Search results for: Possibilistic linear programming

Authors: Mohsen Pirdashti, Masoomeh Omidi, Hemmatollah Pidashti

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Today, advantage of biotechnology especially in environmental issues compared to other technologies is irrefragable. Kimia Gharb Gostar Industries Company, as a largest producer of citric acid in Middle East, applies biotechnology for this goal. Citrogypsum is a by–product of citric acid production and it considered as a valid residuum of this company. At this paper summary of acid citric production and condition of Citrogypsum production in company were introduced in addition to defmition of Citrogypsum production and its applications in world. According to these information and evaluation of present conditions about Iran needing to Citrogypsum, the best priority was introduced and emphasized on strategy selection and proper programming for self-sufficiency. The Delphi technique was used to elicit expert opinions about criteria for evaluating the usages. The criteria identified by the experts were profitability, capacity of production, the degree of investment, marketable, production ease and time production. The Analytical Hierarchy Process (ARP) and Expert Choice software were used to compare the alternatives on the criteria derived from the Delphi process.

Keywords: Analytical Hierarchy Process, ARP, Delphi, Multi- criteria decision making, Citrogypsum

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Authors: Vahid Nademi

Abstract:

In response to widely used wearable medical devices equipped with a continuous glucose monitor (CGM) and insulin pump, the advanced control methods are still demanding to get the full benefit of these devices. Unlike costly clinical trials, implementing effective insulin-glucose control strategies can provide significant contributions to the patients suffering from chronic diseases such as diabetes. This study deals with a key role of two-layer insulin-glucose regulator based on model-predictive-control (MPC) scheme so that the patient’s predicted glucose profile is in compliance with the insulin level injected through insulin pump automatically. It is achieved by iterative optimization algorithm which is called an integrated perturbation analysis and sequential quadratic programming (IPA-SQP) solver for handling uncertainties due to unexpected variations in glucose-insulin values and body’s characteristics. The feasibility evaluation of the discussed control approach is also studied by means of numerical simulations of two case scenarios via measured data. The obtained results are presented to verify the superior and reliable performance of the proposed control scheme with no negative impact on patient safety.

Keywords: Blood glucose monitoring, insulin pump, optimization, predictive control, diabetes disease.

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Authors: József Valyon, Gábor Horváth

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Among neural models the Support Vector Machine (SVM) solutions are attracting increasing attention, mostly because they eliminate certain crucial questions involved by neural network construction. The main drawback of standard SVM is its high computational complexity, therefore recently a new technique, the Least Squares SVM (LS–SVM) has been introduced. In this paper we present an extended view of the Least Squares Support Vector Regression (LS–SVR), which enables us to develop new formulations and algorithms to this regression technique. Based on manipulating the linear equation set -which embodies all information about the regression in the learning process- some new methods are introduced to simplify the formulations, speed up the calculations and/or provide better results.

Keywords: Function estimation, Least–Squares Support VectorMachines, Regression, System Modeling

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Authors: Héctor Rivera-Gómez, Eva Selene Hernández-Gress, Oscar Montaño-Arango, Jose Ramon Corona-Armenta

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This research studies the joint production, maintenance and subcontracting control policy for an unreliable deteriorating manufacturing system. Production activities are controlled by a derivation of the Hedging Point Policy, and given that the system is subject to deterioration, it reduces progressively its capacity to satisfy product demand. Multiple deterioration effects are considered, reflected mainly in the quality of the parts produced and the reliability of the machine. Subcontracting is available as support to satisfy product demand; also, overhaul maintenance can be conducted to reduce the effects of deterioration. The main objective of the research is to determine simultaneously the production, maintenance and subcontracting rate, which minimize the total, incurred cost. A stochastic dynamic programming model is developed and solved through a simulation-based approach composed of statistical analysis and optimization with the response surface methodology. The obtained results highlight the strong interactions between production, deterioration and quality, which justify the development of an integrated model. A numerical example and a sensitivity analysis are presented to validate our results.

Keywords: Deterioration, simulation, subcontracting, production planning.

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Authors: Zhengnan Shi

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In the self-stabilizing algorithmic paradigm, each node has a local view of the system, in a finite amount of time the system converges to a global state with desired property. In a graph G = (V, E), a subset S C V is a 2-packing if Vi c V: IN[i] n SI <1. In this paper, an ID-based, constant space, self-stabilizing algorithm that stabilizes to a maximal 2-packing in an arbitrary graph is proposed. It is shown that the algorithm stabilizes in 0(n3) moves under any scheduler (daemon). Specifically, it is shown that the algorithm stabilizes in linear time-steps under a synchronous daemon where every privileged node moves at each time-step.

