Search results for: Empirical mode decomposition

Authors: A. Sokołowska

Abstract:

The study presents a brief and synthetic discussion of selected conclusions resulting from multidimensional and in-depth empirical studies. Its theoretical part presents the assumptions referring to social responsibility management from the perspective of the specific nature of small enterprise functioning, while the empirical part presents the selected dysfunctions and paradoxes in social responsibility management referring to this group of enterprises. The paper is summarized by a short list of the resulting recommendations.

Keywords: Small enterprise, social responsibility management, social responsibility of small enterprise.

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Authors: S. Al Dandachli, F. Perales, Y. Monerie, F. Jamin, M. S. El Youssoufi, C. Pelissou

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The goal of this research is to study the fracture process and mechanical behavior of concrete under I–II mixed-mode stress, which is essential for ensuring the safety of concrete structures. For this purpose, two-dimensional simulations of three-point bending tests under variable load and geometry on notched cement paste samples of composite samples (cement paste/siliceous aggregate) are modeled by employing Cohesive Zone Models (CZMs). As a result of experimental validation of these tests, the CZM model demonstrates its capacity to predict fracture propagation at the local scale.

Keywords: Concrete, cohesive zone model, microstructure, fracture, three-point flexural test bending.

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Authors: Siddharth Gadkari, Rochish Thaokar

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The effect of viscosity ratio (λ, defined as viscosity of surrounding medium/viscosity of fluid jet) on stability of axisymmetric (m=0) and asymmetric (m=1) modes of perturbation on a liquid-liquid jet in presence of radial electric field (E0 ), is studied using linear stability analysis. The viscosity ratio is shown to have a damping effect on both the modes of perturbation. However the effect was found more pronounced for the m=1 mode as compared to m=1 mode. Investigating the effect of both E0 and λ simultaneously, an operating diagram is generated, which clearly shows the regions of dominance of the two modes for a range of electric field and viscosity ratio values.

Keywords: liquid-liquid jet, axisymmetric perturbation, asymmetric perturbation, radial electric field

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Authors: Komala Kalyanam, Pushpam Indumathi

Abstract:

WiMAX is defined as Worldwide Interoperability for Microwave Access by the WiMAX Forum, formed in June 2001 to promote conformance and interoperability of the IEEE 802.16 standard, officially known as WirelessMAN. The attractive features of WiMAX technology are very high throughput and Broadband Wireless Access over a long distance. A detailed simulation environment is demonstrated with the UGS, nrtPS and ertPS service classes for throughput, delay and packet delivery ratio for a mixed environment of fixed and mobile WiMAX. A simple mobility aspect is considered for the mobile WiMAX and the PMP mode of transmission is considered in TDD mode. The Network Simulator 2 (NS-2) is the tool which is used to simulate the WiMAX network scenario. A simple Priority Scheduler and Weighted Round Robin Schedulers are the WiMAX schedulers used in the research work

Keywords: ertPS, Mobile WiMAX, scheduler.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

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The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

Keywords: Non-linear vibrations, Annular plates, Large vibration amplitudes.

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Authors: Ki Hyun Kim, Jang-Hee Yoo, Kyo Il Chung

Abstract:

This paper proposes a VPN Accelerator Board (VPN-AB), a virtual private network (VPN) protocol designed for trust channel security system (TCSS). TCSS supports safety communication channel between security nodes in internet. It furnishes authentication, confidentiality, integrity, and access control to security node to transmit data packets with IPsec protocol. TCSS consists of internet key exchange block, security association block, and IPsec engine block. The internet key exchange block negotiates crypto algorithm and key used in IPsec engine block. Security Association blocks setting-up and manages security association information. IPsec engine block treats IPsec packets and consists of networking functions for communication. The IPsec engine block should be embodied by H/W and in-line mode transaction for high speed IPsec processing. Our VPN-AB is implemented with high speed security processor that supports many cryptographic algorithms and in-line mode. We evaluate a small TCSS communication environment, and measure a performance of VPN-AB in the environment. The experiment results show that VPN-AB gets a performance throughput of maximum 15.645Gbps when we set the IPsec protocol with 3DES-HMAC-MD5 tunnel mode.

