Search results for: type 2 fuzzy logic systems.

Authors: K. Liagkouras, K. Metaxiotis

Abstract:

Customer relationship management (CRM) systems in business are a reality of the contemporary business world for the last decade or so. Still, there are grey areas regarding the successful implementation and operation of CRM systems in business. This paper, through the systematic study of the CRM implementation paradigm, attempts to identify the most important challenges and opportunities that the CRM systems face in a rapidly changing business world.

Keywords: Customer Relationship Management, CRM, Business, Information Systems.

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Authors: Phutthiwat Waiyawuththanapoom

Abstract:

This study has only one objective which is to identify the different in factors of choosing the distributor for food and non-food OTOP entrepreneur in Thailand. In this research, the types of OTOP product will be divided into two groups which are food and non-food. The sample for the food type OTOP product was the processed fruit and vegetable from Nakorn Pathom province and the sample for the non-food type OTOP product was the court doll from Ang Thong province. The research was divided into 3 parts which were a study of the distribution pattern and how to choose the distributor of the food type OTOP product, a study of the distribution pattern and how to choose the distributor of the non-food type OTOP product and a comparison between 2 types of products to find the differentiation in the factor of choosing distributor. The data and information was collected by using the interview. The populations in the research were 5 producers of the processed fruit and vegetable from Nakorn Pathom province and 5 producers of the court doll from Ang Thong province. The significant factor in choosing the distributor of the food type OTOP product is the material handling efficiency and on-time delivery but for the non-food type OTOP product is focused on the channel of distribution and cost of the distributor.

Keywords: Distributor, OTOP, Food and Non-Food, Selection.

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Authors: Gaurav Kumar, Rakesh Kumar Bajaj

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The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), z_pqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree F_pq instead of  and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.

Keywords: Assignment problem, Interval-valued Intuitionistic Fuzzy Sets, Similarity Measures, score function.

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Authors: S. Carpintero, R. Barcham

Abstract:

Light rail systems have proliferated in Spain in the last decade, following a tendency that is common not only in other European countries but also in other parts of the world. This paper reviews the benefits of light rail systems, both related to environmental issues and mobility issues. It analyses the evolution of light rail projects in Spain and shows that light rail systems in this country have evolved towards an extensive use of public-private partnerships. The analysis of the Spanish projects, however, does not contribute any conclusive evidence about whether public-private partnerships have been more efficient than publicly owned enterprises in building and operating light rail systems.

Keywords: Light rail systems, public-private partnerships, BOT.

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Authors: Debal Saha, NirmalBaranHui

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The present paper discusses the basic concepts and the underlying principles of Multi-Agent Systems (MAS) along with an interdisciplinary exploitation of these principles. It has been found that they have been utilized for lots of research and studies on various systems spanning across diverse engineering and scientific realms showing the need of development of a proper generalized framework. Such framework has been developed for the Multi-Agent Systems and it has been generalized keeping in mind the diverse areas where they find application. All the related aspects have been categorized and a general definition has been given where ever possible.

Keywords: Generalized framework, multiagent systems.

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Authors: Elke Mackensen

Abstract:

Systems Engineering plays a key role during industrial product development of complex technical systems. The need for systems engineers in industry is growing. But there is a gap between the industrial need and the academic education. Normally the academic education is focused on the domain specific design, implementation and testing of technical systems. Necessary systems engineering expertise like knowledge about requirements analysis, product cost estimation, management or social skills are poorly taught. Thus there is the need of new academic concepts for teaching systems engineering skills. This paper presents a project-orientated training concept to prepare students from different technical degree programs for systems engineering activities. The training concept has been initially implemented and applied in the industrial engineering master program of the University of Applied Sciences Offenburg.

Keywords: Educational systems engineering training, requirements analysis, system modelling, SysML.

