Search results for: Proposed Model

Authors: M.Machhout, M.Zeghid, W.El hadj youssef, B.Bouallegue, A.Baganne, R.Tourki

Abstract:

Long number multiplications (n ≥ 128-bit) are a primitive in most cryptosystems. They can be performed better by using Karatsuba-Ofman technique. This algorithm is easy to parallelize on workstation network and on distributed memory, and it-s known as the practical method of choice. Multiplying long numbers using Karatsuba-Ofman algorithm is fast but is highly recursive. In this paper, we propose different designs of implementing Karatsuba-Ofman multiplier. A mixture of sequential and combinational system design techniques involving pipelining is applied to our proposed designs. Multiplying large numbers can be adapted flexibly to time, area and power criteria. Computationally and occupation constrained in embedded systems such as: smart cards, mobile phones..., multiplication of finite field elements can be achieved more efficiently. The proposed designs are compared to other existing techniques. Mathematical models (Area (n), Delay (n)) of our proposed designs are also elaborated and evaluated on different FPGAs devices.

Keywords: finite field, Karatsuba-Ofman, long numbers, multiplication, mathematical model, recursivity.

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Authors: Lenka Ševelová, Aleš Florian

Abstract:

Appropriate and progressive tool for analyzing behavior of low volume roads are probabilistic models used in reliability analyses. The necessary part of the probabilistic model is the deterministic model of structural behavior. The FE model of low volume roads is created in the ANSYS software. It is able to determine the state of stress and deformation in any point of the structure and thus generate data required for the reliability analysis. The paper compares two material constitutive models used for modeling of unbound non-homogenous materials used in low volume roads. The first model is linear elastic model according to Hook theory (H model), the second one is nonlinear elastic-plastic Drucker-Prager model (D-P model).

Keywords: FEA, FEM, geotechnical materials, low volume roads, material constitutive models, pavement.

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Authors: Mesbaholdin Salami, Farzad Movahedi Sobhani, Mohammad Sadegh Ghazizadeh

Abstract:

Evaluation of organizational performance is among the most important measures that help organizations and entities continuously improve their efficiency. Organizations can use the existing data and results from the comparison of units under investigation to obtain an estimation of their performance. The Malmquist Productivity Index (MPI) is an important index in the evaluation of overall productivity, which considers technological developments and technical efficiency at the same time. This article proposed a model based on the multistage MPI, considering limited data (Grey’s theory). This model can evaluate the performance of units using limited and uncertain data in a multistage process. It was applied by the electricity market manager to Iran’s electric power supply chain (EPSC), which contains uncertain data, to evaluate the performance of its actors. Results from solving the model showed an improvement in the accuracy of future performance of the units under investigation, using the Grey’s system theory. This model can be used in all case studies, in which MPI is used and there are limited or uncertain data.

Keywords: Malmquist Index, Grey's Theory, Charnes Cooper & Rhodes (CCR) Model, network data envelopment analysis, Iran electricity power chain.

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Authors: A. Mirrashid, M. Khoshbin, A. Atghaei, H. Shahbazi

Abstract:

In various industries, smoke and fire are two of the most important threats in the workplace. One of the common methods for detecting smoke and fire is the use of infrared thermal and smoke sensors, which cannot be used in outdoor applications. Therefore, the use of vision-based methods seems necessary. The problem of smoke and fire detection is spatiotemporal and requires spatiotemporal solutions. This paper presents a method that uses spatial features along with temporal-based features to detect smoke and fire in the scene. It consists of three main parts; the task of each part is to reduce the error of the previous part so that the final model has a robust performance. This method also uses transformer modules to increase the accuracy of the model. The results of our model show the proper performance of the proposed approach in solving the problem of smoke and fire detection and can be used to increase workplace safety.

Keywords: Attention, fire detection, smoke detection, spatiotemporal.

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Authors: Muhammad Irfan Marwat, Sadaqat Jan, Syed Zafar Ali Shah

Abstract:

Software Architecture plays a key role in software development but absence of formal description of Software Architecture causes different impede in software development. To cope with these difficulties, ontology has been used as artifact. This paper proposes ontology for Software Architectural design based on IEEE model for architecture description and Kruchten 4+1 model for viewpoints classification. For categorization of style and views, ISO/IEC 42010 has been used. Corpus method has been used to evaluate ontology. The main aim of the proposed ontology is to classify and locate Software Architectural design information.

