Search results for: Linear Matrix Inequalities

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

Abstract:

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

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

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Authors: J. Preetha, S. Selvarajan

Abstract:

When neck pain is associated with pain, numbness, or weakness in the arm, shoulder, or hand, further investigation is needed as these are symptoms indicating pressure on one or more nerve roots. Evaluation necessitates a neurologic examination and imaging using an MRI/CT scan. A degenerating disc loses some thickness and is less flexible, causing inter-vertebrae space to narrow. A radiologist diagnoses an Intervertebral Disc Degeneration (IDD) by localizing every inter-vertebral disc and identifying the pathology in a disc based on its geometry and appearance. Accurate localizing is necessary to diagnose IDD pathology. But, the underlying image signal is ambiguous: a disc’s intensity overlaps the spinal nerve fibres. Even the structure changes from case to case, with possible spinal column bending (scoliosis). The inter-vertebral disc pathology’s quantitative assessment needs accurate localization of the cervical region discs. In this work, the efficacy of multilevel set segmentation model, to segment cervical discs is investigated. The segmented images are annotated using a simple distance matrix.

Keywords: Intervertebral Disc Degeneration (IDD), Cervical Disc Localization, multilevel set segmentation.

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Authors: Mokhtar Awang, Wei-Vern Hor, Ehsan Mohammadpour, M Zaki Abdullah, Faiz Ahmad

Abstract:

Chemical and physical functionalization of multiwalled carbon nanotubes (MWCNT) has been commonly practiced to achieve better dispersion of carbon nanotubes (CNTs) in polymer matrix. This work describes various functionalization methods (acidtreatment, non-ionic surfactant treatment with TritonX-100), fabrication of MWCNT/PP nanocomposites via melt blending and characterization of mechanical properties. Microscopy analysis (FESEM, TEM, XPS) showed effective purification of MWCNTs under acid treatment, and better dispersion under both chemical and physical functionalization techniques combined, in their respective order. Tensile tests showed increase in tensile strength for the nanocomposites that contain MWCNTs up to 2 wt%. A decrease in tensile strength was seen in samples that contain 4 wt% of MWCNTs for both raw and Triton X-100 functionalized, signifying MWCNT degradation/rebundling at composition with higher content of MWCNTs. For the acid-treated MWCNTs, however, the tensile results showed slight improvement even at 4wt%, indicating effective dispersion of MWCNTs.

Keywords: Multi walled carbon nanotube (MWCNT), functionalization, dispersion, nanocomposite

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Authors: Zeynep R. Ege, Aydin Akan, Faik N. Oktar, Betul Karademir, Oguzhan Gunduz

Abstract:

Early detection of cancer could save human life and quality in insidious cases by advanced biomedical imaging techniques. Designing targeted detection system is necessary in order to protect of healthy cells. Electrospun nanofibers are efficient and targetable nanocarriers which have important properties such as nanometric diameter, mechanical properties, elasticity, porosity and surface area to volume ratio. In the present study, indocyanine green (ICG) organic dye was stabilized and encapsulated in polymer matrix which polyethylene oxide (PEO) and chitosan (CHI) multilayer nanofibers via co-axial electrospinning method at one step. The co-axial electrospun nanofibers were characterized as morphological (SEM), molecular (FT-IR), and entrapment efficiency of Indocyanine Green (ICG) (confocal imaging). Controlled release profile of PEO/CHI/ICG nanofiber was also evaluated up to 40 hours.

Keywords: Chitosan, coaxial electrospinning, controlled releasing, indocyanine green, nanoprobe, polyethylene oxide.

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Authors: Alexander Efremov

Abstract:

A system for market identification (SMI) is presented. The resulting representations are multivariable dynamic demand models. The market specifics are analyzed. Appropriate models and identification techniques are chosen. Multivariate static and dynamic models are used to represent the market behavior. The steps of the first stage of SMI, named data preprocessing, are mentioned. Next, the second stage, which is the model estimation, is considered in more details. Stepwise linear regression (SWR) is used to determine the significant cross-effects and the orders of the model polynomials. The estimates of the model parameters are obtained by a numerically stable estimator. Real market data is used to analyze SMI performance. The main conclusion is related to the applicability of multivariate dynamic models for representation of market systems.

Keywords: market identification, dynamic models, stepwise regression.