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Authors: Abdulrahim Aljamal

Abstract:

Bay leaves have been shown to improve insulin function in vitro but the effects on people have not been determined. The objective of this study was to determine if bay leaves may be important in the prevention and/or alleviation of type 1 diabetes. Methods: Fifty five people with type 1 diabetes were divided into two groups, 45 given capsules containing 3 g of bay leaves per day for 30 days and 10 given a placebo capsules. Results All the patients consumed bay leaves shows reduced serum glucose with significant decreases 27% after 30 d. Total cholesterol decreased, 21 %, after 30 days with larger decreases in low density lipoprotein (LDL) 24%. High density lipoprotein (HDL) increased 20% and Triglycerides also decreased 26%. There were no significant changes in the placebo group. Conclusion, this study demonstrates that consumption of bay leaves, 3 g/d for 30 days, decreases risk factors for diabetes and cardiovascular diseases and suggests that bay leaves may be beneficial for people with type 1 diabetes.

Keywords: bay leave, cholesterol, diabetes, triglycerides

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Authors: Haitham S. Hamza, Mohamed Maher, Shourok Alaa, Aya Khattab, Hadeal Ismail, Kamilia Hosny

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Radio Frequency Identification (RFID) has become a key technology in the emerging concept of Internet of Things (IoT). Naturally, business applications would require the deployment of various RFID systems developed by different vendors that use different data formats and structures. This heterogeneity poses a challenge in developing real-life IoT systems with RFID, as integration is becoming very complex and challenging. Semantic integration is a key approach to deal with this challenge. To do so, ontology for RFID systems need to be developed in order to annotated semantically RFID systems, and hence, facilitate their integration. Accordingly, in this paper, we propose ontology for RFID systems. The proposed ontology can be used to semantically enrich RFID systems, and hence, improve their usage and reasoning.

Keywords: IoT, RFID, Semantic, sparql, Ontology.

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Authors: Amna Noreen , Kare Olaussen

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We demonstrate that it is possible to compute wave function normalization constants for a class of Schr¨odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P in decimals.

Keywords: Eigenvalue problems, bound states, trapezoidal rule, poisson resummation.

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Authors: Yao-Tien Wang, Hsiang-Fu Yu, Dung Chen Chiou

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In wireless and mobile communications, this progress provides opportunities for introducing new standards and improving existing services. Supporting multimedia traffic with wireless networks quality of service (QoS). In this paper, a grey-fuzzy controller for radio resource management (GF-RRM) is presented to maximize the number of the served calls and QoS provision in wireless networks. In a wireless network, the call arrival rate, the call duration and the communication overhead between the base stations and the control center are vague and uncertain. In this paper, we develop a method to predict the cell load and to solve the RRM problem based on the GF-RRM, and support the present facility has been built on the application-level of the wireless networks. The GF-RRM exhibits the better adaptability, fault-tolerant capability and performance than other algorithms. Through simulations, we evaluate the blocking rate, update overhead, and channel acquisition delay time of the proposed method. The results demonstrate our algorithm has the lower blocking rate, less updated overhead, and shorter channel acquisition delay.

Keywords: radio resource management, grey prediction, fuzzylogic control, wireless networks, quality of service.

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Authors: M. Douak, Z. Aouachria

Abstract:

The aim of our study is to project an optimized wind turbine of Darrieus type. This type of wind turbine is characterized by a low starting torque in comparison with the Savonius rotor allowing them to operate for a period greater than wind speed. This led us to reconsider the Darrieus rotor to optimize a design which will increase its starting torque. The study of a system of monitoring and control of the angle of attack of blade profile, which allows an auto start to wind speeds as low as possible is presented for the straight blade of Darrieus turbine. The study continues to extend to other configurations namely those of parabolic type.

Keywords: Darrieus turbine, pitch angle, self-stating, wind energy.

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Authors: Hasmayadi Abdul Majid, Rohana Musa

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This paper presents the development of a 38.5 kS/s 10-bit low power SAR ADC which is realized in MIMOS’s 0.35 µm CMOS process. The design uses a resistive DAC, a dynamic comparator with pre-amplifier and SAR digital logic to create 10 effective bits while consuming less than 7.8 mW with a 3.3 V power supply.

