Search results for: virtual space

Authors: I. Oral, E. Bozkurt, H. Guzel

Abstract:

The purpose of this study was to investigate the effect of combining Real Experimentation (RE) With Virtual Experimentation (VE) on students- conceptual understanding of photo electric effect. To achieve this, a pre–post comparison study design was used that involved 46 undergraduate students. Two groups were set up for this study. Participants in the control group used RE to learn photo electric effect, whereas, participants in the experimental group used RE in the first part of the curriculum and VE in another part. Achievement test was given to the groups before and after the application as pre-test and post test. The independent samples t- test, one way Anova and Tukey HSD test were used for testing the data obtained from the study. According to the results of analyzes, the experimental group was found more successful than the control group.

Keywords: Computer Based Teaching, Java, Physics Education, Virtual Laboratory.

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Authors: Saead Negahdari, Davood Jalali Vahid

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Nowadays, the importance of energy saving is clearance to everyone. By attention to increasing price of fuels and also the problems of environment pollutions, there are the most efforts for using fuels littler and more optimum in everywhere. This essay studies optimizing of gas consumption in gas-burner space heaters. In oven of each gas-burner space heaters there is two snags to prevent the hot air (the result of combustion of natural gas) to go out of oven of the gas-burner space heaters directly without delivering its heat to the space of favorite environment like a room. These snags cause a excess circulating that helps hot air deliver its heat to the space of favorite environment. It means the exhaust air temperature will be decreased then when there are no snags. This is the aim of this essay to use maximum potential energy of the natural gas to make heat. In this study, by the help of a finite volume software (FLUENT) consumption of the gas-burner space heaters is simulated and optimized. At the end of this writing, by comparing the results of software and experimental results, it will be proved the authenticity of this method.

Keywords: FLUENT, Heat transfer, Oven of Gas-burner spaceheaters, Simulation.

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Authors: Khaja Kamaluddin, Muhammed Yousoof

Abstract:

Available Bit Rate Service (ABR) is the lower priority service and the better service for the transmission of data. On wireline ATM networks ABR source is always getting the feedback from switches about increase or decrease of bandwidth according to the changing network conditions and minimum bandwidth is guaranteed. In wireless networks guaranteeing the minimum bandwidth is really a challenging task as the source is always in mobile and traveling from one cell to another cell. Re establishment of virtual circuits from start to end every time causes the delay in transmission. In our proposed solution we proposed the mechanism to provide more available bandwidth to the ABR source by re-usage of part of old Virtual Channels and establishing the new ones. We want the ABR source to transmit the data continuously (non-stop) inorderto avoid the delay. In worst case scenario at least minimum bandwidth is to be allocated. In order to keep the data flow continuously, priority is given to the handoff ABR call against new ABR call.

Keywords: Bandwidth allocation, Virtual Channel (VC), CBR, ABR, MCR and QOS.

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Authors: Erisasadat Sahebzamani, Núria Forcada, Francisco Lendinez

Abstract:

Global climate change has become increasingly problematic over the past few decades. The construction industry has contributed to greenhouse gas emissions in recent decades. Considering these issues and the high demand for materials in the construction industry, Circular Economy (CE) is considered necessary to keep materials in the loop and extend their useful lives. By providing tangible benefits, Construction 4.0 facilitates the adoption of CE by reducing waste, updating standard work, sharing knowledge, and increasing transparency and stability. This study aims to present a framework for integrating CE and digital tools like Building Information Modeling (BIM) and Virtual Reality (VR) to examine the impact on the construction industry based on stakeholders' perspectives.

Keywords: Circular Economy, Building Information Modeling, Virtual Reality, stakeholder engagement.

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Authors: Nina Robson, Kenneth John Faller II, Vishalkumar Ahir, Arthur Ricardo Deps Miguel Ferreira, John Buchanan, Amarnath Banerjee

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This paper describes the development of a virtual-reality system ARWED, which will be used in physical rehabilitation of patients with reduced upper extremity mobility to increase limb Active Range of Motion (AROM). The ARWED system performs a symmetric reflection and real-time mapping of the patient’s healthy limb on to their most affected limb, tapping into the mirror neuron system and facilitating the initial learning phase. Using the ARWED, future experiments will test the extension of the action-observation priming effect linked to the mirror-neuron system on healthy subjects and then stroke patients.

