Search results for: operators sequence group

Authors: S. Sowmyayani, P. Arockia Jansi Rani

Abstract:

This paper integrates Octagon and Square Search pattern (OCTSS) motion estimation algorithm into H.264/AVC (Advanced Video Coding) video codec in Adaptive Group of Pictures (AGOP) mode. AGOP structure is computed based on scene change in the video sequence. Octagon and square search pattern block-based motion estimation method is implemented in inter-prediction process of H.264/AVC. Both these methods reduce bit rate and computational complexity while maintaining the quality of the video sequence respectively. Experiments are conducted for different types of video sequence. The results substantially proved that the bit rate, computation time and PSNR gain achieved by the proposed method is better than the existing H.264/AVC with fixed GOP and AGOP. With a marginal gain in quality of 0.28dB and average gain in bitrate of 132.87kbps, the proposed method reduces the average computation time by 27.31 minutes when compared to the existing state-of-art H.264/AVC video codec.

Keywords: Block Distortion Measure, Block Matching Algorithms, H.264/AVC, Motion estimation, Search patterns, Shot cut detection.

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Authors: Kolar Jan, Dvorak Vaclav

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In this study, an optimization of supersonic air-to-air ejector is carried out by a recently developed single-objective genetic algorithm based on adaption of sequence of individuals. Adaptation of sequence is based on Shape-based distance of individuals and embedded micro-genetic algorithm. The optimal sequence found defines the succession of CFD-aimed objective calculation within each generation of regular micro-genetic algorithm. A spring-based deformation mutates the computational grid starting the initial individualvia adapted population in the optimized sequence. Selection of a generation initial individual is knowledge-based. A direct comparison of the newly defined and standard micro-genetic algorithm is carried out for supersonic air-to-air ejector. The only objective is to minimize the loose of total stagnation pressure in the ejector. The result is that sequence-adopted micro-genetic algorithm can provide comparative results to standard algorithm but in significantly lower number of overall CFD iteration steps.

Keywords: Grid deformation, Micro-genetic algorithm, shapebased sequence, supersonic ejector.

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Authors: Patsaraporn Somboonsak, Mud-Armeen Munlin

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In April 2009, a new variant of Influenza A virus subtype H1N1 emerged in Mexico and spread all over the world. The influenza has three subtypes in human (H1N1, H1N2 and H3N2) Types B and C influenza tend to be associated with local or regional epidemics. Preliminary genetic characterization of the influenza viruses has identified them as swine influenza A (H1N1) viruses. Nucleotide sequence analysis of the Haemagglutinin (HA) and Neuraminidase (NA) are similar to each other and the majority of their genes of swine influenza viruses, two genes coding for the neuraminidase (NA) and matrix (M) proteins are similar to corresponding genes of swine influenza. Sequence similarity between the 2009 A (H1N1) virus and its nearest relatives indicates that its gene segments have been circulating undetected for an extended period. Nucleic acid sequence Maximum Likelihood (MCL) and DNA Empirical base frequencies, Phylogenetic relationship amongst the HA genes of H1N1 virus isolated in Genbank having high nucleotide sequence homology. In this paper we used 16 HA nucleotide sequences from NCBI for computing sequence relationships similarity of swine influenza A virus using the following method MCL the result is 28%, 36.64% for Optimal tree with the sum of branch length, 35.62% for Interior branch phylogeny Neighber – Join Tree, 1.85% for the overall transition/transversion, and 8.28% for Overall mean distance.

Keywords: Sequence DNA, Relationship of swine, Swineinfluenza, Sequence Similarity

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Authors: Rabha W. Ibrahim

Abstract:

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

Keywords: Fractional calculus, fractional differential equation, Cauchy equation, Riemann-Liouville fractional operators, Volterra integral equation, non-expansive mapping, iterative differential equation.

