Search results for: Pearson correlation coefficient.

Authors: Rajendra M. Galagali, R. G. Tikotkar

Abstract:

Ductile iron samples alloyed with 2.5% Si, 0.78% Cu, 0.421% Mo and 0.151% Ni were austempered at 345 °C and 380 °C for 150 and 180 mins and then tested for wear strength. Ductile iron was also included in the study for comparison purposes. A pin-on-disc machine was employed for wear study. The investigations were carried out for a speed of 3 m/s, under the contact load of 29.43 N with varying sliding distances ranging from 1000 m to 5000 m. The experimental outcome indicates that ADI austempered at 345 °C is more wear resistant than the one austempered at 380 °C. Also for only a sliding distance of 3000 m, both exhibited almost same wear resistance. SEM analysis indicates running sliding marks more or less parallel to one another. Spalled layers and large voids which resemble delamination were observed on worn surface of ADI380. This indicated the occurrence of severe wear. Dark patches observed indicate oxidized surface.

Keywords: Austempered ductile iron, coefficient of friction, dry sliding wear, sliding distance.

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Authors: Cherry Oo, Hnin Min Oo

Abstract:

Software bug localization is one of the most costly tasks in program repair technique. Therefore, there is a high claim for automated bug localization techniques that can monitor programmers to the locations of bugs, with slight human arbitration. Spectrum-based bug localization aims to help software developers to discover bugs rapidly by investigating abstractions of the program traces to make a ranking list of most possible buggy modules. Using the Apache Commons Math library project, we study the diagnostic accuracy using our spectrum-based bug localization metric. Our outcomes show that the greater performance of a specific similarity coefficient, used to inspect the program spectra, is mostly effective on localizing of single line bugs.

Keywords: Software testing, fault localization, program spectra.

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Authors: Jose William Porras Ferreira

Abstract:

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: A. Heidarinasab, V. Moghaddam Nansa

Abstract:

This paper deals with rheological behavior of tomato paste from the view point of time independent properties inclusive of processing variables such as sample temperature which influence on rheological properties as well as breaking temperature and concentration which beside the rheological properties, influence on the quality of final product. With this aim 10 tomato paste samples at various concentrations (17-25%) and breaking temperatures (65- 85 C o ) have been produced. The experimental results showed tomato paste behaves as a non-Newtonian semi-fluid which follows power law model that consistency coefficient (K) is supposed function of breaking temperature, concentration and sample temperature with consideration to superimpose function.

Keywords: Breaking temperature, Concentration, Power law, Rheology, Time independent.

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Authors: S. Malek, N. Zenati-Henda, M. Belhocine, S. Benbelkacem

Abstract:

In geometrical camera calibration, the objective is to determine a set of camera parameters that describe the mapping between 3D references coordinates and 2D image coordinates. In this paper, a technique of calibration and tracking based on both a least squares method is presented and a correlation technique developed as part of an augmented reality system. This approach is fast and it can be used for a real time system

Keywords: Camera calibration, pinhole model, least squares method, augmented reality, strong calibration.

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Authors: K. M. Ngcobo, S. D. Eyono Obono

Abstract:

Science and technology has a major impact on many societal domains such as communication, medicine, food, transportation, etc. However, this dominance of modern technology can have a negative unintended impact on indigenous systems, and in particular on indigenous foods. This problem serves as a motivation to this study whose aim is to examine the perceptions of learners on the usefulness of Information and Communication Technologies (ICTs) for learning about indigenous foods. This aim will be subdivided into two types of research objectives. The design and identification of theories and models will be achieved using literature content analysis. The objective on the empirical testing of such theories and models will be achieved through the survey of Hospitality studies learners from different schools in the iLembe and Umgungundlovu Districts of the South African Kwazulu-Natal province. SPSS is used to quantitatively analyze the data collected by the questionnaire of this survey using descriptive statistics and Pearson correlations after the assessment of the validity and the reliability of the data. The main hypothesis behind this study is that there is a connection between the demographics of learners, their perceptions on the usefulness of ICTs for learning about indigenous foods, and the following personality and eLearning related theories constructs: Computer self-efficacy, Trust in ICT systems, and Conscientiousness; as suggested by existing studies on learning theories. This hypothesis was fully confirmed by the survey conducted by this study except for the demographic factors where gender and age were not found to be determinant factors of learners’ perceptions on the usefulness of ICTs for learning about indigenous foods.