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Authors: Neveen I. Ghali, Nahed El-Dessouki, Mervat A. N., Lamiaa Bakrawi

Abstract:

In this paper we use exponential particle swarm optimization (EPSO) to cluster data. Then we compare between (EPSO) clustering algorithm which depends on exponential variation for the inertia weight and particle swarm optimization (PSO) clustering algorithm which depends on linear inertia weight. This comparison is evaluated on five data sets. The experimental results show that EPSO clustering algorithm increases the possibility to find the optimal positions as it decrease the number of failure. Also show that (EPSO) clustering algorithm has a smaller quantization error than (PSO) clustering algorithm, i.e. (EPSO) clustering algorithm more accurate than (PSO) clustering algorithm.

Keywords: Particle swarm optimization, data clustering, exponential PSO.

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Authors: Alexander Breitholz, Wolfgang Arlt, Ki-Pung Yoo

Abstract:

Group contribution based models are widely used in industrial applications for its convenience and flexibility. Although a number of group contribution models have been proposed, there were certain limitations inherent to those models. Models based on group contribution excess Gibbs free energy are limited to low pressures and models based on equation of state (EOS) cannot properly describe highly nonideal mixtures including acids without introducing additional modification such as chemical theory. In the present study new a new approach derived from quantum chemistry have been used to calculate necessary EOS group interaction parameters. The COSMO-RS method, based on quantum mechanics, provides a reliable tool for fluid phase thermodynamics. Benefits of the group contribution EOS are the consistent extension to hydrogen-bonded mixtures and the capability to predict polymer-solvent equilibria up to high pressures. The authors are confident that with a sufficient parameter matrix the performance of the lattice EOS can be improved significantly.

Keywords: COSMO-RS, Equation of State, Group contribution, Lattice Fluid, Phase equilibria.

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Authors: O. Poleshchuk, E.Komarov

Abstract:

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: Interval type-2 fuzzy sets, fuzzy regression, weighted interval.

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Authors: Kitti Leangkrua

Abstract:

This paper presents a risk-based maintenance strategy of a power transformer in order to optimize operating and maintenance costs. The methodology involves the study and preparation of a database for the collection the technical data and test data of a power transformer. An evaluation of the overall condition of each transformer is performed by a program developed as a result of the measured results; in addition, the calculation of the main equipment separation to the overall condition of the transformer (% HI) and the criteria for evaluating the importance (% ImI) of each location where the transformer is installed. The condition assessment is performed by analysis test data such as electrical test, insulating oil test and visual inspection. The condition of the power transformer will be classified from very poor to very good condition. The importance is evaluated from load criticality, importance of load and failure consequence. The risk matrix is developed for evaluating the risk of each power transformer. The high risk power transformer will be focused firstly. The computerized program is developed for practical use, and the maintenance strategy of a power transformer can be effectively managed.

Keywords: Asset management, risk-based maintenance, power transformer, health index.

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Authors: Ekaterina Artiukhina, Panagiotis Grammelis

Abstract:

Torrefaction of biomass pellets is considered as a useful pretreatment technology in order to convert them into a high quality solid biofuel that is more suitable for pyrolysis, gasification, combustion, and co-firing applications. In the course of torrefaction, the temperature varies across the pellet, and therefore chemical reactions proceed unevenly within the pellet. However, the uniformity of the thermal distribution along the pellet is generally assumed. The torrefaction process of a single cylindrical pellet is modeled here, accounting for heat transfer coupled with chemical kinetics. The drying sub-model was also introduced. The nonstationary process of wood pellet decomposition is described by the system of non-linear partial differential equations over the temperature and mass. The model captures well the main features of the experimental data.

Keywords: Torrefaction, biomass pellets, model, heat and mass transfer.

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Authors: Shield B. Lin, Sameer Abdali

Abstract:

Computer simulations were performed using MATLAB/Simulink for a vibration isolation system for astronaut’s exercise platform. Simulation parameters initially were based on an on-going experiment in a laboratory at NASA Johnson Space Center. The authors expanded later simulations to include other parameters. A discrete proportional-integral-derivative controller with a low-pass filter commanding a linear actuator served as the active control unit to push and pull a counterweight in balancing the disturbance forces. A spring-damper device is used as an optional passive control unit. Simulation results indicated such design could achieve near complete vibration isolation with small displacements of the exercise platform.

Keywords: Control, counterweight, isolation, vibration.