Keywords: TCSS(Trust Channel Security System), VPN(VirtualPrivate Network), IPsec, SSL, Security Processor, Securitycommunication.

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Authors: Martin Ringdorfer, Martin Horn

Abstract:

A robust wheel slip controller for electric vehicles is introduced. The proposed wheel slip controller exploits the dynamics of electric traction drives and conventional hydraulic brakes for achieving maximum energy efficiency and driving safety. Due to the control of single wheel traction motors in combination with a hydraulic braking system, it can be shown, that energy recuperation and vehicle stability control can be realized simultaneously. The derivation of a sliding mode wheel slip controller accessing two drivetrain actuators is outlined and a comparison to a conventionally braked vehicle is shown by means of simulation.

Keywords: Wheel slip control, sliding mode control, vehicle dynamics.

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Authors: Marinka Baghdasaryan, Tigran Mnoyan

Abstract:

The pertinence of modeling the moment of resistance generated by the ore-grinding mill is substantiated. Based on the ranking of technological indices obtained in the result of the survey among the specialists of several beneficiating plants, the factors determining the level of the moment of resistance generated by the mill are revealed. A priori diagram of the ranks is obtained in which the factors are arranged in the descending order of the impact degree on the level of the moment. The obtained model of the moment of resistance shows the technological character of the operation modes of the ore-grinding mill and can be used for improving the operation modes of the system motor-mill and preventing the abnormal mode of the drive synchronous motor.

Keywords: Model, abnormal mode, mill, correlation, moment of resistance, rotational speed.

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Authors: Hongjun Liu, Cunxiao Gao, Jintao Tao, Wei Zhao, Yishan Wang

Abstract:

A compact tunable 10 W picosecond source based on Yb-doped fiber amplification of gain switch laser diode has been demonstrated. A gain switch semiconductor laser diode was used as the seed source, and a multi-stage single mode Yb-doped fiber preamplifier was combined with two large mode area double-clad Yb-doped fiber main amplifiers to construct the amplification system. The tunable pulses with high stability and excellent beam quality (M2<1.2) of 10 W average power 150 ps pulse duration at 1 MHz repetition rate were obtained. The central wavelength with the line width of 2.5-3 nm was tunable from 1053 nm to 1073 nm.

Keywords: Fiber laser, fiber amplifier, picosecond laser, highpower laser

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Authors: Shougi Suliman Abosuliman, Arun Kumar, Firoz Alam

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Disaster preparedness is a key success factor for any effective disaster management practices. This paper evaluates the disaster preparedness and management in Saudi Arabia using an empirical investigation approach. It presents the results of the survey conducted by interviewing representatives of the Saudi decision-makers and administrators responsible for disaster control in Jeddah before, during and after flooding in 2009 and 2010. First, demographics of the respondents are presented, followed by quantitative analysis of their views and experiences regarding the Kingdom’s readiness before and after each flood. This is shown as a series of dependent and independent variables. Following this is a list of respondents’ priorities for disaster preparation in the Kingdom.

Keywords: Disaster response policy, crisis management, effective service delivery.

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Authors: Sundararajan Sangeetha, Joseph Jesu Christopher, Swaminathan Ramakrishnan

