Search results for: AIMMS mathematical software
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2967

Search results for: AIMMS mathematical software

1707 Assessments of Internal Erosion in a Landfill Due to Changes in Groundwater Level

Authors: Siamak Feizi, Gunvor Baardvik

Abstract:

Soil erosion has special consequences for landfills that are more serious than those found at conventional construction sites. Different potential heads between two sides of a landfill and the subsequent movement of water through pores within the soil body could trigger the soil erosion and construction instability. Such condition was encountered in a landfill project in the southern part of Norway. To check the risk of internal erosion due changes in the groundwater level (because of seasonal flooding in the river), a series of numerical simulations by means of Geo-Seep software were conducted. Output of this study provides a total picture of the landfill stability, possibilities of erosions and necessary measures to prevent or reduce the risk for the landfill operator.

Keywords: Erosion, seepage, landfill, stability.

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1706 Mathematical Modeling of Switching Processes in Magnetically Controlled MEMS Switches

Authors: Sergey M. Karabanov, Dmitry V. Suvorov, Dmitry Yu. Tarabrin

Abstract:

The operating principle of magnetically controlled microelectromechanical system (MEMS) switches is based on controlling the beam movement under the influence of a magnetic field. Currently, there is a MEMS switch design with a flexible ferromagnetic electrode in the form of a fixed-terminal beam, with an electrode fastened on a straight or cranked anchor. The basic performance characteristics of magnetically controlled MEMS switches (service life, sensitivity, contact resistance, fast response) are largely determined by the flexible electrode design. To ensure the stable and controlled motion of the flexible electrode, it is necessary to provide the optimal design of a flexible electrode.

Keywords: MEMS switch, magnetic sensitivity, magnetic concentrator.

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1705 Artificial Intelligence Techniques for Controlling Spacecraft Power System

Authors: Hanaa T. El-Madany, Faten H. Fahmy, Ninet M. A. El-Rahman, Hassen T. Dorrah

Abstract:

Advancements in the field of artificial intelligence (AI) made during this decade have forever changed the way we look at automating spacecraft subsystems including the electrical power system. AI have been used to solve complicated practical problems in various areas and are becoming more and more popular nowadays. In this paper, a mathematical modeling and MATLAB–SIMULINK model for the different components of the spacecraft power system is presented. Also, a control system, which includes either the Neural Network Controller (NNC) or the Fuzzy Logic Controller (FLC) is developed for achieving the coordination between the components of spacecraft power system as well as control the energy flows. The performance of the spacecraft power system is evaluated by comparing two control systems using the NNC and the FLC.

Keywords: Spacecraft, Neural network, Fuzzy logic control, Photovoltaic array.

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1704 Evaluation of Traditional Methods in Construction and Their Effects on Reinforced-Concrete Buildings Behavior

Authors: E. H. N. Gashti, M. Zarrini, M. Irannezhad, J. R. Langroudi

Abstract:

Using ETABS software, this study analyzed 23 buildings to evaluate effects of mistakes during construction phase on buildings structural behavior. For modelling, two different loadings were assumed: 1) design loading and 2) loading due to the effects of mistakes in construction phase. Research results determined that considering traditional construction methods for buildings resulted in a significant increase in dead loads and consequently intensified the displacements and base-shears of buildings under seismic loads.

Keywords: Reinforced-concrete buildings, Construction mistakes, Base-shear, displacements, Failure.

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1703 Adaptive Integral Backstepping Motion Control for Inverted Pendulum

Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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1702 Possibilistic Aggregations in the Investment Decision Making

Authors: I. Khutsishvili, G. Sirbiladze, B. Ghvaberidze

Abstract:

This work proposes a fuzzy methodology to support the investment decisions. While choosing among competitive investment projects, the methodology makes ranking of projects using the new aggregation OWA operator – AsPOWA, presented in the environment of possibility uncertainty. For numerical evaluation of the weighting vector associated with the AsPOWA operator the mathematical programming problem is constructed. On the basis of the AsPOWA operator the projects’ group ranking maximum criteria is constructed. The methodology also allows making the most profitable investments into several of the project using the method developed by the authors for discrete possibilistic bicriteria problems. The article provides an example of the investment decision-making that explains the work of the proposed methodology.

