Search results for: flare motion

Authors: Mirabbos Mirkamalov, Zavkiddin Mirtoshev

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The M 1.6 class flare occurred on 6^th of September 2012. Our observations correspond to the active region NOAA 11560 with the heliographic coordinates N04W71. The event took place between 04:00 UT and 04:45 UT, and was close to the solar limb at the western region. The flare temperature correlates with flux peak, increases for a short period (between 04:08 UT and 04:12 UT), rises impulsively, attains a maximum value of about 17 MK at 04:12 UT and gradually decreases after peak value. Around the peak we observe significant emissions of X-ray sources. Flux profiles of the X-ray emission exhibit a progressively faster raise and decline as the higher energy channels are considered.

Keywords: magnetic reconnection, solar atmosphere, solar flare, X-ray emission

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Authors: Khalid Mohammed Idrees

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Endodontic treatment aims to reverse the disease process and thereby eliminate the associated signs of symptoms. When the treatment itself appears to initiate the onset of pain and /or swelling (endodontic flare-up), the result can be distressing to both the patient and the operator. Patient might even consider postoperative symptoms as a bench mark against which the clinician’s skills are measured. Obviously the treatment with the lowest prevalence of postoperative pain is usually the treatment of choice as long as effectiveness and cost are not compromised. Knowledge of the cause and mechanism behind intra appointment flare-up is of utmost importance for the clinician to properly prevent or manage this undesirable condition. This review lecture will discuss the causative factors of flare-up with special attention to the microorganism role, various modalities of preventive measures would be discussed. Those measures are based on scientific evidence combined with the long clinical experience of the lecturer.

Keywords: endodontic flare-up, causative factors, inflammatory mediators, preventive measures

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Authors: Lai Xuejiang, Huang Li, Yang Yi

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To study the potential hazards of the sudden emergency relief of flare stack, the thermal radiation and noise calculation of flare stack is carried out by using Flaresim program 2.0. Thermal radiation and noise analysis should be considered as the sudden emergency relief takes place. According to the Flaresim software simulation results, the thermal radiation and noise meet the requirement.

Keywords: flare stack, thermal radiation, safety assessment, noise

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Authors: B. Daheche, M. T. Hannachi, H. Djebaili

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In this approach, we tried to describe the flare test tubes welded by high frequency induction HF, and its experimental application. The test is carried out ENTTPP (National company of pipe mill and processing of flat products). Usually, the final products (tube) undergo a series of destructive testing (CD) in order to see the efficiency of welding. This test performed on sections of pipe with a length defined in the notice is made under a determined effort (pressure), which depends on its share of other parameters namely mechanical (fracture resistance) and geometry (thickness tube, outside diameter), the variation of this effort is well researched and recorded.

Keywords: flare, destructive testing, pressure, drafts tube, tube finished

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Authors: Benedictus Asriparusa, Lathifah Al Hakimi, Aulia Husada

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A large amount of energy is being wasted by the release of natural gas associated with the oil industry. This release interrupts the environment particularly atmosphere layer condition globally which contributes to global warming impact. This research presents an overview of the methods employed by researchers in PT. Chevron Pacific Indonesia in the Minas area to determine a new prediction method of measuring and reducing gas flaring and its emission. The method emphasizes advanced research which involved analytical studies, numerical studies, modeling, and computer simulations, amongst other techniques. A flaring system is the controlled burning of natural gas in the course of routine oil and gas production operations. This burning occurs at the end of a flare stack or boom. The combustion process releases emissions of greenhouse gases such as NO2, CO2, SO2, etc. This condition will affect the chemical composition of air and environment around the boundary layer mainly during transition season. Transition season in Indonesia is absolutely very difficult condition to predict its pattern caused by the difference of two air mass conditions. This paper research focused on transition season in 2013. A simulation to create the new pattern of the pollutants distribution is needed. This paper has outlines trends in gas flaring modeling and current developments to predict the dominant variables in the pollutants distribution. A Fluent model is used to simulate the distribution of pollutants gas coming out of the stack, whereas WRF model output is used to overcome the limitations of the analysis of meteorological data and atmospheric conditions in the study area. Based on the running model, the most influence factor was wind speed. The goal of the simulation is to predict the new pattern based on the time of fastest wind and slowest wind occurs for pollutants distribution. According to the simulation results, it can be seen that the fastest wind (last of March) moves pollutants in a horizontal direction and the slowest wind (middle of May) moves pollutants vertically. Besides, the design of flare stack in compliance according to EPA Oil and Gas Facility Stack Parameters likely shows pollutants concentration remains on the under threshold NAAQS (National Ambient Air Quality Standards).

