Search results for: Weighted Centroid Modified Simplex Method

Authors: Dini Endah Setyo Rahaju, Dian Retno Sari Dewi

Abstract:

This paper presents an application of the improved QFD method for determining the specifications of kitchen utensils rack. By using the improved method, the subjective nature in original QFD was reduced; particularly in defining the relationship between customer requirement and engineering characteristics. The regression analysis that was used for obtaining the relationship functions between customer requirement and engineering characteristics also accommodated the inaccurateness of the competitive assessment results. The improved method which is represented in the form of a mathematical model had become a formal guidance to allocate the resource for improving the specifications of kitchen utensils rack. The specifications obtained had led to the achievement of the highest feasible customer satisfaction.

Keywords: Customer satisfaction, kitchen utensils rack design, QFD, specifications.

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Authors: Delowar Hossain, Genci Capi

Abstract:

This paper concerns with the problem of deep learning parameters tuning using a genetic algorithm (GA) in order to improve the performance of deep learning (DL) method. We present a GA based DL method for robot object recognition and grasping. GA is used to optimize the DL parameters in learning procedure in term of the fitness function that is good enough. After finishing the evolution process, we receive the optimal number of DL parameters. To evaluate the performance of our method, we consider the object recognition and robot grasping tasks. Experimental results show that our method is efficient for robot object recognition and grasping.

Keywords: Deep learning, genetic algorithm, object recognition, robot grasping.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

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Authors: M. Suresh Kumar, K. Ramani

Abstract:

This paper proposed the comparison made between Multi-Carrier Pulse Width Modulation, Sinusoidal Pulse Width Modulation and Selective Harmonic Elimination Pulse Width Modulation technique for minimization of Total Harmonic Distortion in Cascaded H-Bridge Multi-Level Inverter. In Multicarrier Pulse Width Modulation method by using Alternate Position of Disposition scheme for switching pulse generation to Multi-Level Inverter. Another carrier based approach; Sinusoidal Pulse Width Modulation method is also implemented to define the switching pulse generation system in the multi-level inverter. In Selective Harmonic Elimination method using Genetic Algorithm and Particle Swarm Optimization algorithm for define the required switching angles to eliminate low order harmonics from the inverter output voltage waveform and reduce the total harmonic distortion value. So, the results validate that the Selective Harmonic Elimination Pulse Width Modulation method does capably eliminate a great number of precise harmonics and minimize the Total Harmonic Distortion value in output voltage waveform in compared with Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method. In this paper, comparison of simulation results shows that the Selective Harmonic Elimination method can attain optimal harmonic minimization solution better than Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method.

Keywords: Multi-level inverter, Selective Harmonic Elimination Pulse Width Modulation, Multi-Carrier Pulse Width Modulation, Total Harmonic Distortion, Genetic Algorithm.

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Authors: Benjamin Gorry, Zezhi Chen, Kevin Hammond, Andy Wallace, Greg Michaelson

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This paper describes new computer vision algorithms that have been developed to track moving objects as part of a long-term study into the design of (semi-)autonomous vehicles. We present the results of a study to exploit variable kernels for tracking in video sequences. The basis of our work is the mean shift object-tracking algorithm; for a moving target, it is usual to define a rectangular target window in an initial frame, and then process the data within that window to separate the tracked object from the background by the mean shift segmentation algorithm. Rather than use the standard, Epanechnikov kernel, we have used a kernel weighted by the Chamfer distance transform to improve the accuracy of target representation and localization, minimising the distance between the two distributions in RGB color space using the Bhattacharyya coefficient. Experimental results show the improved tracking capability and versatility of the algorithm in comparison with results using the standard kernel. These algorithms are incorporated as part of a robot test-bed architecture which has been used to demonstrate their effectiveness.

Keywords: Hume, functional programming, autonomous vehicle, pioneer robot, vision.

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Authors: Tao Peng, Jing Zhao, Yanqing Xu, Jing Cai

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Due to missing/ambiguous boundaries between the prostate and neighboring structures, the presence of shadow artifacts, as well as the large variability in prostate shapes, ultrasound prostate segmentation is challenging. To handle these issues, this paper develops a hybrid method for ultrasound prostate segmentation by combining an optimized closed principal curve-based method and the evolutionary neural network; the former can fit curves with great curvature and generate a contour composed of line segments connected by sorted vertices, and the latter is used to express an appropriate map function (represented by parameters of evolutionary neural network) for generating the smooth prostate contour to match the ground truth contour. Both qualitative and quantitative experimental results showed that our proposed method obtains accurate and robust performances.