Keywords: Successive Approximation Register Analog-to- Digital Converter, SAR ADC, Resistive DAC.

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Authors: Carsten Röcker

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This paper presents a set of guidelines for the design of multi-user awareness systems. In a first step, general requirements for team awareness systems are analyzed. In the second part of the paper, the identified requirements are aggregated and transformed into concrete design guidelines for the development of team awareness systems.

Keywords: User Interface Design, Awareness Systems, User- Centered Design, Human Factors.

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Authors: Prashanth C.M., K. Chandrashekar Shet

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In recent past, the Unified Modeling Language (UML) has become the de facto industry standard for object-oriented modeling of the software systems. The syntax and semantics rich UML has encouraged industry to develop several supporting tools including those capable of generating deployable product (code) from the UML models. As a consequence, ensuring the correctness of the model/design has become challenging and extremely important task. In this paper, we present an approach for automatic verification of protocol model/design. As a case study, Session Initiation Protocol (SIP) design is verified for the property, “the CALLER will not converse with the CALLEE before the connection is established between them ". The SIP is modeled using UML statechart diagrams and the desired properties are expressed in temporal logic. Our prototype verifier “UML-SMV" is used to carry out the verification. We subjected an erroneous SIP model to the UML-SMV, the verifier could successfully detect the error (in 76.26ms) and generate the error trace.

Keywords: Unified Modeling Language, Statechart, Verification, Protocol Design, Model Checking.

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Authors: Safaa Al-Ali, Ahmad Shahin, Fadi Chakik

Abstract:

Image coding based on clustering provides immediate access to targeted features of interest in a high quality decoded image. This approach is useful for intelligent devices, as well as for multimedia content-based description standards. The result of image clustering cannot be precise in some positions especially on pixels with edge information which produce ambiguity among the clusters. Even with a good enhancement operator based on PDE, the quality of the decoded image will highly depend on the clustering process. In this paper, we introduce an ambiguity cluster in image coding to represent pixels with vagueness properties. The presence of such cluster allows preserving some details inherent to edges as well for uncertain pixels. It will also be very useful during the decoding phase in which an anisotropic diffusion operator, such as Perona-Malik, enhances the quality of the restored image. This work also offers a comparative study to demonstrate the effectiveness of a fuzzy clustering technique in detecting the ambiguity cluster without losing lot of the essential image information. Several experiments have been carried out to demonstrate the usefulness of ambiguity concept in image compression. The coding results and the performance of the proposed algorithms are discussed in terms of the peak signal-tonoise ratio and the quantity of ambiguous pixels.

Keywords: Ambiguity Cluster, Anisotropic Diffusion, Fuzzy Clustering, Image Compression.

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Authors: Chao Qi, Fuyang Peng, Bo Deng, Xiaoyan Su

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In the upgrade process of enterprise information systems, how to deal with and utilize those legacy systems affects the efficiency of construction and development of the new system. We propose an evaluation system, which comprehensively describes the capacity of legacy information systems in five aspects. Then we propose a practical legacy systems evaluation method. Base on the evaluation result, we can determine the current state of legacy system which was evaluated.

Keywords: Legacy Information Systems, Evaluation IndexSystem, Evaluation Method, Evaluation Level

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Authors: M. Othman, N. Bhuiyan, G. J. Gouw

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In today-s competitive market, most companies develop manufacturing systems that can help in cost reduction and maximum quality. Human issues are an important part of manufacturing systems, yet most companies ignore their effects on production performance. This paper aims to developing an integrated workforce planning system that incorporates the human being. Therefore, a multi-objective mixed integer nonlinear programming model is developed to determine the amount of hiring, firing, training, overtime for each worker type. This paper considers a workforce planning model including human aspects such as skills, training, workers- personalities, capacity, motivation, and learning rates. This model helps to minimize the hiring, firing, training and overtime costs, and maximize the workers- performance. The results indicate that the workers- differences should be considered in workforce scheduling to generate realistic plans with minimum costs. This paper also investigates the effects of human learning rates on the performance of the production systems.