Keywords: flare motion, new prediction, pollutants distribution, transition season, WRF model

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Authors: Viktor Novikov, Yuri Ruzhin

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The studies completed to-date on a relation of the Earth's seismicity and solar processes provide the fuzzy and contradictory results. For verification of an idea that solar flares can trigger earthquakes, we have analyzed a case of a powerful surge of solar flash activity early in September 2017 during approaching the minimum of 24th solar cycle was accompanied by significant disturbances of space weather. On September 6, 2017, a group of sunspots AR2673 generated a large solar flare of X9.3 class, the strongest flare over the past twelve years. Its explosion produced a coronal mass ejection partially directed towards the Earth. We carried out a statistical analysis of the catalogs of earthquakes USGS and EMSC for determination of the effect of solar flares on global seismic activity. New evidence of earthquake triggering due to the Sun-Earth interaction has been demonstrated by simple comparison of behavior of Earth's seismicity before and after the strong solar flare. The global number of earthquakes with magnitude of 2.5 to 5.5 within 11 days after the solar flare has increased by 30 to 100%. A possibility of electric/electromagnetic triggering of earthquake due to space weather disturbances is supported by results of field and laboratory studies, where the earthquakes (both natural and laboratory) were initiated by injection of electrical current into the Earth crust. For the specific case of artificial electric earthquake triggering the current density at a depth of earthquake, sources are comparable with estimations of a density of telluric currents induced by variation of space weather conditions due to solar flares. Acknowledgment: The work was supported by RFBR grant No. 18-05-00255.

Keywords: solar flare, earthquake activity, earthquake triggering, solar-terrestrial relations

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Authors: Sujing Wang, Song Wang, Jian Zhang, Qiang Xu

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Flaring emissions during abnormal operating conditions such as plant start-ups, shut-downs, and upsets in chemical process industries (CPI) are usually significant. Flare minimization can help to save raw material and energy for CPI plants, and to improve local environmental sustainability. In this paper, a systematic methodology based on plant-wide dynamic simulation is presented for CPI plant flare minimizations under abnormal operating conditions. Since off-specification emission sources are inevitable during abnormal operating conditions, to significantly reduce flaring emission in a CPI plant, they must be either recycled to the upstream process for online reuse, or stored somewhere temporarily for future reprocessing, when the CPI plant manufacturing returns to stable operation. Thus, the off-spec products could be reused instead of being flared. This can be achieved through the identification of viable design and operational strategies during normal and abnormal operations through plant-wide dynamic scheduling, simulation, and optimization. The proposed study includes three stages of simulation works: (i) developing and validating a steady-state model of a CPI plant; (ii) transiting the obtained steady-state plant model to the dynamic modeling environment; and refining and validating the plant dynamic model; and (iii) developing flare minimization strategies for abnormal operating conditions of a CPI plant via a validated plant-wide dynamic model. This cost-effective methodology has two main merits: (i) employing large-scale dynamic modeling and simulations for industrial flare minimization, which involves various unit models for modeling hundreds of CPI plant facilities; (ii) dealing with critical abnormal operating conditions of CPI plants such as plant start-up and shut-down. Two virtual case studies on flare minimizations for start-up operation (over 50% of emission savings) and shut-down operation (over 70% of emission savings) of an ethylene plant have been employed to demonstrate the efficacy of the proposed study.

Keywords: flare minimization, large-scale modeling and simulation, plant shut-down, plant start-up

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Authors: Majid Amidpour, Parisa Karimi, Marzieh Joda

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For the last few years, release of burned undesirable by-products has become a challenging issue in oil industries. Flaring, as one of the main sources of air contamination, involves detrimental and long-lasting effects on human health and is considered a substantial reason for energy losses worldwide. This research involves studying the implications of two main flare gas recovery methods at three oil refineries, all in Iran as the case I, case II, and case III in which the production capacities are increasing respectively. In the proposed methods, flare gases are converted into more valuable products, before combustion by the flare networks. The first approach involves collecting, compressing and converting the flare gas to smokeless fuel which can be used in the fuel gas system of the refineries. The other scenario includes utilizing the flare gas as a feed into liquefied petroleum gas (LPG) production unit already established in the refineries. The processes of these scenarios are simulated, and the capital investment is calculated for each procedure. The cumulative profits of the scenarios are evaluated using Net Present Value method. Furthermore, the sensitivity analysis based on total propane and butane mole fraction is carried out to make a rational comparison for LPG production approach, and the results are illustrated for different mole fractions of propane and butane. As the mole fraction of propane and butane contained in LPG differs in summer and winter seasons, the results corresponding to LPG scenario are demonstrated for each season. The results of the simulations show that cumulative profit in fuel gas production scenario and LPG production rate increase with the capacity of the refineries. Moreover, the investment return time in LPG production method experiences a decline, followed by a rising trend with an increase in C₃ and C₄ content. The minimum value of time return occurs at propane and butane sum concentration values of 0.7, 0.6, and 0.7 in case I, II, and III, respectively. Based on comparison of the time of investment return and cumulative profit, fuel gas production is the superior scenario for three case studies.

