structure varies between the communities in Bangladesh.

Keywords: Bangladesh, Cross-Cultural Comparison, Family Structure, Muslim, Santal.

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Authors: N. Veerasamy, C. J. Cheyne

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Users of computer systems may often require the private transfer of messages/communications between parties across a network. Information warfare and the protection and dominance of information in the military context is a prime example of an application area in which the confidentiality of data needs to be maintained. The safe transportation of critical data is therefore often a vital requirement for many private communications. However, unwanted interception/sniffing of communications is also a possibility. An elementary stealthy transfer scheme is therefore proposed by the authors. This scheme makes use of encoding, splitting of a message and the use of a hashing algorithm to verify the correctness of the reconstructed message. For this proof-of-concept purpose, the authors have experimented with the random sending of encoded parts of a message and the construction thereof to demonstrate how data can stealthily be transferred across a network so as to prevent the obvious retrieval of data.

Keywords: Construction, encode, interception, stealthy.

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Authors: Beata Ślusarczyk, Sebastian Kot

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In subjective terms, Polish SME sector occupies a prominent position in the national economic development, in which planning of the management strategies should be primarily based on identifying and meeting the innovation needs. As a research sample, there is chosen a printing sector of industry. SMEs share in printing sector in Poland is estimated at the level of 81% of all enterprises. In recent years, the printing industry achieved one of the highest levels of EU support in Poland. There is a relatively high increase in the development of technological innovations in equipment and the associated significant increase in production capacity. It can be also noticed that on average, every third enterprise belonging to the printing industry has implemented innovations, but not all of them effected in better economic results. Therefore, the aim of this article is to evaluate the impact of the implementation of innovation projects financed from the EU funds for performance of SMEs in the printing industry. As the results of research of EU funds co-financing effects on the development of innovation in the printing industry, it was specified that examined SMEs prefer to implement product innovation to receive a grant to the project at a level between 40% to 60%, the remaining part of the investment is usually covered with equity. The most common type of innovation had indicated a single implementation, related only to the change in process, technology, or organization. The relationship between variables of the EU funds and management of innovative activities was verified. It has been observed that the identified variables arising from the support in a form of the EU funds had a positive effect on the level of earned revenue, the increase in margin and in increase in employment as well. It was confirmed that the implemented innovations supported by the European funds have a positive impact on the performance of the printing companies. Although there is a risk that due to the decreasing demand for printing services such a high level of funding the companies in this sector will significantly increase competition in the long term, that may also contribute to the economic problems of the enterprises belonging to the analyzed branch.

Keywords: Innovations, SMEs, performance, results.

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Authors: Kyoung Kun Lee, Soongyu Kwon, Jong Tae Kim

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An embedded system for SEU(single event upset) test needs to be designed to prevent system failure by high-energy particles during measuring SEU. SEU is a phenomenon in which the data is changed temporary in semiconductor device caused by high-energy particles. In this paper, we present an embedded system for SRAM(static random access memory) SEU test. SRAMs are on the DUT(device under test) and it is separated from control board which manages the DUT and measures the occurrence of SEU. It needs to have considerations for preventing system failure while managing the DUT and making an accurate measurement of SEUs. We measure the occurrence of SEUs from five different SRAMs at three different cyclotron beam energies 30, 35, and 40MeV. The number of SEUs of SRAMs ranges from 3.75 to 261.00 in average.

Keywords: embedded system, single event upset, SRAM

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Authors: Ramazan Hasanzadeh, Leyla Vatandoust

Abstract:

This study examined the efficacy of motivation management training for students’ academic achievement and self-concept. The pretest–posttest quasi-experimental study used a cluster random sampling method to select subjects for the experimental (20 subjects) and control (20 subjects) groups. posttest was conducted with both groups to determine the effect of the training. An academic achievement and academic self-concept questionnaire (grade point average requirement) was used for the pretest and posttest. The results showed that the motivation management training increased academic self-concept and academic achievement.

Keywords: Motivation management, academic self-concept, academic achievement, students.

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Authors: M. Mlhem

Abstract:

Geotechnical engineers face many problematic soils upon construction and they have the choice for replacing these soils with more appropriate soils or attempting to improve the engineering properties of the soil through a suitable soil stabilization technique. Mostly, improving soils is environmental, easier and more economical than other solutions. Stabilization soils technique is applied by introducing a cementing agent or by injecting a substance to fill the pore volume. Chemical stabilizers are divided into two groups: traditional agents such as cement or lime and non-traditional agents such as polymers. This paper studies the effect of epoxy additives on the compression strength of four types of soil and then compares with the effect of cement on the compression strength for the same soils. Overall, the epoxy additives are more effective in increasing the strength for different types of soils regardless its classification. On the other hand, there was no clear relation between studied parameters liquid limit, passing No.200, unit weight and between the strength of samples for different types of soils.

