Search results for: complex nonlinear system.

Authors: Viet Dzung Nguyen, Duc Thuan Nguyen, Tien Dzung Nguyen, Van Thanh Pham

Abstract:

Mammography is the most effective procedure for an early diagnosis of the breast cancer. Nowadays, people are trying to find a way or method to support as much as possible to the radiologists in diagnosis process. The most popular way is now being developed is using Computer-Aided Detection (CAD) system to process the digital mammograms and prompt the suspicious region to radiologist. In this paper, an automated CAD system for detection and classification of massive lesions in mammographic images is presented. The system consists of three processing steps: Regions-Of- Interest detection, feature extraction and classification. Our CAD system was evaluated on Mini-MIAS database consisting 322 digitalized mammograms. The CAD system-s performance is evaluated using Receiver Operating Characteristics (ROC) and Freeresponse ROC (FROC) curves. The archived results are 3.47 false positives per image (FPpI) and sensitivity of 85%.

Keywords: classification, computer-aided detection, featureextraction, mass detection.

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Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

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Authors: L. Nikakhtar, S. Zare

Abstract:

One of the main practical difficulties attended with tunnel construction is related to underground water. Uncontrolled water behavior may cause extra loads on the lining, mechanical instability, and unfavorable environmental problems. Estimating underground water inflow rate to the tunnels is a complex skill. The common calculation methods are: empirical methods, analytical solutions, numerical solutions based on the equivalent continuous porous media. In this research the rate of underground water inflow to the Tabriz metro first line tunnel has been investigated by numerical finite difference method using FLAC^2D software. Comparing results of Heuer analytical method and numerical simulation showed good agreement with each other. Fully coupled and one-way coupled hydro mechanical states as well as water-free conditions in the soil around the tunnel are used in numerical models and these models have been applied to evaluate the loading value on the tunnel support system. Results showed that the fully coupled hydro mechanical analysis estimated more axial forces, moments and shear forces in linings, so this type of analysis is more conservative and reliable method for design of tunnel lining system. As sensitivity analysis, inflow water rates into the tunnel were evaluated in different soil permeability, underground water levels and depths of the tunnel. Result demonstrated that water level in constant depth of the tunnel is more sensitive factor for water inflow rate to the tunnel in comparison of other parameters investigated in the sensitivity analysis.

Keywords: Coupled hydro mechanical analysis, FLAC2D, Tabriz Metro, inflow rate.

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Authors: Vahid Fayaz , Asieh Tavakol

Abstract:

To investigate the applicability of the EDR-2 film for clinical radiation dosimetry, percentage depth-doses, profiles and distributions in open and dynamically wedged fields were measured using film and compared with data from a Treatment Planning system.The validity of the EDR2 film to measure dose in a plane parallel to the beam was tested by irradiating 10 cm×10 cm and 4 cm×4 cm fields from a Siemens, primus linac with a 6MV beam and a source-to-surface distance of 100 cm. The film was placed Horizontally between solid water phantom blocks and marked with pin holes at a depth of 10 cm from the incident beam surface. The film measurement results, in absolute dose, were compared with ion chamber measurements using a Welhoffer scanning water tank system and Treatment Planning system. Our results indicate a maximum underestimate of calculated dose of 8 % with Treatment Planning system.

Keywords: 6MV Photon , EDR-2 film, Radiotherapy, TreatmentPlanning system

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Authors: Shield B. Lin, Ziraguen O. Williams

Abstract:

In a task to assist NASA in analyzing the dynamic forces caused by operational countermeasures of an astronaut’s exercise platform impacting the spacecraft, an active proportional-integral-derivative controller commanding a linear actuator is proposed in a vibration isolation system to regulate the movement of the exercise platform. Computer simulation shows promising results that most exciter forces can be reduced or even eliminated. This paper emphasizes on parameter uncertainties, variations and exciter force variations. Drift and variations of system parameters in the vibration isolation system for astronaut’s exercise platform are analyzed. An active controlled scheme is applied with the goals to reduce the platform displacement and to minimize the force being transmitted to the spacecraft structure. The controller must be robust enough to accommodate the wide variations of system parameters and exciter forces. Computer simulation for the vibration isolation system was performed via MATLAB/Simulink and Trick. The simulation results demonstrate the achievement of force reduction with small platform displacement under wide ranges of variations in system parameters. 