Keywords: Expert evaluations, investment decision making, OWA operator, possibility uncertainty.

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1701 Bubble Growth in a Two Phase Upward Flow in a Miniature Tube

Authors: R. S. Hassani, S. Chikh, L. Tadrist, S. Radev

Abstract:

A bubbly flow in a vertical miniature tube is analyzed theoretically. The liquid and gas phase are co-current flowing upward. The gas phase is injected via a nozzle whose inner diameter is 0.11mm and it is placed on the axis of the tube. A force balance is applied on the bubble at its detachment. The set of governing equations are solved by use of Mathematica software. The bubble diameter and the bubble generation frequency are determined for various inlet phase velocities represented by the inlet mass quality. The results show different behavior of bubble growth and detachment depending on the tube size.

Keywords: Two phase flow, bubble growth, minichannel, generation frequency.

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1700 Development of a Novel Low-Cost Flight Simulator for Pilot Training

Authors: Hongbin Gu, Dongsu Wu, Hui Liu

Abstract:

A novel low-cost flight simulator with the development goals cost effectiveness and high performance has been realized for meeting the huge pilot training needs of airlines. The simulator consists of an aircraft dynamics model, a sophisticated designed low-profile electrical driven motion system with a subsided cabin, a mixed reality based semi-virtual cockpit system, a control loading system and some other subsystems. It shows its advantages over traditional flight simulator by its features achieved with open architecture, software solutions and low-cost hardware.

Keywords: Flight simulator, mixed reality, motion system, control loading system.

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1699 Teaching Students Collaborative Requirements Engineering: Case Study of Red:Wire

Authors: Dagmar Monett, Sven-Erik Kujat, Marvin Hartmann

Abstract:

This paper discusses the use of a template-based approach for documenting high-quality requirements as part of course projects in an undergraduate Software Engineering course. In order to ease some of the Requirements Engineering activities that are performed when defining requirements by using the template, a new CASE tool, RED:WIRE, was first developed and later tested by students attending the course. Two questionnaires were conceived around a study that aims to analyze the new tool’s learnability as well as other obtained results concerning its usability in particular and the Requirements Engineering skills developed by the students in general.

Keywords: CASE tool, collaborative learning, requirements engineering, undergraduate teaching.

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1698 Natural Convection of Water-Based CuO Nanofluids in a Cylindrical Enclosure

Authors: Baha Tulu Tanju, Kamil Kahveci

Abstract:

Buoyancy driven heat transfer of nanofluids in a cylindrical enclosure used as a control unit in the subsea hydrocarbon injection wells is investigated in this study. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. The base fluid is water and CuO is used as nanoparticles. Solution is obtained for nanoparticle solid volume fraction of 8% and for Rayleigh number in the range of 105-107. The results show that nanoparticle usage in the cylindrical electronic control unit has a significant effect on the flow and heat transfer.

Keywords: CuO, enclosure, nanofluid, natural convection

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1697 Novel GPU Approach in Predicting the Directional Trend of the S&P 500

Authors: A. J. Regan, F. J. Lidgey, M. Betteridge, P. Georgiou, C. Toumazou, K. Hayatleh, J. R. Dibble

Abstract:

Our goal is development of an algorithm capable of predicting the directional trend of the Standard and Poor’s 500 index (S&P 500). Extensive research has been published attempting to predict different financial markets using historical data testing on an in-sample and trend basis, with many authors employing excessively complex mathematical techniques. In reviewing and evaluating these in-sample methodologies, it became evident that this approach was unable to achieve sufficiently reliable prediction performance for commercial exploitation. For these reasons, we moved to an out-ofsample strategy based on linear regression analysis of an extensive set of financial data correlated with historical closing prices of the S&P 500. We are pleased to report a directional trend accuracy of greater than 55% for tomorrow (t+1) in predicting the S&P 500.

