Search results for: fuzzy Delphi method

Authors: Azizakhanim Maharramli

Abstract:

The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.

Keywords: parallel method, sequential method, stream method, combined method, nodal method

Procedia PDF Downloads 95

Authors: Mahacine Amrani

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A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.

Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco

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Authors: R. Ramesh, K. K. Shivaraman

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The main aim of this paper is to handle the energy requirement in an efficient manner by merging the advanced digital communication and control technologies for smart grid applications. In order to reduce user home load during peak load hours, utility applies several incentives such as real-time pricing, time of use, demand response for residential customer through smart meter. However, this method provides inconvenience in the sense that user needs to respond manually to prices that vary in real time. To overcome these inconvenience, this paper proposes a convolutional neural network (CNN) with k-means clustering machine learning model which have ability to forecast energy requirement in short term, i.e., hour of the day or day of the week. By integrating our proposed technique with home energy management based on Bluetooth low energy provides predicted value to user for scheduling appliance in advanced. This paper describes detail about CNN configuration and k-means clustering algorithm for short-term energy forecasting.

Keywords: convolutional neural network, fuzzy logic, k-means clustering approach, smart home energy management

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Jiankang Wang, Hongyang Yu

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This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

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Authors: Henry Lau, Dilupa Nakandala, Li Zhao

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In today’s business, it is well-recognized that risk is an important factor that needs to be taken into consideration before a decision is made. Studies indicate that both the number of risks faced by organizations and their potential consequences are growing. Supply chain risk management has become one of the major concerns for practitioners and researchers. Supply chain leaders and scholars are now focusing on the importance of managing supply chain risk. In order to meet the challenge of managing and mitigating supply chain risk (SCR), we must first identify the different dimensions of SCR and assess its relevant probability and severity. SCR has been classified in many different ways, and there are no consistently accepted dimensions of SCRs and several different classifications are reported in the literature. Basically, supply chain risks can be classified into two dimensions namely disruption risk and operational risk. Disruption risks are those caused by events such as bankruptcy, natural disasters and terrorist attack. Operational risks are related to supply and demand coordination and uncertainty, such as uncertain demand and uncertain supply. Disruption risks are rare but severe and hard to manage, while operational risk can be reduced through effective SCM activities. Other SCRs include supply risk, process risk, demand risk and technology risk. In fact, the disorganized classification of SCR has created confusion for SCR scholars. Moreover, practitioners need to identify and assess SCR. As such, it is important to have an overarching framework tying all these SCR dimensions together for two reasons. First, it helps researchers use these terms for communication of ideas based on the same concept. Second, a shared understanding of the SCR dimensions will support the researchers to focus on the more important research objective: operationalization of SCR, which is very important for assessing SCR. In general, fresh food supply chain is subject to certain level of risks, such as supply risk (low quality, delivery failure, hot weather etc.) and demand risk (season food imbalance, new competitors). Effective strategies to mitigate fresh food supply chain risk are required to enhance operations. Before implementing effective mitigation strategies, we need to identify the risk sources and evaluate the risk level. However, assessing the supply chain risk is not an easy matter, and existing research mainly use qualitative method, such as risk assessment matrix. To address the relevant issues, this paper aims to analyze the risk factor of the fresh food supply chain using an approach comprising both fuzzy logic and hierarchical holographic modeling techniques. This novel approach is able to take advantage the benefits of both of these well-known techniques and at the same time offset their drawbacks in certain aspects. In order to develop this integrated approach, substantial research work is needed to effectively combine these two techniques in a seamless way, To validate the proposed integrated approach, a case study in a fresh food supply chain company was conducted to verify the feasibility of its functionality in a real environment.

Keywords: fresh food supply chain, fuzzy logic, hierarchical holographic modelling, operationalization, supply chain risk

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Authors: D. Pugazhenthi, B. Sree Vidya