Keywords: self-stabilization, 2-packing, distributed computing, fault tolerance, graph algorithms

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Authors: Fabian Horn, Reinhard Guthke

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In molecular biology, microarray technology is widely and successfully utilized to efficiently measure gene activity. If working with less studied organisms, methods to design custom-made microarray probes are available. One design criterion is to select probes with minimal melting temperature variances thus ensuring similar hybridization properties. If the microarray application focuses on the investigation of metabolic pathways, it is not necessary to cover the whole genome. It is more efficient to cover each metabolic pathway with a limited number of genes. Firstly, an approach is presented which minimizes the overall melting temperature variance of selected probes for all genes of interest. Secondly, the approach is extended to include the additional constraints of covering all pathways with a limited number of genes while minimizing the overall variance. The new optimization problem is solved by a bottom-up programming approach which reduces the complexity to make it computationally feasible. The new method is exemplary applied for the selection of microarray probes in order to cover all fungal secondary metabolite gene clusters for Aspergillus terreus.

Keywords: bottom-up approach, gene clusters, melting temperature, metabolic pathway, microarray probe design, probe selection

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Authors: M.J. Park, K.H. Kim, O.M. Kwon

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This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.

Keywords: Multi-agent systems, probabilistic self-delay, consensus, Lyapunov method, LMI.

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Authors: Deniz T. Sodiri, Venkat V S S Sastry

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The paper presents an on-line recognition machine (RM) for continuous/isolated, dynamic and static gestures that arise in Flight Deck Officer (FDO) training. RM is based on generic pattern recognition framework. Gestures are represented as templates using summary statistics. The proposed recognition algorithm exploits temporal and spatial characteristics of gestures via dynamic programming and Markovian process. The algorithm predicts corresponding index of incremental input data in the templates in an on-line mode. Accumulated consistency in the sequence of prediction provides a similarity measurement (Score) between input data and the templates. The algorithm provides an intuitive mechanism for automatic detection of start/end frames of continuous gestures. In the present paper, we consider isolated gestures. The performance of RM is evaluated using four datasets - artificial (W TTest), hand motion (Yang) and FDO (tracker, vision-based ). RM achieves comparable results which are in agreement with other on-line and off-line algorithms such as hidden Markov model (HMM) and dynamic time warping (DTW). The proposed algorithm has the additional advantage of providing timely feedback for training purposes.

Keywords: On-line Recognition Algorithm, IsolatedDynamic/Static Gesture Recognition, On-line Markovian/DynamicProgramming, Training in Virtual Environments.

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Authors: Elham Jelodari Mamaghani, Christian Prins, Haoxun Chen

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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: O. Takakuwa, Y. Mano, H. Soyama

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This paper reveals the interaction between hydrogen and surface stress in austenitic stainless steel by X-ray diffraction stress measurement and thermal desorption analysis before and after being charged with hydrogen. The surface residual stress was varied by surface finishing using several disc polishing agents. The obtained results show that the residual stress near surface had a significant effect on hydrogen absorption behavior, that is, tensile residual stress promoted the hydrogen absorption and compressive one did opposite. Also, hydrogen induced equi-biaxial stress and this stress has a linear correlation with hydrogen content.

Keywords: Hydrogen embrittlement, Residual stress, Surface finishing, Stainless steel.

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Authors: A. Ramdane, F.Naceri, S. Ramdane

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in this work, we present a new strategy of direct adaptive control denoted: Extended minimal controller synthesis (EMCS). This algorithm is designed for an induction motor, which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The main motivation of the EMCS control is to enhance the robustness of the MRAC algorithms, i.e. the rejection of bounded effects of rapidly varying external disturbances.