Keywords: Software Architecture Ontology, Semantic based Software Architecture, Software Architecture, Ontology, Software Engineering.

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Authors: S. T. Tan, H. Hashim, W. S. Ho, C. T. Lee

Abstract:

Rapid economic development and population growth in Malaysia had accelerated the generation of solid waste. This issue gives pressure for effective management of municipal solid waste (MSW) to take place in Malaysia due to the increased cost of landfill. This paper discusses optimal planning of waste-to-energy (WTE) using a combinatorial simulation and optimization model through mixed integer linear programming (MILP) approach. The proposed multi-period model is tested in Iskandar Malaysia (IM) as case study for a period of 12 years (2011 -2025) to illustrate the economic potential and tradeoffs involved in this study. In this paper, 3 scenarios have been used to demonstrate the applicability of the model: (1) Incineration scenario (2) Landfill scenario (3) Optimal scenario. The model revealed that the minimum cost of electricity generation from 9,995,855 tonnes of MSW is estimated as USD 387million with a total electricity generation of 50MW /yr in the optimal scenario.

Keywords: Mixed Integer Linear Programming (MILP), optimization, solid waste management (SWM), Waste-to-energy (WTE).

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Authors: Khaleel Sami Hamdan, Dong-Eok Kim, Sang-Ki Moon

Abstract:

An appropriate model to predict the size of the droplets resulting from the break-up with the structures will help in a better understanding and modeling of the two-phase flow calculations in the simulation of a reactor core loss-of-coolant accident (LOCA). A droplet behavior impacting on a hot surface above the Leidenfrost temperature was investigated. Droplets of known size and velocity were impacted to an inclined plate of hot temperature, and the behavior of the droplets was observed by a high-speed camera. It was found that for droplets of Weber number higher than a certain value, the higher the Weber number of the droplet the smaller the secondary droplets. The COBRA-TF model over-predicted the measured secondary droplet sizes obtained by the present experiment. A simple model for the secondary droplet size was proposed using the mass conservation equation. The maximum spreading diameter of the droplets was also compared to previous correlations and a fairly good agreement was found. A better prediction of the heat transfer in the case of LOCA can be obtained with the presented model.

Keywords: Break-up, droplet, impact, inclined hot plate, Leidenfrost temperature, LOCA.

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Authors: Andrey V. Timofeev

Abstract:

A method is proposed for stable detection of seismoacoustic sources in C-OTDR systems that guarantee given upper bounds for probabilities of type I and type II errors. Properties of the proposed method are rigorously proved. The results of practical applications of the proposed method in a real C-OTDRsystem are presented.

Keywords: Guaranteed detection, C-OTDR systems, change point, interval estimation.

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Authors: Meng Fanchao, Zhan Dechen, Xu Xiaofei

Abstract:

Software reuse can be considered as the most realistic and promising way to improve software engineering productivity and quality. Automated assistance for software reuse involves the representation, classification, retrieval and adaptation of components. The representation and retrieval of components are important to software reuse in Component-Based on Software Development (CBSD). However, current industrial component models mainly focus on the implement techniques and ignore the semantic information about component, so it is difficult to retrieve the components that satisfy user-s requirements. This paper presents a method of business component retrieval based on specification matching to solve the software reuse of enterprise information system. First, a business component model oriented reuse is proposed. In our model, the business data type is represented as sign data type based on XML, which can express the variable business data type that can describe the variety of business operations. Based on this model, we propose specification match relationships in two levels: business operation level and business component level. In business operation level, we use input business data types, output business data types and the taxonomy of business operations evaluate the similarity between business operations. In the business component level, we propose five specification matches between business components. To retrieval reusable business components, we propose the measure of similarity degrees to calculate the similarities between business components. Finally, a business component retrieval command like SQL is proposed to help user to retrieve approximate business components from component repository.

Keywords: Business component, business operation, business data type, specification matching.

