Search results for: generalized beam theory

Authors: Ghassan H. Halasa

Abstract:

Elementary particles are created in pairs of equal and opposite momentums at a reference frame at the speed of light. The speed of light reference frame is viewed as a point in space as observed by observer at rest. This point in space is the bang location of the big bang theory. The bang in the big bang theory is not more than sustained flow of pairs of positive and negative elementary particles. Electrons and negative charged elementary particles are ejected from this point in space at velocities faster than light, while protons and positively charged particles obtain velocities lower than light. Subsonic masses are found to have real and positive charge, while supersonic masses are found to be negative and imaginary indicating that the two masses are of different entities. The electron-s super-sonic speed, as viewed by rest observer was calculated and found to be less than the speed of light and is little higher than the electron speed in Bohr-s orbit. The newly formed hydrogen gas temperature was found to be in agreement with temperatures found on newly formed stars. Universe expansion was found to be in agreement. Partial mass and charge elementary particles and particles with momentum only were explained in the context of this theoretical approach.

Keywords: Evolution of Matter, Multidimensional spaces, relativity, Big Bang Theory

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Authors: Sun Lim, Bong-Seok Kim

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This paper presents an adaptive nonlinear position controller with velocity constraint, capable of combining the input-output linearization technique and Lyapunov stability theory. Based on the Lyapunov stability theory, the adaptation law of the proposed controller is derived along with the verification of the overall system-s stability. Computer simulation results demonstrate that the proposed controller is robust and it can ensure transient stability of BLDCM, under the occurrence of a large sudden fault.

Keywords: BLDC Motor Control, Backstepping Control, Adaptive nonlinear control

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Authors: Joseph Ignagni, Rebecca E. Deen

Abstract:

There are many views on how human decision makers behave. In this work, the Justices of the United States Supreme Court will be viewed in terms of constrained maximization and cognitivecybernetic theory. This paper will integrate research in such fields as law, political science, psychology, economics and decision making theory. It will be argued that due to its heavy workload, the Supreme Court is forced to make decisions in a boundedly rational manner. The ideas and theory put forward here will be tested in the area of the Court’s decisions involving religion. Therefore, the cases involving the U.S. Constitution’s Free Exercise Clause and Establishment Clause will be analyzed. Also, variables such as the U.S. government’s involvement in these cases will be considered. The years to be studied will be 1987-2011.

Keywords: Establishment Clause, Free Exercise Clause, U.S. Constitution, U.S. Supreme Court.

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Authors: Nurul Diyana, A., Zainul Abidin, N.

Abstract:

Social cognitive theory explains the power to inaugurate change is determined by the mutual influence of personal proclivity and social factors which will shape ones- motivations and expectations. In construction industry, green concept offers an opportunity to leave a lighter footprint on the environment. This opportunity, however, has not been fully grasped by many countries. As such, venturing into green construction for many practitioners would be their maiden experience. Decision to venture into new practice such as green construction will be influenced by certain drivers. This paper explores these drivers which is further expanded into motivational factors and later becomes the platform upon which expectation for green construction stands. This theoretical concept of motivation and expectations, which is adapted from social cognitive theory, focus on developers- view because of their crucial role in green application. This conceptual framework, which serves as the basis for further research, will benefit the industry as it elucidate cognitive angles to attract more new entrants to green business.

Keywords: Developers, Green Construction, Motivation, Expectation, Social Cognitive Theory.

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Authors: Raya Harkouss, Bilal Hamad

Abstract:

Self-Consolidating Concrete (SCC) is considered as a relatively new technology created as an effective solution to problems associated with low quality consolidation. A SCC mix is defined as successful if it flows freely and cohesively without the intervention of mechanical compaction. The construction industry is showing high tendency to use SCC in many contemporary projects to benefit from the various advantages offered by this technology.

At this point, a main question is raised regarding the effect of enhanced fluidity of SCC on the structural behavior of high strength self-consolidating reinforced concrete.