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Cloud computing is one of the emerging technologies that enables end users to use the services of cloud on ‘pay per usage’ strategy. This technology grows in a fast pace and so is its security threat. One among the various services provided by cloud is storage. In this service, security plays a vital factor for both authenticating legitimate users and protection of information. This paper brings in efficient ways of authenticating users as well as securing information on the cloud. Initial phase proposed in this paper deals with an authentication technique using multi-factor and multi-dimensional authentication system with multi-level security. Unique identification and slow intrusive formulates an advanced reliability on user-behaviour based biometrics than conventional means of password authentication. By biometric systems, the accounts are accessed only by a legitimate user and not by a nonentity. The biometric templates employed here do not include single trait but multiple, viz., iris and finger prints. The coordinating stage of the authentication system functions on Ensemble Support Vector Machine (SVM) and optimization by assembling weights of base SVMs for SVM ensemble after individual SVM of ensemble is trained by the Artificial Fish Swarm Algorithm (AFSA). Thus it helps in generating a user-specific secure cryptographic key of the multimodal biometric template by fusion process. Data security problem is averted and enhanced security architecture is proposed using encryption and decryption system with double key cryptography based on Fuzzy Neural Network (FNN) for data storing and retrieval in cloud computing . The proposing scheme aims to protect the records from hackers by arresting the breaking of cipher text to original text. This improves the authentication performance that the proposed double cryptographic key scheme is capable of providing better user authentication and better security which distinguish between the genuine and fake users. Thus, there are three important modules in this proposed work such as 1) Feature extraction, 2) Multimodal biometric template generation and 3) Cryptographic key generation. The extraction of the feature and texture properties from the respective fingerprint and iris images has been done initially. Finally, with the help of fuzzy neural network and symmetric cryptography algorithm, the technique of double key encryption technique has been developed. As the proposed approach is based on neural networks, it has the advantage of not being decrypted by the hacker even though the data were hacked already. The results prove that authentication process is optimal and stored information is secured.

Keywords: artificial fish swarm algorithm (AFSA), biometric authentication, decryption, encryption, fingerprint, fusion, fuzzy neural network (FNN), iris, multi-modal, support vector machine classification

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Authors: Aakansha Gupta, Neha Vadnere, Tapasvi Soni, M. Anbarsi

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Protein secondary structure prediction is one of the most important goals pursued by bioinformatics and theoretical chemistry; it is highly important in medicine and biotechnology. Some aspects of protein functions and genome analysis can be predicted by secondary structure prediction. This is used to help annotate sequences, classify proteins, identify domains, and recognize functional motifs. In this paper, we represent protein secondary structure as a mathematical model. To extract and predict the protein secondary structure from the primary structure, we require a set of parameters. Any constants appearing in the model are specified by these parameters, which also provide a mechanism for efficient and accurate use of data. To estimate these model parameters there are many algorithms out of which the most popular one is the EM algorithm or called the Expectation Maximization Algorithm. These model parameters are estimated with the use of protein datasets like RS126 by using the Bayesian Probabilistic method (data set being categorical). This paper can then be extended into comparing the efficiency of EM algorithm to the other algorithms for estimating the model parameters, which will in turn lead to an efficient component for the Protein Secondary Structure Prediction. Further this paper provides a scope to use these parameters for predicting secondary structure of proteins using machine learning techniques like neural networks and fuzzy logic. The ultimate objective will be to obtain greater accuracy better than the previously achieved.

Keywords: model parameters, expectation maximization algorithm, protein secondary structure prediction, bioinformatics

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Mei-Jie Xu, Yang Zhong

Abstract:

Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

Procedia PDF Downloads 598

Authors: Musarrat Jabeen

Abstract:

Thoughtful intelligence offers a sustainable position to enhance the influence of decision-makers. Thoughtful Intelligence implies the understanding to realize the impact of one’s thoughts, words and actions on the survival, dignity and development of the individuals, groups and nations. Thoughtful intelligence has received minimal consideration in the area of Decision Support Systems, with an end goal to evaluate the quantity of knowledge and its viability. This pattern degraded the imbibed contribution of thoughtful intelligence required for sustainable decision making. Given the concern, this paper concentrates on the question: How to present a model of Thoughtful Decision Support System (TDSS)? The aim of this paper is to appreciate the concepts of thoughtful intelligence and insinuate a Decision Support System based on thoughtful intelligence. Thoughtful intelligence includes three dynamic competencies: i) Realization about long term impacts of decisions that are made in a specific time and space, ii) A great sense of taking actions, iii) Intense interconnectivity with people and nature and; seven associate competencies, of Righteousness, Purposefulness, Understanding, Contemplation, Sincerity, Mindfulness, and Nurturing. The study utilizes two methods: Focused group discussion to count prevailing Decision Support Systems; 70% results of focus group discussions found six decision support systems and the positive inexistence of thoughtful intelligence among decision support systems regarding sustainable decision making. Delphi focused on defining thoughtful intelligence to model (TDSS). 65% results helped to conceptualize (definition and description) of thoughtful intelligence. TDSS is offered here as an addition in the decision making literature. The clients are top leaders.