Keywords: E-learning, Indigenous Foods, Information and Communication Technologies, Learning Theories, Personality.

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Authors: M. Vijaya Kini, R. S. Pai, D. Srikanth Rao, Satish Shenoy B, R. Pai

Abstract:

The stability characteristics of water lubricated journal bearings having three axial grooves are obtained theoretically. In this lubricant (water) is fed under pressure from one end of the bearing, through the 3-axial grooves (groove angles may vary). These bearings can use the process fluid as the lubricant, as in the case of feed water pumps. The Reynolds equation is solved numerically by the finite difference method satisfying the boundary conditions. The stiffness and damping coefficient for various bearing number and eccentricity ratios, assuming linear pressure drop along the groove, shows that smaller groove angles better results.

Keywords: 3-axial groove, dynamic characteristics, groovelocation, water lubricated bearings.

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Authors: Tadeusz Witkowski, Paweł Antczak, Arkadiusz Antczak

Abstract:

In the paper we discuss the influence of the route flexibility degree, the open rate of operations and the production type coefficient on makespan. The flexible job-open shop scheduling problem FJOSP (an extension of the classical job shop scheduling) is analyzed. For the analysis of the production process we used a hybrid heuristic of the GRASP (greedy randomized adaptive search procedure) with simulated annealing algorithm. Experiments with different levels of factors have been considered and compared. The GRASP+SA algorithm has been tested and illustrated with results for the serial route and the parallel one.

Keywords: Makespan, open shop, route flexibility, serial and parallel route, simulation modeling, type of production.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

This paper studies mechanical buckling of functionally graded beams subjected to axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of dimensionless geometrical parameter, functionally graded index and foundation coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Mechanical Buckling, Functionally graded beam- Engesser-Timoshenko beam theory

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Authors: Vinti Davar

Abstract:

Background: Worldwide, at least 2.8 million people die each year as a result of being overweight or obese, and 35.8 million (2.3%) of global DALYs are caused by overweight or obesity. Obesity is acknowledged as one of the burning public health problems reducing life expectancy and quality of life. The body composition analysis of the university population is essential in assessing the nutritional status, as well as the risk of developing diseases associated with abnormal body fat content so as to make nutritional recommendations. Objectives: The main aim was to determine the prevalence of obesity and overweight in University students using Anthropometric analysis and BIA methods. Material and Methods: In this cross-sectional study, 283 university students participated. The body composition analysis was undertaken by using mainly: i) Anthropometric Measurement: Height, Weight, BMI, waist circumference, hip circumference and skin fold thickness, ii) Bio-electrical impedance was used for analysis of body fat mass, fat percent and visceral fat which was measured by Tanita SC-330P Professional Body Composition Analyzer. The data so collected were compiled in MS Excel and analyzed for males and females using SPSS 16. Results and Discussion: The mean age of the male (n= 153) studied subjects was 25.37 ±2.39 years and females (n=130) was 22.53 ±2.31. The data of BIA revealed very high mean fat per cent of the female subjects i.e. 30.3±6.5 per cent whereas mean fat per cent of the male subjects was 15.60±6.02 per cent indicating a normal body fat range. The findings showed high visceral fat of both males (12.92±3.02) and females (16.86±4.98). BMI, BF% and WHR were higher among females, and BMI was higher among males. The most evident correlation was verified between BF% and WHR for female students (r=0.902; p<0.001). The correlation of BFM and BF% with thickness of triceps, sub scapular and abdominal skin folds and BMI was significant (P<0.001). Conclusion: The studied data made it obvious that there is a need to initiate lifestyle changing strategies especially for adult females and encourage them to improve their dietary intake to prevent incidence of noncommunicable diseases due to obesity and high fat percentage.

Keywords: Anthropometry, bioelectrical impedance, body fat percentage, obesity.