Keywords: control, counterweight, isolation, vibration

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

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In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

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Authors: Bakari M. M. Mwinyiwiwa, Mighanda J. Manyahi, Nicodemu Gregory, Alex L. Kyaruzi

Abstract:

Microgrids are increasingly being considered to provide electricity for the expanding energy demand in the grid distribution network and grid isolated areas. However, the technical challenges associated with the operation and controls are immense. Management of dynamic power balances, power flow, and network voltage profiles imposes unique challenges in the context of microgrids. Stability of the microgrid during both grid-connected and islanded mode is considered as the major challenge during its operation. Traditional control methods have been employed are based on the assumption of linear loads. For instance the concept of PQ, voltage and frequency control through decoupled PQ are some of very useful when considering linear loads, but they fall short when considering nonlinear loads. The deficiency of traditional control methods of microgrid suggests that more research in the control of microgrids should be done. This research aims at introducing the dq technique concept into decoupled PQ for dynamic load demand control in inverter interfaced DG system operating as isolated LV microgrid. Decoupled PQ in exact mathematical formulation in dq frame is expected to accommodate all variations of the line parameters (resistance and inductance) and to relinquish forced relationship between the DG variables such as power, voltage and frequency in LV microgrids and allow for individual parameter control (frequency and line voltages). This concept is expected to address and achieve accurate control, improve microgrid stability and power quality at all load conditions.

Keywords: Decoupled PQ, microgrid, multisource, renewable energy, dq control.

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Authors: Worawit Somha, Hiroyuki Yamauchi

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This paper proposes, for the first time, how the challenges facing the guard-band designs including the margin assist-circuits scheme for the screening-test in the coming process generations should be addressed. The increased screening error impacts are discussed based on the proposed statistical analysis models. It has been shown that the yield-loss caused by the misjudgment on the screening test would become 5-orders of magnitude larger than that for the conventional one when the amplitude of random telegraph noise (RTN) caused variations approaches to that of random dopant fluctuation. Three fitting methods to approximate the RTN caused complex Gamma mixtures distributions by the simple Gaussian mixtures model (GMM) are proposed and compared. It has been verified that the proposed methods can reduce the error of the fail-bit predictions by 4-orders of magnitude.

Keywords: Mixtures of Gaussian, Random telegraph noise, EM algorithm, Long-tail distribution, Fail-bit analysis, Static random access memory, Guard band design.

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Authors: Jian Wang, Lu Yang, Jiong Peng

Abstract:

Internal circulation two-platen clamping system for injection molding machine (IMM) has many potential advantages on energy-saving. In order to estimate its properties, experiments were carried out in this paper. Displacement and pressure of the components were measured. In comparison, the model of hydraulic clamping system was established by using AMESim. The related parameters as well as the energy consumption could be calculated. According to the analysis, the hydraulic system was optimized in order to reduce the energy consumption.

Keywords: AMESim, energy-saving, injection molding machine, internal circulation.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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Authors: Young-Lim Choi, Nak-Yun Choi, Jae-Yong Seo, Sang-Il Park, Jong-Wook Kim

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This paper proposes a prototype of a lower-limb rehabilitation system for recovering and strengthening patients- injured lower limbs. The system is composed of traction motors for each leg position, a treadmill as a walking base, tension sensors, microcontrollers controlling motor functions and a main system with graphic user interface. For derivation of reference or normal velocity profiles of the body segment point, kinematic method is applied based on the humanoid robot model using the reference joint angle data of normal walking.

Keywords: Rehabilitation, lower limb, treadmill, humanoid robot.

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Authors: Chakkrit Snae, Michael Brueckner

Abstract:

In this paper the authors present the framework of a system for assisting users through counseling on personal health, the Personal Health Assistance Service Expert System (PHASES). Personal health assistance systems need Personal Health Records (PHR), which support wellness activities, improve the understanding of personal health issues, enable access to data from providers of health services, strengthen health promotion, and in the end improve the health of the population. This is especially important in societies where the health costs increase at a higher rate than the overall economy. The most important elements of a healthy lifestyle are related to food (such as balanced nutrition and diets), activities for body fitness (such as walking, sports, fitness programs), and other medical treatments (such as massage, prescriptions of drugs). The PHASES framework uses an ontology of food, which includes nutritional facts, an expert system keeping track of personal health data that are matched with medical treatments, and a comprehensive data transfer between patients and the system.