Keywords: Physical rehabilitation, mirror neuron, virtual reality, stroke therapy.

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Authors: Galeano R. Katherine, Rincon L. David, Luengas C. Lely

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This paper describes the development of an electronic instrument that looks like a flute, which is able to sense the basic musical notes being executed by a specific user. The principal function of the instrument is to teach how to play a flute. This device will generate a significant academic impact, in a field of virtual reality interactive that combine art and technology. With this example is expected to contribute in research and implementation of teaching devices around the world.

Keywords: Flute, Hardware, Learning, Virtual Reality.

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Authors: Sadia Idrees, Gianpaolo Vignali, Simeon Gill

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The study aims to establish the virtual size and fit technology features to enhance fashion online retailing platforms, utilising digital human measurements to provide customised style and function to consumers. A few firms in the UK have launched advanced interactive fashion shopping domains for personalised shopping globally, aided by the latest internet technology. Virtual size and fit interfaces have a great potential to provide a personalised better-fitted garment to promote mass customisation globally. Made-to-measure clothing, consuming unstitched fabric is a common practice offered by fashion brands in Pakistan. This product is regarded as economical and sustainable to be utilised by consumers in Pakistan. Although the manual sizing system is practiced to sell garments online, virtual size and fit visualisation and recommendation technologies are uncommon in Pakistani fashion interfaces. A comparative assessment of Pakistani fashion brand websites and UK technology-driven fashion interfaces was conducted to highlight the vast potential of the virtual size and fit technology. The results indicated that web 2.0 technology adopted by Pakistani apparel brands has limited features, whereas companies practicing web 3.0 technology provide interactive online real-store shopping experience leading to enhanced customer satisfaction and globalisation of brands.

Keywords: E-commerce, mass customization, virtual size and fit, web 3.0 technology.

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Authors: Muhammed Çetin, Yılmaz Tunçer, Nejat Ekmekçi

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In this paper, the translation surfaces in 3-dimensional Euclidean space generated by two space curves have been investigated. It has been indicated that Scherk surface is not only minimal translation surface.

Keywords: Minimal surface, Surface of Scherk, Translationsurface

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Authors: M. M. Fateh, A. Izadbakhsh

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A robust control approach is proposed for a high speed manipulator using a hybrid computed torque control approach in the state space. The high-speed manipulator is driven by permanent magnet dc motors to track a trajectory in the joint space in the presence of disturbances. Tracking problem is analyzed in the state space where the completed models are considered for actuators. The proposed control approach can guarantee the stability and a satisfactory tracking performance. A two-link elbow manipulator driven by electrical actuators is simulated and results are shown to satisfy conditions under technical specifications.

Keywords: Computed torque, manipulator, robust control, state space.

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Authors: Lili Chen, Chao Yuan

Abstract:

On path space kQ, there is a trivial kQ^a-module structure determined by the multiplication of path algebra kQ^a and a trivial kQ^c-comodule structure determined by the comultiplication of path coalgebra kQ^c. In this paper, on path space kQ, a nontrivial kQ^a-module structure is defined, and it is proved that this nontrivial left kQ^a-module structure is isomorphic to the dual module structure of trivial right kQ^c-comodule. Dually, on path space kQ, a nontrivial kQ^c-comodule structure is defined, and it is proved that this nontrivial right kQ^c-comodule structure is isomorphic to the dual comodule structure of trivial left kQ^a-module. Finally, the trivial and nontrivial module structures on path space are compared from the aspect of submodule, and the trivial and nontrivial comodule structures on path space are compared from the aspect of subcomodule.

Keywords: Quiver, path space, module, comodule, dual.

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Authors: Karim Sobh, Khaled El-Ayat, Fady Morcos, Amr El-Kadi

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Distributed applications deployed on LEO satellites and ground stations require substantial communication between different members in a constellation to overcome the earth coverage barriers imposed by GEOs. Applications running on LEO constellations suffer the earth line-of-sight blockage effect. They need adequate lab testing before launching to space. We propose a scalable cloud-based network simulation framework to simulate problems created by the earth line-of-sight blockage. The framework utilized cloud IaaS virtual machines to simulate LEO satellites and ground stations distributed software. A factorial ANOVA statistical analysis is conducted to measure simulator overhead on overall communication performance. The results showed a very low simulator communication overhead. Consequently, the simulation framework is proposed as a candidate for testing LEO constellations with distributed software in the lab before space launch.