Keywords: flare gas reduction, liquefied petroleum gas, fuel gas, net present value method, sensitivity analysis

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Authors: Ismahafezi Ismail, Mohd Shahrizal Sunar

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The motion of a realistic 3D humanoid character is very important especially for the industries developing computer animations and games. However, this type of motion is seen with a very complex dimensional data as well as body position, orientation, and joint rotation. Integrated Style Motion Editor (ISME), on the other hand, is a method used to alter the 3D humanoid motion capture data utilised in computer animation and games development. Therefore, this study was carried out with the purpose of demonstrating a method that is able to manipulate and deform different motion styles by integrating Key Pose Deformation Technique and Trajectory Control Technique. This motion editing method allows the user to generate new motions from the original motion capture data using a simple interface control. Unlike the previous method, our method produces a realistic humanoid motion style in real time.

Keywords: computer animation, humanoid motion, motion capture, motion editing

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Authors: Amritpal Singh Nafria, Rohit Sharma, Md. Shami Ansari

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Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion.

Keywords: velocity-time graph, fundamental equations, additional equations, requisite conditions, importance and educational benefits

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Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

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Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: kinematic constraints, motion planning, trigonometric function, 6-DOF robots

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Authors: Baris Can Yalcin

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Motion sensors have been commonly used as a valuable component in mechatronic systems, however, many mechatronic designs and applications that need motion sensors cost enormous amount of money, especially high-tech systems. Design of a software for communication protocol between data acquisition card and motion sensor is another issue that has to be solved. This study presents how to design a low cost motion data acquisition setup consisting of MPU 6050 motion sensor (gyro and accelerometer in 3 axes) and Arduino Mega2560 microcontroller. Design parameters are calibration of the sensor, identification and communication between sensor and data acquisition card, interpretation of data collected by the sensor.

Keywords: design, mechatronics, motion sensor, data acquisition

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Authors: Ibrahim Hassan

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Motion typography is one of the most important types of visual communication based on display. Through the digital display media, we can control the text properties (size, direction, thickness, color, etc.). The use of motion typography in visual communication made it have several images. We need to adjust the terminology and clarify the different differences between them, so relying on the word motion typography -considered a general term- is not enough to separate the different communicative functions of the moving text. In this paper, we discuss the different effects of motion typography on Arabic writing and how we can achieve harmony between the movement and the letterform, and we will, during our experiments, present a new type of text movement.

Keywords: Arabic typography, motion typography, kinetic typography, fluid typography, temporal typography

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Authors: Alireza Abbasi Moshaii, Farshid Najafi

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In this paper a new model for centre of motion creating is proposed. This new method uses cables. So, it is very useful in robots because it is light and has easy assembling process. In the robots which need to be in touch with some things this method is very good. It will be described in the following. The accuracy of the idea is proved by an experiment. This system could be used in the robots which need a fixed point in the contact with some things and make a circular motion. Such as dancer, physician or repair robots.

Keywords: centre of motion, robotic cables, permanent touching, mechatronics engineering

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Authors: Areena Bhatti

Abstract:

The geometric arrangement of planet and moon is the result of a self-organizing system. In our solar system, the planets and moons are constantly orbiting around the sun. The aim of this theory is to compare the motion of a solar system with the motion of water droplet when poured into a water body. The basic methodology is to compare both motions to know how they are related to each other. The difference between both systems will be that one is extremely fast, and the other is extremely slow. The role of this theory is that by looking at the fast system we can conclude how slow the system will get to an end. Just like ripples are formed around water droplet that move away from the droplet and water droplet forming those ripples become small in size will tell us how solar system will behave in the same way. So it is concluded that large and small systems can work under the same process but with different motions of time, and motion of the solar system is the slowest form of water droplet motion.

Keywords: motion, water, sun, time

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Authors: Insaf Ajili, Malik Mallem, Jean-Yves Didier

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Motion recognition from videos is actually a very complex task due to the high variability of motions. This paper describes the challenges of human motion recognition, especially motion representation step with relevant features. Our descriptor vector is inspired from Laban Movement Analysis method. We propose discriminative features using the Random Forest algorithm in order to remove redundant features and make learning algorithms operate faster and more effectively. We validate our method on MSRC-12 and UTKinect datasets.