Keywords: Additives, clay, compression strength, epoxy, stabilization.

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Authors: Byung – wan Jo, Jung – hoon Park, Jang - wook Kim

Abstract:

Recently, as information industry and mobile communication technology are developing, this study is conducted on the new concept of intelligent structures and maintenance techniques that applied wireless sensor network, USN (Ubiquitous Sensor Network), to social infrastructures such as civil and architectural structures on the basis of the concept of Ubiquitous Computing that invisibly provides human life with computing, along with mutually cooperating, compromising and connecting networks each other by having computers within all objects around us. Therefore, the purpose of this study is to investigate the capability of wireless communication of sensor node embedded in reinforced concrete structure with a basic experiment on an electric wave permeability of sensor node by fabricating molding with variables of concrete thickness and steel bars that are mostly used in constructing structures to determine the feasibility of application to constructing structures with USN. At this time, with putting the pitches of steel bars, the thickness of concrete placed, and the intensity of RF signal of a transmitter-receiver as variables and when wireless communication module was installed inside, the possible communication distance of plain concrete and the possible communication distance by the pitches of steel bars was measured in the horizontal and vertical direction respectively. Besides, for the precise measurement of diminution of an electric wave, the magnitude of an electric wave in the range of used frequencies was measured by using Spectrum Analyzer. The phenomenon of diminution of an electric wave was numerically analyzed and the effect of the length of wavelength of frequencies was analyzed by the properties of a frequency band area. As a result of studying the feasibility of an application to constructing structures with wireless sensor, in case of plain concrete, it shows 45cm for the depth of permeability and in case of reinforced concrete with the pitches of 5cm, it shows 37cm and 45cm for the pitches of 15cm.

Keywords: Ubiquitous, Concrete, Permeability, Wireless, Sensor

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Authors: N. Greco, S. Impedovo, R.Modugno, G. Pirlo

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This paper presents a new technique for generating sets of synthetic classifiers to evaluate abstract-level combination methods. The sets differ in terms of both recognition rates of the individual classifiers and degree of similarity. For this purpose, each abstract-level classifier is considered as a random variable producing one class label as the output for an input pattern. From the initial set of classifiers, new slightly different sets are generated by applying specific operators, which are defined at the purpose. Finally, the sets of synthetic classifiers have been used to estimate the performance of combination methods for abstract-level classifiers. The experimental results demonstrate the effectiveness of the proposed approach.

Keywords: Abstract-level Classifier, Dempster-Shafer Rule, Multi-expert Systems, Similarity Index, System Evaluation

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: B. Prabhakara Rao, M. V. H. Bhaskara Murthy

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An Ad hoc wireless network comprises of mobile terminals linked and communicating with each other sans the aid of traditional infrastructure. Optimized Link State Protocol (OLSR) is a proactive routing protocol, in which routes are discovered/updated continuously so that they are available when needed. Hello messages generated by a node seeks information about its neighbor and if the latter fails to respond to a specified number of hello messages regulated by neighborhood hold time, the node is forced to assume that the neighbor is not in range. This paper proposes to evaluate OLSR routing protocol in a random mobility network having various neighborhood hold time intervals. The throughput and delivery ratio are also evaluated to learn about its efficiency for multimedia loads.

Keywords: Ad hoc Network, Optimized Link State Routing, Multimedia traffic

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Authors: Emad T. Khalaf, Norrozila Sulaiman

Abstract:

Many researchers are working on information hiding techniques using different ideas and areas to hide their secrete data. This paper introduces a robust technique of hiding secret data in image based on LSB insertion and RSA encryption technique. The key of the proposed technique is to encrypt the secret data. Then the encrypted data will be converted into a bit stream and divided it into number of segments. However, the cover image will also be divided into the same number of segments. Each segment of data will be compared with each segment of image to find the best match segment, in order to create a new random sequence of segments to be inserted then in a cover image. Experimental results show that the proposed technique has a high security level and produced better stego-image quality.