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Authors: B. Bellakhdhar, A. Dogui, J.L. Ligier

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Simplified coupled engine block-crankshaft models based on beam theory provide an efficient substitute to engine simulation in the design process. These models require accurate definition of the main bearing stiffness. In this paper, an investigation of this stiffness is presented. The clearance effect is studied using a smooth bearing model. It is manifested for low shaft displacement. The hydrodynamic assessment model shows that the oil film has no stiffness for low loads and it is infinitely rigid for important loads. The deformation stiffness is determined using a suitable finite elements model based on real CADs. As a result, a main bearing behaviour law is proposed. This behaviour law takes into account the clearance, the hydrodynamic sustention and the deformation stiffness. It ensures properly the transition from the configuration low rigidity to the configuration high rigidity.

Keywords: Clearance, deformation stiffness, main bearing behaviour law, oil film stiffness

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Authors: Guoyuan Qi , Yskandar Hamam, Barend Jacobus van Wyk, Shengzhi Du

Abstract:

The majority of existing predictors for time series are model-dependent and therefore require some prior knowledge for the identification of complex systems, usually involving system identification, extensive training, or online adaptation in the case of time-varying systems. Additionally, since a time series is usually generated by complex processes such as the stock market or other chaotic systems, identification, modeling or the online updating of parameters can be problematic. In this paper a model-free predictor (MFP) for a time series produced by an unknown nonlinear system or process is derived using tracking theory. An identical derivation of the MFP using the property of the Newton form of the interpolating polynomial is also presented. The MFP is able to accurately predict future values of a time series, is stable, has few tuning parameters and is desirable for engineering applications due to its simplicity, fast prediction speed and extremely low computational load. The performance of the proposed MFP is demonstrated using the prediction of the Dow Jones Industrial Average stock index.

Keywords: Forecast, model-free predictor, prediction, time series

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Authors: Essam Al Daoud

Abstract:

Intrusion detection is a mechanism used to protect a system and analyse and predict the behaviours of system users. An ideal intrusion detection system is hard to achieve due to nonlinearity, and irrelevant or redundant features. This study introduces a new anomaly-based intrusion detection model. The suggested model is based on particle swarm optimisation and nonlinear, multi-class and multi-kernel support vector machines. Particle swarm optimisation is used for feature selection by applying a new formula to update the position and the velocity of a particle; the support vector machine is used as a classifier. The proposed model is tested and compared with the other methods using the KDD CUP 1999 dataset. The results indicate that this new method achieves better accuracy rates than previous methods.

Keywords: Feature selection, Intrusion detection, Support vector machine, Particle swarm.

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Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane

Abstract:

LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.

Keywords: Hysteresis, LuGre model, operator, (strong) consistency.

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Authors: Abdelali Joumad, Abdelaziz Nasroallah

Abstract:

In unsupervised segmentation context, we propose a bi-dimensional hidden Markov chain model (X,Y) that we adapt to the image segmentation problem. The bi-dimensional observed process Y = (Y 1, Y 2) is such that Y 1 represents the noisy image and Y 2 represents a noisy supplementary information on the image, for example a noisy proportion of pixels of the same type in a neighborhood of the current pixel. The proposed model can be seen as a competitive alternative to the Hilbert-Peano scan. We propose a bayesian algorithm to estimate parameters of the considered model. The performance of this algorithm is globally favorable, compared to the bi-dimensional EM algorithm through numerical and visual data.

Keywords: Image segmentation, Hidden Markov chain with a bi-dimensional observed process, Peano-Hilbert scan, Bayesian approach, MCMC methods, Bi-dimensional EM algorithm.

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Authors: Cheng-Chi Lee, Min-Shiang Hwang, Shu-Yin Hsiao

Abstract:

Network exchange is now widely used. However, it still cannot avoid the problems evolving from network exchange. For example. A buyer may not receive the order even if he/she makes the payment. For another example, the seller possibly get nothing even when the merchandise is sent. Some studies about the fair exchange have proposed protocols for the design of efficiency and exploited the signature property to specify that two parties agree on the exchange. The information about purchased item and price are disclosed in this way. This paper proposes a new fair network payment protocol with off-line trusted third party. The proposed protocol can protect the buyers- purchase message from being traced. In addition, the proposed protocol can meet the proposed requirements. The most significant feature is Non-transfer property we achieved.