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In this work, the primary compressive strength components of human femur trabecular bone are qualitatively assessed using image processing and wavelet analysis. The Primary Compressive (PC) component in planar radiographic femur trabecular images (N=50) is delineated by semi-automatic image processing procedure. Auto threshold binarization algorithm is employed to recognize the presence of mineralization in the digitized images. The qualitative parameters such as apparent mineralization and total area associated with the PC region are derived for normal and abnormal images.The two-dimensional discrete wavelet transforms are utilized to obtain appropriate features that quantify texture changes in medical images .The normal and abnormal samples of the human femur are comprehensively analyzed using Harr wavelet.The six statistical parameters such as mean, median, mode, standard deviation, mean absolute deviation and median absolute deviation are derived at level 4 decomposition for both approximation and horizontal wavelet coefficients. The correlation coefficient of various wavelet derived parameters with normal and abnormal for both approximated and horizontal coefficients are estimated. It is seen that in almost all cases the abnormal show higher degree of correlation than normals. Further the parameters derived from approximation coefficient show more correlation than those derived from the horizontal coefficients. The parameters mean and median computed at the output of level 4 Harr wavelet channel was found to be a useful predictor to delineate the normal and the abnormal groups.

Keywords: Image processing, planar radiographs, trabecular bone and wavelet analysis.

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Authors: Marziyeh Yousefi, Hossein Nassaji

Abstract:

This paper reports the results of a meta-analysis of studies on the effects of instruction mode on learning second language pragmatics during the last decade (from 2006 to 2016). After establishing related inclusion/ exclusion criteria, 39 published studies were retrieved and included in the present meta-analysis. Studies were later coded for face-to-face and computer-assisted mode of instruction. Statistical procedures were applied to obtain effect sizes. It was found that Computer-Assisted-Language-Learning studies generated larger effects than Face-to-Face instruction.

Keywords: Meta-analysis, effect size, pragmatics, computer-assisted language learnin, face-to-face instruction, comprehensive meta-analysis software.

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Authors: Jun Yu, Yat-Hei Lam, Boris Grinberg, Kevin Chai Tshun Chuan

Abstract:

This paper presents a 5-V to 30-V current-mode boost converter for powering the drive circuit of a micro-electro-mechanical sensor. The design of a transconductance amplifier and an integrated current sensing circuit are presented. In addition, essential building blocks for power-on protection such as a soft-start and clamp block and supply and clock ready block are discussed in details. The chip is fabricated in a 0.18-μm CMOS process. Measurement results show that the soft-start and clamp block can effectively limit the inrush current during startup and protect the boost converter from startup failure.

Keywords: Boost Converter, Current Sensing, Power-on protection, Step-up Converter, Soft-start.

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Authors: T.C. Manjunath

Abstract:

This paper deals with the design of a moving sliding surface in a variable structure plant for a second order system. The chattering phenomena is also dealt with during the switching process for an unstable sliding surface condition. The simulation examples considered in this paper shows the effectiveness of the sliding mode control method used for the design of the moving sliding surfaces. A simulink model of the continuous system was also developed in MATLAB-SIMULINK for the design and hence demonstrated. The phase portraits and the state plots shows the demonstration of the powerful control technique which can be applied for second order systems.

Keywords: Sliding mode control, VSC, Reaching phase, Sliding phase, Moving surfaces, Chattering, Trajectories.

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Authors: Gabriel Sitler, Yousef Sardahi, Asad Salem

Abstract:

This paper presents an optimal and robust sliding mode controller (SMC) to regulate the position of the knee joint angle for patients suffering from knee injuries. The controller imitates the role of active orthoses that produce the joint torques required to overcome gravity and loading forces and regain natural human movements. To this end, a mathematical model of the shank, the lower part of the leg, is derived first and then used for the control system design and computer simulations. The design of the controller is carried out in optimal and multi-objective settings. Four objectives are considered: minimization of the control effort and tracking error; and maximization of the control signal smoothness and closed-loop system’s speed of response. Optimal solutions in terms of the Pareto set and its image, the Pareto front, are obtained. The results show that there are trade-offs among the design objectives and many optimal solutions from which the decision-maker can choose to implement. Also, computer simulations conducted at different points from the Pareto set and assuming knee squat movement demonstrate competing relationships among the design goals. In addition, the proposed control algorithm shows robustness in tracking a standard gait signal when accounting for uncertainty in the shank’s parameters.

Keywords: Optimal control, multi-objective optimization, sliding mode control, wearable knee exoskeletons.