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Authors: Harsh Vikram Singh, S. P. Singh, Anand Mohan

Abstract:

This paper discusses a new heavy tailed distribution based data hiding into discrete cosine transform (DCT) coefficients of image, which provides statistical security as well as robustness against steganalysis attacks. Unlike other data hiding algorithms, the proposed technique does not introduce much effect in the stegoimage-s DCT coefficient probability plots, thus making the presence of hidden data statistically undetectable. In addition the proposed method does not compromise on hiding capacity. When compared to the generic block DCT based data-hiding scheme, our method found more robust against a variety of image manipulating attacks such as filtering, blurring, JPEG compression etc.

Keywords: Information Security, Robust Steganography, Steganalysis, Pareto Probability Distribution function.

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Authors: B. Chetti, W. A. Crosby

Abstract:

The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: Two-lobe bearing, thermal effect, static and dynamic characteristics.

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Authors: Z. Pavlík, A. Trník, M. Pavlíková, M. Keppert, R. Černý

Abstract:

A new type of lightweight plaster with the thermal capacity enhanced by PCM (Phase Change Material) addition is analyzed. The basic physical characteristics, namely the bulk density, matrix density, total open porosity, and pore size distribution are measured at first. For description of mechanical properties, compressive strength measurements are done. The thermal properties are characterized by transient impulse techniques as well as by DSC analysis that enables determination of the specific heat capacity as a function of temperature. The resistivity against the liquid water ingress is described by water absorption coefficient measurement. The experimental results indicate a good capability of the designed plaster to moderate effectively the interior climate of buildings.

Keywords: Lime-pozzolan plaster, PCM addition, enhanced thermal capacity, DSC analysis.

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Authors: María Jesús Luengo-Valderrey, Mónica Moso-Díez

Abstract:

In the knowledge-based economy, innovation is considered essential in order to achieve survival and growth in organizations. On the other hand, knowledge management is currently understood as one of the keys to innovation process. Both factors are generally admitted as generators of competitive advantage in organizations. Specifically, activities on R&D&I and those that generate internal knowledge have a positive influence in innovation results. This paper examines this effect and if it is similar or not is what we aimed to quantify in this paper. We focus on the impact that proportion of knowledge workers, the R&D&I investment, the amounts destined for ICTs and training for innovation have on the variation of tangible and intangibles returns for the sector of high and medium technology in Spain. To do this, we have performed an empirical analysis on the results of questionnaires about innovation in enterprises in Spain, collected by the National Statistics Institute. First, using clusters methodology, the behavior of these enterprises regarding knowledge management is identified. Then, using SEM methodology, we performed, for each cluster, the study about cause-effect relationships among constructs defined through variables, setting its type and quantification. The cluster analysis results in four groups in which cluster number 1 and 3 presents the best performance in innovation with differentiating nuances among them, while clusters 2 and 4 obtained divergent results to a similar innovative effort. However, the results of SEM analysis for each cluster show that, in all cases, knowledge workers are those that affect innovation performance most, regardless of the level of investment, and that there is a strong correlation between knowledge workers and investment in knowledge generation. The main findings reached is that Spanish high and medium technology companies improve their innovation performance investing in internal knowledge generation measures, specially, in terms of R&D activities, and underinvest in external ones. This, and the strong correlation between knowledge workers and the set of activities that promote the knowledge generation, should be taken into account by managers of companies, when making decisions about their investments for innovation, since they are key for improving their opportunities in the global market.

Keywords: High and medium technology sector, innovation, knowledge management, Spanish companies.

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Authors: T. Tchawe Moukam, N. Ngongang François, D. Thomas, K. Bienvenu, T. -Toko Dénis

Abstract:

Since the expression of the coefficient of friction by Colebrook-White which turns out to be an implicit equation, equations have been developed to facilitate their applicability. In this work, this equation was applied to the penstock of the Three Gorges dam in order to observe the evolution of the turbulent boundary layer and the friction along the walls. Thus, the study is being carried out using a 3D digital approach in FLUENT in order to take into account the wall effects. It appears that according to the position of the portions, we have a variation in the evolutions of the turbulent friction and of the values of the boundary layer. We also observe that the inclination of the pipe has a significant influence on this turbulent friction; similarly, one could not make a fair evaluation of the latter without specifying the choice and location of the wall.