A three phase research program was conducted at the American University of Beirut (AUB) to address this concern. The first two phases consisted of comparative studies conducted on concrete and mortar mixes prepared with second generation Sulphonated Naphtalene-based superplasticizer (SNF) or third generation Polycarboxylate Ethers-based superplasticizer (PCE). The third phase of the research program investigates and compares the structural performance of high strength reinforced concrete beam specimens prepared with two different generations of superplasticizers that formed the unique variable between the concrete mixes. The beams were designed to test and exhibit flexure, shear, or bond splitting failure.

The outcomes of the experimental work revealed comparable resistance of beam specimens cast using self-compacting concrete and conventional vibrated concrete. The dissimilarities in the experimental values between the SCC and the control VC beams were minimal, leading to a conclusion, that the high consistency of SCC has little effect on the flexural, shear and bond strengths of concrete members.

Keywords: Self-consolidating concrete (SCC), high-strength concrete, concrete admixtures, mechanical properties of hardened SCC, structural behavior of reinforced concrete beams.

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Authors: Olli Luoma, Johannes Tuikkala, Olli Nevalainen

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In this paper, we propose a novel improvement for the generalized Lloyd Algorithm (GLA). Our algorithm makes use of an M-tree index built on the codebook which makes it possible to reduce the number of distance computations when the nearest code words are searched. Our method does not impose the use of any specific distance function, but works with any metric distance, making it more general than many other fast GLA variants. Finally, we present the positive results of our performance experiments.

Keywords: Clustering, GLA, M-Tree, Vector Quantization .

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Authors: J. Ranjbarn, A. Alibeigloo

Abstract:

In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied.

Keywords: Nano-scale spherical shell, nonlocal elasticity theory, thermomechanical shock.

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Authors: B. Tondu, N. Bardou

Abstract:

The recent development of humanoid robots has led robot designers to imagine a great variety of anthropomorphic forms for human-like machine. Which form is the best ? We try to answer this question from a double meaning of the anthropomorphism : a positive anthropomorphism corresponing to the realization of an effective anthropomorphic form object and a negative one corresponding to our natural tendency in certain circumstances to give human attributes to non-human beings. We postulate that any humanoid robot is concerned by both these two anthropomorphism kinds. We propose to use gestalt theory and Heider-s balance theory in order to analyze how negative anthropomorphism can influence our perception of human-like robots. From our theoretical approach we conclude that an “even shape" as defined by gestalt theory is not a sufficient condition for a good integration of future humanoid robots into a human community. Aesthetic perception of the robot cannot be splitted from a social perception : a humanoid robot, any how the efforts made for improving its appearance, could be rejected if it is devoted to a task with too high affective implications.

Keywords: Robot appearance, humanoid robot, uncanny valley, human-robot-interaction.

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Authors: Teresa L. Ju, Szu-Yuan Sun, Pei-Ju Chao, Chang-Yao Wu

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This study aims to examine the factors affecting knowledge sharing behavior in knowledge-based electronic communities (e-communities) because quantity and quality of knowledge shared among the members play a critical role in the community-s sustainability. Past research has suggested three perspectives that may affect the quantity and quality of knowledge shared: economics, social psychology, and social ecology. In this study, we strongly believe that an economic perspective may be suitable to validate factors influencing newly registered members- knowledge contribution at the beginning of relationship development. Accordingly, this study proposes a model to validate the factors influencing members- knowledge sharing based on Transaction Cost Theory. By doing so, we may empirically test our hypotheses in various types of e-communities to determine the generalizability of our research models.

Keywords: Electronic community, individual behavior, knowledge sharing, transaction cost theory.

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Authors: Abilio Avila, Orestis Terzidis

Abstract:

A fundamental principle of Grounded Theory (GT) is to prevent the formation of preconceived theories. This implies the need to start a research study with an open mind and to avoid being absorbed by the existing literature. However, to start a new study without an understanding of the research domain and its context can be extremely challenging. This paper presents a research approach that simultaneously supports a researcher to identify and to focus on critical areas of a research project and prevent the formation of prejudiced concepts by the current body of literature. This approach comprises of four stages: Selection of secondary case studies, analysis of secondary case studies, development of an initial conceptual framework, development of an initial interview guide. The analysis of secondary case studies as a starting point for a research project allows a researcher to create a first understanding of a research area based on real-world cases without being influenced by the existing body of theory. It enables a researcher to develop through a structured course of actions a firm guide that establishes a solid starting point for further investigations. Thus, the described approach may have significant implications for GT researchers who aim to start a study within a given research area.