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Authors: Yiwan Guo, Fahui Zhai

Abstract:

In this paper, the similarity invariant and the upper semi-continuity of spherical spectrum, and the spherical spectrum properties for infinite direct sums of quaternionic operators are characterized, respectively. As an application of some results established, a concrete example about the computation of the spherical spectrum of a compact quaternionic operator with form of infinite direct sums of quaternionic matrices is also given.

Keywords: Spherical spectrum, Quaternionic operator, Upper semi-continuity, Direct sum of operators.

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Authors: Pa Pa Lin

Abstract:

This research work is concerned with the eigenvalue problem for the integral operators which are obtained by linearization of a nonlocal evolution equation. The purpose of section II.A is to describe the nature of the problem and the objective of the project. The problem is related to the “stable solution" of the evolution equation which is the so-called “instanton" that describe the interface between two stable phases. The analysis of the instanton and its asymptotic behavior are described in section II.C by imposing the Green function and making use of a probability kernel. As a result , a classical Theorem which is important for an instanton is proved. Section III devoted to a study of the integral operators related to interface dynamics which concern the analysis of the Cauchy problem for the evolution equation with initial data close to different phases and different regions of space.

Keywords: Evolution, Green function, instanton, integral operators.

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Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of (∈, ∈∨q)-fuzzy subalgebras, (∈,∈∨q)-fuzzy ideals and (∈,∈∨q)-fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, (∈, ∈∨q)-fuzzy subalgebras, (∈, ∈∨q)-fuzzy ideals, (∈, ∈∨q)-fuzzy quotient algebras.

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Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, generalized fuzzy subalgebras, generalized fuzzy ideals, generalized fuzzy quotient algebras.

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Authors: T. Balasubramanian, A. Pandiarani

Abstract:

In this paper we introduce some subspaces of fuzzy entire sequence space. Some general properties of these sequence spaces are discussed. Also some inclusion relation involving the spaces are obtained. Mathematics Subject Classification: 40A05, 40D25.

Keywords: Fuzzy Numbers, Entire sequences, completeness, Fuzzy entire sequences

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Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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Authors: R. Khaniki, M.B. Menhaj, H. Eliasi

Abstract:

This paper describes the application of a model predictive controller to the problem of batch reactor temperature control. Although a great deal of work has been done to improve reactor throughput using batch sequence control, the control of the actual reactor temperature remains a difficult problem for many operators of these processes. Temperature control is important as many chemical reactions are sensitive to temperature for formation of desired products. This controller consist of two part (1) a nonlinear control method GLC (Global Linearizing Control) to create a linear model of system and (2) a Model predictive controller used to obtain optimal input control sequence. The temperature of reactor is tuned to track a predetermined temperature trajectory that applied to the batch reactor. To do so two input signals, electrical powers and the flow of coolant in the coil are used. Simulation results show that the proposed controller has a remarkable performance for tracking reference trajectory while at the same time it is robust against noise imposed to system output.

Keywords: Generalized Predictive Control (GPC), TemperatureControl, Global Linearizing Control (GLC), Batch Reactor.

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Authors: R. Khaniki, M.B. Menhaj, H. Eliasi

Abstract:

This paper describes the application of a model predictive controller to the problem of batch reactor temperature control. Although a great deal of work has been done to improve reactor throughput using batch sequence control, the control of the actual reactor temperature remains a difficult problem for many operators of these processes. Temperature control is important as many chemical reactions are sensitive to temperature for formation of desired products. This controller consist of two part (1) a nonlinear control method GLC (Global Linearizing Control) to create a linear model of system and (2) a Model predictive controller used to obtain optimal input control sequence. The temperature of reactor is tuned to track a predetermined temperature trajectory that applied to the batch reactor. To do so two input signals, electrical powers and the flow of coolant in the coil are used. Simulation results show that the proposed controller has a remarkable performance for tracking reference trajectory while at the same time it is robust against noise imposed to system output.

Keywords: Generalized Predictive Control (GPC), TemperatureControl, Global Linearizing Control (GLC), Batch Reactor.