Keywords: Hydroelectric dam, penstock, turbulent friction, boundary layer, CFD.

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Authors: Ilze Beitane, Inga Ciprovica

Abstract:

The influence of lactulose and inulin on rheological properties of fermented milk during storage was studied.Pasteurized milk, freeze-dried starter culture Bb-12 (Bifidobacterium lactis, Chr. Hansen, Denmark), inulin – RAFTILINE®HP (ORAFI, Belgium) and syrup of lactulose (Duphalac®, the Netherlands) were used for experiments. The fermentation process was realized at 37 oC for 16 hours and the storage of products was provided at 4 oC for 7 days. Measurements were carried out by BROOKFIELD standard methods and the flow curves were described by Herschel-Bulkley model. The results of dispersion analysis have shown that both the concentration of prebiotics (p=0.04<0.05) and shelf life (p=0.003<0.05) have a significant influence on the apparent viscosity of the product.

Keywords: Apparent viscosity, B.lactis, consistency coefficient, flow behavior index, prebiotics.

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Authors: Rui Antunes

Abstract:

This article presents the implementation of several different e/b-Learning collaborative activities, used to improve the students learning process in an high school Polytechnic Institution. A new learning model arises, based on a combination between face-toface and distance leaning. Learning is now becoming centered with the development of collaborative activities, and its actors (teachers and students) have to be re-socialized to a new e/b-Learning paradigm. Measuring approaches are proposed for this model and results are presented, showing prospective correlation between students learning success and the use of online collaborative activities.

Keywords: e/b-Learning, Collaborative Learning, TeachingCommunities, Web-based Courseware

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Authors: V. Kesornpatumanun, P. Boonek, W. Silabut, N. Homsup, W. Kuhirun

Abstract:

This paper increases directivity and gain of Small Planar Dipole Antenna (SPDA) by using Symmetrical Pyramidal Block (SPB) which operates in X band at 11 GHz. The SPB consists four sides; each of which is metamaterial with Epsilon Negative Medium (ENG) and Epsilon Near-Zero (ENZ). The results simulated using the High Frequency Structure Simulator (HFSS) show that the SPB is capable of enhancing directivity and gain for the SPDA with maximum gain of 2.46 dB. The reflection coefficient is -13.7037 dB with narrow beam width.

Keywords: Small Planar Dipole Antenna, Symmetrical Pyramidal Block, metamaterials, Epsilon Near-Zero, Epsilon Negative Medium.

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Authors: Zhu Jiaming, Yu Mengna

Abstract:

In this article, models based on quantitative analysis, physical geometry and regression analysis are established, by using analytic hierarchy process analysis, fuzzy cluster analysis, fuzzy photographic and data fitting. The reasons of various leaf shapes among different species and the differences between the leaf shapes on same tree have been solved by using software, such as Eviews, VB and Matlab. We also successfully estimate the leaf mass of a tree and the correlation with the tree profile.

Keywords: Leaf shape; Mass; Fuzzy cluster; Regression analysis; Eviews; Matlab

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Authors: Samrand Rashahmadi, Morteza Abbaszadeh, Sana Hoseyni, Raziyeh Alizadeh

Abstract:

Design of a constant chord propeller is presented in this paper in order to reduce propeller-s design procedure-s costs. The design process was based on Lock and Goldstein-s techniques of propeller design and analysis. In order to calculate optimum chord of propeller, chord of a referential element is generalized as whole blades chord. The design outcome which named CS-X-1 is modeled & analyzed by CFD methods using K-ε: R.N.G turbulence model. Convergence of results of two codes proved that outcome results of design process are reliable. Design result is a two-blade propeller with a total diameter of 1.1 meter, radial velocity of 3000 R.P.M, efficiency above .75 and power coefficient near 1.05.