Keywords: Grounded theory, qualitative research, secondary case studies, secondary data analysis, interview guide.

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Authors: Dany Ng Cheong Vee, Preethee Nunkoo Gonpot, Noor-Ul-Hacq Sookia

Abstract:

In this paper, we consider the application of Extreme Value Theory as a risk measurement tool. The Value at Risk, for a set of indices, from six Stock Exchanges of Frontier markets is calculated using the Peaks over Threshold method and the performance of the model index-wise is evaluated using coverage tests and loss functions. Our results show that “fattailedness” alone of the data is not enough to justify the use of EVT as a VaR approach. The structure of the returns dynamics is also a determining factor. This approach works fine in markets which have had extremes occurring in the past thus making the model capable of coping with extremes coming up (Colombo, Tunisia and Zagreb Stock Exchanges). On the other hand, we find that indices with lower past than present volatility fail to adequately deal with future extremes (Mauritius and Kazakhstan). We also conclude that using EVT alone produces quite static VaR figures not reflecting the actual dynamics of the data.

Keywords: Extreme Value theory, Financial Crisis 2008, Frontier Markets, Value at Risk.

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Authors: Rodrigo Barreiros Leal, Aracéli Cristina de Sousa Ferreira

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This study examines the possibility to apply the theory of multidimensional accounting (momentum accounting) in a Brazilian Navy-s Services Provider Military Organization (Organização Militar Prestadora de Serviços - OMPS). In general, the core of the said theory is the fact that Accounting does not recognize the inertia of transactions occurring in an entity, and that occur repeatedly in some cases, regardless of the implementation of new actions by its managers. The study evaluates the possibility of greater use of information recorded in the financial statements of the unit of analysis, within the strategic decisions of the organization. As a research strategy, we adopted the case study. The results infer that it is possible to use the theory in the context of a multidimensional OMPS, promoting useful information for decision-making and thereby contributing to the strengthening of the necessary alignment of its administration with the current desires of the Brazilian society.

Keywords: Multidimensional Accounting, Public Management, Decision Making.

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Authors: Alexandr A. Penin

Abstract:

Application of projective geometry to the theory of two-ports and cascade circuits with a load change is considered. The equations linking the input and output of a two-port are interpreted as projective transformations which have the invariant as a cross-ratio of four points. This invariant has place for all regime parameters in all parts of a cascade circuit. This approach allows justifying the definition of a regime and its change, to calculate a circuit without explicitly finding the aparameters, to transmit accurately an analogue signal through the unstable two-port.

Keywords: Circuit regime, geometric circuit theory, projective geometry, two-port.

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Authors: Soon-Hyun Park, Takami Matsuo

Abstract:

This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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Authors: Maslina Darus, Khalifa Al-Shaqsi

Abstract:

In this paper, a generalized derivatives operator n λ,βf introduced by the authors will be discussed. Some subordination and superordination results involving this operator for certain normalized analytic functions in the open unit disk will be investigated. Our results extend corresponding previously known results.

Keywords: Analytic functions, Univalent functions, Derivative operator, Differential subordination, Differential superordination.

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Authors: Arkady Bolotin

Abstract:

In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, there are hardly any applications of possibility theory in biology or medicine. The aim of this work is to demonstrate the use of possibility theory in an epidemiological study. In the paper, we build the possibility distribution for the controlled bloodstream concentrations of any physiologically active substance through few approximate considerations. This possibility distribution is tested later against the empirical histograms obtained from the panel study of the eight different physiologically active substances in 417 individuals.

Keywords: Possibility distributions, physiologically activesubstances, bloodstream concentrations.