Keywords: Human Factors, Learning Curves, Workers' Differences, Workforce Scheduling

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Authors: T. Kosáros, D. Gál, F. Pekár, Gy. Lakatos

Abstract:

Periphyton development and composition were studied in three different treatments: (i) two fishpond units of wetland-type wastewater treatment pond systems, (ii) two fishponds in combined intensive-extensive fish farming systems and (iii) three traditional polyculture fishponds. Results showed that amounts of periphyton developed in traditional polyculture fishponds (iii) were different compared to the other treatments (i and ii), where the main function of ponds was stated wastewater treatment. Negative correlation was also observable between water quality parameters and periphyton production. The lower trophity, halobity and saprobity level of ponds indicated higher amount of periphyton. The dry matter content of periphyton was significantly higher in the samples, which were developed in traditional polyculture fishponds (2.84±3.02 g m-2 day-1, whereby the ash content in dry matter 74%), than samples taken from (i) (1.60±2.32 g m-2 day-1, 61%) and (ii) fishponds (0.65±0.45 g m-2 day-1, 81%).

Keywords: Artificial substrate, fishpond, periphyton, waterquality

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Authors: Arash Taheri, Meysam Mohammadi-Amin, Seyed Hossein Moosavy

Abstract:

Medical applications are among the most impactful areas of microrobotics. The ultimate goal of medical microrobots is to reach currently inaccessible areas of the human body and carry out a host of complex operations such as minimally invasive surgery (MIS), highly localized drug delivery, and screening for diseases at their very early stages. Miniature, safe and efficient propulsion systems hold the key to maturing this technology but they pose significant challenges. A new type of propulsion developed recently, uses multi-flagella architecture inspired by the motility mechanism of prokaryotic microorganisms. There is a lack of efficient methods for designing this type of propulsion system. The goal of this paper is to overcome the lack and this way, a numerical strategy is proposed to design multi-flagella propulsion systems. The strategy is based on the implementation of the regularized stokeslet and rotlet theory, RFT theory and new approach of “local corrected velocity". The effects of shape parameters and angular velocities of each flagellum on overall flow field and on the robot net forces and moments are considered. Then a multi-layer perceptron artificial neural network is designed and employed to adjust the angular velocities of the motors for propulsion control. The proposed method applied successfully on a sample configuration and useful demonstrative results is obtained.

Keywords: Artificial Neural Network, Biomimetic Microrobots, Flagellar Propulsion, Swimming Robots.

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Authors: L. Ngowi, N. H. Mvungi

Abstract:

This paper critically examines the evolution of socio-technical systems theory, its practices, and challenges in system design and development. It examines concepts put forward by researchers focusing on the application of the theory in software engineering. There are various methods developed that use socio-technical concepts based on systems engineering without remarkable success. The main constraint is the large amount of data and inefficient techniques used in the application of the concepts in system engineering for developing time-bound systems and within a limited/controlled budget. This paper critically examines each of the methods, highlight bottlenecks and suggest the way forward. Since socio-technical systems theory only explains what to do, but not how doing it, hence engineers are not using the concept to save time, costs and reduce risks associated with new frameworks. Hence, a new framework, which can be considered as a practical approach is proposed that borrows concepts from soft systems method, agile systems development and object-oriented analysis and design to bridge the gap between theory and practice. The approach will enable the development of systems using socio-technical systems theory to attract/enable the system engineers/software developers to use socio-technical systems theory in building worthwhile information systems to avoid fragilities and hostilities in the work environment.

Keywords: Socio-technical systems, human centered design, software engineering, cognitive engineering, soft systems, systems engineering.