Keywords: Personal health assistance service, expert system, ontologies, knowledge management, information technology.

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Authors: Achim Washington, Reece Clothier, Jose Silva

Abstract:

System Safety Regulations (SSR) are a central component to the airworthiness certification of Unmanned Aircraft Systems (UAS). There is significant debate on the setting of appropriate SSR for UAS. Putting this debate aside, the challenge lies in how to apply the system safety process to UAS, which lacks the data and operational heritage of conventionally piloted aircraft. The limited knowledge and lack of operational data result in uncertainty in the system safety assessment of UAS. This uncertainty can lead to incorrect compliance findings and the potential certification and operation of UAS that do not meet minimum safety performance requirements. The existing system safety assessment and compliance processes, as used for conventional piloted aviation, do not adequately account for the uncertainty, limiting the suitability of its application to UAS. This paper discusses the challenges of undertaking system safety assessments for UAS and presents current and envisaged research towards addressing these challenges. It aims to highlight the main advantages associated with adopting a risk based framework to the System Safety Performance Requirement (SSPR) compliance process that is capable of taking the uncertainty associated with each of the outputs of the system safety assessment process into consideration. Based on this study, it is made clear that developing a framework tailored to UAS, would allow for a more rational, transparent and systematic approach to decision making. This would reduce the need for conservative assumptions and take the risk posed by each UAS into consideration while determining its state of compliance to the SSR.

Keywords: Part 1309 regulations, unmanned aircraft systems, system safety, uncertainty.

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Authors: Amin Alvani

Abstract:

Multiple sclerosis (MS) is a chronic, often disabling disease in which the immune system attacks the myelin sheath of neurons in the central nervous system. The purpose of this study was to explore the correlation between the Behavioral Inhibition/Approach System (BIS-BAS) and Perceived Stress (PS), while controlling for White Blood Cell (WBC) count. 60 MS patients (36.7% male, 63.3% female; aged 15-65 years) participated in this study. They completed a demographic questionnaire, underwent a complete blood cell (CBC) test, filled out the Behavioral Activation and Behavioral Inhibition Scale (BIS-BAS), and responded to the Perceived Stress Questionnaire (PSS-14). The results indicated a significant relationship between the BAS-Reward Responsiveness (BAS-RR) subscale and PS, particularly in a subset of MS patients with increased WBC counts.

Keywords: Behavioral inhibition/approach system, multiple sclerosis, perceived stress, white blood cell.

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Authors: Gautam Sarkar, Anjan Rakshit, Amitava Chatterjee, Kesab Bhattacharya

Abstract:

The present paper describes the development of a low cost, highly accurate low capacitance measurement system that can be used over a range of 0 – 400 pF with a resolution of 1 pF. The range of capacitance may be easily altered by a simple resistance or capacitance variation of the measurement circuit. This capacitance measurement system uses quad two-input NAND Schmitt trigger circuit CD4093B with hysteresis for the measurement and this system is integrated with PIC 18F2550 microcontroller for data acquisition purpose. The microcontroller interacts with software developed in the PC end through USB architecture and an attractive graphical user interface (GUI) based system is developed in the PC end to provide the user with real time, online display of capacitance under measurement. The system uses a differential mode of capacitance measurement, with reference to a trimmer capacitance, that effectively compensates lead capacitances, a notorious error encountered in usual low capacitance measurements. The hysteresis provided in the Schmitt-trigger circuits enable reliable operation of the system by greatly minimizing the possibility of false triggering because of stray interferences, usually regarded as another source of significant error. The real life testing of the proposed system showed that our measurements could produce highly accurate capacitance measurements, when compared to cutting edge, high end digital capacitance meters.

Keywords: Capacitance measurement, NAND Schmitt trigger, microcontroller, GUI, lead compensation, hysteresis.