Keywords: steganography; LSB Matching; RSA Encryption; data segments

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Authors: Omid Gervei, Ahmad Ayatollahi, Navid Gervei

Abstract:

In this paper we present an approach for 3D face recognition based on extracting principal components of range images by utilizing modified PCA methods namely 2DPCA and bidirectional 2DPCA also known as (2D) 2 PCA.A preprocessing stage was implemented on the images to smooth them using median and Gaussian filtering. In the normalization stage we locate the nose tip to lay it at the center of images then crop each image to a standard size of 100*100. In the face recognition stage we extract the principal component of each image using both 2DPCA and (2D) 2 PCA. Finally, we use Euclidean distance to measure the minimum distance between a given test image to the training images in the database. We also compare the result of using both methods. The best result achieved by experiments on a public face database shows that 83.3 percent is the rate of face recognition for a random facial expression.

Keywords: 3D face recognition, 2DPCA, (2D) 2 PCA, Rangeimage

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Authors: Xu Guoliang, Tan Qingping

Abstract:

Color printing proceeds with multiple halftone separations overlay. Because of separation overlay misalignment in printing, the percentage of different primary color combination may vary and it will result in color shift. In traditional printing procedure with AM halftone, every separation has different screening angle to make the superposition pattern in a random style, which will reduce the color shift. To evaluate the color shift of printing with hybrid halftoning, we simulate printing procedure with halftone images overlay and calculate the color difference between expected color and color in different overlay misalignment configurations. The color difference for hybrid halftone and AM halftone is very close. So the color shift for hybrid halftone is acceptable with current color printing procedure.

Keywords: color printing, AM halftone, Hybrid halftone, misalignment, color shift, Neugebauer Color Equation

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Authors: Zina Benouaret, Djamil Aissani

Abstract:

In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis.

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Authors: Gilberto Gonzalez-A, Octavio Barriga

Abstract:

A bond graph model of a hydroelectric plant is proposed. In order to analyze the system some structural properties of a bond graph are used. The structural controllability of the hydroelctric plant is described. Also, the steady state of the state variables applying the bond graph in a derivative causality assignment is obtained. Finally, simulation results of the system are shown.

Keywords: Bond graph, hydraulic plant, steady state.

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Authors: Zhe JIN, Motomichi TOYAMA

Abstract:

In this paper, we propose a fixed formatting method of PPX(Pretty Printer for XML). PPX is a query language for XML database which has extensive formatting capability that produces HTML as the result of a query. The fixed formatting method is to completely specify the combination of variables and layout specification operators within the layout expression of the GENERATE clause of PPX. In the experiment, a quick comparison shows that PPX requires far less description compared to XSLT or XQuery programs doing the same tasks.

Keywords: PPX, XML, HTML, XSLT, XQuery, fixed formatting method.

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Authors: Cholpassorn Sitthiwarongchai, Chutikarn Sriviboon

Abstract:

The two primary objectives of this research were (1)  to examine the current knowledge and actual circumstance of  agricultural workers about mangosteen product processing; and (2) to  analyze and evaluate ways to develop capacity of mangosteen  product processing. The population of this study was 15,125 people  who work in the agricultural sector, in this context, mangosteen  production, in the eastern part of Thailand that included Chantaburi  Province, Rayong Province, Trad Province and Pracheenburi  Province. The sample size based on Yamane’s calculation with 95%  reliability was therefore 392 samples. Mixed method was employed  included questionnaire and focus group discussion with  Connoisseurship Model used in order to collect quantitative and  qualitative data. Key informants were used in the focus group  including agricultural business owners, academic people in agro food  processing, local academics, local community development staff,  OTOP subcommittee, and representatives of agro processing  industry professional organizations. The study found that the  majority of the respondents agreed with a high level (in five- rating  scale) towards most of variables of knowledge management in agro  food processing. The result of the current knowledge and actual  circumstance of agricultural human resource in an arena of  mangosteen product processing revealed that mostly, the respondents  agreed at a high level to establish 7 variables. The guideline to  developing the body of knowledge in order to enhance the capacity  of the agricultural workers in mangosteen product processing was  delivered in the focus group discussion. The discussion finally  contributed to an idea to produce manuals for mangosteen product  processing methods, with 4 products chosen: (1) mangosteen soap;  (2) mangosteen juice; (3) mangosteen toffee; and (4) mangosteen  preserves or jam.

Keywords: Capacity Enhancement, Agricultural Workers, Mangosteen Product Processing.

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Authors: K. Suganya Devi, P. Srinivasan, M. P. Vaishnave, G. Arutperumjothi

Abstract:

Today’s internet world is highly prone to various online attacks, of which the most harmful attack is phishing. The attackers host the fake websites which are very similar and look alike. We propose an image based authentication using steganography and visual cryptography to prevent phishing. This paper presents a secure steganographic technique for true color (RGB) images and uses Discrete Cosine Transform to compress the images. The proposed method hides the secret data inside the cover image. The use of visual cryptography is to preserve the privacy of an image by decomposing the original image into two shares. Original image can be identified only when both qualified shares are simultaneously available. Individual share does not reveal the identity of the original image. Thus, the existence of the secret message is hard to be detected by the RS steganalysis.