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Authors: A. Boualouch, A. Essadki, T. Nasser, A. Boukhriss, A. Frigui

Abstract:

This paper presents a power control for a Doubly Fed Induction Generator (DFIG) using in Wind Energy Conversion System (WECS) connected to the grid. The proposed control strategy employs two nonlinear controllers, Backstipping (BSC) and slidingmode controller (SMC) scheme to directly calculate the required rotor control voltage so as to eliminate the instantaneous errors of active and reactive powers. In this paper the advantages of BSC and SMC are presented, the performance and robustness of this two controller’s strategy are compared between them. First, we present a model of wind turbine and DFIG machine, then a synthesis of the controllers and their application in the DFIG power control. Simulation results on a 1.5MW grid-connected DFIG system are provided by MATLAB/Simulink.

Keywords: Backstipping, DFIG, power control, sliding-mode, WESC.

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Authors: Ali Ben Abbes, ImedRiadh Farah, Vincent Barra

Abstract:

Remotely sensed data are a significant source for monitoring and updating databases for land use/cover. Nowadays, changes detection of urban area has been a subject of intensive researches. Timely and accurate data on spatio-temporal changes of urban areas are therefore required. The data extracted from multi-temporal satellite images are usually non-stationary. In fact, the changes evolve in time and space. This paper is an attempt to propose a methodology for changes detection in urban area by combining a non-stationary decomposition method and stochastic modeling. We consider as input of our methodology a sequence of satellite images I₁, I₂, … I_n at different periods (t = 1, 2, ..., n). Firstly, a preprocessing of multi-temporal satellite images is applied. (e.g. radiometric, atmospheric and geometric). The systematic study of global urban expansion in our methodology can be approached in two ways: The first considers the urban area as one same object as opposed to non-urban areas (e.g. vegetation, bare soil and water). The objective is to extract the urban mask. The second one aims to obtain a more knowledge of urban area, distinguishing different types of tissue within the urban area. In order to validate our approach, we used a database of Tres Cantos-Madrid in Spain, which is derived from Landsat for a period (from January 2004 to July 2013) by collecting two frames per year at a spatial resolution of 25 meters. The obtained results show the effectiveness of our method.

Keywords: Multi-temporal satellite image, urban growth, Non-stationarity, stochastic modeling.

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Authors: Atjanakul W, Chutima S., Kamnerdthong T.

Abstract:

Shipping comb is mounted on Head Stack Assembly (HSA) to prevent collision of the heads, maintain the gap between suspensions and protect HSA tips from unintentional contact damaged in the manufacturing process. Failure analysis of shipping comb in hard disk drive production processes is proposed .Field observations were performed to determine the fatal areas on shipping comb and their failure fraction. Root cause failure analysis (RCFA) is applied to specify the failure causes subjected to various loading conditions. For reliability improvement, failure mode and effects analysis (FMEA) procedure to evaluate the risk priority is performed. Consequently, the more suitable information design criterions were obtained.

Keywords: Shipping comb, Hard disk drive, Root cause failureanalysis, Failure mode and effects analysis

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Authors: S. Zeković, M. Vujošević, T. Maričić

Abstract:

The paper provides a comprehensive analysis of the sustainable development in the Belgrade Metropolitan Region - BMA (level NUTS 2) preliminary evaluating the three chosen components: 1) economic growth and developmental changes; 2) competitiveness; and 3) territorial concentration and industrial specialization. First, we identified the main results of development changes and economic growth by applying Shift-share analysis on the metropolitan level. Second, the empirical evaluation of competitiveness in the BMA is based on the analysis of absolute and relative values of eight indicators by Spider method. Paper shows that the consideration of the national share, industrial mix and metropolitan/regional share in total Shift share of the BMA, as well as economic/functional specialization of the BMA indicate very strong process of deindustrialization. Allocative component of the BMA economic growth has positive value, reflecting the above-average sector productivity compared to the national average. Third, the important positive role of metropolitan/regional component in decomposition of the BMA economic growth is highlighted as one of the key results. Finally, comparative analysis of the industrial territorial concentration in the BMA in relation to Serbia is based on location quotient (LQ) or Balassa index as a valid measure. The results indicate absolute and relative differences in decrease of industry territorial concentration as well as inefficiency of utilizing territorial capital in the BMA. Results are important for the increase of regional competitiveness and territorial distribution in this area as well as for improvement of sustainable metropolitan and sector policies, planning and governance on this level.