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Authors: Jeffrey L. Duffany

Abstract:

Graph coloring is an important problem in computer science and many algorithms are known for obtaining reasonably good solutions in polynomial time. One method of comparing different algorithms is to test them on a set of standard graphs where the optimal solution is already known. This investigation analyzes a set of 50 well known graph coloring instances according to a set of complexity measures. These instances come from a variety of sources some representing actual applications of graph coloring (register allocation) and others (mycieleski and leighton graphs) that are theoretically designed to be difficult to solve. The size of the graphs ranged from ranged from a low of 11 variables to a high of 864 variables. The method used to solve the coloring problem was the square of the adjacency (i.e., correlation) matrix. The results show that the most difficult graphs to solve were the leighton and the queen graphs. Complexity measures such as density, mobility, deviation from uniform color class size and number of block diagonal zeros are calculated for each graph. The results showed that the most difficult problems have low mobility (in the range of .2-.5) and relatively little deviation from uniform color class size.

Keywords: graph coloring, complexity, algorithm.

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Authors: S. Tunmee, P. Wongpanya, I. Toda, X. L. Zhou, Y. Nakaya, N. Konkhunthot, S. Arakawa, H. Saitoh

Abstract:

The hydrogenated amorphous carbon films (α-C:H) were deposited on p-type Si (100) substrates at different thicknesses by radio frequency plasma enhanced chemical vapor deposition technique (rf-PECVD). Raman spectra display asymmetric diamond-like carbon (DLC) peaks, representative of the α-C:H films. The decrease of intensity ID/IG ratios revealed the sp3 content arise at different thicknesses of the α-C:H films. In terms of mechanical properties, the high hardness and elastic modulus values showed the elastic and plastic deformation behaviors related to sp3 content in amorphous carbon films. Electrochemical properties showed that the α-C:H films exhibited excellent corrosion resistance in air-saturated 3.5 wt.% NaCl solution for pH 2 at room temperature. Thickness increasing affected the small sp2 clusters in matrix, restricting the velocity transfer and exchange of electrons. The deposited α-C:H films exhibited excellent mechanical properties and corrosion resistance.

Keywords: Thickness, Mechanical properties, Electrochemical corrosion properties, α-C:H film.

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Authors: Ahmed Zaafouri, Mounir Sayadi, Farhat Fnaiech

Abstract:

In this paper, we present a method for edge segmentation of satellite images based on 2-D Phase Congruency (PC) model. The proposed approach is composed by two steps: The contextual non linear smoothing algorithm (CNLS) is used to smooth the input images. Then, the 2D stretched Gabor filter (S-G filter) based on proposed angular variation is developed in order to avoid the multiple responses in the previous work. An assessment of our proposed method performance is provided in terms of accuracy of satellite image edge segmentation. The proposed method is compared with others known approaches.

Keywords: Edge segmentation, Phase congruency model, Satellite images, Stretched Gabor filter

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

Abstract:

In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.

Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure

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Authors: Muhammad Saiful Fadhil Reyhan, Yusnita Rahayu, Fadhel Muhammadsyah

Abstract:

This paper proposed a design of 16 elements, 8x2 linear fed patch antenna array with 16 ports, for 28 GHz, mm-wave band 5G for base station. The phased array covers along the azimuth plane to provide the coverage to the users in omnidirectional. The proposed antenna is designed RT Duroid 5880 substrate with the overall size of 85x35.6x0.787 mm³. The array is operating from 27.43 GHz to 28.34 GHz with a 910 MHz impedance bandwidth. The gain of the array is 18.3 dB, while the suppression of the side lobes is -1.0 dB. The main lobe direction of the array is 15 deg. The array shows a high array gain throughout the impedance bandwidth with overall of VSWR is below 1.12. The design will be proposed in single element and 16 elements antenna.

Keywords: 5G antenna, 28 GHz, MIMO, omnidirectional, phased array, base station, broadband.

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Authors: George Cristian Gruia, Michal Kavan

Abstract:

The article describes a case study on one of Czech Republic-s manufacturing middle size enterprises (ME), where due to the European financial crisis, production lines had to be redesigned and optimized in order to minimize the total costs of the production of goods. It is considered an optimization problem of minimizing the total cost of the work load, according to the costs of the possible locations of the workplaces, with an application of the Greedy algorithm and a partial analogy to a Set Packing Problem. The displacement of working tables in a company should be as a one-toone monotone increasing function in order for the total costs of production of the goods to be at minimum. We use a heuristic approach with greedy algorithm for solving this linear optimization problem, regardless the possible greediness which may appear and we apply it in a Czech ME.