Keywords: Financial algorithm, GPU, S&P 500, stock market prediction.

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1696 Energy Separation Mechanism in Uni-Flow Vortex Tube Using Compressible Vortex Flow

Authors: Hiroshi Katanoda, Mohd Hazwan bin Yusof

Abstract:

A theoretical investigation from the view point of gas-dynamics and thermodynamics was carried out, in order to clarify the energy separation mechanism in a viscous compressible vortex, as a primary flow element in a uni-flow vortex tube. The mathematical solutions of tangential velocity, density and temperature in a viscous compressible vortical flow were used in this study.It is clear that a total temperature in the vortex core falls well below that distant from the vortex core in the radial direction, causing aregion with higher total temperature,compared to the distant region,peripheral to the vortex core.

Keywords: Energy separation mechanism, theoretical analysis, vortex tube, vortical flow.

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1695 Some Solitary Wave Solutions of Generalized Pochhammer-Chree Equation via Exp-function Method

Authors: Kourosh Parand, Jamal Amani Rad

Abstract:

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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1694 A Study on the Heading of Spur Gears: Numerical Analysis and Experiments

Authors: M.Zadshakouyan, E.Abdi Sobbouhi, H.Jafarzadeh

Abstract:

In this study, the precision heading process of spur gears has been investigated by means of numerical analysis. The effect of some parameters such as teeth number and module on the forming force and material flow were presented. The simulation works were performed rigid-plastic finite element method using DEFORM 3D software. In order to validate the estimated numerical results, they were compared with those obtained experimentally during heading of spur gear using lead as a model material. Results showed that the optimum number of gear teeth is between 10 to 20, that is because of being the specific pressure in its minimum value.

Keywords: Heading, spur gear, numerical analysis, experiments.

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1693 Supply Air Pressure Control of HVAC System Using MPC Controller

Authors: P. Javid, A. Aeenmehr, J. Taghavifar

Abstract:

In this paper, supply air pressure of HVAC system has been modeled with second-order transfer function plus dead-time. In HVAC system, the desired input has step changes, and the output of proposed control system should be able to follow the input reference, so the idea of using model based predictive control is proceeded and designed in this paper. The closed loop control system is implemented in MATLAB software and the simulation results are provided. The simulation results show that the model based predictive control is able to control the plant properly.

Keywords: Air conditioning system, GPC, dead time, Air supply control.

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1692 The Threats of Deforestation, Forest Fire, and CO2 Emission toward Giam Siak Kecil Bukit Batu Biosphere Reserve in Riau, Indonesia

Authors: S. B. Rushayati, R. Meilani, R. Hermawan

Abstract:

A biosphere reserve is developed to create harmony amongst economic development, community development, and environmental protection, through partnership between human and nature. Giam Siak Kecil Bukit Batu Biosphere Reserve (GSKBB BR) in Riau Province, Indonesia, is unique in that it has peat soil dominating the area, many springs essential for human livelihood, high biodiversity. Furthermore, it is the only biosphere reserve covering privately managed production forest areas. In this research, we aimed at analyzing the threat of deforestation and forest fire, and the potential of CO2 emission at GSKBB BR. We used Landsat image, arcView software, and ERDAS IMAGINE 8.5 Software to conduct spatial analysis of land cover and land use changes, calculated CO2 emission based on emission potential from each land cover and land use type, and exercised simple linear regression to demonstrate the relation between CO2 emission potential and deforestation. The result showed that, beside in the buffer zone and transition area, deforestation also occurred in the core area. Spatial analysis of land cover and land use changes from years 2010, 2012, and 2014 revealed that there were changes of land cover and land use from natural forest and industrial plantation forest to other land use types, such as garden, mixed garden, settlement, paddy fields, burnt areas, and dry agricultural land. Deforestation in core area, particularly at the Giam Siak Kecil Wildlife Reserve and Bukit Batu Wildlife Reserve, occurred in the form of changes from natural forest in to garden, mixed garden, shrubs, swamp shrubs, dry agricultural land, open area, and burnt area. In the buffer zone and transition area, changes also happened, what once swamp forest changed into garden, mixed garden, open area, shrubs, swamp shrubs, and dry agricultural land. Spatial analysis on land cover and land use changes indicated that deforestation rate in the biosphere reserve from 2010 to 2014 had reached 16 119 ha/year. Beside deforestation, threat toward the biosphere reserve area also came from forest fire. The occurrence of forest fire in 2014 had burned 101 723 ha of the area, in which 9 355 ha of core area, and 92 368 ha of buffer zone and transition area. Deforestation and forest fire had increased CO2 emission as much as 24 903 855 ton/year.

Keywords: Biosphere reserve, CO2 emission, deforestation, forest fire.

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1691 Energy Requirement for Cutting Corn Stalks (Single Cross 704 Var.)

Authors: M. Azadbakht, A. Rezaei Asl, K. Tamaskani Zahedi

Abstract:

Corn is cultivated in most countries because of high consumption, quality, and food value. This study evaluated needed energy for cutting corn stems in different levels of cutting height and moisture content. For this reason, test device was fabricated and then calibrated. The device works on the principle of conservation of energy. The results were analyzed using split plot design and SAS software. The results showed that effect of height and moisture content and their interaction effect on cutting energy are significant (P<1%). The maximum cutting energy was 3.22 kJ in 63 (w.b.%) moisture content and the minimum cutting energy was 1.63 kJ in 83.25 (w.b.%) moisture content.

Keywords: Cutting energy, Corn stalk, Cutting height, Moisture content, Impact cutting.

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1690 Design and Implementation of Project Time Management Risk Assessment Tool for SME Projects using Oracle Application Express

Authors: Abdullahi Mohamud Sharif, Mohd. Zaidi Abd. Rozan

Abstract:

Risk Assessment Tool (RAT) is an expert system that assesses, monitors, and gives preliminary treatments automatically based on the project plan. In this paper, a review was taken out for the current project time management risk assessment tools for SME software development projects, analyze risk assessment parameters, conditions, scenarios, and finally propose risk assessment tool (RAT) model to assess, treat, and monitor risks. An implementation prototype system is developed to validate the model.

Keywords: Project Time Management, Risk Assessment Tool(RAT), Small and Medium Enterprises (SME).

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1689 Vibration Control of MDOF Structure under Earthquake Excitation using Passive Control and Active Control

Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

Abstract:

In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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1688 Modeling of a Novel Dual-Belt Continuously Variable Transmission for Automobiles

Authors: Y. Q. Chen, P. K. Wong, Z. C. Xie, H. W. Wu, K. U. Chan, J., L. Huang

Abstract:

It is believed that continuously variable transmission (CVT) will dominate the automotive transmissions in the future. The most popular design is Van Doorne-s CVT with single metal pushing V-belt. However, it is only applicable to low power passenger cars because its major limitation is low torque capacity. Therefore, this research studies a novel dual-belt CVT system to overcome the limitation of traditional single-belt CVT, such that it can be applicable to the heavy-duty vehicles. This paper presents the mathematical model of the design and its experimental verification. Experimental and simulated results show that the model developed is valid and the proposed dual-belt CVT can really overcome the traditional limitation of single-belt Van Doorne-s CVT.

Keywords: Analytical model, CVT, Dual belts, Torque capacity.