Keywords: Belgrade Metropolitan Area (BMA), Comprehensive analysis/evaluation, economic growth and competitiveness, sustainable development.

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Authors: Valentin Florentin Dumitru

Abstract:

The need to use high volumes of data and the high competition are only two reasons which make necessary the use of information technologies. The objective of our research is to establish the impact of information technologies on the accounting department of the Romanian companies. In order to achieve it, starting from the literature review we made an empirical research based on a questionnaire. We investigated the types of technologies used, the reasons which led to the implementation of certain technologies, the benefits brought by the use of the information technologies, the difficulties brought by the implementation and the future effects of the applications. The conclusions show that there is an evolution in the degree of implementation of the information technologies in the Romanian companies, compared with the results of other studies conducted a few years before.

Keywords: Information technologies, impact, company, Romania, empirical study.

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Authors: Sun Ailu, Zhao Wanmin

Abstract:

In the process of rapid urbanization, old urban renewal is an important task in China's urban construction. This study, using status survey and Analytic Hierarchy Process (AHP) method, taking Chongqing of China as an example, puts forward the problems faced by the old urban area from the aspects of function, facilities and environment. Further, this study summarizes the types of the old urban area and proposes space renewal strategies for three typical old urban areas, such as old residential area, old factory and old market. These old urban areas are confronted with the problems of functional layout confounding, lack of infrastructure and poor living environment. At last, this paper proposes spatial strategies for urban renewal, which are hoped to be useful for urban renewal management in China.

Keywords: Old urban renewal, renewal mode, renewal strategy, Chongqing, China.

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Authors: Linda, Sau-ling Lai

Abstract:

This paper adopts a notion of expectation-perception gap of systems users as information systems (IS) failure. Problems leading to the expectation-perception gap are identified and modelled as five interrelated discrepancies or gaps throughout the process of information systems development (ISD). It describes an empirical study on how systems developers and users perceive the size of each gap and the extent to which each problematic issue contributes to the gap. The key to achieving success in ISD is to keep the expectationperception gap closed by closing all 5 pertaining gaps. The gap model suggests that most factors in IS failure are related to organizational, cognitive and social aspects of information systems design. Organization requirement analysis, being the weakest link of IS development, is particularly worthy of investigation.

Keywords: Information Systems Development, Expectation- Perception Gap, Gap Analysis, Organization Analysis.

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Authors: Nargess Mottaghi Golshan, Siti Zaleha Abdul Rasid

Abstract:

Purpose:This paper aims to gain insights to the influential factors of ERM adoptions by public listed firms in Malaysia. Findings:The two factors of financial leverage and auditor type were found to be significant influential factors for ERM adoption. In other words the findings indicated that firms with higher financial leverage and with a Big Four auditor are more likely to have a form of ERM framework in place. Originality/Value:Since there are relatively few studies conducted in this area and specially in developing economies like Malaysia, this study will broaden the scope of literature by providing novel empirical evidence.

Keywords: Enterprise risk management, risk, public listed company.