Keywords: Czech, greedy algorithm, minimize, total costs.

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Authors: Saeed Sarabadan, Kamal Rashedi

Abstract:

This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: Chutima Prommak, Airisa Jantaweetip

Abstract:

This paper presents a hybrid association control scheme that can maintain load balancing among access points in the wireless LANs and can satisfy the quality of service requirements of the multimedia traffic applications. The proposed model is mathematically described as a linear programming model. Simulation study and analysis were conducted in order to demonstrate the performance of the proposed hybrid load balancing and association control scheme. Simulation results shows that the proposed scheme outperforms the other schemes in term of the percentage of blocking and the quality of the data transfer rate providing to the multimedia and real-time applications.

Keywords: Association control, Load balancing, Wireless LANs

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Authors: M. H. Kargarnovin, A. Mamandi

Abstract:

This paper presents investigation effects of a sharp edged gust on aeroelastic behavior and time-domain response of a typical section model using Jones approximate aerodynamics for pure plunging motion. Flutter analysis has been done by using p and p-k methods developed for presented finite-state aerodynamic model for a typical section model (airfoil). Introduction of gust analysis as a linear set of ordinary differential equations in a simplified procedure has been carried out by using transformation into an eigenvalue problem.

Keywords: Aeroelastic response, jones approximation, pure plunging motion, sharp edged gust.

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Authors: Young Sik Kim, Tae Kwon Ha

Abstract:

Effect of Zn addition on the microstructure and mechanical properties of Mg-Zn alloys with Zn contents from 6 to 10 weight percent was investigated in this study. Through calculation of phase equilibria of Mg-Zn alloys, carried out by using FactSage® and FTLite database, solution treatment temperature was decided as temperatures from 300 to 400oC, where supersaturated solid solution can be obtained. Solid solution treatment of Mg-Zn alloys was successfully conducted at 380oC and supersaturated microstructure with all beta phase resolved into matrix was obtained. After solution treatment, hot rolling was successfully conducted by reduction of 60%. Compression and tension tests were carried out at room temperature on the samples as-cast, solution treated, hot-rolled and recrystallized after rolling. After solid solution treatment, each alloy was annealed at temperatures of 180 and 200oC for time intervals from 1 min to 48 hrs and hardness of each condition was measured by micro-Vickers method. Peak aging conditions were deduced as at the temperature of 200oC for 10 hrs. By addition of Zn by 10 weight percent, hardness and strength were enhanced.

Keywords: Mg-Zn alloy, Heat treatment, Microstructure, Mechanical properties, Hardness.

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Authors: Yousef Abu Nahleh, Alhasan Hakami, Arun Kumar, Fugen Daver

Abstract:

This study considers the problem of calculating safety stocks in disaster situations inventory systems that face demand uncertainties. Safety stocks are essential to make the supply chain, which is controlled by forecasts of customer needs, in response to demand uncertainties and to reach predefined goal service levels. To solve the problem of uncertainties due to the disaster situations affecting the industry sector, the concept of Emergency Safety Stock (ESS) was proposed. While there exists a huge body of literature on determining safety stock levels, this literature does not address the problem arising due to the disaster and dealing with the situations. In this paper, the problem of improving the Order Quantity Model to deal with uncertainty of demand due to disasters is managed by incorporating a new idea called ESS which is based on the probability of disaster occurrence and uses probability matrix calculated from the historical data. 

Keywords: Emergency Safety Stocks, Safety stocks, Order Quantity Model, Supply chain.

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Authors: Jan Erik Stellet

Abstract:

This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it is investigated how changes to the adaptation gain affect the system performance. Furthermore, variations in the reference model parameters, that is changing the desired closed-loop behaviour are examinded.

Keywords: Adaptive control systems, Adaptation gain, MIT rule, Lyapunov rule, Model reference adaptive control.

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Authors: B. S. Saini, Dilbag Singh, Moin Uddin, Vinod Kumar

Abstract:

The RR interval series is non-stationary and unevenly spaced in time. For estimating its power spectral density (PSD) using traditional techniques like FFT, require resampling at uniform intervals. The researchers have used different interpolation techniques as resampling methods. All these resampling methods introduce the low pass filtering effect in the power spectrum. The lomb transform is a means of obtaining PSD estimates directly from irregularly sampled RR interval series, thus avoiding resampling. In this work, the superiority of Lomb transform method has been established over FFT based approach, after applying linear and cubicspline interpolation as resampling methods, in terms of reproduction of exact frequency locations as well as the relative magnitudes of each spectral component.