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Authors: Seung You Na, Daejung Shin, Jin Young Kim, Joo Hyun Jung, Yong-Gwan Won

Abstract:

To explore pipelines is one of various bio-mimetic robot applications. The robot may work in common buildings such as between ceilings and ducts, in addition to complicated and massive pipeline systems of large industrial plants. The bio-mimetic robot finds any troubled area or malfunction and then reports its data. Importantly, it can not only prepare for but also react to any abnormal routes in the pipeline. The pipeline monitoring tasks require special types of mobile robots. For an effective movement along a pipeline, the movement of the robot will be similar to that of insects or crawling animals. During its movement along the pipelines, a pipeline monitoring robot has an important task of finding the shapes of the approaching path on the pipes. In this paper we propose an effective solution to the pipeline pattern recognition, based on the fuzzy classification rules for the measured IR distance data.

Keywords: Bio-mimetic robots, Plant pipes monitoring, Pipepattern recognition.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

In this paper, delay-dependent stability analysis for neutral type neural networks with uncertain paramters and time-varying delay is studied. By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments, a novel sufficient condition is established to guarantee the globally asymptotically stability of the considered system. Finally, a numerical example is provided to illustrate the usefulness of the proposed main results.

Keywords: Neutral type neural networks, Time-varying delay, Stability, Linear matrix inequality(LMI).

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Authors: Shiuh-Jer Huang, Yu-Chi Liu, Su-Hai Hsiang

Abstract:

A novel low-cost impedance control structure is proposed for monitoring the contact force between end-effector and environment without installing an expensive force/torque sensor. Theoretically, the end-effector contact force can be estimated from the superposition of each joint control torque. There have a nonlinear matrix mapping function between each joint motor control input and end-effector actuating force/torques vector. This new force control structure can be implemented based on this estimated mapping matrix. First, the robot end-effector is manipulated to specified positions, then the force controller is actuated based on the hall sensor current feedback of each joint motor. The model-free fuzzy sliding mode control (FSMC) strategy is employed to design the position and force controllers, respectively. All the hardware circuits and software control programs are designed on an Altera Nios II embedded development kit to constitute an embedded system structure for a retrofitted Mitsubishi 5 DOF robot. Experimental results show that PI and FSMC force control algorithms can achieve reasonable contact force monitoring objective based on this hardware control structure.

Keywords: Robot, impedance control, fuzzy sliding mode control, contact force estimator.

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Authors: Kuang-Hsiung Tan, Chih-Chan Hu, Chien-Wu Lan, Shih-Sung Lin, Te-Jen Chang

Abstract:

An active islanding detection method using disturbance signal injection with intelligent controller is proposed in this study. First, a DC\AC power inverter is emulated in the distributed generator (DG) system to implement the tracking control of active power, reactive power outputs and the islanding detection. The proposed active islanding detection method is based on injecting a disturbance signal into the power inverter system through the d-axis current which leads to a frequency deviation at the terminal of the RLC load when the utility power is disconnected. Moreover, in order to improve the transient and steady-state responses of the active power and reactive power outputs of the power inverter, and to further improve the performance of the islanding detection method, two probabilistic fuzzy neural networks (PFNN) are adopted to replace the traditional proportional-integral (PI) controllers for the tracking control and the islanding detection. Furthermore, the network structure and the online learning algorithm of the PFNN are introduced in detail. Finally, the feasibility and effectiveness of the tracking control and the proposed active islanding detection method are verified with experimental results.

Keywords: Distributed generators, probabilistic fuzzy neural network, islanding detection, non-detection zone.

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Authors: Sara Sharifi Rad, Hassan Haghighi

Abstract:

Due to important issues, such as deadlock, starvation, communication, non-deterministic behavior and synchronization, concurrent systems are very complex, sensitive, and error-prone. Thus ensuring reliability and accuracy of these systems is very essential. Therefore, there has been a big interest in the formal specification of concurrent programs in recent years. Nevertheless, some features of concurrent systems, such as dynamic process creation, scheduling and starvation have not been specified formally yet. Also, some other features have been specified partially and/or have been described using a combination of several different formalisms and methods whose integration needs too much effort. In other words, a comprehensive and integrated specification that could cover all aspects of concurrent systems has not been provided yet. Thus, this paper makes two major contributions: firstly, it provides a comprehensive formal framework to specify all well-known features of concurrent systems. Secondly, it provides an integrated specification of these features by using just a single formal notation, i.e., the Z language.