Keywords: LEO, Cloud Computing, Constellation, Satellite, Network Simulation, Netfilter.

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Authors: A. Braeken, L. Sterckx, A. Touhafi, Y. Verbelen

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When studying electronics, hands-on experience is considered to be very valuable for a better understanding of the concepts of electricity and electronics. Students lacking sufficient time in the lab are often put at disadvantage. A way to overcome this, is by using interactive multimedia in a virtual environment. Instead of proposing another new ad-hoc simulator for e-learning, we propose in this paper an e-learning platform integrating the SPICE simulator as a web service. This enables to make use of all the functions of the de-facto standard simulator SPICE inelectronics when developing new simulations.

Keywords: E-learning, SPICE, virtual experiments, web service.

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Authors: Kwan Hee Han, Jun Woo Park, Seock Kyu Yoo, Geon Lee

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As business environments are rapidly changing, the manufacturing system must be reconfigured to adapt to various customer needs. In order to cope with this challenge, it is quintessential to test industrial control logic rapidly and easily in the design time, and monitor operational behavior in the run time of automated manufacturing system. Proposed integrated model for virtual prototyping and operational monitoring of industrial control logic is to improve limitations of current ladder programming practices and general discrete event simulation method. Each plant layout model using HMI package and object-oriented control logic model is designed independently and is executed simultaneously in integrated manner to reflect design practices of automation system in the design time. Control logic is designed and executed using UML activity diagram without considering complicated control behavior to deal with current trend of reconfigurable manufacturing. After the physical installation, layout model of virtual prototype constructed in the design time is reused for operational monitoring of system behavior during run time.

Keywords: automated manufacturing system, HMI, monitoring, object-oriented, PLC, virtual prototyping

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Authors: Afzeri, A.G.E Sujtipto, R. Muhida, M. Konneh, Darmawan

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Increasing the demand for effectively use of the production facility requires the tools for sharing the manufacturing facility through remote operation of the machining process. This research introduces the methodology of machining technology for direct remote operation of networked milling machine. The integrated tools with virtual simulation, remote desktop protocol and Setup Free Attachment for remote operation of milling process are proposed. Accessing and monitoring of machining operation is performed by remote desktop interface and 3D virtual simulations. Capability of remote operation is supported by an auto setup attachment with a reconfigurable pin type setup free technology installed on the table of CNC milling machine to perform unattended machining process. The system is designed using a computer server and connected to a PC based controlled CNC machine for real time monitoring. A client will access the server through internet communication and virtually simulate the machine activity. The result has been presented that combination between real time virtual simulation and remote desktop tool is enabling to operate all machine tool functions and as well as workpiece setup..

Keywords: Remote Desktop, PC Based CNC, Remote Machining.

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Authors: U. Yerlikaya, R. T. Balkan

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In this research, a method is developed to obtain high-dimensional configuration space for path planning problems. In typical cases, the path planning problems are solved directly in the 3-dimensional (D) workspace. However, this method is inefficient in handling the robots with various geometrical and mechanical restrictions. To overcome these difficulties, path planning may be formalized and solved in a new space which is called configuration space. The number of dimensions of the configuration space comes from the degree of freedoms of the system of interest. The method can be applied in two ways. In the first way, the point clouds of all the bodies of the system and interaction of them are used. The second way is performed via using the clearance function of simulation software where the minimum distances between surfaces of bodies are simultaneously measured. A double-turret system is held in the scope of this study. The 4-D configuration space of a double-turret system is obtained in these two ways. As a result, the difference between these two methods is around 1%, depending on the density of the point cloud. The disparity between the two forms steadily decreases as the point cloud density increases. At the end of the study, in order to verify 4-D configuration space obtained, 4-D path planning problem was realized as 2-D + 2-D and a sample path planning is carried out with using A* algorithm. Then, the accuracy of the configuration space is proved using the obtained paths on the simulation model of the double-turret system.

Keywords: A* Algorithm, autonomous turrets, high-dimensional C-Space, manifold C-Space, point clouds.