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Authors: Ziraguen O. Williams, Shield B. Lin, Fouad N. Matari, Leslie J. Quiocho

Abstract:

In a task to assist NASA in analyzing the dynamic forces caused by operational countermeasures of an astronaut’s exercise platform impacting the spacecraft, feedback delay and signal noise were added to a simulation model of an active controlled vibration isolation and stabilization system to regulate the movement of the exercise platform. Two additional simulation tools used in this study were Trick and MBDyn, software simulation environments developed at the NASA Johnson Space Center. Simulation results obtained from these three tools were very similar. All simulation results support the hypothesis that an active controlled vibration isolation and stabilization system outperforms a passive controlled system even with the addition of feedback delay and signal noise to the active controlled system. In this paper, squat exercise was used in creating excited force to the simulation model. The exciter force from squat exercise was calculated from motion capture of an exerciser. The simulation results demonstrate much greater transmitted force reduction in the active controlled system than the passive controlled system.

Keywords: Astronaut, counterweight, stabilization, vibration.

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Authors: Ali A. Ofoghi

Abstract:

While the shear walls are not economical in buildings, thin shear walls are widely used in the buildings. In the present study, the ratio of different loads to their plasticity and seismic behavior of the wall under different loads have been investigated. Modeling and analysis are carried out by the finite element analysis software ABAQUS. The results show that any increase in the exerted loads will have adverse effects on the seismic behavior of the thin shear walls and causes the wall to collapse by small displacements.

Keywords: Thin shear wall, nonlinear dynamic analysis, reinforced concrete, plasticity.

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Authors: R. Prakash, B. Meenakshipriya, R. Kumaravelan

Abstract:

Fresh water is one of the resources which is getting depleted day by day. A wise method to address this issue is by the application of renewable energy-sun irradiation and by means of decentralized, cheap, energetically self-sufficient, robust and simple to operate plants, distillates can be obtained from sea, river or even sewage. Solar desalination is a technique used to desalinate water using solar energy. The present work deals with the comprehensive design and simulation of solar tracking system using LabVIEW, temperature and mass flow rate control of the solar desalination plant using LabVIEW and also analysis of single phase inverter circuit with LC filters for solar pumping system in MATLAB. The main objective of this work is to improve the performance of solar desalination system using automatic tracking system, output control using temperature and mass flow rate control system and also to reduce the harmonic distortion in the solar pumping system by means of LC filters. The simulation of single phase inverter was carried out using MATLAB and the output waveforms were analyzed. Simulations were performed for optimum output temperature control, which in turn controls the mass flow rate of water in the thermal collectors. Solar tracking system was accomplished using LABVIEW and was tested successfully. The thermal collectors are tracked in accordance with the sun’s irradiance levels, thereby increasing the efficiency of the thermal collectors.

Keywords: Desalination, Electro dialysis, LabVIEW, MATLAB, PWM inverter, Reverse osmosis.

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Authors: Jae-Min Yu, Hyoung-Ho Doh, Ji-Su Kim, Dong-Ho Lee, Sung-Ho Nam

Abstract:

A reconfigurable manufacturing system (RMS) is an advanced system designed at the outset for rapid changes in its hardware and software components in order to quickly adjust its production capacity and functionally. Among various operational decisions, this study considers the scheduling problem that determines the input sequence and schedule at the same time for a given set of parts. In particular, we consider the practical constraints that the numbers of pallets/fixtures are limited and hence a part can be released into the system only when the fixture required for the part is available. To solve the integrated input sequencing and scheduling problems, we suggest a priority rule based approach in which the two sub-problems are solved using a combination of priority rules. To show the effectiveness of various rule combinations, a simulation experiment was done on the data for a real RMS, and the test results are reported.

Keywords: Reconfigurable manufacturing system, scheduling, priority rules, multiple process plans, pallets/fixtures

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Authors: E. Supriyanto, S. C. Seow

Abstract:

Early Intervention Program (EIP) is required to improve the overall development of children with Trisomy 21 (Down syndrome). In order to help trainer and parent in the implementation of EIP, a support system has been developed. The support system is able to screen data automatically, store and analyze data, generate individual EIP (curriculum) with optimal training duration and to generate training automatically. The system consists of hardware and software where the software has been implemented using Java language and Linux Fedora. The software has been tested to ensure the functionality and reliability. The prototype has been also tested in Down syndrome centers. Test result shows that the system is reliable to be used for generation of an individual curriculum which includes the training program to improve the motor, cognitive, and combination abilities of Down syndrome children under 6 years.