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Authors: Yuka Kawakami, Tomoyuki Yokogawa, Hisashi Miyazaki, Sousuke Amasaki, Yoichiro Sato, Michiyoshi Hayase

Abstract:

In this paper, we proposed a method for detecting consistency violation between state machine diagrams and a sequence diagram defined in UML 2.0 using SMV. We extended a method expressing these diagrams defined in UML 1.0 with boolean formulas so that it can express a sequence diagram with combined fragments introduced in UML 2.0. This extension made it possible to represent three types of combined fragment: alternative, option and parallel. As a result of experiment, we confirmed that the proposed method could detect consistency violation correctly with SMV.

Keywords: UML, model checking, SMV, sequence diagram.

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Authors: M. Moosavi, H. Khatibzadeh

Abstract:

In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.

Keywords: Fixed point, Hadamard space, proximal point algorithm, quasi-nonexpansive sequence of mappings, resolvent.

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Authors: Yilun Shang

Abstract:

Let {Xi}i≥1 be a martingale difference sequence with Xi = Si - Si-1. Under some regularity conditions, we show that (X2 1+· · ·+X2N n)-1/2SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided.

Keywords: central limit theorem, martingale difference sequence, backward martingale.

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Authors: M. V. A. Raju Bahubalendruni, Bibhuti Bhusan Biswal, B. B. V. L. Deepak

Abstract:

Achieving an appropriate assembly sequence needs deep verification for its physical feasibility. For this purpose, industrial engineers use several assembly predicates; namely, liaison, geometric feasibility, stability and mechanical feasibility. However, testing an assembly sequence for these predicates requires huge assembly information. Extracting such assembly information from an assembled product is a time consuming and highly skillful task with complex reasoning methods. In this paper, computer aided methods are proposed to extract all the necessary assembly information from computer aided design (CAD) environment in order to perform the assembly sequence planning efficiently. These methods use preliminary capabilities of three-dimensional solid modelling and assembly modelling methods used in CAD software considering equilibrium laws of physical bodies.

Keywords: Assembly automation, assembly attributes, assembly sequence generation, computer aided design.

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Authors: Manpreet Singh, Parminder Kaur Wadhwa, Surinder Kaur

Abstract:

The drug discovery process starts with protein identification because proteins are responsible for many functions required for maintenance of life. Protein identification further needs determination of protein function. Proposed method develops a classifier for human protein function prediction. The model uses decision tree for classification process. The protein function is predicted on the basis of matched sequence derived features per each protein function. The research work includes the development of a tool which determines sequence derived features by analyzing different parameters. The other sequence derived features are determined using various web based tools.

Keywords: Sequence Derived Features, decision tree.

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Authors: Fatemeh Afsharnia, Mohammad Amin Asoodar, Abbas Abdeshahi, Afshin Marzban

Abstract:

A repairable mechanical system (as agricultural tractor) is subject to deterioration or repeated failure and needs a repair shops and also operator’s capability for the repair and maintenance operations. Data are based on field visits and interviews with 48MF 285 tractor operators from 14 villages collected in north of Khouzestan province. The results showed that most operators were lack the technical skill to service and repair tractors due to insufficient training, specific education and work experience. Inadequate repair and maintenance facilities, such as workshops, mechanics and spare parts depots cause delays in repair work in the survey areas. Farmers do not keep accurate service records and most of them disregard proper maintenance and service of their tractors, such as changing engine oil without following the manufacturer’s recommendations. Since, Repair and maintenance facilities should be established in village areas to guarantee timely repair in case of breakdowns and to make spare parts available at low price. The operators should keep service records accurately and adhere to maintenance and service schedules according to the manufacturer’s instructions. They should also be encouraged to do the service and maintain their tractors properly.

Keywords: Operators’ capability, Facilities availability, Repair and maintenance, MF 285 tractors.