Keywords: Ultrasound prostate segmentation, optimized closed polygonal segment method, evolutionary neural network, smooth mathematical model.

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Authors: J. Tonkonogij, A. Pedišius, A. Stankevičius

Abstract:

The new semi-experimental method for simulation of the turbine flow meters rotation in the transitional flow has been developed. The method is based on the experimentally established exponential low of changing of dimensionless relative turbine gas meter rotation frequency and meter inertia time constant. For experimental evaluation of the meter time constant special facility has been developed. The facility ensures instant switching of turbine meter under test from one channel to the other channel with different flow rate and measuring the meter response. The developed method can be used for evaluation and predication of the turbine meters response and dynamic error in the transitional flow with any arbitrary law of flow rate changing. The examples of the method application are presented.

Keywords: Dynamic error, pulsing flow, numerical simulation, response, turbine gas meters.

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Authors: Jieer Wu, Zheshu Ma

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Nondestructive testing in engineering is an inverse Cauchy problem for Laplace equation. In this paper the problem of nondestructive testing is expressed by a Laplace-s equation with third-kind boundary conditions. In order to find unknown values on the boundary, the method of fundamental solution is introduced and realized. Because of the ill-posedness of studied problems, the TSVD regularization technique in combination with L-curve criteria and Generalized Cross Validation criteria is employed. Numerical results are shown that the TSVD method combined with L-curve criteria is more efficient than the TSVD method combined with GCV criteria. The abstract goes here.

Keywords: ill-posed, TSVD, Laplace's equation, inverse problem, L-curve, Generalized Cross Validation.

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Authors: Y. Rhazali, Y. Hadi, A. Mouloudi

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This paper proposes a method to automatic transformation of CIM level to PIM level respecting the MDA approach. Our proposal is based on creating a good CIM level through well-defined rules allowing as achieving rich models that contain relevant information to facilitate the task of the transformation to the PIM level. We define, thereafter, an appropriate PIM level through various UML diagram. Next, we propose set rules to move from CIM to PIM. Our method follows the MDA approach by considering the business dimension in the CIM level through the use BPMN, standard modeling business of OMG, and the use of UML in PIM advocated by MDA in this level.

Keywords: Model transformation, MDA, CIM, PIM.

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Authors: Davood Mostofinejad, Seyed Amirali Mostafavizadeh, Amirhomayoon Tabatabaei Kashani

Abstract:

One of the most common practices for strengthening the reinforced concrete structures is the application of FRP (Fiber Reinforce Plastic) sheets to increase the flexural and shear strengths of the member. The elastic modulus of FRP is considerably higher than that of concrete. This will result in debonding between the FRP sheets and concrete surface. With conventional surface preparation of concrete, the ultimate capacity of the FRP sheets can hardly be achieved. New methods for preparation of the bonding surface have shown improvements in reducing the premature debonding of FRP sheets from concrete surface. The present experimental study focuses on the application of grooving method to postpone debonding of the FRP sheets attached to the side faces of concrete beams for shear strengthening. Comparison has also been made with conventional surface preparation method. This study clearly shows the efficiency of grooving method compared to surface preparation method, in preventing the debonding phenomenon and in increasing the load carrying capacity of FRP.

Keywords: FRP composite, grooving, rehabilitation, reinforced concrete, shear strengthening, surface preparation.

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Authors: P. Volakova, M. Mika, V. Verner, B. Klapste, O. Jankovsky

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We successfully developed and tested a new separation layer solving problems with unmanageable deposits inside the boilers of Zluticka Heating Plant. The deposits are mainly created by glass-forming melts. We plotted straw ash compositions in K2OCaO- SiO2 phase diagram and illustrated that they are in the area of low-melting eutectic points. To prevent the melting of ash and the formation of deposits, we modified ash compositions by injecting additives into biomass fuel, and thus effectively suppressed deposits in a burner.

Keywords: Biomass, straw, combustion, deposit, heat, additives

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Authors: Samraj Andrews, Ramaswamy Palaniappan, Nidal Kamel

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In single trial analysis, when using Principal Component Analysis (PCA) to extract Visual Evoked Potential (VEP) signals, the selection of principal components (PCs) is an important issue. We propose a new method here that selects only the appropriate PCs. We denote the method as selective eigen-rate (SER). In the method, the VEP is reconstructed based on the rate of the eigen-values of the PCs. When this technique is applied on emulated VEP signals added with background electroencephalogram (EEG), with a focus on extracting the evoked P3 parameter, it is found to be feasible. The improvement in signal to noise ratio (SNR) is superior to two other existing methods of PC selection: Kaiser (KSR) and Residual Power (RP). Though another PC selection method, Spectral Power Ratio (SPR) gives a comparable SNR with high noise factors (i.e. EEGs), SER give more impressive results in such cases. Next, we applied SER method to real VEP signals to analyse the P3 responses for matched and non-matched stimuli. The P3 parameters extracted through our proposed SER method showed higher P3 response for matched stimulus, which confirms to the existing neuroscience knowledge. Single trial PCA using KSR and RP methods failed to indicate any difference for the stimuli.