Keywords: Early intervention program (curriculum), Trisomy21, support system, Java.

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Authors: Nittaya Kerdprasop, Kittisak Kerdprasop

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Data mining (DM) is the process of finding and extracting frequent patterns that can describe the data, or predict unknown or future values. These goals are achieved by using various learning algorithms. Each algorithm may produce a mining result completely different from the others. Some algorithms may find millions of patterns. It is thus the difficult job for data analysts to select appropriate models and interpret the discovered knowledge. In this paper, we describe a framework of an intelligent and complete data mining system called SUT-Miner. Our system is comprised of a full complement of major DM algorithms, pre-DM and post-DM functionalities. It is the post-DM packages that ease the DM deployment for business intelligence applications.

Keywords: Business intelligence, data mining, functionalprogramming, intelligent system.

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Authors: Ibrahim Shaker, Amr El Hossany, Moustafa Osman, Mohamed El Raey

Abstract:

This paper will explore integration model between GIS–SCADA system and enclosure quantification model to approach the impact of failure-safe event. There are real demands to identify spatial objects and improve control system performance. Nevertheless, the employed methodology is predicting electro-mechanic operations and corresponding time to environmental incident variations. Open processing, as object systems technology, is presented for integration enclosure database with minimal memory size and computation time via connectivity drivers such as ODBC:JDBC during main stages of GIS–SCADA connection. The function of Geographic Information System is manipulating power distribution in contrast to developing issues. In other ward, GIS-SCADA systems integration will require numerical objects of process to enable system model calibration and estimation demands, determine of past events for analysis and prediction of emergency situations for response training.

Keywords: Air dispersion model, integration power system, SCADA systems, GIS system, environmental management.

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Authors: J.-P. Skön, M. Johansson, O. Kauhanen, M. Raatikainen, K. Leiviskä, M. Kolehmainen

Abstract:

The building sector is the largest energy consumer and CO2 emitter in the European Union (EU) and therefore the active reduction of energy consumption and elimination of energy wastage are among the main goals in it. Healthy housing and energy efficiency are affected by many factors which set challenges to monitoring, control and research of indoor air quality (IAQ) and energy consumption, especially in old buildings. These challenges include measurement and equipment costs, for example. Additionally, the measurement results are difficult to interpret and their usage in the ventilation control is also limited when taking into account the energy efficiency of housing at the same time. The main goal of this study is to develop a cost-effective building monitoring and control system especially for old buildings. The starting point or keyword of the development process is a wireless system; otherwise the installation costs become too high. As the main result, this paper describes an idea of a wireless building monitoring and control system. The first prototype of the system has been installed in 10 residential buildings and in 10 school buildings located in the City of Kuopio, Finland.

Keywords: Energy efficiency, Indoor air quality, Monitoring system, Building automation

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Authors: Suwaree Yordchim, Toby J. Gibbs

Abstract:

The objective is to study the satisfaction on English with an online learning. Online learning system mainly consists of English lessons, exercises, tests, web boards, and supplementary lessons for language practice. The sample groups are 80 Thai students studying English for Business Communication, majoring in Hotel and Lodging Management. The data are analyzed by mean, standard deviation (S.D.) value from the questionnaires. The results were found that the most average of satisfaction on academic aspects are technological searching tool through E-learning system that support the students’ learning (4.51), knowledge evaluation on pre-post learning and teaching (4.45), and change for project selections according to their interest, subject contents including practice in the real situations (4.45), respectively.

Keywords: English Learning, Online System, Satisfaction.

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Authors: Chiung-Ju Huang

Abstract:

This study examines whether the Taiwan’s public debt is sustainable utilizing an unrestricted two-regime threshold autoregressive (TAR) model with an autoregressive unit root. The empirical results show that Taiwan’s public debt appears as a nonlinear series and is stationary in regime 1 but not in regime 2. This result implies that while Taiwan’s public debt was mostly sustainable over the 1996 to 2013 period examined in the study, it may no longer be sustainable in the most recent two years as the public debt ratio has increased cumulatively to 3.618%.

Keywords: Nonlinearity, public debt, sustainability, threshold autoregressive model.