Keywords: Image security, random LSB, steganography, visual cryptography.

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Authors: H. K. Hwang, Zekeriya Aliyazicioglu, Solomon Wu, Hung Lu, Nick Wilkins, Daniel Kerr

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Multiple-input multiple-output (MIMO) radar has received increasing attention in recent years. MIMO radar has many advantages over conventional phased array radar such as target detection,resolution enhancement, and interference suppression. In this paper, the results are presented from a simulation study of MIMO uniformly-spaced linear array (ULA) antennas. The performance is investigated under varied parameters, including varied array size, pseudo random (PN) sequence length, number of snapshots, and signal to noise ratio (SNR). The results of MIMO are compared to a traditional array antenna.

Keywords: Multiple-input multiple-output (MIMO) radar, phased array antenna, target detection, radar signal processing.

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Authors: Collins C. Chiemeke

Abstract:

Multichannel Analysis of Surface Wave (MASW) seismic method is widely used in geotechnical engineering for the measurement of shear wave velocity and evaluation of material property. This method was recently conducted at a Dam site located in Zaria, within the basement complex of northern Nigeria. The aim of this experiment was to make use of the MASW method in evaluating the strength of material properties of a section of the Dam embankment, which is vital to ascertain the safety of the Dam. The result revealed that, the material embankment showed general increase of shear wave velocity with depth. The range of shear wave velocities and the determined Poisson’s ratio falls within the normal range of consolidated rock material, indicating the Dam embankment is still consolidated. The range of shear modulus determined, also shows that the Dam embankment is rigid enough to withstand the shear stress imposed by the impounded water.

Keywords: Dam, MASW, Multichannel Analysis of Surface Wave, Seismic.

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Authors: M. Amelsakhi, A. Sohrabi-Bidar, A. Shareghi

Abstract:

One of the most important issues about the structural damages caused by earthquake is the evaluating of the spectral response of the site on which the construction is built. This fact has demonstrated during many earlier earthquakes and many researchers’ reports have concerned with it. According to these reports, features of the site materials and geometry of the ground surface are considered the main factors. This study concentrates on the specific form of topographies like hills. Assessing of spectral responses of different points on the hills and beside demonstrates considerable differences between 1D and 2D methods of geotechnical analyses. A general trend of amplifications on the top of the hills and de-amplifications near the toe of the hills has been appeared within the acceleration, velocity and displacement response spectrums of horizontal motion. Evaluating of spectral responses of different sizes of the hills revealed that as much as the hill-size enlarges differences between spectral responses of 1D and 2D analyses transfers to longer range of periods and becomes wider.

Keywords: Topography effect, Amplification ratio, Response spectrum.

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Authors: S. K. Khosrowshahi, E. Güler

Abstract:

This study investigates the reinforcement function of geosynthetics on the shear strength and strain profile of sand. Conducting a series of simple shear tests, the shearing behavior of the samples under static and cyclic loads was evaluated. Three different types of geosynthetics including geotextile and geonets were used as the reinforcement materials. An image processing analysis based on the optical flow method was performed to measure the lateral displacements and estimate the shear strains. It is shown that besides improving the shear strength, the geosynthetic reinforcement leads a remarkable reduction on the shear strains. The improved layer reduces the required thickness of the soil layer to resist against shear stresses. Consequently, the geosynthetic reinforcement can be considered as a proper approach for the sustainable designs, especially in the projects with huge amount of geotechnical applications like subgrade of the pavements, roadways, and railways.

Keywords: Image processing, soil reinforcement, geosynthetics, simple shear test, shear strain profile.

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Authors: Soma Roychowdhury

Abstract:

This paper deals with a periodic-review substitutable inventory system for a finite and an infinite number of periods. Here an upward substitution structure, a substitution of a more costly item by a less costly one, is assumed, with two products. At the beginning of each period, a stochastic demand comes for the first item only, which is quality-wise better and hence costlier. Whenever an arriving demand finds zero inventory of this product, a fraction of unsatisfied customers goes for its substitutable second item. An optimal ordering policy has been derived for each period. The results are illustrated with numerical examples. A sensitivity analysis has been done to examine how sensitive the optimal solution and the maximum profit are to the values of the discount factor, when there is a large number of periods.

Keywords: Multi-period model, inventory, random demand, upward substitution.

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