Keywords: Adaptive Control, Simple model reference adaptive control (SMRAC), Extended Minimal Controller synthesis (EMCS), Induction Motor (IM)

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Authors: Cecilia Nugraheni, Luciana Abednego

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Sudoku is a kind of logic puzzles. Each puzzle consists of a board, which is a 9×9 cells, divided into nine 3×3 subblocks and a set of numbers from 1 to 9. The aim of this puzzle is to fill in every cell of the board with a number from 1 to 9 such that in every row, every column, and every subblock contains each number exactly one. Sudoku puzzles belong to combinatorial problem (NP complete). Sudoku puzzles can be solved by using a variety of techniques/algorithms such as genetic algorithms, heuristics, integer programming, and so on. In this paper, we propose a new approach for solving Sudoku which is by modelling them as block-world problems. In block-world problems, there are a number of boxes on the table with a particular order or arrangement. The objective of this problem is to change this arrangement into the targeted arrangement with the help of two types of robots. In this paper, we present three models for Sudoku. We modellized Sudoku as parameterized multi-agent systems. A parameterized multi-agent system is a multi-agent system which consists of several uniform/similar agents and the number of the agents in the system is stated as the parameter of this system. We use Temporal Logic of Actions (TLA) for formalizing our models.

Keywords: Sudoku puzzle, block world problem, parameterized multi agent systems modelling, Temporal Logic of Actions.

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Authors: Abeer Amayri, Akif A. Bulgak

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Due to today’s globalization as well as outsourcing practices of the companies, the Supply Chain (SC) performances have become more dependent on the efficient movement of material among places that are geographically dispersed, where there is more chance for disruptions. One such disruption is the quality and delivery uncertainties of outsourcing. These uncertainties could lead the products to be unsafe and, as is the case in a number of recent examples, companies may have to end up in recalling their products. As a result of these problems, there is a need to develop a methodology for selecting suppliers globally in view of risks associated with low quality and late delivery. Accordingly, we developed a two-stage stochastic model that captures the risks associated with uncertainty in quality and delivery as well as a solution procedure for the model. The stochastic model developed simultaneously optimizes supplier selection and purchase quantities under price discounts over a time horizon. In particular, our target is the study of global organizations with multiple sites and multiple overseas suppliers, where the pricing is offered in suppliers’ local currencies. Our proposed methodology is applied to a case study for a US automotive company having two assembly plants and four potential global suppliers to illustrate how the proposed model works in practice.

Keywords: Global supply chains, quality, stochastic programming, supplier selection.

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Authors: Ming-Tsang Wu

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The purpose of this study was to explore the correlation between leisure participation and perceived wellness, with the students of a nursing college in southern Taiwan as the subjects. One thousand six hundred and ninety-six (1,696) surveys were sent, and 1,408 surveys were received for an 83.02% valid response rate. Using canonical correlation analysis to analyze the data, the results showed that the linear combination of the two sets of variable produces five significant canonical variates. Out of the five canonical variates, only the first has sufficient explanatory power. The canonical correlation coefficient of first canonical variate is 0.660. This indicated that leisure participation and perceived wellness are significantly correlated.

Keywords: Leisure, perceived wellness.

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Authors: Markus Kaiser, Johannes Buchmann

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In this article, a formal specification and verification of the Rabin public-key scheme in a formal proof system is presented. The idea is to use the two views of cryptographic verification: the computational approach relying on the vocabulary of probability theory and complexity theory and the formal approach based on ideas and techniques from logic and programming languages. A major objective of this article is the presentation of the first computer-proved implementation of the Rabin public-key scheme in Isabelle/HOL. Moreover, we explicate a (computer-proven) formalization of correctness as well as a computer verification of security properties using a straight-forward computation model in Isabelle/HOL. The analysis uses a given database to prove formal properties of our implemented functions with computer support. The main task in designing a practical formalization of correctness as well as efficient computer proofs of security properties is to cope with the complexity of cryptographic proving. We reduce this complexity by exploring a light-weight formalization that enables both appropriate formal definitions as well as efficient formal proofs. Consequently, we get reliable proofs with a minimal error rate augmenting the used database, what provides a formal basis for more computer proof constructions in this area.

Keywords: public-key encryption, Rabin public-key scheme, formalproof system, higher-order logic, formal verification.

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Authors: Rami Rashkovits, Ilana Lavy

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In this study we present our developed formative assessment tool for students' assignments. The tool enables lecturers to define assignments for the course and assign each problem in each assignment a list of criteria and weights by which the students' work is evaluated. During assessment, the lecturers feed the scores for each criterion with justifications. When the scores of the current assignment are completely fed in, the tool automatically generates reports for both students and lecturers. The students receive a report by email including detailed description of their assessed work, their relative score and their progress across the criteria along the course timeline. This information is presented via charts generated automatically by the tool based on the scores fed in. The lecturers receive a report that includes summative (e.g., averages, standard deviations) and detailed (e.g., histogram) data of the current assignment. This information enables the lecturers to follow the class achievements and adjust the learning process accordingly. The tool was examined on two pilot groups of college students that study a course in (1) Object-Oriented Programming (2) Plane Geometry. Results reveal that most of the students were satisfied with the assessment process and the reports produced by the tool. The lecturers who used the tool were also satisfied with the reports and their contribution to the learning process.