Keywords: thoughtful intelligence, sustainable decision making, thoughtful decision support system

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Guettal Djaouida, Ziadi Abdelkader

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In this paper, we study a coupling of the Alienor method with the algorithm of Piyavskii-Shubert. The classical multidimensional global optimization methods involves great difficulties for their implementation to high dimensions. The Alienor method allows to transform a multivariable function into a function of a single variable for which it is possible to use efficient and rapid method for calculating the the global optimum. This simplification is based on the using of a reducing transformation called Alienor.

Keywords: global optimization, reducing transformation, α-dense curves, Alienor method, Piyavskii-Shubert algorithm

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: exponential smoothing method, open data, operation estimation, train schedule

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Authors: Mahshid Arabi

Abstract:

With the rapid expansion of digital technologies and the internet, information security has become a critical priority for organizations and individuals. The widespread use of digital tools such as smartphones and internet networks facilitates the storage of vast amounts of data, but simultaneously, vulnerabilities and security threats have significantly increased. The aim of this study is to examine and analyze modern methods of information security management and to develop a comprehensive model to counteract threats and information misuse. This study employs a mixed-methods approach, including both qualitative and quantitative analyses. Initially, a systematic review of previous articles and research in the field of information security was conducted. Then, using the Delphi method, interviews with 30 information security experts were conducted to gather their insights on security challenges and solutions. Based on the results of these interviews, a comprehensive model for information security management was developed. The proposed model includes advanced encryption techniques, machine learning-based intrusion detection systems, and network security protocols. AES and RSA encryption algorithms were used for data protection, and machine learning models such as Random Forest and Neural Networks were utilized for intrusion detection. Statistical analyses were performed using SPSS software. To evaluate the effectiveness of the proposed model, T-Test and ANOVA statistical tests were employed, and results were measured using accuracy, sensitivity, and specificity indicators of the models. Additionally, multiple regression analysis was conducted to examine the impact of various variables on information security. The findings of this study indicate that the comprehensive proposed model reduced cyber-attacks by an average of 85%. Statistical analysis showed that the combined use of encryption techniques and intrusion detection systems significantly improves information security. Based on the obtained results, it is recommended that organizations continuously update their information security systems and use a combination of multiple security methods to protect their data. Additionally, educating employees and raising public awareness about information security can serve as an effective tool in reducing security risks. This research demonstrates that effective and up-to-date information security management requires a comprehensive and coordinated approach, including the development and implementation of advanced techniques and continuous training of human resources.

Keywords: data protection, digital technologies, information security, modern management

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Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

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Authors: Juan F. P. Ramírez, Jésica A. L. Isaza, Benjamín A. Rojano

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This study proposes a novel use of a method to determine the mechanical properties of fruits by the use of the indentation tests. The method combines experimental results with a numerical finite elements model. The results presented correspond to a simplified numerical modeling of banana. The banana was assumed as one-layer material with an isotropic linear elastic mechanical behavior, the Young’s modulus found is 0.3Mpa. The method will be extended to multilayer models in further studies.

Keywords: finite element method, fruits, inverse analysis, mechanical properties

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Authors: Amara Prakasa Rao, N. V. S. N. Sarma

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This paper describes the synthesis of linear array geometry with minimum sidelobe level and null control using the Taguchi method. Based on the concept of the orthogonal array, Taguchi method effectively reduces the number of tests required in an optimization process. Taguchi method has been successfully applied in many fields such as mechanical, chemical engineering, power electronics, etc. Compared to other evolutionary methods such as genetic algorithms, simulated annealing and particle swarm optimization, the Taguchi method is much easier to understand and implement. It requires less computational/iteration processing to optimize the problem. Different cases are considered to illustrate the performance of this technique. Simulation results show that this method outperforms the other evolution algorithms (like GA, PSO) for smart antenna systems design.

Keywords: array factor, beamforming, null placement, optimization method, orthogonal array, Taguchi method, smart antenna system

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Authors: Zuhier Altawallbeh

Abstract:

This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

Procedia PDF Downloads 465