Keywords: Single rotating propeller, Design, C.F.D. test, constant chord

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Authors: M. H. Nagrial, J. Rizk, A. Hellany

Abstract:

This paper presents the design, analysis and development of permanent magnet (PM) torque couplers. These couplers employ rare-earth magnets. Based on finite element analysis and earlier analytical works both concentric and face-type synchronous type couplers have been designed and fabricated. The experimental performance has good correlation with finite element calculations.

Keywords: Finite Element Analysis, Synchronous TorqueCouplers, Permanent Magnet Torque Couplers

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Authors: Liberty L Mguni, Reinout Meijboom, Kalala Jalama

Abstract:

Nano-MgO was successfully deposited on titania using deposition-precipitation method. The catalyst produced was characterised using FTIR, XRD, BET and XRF and its activity was tested on the transesterification reaction of soybean oil to biodiesel. The catalyst activity improved when the reaction temperature was increasedfrom 150 and 225 OC. It was also observed that increasing the reaction time above 1h had no significant benefit on conversion. The stability fixed MgO on TiO2 was investigated using XRF and ICP-OES. It was observed that MgO loss during the reaction was between 0.5-2.3 percent and that there was no correlation between the reaction temperature and the MgO loss.

Keywords: Nano-MgO, TiO2, transesterification

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Authors: Ayesha S. Rahman, Khaled Haddad, Ataur Rahman

Abstract:

At-site flood frequency analysis is used to estimate flood quantiles when at-site record length is reasonably long. In Australia, FLIKE software has been introduced for at-site flood frequency analysis. The advantage of FLIKE is that, for a given application, the user can compare a number of most commonly adopted probability distributions and parameter estimation methods relatively quickly using a windows interface. The new version of FLIKE has been incorporated with the multiple Grubbs and Beck test which can identify multiple numbers of potentially influential low flows. This paper presents a case study considering six catchments in eastern Australia which compares two outlier identification tests (original Grubbs and Beck test and multiple Grubbs and Beck test) and two commonly applied probability distributions (Generalized Extreme Value (GEV) and Log Pearson type 3 (LP3)) using FLIKE software. It has been found that the multiple Grubbs and Beck test when used with LP3 distribution provides more accurate flood quantile estimates than when LP3 distribution is used with the original Grubbs and Beck test. Between these two methods, the differences in flood quantile estimates have been found to be up to 61% for the six study catchments. It has also been found that GEV distribution (with L moments) and LP3 distribution with the multiple Grubbs and Beck test provide quite similar results in most of the cases; however, a difference up to 38% has been noted for flood quantiles for annual exceedance probability (AEP) of 1 in 100 for one catchment. This finding needs to be confirmed with a greater number of stations across other Australian states.

Keywords: Floods, FLIKE, probability distributions, flood frequency, outlier.

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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: M. Karami Khorramabadi, P. Khazaeinejad

Abstract:

The static stability analysis of stiffened functionally graded cylindrical shells by isotropic rings and stringers subjected to axial compression is presented in this paper. The Young's modulus of the shell is taken to be function of the thickness coordinate. The fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical axial loads. The effects of material properties, geometric size and different material coefficient on the critical axial loads are examined. The analytical results are compared and validated using the finite element model.

Keywords: Functionally graded material, Stability, Stiffened cylindrical shell, Finite element analysis

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

Abstract:

In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even-dough decreases at these extreme wind speeds but are not infinite. Moreover, we also fund that it is possible to stabilize the power coefficient (stabilizing the output power)above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque.

Keywords: Probability, Stochastic, Probability density function, Turbulence.

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Authors: Mahdi Masoumi, Mehrdad Ardebilipoor, Seyed Aidin Bassam

Abstract:

This paper proposes a novel frequency offset (FO) estimator for orthogonal frequency division multiplexing. Simplicity is most significant feature of this algorithm and can be repeated to achieve acceptable accuracy. Also fractional and integer part of FO is estimated jointly with use of the same algorithm. To do so, instead of using conventional algorithms that usually use correlation function, we use DFT of received signal. Therefore, complexity will be reduced and we can do synchronization procedure by the same hardware that is used to demodulate OFDM symbol. Finally, computer simulation shows that the accuracy of this method is better than other conventional methods.

Keywords: DFT, Estimator, Frequency Offset, IEEE802.11a, OFDM.

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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