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Authors: Lalith Edirisinghe, Zhihong Jin, A.W. Wijeratne, Hansa Edirisinghe, Lakshmi Ranwala Rashika Mudunkotuwa

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A paradigm shift in container inventory management (CIM) is a long-awaited industry need. Virtual container yard (VCY) is a concept developed in 2013 and its primary objective is to minimize shipping transport cost through implementing container exchange between carriers. Shipping lines always try to maintain lower container idle time and provide higher customer satisfaction. However, it is disappointing to note that carriers turn a blind eye to the escalating cost resulted from the present inefficient CIM mechanism. The cost of empty container management is simply transferred to the importers and exporters as freight adjustments. It also creates an environmental hazard. Therefore, it has now become a problem for the society. Therefore, a paradigm shift may be required as the present CIM system is not working for common interests of human beings as it should be.

Keywords: Virtual container yard, imbalance, management, inventory, container inventory management.

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Authors: Mahdi Zolfaghari, Seyed Hossein Hosseinian, Hossein Askarian Abyaneh, Mehrdad Abedi

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This paper presents a virtual active power filter (VAPF) using vehicle to grid (V2G) technology to maintain power quality requirements. The optimal discrete operation of the power converter of electric vehicle (EV) is based on recognizing desired switching states using the model predictive control (MPC) algorithm. A fast dynamic response, lower total harmonic distortion (THD) and good reference tracking performance are realized through the presented control strategy. The simulation results using MATLAB/Simulink validate the effectiveness of the scheme in improving power quality as well as good dynamic response in power transferring capability.

Keywords: Virtual active power filter, V2G technology, model predictive control, electric vehicle, power quality.

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Authors: Süha Yılmaz, Melih Turgut

Abstract:

In this paper, a method to calculate Frenet Apparatus of the curves in five dimensional Euclidean space is presented.

Keywords: Classical Differential Geometry, Euclidean-5 space, Frenet Apparatus.

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Authors: Kuo-Yang Cheng, Yi-Lun Pan, Chang-Hsing Wu, His-En Yu, Hui-Shan Chen, Weicheng Huang

Abstract:

The main mission of Ezilla is to provide a friendly interface to access the virtual machine and quickly deploy the high performance computing environment. Ezilla has been developed by Pervasive Computing Team at National Center for High-performance Computing (NCHC). Ezilla integrates the Cloud middleware, virtualization technology, and Web-based Operating System (WebOS) to form a virtual computer in distributed computing environment. In order to upgrade the dataset and speedup, we proposed the sensor observation system to deal with a huge amount of data in the Cassandra database. The sensor observation system is based on the Ezilla to store sensor raw data into distributed database. We adopt the Ezilla Cloud service to create virtual machines and login into virtual machine to deploy the sensor observation system. Integrating the sensor observation system with Ezilla is to quickly deploy experiment environment and access a huge amount of data with distributed database that support the replication mechanism to protect the data security.

Keywords: Cloud, Virtualization, Cassandra, WebOS

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Authors: Johan Wall, Johan Fredin, Anders Jönsson, Göran Broman

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Designing modern machine tools is a complex task. A simulation tool to aid the design work, a virtual machine, has therefore been developed in earlier work. The virtual machine considers the interaction between the mechanics of the machine (including structural flexibility) and the control system. This paper exemplifies the usefulness of the virtual machine as a tool for product development. An optimisation study is conducted aiming at improving the existing design of a machine tool regarding weight and manufacturing accuracy at maintained manufacturing speed. The problem can be categorised as constrained multidisciplinary multiobjective multivariable optimisation. Parameters of the control and geometric quantities of the machine are used as design variables. This results in a mix of continuous and discrete variables and an optimisation approach using a genetic algorithm is therefore deployed. The accuracy objective is evaluated according to international standards. The complete systems model shows nondeterministic behaviour. A strategy to handle this based on statistical analysis is suggested. The weight of the main moving parts is reduced by more than 30 per cent and the manufacturing accuracy is improvement by more than 60 per cent compared to the original design, with no reduction in manufacturing speed. It is also shown that interaction effects exist between the mechanics and the control, i.e. this improvement would most likely not been possible with a conventional sequential design approach within the same time, cost and general resource frame. This indicates the potential of the virtual machine concept for contributing to improved efficiency of both complex products and the development process for such products. Companies incorporating such advanced simulation tools in their product development could thus improve its own competitiveness as well as contribute to improved resource efficiency of society at large.