Keywords: Computer-based formative assessment tool, science education.

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Authors: Yudia Mailani Putri, Martalena Purba, B. J. Istiti Kandarina

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Background: Obesity has been recognized as a global health problem. Individuals classified as overweight and obese are increasing at an alarming rate. This condition is associated with psychological and physiological problems. as a person reaches adulthood, somatic growth ceases. At this stage, the human body has developed fully, to a stable state. As the capital of Riau Province in Indonesia, Pekanbaru is dominated by Malay ethnic population habitually consuming cholesterol-rich fatty foods as a daily menu, a trigger to the onset of obesity resulting in high prevalence of degenerative diseases. Research objectives: The aim of this study is elaborating the relationship between high-fat consumption pattern, stress level, physical activity and the incidence of obesity in adult women in Pekanbaru city. Research Methods: Among the combined research methods applied in this study, the first stage is quantitative observational, analytical cross-sectional research design with adult women aged 20-40 living in Pekanbaru city. The sample consists of 200 women with BMI≥25. Sample data is processed with univariate, bivariate (correlation and simple linear regression) and multivariate (multiple linear regression) analysis. The second phase is qualitative descriptive study purposive sampling by in-depth interviews. six participants withdrew from the study. Results: According to the results of the bivariate analysis, there are relationships between the incidence of obesity and the pattern of high fat foods consumption (energy intake (p≤0.000; r = 0.536), protein intake (p≤0.000; r=0.307), fat intake (p≤0.000; r=0.416), carbohydrate intake (p≤0.000; r=0.430), frequency of fatty food consumption (p≤0.000; r=0.506) and frequency of viscera foods consumption (p≤0.000; r=0.535). There is a relationship between physical activity and incidence of obesity (p≤0.000; r=-0.631). However, there is no relationship between the level of stress (p=0.741; r=0.019-) and the incidence of obesity. Physical activity is a predominant factor in the incidence of obesity in adult women in Pekanbaru city. Conclusion: There are relationships between high-fat food consumption pattern, physical activity and the incidence of obesity in Pekanbaru city whereas physical activity is a predominant factor in the occurrence of obesity, supported by the unchangeable pattern of high-fat foods consumption.

Keywords: Obesity, adult, high in fat, stress, physical activity, consumption pattern.

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Authors: Swarniv Chandra, Basudev Ghosh

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Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: Padmakumar S., Vivek Agarwal, Kallol Roy

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A model based fault detection and diagnosis technique for DC motor is proposed in this paper. Fault detection using Kalman filter and its different variants are compared. Only incipient faults are considered for the study. The Kalman Filter iterations and all the related computations required for fault detection and fault confirmation are presented. A second order linear state space model of DC motor is used for this work. A comparative assessment of the estimates computed from four different observers and their relative performance is evaluated.

Keywords: DC motor model, Fault detection and diagnosis Kalman Filter, Unscented Kalman Filter

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Authors: Rahul Bansal, Sudipta Majumdar

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This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

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The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: Ju H. Park, S.M. Lee

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In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.

Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.

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Authors: Husna Hasan, Norfatin Salam, Mohd Bakri Adam

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Extreme temperature of several stations in Malaysia is modelled by fitting the monthly maximum to the Generalized Extreme Value (GEV) distribution. The Mann-Kendall (MK) test suggests a non-stationary model. Two models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. Results show that half of the stations favour a model which is linear for the location parameters. The return level is the level of events (maximum temperature) which is expected to be exceeded once, on average, in a given number of years, is obtained.

Keywords: Extreme temperature, extreme value, return level.