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Authors: Shanshan Li

Abstract:

Beginning with the debate of concept, this essay explains the historical source and development of flexible housing in China. In the former part, the flexibility contained in traditional house is explored. While in the latter, the relevant practices in modern times are systematically analyzed as three phases–the Embryonic Period (1949 - 1980), the Systematic Practice (1981 - 2000), as well as the Integrated Trend and Prosperity (2001 - present). As a conclusion, the generalized flexibility is tentatively discussed.

Keywords: Flexibility, Long-term effectiveness, Variety, Social background.

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Authors: Hae-Yeoun Lee, In-Koo Kang, Heung-Kyu Lee

Abstract:

This paper addresses an efficient technique to embed and detect digital fingerprint code. Orthogonal modulation method is a straightforward and widely used approach for digital fingerprinting but shows several limitations in computational cost and signal efficiency. Coded modulation method can solve these limitations in theory. However it is difficult to perform well in practice if host signals are not available during tracing colluders, other kinds of attacks are applied, and the size of fingerprint code becomes large. In this paper, we propose a hybrid modulation method, in which the merits of or-thogonal modulation and coded modulation method are combined so that we can achieve low computational cost and high signal efficiency. To analyze the performance, we design a new fingerprint code based on GD-PBIBD theory and modulate this code into images by our method using spread-spectrum watermarking on frequency domain. The results show that the proposed method can efficiently handle large fingerprint code and trace colluders against averaging attacks.

Keywords: Fingerprinting, GD-PBIBD theory, Hybrid modulationtechnique.

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Authors: Mesbaholdin Salami, Farzad Movahedi Sobhani, Mohammad Sadegh Ghazizadeh

Abstract:

Evaluation of organizational performance is among the most important measures that help organizations and entities continuously improve their efficiency. Organizations can use the existing data and results from the comparison of units under investigation to obtain an estimation of their performance. The Malmquist Productivity Index (MPI) is an important index in the evaluation of overall productivity, which considers technological developments and technical efficiency at the same time. This article proposed a model based on the multistage MPI, considering limited data (Grey’s theory). This model can evaluate the performance of units using limited and uncertain data in a multistage process. It was applied by the electricity market manager to Iran’s electric power supply chain (EPSC), which contains uncertain data, to evaluate the performance of its actors. Results from solving the model showed an improvement in the accuracy of future performance of the units under investigation, using the Grey’s system theory. This model can be used in all case studies, in which MPI is used and there are limited or uncertain data.

Keywords: Malmquist Index, Grey's Theory, Charnes Cooper & Rhodes (CCR) Model, network data envelopment analysis, Iran electricity power chain.

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Authors: Anil Kumar, S. Deswal

Abstract:

The mathematical equation for Separation of the binary aqueous solution is developed by using the Spiegler- Kedem theory. The characteristics of a B-9 hollow fibre module of Du Pont are determined by using these equations and their results are compared with the experimental results of Ohya et al. The agreement between these results is found to be excellent.

Keywords: Binary aqueous solution, modeling, reverse osmosis module, Spiegler-Kedem theory.

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Authors: I. Habi, M. Bouguerra, D. Ouahdi, H. Meglouli

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In this paper, we apply the PQ theory with shunt active power filter in an unbalanced and distorted power system voltage to compensate the perturbations generated by non linear load. The power factor is also improved in the current source. The PLL system is used to extract the fundamental component of the even sequence under conditions mentioned of the power system voltage.

Keywords: Converter, power filter, harmonies, non-linear load, pq theory, PLL, unbalanced voltages, distorted voltages.

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Authors: Aziza Altaibayeva, Ertan Gudekli, Ratbay Myrzakulov

Abstract:

In this letter, we explore exact solutions for the Horava-Lifshitz gravity. We use of an extension of this theory with first order dynamical lapse function. The equations of motion have been derived in a fully consistent scenario. We assume that there are some spherically symmetric families of exact solutions of this extended theory of gravity. We obtain exact solutions and investigate the singularity structures of these solutions. Specially, an exact solution with the regular horizon is found.