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Authors: A.Goel, M. Agrawal, P. Gupta Poddar

Abstract:

Selected Mapping (SLM) is a PAPR reduction technique, which converts the OFDM signal into several independent signals by multiplication with the phase sequence set and transmits one of the signals with lowest PAPR. But it requires the index of the selected signal i.e. side information (SI) to be transmitted with each OFDM symbol. The PAPR reduction capability of the SLM scheme depends on the selection of phase sequence set. In this paper, we have proposed a new phase sequence set generation scheme based on M-ary chaotic sequence and a mapping scheme to map quaternary data to concentric circle constellation (CCC) is used. It is shown that this method does not require SI and provides better SER performance with good PAPR reduction capability as compared to existing SLMOFDM methods.

Keywords: Orthogonal frequency division multiplexing (OFDM), Peak-to-average power ratio (PAPR), Selected mapping (SLM), Side information (SI)

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Authors: B. Falah, N. E. Abakouy

Abstract:

Due to its high computational cost, mutation testing has been neglected by researchers. Recently, many cost and mutants’ reduction techniques have been developed, improved, and experimented, but few of them has relied the possibility of reducing the cost of mutation testing on the program type of the application under test. This paper is a comparative study between four operators’ selection techniques (mutants sampling, class level operators, method level operators, and all operators’ selection) based on the program code type of each application under test. It aims at finding an alternative approach to reveal the effect of code type on mutation testing score. The result of our experiment shows that the program code type can affect the mutation score and that the programs using polymorphism are best suited to be tested with mutation testing.

Keywords: Equivalent mutant, killed mutant, mutation score, mutation testing, program code type.

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Authors: Justinian Anatory, Ekael Stephen Manase

Abstract:

In recent years, the adoption of mobile phones has been exceptionally rapid in many parts of the world, and Tanzania is not exceptional. We are witnessing a number of new mobile network operators being licensed from time to time by Tanzania Communications Regulatory Authority (TCRA). This makes competition in the telecommunications market very stiff. All mobile phone companies are struggling to earn more new customers into their networks. This trend courses a stiff competition. The various measures are being taken by different companies including, lowering tariff, and introducing free short messages within and out of their networks, and free calls during off-peak periods. This paper is aimed at investigating the influence of tariffs on students’ mobile customers in selecting their mobile network operators. About seventy seven students from high learning institutions in Dodoma Municipality, Tanzania, participated in responding to the prepared questionnaires. The sought information was aimed at determining if tariffs influenced students into selection of their current mobile operators. The results indicate that tariffs were the major driving factor in selection of mobile operators. However, female mobile customers were found to be more easily attracted into subscribing to a mobile operator due to low tariffs, a bigger number of free short messages or discounted call charges than their fellow male customers.

Keywords: Consumer Buying, mobile operators, tariff.

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Authors: Abhijit Mitra

Abstract:

Maximal length sequences (m-sequences) are also known as pseudo random sequences or pseudo noise sequences for closely following Golomb-s popular randomness properties: (P1) balance, (P2) run, and (P3) ideal autocorrelation. Apart from these, there also exist certain other less known properties of such sequences all of which are discussed in this tutorial paper. Comprehensive proofs to each of these properties are provided towards better understanding of such sequences. A simple test is also proposed at the end of the paper in order to distinguish pseudo noise sequences from truly random sequences such as Bernoulli sequences.

Keywords: Maximal length sequence, pseudo noise sequence, punctured de Bruijn sequence, auto-correlation, Bernoulli sequence, randomness tests.

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Authors: M. T. Yazdani Sabouni, Rasaratnam Logendran

Abstract:

We consider a typical problem in the assembly of printed circuit boards (PCBs) in a two-machine flow shop system to simultaneously minimize the weighted sum of weighted tardiness and weighted flow time. The investigated problem is a group scheduling problem in which PCBs are assembled in groups and the interest is to find the best sequence of groups as well as the boards within each group to minimize the objective function value. The type of setup operation between any two board groups is characterized as carryover sequence-dependent setup time, which exactly matches with the real application of this problem. As a technical constraint, all of the boards must be kitted before the assembly operation starts (kitting operation) and by kitting staff. The main idea developed in this paper is to completely eliminate the role of kitting staff by assigning the task of kitting to the machine operator during the time he is idle which is referred to as integration of internal (machine) and external (kitting) setup times. Performing the kitting operation, which is a preparation process of the next set of boards while the other boards are currently being assembled, results in the boards to continuously enter the system or have dynamic arrival times. Consequently, a dynamic PCB assembly system is introduced for the first time in the assembly of PCBs, which also has characteristics similar to that of just-in-time manufacturing. The problem investigated is computationally very complex, meaning that finding the optimal solutions especially when the problem size gets larger is impossible. Thus, a heuristic based on Genetic Algorithm (GA) is employed. An example problem on the application of the GA developed is demonstrated and also numerical results of applying the GA on solving several instances are provided.

Keywords: Genetic algorithm, Dynamic PCB assembly, Carryover sequence-dependent setup times, Multi-objective.

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Authors: Daniela I. Borissova, Ivan C. Mustakerov

Abstract:

The paper addresses a problem of optimal staffing in open shop environment. The problem is to determine the optimal number of operators serving a given number of machines to fulfill the number of independent operations while minimizing staff idle. Using a Gantt chart presentation of the problem it is modeled as twodimensional cutting stock problem. A mixed-integer programming model is used to get minimal job processing time (makespan) for fixed number of machines' operators. An algorithm for optimal openshop staffing is developed based on iterative solving of the formulated optimization task. The execution of the developed algorithm provides optimal number of machines' operators in the sense of minimum staff idle and optimal makespan for that number of operators. The proposed algorithm is tested numerically for a real life staffing problem. The testing results show the practical applicability for similar open shop staffing problems.

Keywords: Integer programming, open shop problem, optimal staffing.

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Authors: Ibrahim M. Hussain

Abstract:

Three new algorithms based on minimization of autocorrelation of transmitted symbols and the SLM approach which are computationally less demanding have been proposed. In the first algorithm, autocorrelation of complex data sequence is minimized to a value of 1 that results in reduction of PAPR. Second algorithm generates multiple random sequences from the sequence generated in the first algorithm with same value of autocorrelation i.e. 1. Out of these, the sequence with minimum PAPR is transmitted. Third algorithm is an extension of the second algorithm and requires minimum side information to be transmitted. Multiple sequences are generated by modifying a fixed number of complex numbers in an OFDM data sequence using only one factor. The multiple sequences represent the same data sequence and the one giving minimum PAPR is transmitted. Simulation results for a 256 subcarrier OFDM system show that significant reduction in PAPR is achieved using the proposed algorithms.

Keywords: Aperiodic autocorrelation, OFDM, PAPR, SLM, wireless communication.

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Authors: M.R. Osman, F. Abas, M.S. Noh, A. Mohamad Suffian, O. Ilhamah, H.Z. Zarir, A.B. Wahida, P. Noor Faradila, M.F. Siti Atiqah

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Safety Health and Environment Code of Practice (SHE COP) was developed to help road transportation operators to manage its operation in a systematic and safe manner. A study was conducted to determine the effectiveness of SHE COP implementation during non-OPS period. The objective of the study is to evaluate the implementations of SHE COP among bus operators during wee hour operations. The data was collected by completing a set of checklist after observing the activities during pre departure, during the trip, and upon arrival. The results show that there are seven widely practiced SHE COP elements. 22% of the buses have average speed exceeding the maximum permissible speed on the highways (90 km/h), with 13% of the buses were travelling at the speed of more than 100 km/h. The statistical analysis shows that there is only one significant association which relates speeding with prior presence of enforcement officers.

Keywords: Safety practices, speeding, wee hour.

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Authors: Rabah Diabi

Abstract:

As known, the guard wires of overhead high voltage are usually grounded through the grounding systems of support and of the terminal stations. They do affect the zero sequence impedance value of the line, Z0, which is generally, calculated assuming that the wires guard are at ground potential. In this way it is not considered the effect of the resistances of earth of supports and stations. In this work is formed a formula for the calculation of Z0 which takes account of said resistances. Is also proposed a method of calculating the impedance zero sequence overhead lines in which, in various sections or spans, the guard wires are connected to the supports, or isolated from them, or are absent. Parametric analysis is given for lines 220 kV and 400 kV, which shows the extent of the errors made with traditional methods of calculation.