Keywords: discriminative LMA features, features reduction, human motion recognition, random forest

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified.

Keywords: mixed Gaussian processes, Sub-fractional Brownian motion, sample paths

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Authors: Giovanni Incerti

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The paper presents a method for a simple and immediate motion planning of a SCARA robot, whose end-effector has to move along a given trajectory; the calculation procedure requires the user to define in analytical form or by points the trajectory to be followed and to assign the curvilinear abscissa as function of the time. On the basis of the geometrical characteristics of the robot, a specifically developed program determines the motion laws of the actuators that enable the robot to generate the required movement; this software can be used in all industrial applications for which a SCARA robot has to be frequently reprogrammed, in order to generate various types of trajectories with different motion times.

Keywords: motion planning, SCARA robot, trajectory tracking, analytical form

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified.

Keywords: fractal dimensions, mixed gaussian processes, sample paths, sub-fractional brownian motion

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Authors: N. Tahouni, M. Gholami, M. H. Panjeshahi

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Gas flaring is one of the most GHG emitting sources in the oil and gas industries. It is also a major way for wasting such an energy that could be better utilized and even generates revenue. Minimize flaring is an effective approach for reducing GHG emissions and also conserving energy in flaring systems. Integrating waste and flared gases into the fuel gas networks (FGN) of refineries is an efficient tool. A fuel gas network collects fuel gases from various source streams and mixes them in an optimal manner, and supplies them to different fuel sinks such as furnaces, boilers, turbines, etc. In this article we use fuel gas network model proposed by Hasan et al. as a base model and modify some of its features and add constraints on emission pollution by gas flaring to reduce GHG emissions as possible. Results for a refinery case study showed that integration of flare gas stream with waste and natural gas streams to construct an optimal FGN can significantly reduce total annualized cost and flaring emissions.

Keywords: flaring, fuel gas network, GHG emissions, stream

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Authors: M. V. Chidananda Murthy, M. Z. Kurian, H. S. Guruprasad

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Image restoration in the process of communication is one of the emerging fields in the image processing. The motion analysis processing is the simplest case to detect motion in an image. Applications of motion analysis widely spread in many areas such as surveillance, remote sensing, film industry, navigation of autonomous vehicles, etc. The scene may contain multiple moving objects, by using motion analysis techniques the blur caused by the movement of the objects can be enhanced by filling-in occluded regions and reconstruction of transparent objects, and it also removes the motion blurring. This paper presents the design and comparison of various motion detection and enhancement filters. Median filter, Linear image deconvolution, Inverse filter, Pseudoinverse filter, Wiener filter, Lucy Richardson filter and Blind deconvolution filters are used to remove the blur. In this work, we have considered different types and different amount of blur for the analysis. Mean Square Error (MSE) and Peak Signal to Noise Ration (PSNR) are used to evaluate the performance of the filters. The designed system has been implemented in Matlab software and tested for synthetic and real-time images.

Keywords: image enhancement, motion analysis, motion detection, motion estimation

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Authors: Kazuo Kiguchi, Kouta Ikegami

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In the case of physically weak persons, not only motor abilities, but also sensory abilities are sometimes deteriorated. The concept of perception-assist has been proposed to assist the sensory ability of the physically weak persons with a power-assist robot. Since upper-limb motion is very important in daily living, perception-assist for upper-limb motion has been proposed to assist upper-limb motion in daily living. A virtual tunnel was applied to modify the user’s upper-limb motion if it was necessary. In this paper, effective shape of the virtual tunnel which is applied in the perception-assist for upper-limb motion is proposed. Not only the position of the grasped tool but also the angle of the grasped tool are modified if it is necessary. Therefore, the upper-limb motion in daily living can be effectively modified to realize certain proper daily motion. The effectiveness of the proposed virtual tunnel was evaluated by performing the experiments.

Keywords: motion modification, power-assist robots, perception-assist, upper-limb motion

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Authors: Mohammad Saleh Vahdatpour, Yanqing Zhang

Abstract:

Understanding the neural mechanisms underlying motion detection in the human visual system has long been a fascinating challenge in neuroscience and artificial intelligence. This paper presents a spiking neural network model inspired by the processing of motion information in the primate visual system, particularly focusing on the Middle Temporal (MT) area. In our study, we propose a multi-layer spiking neural network model to perform motion detection tasks, leveraging the idea that synaptic delays in neuronal communication are pivotal in motion perception. Synaptic delay, determined by factors like axon length and myelin insulation, affects the temporal order of input spikes, thereby encoding motion direction and speed. Overall, our spiking neural network model demonstrates the feasibility of capturing motion detection principles observed in the primate visual system. The combination of synaptic delays, learning mechanisms, and shared weights and delays in SMD provides a promising framework for motion perception in artificial systems, with potential applications in computer vision and robotics.