Keywords: E-commerce, digital signature, fair exchange, security.

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Authors: S.K. Satpathy, S.K. Nayak, K. K. Nagwanshi, S. Panda, C. Ardil

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Image restoration involves elimination of noise. Filtering techniques were adopted so far to restore images since last five decades. In this paper, we consider the problem of image restoration degraded by a blur function and corrupted by random noise. A method for reducing additive noise in images by explicit analysis of local image statistics is introduced and compared to other noise reduction methods. The proposed method, which makes use of an a priori noise model, has been evaluated on various types of images. Bayesian based algorithms and technique of image processing have been described and substantiated with experimentation using MATLAB.

Keywords: Image Restoration, Probability DensityFunction (PDF), Neural Networks, Bayesian Classifier.

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Authors: Rohit Gupta, Ruchika

Abstract:

In this paper, a PSO based fractional order PID (FOPID) controller is proposed for concentration control of an isothermal Continuous Stirred Tank Reactor (CSTR) problem. CSTR is used to carry out chemical reactions in industries, which possesses complex nonlinear dynamic characteristics. Particle Swarm Optimization algorithm technique, which is an evolutionary optimization technique based on the movement and intelligence of swarm is proposed for tuning of the controller for this system. Comparisons of proposed controller with conventional and fuzzy based controller illustrate the superiority of proposed PSO-FOPID controller.

Keywords: CSTR, Fractional Order PID Controller, Partical Swarm Optimization.

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Authors: Po-Wen Chen, Jin-Yu Wu, Md. Manirul Ali, Yang Peng, Chen-Te Chang, Der-Jun Jan

Abstract:

Dynamics of cathode spot has become a major part of vacuum arc discharge with its high academic interest and wide application potential. In this article, using a three-dimensional statistical model, we simulate the distribution of the ignition probability of a new cathode spot occurring in different magnetic pressure on old cathode spot surface and at different arcing time. This model for the ignition probability of a new cathode spot was proposed in two typical situations, one by the pure isotropic random walk in the absence of an external magnetic field, other by the retrograde motion in external magnetic field, in parallel with the cathode surface. We mainly focus on developed relationship between the ignition probability density distribution of a new cathode spot and the external magnetic field.

Keywords: Cathode spot, vacuum arc discharge, transverse magnetic field, random walk.

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Authors: Fauziah Sh. Ahmad, Rosmini Omar, Siti Zaleha Abdul Rasid, Muslim Amin

Abstract:

The purpose of this paper is to examine the inter relationships among various leadership branding constructs of entrepreneurs in small and medium sized enterprises (SMEs). We employ a quantitative structural equation modeling through a new leadership branding engagement model comprises constructs of leader-s or entrepreneur-s personality, branding practice and customer engagement. The results confirm that there are significant relationships between the three constructs and the major fit indices indicate that the data fits the proposed model. The findings provide insights and fill in the literature gaps on statistically validated representation of leadership branding for SMEs across new economic regions of Malaysia that may implicate other economic zones with similar situations. This study extends the establishment of a leadership branding engagement model with a new mechanism of using leaders- personality as a predictor to branding practice and customer engagement performance.

Keywords: Leadership Branding, Malaysia Brands, Customer Engagement, SME Branding.

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Authors: Almutasim Billa A. Alanazi, Hal S. Tharp

Abstract:

Artificial Intelligence (AI), specifically Reinforcement Learning (RL), has proven helpful in many control path planning technologies by maximizing and enhancing their performance, such as navigation systems. Since it learns from experience by interacting with the environment to determine the optimal policy, the optimal policy takes the best action in a particular state, accounting for the long-term rewards. Most navigation systems focus primarily on "arriving faster," overlooking safety and efficiency while estimating the optimum path, as safety and efficiency are essential factors when planning for a long-distance journey. This paper represents an RL control model that proposes a control mechanism for improving navigation systems. Also, the model could be applied to other control path planning applications because it is adjustable and can accept different properties and parameters. However, the navigation system application has been taken as a case and evaluation study for the proposed model. The model utilized a Q-learning algorithm for training and updating the policy. It allows the agent to analyze the quality of an action made in the environment to maximize rewards. The model gives the ability to update rewards regularly based on safety and efficiency assessments, allowing the policy to consider the desired safety and efficiency benefits while making decisions, which improves the quality of the decisions taken for path planning compared to the conventional RL approaches.