Keywords: Overhead line, power system, zero sequence, wire guard, grounding.

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Authors: Yuan-Jye Tseng, Fang-Yu Yu, Feng-Yi Huang

Abstract:

A green design for assembly model is presented to integrate design evaluation and assembly and disassembly sequence planning by evaluating the three activities in one integrated model. For an assembled product, an assembly sequence planning model is required for assembling the product at the start of the product life cycle. A disassembly sequence planning model is needed for disassembling the product at the end. In a green product life cycle, it is important to plan how a product can be disassembled, reused, or recycled, before the product is actually assembled and produced. Given a product requirement, there may be several design alternative cases to design the same product. In the different design cases, the assembly and disassembly sequences for producing the product can be different. In this research, a new model is presented to concurrently evaluate the design and plan the assembly and disassembly sequences. First, the components are represented by using graph based models. Next, a particle swarm optimization (PSO) method with a new encoding scheme is developed. In the new PSO encoding scheme, a particle is represented by a position matrix defining an assembly sequence and a disassembly sequence. The assembly and disassembly sequences can be simultaneously planned with an objective of minimizing the total of assembly costs and disassembly costs. The test results show that the presented method is feasible and efficient for solving the integrated design evaluation and assembly and disassembly sequence planning problem. An example product is implemented and illustrated in this paper.

Keywords: green design, assembly and disassembly sequence planning, green design for assembly, particle swarm optimization.

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Authors: Justinian Anatory, Ekael Stephen Manase

Abstract:

The use of mobile phones is growing tremendously all over the world. In Tanzania there are a number of operators licensed by Tanzania Communications Regulatory Authority (TCRA) aiming at attracting customers into their networks. So far telecommunications market competition has been very stiff. Various measures are being taken by mobile operators to survive in the market. Such measure include introducing of different air time bundles on daily, weekly and monthly at lower tariffs. Other measures include the introduction of normal tariff, tourist package and one network. Despite of all these strategies, there is a dynamic competition in the market which needs to be explored. Some influences which attract customers to choose a certain mobile operator are of particular interest. This paper is investigating if the network effects and Quality of Services (QoS) influence mobile customers in selection of their mobile network operators. Seventy seven students from high learning institutions in Dodoma Municipality in Tanzania participated in responding to prepared questionnaires. The data was analyzed using Statistical Package for Social Science (SPSS) Software. The results indicate that, network coverage does influence customers in selection of mobile operators. In addition, this paper proposes further research in some areas especially where the study came up with different findings from what the theory has in place.

Keywords: Network effects, Quality of services, Consumer Buying, mobile operators.

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Authors: Chithra R, Pallab Maji, Sarat Kumar Patra, Girija Sankar Rath

Abstract:

The successful use of CDMA technology is based on the construction of large families of encoding sequences with good correlation properties. This paper discusses PN sequence generation based on Residue Arithmetic with an effort to improve the performance of existing interference-limited CDMA technology for mobile cellular systems. All spreading codes with residual number system proposed earlier did not consider external interferences, multipath propagation, Doppler effect etc. In literature the use of residual arithmetic in DS-CDMA was restricted to encoding of already spread sequence; where spreading of sequence is done by some existing techniques. The novelty of this paper is the use of residual number system in generation of the PN sequences which is used to spread the message signal. The significance of cross-correlation factor in alleviating multi-access interference is also discussed. The RNS based PN sequence has superior performance than most of the existing codes that are widely used in DS-CDMA applications. Simulation results suggest that the performance of the proposed system is superior to many existing systems.

Keywords: Direct-Sequence Code Division Multiple Access (DSCDMA), Multiple-Access Interference (MAI), PN Sequence, Residue Number System (RNS).

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