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1687 Retina Based Mouse Control (RBMC)

Authors: Arslan Qamar Malik, Jehanzeb Ahmad

Abstract:

The paper presents a novel idea to control computer mouse cursor movement with human eyes. In this paper, a working of the product has been described as to how it helps the special people share their knowledge with the world. Number of traditional techniques such as Head and Eye Movement Tracking Systems etc. exist for cursor control by making use of image processing in which light is the primary source. Electro-oculography (EOG) is a new technology to sense eye signals with which the mouse cursor can be controlled. The signals captured using sensors, are first amplified, then noise is removed and then digitized, before being transferred to PC for software interfacing.

Keywords: Human Computer Interaction, Real-Time System, Electro-oculography, Signal Processing.

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1686 Modeling UWSN Simulators – A Taxonomy

Authors: Christhu Raj, Rajeev Sukumaran

Abstract:

In this research article of modeling Underwater Wireless Sensor Network Simulators, we provide a comprehensive overview of the various currently available simulators used in UWSN modeling. In this work, we compare their working environment, software platform, simulation language, key features, limitations and corresponding applications. Based on extensive experimentation and performance analysis, we provide their efficiency for specific applications. We have also provided guidelines for developing protocols in different layers of the protocol stack, and finally these parameters are also compared and tabulated. This analysis is significant for researchers and designers to find the right simulator for their research activities.

Keywords: Underwater Wireless Sensor networks (UWSN), SUNSET, NS2, OPNET, WOSS, DESERT, RECORDS, Aqua- Sim, Aqua- Net Mate.

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1685 Mathematical Modelling of Transport Phenomena in Radioactive Waste-Cement-Bentonite Matrix

Authors: Ilija Plecas, Uranija Kozmidis-Luburic, Radojica Pesic

Abstract:

The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: bentonite, cement , radioactive waste, composite, disposal, diffusion

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1684 Methodology for Obtaining Static Alignment Model

Authors: Lely A. Luengas, Pedro R. Vizcaya, Giovanni Sánchez

Abstract:

In this paper, a methodology is presented to obtain the Static Alignment Model for any transtibial amputee person. The proposed methodology starts from experimental data collected on the Hospital Militar Central, Bogotá, Colombia. The effects of transtibial prosthesis malalignment on amputees were measured in terms of joint angles, center of pressure (COP) and weight distribution. Some statistical tools are used to obtain the model parameters. Mathematical predictive models of prosthetic alignment were created. The proposed models are validated in amputees and finding promising results for the prosthesis Static Alignment. Static alignment process is unique to each subject; nevertheless the proposed methodology can be used in each transtibial amputee.

Keywords: Information theory, prediction model, prosthetic alignment, transtibial prosthesis.

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1683 Representation of Coloured Petri Net in Abductive Logic Programming (CPN-LP) and Its Application in Modeling an Intelligent Agent

Authors: T. H. Fung

Abstract:

Coloured Petri net (CPN) has been widely adopted in various areas in Computer Science, including protocol specification, performance evaluation, distributed systems and coordination in multi-agent systems. It provides a graphical representation of a system and has a strong mathematical foundation for proving various properties. This paper proposes a novel representation of a coloured Petri net using an extension of logic programming called abductive logic programming (ALP), which is purely based on classical logic. Under such a representation, an implementation of a CPN could be directly obtained, in which every inference step could be treated as a kind of equivalence preserved transformation. We would describe how to implement a CPN under such a representation using common meta-programming techniques in Prolog. We call our framework CPN-LP and illustrate its applications in modeling an intelligent agent.

Keywords: Abduction, coloured petri net, intelligent agent, logic programming.

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1682 Multi-Agent Approach for Monitoring and Control of Biotechnological Processes

Authors: Ivanka Valova

Abstract:

This paper is aimed at using a multi-agent approach to monitor and diagnose a biotechnological system in order to validate certain control actions depending on the process development and the operating conditions. A multi-agent system is defined as a network of interacting software modules that collectively solve complex tasks. Remote monitoring and control of biotechnological processes is a necessity when automated and reliable systems operating with no interruption of certain activities are required. The advantage of our approach is in its flexibility, modularity and the possibility of improving by acquiring functionalities through the integration of artificial intelligence.