Keywords: Artificial intelligence, control system, navigation systems, reinforcement learning.

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Authors: Fatemeh Amiri, Caro Lucas, Nasser Yazdani

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As the network based technologies become omnipresent, demands to secure networks/systems against threat increase. One of the effective ways to achieve higher security is through the use of intrusion detection systems (IDS), which are a software tool to detect anomalous in the computer or network. In this paper, an IDS has been developed using an improved machine learning based algorithm, Locally Linear Neuro Fuzzy Model (LLNF) for classification whereas this model is originally used for system identification. A key technical challenge in IDS and LLNF learning is the curse of high dimensionality. Therefore a feature selection phase is proposed which is applicable to any IDS. While investigating the use of three feature selection algorithms, in this model, it is shown that adding feature selection phase reduces computational complexity of our model. Feature selection algorithms require the use of a feature goodness measure. The use of both a linear and a non-linear measure - linear correlation coefficient and mutual information- is investigated respectively

Keywords: anomaly Detection, feature selection, Locally Linear Neuro Fuzzy (LLNF), Mutual Information (MI), liner correlation coefficient.

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Authors: L. Gaile, I. Radinsh

Abstract:

Based on experimental data using accelerometry technology there was developed an analytical model that approximates human induced ground reaction forces in vertical, longitudinal and lateral directions ascending and descending the stairs. Proposed dynamic loading factors and corresponding phase shifts for the first five harmonics of continuous walking force history in case of stair ascend and descend. Into account is taken imperfectness of individual footfall forcing functions, differences between continuous walking force histories among individuals. There is proposed mean synthetic continuous walking force history that can be used in numerical simulations of human movement on the stairs.

Keywords: footfall, ground reaction forces, human loads, serviceability, stair vibration, walking

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Authors: Elham Jelodari Mamaghani, Christian Prins, Haoxun Chen

Abstract:

In this paper, there is concentration on collaborative transportation planning (CTP) among multiple carriers with pickup and delivery requests and time windows. This problem is a vehicle routing problem with constraints from standard vehicle routing problems and new constraints from a real-world application. In the problem, each carrier has a finite number of vehicles, and each request is a pickup and delivery request with time window. Moreover, each carrier has reserved requests, which must be served by itself, whereas its exchangeable requests can be outsourced to and served by other carriers. This collaboration among carriers can help them to reduce total transportation costs. A mixed integer programming model is proposed to the problem. To solve the model, a hybrid algorithm that combines Genetic Algorithm and Simulated Annealing (GASA) is proposed. This algorithm takes advantages of GASA at the same time. After tuning the parameters of the algorithm with the Taguchi method, the experiments are conducted and experimental results are provided for the hybrid algorithm. The results are compared with those obtained by a commercial solver. The comparison indicates that the GASA significantly outperforms the commercial solver.

Keywords: Centralized collaborative transportation, collaborative transportation with pickup and delivery, collaborative transportation with time windows, hybrid algorithm of GA and SA.

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Authors: Snehal R. Pathak, Sachin S. Munnoli

Abstract:

Evaluation of dynamic earth pressure on retaining wall is a topic of primary importance. In present paper, dynamic active earth pressure and displacement of flexible cantilever retaining wall has been evaluated analytically using 2-DOF mass-spring-dashpot model by incorporating both wall and backfill properties. The effect of wall flexibility on dynamic active earth pressure and wall displacement are studied and presented in graphical form. The obtained results are then compared with the various conventional methods, experimental analysis and also with PLAXIS analysis. It is observed that the dynamic active earth pressure decreases with increase in the wall flexibility while wall displacement increases linearly with flexibility of the wall. The results obtained by proposed 2-DOF analytical model are found to be more realistic and economical.

Keywords: Earth pressure, earthquake, 2-DOF model, plaxis, wall movement, retaining walls.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.

Keywords: Artificial Intelligent, Soft Computing, NeuralNetworks, Genetic Algorithms, Hopfield Neural Networks, andAssociative Memories.