Keywords: Machine tools, Mechatronics, Non-deterministic, Optimisation, Product development, Virtual machine

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Authors: A. Montazar

Abstract:

The great challenge of the agricultural sector is to produce more crop from less water, which can be achieved by increasing crop water productivity. The modernization of the irrigation systems offers a number of possibilities to expand the economic productivity of water and improve the virtual water status. The objective of the present study is to assess the global water productivity (GWP) within the major irrigation command areas of I.R. Iran. For this purpose, fourteen irrigation command areas where located in different areas of Iran were selected. In order to calculate the global water productivity of irrigation command areas, all data on the delivered water to cropping pattern, cultivated area, crops water requirement, and yield production rate during 2002-2006 were gathered. In each of the command areas it seems that the cultivated crops have a higher amount of virtual water and thus can be replaced by crops with less virtual water. This is merely suggested due to crop water consumption and at the time of replacing crops, economic value as well as cultural and political factors must be considered. The results indicated that the lowest GWP belongs to Mahyar and Borkhar irrigation areas, 0.24 kg m-3, and the highest is that of the Dez irrigation area, 0.81 kg m-3. The findings demonstrated that water management in the two irrigation areas is just efficient. The difference in the GWP of irrigation areas is due to variations in the cropping pattern, amount of crop productions, in addition to the effective factors in the water use efficiency in the irrigation areas.

Keywords: Iran, Irrigation command area, Water productivity, Virtual water.

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Authors: Zullina H. Shaari, Amzairi Amar, Abdul Mutalib Embong, Hezlina Hashim

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University websites are considered as one of the brand primary touch points for multiple stakeholders, but most of them did not have great designs to create favorable impressions. Some of the elements that web designers should carefully consider are the appearance, the content, the functionality, usability and search engine optimization. However, priority should be placed on website simplicity and negative space. In terms of content, previous research suggests that universities should include reputation, learning environment, graduate career prospects, image destination, cultural integration, and virtual tour on their websites. The study examines how top 200 world ranking science and technology-based universities present their brands online and whether the websites capture the content dimensions. Content analysis of the websites revealed that the top ranking universities captured these dimensions at varying degree. Besides, the UK-based university had better priority on website simplicity and negative space compared to the Malaysian-based university.

Keywords: Science and technology programs, top-ranked universities, online brands, university websites.

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Authors: Maryam Khalili, Fateme Ghanei

Abstract:

As one of the most significant phenomena of industrialized societies, tourism plays a key role in encouraging regional developments and enhancing higher standards of living for local communities in particular. Traveling is a formative experience endowed with lessons on various aspects of life. It allows us learning how to enhance the social position as well as the social relationships. However, people forget the need to travel and gain first-hand experiences as they have to cope with the ever-increasing rate of stress created by the disorders and routines of the urban dwelling style. In this paper, various spaces of such experiences were explored through a virtual tour with two underlying aims: 1) encouraging, informing, and educating the community in terms of tourism development, and 2) introducing a temporary release from the routines. This study enjoyed a practical-qualitative research methodology, and the required data were collected through observation and using a multiple-response questionnaire. The participants (19-48 years old) included 41 citizens of both genders (63.4% male and 36.6% female) from two regions in Tehran, selected by cluster-probability sampling. The results led to development of a spatial design for a virtual tour experience in Tehran where different areas are explored to both raise people’s awareness and educate them on their cultural heritage.

Keywords: Ecotourism, education, gamification, social interaction, urban design, virtual tour.

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Authors: Xing Jiankuan, Qin Zheng, Zhang Jinxue

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Decentralized Tuple Space (DTS) implements tuple space model among a series of decentralized hosts and provides the logical global shared tuple repository. Replication has been introduced to promote performance problem incurred by remote tuple access. In this paper, we propose a replication approach of DTS allowing replication policies self-adapting. The accesses from users or other nodes are monitored and collected to contribute the decision making. The replication policy may be changed if the better performance is expected. The experiments show that this approach suitably adjusts the replication policies, which brings negligible overhead.

Keywords: Decentralization, Replication Management, SelfAdaption, Tuple Space.