Keywords: Electroencephalogram, P3, Single trial VEP.

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Authors: Samera Salimpour Abkenar

Abstract:

In traditional dyeing of natural fibers with natural dyes, metal salts are commonly used to increase color stability. This method always carries the risk of environmental pollution (contamination of arable soils and fresh groundwater) due to the release of dyeing effluents containing large amounts of metal. Therefore, researchers are always looking for new methods to obtain a green dyeing system. In this research, the use of the enzymatic dyeing method to prevent environmental pollution with metals and reduce production costs has been proposed. After degumming and bleaching, raw silk fabrics were dyed with natural dyes (Madder and Sumac) by three methods (pre-mordanting with a metal salt, one-step enzymatic dyeing, and two-step enzymatic dyeing). Results show that silk dyed with natural dyes by the enzymatic method has higher color strength and colorfastness than the pretreated with a metal salt. Also, the amount of remained dyes in the dyeing wastewater is significantly reduced by the enzymatic method. It is found that the enzymatic dyeing method leads to improvement of dye absorption, color strength, soft hand, no change in color shade, low production costs (due to low dyeing temperature), and a significant reduction in environmental pollution.

Keywords: Eco-friendly, natural dyes, silk, traditional dyeing.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).

Keywords: Homotopy perturbation method, Exact solution, Cauchy problem, inhomogeneous wave equation

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Authors: J. Nisar, S. Halim

Abstract:

The additional relationships i.e., start-to-start, finish-to-finish, and start-to-finish, between activity in Precedence Diagram Method (PDM) provides a more flexible schedule than traditional Critical Path Method (CPM). But, changing the duration of critical activities in the PDM network will have an anomalous effect on the critical path and the project completion date. In this study, we classified the critical activities in two groups i.e., 1. activity on single critical path and 2. activity on multi-critical paths, and six classes i.e., normal, reverse, neutral, perverse, decrease-reverse and increase-normal, based on their effects on project duration in PDM. Furthermore, we determined the maximum float of time by which the duration each type of critical activities can be changed without effecting the project duration. This study would help the project manager to clearly understand the behavior of each critical activity on critical path, and he/she would be able to change the project duration by shortening or lengthening activities based on project budget and project deadline.

Keywords: Construction project management, critical path method, project scheduling, precedence diagram method.

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Authors: Khaled M. El Naggar

Abstract:

This paper introduces a digital method for fault section identification in transmission lines. The method uses digital set of the measured short circuit current to locate faults in electrical power systems. The digitized current is used to construct a set of overdetermined system of equations. The problem is then constructed and solved using the proposed digital optimization technique to find the fault distance. The proposed optimization methodology is an application of simulated annealing optimization technique. The method is tested using practical case study to evaluate the proposed method. The accurate results obtained show that the algorithm can be used as a powerful tool in the area of power system protection.

Keywords: Optimization, estimation, faults, measurement, high voltage, simulated annealing.

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Authors: Andrey V. Timofeev, Viktor M. Denisov

Abstract:

A robust sequential nonparametric method is proposed for adaptation to background noise parameters for real-time. The distribution of background noise was modelled like to Huber contamination mixture. The method is designed to operate as an adaptation-unit, which is included inside a detection subsystem of an integrated multichannel monitoring system. The proposed method guarantees the given size of a nonasymptotic confidence set for noise parameters. Properties of the suggested method are rigorously proved. The proposed algorithm has been successfully tested in real conditions of a functioning C-OTDR monitoring system, which was designed to monitor railways.

Keywords: Guaranteed estimation, multichannel monitoring systems, non-asymptotic confidence set, contamination mixture.

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Authors: M. Zarebnia, S. Khani

Abstract:

In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

Keywords: Hammerstein integral equations, quasi-interpolation, Nystrom’s method.

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Authors: Kourosh Parand, Zahra Delafkar, Fatemeh Baharifard

Abstract:

The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.