Keywords: neural network, motion detection, signature detection, convolutional neural network

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Authors: Koichi Kurita

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In this study, we propose a real-time data collection technique for the detection of human walking motion from the charge generated on the human body. This technique is based on the detection of a sub-picoampere electrostatic induction current, generated by the motion, flowing through the electrode of a wireless portable sensor attached to the subject. An FFT analysis of the wave-forms of the electrostatic induction currents generated by the walking motions showed that the currents generated under normal and restricted walking conditions were different. Moreover, we carried out a cepstrum analysis to detect any differences in the walking style. Results suggest that a slight difference in motion, either due to the individual’s gait or a splinted leg, is directly reflected in the electrostatic induction current generated by the walking motion. The proposed wireless portable sensor enables the detection of even subtle differences in walking motion.

Keywords: human walking motion, motion measurement, current measurement, electrostatic induction

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Authors: Najm Alotaibi

Abstract:

Human motion capture has become one of the major area of interest in the field of computer vision. Some of the major application areas that have been rapidly evolving include the advanced human interfaces, virtual reality and security/surveillance systems. This study provides a brief overview of the techniques and applications used for the markerless human motion capture, which deals with analyzing the human motion in the form of mathematical formulations. The major contribution of this research is that it classifies the computer vision based techniques of human motion capture based on the taxonomy, and then breaks its down into four systematically different categories of tracking, initialization, pose estimation and recognition. The detailed descriptions and the relationships descriptions are given for the techniques of tracking and pose estimation. The subcategories of each process are further described. Various hypotheses have been used by the researchers in this domain are surveyed and the evolution of these techniques have been explained. It has been concluded in the survey that most researchers have focused on using the mathematical body models for the markerless motion capture.

Keywords: human motion capture, computer vision, vision-based, tracking

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Authors: Seongsoo Lee

Abstract:

Motion estimation occupies the heaviest computation in HEVC (high efficiency video coding). Many fast algorithms such as TZS (test zone search) have been proposed to reduce the computation. Still the huge computation of the motion estimation is a critical issue in the implementation of HEVC video codec. In this paper, motion estimator architecture with optimized number of PEs (processing element) is presented by exploiting early termination. It also reduces hardware size by exploiting parallel processing. The presented motion estimator architecture has 8 PEs, and it can efficiently perform TZS with very high utilization of PEs.

Keywords: motion estimation, test zone search, high efficiency video coding, processing element, optimization

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Authors: Valeria Bondarenko

Abstract:

In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

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Authors: S. M. Kulkarni, D. S. Bormane, S. L. Nalbalwar

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The rapid development in the technology have dramatic impact on the medical health care field. Medical data base obtained with latest machines like CT Machine, MRI scanner requires large amount of memory storage and also it requires large bandwidth for transmission of data in telemedicine applications. Thus, there is need for video compression. As the database of medical images contain number of frames (slices), hence while coding of these images there is need of motion estimation. Motion estimation finds out movement of objects in an image sequence and gets motion vectors which represents estimated motion of object in the frame. In order to reduce temporal redundancy between successive frames of video sequence, motion compensation is preformed. In this paper three step search (TSS) block matching algorithm is implemented on different types of video sequences. It is shown that three step search algorithm produces better quality performance and less computational time compared with exhaustive full search algorithm.

Keywords: block matching, exhaustive search motion estimation, three step search, video compression

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Authors: Kyeong-Ri Ko, Seong Bong Bae, Jang Sik Choi, Sung Bum Pan

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A simple method for testing the posture imbalance of the human body is to check for differences in the bilateral shoulder and pelvic height of the target. In this paper, to check for spinal disorders the authors have studied ways to establish a motion capture system to obtain and express motions of 4-joints, and to acquire data based on this system. The 4 sensors are attached to the both shoulders and pelvis. To verify the established system, the normal and abnormal postures of the targets listening to a lecture were obtained using the established 4-joint based motion capture system. From the results, it was confirmed that the motions taken by the target was identical to the 3-dimensional simulation.

Keywords: inertial sensor, motion capture, motion data acquisition, posture imbalance

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Authors: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional g-Brownian motion, Taylor's series of fractional order, uncertain volatility

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