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Authors: Shahzadah Fahad Qureshi, Jianqing Zhang

Abstract:

The wisest economic decision of United States in the 20th century was establishing the favorable international monetary system, and capturing the leadership position in it. This decision gave economic hegemony to the US for the next more than 7 decades. The continuation of this hegemony till the next decade seems difficult as the US economy is under continuous streams of recessions since 2007. On the other hand, Chinese economy is progressing with a very fast speed and is estimated to pass the US economy till 2025, in various aspects. Will the US be able to continue its leadership in the IMS? Will China replace US in the international monetary system? The answers to these questions have been explored by comparing the economic competitiveness of US and China, with respect to each other. The paper concludes that the change in global economic environment will compel US to share the leadership of international monetary system with China. This sharing will solve most problems of the current IMS, but will also birth some new problems.

Keywords: Economic competitiveness, Global economic environment (GEE), International monetary fund (IMF), International monetary system (IMS)

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Authors: Md. Zahangir Alom, Mei-Lan Piao, Md. Ashraful Alam, Nam Kim, Jae-Hyeung Park

Abstract:

A new approach for facial expressions recognition based on face context and adaptively weighted sub-pattern PCA (Aw-SpPCA) has been presented in this paper. The facial region and others part of the body have been segmented from the complex environment based on skin color model. An algorithm has been proposed to accurate detection of face region from the segmented image based on constant ratio of height and width of face (δ= 1.618). The paper also discusses on new concept to detect the eye and mouth position. The desired part of the face has been cropped to analysis the expression of a person. Unlike PCA based on a whole image pattern, Aw-SpPCA operates directly on its sub patterns partitioned from an original whole pattern and separately extracts features from them. Aw-SpPCA can adaptively compute the contributions of each part and a classification task in order to enhance the robustness to both expression and illumination variations. Experiments on single standard face with five types of facial expression database shows that the proposed method is competitive.

Keywords: Aw-SpPC, Expressoin Recognition, Face context, Face Detection, PCA

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Authors: Daniela I. Borissova, Ivan C. Mustakerov, Evgeni D. Bantutov

Abstract:

Nowadays the devices of night vision are widely used both for military and civil applications. The variety of night vision applications require a variety of the night vision devices designs. A web-based architecture of a software system for design assessment before producing of night vision devices is developed. The proposed architecture of the web-based system is based on the application of a mathematical model for designing of night vision devices. An algorithm with two components – for iterative design and for intelligent design is developed and integrated into system architecture. The iterative component suggests compatible modules combinations to choose from. The intelligent component provides compatible combinations of modules  satisfying given user requirements to device parameters. The proposed web-based architecture of a system for design assessment of night vision devices is tested via a prototype of the system. The testing showed the applicability of both iterative and intelligent components of algorithm. 

Keywords: Night vision devices, design modeling, software architecture, web-based system.

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Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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Authors: Oscar E. Ruiz, Carlos Cadavid, Juan G. Lalinde, Ricardo Serrano, Guillermo Peris-Fajarnes

Abstract:

The Boundary Representation of a 3D manifold contains FACES (connected subsets of a parametric surface S : R2 -! R3). In many science and engineering applications it is cumbersome and algebraically difficult to deal with the polynomial set and constraints (LOOPs) representing the FACE. Because of this reason, a Piecewise Linear (PL) approximation of the FACE is needed, which is usually represented in terms of triangles (i.e. 2-simplices). Solving the problem of FACE triangulation requires producing quality triangles which are: (i) independent of the arguments of S, (ii) sensitive to the local curvatures, and (iii) compliant with the boundaries of the FACE and (iv) topologically compatible with the triangles of the neighboring FACEs. In the existing literature there are no guarantees for the point (iii). This article contributes to the topic of triangulations conforming to the boundaries of the FACE by applying the concept of parameterindependent Gabriel complex, which improves the correctness of the triangulation regarding aspects (iii) and (iv). In addition, the article applies the geometric concept of tangent ball to a surface at a point to address points (i) and (ii). Additional research is needed in algorithms that (i) take advantage of the concepts presented in the heuristic algorithm proposed and (ii) can be proved correct.

Keywords: surface triangulation, conforming triangulation, surfacesampling, Gabriel complex.

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