Keywords: Multi-agent approach, artificial intelligence, biotechnological processes, anaerobic biodegradation.

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1681 Proposed Program for Developing Some Concepts for Nursery School Children in Egypt Using Artistic Activities

Authors: Ebtehag Tolba

Abstract:

The study presents a proposed program for nursery school children in Egypt. The program consists of a collection of artistic activities and aims to develop the language, mathematical, and artistic skills of preschool children. Furthermore, the researcher has presented a questionnaire to experts about the link between the target group and the content. Finally, the proposed program was applied to group of 30 children. In addition, the researcher has prepared another questionnaire for measuring the effect of the program. This questionnaire was used as a pre-test and post-test, and at the end of the study, a significant difference was determined in favour of the post-test results.

Keywords: Developing, concepts, nursery, children, artistic activities.

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1680 Performance Analysis of a Free-Space Optical Code Division Multiple Access through Atmospheric Turbulence Channel

Authors: Tanveer Ahmed Bhuiyan, Samiul Hayder Choudhury, Asif Al - Rasheed, S.P. Majumder

Abstract:

In this paper, the effect of atmospheric turbulence on bit error probability in free-space optical CDMA scheme with Sequence Inverse Keyed (SIK) optical correlator receiver is analyzed. Here Intensity Modulation scheme is considered for transmission. The turbulence induced fading is described by the newly introduced gamma-gamma pdf[1] as a tractable mathematical model for atmospheric turbulence. Results are evaluated with Gold and Kasami code & it is shown that Gold sequence can be used for more efficient transmission than Kasami sequence in an atmospheric turbulence channel.

Keywords: CDMA, gamma-gamma pdf, atmospheric turbulence, Kasami, Gold, SIK, BER, Power Penalty, FSO.

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1679 LumaCert: Conception and Creation of New Digital Certificate for Online User Authentication in e-Banking Systems

Authors: Artan Luma, Betim Prevalla, Besart Qoku, Bujar Raufi

Abstract:

Electronic banking must be secure and easy to use and many banks heavily advertise an apparent of 100% secure system which is contestable in many points. In this work, an alternative approach to the design of e-banking system, through a new solution for user authentication and security with digital certificate called LumaCert is introduced. The certificate applies new algorithm for asymmetric encryption by utilizing two mathematical operators called Pentors and UltraPentors. The public and private key in this algorithm represent a quadruple of parameters which are directly dependent from the above mentioned operators. The strength of the algorithm resides in the inability to find the respective Pentor and UltraPentor operator from the mentioned parameters.

Keywords: Security, Digital Certificate, Cryptography.

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1678 Analysis of FWM Penalties in DWDM Systems Based on G.652, G.653, and G.655 Optical Fibers

Authors: Paula B. Harboe, Edilson da Silva, José R. Souza

Abstract:

This paper presents an investigation of the power penalties imposed by four-wave mixing (FWM) on G.652 (Single- Mode Fiber - SMF), G.653 (Dispersion-Shifted Fiber - DSF), and G.655 (Non-Zero Dispersion-Shifted Fiber - NZDSF) compliant fibers, considering the DWDM grids suggested by the ITU-T Recommendations G.692, and G.694.1, with uniform channel spacing of 100, 50, 25, and 12.5 GHz. The mathematical/numerical model assumes undepleted pumping, and shows very clearly the deleterious effect of FWM on the performance of DWDM systems, measured by the signal-to-noise ratio (SNR). The results make it evident that non-uniform channel spacing is practically mandatory for WDM systems based on DSF fibers.

Keywords: DWDM systems, Four-Wave Mixing (FWM), G.652, G.653, G.655 compliant fibers, Signal-to-noise ratio.

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