Keywords: Tau method, semi-infinite, nonlinear ODE, rational Chebyshev, porous media.

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Authors: O. Ikpotokin

Abstract:

In any production process, every product is aimed to attain a certain standard, but the presence of assignable cause of variability affects our process, thereby leading to low quality of product. The ability to identify and remove this type of variability reduces its overall effect, thereby improving the quality of the product. In case of a univariate control chart signal, it is easy to detect the problem and give a solution since it is related to a single quality characteristic. However, the problems involved in the use of multivariate control chart are the violation of multivariate normal assumption and the difficulty in identifying the quality characteristic(s) that resulted in the out of control signals. The purpose of this paper is to examine the use of non-parametric control chart (the bootstrap approach) for obtaining control limit to overcome the problem of multivariate distributional assumption and the p-value method for detecting out of control signals. Results from a performance study show that the proposed bootstrap method enables the setting of control limit that can enhance the detection of out of control signals when compared, while the p-value method also enhanced in identifying out of control variables.

Keywords: Bootstrap control limit, p-value method, out-of-control signals, p-value, quality characteristics.

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Authors: Z. Pavlík, J. Fořt, J. Žumár, M. Pavlíková, R. Černý

Abstract:

The cup method is applied for the measurement of water vapor transport properties of porous materials worldwide. However, in practical applications the experimental results are often used without taking into account some secondary effects which can play an important role under specific conditions. In this paper, the effect of temperature on water vapor transport properties of cellular concrete is studied, together with the influence of sample thickness. At first, the bulk density, matrix density, total open porosity and sorption and desorption isotherms are measured for material characterization purposes. Then, the steady state cup method is used for determination of water vapor transport properties, whereas the measurements are performed at several temperatures and for three different sample thicknesses.

Keywords: Water vapor transport, cellular concrete, cup method, temperature, sample thickness.

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Authors: Amir Moslemi, Amir Movafeghi, Shahab Moradi

Abstract:

One of the most important challenging factors in medical images is nominated as noise. Image denoising refers to the improvement of a digital medical image that has been infected by Additive White Gaussian Noise (AWGN). The digital medical image or video can be affected by different types of noises. They are impulse noise, Poisson noise and AWGN. Computed tomography (CT) images are subjects to low quality due to the noise. Quality of CT images is dependent on absorbed dose to patients directly in such a way that increase in absorbed radiation, consequently absorbed dose to patients (ADP), enhances the CT images quality. In this manner, noise reduction techniques on purpose of images quality enhancement exposing no excess radiation to patients is one the challenging problems for CT images processing. In this work, noise reduction in CT images was performed using two different directional 2 dimensional (2D) transformations; i.e., Curvelet and Contourlet and Discrete Wavelet Transform (DWT) thresholding methods of BayesShrink and AdaptShrink, compared to each other and we proposed a new threshold in wavelet domain for not only noise reduction but also edge retaining, consequently the proposed method retains the modified coefficients significantly that result good visual quality. Data evaluations were accomplished by using two criterions; namely, peak signal to noise ratio (PSNR) and Structure similarity (Ssim).

Keywords: Computed Tomography (CT), noise reduction, curve-let, contour-let, Signal to Noise Peak-Peak Ratio (PSNR), Structure Similarity (Ssim), Absorbed Dose to Patient (ADP).

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Authors: A. K. Sethi, R. N. Patra, B. Nayak

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In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant r (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

Keywords: Bulk viscosity, Lyra geometry, generalized Chaplygin gas, cosmology.

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Authors: B. R. Madushan, S. B. Navaratne, I. Wickramasinghe

Abstract:

Toddy sediment (TS) was cultured in a PDA medium to determine initial yeast load, and also it was undergone sun, shade, solar, dehumidified cold air (DCA) and hot air oven (at 400, 500 and 60oC) drying with a view to preserve viability of yeast. Thereafter, this study was conducted according to two factor factorial design in order to determine best preservation method. Therein the dried TS from the best drying method was taken and divided into two portions. One portion was mixed with 3: 7 ratio of TS: rice flour and the mixture was divided in to two again. While one portion was kept under in house condition the other was in a refrigerator. Same procedure was followed to the rest portion of TS too but it was at the same ratio of corn flour. All treatments were vacuum packed in triple laminate pouches and the best preservation method was determined in terms of leavening index (LI). The TS obtained from the best preservation method was used to make foods (bread and hopper) and organoleptic properties of it were evaluated against same of ordinary foods using sensory panel with a five point hedonic scale. Results revealed that yeast load or fresh TS was 58×106 CFU/g. The best drying method in preserving viability of yeast was DCA because LI of this treatment (96%) is higher than that of other three treatments. Organoleptic properties of foods prepared from best preservation method are as same as ordinary foods according to Duo trio test.