Keywords: Concurrent systems, Formal methods, Formal specification, Z language

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Authors: Changjin Xu, Yusen Wu

Abstract:

In this paper, a asymptotically periodic predator-prey model with Modified Leslie-Gower and Holling-Type II schemes is investigated. Some sufficient conditions for the uniformly strong persistence of the system are established. Our result is an important complementarity to the earlier results.

Keywords: Predator-prey model, uniformly strong persistence, asymptotically periodic, Holling-type II.

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Authors: Amid Ranjkesh, Milan Ambrožič, Samo Kralj

Abstract:

We study the typical domain size and configuration character of a randomly perturbed system exhibiting continuous symmetry breaking. As a model system we use rod-like objects within a cubic lattice interacting via a Lebwohl–Lasher-type interaction. We describe their local direction with a headless unit director field. An example of such systems represents nematic LC or nanotubes. We further introduce impurities of concentration p, which impose the random anisotropy field-type disorder to directors. We study the domain-type pattern of molecules as a function of p, anchoring strength w between a neighboring director and impurity, temperature, history of samples. In simulations we quenched the directors either from the random or homogeneous initial configuration. Our results show that a history of system strongly influences: i) the average domain coherence length; and ii) the range of ordering in the system. In the random case the obtained order is always short ranged (SR). On the contrary, in the homogeneous case, SR is obtained only for strong enough anchoring and large enough concentration p. In other cases, the ordering is either of quasi long range (QLR) or of long range (LR). We further studied memory effects for the random initial configuration. With increasing external ordering field B either QLR or LR is realized.

Keywords: Lebwohl-Lasher model, liquid crystals, disorder, memory effect, orientational order.

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Authors: Rita SahaRay, Ganesh Dutta

Abstract:

In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks, not necessarily of same size. Assuming the block sizes to be even for all blocks, for the case n ≡ 2 (mod 4), optimal designs are obtained with respect to type 1 and type 2 optimality criteria in the class of designs providing estimation of all main effects orthogonal to the block effects. In practice, such orthogonal estimation of main effects is often a desirable condition. In the wider class of all available m two level even sized blocked main effects plans, where the factors do not occur at high and low levels equally often in each block, E-optimal designs are also characterized. Simple construction methods based on Hadamard matrices and Kronecker product for these optimal designs are presented.

Keywords: Design matrix, Hadamard matrix, Kronecker product, type 1 criteria, type 2 criteria.

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Authors: Dariush Semnani, Mohammad Sheikhzadeh

Abstract:

Circular knitting machine makes the fabric with more than two knitting tools. Variation of yarn tension between different knitting tools causes different loop length of stitches duration knitting process. In this research, a new intelligent method is applied to control loop length of stitches in various tools based on ideal shape of stitches and real angle of stitches direction while different loop length of stitches causes stitches deformation and deviation those of angle. To measure deviation of stitch direction against variation of tensions, image processing technique was applied to pictures of different fabrics with constant front light. After that, the rate of deformation is translated to needed compensation of loop length cam degree to cure stitches deformation. A fuzzy control algorithm was applied to loop length modification in knitting tools. The presented method was experienced for different knitted fabrics of various structures and yarns. The results show that presented method is useable for control of loop length variation between different knitting tools based on stitch deformation for various knitted fabrics with different fabric structures, densities and yarn types.

Keywords: Circular knitting, Radon transformation, Knittedfabric, Regularity, Fuzzy control

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Authors: Lina Wu, Ye Li, Jia Liu

Abstract:

We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: Differential Forms, Hölder Inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series.

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