Keywords: Quantum gravity, Horava-Lifshitz gravity, black hole, spherically symmetric space times.

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Authors: Yehuda Roth

Abstract:

In quantum theory, a system’s time evolution is predictable unless an observer performs measurement, as the measurement process can randomize the system. This randomness appears when the measuring device does not accurately describe the measured item, i.e., when the states characterizing the measuring device appear as a superposition of those being measured. When such a mismatch occurs, the measured data randomly collapse into a single eigenstate of the measuring device. This  scenario resembles the interpretation process in which the observer does not experience an objective reality but interprets it based on preliminary descriptions initially ingrained into his/her mind. This distinction is the motivation for the present study in which the collapse scenario is regarded as part of the interpretation process of the observer. By adopting the formalism of the quantum theory, we present a complete mathematical approach that describes the interpretation process. We demonstrate this process by applying the proposed interpretation formalism to the ambiguous image "My wife and mother-in-law" to identify whether a woman in the picture is young or old.

Keywords: Interpretation, ambiguous images, data reception, state matching, classification, determination.

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Authors: Chigbogu G. Ozoegwu, Sam N. Omenyi

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The objective in this work is to generate and discuss the stability results of fully-immersed end-milling process with parameters; tool mass m=0.0431kg,tool natural frequency ω_n = 5700 rads^-1, damping factor ξ=0.002 and workpiece cutting coefficient C=3.5x10^7 Nm^-7/4. Different no of teeth is considered for the end-milling. Both 1-DOF and 2-DOF chatter models of the system are generated on the basis of non-linear force law. Chatter stability analysis is carried out using a modified form (generalized for both 1-DOF and 2-DOF models) of recently developed method called Full-discretization. The full-immersion three tooth end-milling together with higher toothed end-milling processes has secondary Hopf bifurcation lobes (SHBL’s) that exhibit one turning (minimum) point each. Each of such SHBL is demarcated by its minimum point into two portions; (i) the Lower Spindle Speed Portion (LSSP) in which bifurcations occur in the right half portion of the unit circle centred at the origin of the complex plane and (ii) the Higher Spindle Speed Portion (HSSP) in which bifurcations occur in the left half portion of the unit circle. Comments are made regarding why bifurcation lobes should generally get bigger and more visible with increase in spindle speed and why flip bifurcation lobes (FBL’s) could be invisible in the low-speed stability chart but visible in the high-speed stability chart of the fully-immersed three-tooth miller.

Keywords: Chatter, flip bifurcation, modified full-discretization map stability lobe, secondary Hopf bifurcation.

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Authors: Eid Alotaibi

Abstract:

The purpose of this study is to investigate the impact of tourists’ culture on perception and evaluation of hotel service experience and behavioral intentions. Drawing on Hofested’s cultural dimensions, this study seeks to further contribute towards understanding the effect of culture on perception and evaluation of hotels’ services, and whether there are differences between Saudi and European tourists’ perceptions of hotel services evaluation. A descriptive cross-sectional design was used in this study. Data were collected from tourists staying in five-star hotels in Saudi Arabia using the self-completion technique. The findings show that evaluations of hotel services differ from one culture to another. T-test results reveal that Saudis were more tolerant and reported significantly higher levels of satisfaction, were more likely to return and recommend the hotel, and perceived the price for the hotel stay as being good value for money as compared to their European counterparts. The sample was relatively small and specific to only five-star hotel evaluations. As a result, findings cannot be generalized to the wider tourist population. The results of this research have important implications for management within the Saudi hospitality industry. The study contributes to the tourist cultural theory by emphasizing the relative importance of cultural dimensions in-service evaluation. The author argues that no studies could be identified that compare Saudis and Europeans in their evaluations of their experiences staying at hotels. Therefore, the current study would enhance understanding of the effects of cultural factors on service evaluations and provide valuable input for international market segmentation and resource allocation in the Saudi hotel industry.

Keywords: Culture, tourist, service experience, hotel industry, Hofested’s cultural dimensions.