Keywords: Biological leavening agent, coconut toddy, fermentation, yeast.

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Authors: Mariani Md Nor, Y. Saeednia

Abstract:

Self-directed learning (SDL) was developed initially for adult learning. Guglielmino constructed a scale to measure SDL. Recent researchers have applied this concept to children. Although there are sufficient theoretical evidences to present the possibility of applying this concept to children, empirical evidences were not provided. This study aimed to examine the quality of SDL and construct a scale to measure SDL among young children. A modified scale of Guglielmino-s scale was constructed and piloted with 183 subjects of age 9. Findings suggest that the qualities of SDL in young ages are apparently congruent with that of adults.

Keywords: SDLR, Self-Directed Learning, Young Children.

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Authors: V. Manush Nandan, K. Lokdeep, R. Vimal, K. Hari Hara Subramanyan, C. Aswin, V. Logeswaran

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Natural fibers have attained the potential market in the composite industry because of the huge environmental impact caused by synthetic fibers. Among the natural fibers, jute fibers are the most abundant plant fibers which are manufactured mainly in countries like India. Even though there is a good motive to utilize the natural supplement, the strength of the natural fiber composites is still a topic of discussion. In recent days, many researchers are showing interest in the chemical modification of the natural fibers to increase various mechanical and thermal properties. In the present study, jute fibers have been modified chemically using glutaric anhydride at different concentrations of 5%, 10%, 20%, and 30%. The glutaric anhydride solution is prepared by dissolving the different quantity of glutaric anhydride in benzene and dimethyl-sulfoxide using sodium formate catalyst. The jute fiber mats have been treated by the method of retting at various time intervals of 3, 6, 12, 24, and 36 hours. The modification structure of the treated fibers has been confirmed with infrared spectroscopy. The degree of modification increases with an increase in retention time, but higher retention time has damaged the fiber structure. The unmodified fibers and glutarylated fibers at different retention times are reinforced with epoxy matrix under room temperature. The tensile strength and flexural strength of the composites are analyzed in detail. Among these, the composite made with glutarylated fiber has shown good mechanical properties when compared to those made of unmodified fiber.

Keywords: Flexural properties, glutarylation, glutaric anhydride, tensile properties.

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: Inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness.

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Authors: G. Kehl, P. Wagner

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A novel simulation method to determine the displacements of machine tools due to thermal factors is presented. The specific characteristic of this method is the employment of original CAD data from the design process chain, which is interpreted by an algorithm in terms of geometry-based allocation of convection and radiation parameters. Furthermore analogous models relating to the thermal behaviour of machine elements are automatically implemented, which were gained by extensive experimental testing with thermography imaging. With this a transient simulation of the thermal field and in series of the displacement of the machine tool is possible simultaneously during the design phase. This method was implemented and is already used industrially in the design of machining centres in order to improve the quality of herewith manufactured workpieces.

Keywords: Accuracy, design process, finite element analysis, machine tools, thermal simulation.

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Authors: Hubert Klar

Abstract:

High double excitation of two-electron atoms has been investigated using hyperpherical coordinates within a modified adiabatic expansion technique. This modification creates a novel fictitious force leading to a spontaneous exchange symmetry breaking at high double excitation. The Pauli principle must therefore be regarded as approximation valid only at low excitation energy. Threshold electron scattering from high Rydberg states shows an unexpected time reversal symmetry breaking. At threshold for double escape we discover a broad (few eV) Cooper pair.

Keywords: Correlation, resonances, threshold ionization, Cooper pair.

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Authors: Tunjo Peric, Zoran Babic

Abstract:

The authors of this work indicate by means of a concrete example that it is possible to apply efficaciously the method of multiple criteria programming in dealing with the problem of determining the optimal production plan for a certain period of time. The work presents: (1) the selection of optimization criteria, (2) the setting of the problem of determining an optimal production plan, (3) the setting of the model of multiple criteria programming in finding a solution to a given problem, (4) the revised surrogate trade-off method, (5) generalized multicriteria model for solving production planning problem and problem of choosing technological variants in the metal manufacturing industry. In the final part of this work the authors reflect on the application of the method of multiple criteria programming while determining the optimal production plan in manufacturing enterprises.

Keywords: multi-criteria programming, production planning, technological variant, Surrogate Worth Trade-off Method.

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