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Authors: Romain Bosquet, Pierre-Olivier Vandanjon, Alex Coiret, Tristan Lorino

Abstract:

In the hardening energy context, the transport sector which constitutes a large worldwide energy demand has to be improving for decrease energy demand and global warming impacts. In a controversial situation where subsists an increasing demand for long-distance and high-speed travels, high-speed trains offer many advantages, as consuming significantly less energy than road or air transports. At the project phase of new rail infrastructures, it is nowadays important to characterize accurately the energy that will be induced by its operation phase, in addition to other more classical criteria as construction costs and travel time. Current literature consumption models used to estimate railways operation phase are obsolete or not enough accurate for taking into account the newest train or railways technologies. In this paper, an updated model of consumption for high-speed is proposed, based on experimental data obtained from full-scale tests performed on a new high-speed line. The assessment of the model is achieved by identifying train parameters and measured power consumptions for more than one hundred train routes. Perspectives are then discussed to use this updated model for accurately assess the energy impact of future railway infrastructures.

Keywords: High-speed train, energy, model, track profile, infrastructure

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Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur

Abstract:

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.

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Authors: Muhammad Marsudi, Dzuraidah Abdul Wahab, Che Hassan Che Haron

Abstract:

Modeling of a manufacturing system enables one to identify the effects of key design parameters on the system performance and as a result to make correct decision. This paper proposes a manufacturing system modeling approach using a spreadsheet model based on queuing network theory, in which a static capacity planning model and stochastic queuing model are integrated. The model was used to improve the existing system utilization in relation to product design. The model incorporates few parameters such as utilization, cycle time, throughput, and batch size. The study also showed that the validity of developed model is good enough to apply and the maximum value of relative error is 10%, far below the limit value 32%. Therefore, the model developed in this study is a valuable alternative model in evaluating a manufacturing system

Keywords: Manufacturing system, product design, spreadsheet model, utilization.

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Authors: Ririn Dewi Cahyani, Muh. Hisjam, Wahyudi Sutopo, Kuncoro Harto Widodo

Abstract:

Availability of raw materials is important for Indonesia as a furniture exporting country. Teak log as raw materials is supplied to the furniture industry by Perum Perhutani (PP). PP needs to involve carbon trading for nature conservation. PP also has an obligation in the Corporate Social Responsibility program. PP and furniture industry also must prosecute the regulations related to ecological issues and labor rights. This study has the objective to create the relationship model between supplier and manufacturer to fulfill teak log demand that involving teak forest carbon sequestration. A model is formulated as Goal Programming to get the favorable solution for teak log procurement and support carbon sequestration that considering economical, ecological, and social aspects of both supplier and manufacturer. The results show that the proposed model can be used to determine the teak log quantity involving carbon trading to achieve the seven goals to be satisfied the sustainability considerations.

Keywords: Availability of teak log, support carbon sequestration, goal programming, sustainability consideration.

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Authors: Vikas Tewari, K.R. Pardasani

Abstract:

Calcium is very important for communication among the neurons. It is vital in a number of cell processes such as secretion, cell movement, cell differentiation. To reduce the system of reactiondiffusion equations of [Ca2+] into a single equation, two theories have been proposed one is excess buffer approximation (EBA) other is rapid buffer approximation (RBA). The RBA is more realistic than the EBA as it considers both the mobile and stationary endogenous buffers. It is valid near the mouth of the channel. In this work we have studied the effects of different types of buffers on calcium diffusion under RBA. The novel thing studied is the effect of sodium ions on calcium diffusion. The model has been made realistic by considering factors such as variable [Ca2+], [Na+] sources, sodium-calcium exchange protein(NCX), Sarcolemmal Calcium ATPase pump. The proposed mathematical leads to a system of partial differential equations which has been solved numerically to study the relationships between different parameters such as buffer concentration, buffer disassociation rate, calcium permeability. We have used Forward Time Centred Space (FTCS) approach to solve the system of partial differential equations.

Keywords: rapid buffer approximation, sodium-calcium exchangeprotein, Sarcolemmal Calcium ATPase pump, buffer disassociationrate, forward time centred space.

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