Keywords: HRV, Lomb Transform, Resampling, RR-intervals.

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Authors: A. M. Sagir

Abstract:

In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: C. Porkodi, R. Arumuganathan

Abstract:

In this paper a Public Key Cryptosystem is proposed using the number theoretic transforms (NTT) over a ring of integer modulo a composite number. The key agreement is similar to ElGamal public key algorithm. The security of the system is based on solution of multivariate linear congruence equations and discrete logarithm problem. In the proposed cryptosystem only fixed numbers of multiplications are carried out (constant complexity) and hence the encryption and decryption can be done easily. At the same time, it is very difficult to attack the cryptosystem, since the cipher text is a sequence of integers which are interrelated. The system provides authentication also. Using Mathematica version 5.0 the proposed algorithm is justified with a numerical example.

Keywords: Cryptography, decryption, discrete logarithm problem encryption, Integer Factorization problem, Key agreement, Number Theoretic Transform.

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Authors: Nina Øystad-Larsen, Miran Cemalovic, Amir M. Kaynia

Abstract:

The nonlinear static and dynamic analysis procedures presented in EN 1998-1 for the structural response of a RC wall-frame building are assessed. The structure is designed according to the guidelines for high ductility (DCH) in 1998-1. The finite element packages SeismoStruct and OpenSees are utilized and evaluated. The structural response remains nearly in the elastic range even though the building was designed for high ductility. The overstrength is a result of oversized and heavily reinforced members, with emphasis on the lower storey walls. Nonlinear response history analysis in the software packages give virtually identical results for displacements.

Keywords: Behaviour factor, Dual system, OpenSEES, Overstrength, SeismoStruct.

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Authors: F. Abbas Pour Khotbehsara, B. Salehpour, A. Kianvash

Abstract:

Many industrial materials like magnets need to be tested for the radiation environment expected at linear colliders (LC) where the accelerator and detectors will be subjected to large influences of beta, neutron and gamma’s over their life Gamma irradiation of the permanent sample magnets using a 60Co source was investigated up to an absorbed dose of 700Mrad shows a negligible effect on some magnetic properties of Nd-Fe-B. In this work it has been tried to investigate the change of some important properties of Barium hexa ferrite. Results showed little decreases of magnetic properties at doses rang of 0.5 to 2.5 Mrad. But at the gamma irradiation dose up to 10 Mrad it is showed a few increase of properties. Also study of gamma irradiation of Nd-Fe-B showed considerably increase of magnetic properties.

Keywords: Gamma ray irradiation, Hard Ferrite, Magnetic coefficient, Radiation dose.

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Authors: Gaurav Kumar, Dharmbir Prasad, Rudra Pratap Singh

Abstract:

In the current work, adaptive extended Kalman filter (AEKF) is presented for solution of ground radar based ballistic missile (BM) tracking problem in re-entry phase with unknown ballistic coefficient. The estimation of trajectory of any BM in re-entry phase is extremely difficult, because of highly non-linear motion of BM. The estimation accuracy of AEKF has been tested for a typical test target tracking problem adopted from literature. Further, the approach of AEKF is compared with extended Kalman filter (EKF). The simulation result indicates the superiority of the AEKF in solving joint parameter and state estimation problems.

Keywords: Adaptive, AEKF, ballistic missile, EKF, re-entry phase, target tracking.

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Authors: Sh. Mirhosseini, Y. Haghighatfar, M. Sedighi

Abstract:

Forced vibration problem of a delaminated beam made of fiber metal laminates is studied in this paper. Firstly, a delamination is considered to divide the beam into four sections. The classic beam theory is assumed to dominate each section. The layers on two sides of the delamination are constrained to have the same deflection. This hypothesis approves the conditions of compatibility as well. Consequently, dynamic response of the beam is obtained by the means of differential transform method (DTM). In order to verify the correctness of the results, a model is constructed using commercial software ABAQUS 6.14. A linear spring with constant stiffness takes the effect of contact between delaminated layers into account. The attained semi-analytical outcomes are in great agreement with finite element analysis.

Keywords: Delamination, forced vibration, finite element modelling, natural frequency.

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