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Authors: Rakesh Prajapati, Purvik Patel, Avadhoot Rajurkar

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Nowadays, manufacturing industries augment their production lines with modern machining centers backed by CAM software. Several attempts are being made to cut down the programming time for machining complex geometries. Special programs/software have been developed to generate the digital numerical data and to prepare NC programs by using suitable post-processors for different machines. By selecting the tools and manufacturing process then applying tool paths and NC program are generated. More and more complex mechanical parts that earlier were being cast and assembled/manufactured by other processes are now being machined. Majority of these parts require lots of pocketing operations and find their applications in die and mold, turbo machinery, aircraft, nuclear, defense etc. Pocketing operations involve removal of large quantity of material from the metal surface. The modeling of warm cast and clamping a piece of food processing parts which the used of Pro-E and MasterCAM^® software. Pocketing operation has been specifically chosen for toolpath optimization. Then after apply Pocketing toolpath, Multi Tool Selection and Reduce Air Time give the results of software simulation time and experimental machining time.

Keywords: Toolpath, part program, optimization, pocket.

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Authors: Chimaobi V. Okolo, Afamefuna J. Ani, Ebere U. Okolo

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This paper seeks to assess the implications of insurance to foreign direct investment inflow in Nigeria. Multiple linear regression technique and correlation matrix test were employed to measure the extent to which foreign direct investment was influenced. The result showed that insurance premium (IP), asset size of insurance industry (AS), and total investment of the industry (TI) impacted significantly and positively on foreign direct investment inflow in Nigeria. There should be effective risk transfer mechanism and financial intermediation, which gives the investor confidence in the risk management strength of the host country.

Keywords: Foreign direct investment, insurance.

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Authors: Miaomiao Yang, Shouming Zhong

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This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability , Neural networks, Linear matrix inequality, Lyapunov-Krasovskii, Time-varying.

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Authors: Isaac O. Asante, Yushi Jiang, Hailin Tao

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Livestreaming marketing, the new electronic commerce element, has become an optional marketing channel following the COVID-19 pandemic, and many sellers are leveraging the features presented by livestreaming to increase sales. This study was conducted to measure real-time observable interactions between consumers and sellers. Based on the affordance theory, this study conceptualized constructs representing the interactive features and examined how they drive consumers’ purchase willingness during livestreaming sessions using 1238 datasets from Amazon Live, following the manual observation of transaction records. Using structural equation modeling, the ordinary least square regression suggests that live viewers, new followers, live chats, and likes positively affect purchase willingness. The Sobel and Monte Carlo tests show that new followers, live chats, and likes significantly mediate the relationship between live viewers and purchase willingness. The study presents a way of measuring interactions in livestreaming commerce and proposes a way to manually gather data on consumer behaviors in livestreaming platforms when the application programming interface (API) of such platforms does not support data mining algorithms.

Keywords: Livestreaming marketing, live chats, live viewers, likes, new followers, purchase willingness.

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Authors: Atman Jbari, Abdellah Adib, Driss Aboutajdine

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This paper addresses the problem of blind source separation (BSS). To recover original signals, from linear instantaneous mixtures, we propose a new contrast function based on the use of a double referenced system. Our approach assumes statistical independence sources. The reference vectors will be incrusted in the cumulant to evaluate the independence. The estimation of the separating matrix will be performed in two steps: whitening observations and joint diagonalization of a set of referenced cumulant matrices. Computer simulations are presented to demonstrate the effectiveness of the suggested approach.

Keywords: Blind source separation, Referenced Cumulant, Contrast, Joint Diagonalization.

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Authors: Liton Jude Rozario, Mohammad Reduanul Haque, Md. Ziarul Islam, Mohammad Shorif Uddin

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Face recognition is a technique to automatically identify or verify individuals. It receives great attention in identification, authentication, security and many more applications. Diverse methods had been proposed for this purpose and also a lot of comparative studies were performed. However, researchers could not reach unified conclusion. In this paper, we are reporting an extensive quantitative accuracy analysis of four most widely used face recognition algorithms: Principal Component Analysis (PCA), Independent Component Analysis (ICA), Linear Discriminant Analysis (LDA) and Support Vector Machine (SVM) using AT&T, Sheffield and Bangladeshi people face databases under diverse situations such as illumination, alignment and pose variations.

Keywords: PCA, ICA, LDA, SVM, face recognition, noise.

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Authors: M. Ouassaid, M. Cherkaoui, A. Nejmi, M. Maaroufi

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This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation results are presented to show the effectiveness of the approach.

Keywords: Integral action, Lyapunov Technique, Non Linear Control, Permanent Magnet Synchronous Motors, Torque Control, Stability.

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