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Authors: Sa-aat Niwitpong

Abstract:

Recent articles have addressed the problem to construct the confidence intervals for the mean of a normal distribution where the parameter space is restricted, see for example Wang [Confidence intervals for the mean of a normal distribution with restricted parameter space. Journal of Statistical Computation and Simulation, Vol. 78, No. 9, 2008, 829–841.], we derived, in this paper, analytic expressions of the coverage probability and the expected length of confidence interval for the normal mean when the whole parameter space is bounded. We also construct the confidence interval for the normal variance with restricted parameter for the first time and its coverage probability and expected length are also mathematically derived. As a result, one can use these criteria to assess the confidence interval for the normal mean and variance when the parameter space is restricted without the back up from simulation experiments.

Keywords: Confidence interval, coverage probability, expected length, restricted parameter space.

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Authors: Dai Zhimei, Hua Chen

Abstract:

The exploration of urban spatial evolution is an important part of urban development research. Therefore, the evolutionary modern Yangzhou urban spatial texture was taken as the research object, and Spatial Syntax was used as the main research tool, this paper explored Yangzhou spatial evolution law and its driving factors from the urban street network scale, district scale and street scale. The study has concluded that at the urban scale, Yangzhou urban spatial evolution is the result of a variety of causes, including physical and geographical condition, policy and planning factors, and traffic conditions, and the evolution of space also has an impact on social, economic, environmental and cultural factors. At the district and street scales, changes in space will have a profound influence on the history of the city and the activities of people. At the end of the article, the matters needing attention during the evolution of urban space were summarized.

Keywords: Space Syntax, spatial texture, urban space, Yangzhou.

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Authors: Kiran Ijaz, Umar Manzoor, Arshad Ali Shahid

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In this paper we present an extension to Vision Based LRTA* (VLRTA*) known as Vision Based Moving Target Search (VMTS) for capturing unknown moving target in unknown territory with randomly generated obstacles. Target position is unknown to the agents and they cannot predict its position using any probability method. Agents have omni directional vision but can see in one direction at some point in time. Agent-s vision will be blocked by the obstacles in the search space so agent can not see through the obstacles. Proposed algorithm is evaluated on large number of scenarios. Scenarios include grids of sizes from 10x10 to 100x100. Grids had obstacles randomly placed, occupying 0% to 50%, in increments of 10%, of the search space. Experiments used 2 to 9 agents for each randomly generated maze with same obstacle ratio. Observed results suggests that VMTS is effective in locate target time, solution quality and virtual target. In addition, VMTS becomes more efficient if the number of agents is increased with proportion to obstacle ratio.

Keywords: Vision, MTS, Unknown Target, Coordination, VMTS, Multi-Agent.

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Authors: Zhou Yingkun, Xu Guorui, Wei Siming, Huang Yongzhang

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With the increasing of the penetration of renewable energy in power system, the whole inertia of the power system is declining, which will endanger the frequency stability of the power system. In order to enhance the inertia, virtual synchronous generator (VSG) has been proposed. In addition, the motor-generator pair (MGP) system is proposed to enhance grid inertia. Both of them need additional equipment to provide instantaneous energy, so the economic problem should be considered. In this paper, the basic working principle of MGP system and VSG are introduced firstly. Then, the technical characteristics and economic investment of MGP/VSG are compared by calculation and simulation. The results show that the MGP system can provide same inertia with less cost than VSG.

Keywords: High renewable energy penetration, inertia of power system, virtual synchronous generator, motor-generator pair system, techno-economic analysis.

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Authors: Behnam Shirkhanghah, Vahid Shahbaznejhad-Fard, Houshyar Eimani-Kalesar, Babak Pahlevan

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Flat double-layer grid is from category of space structures that are formed from two flat layers connected together with diagonal members. Increased stiffness and better seismic resistance in relation to other space structures are advantages of flat double layer space structures. The objective of this study is assessment and calculation of Behavior factor of flat double layer space structures. With regarding that these structures are used widely but Behavior factor used to design these structures against seismic force is not determined and exact, the necessity of study is obvious. This study is theoretical. In this study we used structures with span length of 16m and 20 m. All connections are pivotal. ANSYS software is used to non-linear analysis of structures.

Keywords: Behavior factor, Double-layer, Intensified resistance, Non-linear analysis

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Authors: Süha Yılmaz, Melih Turgut

Abstract:

These In this work, a regular unit speed curve in six dimensional Euclidean space, whose Frenet curvatures are constant, is considered. Thereafter, a method to calculate Frenet apparatus of this curve is presented.

Keywords: Classical Differential Geometry, Euclidean 6-space, Frenet Apparatus of the curves.

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