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Authors: Zuhaib Ashfaq Khan, Imran Khan, Nandana Rajatheva

Abstract:

In this paper, hybrid FDMA-TDMA access technique in a cooperative distributive fashion introducing and implementing a modified protocol introduced in [1] is analyzed termed as Power and Cooperation Diversity Gain Protocol (PCDGP). A wireless network consists of two users terminal , two relays and a destination terminal equipped with two antennas. The relays are operating in amplify-and-forward (AF) mode with a fixed gain. Two operating modes: cooperation-gain mode and powergain mode are exploited from source terminals to relays, as it is working in a best channel selection scheme. Vertical BLAST (Bell Laboratories Layered Space Time) or V-BLAST with minimum mean square error (MMSE) nulling is used at the relays to perfectly detect the joint signals from multiple source terminals. The performance is analyzed using binary phase shift keying (BPSK) modulation scheme and investigated over independent and identical (i.i.d) Rayleigh, Ricean-K and Nakagami-m fading environments. Subsequently, simulation results show that the proposed scheme can provide better signal quality of uplink users in a cooperative communication system using hybrid FDMATDMA technique.

Keywords: Cooperation Diversity, Best Channel Selectionscheme, MIMO relay networks, V-BLAST, QRdecomposition, and MMSE.

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

Abstract:

This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: Differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control.

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Authors: Mohamad Mahdavi, Mojtaba Mahdavi

Abstract:

This paper tries to represent a new method for computing the reliability of a system which is arranged in series or parallel model. In this method we estimate life distribution function of whole structure using the asymptotic Extreme Value (EV) distribution of Type I, or Gumbel theory. We use EV distribution in minimal mode, for estimate the life distribution function of series structure and maximal mode for parallel system. All parameters also are estimated by Moments method. Reliability function and failure (hazard) rate and p-th percentile point of each function are determined. Other important indexes such as Mean Time to Failure (MTTF), Mean Time to repair (MTTR), for non-repairable and renewal systems in both of series and parallel structure will be computed.

Keywords: Reliability, extreme value, parallel, series, lifedistribution

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Authors: Mabel A. Leva

Abstract:

This study defines a methodology to compute unitary costs for freight transportation modes. The main objective was to gather relevant costs data to support the formulation and evaluation of railway, road, pipelines and port projects. This article will concentrate on the following steps: Compilation and analysis of relevant modal cost studies, Methodological adjustments to make cost figures comparable between studies, Definition of typology and scope of transportation modes, Analysis and validation of cost values for relevant freight transportation modes in Chile. In order to define the comparison methodology for the costs between the different transportation modes, it was necessary to consider that the relevant cost depends on who performs the comparison. Thus, for the transportation user (e.g. exporter) the pertinent costs are the mode tariffs, whereas from the operators perspective (e.g. rail manager), the pertinent costs are the operating costs of each mode.

Keywords: Intermodal costs, Logistics, Transportation costs.

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Authors: Vilma Deltuvaitė

Abstract:

Comparisons of financial development across countries are central to answering many of the questions on factors leading to economic development. For this reason this study analyzes the implications of financial system’s development on country’s economic development. The aim of the article: to analyze the impact of financial system’s development on economic development. The following research methods were used: systemic, logical and comparative analysis of scientific literature, analysis of statistical data, time series model (Autoregressive Distributed Lag (ARDL) Model). The empirical results suggest about positive short and long term effect of stock market development on GDP per capita.

Keywords: Banking sector, economic development, financial system’s development, stock market, private bond market.

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Authors: Wang liguo, Wang zongmin, Kong ying

Abstract:

A novel interpolation scheme to extend usable spectrum and upconvert in high performance D/A converters is addressed in this paper. By adjusting the pulse width of cycle and the production circuit of code, the expansion code is a null code or complementary code that is interpolation process. What the times and codes of interpolation decide DAC works in one of a normal mode or multi-mixer mode so that convert the input digital data signal into normal signal or a mixed analog signal having a mixer frequency that is higher than the data frequency. Simulation results show that the novel scheme and apparatus most extend the usable frequency spectrum into fifth to sixth Nyquist zone beyond conventional DACs.

Keywords: interpolation, upconversion, modulation, switching function, duty cycle.

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Authors: Nidhal Jamia, Sami El-Borgi

Abstract:

In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: Functionally graded piezoelectric material, mixed-mode crack, non-local theory, Schmidt method.

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