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Authors: Sahil, Rajeev Saha, Sanjeev Kumar

Abstract:

Material selection is one of the key issues for the production of reliable and quality products in industries. A number of materials are available for a single product due to which material selection become a difficult task. The aim of this paper is to select appropriate material for gear used in fuel pump by using Graph Theory and Matrix Approach (GTMA). GTMA is a logical and systematic approach that can be used to model and analyze various engineering systems. In present work, four alternative material and their seven attributes are used to identify the best material for given product.

Keywords: Material, GTMA, MADM, digraph, decision making.

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Authors: Mert Bal, Hayri Sever, Oya Kalıpsız

Abstract:

Medical Decision Support Systems (MDSSs) are sophisticated, intelligent systems that can provide inference due to lack of information and uncertainty. In such systems, to model the uncertainty various soft computing methods such as Bayesian networks, rough sets, artificial neural networks, fuzzy logic, inductive logic programming and genetic algorithms and hybrid methods that formed from the combination of the few mentioned methods are used. In this study, symptom-disease relationships are presented by a framework which is modeled with a formal concept analysis and theory, as diseases, objects and attributes of symptoms. After a concept lattice is formed, Bayes theorem can be used to determine the relationships between attributes and objects. A discernibility relation that forms the base of the rough sets can be applied to attribute data sets in order to reduce attributes and decrease the complexity of computation.

Keywords: Formal Concept Analysis, Rough Set Theory, Granular Computing, Medical Decision Support System.

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Authors: X. Mercilin Raajini, R. Raja Kumar, P. Indumathi, V. Praveen

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Many cluster based routing protocols have been proposed in the field of wireless sensor networks, in which a group of nodes are formed as clusters. A cluster head is selected from one among those nodes based on residual energy, coverage area, number of hops and that cluster-head will perform data gathering from various sensor nodes and forwards aggregated data to the base station or to a relay node (another cluster-head), which will forward the packet along with its own data packet to the base station. Here a Game Theory based Diligent Energy Utilization Algorithm (GTDEA) for routing is proposed. In GTDEA, the cluster head selection is done with the help of game theory, a decision making process, that selects a cluster-head based on three parameters such as residual energy (RE), Received Signal Strength Index (RSSI) and Packet Reception Rate (PRR). Finding a feasible path to the destination with minimum utilization of available energy improves the network lifetime and is achieved by the proposed approach. In GTDEA, the packets are forwarded to the base station using inter-cluster routing technique, which will further forward it to the base station. Simulation results reveal that GTDEA improves the network performance in terms of throughput, lifetime, and power consumption.

Keywords: Cluster head, Energy utilization, Game Theory, LEACH, Sensor network.

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Authors: Aisha Tarek Noour, Nick Hubbard

Abstract:

Learner motivation is considered to be an important component for the Blended e-Learning (BL) Method. BL is an effective learning method in multiple domains, which opens several opportunities for its participants to engage in the learning environment. This research explores the learners’ perspective of BL according to the Self-Determination Theory (SDT). It identifies the opportunities and challenges for using the BL in Logistics Education (LE) in Egyptian Higher Education (HE). SDT is approached from different perspectives within the relationship between Intrinsic Motivation (IM), Extrinsic Motivation (EM) and Amotivation (AM). A self-administered face-to-face questionnaire was used to collect data from learners who were geographically widely spread around three colleges of International Transport and Logistics (CILTs) at the Arab Academy for Science, Technology and Maritime Transport (AAST&MT) in Egypt. Six hundred and sixteen undergraduates responded to a questionnaire survey. Respondents were drawn from three branches in Greater Cairo, Alexandria, and Port Said. The data analysis used was SPSS 22 and AMOS 18.

Keywords: Intrinsic Motivation, Extrinsic Motivation, Amotivation, Blended e-Learning, Self Determination Theory.

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Authors: Nidhal Jamia, Sami El-Borgi

Abstract:

In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: Functionally graded piezoelectric material, mixed-mode crack, non-local theory, Schmidt method.

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